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.
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 Results for `Bouncing' Gaussian Wave Packets
NASA Astrophysics Data System (ADS)
Belloni, M.; Doncheski, M. A.; Robinett, R. W.
2005-01-01
We consider time-dependent Gaussian wave packet solutions of the Schrödinger equation, with arbitrary initial central position, x0, and momentum, p0, for an otherwise free particle, but with an infinite wall at x = 0, so-called bouncing wave packets. We show how difference or mirror solutions of the form ψ(x,t) - ψ(-x,t) can, in this case, be normalized exactly, allowing for the evaluation of a number of time-dependent expectation values and other quantities in closed form. For example, we calculate langp2rangt explicitly which illustrates how the free-particle kinetic (and hence total energy) is affected by the presence of the distant boundary. We also discuss the time dependence of the expectation values of position, langxrangt, and momentum, langprangt, and their relation to the impulsive force during the `collision' with the wall. Finally, the x0, p0 → 0 limit is shown to reduce a special case of a non-standard free-particle Gaussian solution. The addition of this example to the literature then expands of the relatively small number of Gaussian solutions to quantum mechanical problems with familiar classical analogs (free particle, uniform acceleration, harmonic oscillator, unstable oscillator, and uniform magnetic field) available in closed form.
Partial transpose of random quantum states: Exact formulas and meanders
Fukuda, Motohisa; Sniady, Piotr
2013-04-15
We investigate the asymptotic behavior of the empirical eigenvalues distribution of the partial transpose of a random quantum state. The limiting distribution was previously investigated via Wishart random matrices indirectly (by approximating the matrix of trace 1 by the Wishart matrix of random trace) and shown to be the semicircular distribution or the free difference of two free Poisson distributions, depending on how dimensions of the concerned spaces grow. Our use of Wishart matrices gives exact combinatorial formulas for the moments of the partial transpose of the random state. We find three natural asymptotic regimes in terms of geodesics on the permutation groups. Two of them correspond to the above two cases; the third one turns out to be a new matrix model for the meander polynomials. Moreover, we prove the convergence to the semicircular distribution together with its extreme eigenvalues under weaker assumptions, and show large deviation bound for the latter.
Exact semiclassical wave equation for stochastic quantum optics
NASA Astrophysics Data System (ADS)
Diósi, Lajos
1996-02-01
Semiclassical (stochastic) wave equations are proposed for the coupled dynamics of atomic quantum states and semiclassical radiation field. All relevant predictions of standard unitary quantum dynamics are exactly reproducible in the framework of the stochastic wave equation model. We stress in such a way that the concept of stochastic wave equations is not to be restricted to the widely used Markovian approximation.
Electromagnetic shock wave in nonlinear vacuum: exact solution.
Kovachev, Lubomir M; Georgieva, Daniela A; Kovachev, Kamen L
2012-10-01
An analytical approach to the theory of electromagnetic waves in nonlinear vacuum is developed. The evolution of the pulse is governed by a system of nonlinear wave vector equations. An exact solution with its own angular momentum in the form of a shock wave is obtained.
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 controllability of partial integrodifferential equations with mixed boundary conditions
NASA Astrophysics Data System (ADS)
Sakthivel, K.; Balachandran, K.; Lavanya, R.
2007-01-01
In this work the exact controllability of linear parabolic integrodifferential equations with mixed boundary conditions are studied. Carleman estimate for the linearized problem providing the observability results is fundamental to the analysis and by duality it provides exact global controllability.
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.
Partial-wave expansions of angular spectra of plane waves.
Lock, James A
2006-11-01
Focused electromagnetic beams are frequently modeled by either an angular spectrum of plane waves or a partial-wave sum of spherical multipole waves. The connection between these two beam models is explored here. The partial-wave expansion of an angular spectrum containing evanescent components is found to possess only odd partial waves. On the other hand, the partial-wave expansion of an alternate angular spectrum constructed so as to be free of evanescent components contains all partial waves but describes a propagating beam with a small amount of standing-wave component mixed in. A procedure is described for minimizing the standing-wave component so as to more accurately model a purely forward propagating experimental beam.
Partial-wave expansions of angular spectra of plane waves
NASA Astrophysics Data System (ADS)
Lock, James A.
2006-11-01
Focused electromagnetic beams are frequently modeled by either an angular spectrum of plane waves or a partial-wave sum of spherical multipole waves. The connection between these two beam models is explored here. The partial-wave expansion of an angular spectrum containing evanescent components is found to possess only odd partial waves. On the other hand, the partial-wave expansion of an alternate angular spectrum constructed so as to be free of evanescent components contains all partial waves but describes a propagating beam with a small amount of standing-wave component mixed in. A procedure is described for minimizing the standing-wave component so as to more accurately model a purely forward propagating experimental beam.
Exact Steady Azimuthal Edge Waves in Rotating Fluids
NASA Astrophysics Data System (ADS)
Ionescu-Kruse, Delia
2016-09-01
The full problem of water waves travelling along a constant sloping beach with the shoreline parallel to the Equator, written in a moving frame with the origin at a point on the rotating Earth is introduced. An exact steady solution of this problem moving only in the azimuthal direction, with no variations in this direction, is obtained. The solution is discussed in turn in spherical coordinates, in cylindrical coordinates and in the tangent-plan approximations.
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.
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.
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
S-Wave Dispersion Relations: Exact Left Hand E-Plane Discontinuity from the Born Series
NASA Technical Reports Server (NTRS)
Bessis, D.; Temkin, A.
1999-01-01
We show, for a superposition of Yukawa potentials, that the left hand cut discontinuity in the complex E plane of the (S-wave) scattering amplitude is given exactly, in an interval depending on n, by the discontinuity of the Born series stopped at order n. This also establishes an inverse and unexpected correspondence of the Born series at positive high energies and negative low energies. We can thus construct a viable dispersion relation (DR) for the partial (S-) wave amplitude. The high numerical precision achievable by the DR is demonstrated for the exponential potential at zero scattering energy. We also briefly discuss the extension of our results to Field Theory.
Waves on a vortex filament: exact solutions of dynamical equations
NASA Astrophysics Data System (ADS)
Brugarino, Tommaso; Mongiovi, Maria Stella; Sciacca, Michele
2014-09-01
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.
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.
Stokes waves revisited: Exact solutions in the asymptotic limit
NASA Astrophysics Data System (ADS)
Davies, Megan; Chattopadhyay, Amit K.
2016-03-01
The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic "secular variation" in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n -ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.
NASA Astrophysics Data System (ADS)
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.
Wave Attenuation in Partially Saturated Porous Solids.
NASA Astrophysics Data System (ADS)
Yin, Chuan-Sheng
1992-01-01
This thesis consists of three independent papers. Paper 1 studies effects of pulsating gas pockets on wave propagation in partially saturated porous solids containing both liquid and gas phases. On the basis of Biot theory, an analytic solution for the White model for study of the effects of saturation history on wave attenuation is derived. One of the most significant findings of this work is that when the average spacing among the neighboring gas pockets is of the order of the boundary-layer thickness associated with the slow compressional (or P2) wave, the attenuation of the compressional (or P) wave due to local fluid flow reaches its maximum. Results of Paper 1 bear direct applications to seismic and logging responses of partially saturated rocks in prospecting for petroleum, and monitoring of oil and natural gas reservoirs. Paper 2 presents the results of the experimental studies of the effects of partial liquid/gas saturation on extensional wave attenuation in Berea sandstones. Two experimental methods are used; one is the resonant-bar method and the other the forced-deformation method. It is found that the wave attenuation depends on sample-saturation history (drainage or imbibition), as well as boundary-flow conditions, and the degree of saturation. The attenuation caused by "flowable" liquid is sensitive only in the region of low degree of gas saturation. An open-pore boundary tends to induce higher attenuation. The results obtained by the forced-deformation method show that the magnitude of the attenuation decreases substantially with decreasing frequency to the extent that no attenuation peak was apparent at frequencies below 100 Hz. Paper 3 analyzes extensional wave propagation in a porous fluid-saturated hollow-cylinder of infinite extent. Analytic solutions of complex Young's modulus for the long wavelength limit was obtained for a hollow -cylinder with open-pore inner surface. A simplified formula for estimating the frequency at which the
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.
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
The new BNL partial wave analysis programs
Cummings, J.P.; Weygand, D.P.
1997-07-29
Experiment E852 at Brookhaven National Laboratory is a meson spectroscopy experiment which took data at the Multi-Particle Spectrometer facility of the Alternating Gradient Syncrotron. Upgrades to the spectrometer`s data acquisition and trigger electronics allowed over 900 million data events, of numerous topologies, to be recorded to tape in 1995 running alone. One of the primary goals of E852 is identification of states beyond the quark model, i.e., states with gluonic degrees of freedom. Identification of such states involves the measurement of a systems spin-parity. Such a measurement is usually done using Partial Wave Analysis. Programs to perform such analyses exist, in fact, one was written at BNL and used in previous experiments by some of this group. This program, however, was optimized for a particular final state, and modification to allow analysis of the broad range of final states in E852 would have been difficult. The authors therefore decided to write a new program, with an eye towards generality that would allow analysis of a large class of reactions.
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.
Exact Travelling Wave Solutions of the Schamel-Korteweg-de Vries Equation
NASA Astrophysics Data System (ADS)
Lee, Jonu; Sakthivel, Rathinasamy
2011-12-01
The Schamel-Korteweg-de Vries (S-KdV) equation containing a square root nonlinearity is a very attractive model for the study of ion-acoustic waves in plasma and dusty plasma. In this work, we obtain exact travelling wave solutions of the S-KdV equation by employing the exp function method. In general, the exact travelling wave solutions will be helpful in the theoretical and numerical study of the nonlinear evolution equations. The work emphasizes the power of the method in providing distinct solutions of different physical problems.
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 a Higher-Dimensional Nonlinear Evolution Equation
NASA Astrophysics Data System (ADS)
Lee, Jonu; Sakthivel, Rathinasamy; Wazzan, Luwai
The exact traveling wave solutions of (4 + 1)-dimensional nonlinear Fokas equation is obtained by using three distinct methods with symbolic computation. The modified tanh-coth method is implemented to obtain single soliton solutions whereas the extended Jacobi elliptic function method is applied to derive doubly periodic wave solutions for this higher-dimensional integrable equation. The Exp-function method gives generalized wave solutions with some free parameters. It is shown that soliton solutions and triangular solutions can be established as the limits of the Jacobi doubly periodic wave solutions.
Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents.
Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan
2014-04-01
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.
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
NASA Technical Reports Server (NTRS)
Barnes, A.
1983-01-01
An exact nonlinear solution is found to the relativistic kinetic and electrodynamic equations (in their hydromagnetic limit) that describes the large-amplitude fast-mode magnetoacoustic wave propagating normal to the magnetic field in a collisionless, previously uniform plasma. It is pointed out that a wave of this kind will be generated by transverse compression of any collisionless plasma. The solution is in essence independent of the detailed form of the particle momentum distribution functions. The solution is obtained, in part, through the method of characteristics; the wave exhibits the familiar properties of steepening and shock formation. A detailed analysis is given of the ultrarelativistic limit of this wave.
The exact distributions of F(IS) 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 F IS. Understanding how those mating systems impact the possible distributions of F IS 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 F IS, the probabilities of positive and negative F IS, the probabilities of fixation and the probabilities to observe changes in the sign of F IS 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 F IS and the occurrence of extreme values. It also drastically modified the probability to change the sign of F IS value at one locus over one generation. When mutation prevailed over genetic drift, increasing rates of asexuality continuously increased the variance of F IS that reached its highest value in fully asexual populations. In consequence, even ancient asexual populations showed the entire F IS spectrum, including strong positive F IS. The prevalence of heterozygous loci only occurred in full asexual populations when genetic drift dominated.
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
Cylindrical gravitational waves with two degrees of freedom: An exact solution
NASA Astrophysics Data System (ADS)
Piran, T.; Safier, P. N.; Katz, J.
1986-07-01
The exact two-parameter solution of Einstein's equations described below represents ingoing and outgoing cylindrical gravitational waves with two degrees of polarization. It has been obtained from the Kerr metric by applying a well-known trick but, unlike the Kerr metric, it has no singularities.
A new class of exact solutions with shock waves in gas dynamics
NASA Astrophysics Data System (ADS)
Poslavskii, S. A.
1985-10-01
New exact solutions are obtained for one-dimensional gasdynamic equations with strong shock waves propagating in a moving medium, with gas flow behind the shock wave described by a solution with uniform deformation. Solutions are then presented for a problem concerning explosion without counterpressure in a uniformly expanding (contracting) gas with an arbitrary adiabatic exponent and a nonuniform initial density distribution. A solution is also presented for the problem of cavity collapse in a dust cloud with the formation of a shock wave.
Lerma H, S.
2010-07-15
The structure of the exact wave function of the isovectorial pairing Hamiltonian with nondegenerate single-particle levels is discussed. The way that the single-particle splittings break the quartet condensate solution found for N=Z nuclei in a single degenerate level is established. After a brief review of the exact solution, the structure of the wave function is analyzed and some particular cases are considered where a clear interpretation of the wave function emerges. An expression for the exact wave function in terms of the isospin triplet of pair creators is given. The ground-state wave function is analyzed as a function of pairing strength, for a system of four protons and four neutrons. For small and large values of the pairing strength a dominance of two-pair (quartets) scalar couplings is found, whereas for intermediate values enhancements of the nonscalar couplings are obtained. A correlation of these enhancements with the creation of Cooper-like pairs is observed.
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.
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.
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.
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
Exact solution to plane-wave scattering by an ideal "left-handed" wedge.
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 = micro = -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.
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.
NASA Astrophysics Data System (ADS)
Shvartsburg, Aleksandr B.
1998-03-01
An analysis is made of propagation of electromagnetic waves in media which are nonstationary because of relaxation of the refractive index. A series of models of oscillatory and transient regimes of such relaxation is developed. Several characteristic times are used in these models and exact analytic solutions of the Maxwell equations can be obtained for these regimes. In contrast to the traditional approaches, the exact solutions are obtained without assuming smallness or slowness of temporal variations of the parameters of the medium and these solutions are valid even when the characteristic relaxation time is comparable with the period of oscillations of the wave field. A nonstationary generalisation of the Fresnel formulae is derived. It is shown that waves reflected from a nonstationary surface experience amplitude and frequency modulation, and the modulation effect is localised in an interval of the order of one relaxation time. It is shown that a short broadband perturbation pulse forms in the reflected wave and that this pulse contains one or several oscillations of the field. It should be possible to use nonstationary broadening of the spectrum of a probe wave reflected from a surface perturbed by a powerful laser pulse in estimating the relaxation times of fast optical processes.
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.
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.
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.
Bohmian mechanics in the exact factorization of electron-nuclear wave functions
NASA Astrophysics Data System (ADS)
Suzuki, Yasumitsu; Watanabe, Kazuyuki
2016-09-01
The exact factorization of an electron-nuclear wave function [A. Abedi, N. T. Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010), 10.1103/PhysRevLett.105.123002] allows us to define the rigorous nuclear time-dependent Schrödinger equation (TDSE) with a time-dependent potential-energy surface (TDPES) that fully accounts for the coupling to the electronic motion and drives the nuclear wave-packet dynamics. Here, we study whether the propagation of multiple classical trajectories can reproduce the quantum nuclear motion in strong-field processes when their motions are governed by the quantum Hamilton-Jacobi equation derived by applying Bohmian mechanics to this exact nuclear TDSE. We demonstrate that multiple classical trajectories propagated by the force from the gradient of the exact TDPES plus the Bohmian quantum potential can reproduce the strong-field dissociation dynamics of a one-dimensional model of the H2 + molecule. Our results show that the force from the Bohmian quantum potential plays a non-negligible role in yielding quantum nuclear dynamics in the strong-field process studied here, where ionization and/or splitting of nuclear probability density occurs.
Comparison of spherical wave ray tracing and exact boundary value solutions for spherical radomes
NASA Astrophysics Data System (ADS)
Bloom, D. A.; Overfelt, P. L.; White, D. J.
Much radome analysis is based on plane wave ray tracing techniques which combine conceptual simplicity with reasonable accuracy. As increasing demands on the performance of airborne antennas necessitate more accurate methods of analysis for the enclosing radome, an exact idea of the limits of applicability of the ray-optical approximation becomes more critical. In an effort to contribute to this subject, we have taken a single layer spherical radome excited by a dipole source oriented parallel to the z-axis and computed its transmitted electric and magnetic fields using a spherical wave ray tracing technique and also by solving the electromagnetic boundary value problem exactly. The exact solution is used as a standard against which the ray tracing approximation can be compared. In this paper, we compare the field patterns of the two solutions by varying the dipole offset distance, the observation point position, wall thickness, dielectric constant, wavelength, and curvature. Parameter values and the compared field patterns are examined in terms of the theory, and conclusions are drawn as to which parameters affect agreement most strongly.
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.
Dyadic analysis of partially coherent submillimeter-wave antenna systems
NASA Astrophysics Data System (ADS)
Withington, S.; Yassin, G.; Murphy, J. A.
2001-08-01
We describe a procedure for simulating the behavior of partially coherent submillimeter-wave antenna systems. The procedure is based on the principle that the second-order statistical properties of any partially coherent vector field can be decomposed into a sum of fully coherent, but completely uncorrelated, natural modes. Any of the standard electromagnetic analysis techniques-physical optics, geometrical theory of diffraction, etc.-can be used to propagate and scatter the modes individually, and the statistical properties of the total transformed field reconstructed at the output surface by means of superposition. In the case of modal optics-plane waves, Gaussian optics, waveguide mode matching, etc.-the properties of the field can be traced directly by means of scattering matrices. The overall procedure is of considerable value for calculating the behavior of astronomical instruments comprising planar and waveguide multimode bolometers, submillimeter-wave optical components, and large reflecting antennas.
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
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.
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.
An Exact Transfer Matrix Formulation of Plane Sound Wave Transmission in Inhomogeneous Ducts
NASA Astrophysics Data System (ADS)
Dockumaci, E.
1998-11-01
The impedance, or the reflection coefficient, of plane sound waves in inhomogeneous ducts satisfies a Riccati equation. The present paper shows that the duct impedance matrix, or the scattering matrix, can be related explicitly to the solutions of the associated linear equation of the Riccati equation for duct impedance, or reflection coefficient, respectively. New exact analytical scattering matrix solutions, which follow as consequences of this connection, are given for two significant duct acoustics problems, namely, the sound transmission in non-uniform ducts carrying an incompressible subsonic low Mach number mean flow transmission of sound in uniform ducts with a full quadratic axial mean temperature gradient.
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.
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
Ray and wave aberrations revisited: a Huygens-like construction yields exact relations.
Restrepo, John; Stoerck, Pawel J; Ihrke, Ivo
2016-02-01
The aberrations of an optical system can be described in terms of the wave aberrations, defined as the departure from the ideal spherical wavefront; or the ray aberrations, which are in turn the deviations from the paraxial ray intersections measured in the image plane. The classical connection between the two descriptions is an approximation, the error of which has, to our knowledge, so far not been quantified analytically. We derive exact analytical equations for computing the wavefront surface, the aberrated ray directions, and the transverse ray aberrations in terms of the wave aberrations (OPD) and the reference sphere. We introduce precise conditions for a function to be an OPD function, show that every such function has an associated wavefront, and study the error arising from the classical approximation. We establish strict conditions for the error to be small. We illustrate our results with numerical simulations. Our results show that large numerical apertures and OPD functions with strong gradients yield larger approximation errors.
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
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.
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.
Can the effective string see higher partial waves?
Gubser, S.S.
1997-10-01
The semiclassical cross sections for arbitrary partial waves of ordinary scalars to fall into certain five-dimensional black holes have a form that seems capable of explanation in terms of the effective string model. The kinematics of these processes is analyzed in detail on the effective string and is shown to reproduce the correct functional form of the semiclassical cross sections. But it is necessary to choose a peculiar value of the effective string tension to obtain the correct scaling properties. Furthermore, the assumptions of locality and statistics combine to forbid the effective string from absorbing more than a finite number of partial waves. The relation of this limitation to cosmic censorship is discussed. {copyright} {ital 1997} {ital The American Physical Society}
Impact of plunging breaking waves on a partially submerged cube
NASA Astrophysics Data System (ADS)
Wang, A.; Ikeda, C.; Duncan, J. H.
2013-11-01
The impact of a deep-water plunging breaking wave on a partially submerged cube is studied experimentally in a tank that is 14.8 m long and 1.2 m wide with a water depth of 0.91 m. The breakers are created from dispersively focused wave packets generated by a programmable wave maker. The water surface profile in the vertical center plane of the cube is measured using a cinematic laser-induced fluorescence technique with movie frame rates ranging from 300 to 4,500 Hz. The pressure distribution on the front face of the cube is measured with 24 fast-response sensors simultaneously with the wave profile measurements. The cube is positioned vertically at three heights relative to the mean water level and horizontally at a distance from the wave maker where a strong vertical water jet is formed. The portion of the water surface between the contact point on the front face of the cube and the wave crest is fitted with a circular arc and the radius and vertical position of the fitted circle is tracked during the impact. The vertical acceleration of the contact point reaches more than 50 times the acceleration of gravity and the pressure distribution just below the free surface shows a localized high-pressure region with a very high vertical pressure gradient. This work is supported by the Office of Naval Research under grant N000141110095.
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
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.
NASA Astrophysics Data System (ADS)
Miroshnikov, Victor
2015-11-01
The Navier-Stokes system of PDEs is reduced to a system of the vorticity, continuity, Helmholtz, and Lamb-Helmholtz PDEs. The periodic Dirichlet problems are formulated for conservative internal waves vanishing at infinity in upper and lower domains. Stationary kinematic Fourier (SKF) structures, stationary kinematic Euler-Fourier (SKEF) structures, stationary dynamic Euler-Fourier (SDEF) structures, and SKEF-SDEF structures of three spatial variables and time are constructed to consider kinematic and dynamic problems of the three-dimensional theory of the Newtonian flows with harmonic velocity. Exact solutions for propagation and interaction of N internal waves in the upper and lower domains are developed by the method of decomposition in invariant structures and implemented through experimental and theoretical programming in Maple. Main results are summarized in a global existence theorem for the strong solutions. The SKEF, SDEF, and SKEF-SDEF structures of the cumulative flows are visualized by two-parametric surface plots for six fluid-dynamic variables.
Exact density functional and wave function embedding schemes based on orbital localization
NASA Astrophysics Data System (ADS)
Hégely, Bence; Nagy, Péter R.; Ferenczy, György G.; Kállay, Mihály
2016-08-01
Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.
Ruban, V P
2008-12-01
It is demonstrated that a standard coupled-mode theory can successfully describe weakly nonlinear gravity water waves in Bragg resonance with a periodic one-dimensional topography. Analytical solutions for gap solitons provided by this theory are in reasonable agreement with numerical simulations of the exact equations of motion for ideal planar potential free-surface flows, even for strongly nonlinear waves. In numerical experiments, self-localized groups of nearly standing water waves can exist up to hundreds of wave periods. Generalizations of the model to the three-dimensional case are also derived. PMID:19256946
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.
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.
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)
Naz, R.; Khan, M. D.; Naeem, I.
2013-04-01
The conservation laws for (1+1)-dimensional non-linear generalized regularized long wave (GRLW) equation are derived via partial Noether approach after increasing its order. The GRLW equation is a third-order partial differential equation. We convert GRLW equation to fourth order equation by assuming new dependent variable v to be the derivative of original dependent variable u by setting either u=vx or u=vt. The partial Noether's approach is then used to derive the conservation laws. The derived conserved vectors are adjusted to satisfy the divergence relationship. Finally, the conservation laws are expressed in the variable u and they constitute the conservation laws for the third-order GRLW equation. The Lie point symmetries for GRLW equation are computed. The double reduction theory based on symmetry and its associated conserved vector is utilized and two independent exact solutions are obtained. Moreover, the Lie symmetry method is used to derive an invariant solution. One of the solutions obtained by the double reduction method is the same as derived by Lie symmetry method. The second solution constructed by the double reduction theory is not obtained by the Lie symmetry method. A similar analysis is performed for regularized long wave (RLW) and modified Benjamin-Bona-Mahoney (MBBM) equations.
Brunet, Eric; Derrida, Bernard
2004-01-01
We calculate exactly the velocity and diffusion constant of a microscopic stochastic model of N evolving particles which can be described by a noisy traveling-wave equation with a noise of order N(-1/2). Our model can be viewed as the infinite range limit of a directed polymer in random medium with N sites in the transverse direction. Despite some peculiarities of the traveling-wave equations in the absence of noise, our exact solution allows us to test the validity of a simple cutoff approximation and to show that, in the weak noise limit, the position of the front can be completely described by the effect of the noise on the first particle. PMID:15324128
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. 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.
Godin, O A; Chapman, D M
2001-10-01
In the upper tens of meters of ocean bottom, unconsolidated marine sediments consisting of clay, silt, or fine sand with high porosity are "almost incompressible" in the sense that the shear wave velocity is much smaller than the compressional wave velocity. The shear velocity has very large gradients close to the ocean floor leading to strong coupling of compressional and shear waves in such "soft" sediments. The weak compressibility opens an avenue for developing a theory of elastic wave propagation in continuously stratified soft sediments that fully accounts for the coupling. Elastic waves in soft sediments consist of "fast" waves propagating with velocities close to the compressional velocity and "slow" waves propagating with velocities on the order of the shear velocity. For the slow waves, the theory predicts the existence of surface waves at the ocean-sediment boundary. In the important special case of the power-law depth-dependence of shear rigidity, phase and group velocities of the interface waves are shown to scale as a certain power of frequency. An explicit, exact solution was obtained for the surface waves in sediments characterized by constant density and a linear increase of shear rigidity with depth, that is, for the case of shear speed proportional to the square root of the depth below the sediment-water interface. Asymptotic and perturbation techniques were used to extend the result to more general environments. Theoretical dispersion relations agreed well with numerical simulations and available experimental data and, as demonstrated in a companion paper [D. M. F. Chapman and O. A. Godin, J. Acoust. Soc. Am 110, 1908 (2001)] led to a simple and robust inversion of interface wave travel times for shear velocity profiles in the sediment.
H-He elastic scattering at low energies: Contribution of nonzero partial waves
Sinha, Prabal K.; Ghosh, A.S.
2005-01-01
The present study reports the nonzero partial wave elastic cross sections together with s-wave results for the scattering of an antihydrogen atom off a gaseous helium target at thermal energies (up to 10{sup -2} a.u.). We have used a nonadiabatic atomic orbital method having different basis sets to investigate the system. The consideration of all the significant partial waves (up to J=24) reduces the oscillatory nature present in the individual partial wave cross section. The added elastic cross section is almost constant up to 10{sup -7} a.u. and then decreases steadily and very slowly with increasing energy.
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.
NASA Astrophysics Data System (ADS)
Erokhin, N. S.; Zakharov, V. E.; Zol'nikova, N. N.; Mikhailovskaya, L. A.
2015-02-01
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.
NASA Astrophysics Data System (ADS)
Kong, Chao; Hai, Kuo; Tan, Jintao; Chen, Hao; Hai, Wenhua
2016-03-01
Nonlinear Kronig-Penney model has been frequently employed to study transmission problem of electron wave in a doped semiconductor superlattice or in a nonlinear electrified chain. Here from an integral equation we derive a novel exact solution of the problem, which contains a simple nonlinear map connecting transmission coefficient with system parameters. Consequently, we propose a scheme to manipulate electronic distribution and transmission by adjusting the system parameters. A new quantum coherence effect is evidenced by the strict expression of transmission coefficient, which results in the aperiodic electronic distributions and different transmission coefficients including the approximate zero transmission and total transmission, and the multiple transmissions. The method based on the concise exact solution can be applied directly to some nonlinear cold atomic systems and a lot of linear Kronig-Penney systems, and also can be extended to investigate electronic transport in different discrete nonlinear systems.
Analytical expressions for partial wave two-body Coulomb transition matrices at ground-state energy
NASA Astrophysics Data System (ADS)
Kharchenko, V. F.
2016-11-01
Leaning upon the Fock method of the stereographic projection of the three-dimensional momentum space onto the four-dimensional unit sphere the possibility of the analytical solving of the Lippmann-Schwinger integral equation for the partial wave two-body Coulomb transition matrix at the ground bound state energy has been studied. In this case new expressions for the partial p-, d- and f-wave two-body Coulomb transition matrices have been obtained in the simple analytical form. The developed approach can also be extended to determine analytically the partial wave Coulomb transition matrices at the energies of excited bound states.
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
Exact solutions for two nonlinear wave equations with nonlinear terms of any order
NASA Astrophysics Data System (ADS)
Chen, Yong; Li, Biao; Zhang, Hongqing
2005-03-01
In this paper, based on a variable-coefficient balancing-act method, by means of an appropriate transformation and with the help of Mathematica, we obtain some new types of solitary-wave solutions to the generalized Benjamin-Bona-Mahony (BBM) equation and the generalized Burgers-Fisher (BF) equation with nonlinear terms of any order. These solutions fully cover the various solitary waves of BBM equation and BF equation previously reported.
Imaging of s and d partial-wave interference in quantum scattering of identical bosonic atoms.
Thomas, Nicholas R; Kjaergaard, Niels; Julienne, Paul S; Wilson, Andrew C
2004-10-22
We report on the direct imaging of s and d partial-wave interference in cold collisions of atoms. Two ultracold clouds of 87Rb atoms were accelerated by magnetic fields to collide at energies near a d-wave shape resonance. The resulting halos of scattered particles were imaged using laser absorption. By scanning across the resonance we observed a marked evolution of the scattering patterns due to the energy dependent phase shifts for the interfering s and d waves. Since only two partial-wave states are involved in the collision process the scattering yield and angular distributions have a simple interpretation in terms of a theoretical model.
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.
Pseudo Rayleigh wave in a partially saturated non-dissipative porous solid
NASA Astrophysics Data System (ADS)
Sharma, M. D.
2016-09-01
Propagation of surface waves is studied at the pervious boundary of a porous solid saturated with a mixture of two immiscible fluids. An approach, based on continuum mixture theory, is used to derive a secular equation for the propagation of harmonic waves at the stress-free plane surface of this non-dissipative medium. Numerical analysis shows that this secular equation may not represent the propagation of true surface wave in the porous aggregate. Then, this equation is solved numerically for the propagation of pseudo Rayleigh wave or the leaky surface waves. To ensure the existence of pseudo Rayleigh wave, capillary effect between two (wetting and non-wetting) pore-fluids is related to the partial saturation. Effects of porosity and partial saturation coupled with capillary effect are observed on the phase velocity of pseudo Rayleigh waves in sandstone saturated with water-CO2 mixture.
NASA Astrophysics Data System (ADS)
Li, Biao; Chen, Yong; Zhang, Hongqing
2004-02-01
In this paper, by introducing some proper transformations, the applied range of the homogenous balance (HB) method is extended. With the help of Mathematica, we obtain three auto-Bäcklund transformations (BT) for the generalized Fithugh-Nagumo equation, the generalized Burgers-Fisher equation, the generalized Burgers-Huxley equation, respectively, by use of the extended HB method. From these BTs, some exact solutions for these equations are derived.
New Exact Traveling Wave Solutions of Some Nonlinear Higher-Dimensional Physical Models
NASA Astrophysics Data System (ADS)
Kim, Hyunsoo; Sakthivel, Rathinasamy
2012-08-01
In this paper, some new traveling wave solutions of the (4 + 1)-dimensional Fokas equation, (3 + 1)-dimensional Jumbo-Miwa equation and (2 + 1)-dimensional Boiti-Leon-Pempinelli equation are obtained through the ({GG)-expansion technique. The key idea of this technique is to take full advantage of a Riccati equation involving two parameters and use its solutions in obtaining the traveling wave solutions. The results reveal that this technique is very effective and powerful for solving higher-dimensional nonlinear problems arising in mathematical physics.
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.
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.
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
Overall coherence and coherent-mode expansion of spectrally partially coherent plane-wave pulses.
Lajunen, Hanna; Tervo, Jani; Vahimaa, Pasi
2004-11-01
The modal theory for spectrally partially coherent nonstationary plane waves is introduced. The theory is first developed in the space-frequency domain and then extended to the space-time domain. Propagation properties of the coherent modes are analyzed. The concept of the overall degree of coherence is extended to the domain of nonstationary fields, and it is shown that the overall degree of coherence of partially coherent plane-wave pulses is the same in the space-frequency and space-time domains. The theory is applied to the recently introduced concept of spectrally Gaussian Schell-model plane-wave pulses.
Overall coherence and coherent-mode expansion of spectrally partially coherent plane-wave pulses
NASA Astrophysics Data System (ADS)
Lajunen, Hanna; Tervo, Jani; Vahimaa, Pasi
2004-11-01
The modal theory for spectrally partially coherent nonstationary plane waves is introduced. The theory is first developed in the space-frequency domain and then extended to the space-time domain. Propagation properties of the coherent modes are analyzed. The concept of the overall degree of coherence is extended to the domain of nonstationary fields, and it is shown that the overall degree of coherence of partially coherent plane-wave pulses is the same in the space-frequency and space-time domains. The theory is applied to the recently introduced concept of spectrally Gaussian Schell-model plane-wave pulses.
Extracting scattering phase shifts in higher partial waves from lattice QCD calculations
Luu, Thomas; Savage, Martin J.
2011-06-01
Lüscher’s method is routinely used to determine meson-meson, meson-baryon, and baryon-baryon s-wave scattering amplitudes below inelastic thresholds from lattice QCD calculations—presently at unphysical light-quark masses. In this work we review the formalism and develop the requisite expressions to extract phase shifts describing meson-meson scattering in partial waves with angular momentum l≤6 and l=9. The implications of the underlying cubic symmetry, and strategies for extracting the phase shifts from lattice QCD calculations, are presented, along with a discussion of the signal-to-noise problem that afflicts the higher partial waves.
Treatment of ion-atom collisions using a partial-wave expansion of the projectile wavefunction
Foster, M; Colgan, J; Wong, T G; Madison, D H
2008-01-01
We present calculations of ion-atom collisions using a partial-wave expansion of the projectile wavefunction. Most calculations of ion-atom collisions have typically used classical or plane-wave approximations for the projectile wavefunction, since partial-wave expansions are expected to require prohibitively large numbers of terms to converge scattering quantities. Here we show that such calculations are possible using modern high-performance computing. We demonstrate the utility of our method by examining elastic scattering of protons by hydrogen and helium atoms, problems familiar to undergraduate students of atomic scattering. Application to ionization of helium using partial-wave expansions of the projectile wavefunction, which has long been desirable in heavy-ion collision physics, is thus quite feasible.
Exact soliton-on-plane-wave solutions for two-component Bose-Einstein condensates.
Li, Lu; Malomed, Boris A; Mihalache, Dumitru; Liu, W M
2006-06-01
By means of the Darboux transformation, we obtain analytical solutions for a soliton set on top of a plane-wave background in coupled Gross-Pitaevskii equations describing a binary Bose-Einstein condensate. We consider basic properties of the solutions with and without the cross interaction [cross phase modulation (XPM)] between the two components of the background. In the absence of the XPM, this solutions maintain properties of one-component condensates, such as the modulation instability (MI); in the presence of the cross interaction, the solutions exhibit different properties, such as restriction of the MI and soliton splitting.
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.
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
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.
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.
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.
Petrović, Nikola Z; Belić, Milivoj; Zhong, Wei-Ping
2011-02-01
We obtain exact traveling wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with variable coefficients and polynomial Kerr nonlinearity of an arbitrarily high order. Exact solutions, given in terms of Jacobi elliptic functions, are presented for the special cases of cubic-quintic and septic models. We demonstrate that the widely used method for finding exact solutions in terms of Jacobi elliptic functions is not applicable to the nonlinear Schrödinger equation with saturable nonlinearity.
Large-Scale Patterns of Waves in Partial Ice Cover in the Arctic Ocean
NASA Astrophysics Data System (ADS)
Smith, M.; Thomson, J. M.; Rogers, W.
2014-12-01
Surface waves are becoming a central feature of the emerging Arctic Ocean; however, few direct measurements of waves have been made. We present multi-year time series of wave height and ice draft from moorings at two locations in the Beaufort Sea, as well as wavelength and direction estimated from high-resolution satellite imagery. In situ wave and ice data are used to examine large-scale spatial and temporal patterns of waves in the previously ice-covered Arctic Ocean. In particular, we investigate the dependence of waves on ice-controlled fetch, and wave physics in partial ice cover in the Beaufort Sea. These results are compared with WaveWatch III hindcasts to evaluate the model's accuracy in the marginal ice zone. We will expand on the approach of Thomson and Rogers (2014), who found that the energy of waves in the Arctic is directly correlated with open water distances. Incorporating new (2014) data collected throughout the marginal ice zone, we will examine adjustments to conventional fetch scaling laws in the presence of partial ice cover.
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.
Robustness, Death of Spiral Wave in the Network of Neurons under Partial Ion Channel Block
NASA Astrophysics Data System (ADS)
Ma, Jun; Huang, Long; Wang, Chun-Ni; Pu, Zhong-Sheng
2013-02-01
The development of spiral wave in a two-dimensional square array due to partial ion channel block (Potassium, Sodium) is investigated, the dynamics of the node is described by Hodgkin—Huxley neuron and these neurons are coupled with nearest neighbor connection. The parameter ratio xNa (and xK), which defines the ratio of working ion channel number of sodium (potassium) to the total ion channel number of sodium (and potassium), is used to measure the shift conductance induced by channel block. The distribution of statistical variable R in the two-parameter phase space (parameter ratio vs. poisoning area) is extensively calculated to mark the parameter region for transition of spiral wave induced by partial ion channel block, the area with smaller factors of synchronization R is associated the parameter region that spiral wave keeps alive and robust to the channel poisoning. Spiral wave keeps alive when the poisoned area (potassium or sodium) and degree of intoxication are small, distinct transition (death, several spiral waves coexist or multi-arm spiral wave emergence) occurs under moderate ratio xNa (and xK) when the size of blocked area exceeds certain thresholds. Breakup of spiral wave occurs and multi-arm of spiral waves are observed when the channel noise is considered.
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.
Scattering of a partially-coherent wave from a material circular cylinder.
Hyde, Milo W; Bogle, Andrew E; Havrilla, Michael J
2013-12-30
The case of a partially-coherent wave scattered from a material circular cylinder is investigated. Expressions for the TMz and TEz scattered-field cross-spectral density functions are derived by utilizing the plane-wave spectrum representation of electromagnetic fields and cylindrical wave transformations. From the analytical scattered-field cross-spectral density functions, the mean scattering widths are derived and subsequently validated via comparison with those computed from Method of Moments Monte Carlo simulations. The analytical relations as well as the simulation results are discussed and physically interpreted. Key insights are noted and subsequently analyzed.
Aruldoss, C K; Dragomir, N M; Roberts, A
2007-10-01
We report on the application of a simple propagation-based phase-space tomographic technique to the determination of characteristic projections through the mutual optical intensity and the generalized radiance of a scalar, quasi-monochromatic partially coherent wave field. This method is applied to the reconstruction of the coherence functions of an initially spatially coherent optical wave field that has propagated through a suspension of polystyrene microspheres. As anticipated, we see that the field separates into a ballistic, or unscattered, component and a scattered component with a much shorter coherence length. Good agreement is obtained between experimental results and the results of a model based on a wave-transport equation.
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.
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.
Hendrick, R.E.
1981-01-10
This report details progress toward completion of a long-term pion-nucleon partial wave analysis, summarizing results and conclusions to date. The report also discussed progress in using partial wave and resonance parameter results to test dynamical models of the baryon and in better understanding interquark forces within baryons.
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.
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
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.
Breaking Wave Impact on a Partially Submerged Rigid Cube in Deep Water
NASA Astrophysics Data System (ADS)
Ikeda, C. M.; Choquette, M.; Duncan, J. H.
2011-11-01
The impact of a plunging breaking wave on a partially submerged cube is studied experimentally. The experiments are performed in a wave tank that is 14.8 m long, 1.15 m wide and 2.2 m high with a water depth of 0.91 m. A single repeatable plunging breaker is generated from a dispersively focused wave packet (average frequency of 1.4 Hz) that is created with a programmable wave maker. The rigid (L = 30 . 5 cm) cube is centered in the width of the tank and mounted from above with one face oriented normal to the oncoming wave. The position of the center of the front face of the cube is varied from the breaker location (xb ~ 6 . 35 m) to xb + 0 . 05 m in the streamwise direction and from - 0 . 25 L to 0 . 25 L vertically relative to the mean water level. A high-speed digital camera is used to record both white-light and laser-induced fluorescence (LIF) movies of the free surface shape in front of the cube before and after the wave impact. When the wave hits the cube just as the plunging jet is formed, a high-velocity vertical jet is created and the trajectory and maximum height of the jet are strongly influenced by the vertical position of the cube. Supported by the Office of Naval Research, Contract Monitor R. D. Joslin.
PARTIAL REFLECTION AND TRAPPING OF A FAST-MODE WAVE IN SOLAR CORONAL ARCADE LOOPS
Kumar, Pankaj; Innes, D. E.
2015-04-20
We report on the first direct observation of a fast-mode wave propagating along and perpendicular to cool (171 Å) arcade loops observed by the Solar Dynamics Observatory/Atmospheric Imaging Assembly (AIA). The wave was associated with an impulsive/compact flare near the edge of a sunspot. The EUV wavefront expanded radially outward from the flare center and decelerated in the corona from 1060 to 760 km s{sup −1} within ∼3–4 minutes. Part of the EUV wave propagated along a large-scale arcade of cool loops and was partially reflected back to the flare site. The phase speed of the wave was about 1450 km s{sup −1}, which is interpreted as a fast-mode wave. A second overlying loop arcade, orientated perpendicular to the cool arcade, is heated and becomes visible in the AIA hot channels. These hot loops sway in time with the EUV wave, as it propagated to and fro along the lower loop arcade. We suggest that an impulsive energy release at one of the footpoints of the arcade loops causes the onset of an EUV shock wave that propagates along and perpendicular to the magnetic field.
Raman rogue waves in a partially mode-locked fiber laser.
Runge, Antoine F J; Aguergaray, Claude; Broderick, Neil G R; Erkintalo, Miro
2014-01-15
We report on an experimental study of spectral fluctuations induced by intracavity Raman conversion in a passively partially mode-locked, all-normal dispersion fiber laser. Specifically, we use dispersive Fourier transformation to measure single-shot spectra of Raman-induced noise-like pulses, demonstrating that for low cavity gain values Raman emission is sporadic and follows rogue-wave-like probability distributions, while a saturated regime with Gaussian statistics is obtained for high pump powers. Our experiments further reveal intracavity rogue waves originating from cascaded Raman dynamics. PMID:24562136
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.
Renormalized effective actions in radially symmetric backgrounds: Partial wave cutoff method
Dunne, Gerald V.; Hur, Jin; Lee, Choonkyu
2006-10-15
The computation of the one-loop effective action in a radially symmetric background can be reduced to a sum over partial-wave contributions, each of which is the logarithm of an appropriate one-dimensional radial determinant. While these individual radial determinants can be evaluated simply and efficiently using the Gel'fand-Yaglom method, the sum over all partial-wave contributions diverges. A renormalization procedure is needed to unambiguously define the finite renormalized effective action. Here we use a combination of the Schwinger proper-time method, and a resummed uniform DeWitt expansion. This provides a more elegant technique for extracting the large partial-wave contribution, compared to the higher-order radial WKB approach which had been used in previous work. We illustrate the general method with a complete analysis of the scalar one-loop effective action in a class of radially separable SU(2) Yang-Mills background fields. We also show that this method can be applied to the case where the background gauge fields have asymptotic limits appropriate to uniform field strengths, such as, for example, in the Minkowski solution, which describes an instanton immersed in a constant background. Detailed numerical results will be presented in a sequel.
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.
Ebrahimi, V.; Esfandyari-Kalejahi, A.
2014-09-15
In this paper, first we represent the differences between spatial and temporal dispersions and their dependence on the measurement techniques for electrostatic waves in unmagnetized collisionless plasma. Then, three different experimental data are compared to the solutions of exact nonextensive dispersion relations for electron-ion and pair plasma. The results confirm the existence of new acoustic plasma waves. Furthermore, these comparisons yield a Maxwellian and a nonextensive plasma with nonextensive parameter q larger than one, and a Maxwellian plasma with some abnormal dispersion properties.
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)
Zhao, J.; Yi, X.; Shen, X.; Wang, R.; Yeh, P.
We investigate the effect of beam coherence on four-wave mixing via reflection gratings in photorefractive media. For the case of phase conjugation, the results of our theoretical analysis indicate that partial coherence always leads to a drop of signal gain and phase conjugate reflectivity in non-depleted cases. In general, the mutual coherence of the signal beam and the pump beam can be enhanced due to the process of wave mixing. The mutual coherence of the phase conjugate beam and one of the pump beams depends on the beam intensity ratio as well as the optical path difference. This is distinctly different from the four-wave mixing case with a transmission grating.
NASA Astrophysics Data System (ADS)
Santucci, F.; Santini, P. M.
2016-10-01
We study the generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one-dimensional waves in the absence of dispersion and dissipation, and arising in several physical contexts, like acoustics, plasma physics, hydrodynamics and nonlinear optics. In 2 + 1 dimensions and with quadratic nonlinearity, this equation is integrable through a novel inverse scattering transform, and it has been recently shown to be a prototype model equation in the description of the two-dimensional wave breaking of localized initial data. In higher dimensions and with higher nonlinearity, the generalized dKP equations are not integrable, but their invariance under motions on the paraboloid allows one to construct in this paper a family of exact solutions describing waves constant on their paraboloidal wave front and breaking simultaneously in all points of it, developing after breaking either multivaluedness or single-valued discontinuous profiles (shocks). Then such exact solutions are used to build the longtime behavior of the solutions of the Cauchy problem, for small and localized initial data, showing that wave breaking of small initial data takes place in the longtime regime if and only if m(n-1)≤slant 2. Lastly, the analytic aspects of such wave breaking are investigated in detail in terms of the small initial data, in both cases in which the solution becomes multivalued after breaking or it develops a shock. These results, contained in the 2012 master’s thesis of one of the authors (FS) [1], generalize those obtained in [2] for the dKP equation in n+1 dimensions with quadratic nonlinearity, and are obtained following the same strategy.
NASA Astrophysics Data System (ADS)
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.
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.
Nucleon-nucleon scattering in the 1S0 partial wave in the modified Weinberg approach
NASA Astrophysics Data System (ADS)
Gasparyan, A. M.; Epelbaum, E.; Gegelia, J.; Krebs, H.
2016-03-01
Nucleon-nucleon scattering in the 1S0 partial wave is considered in chiral effective field theory within the recently suggested renormalizable formulation based on the Kadyshevsky equation. Contact interactions are taken into account beyond the leading-order approximation. The subleading contact terms are included non-perturbatively by means of subtractive renormalization. The dependence of the phase shifts on the choice of the renormalization condition is discussed. Perturbative inclusion of the subleading contact interaction is found to be justified only very close to threshold. The low-energy theorems are reproduced significantly better compared with the leading order results.
Evaporative cooling of metastable helium in the multi-partial-wave regime
Nguyen, Scott V.; Doret, S. Charles; Connolly, Colin B.; Michniak, Robert A.; Doyle, John M.; Ketterle, Wolfgang
2005-12-15
Metastable helium is buffer gas cooled, magnetically trapped, and evaporatively cooled in large numbers. 10{sup 11} {sup 4}He{sup *} atoms are trapped at an initial temperature of 400 mK and evaporatively cooled into the ultracold regime, resulting in a cloud of 2{+-}0.5x10{sup 9} atoms at 1.4{+-}0.2 mK. Efficient evaporation indicates low collisional loss for {sup 4}He{sup *} in both the ultracold and multi-partial-wave regime, in agreement with theory.
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.
NASA Astrophysics Data System (ADS)
Dembiński, S. T.; Makowski, A. J.; Pepłowski, P.; Wolniewicz, L.
1996-04-01
We attempt to show both analytically and numerically that a recent work by Willemsen
NASA Astrophysics Data System (ADS)
Xiao, Xifeng
One of the main drawbacks that prevent the extensive application of free space laser communications is the atmospheric turbulence through which the beam must propagate. For the past four decades, much attention has been devoted to finding different methods to overcome this difficulty. A partially coherent beam (PCB) has been recognized as an effective approach to improve the performance of an atmospheric link. It has been examined carefully with most analyses considering the Gaussian Schell-model (GSM) beam. However, practical PCBs may not follow GSM theory and are better examined through some numerical simulation approach such as a wave optics simulation. Consequently, an approach for modeling the spatially PCB in wave optics simulation is presented here. The approach involves the application of a sequence of random phase screens to an initial beam field and the summation of the intensity results after propagation. The relationship between the screen parameters and the spatial coherence function for the beam is developed and the approach is verified by comparing results with analytic formulations for a Gaussian Schell-model (GSM) beam. A variety of simulation studies were performed for this dissertation. The propagation through turbulence of a coherent beam and a particular version of a PCB, a pseudo-partially coherent beam (PPCB), is analyzed. The beam is created with a sequence of several Gaussian random phase screens for each atmospheric realization. The average intensity profiles, the scintillation index and aperture averaging factor for a horizontal propagation scenario are examined. Comparisons between these results and their corresponding analytic results for the well-known GSM beam are also made. Cumulative probability density functions for the received irradiance are initially investigated. Following the general simulation investigations, a performance metric is proposed as a general measure for optimizing the transverse coherence length of a partial
NASA Astrophysics Data System (ADS)
Syrotyuk, S. V.; Kynash, Yu. E.; Sobchuk, I. S.
1997-03-01
The formula for calculating the spectrum gradient gk = gradk E(k) at an arbitrary point k in the Brillouin zone has been derived on the basis of the new completely orthogonalized plane wave formalism (COPW). This important physical quantity has been obtained within the COPW basis for the first time. It displays a true plane wave basis limit.
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
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.
Bulanov, Sergei V; Esirkepov, Timur Zh; Kando, Masaki; Koga, James K; Bulanov, Stepan S
2011-11-01
When the parameters of electron-extreme power laser interaction enter the regime of dominated radiation reaction, the electron dynamics changes qualitatively. The adequate theoretical description of this regime becomes crucially important with the use of the radiation friction force either in the Lorentz-Abraham-Dirac form, which possesses unphysical runaway solutions, or in the Landau-Lifshitz form, which is a perturbation valid for relatively low electromagnetic wave amplitude. The goal of the present paper is to find the limits of the Landau-Lifshitz radiation force applicability in terms of the electromagnetic wave amplitude and frequency. For this, a class of the exact solutions to the nonlinear problems of charged particle motion in the time-varying electromagnetic field is used.
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.
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
Partial-wave expansion for photoproduction of two pseudoscalars on a nucleon
NASA Astrophysics Data System (ADS)
Fix, A.; Arenhövel, H.
2012-03-01
The amplitudes for photoproduction of two pseudoscalars on a nucleon are expanded in the overall center-of-momentum (c.m.) frame in a model-independent way with respect to the contribution of the final-state partial wave of total angular momentum J and its projection on the normal to the plane spanned by the momenta of the final particles. The expansion coefficients, which are analogs to the multipole amplitudes for single-meson photoproduction, contain the complete information about the reaction dynamics. Results of an explicit evaluation are presented for the moments Wjm of the inclusive angular distribution of an incident photon beam with respect to the c.m. coordinate system defined by the final particles, taking photoproduction of π0π0 and π0η as an example.
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.
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.
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
Partial-wave analysis of n +241Am reaction cross sections in the resonance region
NASA Astrophysics Data System (ADS)
Noguere, G.; Bouland, O.; Kopecky, S.; Lampoudis, C.; Schillebeeckx, P.; Plompen, A.; Gunsing, F.; Sage, C.; Sirakov, I.
2015-07-01
Cross sections for neutron-induced reactions of 241Am in the resonance region have been evaluated. Results of time-of-flight cross section experiments carried out at the GELINA, LANSCE, ORELA and Saclay facilities have been combined with optical model calculations to derive consistent cross sections from the thermal energy region up to the continuum region. Resolved resonance parameters were derived from a resonance shape analysis of transmissions, capture yields, and fission yields in the energy region up to 150 eV using the refit code. From a statistical analysis of these parameters, a neutron strength function (104S0=1.01 ±0.12 ), mean level spacing (D0=0.60 ±0.01 eV) and average radiation width (<Γγ 0>=43.3 ±1.1 meV) for s -wave resonances were obtained. Neutron strength functions for higher partial waves (l >0 ) together with channel and effective scattering radii were deduced from calculations based on a complex mean-field optical model potential, applying an equivalent hard-sphere scattering radius approximation.
X-ray standing wave analysis of nanostructures using partially coherent radiation
Tiwari, M. K. Das, Gangadhar; Bedzyk, M. J.
2015-09-07
The effect of longitudinal (or temporal) coherence on total reflection assisted x-ray standing wave (TR-XSW) analysis of nanoscale materials is quantitatively demonstrated by showing how the XSW fringe visibility can be strongly damped by decreasing the spectral resolution of the incident x-ray beam. The correction for nonzero wavelength dispersion (δλ ≠ 0) of the incident x-ray wave field is accounted for in the model computations of TR-XSW assisted angle dependent fluorescence yields of the nanostructure coatings on x-ray mirror surfaces. Given examples include 90 nm diameter Au nanospheres deposited on a Si(100) surface and a 3 nm thick Zn layer trapped on top a 100 nm Langmuir-Blodgett film coating on a Au mirror surface. Present method opens up important applications, such as enabling XSW studies of large dimensioned nanostructures using conventional laboratory based partially coherent x-ray sources.
Fast solution of elliptic partial differential equations using linear combinations of plane waves
NASA Astrophysics Data System (ADS)
Pérez-Jordá, José M.
2016-02-01
Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations A x =b , where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O (N logN ) memory and executing an iteration in O (N log2N ) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.
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.
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.
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
Hansson, T; Lisak, M; Anderson, D
2012-02-10
It is shown that the evolution equations describing partially coherent wave propagation in noninstantaneous Kerr media are integrable and have an infinite number of invariants. A recursion relation for generating these invariants is presented, and it is demonstrated how to express them in the coherent density, self-consistent multimode, mutual coherence, and Wigner formalisms.
El-Ocla, Hosam
2006-08-01
The characteristics of a radar cross section (RCS) of partially convex targets with large sizes up to five wavelengths in free space and random media are studied. The nature of the incident wave is an important factor in remote sensing and radar detection applications. I investigate the effects of beam wave incidence on the performance of RCS, drawing on the method I used in a previous study on plane-wave incidence. A beam wave can be considered a plane wave if the target size is smaller than the beam width. Therefore, to have a beam wave with a limited spot on the target, the target size should be larger than the beam width (assuming E-wave incidence wave polarization. The effects of the target configuration, random medium parameters, and the beam width on the laser RCS and the enhancement in the radar cross section are numerically analyzed, resulting in the possibility of having some sort of control over radar detection using beam wave incidence.
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.
An Embedded Cluster Self-Consistent Partial Wave Method using Divide and Conquer
Averill, Frank; Painter, Gayle S
2008-04-01
An efficient approach to extending the spatial scale of electronic structure calculations is described in this work. The method is formulated as a combination of the interacting fragments concept of Harris [J. Harris, Phys. Rev. B 31, 1770 (1985)] and the D&C method of Yang [W. Yang, Phys. Rev. Lett. 66, 1438 (1991)], which recognizes the intrinsic locality of electron bonding and is devised to optimize the total electron charge density within an approximate representation of partitioned components. Beginning with a brief review of D&C concepts, we report results from this new method using the D&C as an embedding method for coupling an atomic cluster to its extended environment. The convergence properties as implemented within the self-consistent partial wave linear variational method (SCPW) are illustrated through various applications. In particular, results from a study of the adsorption of La atoms at the prism plane of -Si3N4 demonstrate the practicality of the SCPW using D&C as an embedding technique. PACS numbers: 71.15.Mb, 31.15.Ew, 31.50.Bc
Partial wave analyses of J/ψ→γππ and γππ
NASA Astrophysics Data System (ADS)
BES Collaboration; Ablikim, M.; Bai, J. Z.; Ban, Y.; Bian, J. G.; Cai, X.; Chen, H. F.; Chen, H. S.; Chen, H. X.; Chen, J. C.; Chen, Jin; Chen, Y. B.; Chi, S. P.; Chu, Y. P.; Cui, X. Z.; Dai, Y. S.; Diao, L. Y.; Deng, Z. Y.; Dong, Q. F.; Du, S. X.; Fang, J.; Fang, S. S.; Fu, C. D.; Gao, C. S.; Gao, Y. N.; Gu, S. D.; Gu, Y. T.; Guo, Y. N.; Guo, Y. Q.; Guo, Z. J.; Harris, F. A.; He, K. L.; He, M.; Heng, Y. K.; Hu, H. M.; Hu, T.; Huang, G. S.; Huang, X. T.; Ji, X. B.; Jiang, X. S.; Jiang, X. Y.; Jiao, J. B.; Jin, D. P.; Jin, S.; Jin, Yi; Lai, Y. F.; Li, G.; Li, H. B.; Li, H. H.; Li, J.; Li, R. Y.; Li, S. M.; Li, W. D.; Li, W. G.; Li, X. L.; Li, X. N.; Li, X. Q.; Li, Y. L.; Liang, Y. F.; Liao, H. B.; Liu, B. J.; Liu, C. X.; Liu, F.; Liu, Fang; Liu, H. H.; Liu, H. M.; Liu, J.; Liu, J. B.; Liu, J. P.; Liu, Q.; Liu, R. G.; Liu, Z. A.; Lou, Y. C.; Lu, F.; Lu, G. R.; Lu, J. G.; Luo, C. L.; Ma, F. C.; Ma, H. L.; Ma, L. L.; Ma, Q. M.; Ma, X. B.; Mao, Z. P.; Mo, X. H.; Nie, J.; Olsen, S. L.; Peng, H. P.; Ping, R. G.; Qi, N. D.; Qin, H.; Qiu, J. F.; Ren, Z. Y.; Rong, G.; Shan, L. Y.; Shang, L.; Shen, C. P.; Shen, D. L.; Shen, X. Y.; Sheng, H. Y.; Sun, H. S.; Sun, J. F.; Sun, S. S.; Sun, Y. Z.; Sun, Z. J.; Tan, Z. Q.; Tang, X.; Tong, G. L.; Varner, G. S.; Wang, D. Y.; Wang, L.; Wang, L. L.; Wang, L. S.; Wang, M.; Wang, P.; Wang, P. L.; Wang, W. F.; Wang, Y. F.; Wang, Z.; Wang, Z. Y.; Wang, Zhe; Wang, Zheng; Wei, C. L.; Wei, D. H.; Wu, N.; Xia, X. M.; Xie, X. X.; Xu, G. F.; Xu, X. P.; Xu, Y.; Yan, M. L.; Yang, H. X.; Yang, Y. X.; Ye, M. H.; Ye, Y. X.; Yi, Z. Y.; Yu, G. W.; Yuan, C. Z.; Yuan, J. M.; Yuan, Y.; Zang, S. L.; Zeng, Y.; Zeng, Yu; Zhang, B. X.; Zhang, B. Y.; Zhang, C. C.; Zhang, D. H.; Zhang, H. Q.; Zhang, H. Y.; Zhang, J. W.; Zhang, J. Y.; Zhang, S. H.; Zhang, X. M.; Zhang, X. Y.; Zhang, Yiyun; Zhang, Z. P.; Zhao, D. X.; Zhao, J. W.; Zhao, M. G.; Zhao, P. P.; Zhao, W. R.; Zhao, Z. G.; Zheng, H. Q.; Zheng, J. P.; Zheng, Z. P.; Zhou, L.; Zhou, N. F.; Zhu, K. J.; Zhu, Q. M.; Zhu, Y. C.; Zhu, Y. S.; Zhu, Yingchun; Zhu, Z. A.; Zhuang, B. A.; Zhuang, X. A.; Zou, B. S.
2006-11-01
Results are presented on J/ψ radiative decays to ππ and ππ based on a sample of 58M J/ψ events taken with the BES II detector. Partial wave analyses are carried out using the relativistic covariant tensor amplitude method in the 1.0 to 2.3GeV/cππ mass range. There are conspicuous peaks due to the f(1270) and two 0 states in the 1.45 and 1.75 GeV/c mass regions. The first 0 state has a mass of 1466±6±20MeV/c, a width of 108-11+14±25MeV/c, and a branching fraction B(J/ψ→γf(1500)→γππ)=(0.67±0.02±0.30)×10. Spin 0 is strongly preferred over spin 2. The second 0 state peaks at 1765-3+4±13MeV/c with a width of 145±8±69MeV/c. If this 0 is interpreted as coming from f(1710), the ratio of its branching fractions to ππ and KK¯ is 0.41-0.17+0.11.
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.
Almassalha, Luay M.; Bauer, Greta M.; Chandler, John E.; Gladstein, Scott; Cherkezyan, Lusik; Stypula-Cyrus, Yolanda; Weinberg, Samuel; Zhang, Di; Thusgaard Ruhoff, Peder; Roy, Hemant K.; Subramanian, Hariharan; Chandel, Navdeep S.; Szleifer, Igal; Backman, Vadim
2016-01-01
The organization of chromatin is a regulator of molecular processes including transcription, replication, and DNA repair. The structures within chromatin that regulate these processes span from the nucleosomal (10-nm) to the chromosomal (>200-nm) levels, with little known about the dynamics of chromatin structure between these scales due to a lack of quantitative imaging technique in live cells. Previous work using partial-wave spectroscopic (PWS) microscopy, a quantitative imaging technique with sensitivity to macromolecular organization between 20 and 200 nm, has shown that transformation of chromatin at these length scales is a fundamental event during carcinogenesis. As the dynamics of chromatin likely play a critical regulatory role in cellular function, it is critical to develop live-cell imaging techniques that can probe the real-time temporal behavior of the chromatin nanoarchitecture. Therefore, we developed a live-cell PWS technique that allows high-throughput, label-free study of the causal relationship between nanoscale organization and molecular function in real time. In this work, we use live-cell PWS to study the change in chromatin structure due to DNA damage and expand on the link between metabolic function and the structure of higher-order chromatin. In particular, we studied the temporal changes to chromatin during UV light exposure, show that live-cell DNA-binding dyes induce damage to chromatin within seconds, and demonstrate a direct link between higher-order chromatin structure and mitochondrial membrane potential. Because biological function is tightly paired with structure, live-cell PWS is a powerful tool to study the nanoscale structure–function relationship in live cells. PMID:27702891
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.
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)
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.
Effect of H-wave polarization on laser radar detection of partially convex targets in random media.
El-Ocla, Hosam
2010-07-01
A study on the performance of laser radar cross section (LRCS) of conducting targets with large sizes is investigated numerically in free space and random media. The LRCS is calculated using a boundary value method with beam wave incidence and H-wave polarization. Considered are those elements that contribute to the LRCS problem including random medium strength, target configuration, and beam width. The effect of the creeping waves, stimulated by H-polarization, on the LRCS behavior is manifested. Targets taking large sizes of up to five wavelengths are sufficiently larger than the beam width and are sufficient for considering fairly complex targets. Scatterers are assumed to have analytical partially convex contours with inflection points.
Exactly conservation integrators
Shadwick, B.A.; Bowman, J.C.; Morrison, P.J.
1999-03-01
Traditional explicit numerical discretizations of conservative systems generically predict artificial secular drifts of any nonlinear invariants. In this work the authors present a general approach for developing explicit nontraditional algorithms that conserve such invariants exactly. They illustrate the method by applying it to the three-wave truncation of the Euler equations, the Lotka-Volterra predator-prey model, and the Kepler problem. The ideas are discussed in the context of symplectic (phase-space-conserving) integration methods as well as nonsymplectic conservative methods. They comment on the application of the method to general conservative systems.
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.
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.
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.
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
Dunne, Gerald V.; Hur, Jin; Lee, Choonkyu; Min, Hyunsoo
2008-02-15
Our previously developed calculational method (the partial-wave cutoff method) is employed to evaluate explicitly scalar one-loop effective actions in a class of radially symmetric background gauge fields. Our method proves to be particularly effective when it is used in conjunction with a systematic WKB series for the large partial-wave contribution to the effective action. By comparing these numerically exact calculations against the predictions based on the large-mass expansion and derivative expansion, we discuss the validity ranges of the latter approximation methods.
Ultrasonic wave propagation on an inclined solid half-space partially immersed in a liquid
NASA Astrophysics Data System (ADS)
Dao, Cac Minh
The interaction between a bounded ultrasonic beam and a liquid wedge over a solid half-space is studied theoretically as well as experimentally. A semi-analytical technique called Distributed Point Source Method (DPSM) is adopted for modeling the ultrasonic field in a wedge-shaped fluid structure on a solid half-space. This study is important for analyzing and understanding the propagation of ultrasonic waves used for underwater communications and inspections. A better understanding of the elastic wave propagation in water and in submerged marine strata near the seashore requires extensive investigations of such problem geometries. The semi-analytical technique used in this dissertation considers a bounded acoustic beam striking a fluid-solid interface between a fluid wedge and a solid half-space. Solution of this problem is beyond the scope of the currently available analytical methods when the beam is bounded. However, it is important to model the bounded beams because, in all underwater communications and inspections, bounded beams are used. Currently, only numerical method [Boundary Element Method (BEM) or Finite Element Method (FEM)] based packages (e.g., PZFlex) are in principle capable of modeling ultrasonic fields in such structures. However, these packages are not very accurate and are very CPU-intensive for high-frequency ultrasonic problems. At high frequencies, FEM- and BEM-based packages require huge amount of computation memory and time for their executions that the DPSM technique can avoid. The effect of the angle variation between the fluid-solid interface and the fluid wedge on the wave propagation characteristics is studied and presented.
Kushiyama, Yasunori; Honjo, Haruo; Niwa, Ryoko; Takanari, Hiroki; Yamazaki, Masatoshi; Takemoto, Yoshio; Sakuma, Ichiro; Kodama, Itsuo; Kamiya, Kaichiro
2016-09-01
It has been reported that blockade of the inward rectifier K(+) current (IK1) facilitates termination of ventricular fibrillation. We hypothesized that partial IK1 blockade destabilizes spiral wave (SW) re-entry, leading to its termination. Optical action potential (AP) signals were recorded from left ventricles of Langendorff-perfused rabbit hearts with endocardial cryoablation. The dynamics of SW re-entry were analyzed during ventricular tachycardia (VT), induced by cross-field stimulation. Intercellular electrical coupling in the myocardial tissue was evaluated by the space constant. In separate experiments, AP recordings were made using the microelectrode technique from right ventricular papillary muscles of rabbit hearts. Ba(2+) (10-50 μM) caused a dose-dependent prolongation of VT cycle length and facilitated termination of VT in perfused hearts. Baseline VT was maintained by a stable rotor, where an SW rotated around an I-shaped functional block line (FBL). Ba(2+) at 10 μM prolonged I-shaped FBL and phase-singularity trajectory, whereas Ba(2+) at 50 μM transformed the SW rotation dynamics from a stable linear pattern to unstable circular/cycloidal meandering. The SW destabilization was not accompanied by SW breakup. Under constant pacing, Ba(2+) caused a dose-dependent prolongation of APs, and Ba(2+) at 50 μM decreased conduction velocity. In papillary muscles, Ba(2+) at 50 μM depolarized the resting membrane potential. The space constant was increased by 50 μM Ba(2+) Partial IK1 blockade destabilizes SW rotation dynamics through a combination of prolongation of the wave length, reduction of excitability, and enhancement of electrotonic interactions, which facilitates termination of ventricular tachyarrhythmias. PMID:27422985
Kushiyama, Yasunori; Honjo, Haruo; Niwa, Ryoko; Takanari, Hiroki; Yamazaki, Masatoshi; Takemoto, Yoshio; Sakuma, Ichiro; Kodama, Itsuo; Kamiya, Kaichiro
2016-09-01
It has been reported that blockade of the inward rectifier K(+) current (IK1) facilitates termination of ventricular fibrillation. We hypothesized that partial IK1 blockade destabilizes spiral wave (SW) re-entry, leading to its termination. Optical action potential (AP) signals were recorded from left ventricles of Langendorff-perfused rabbit hearts with endocardial cryoablation. The dynamics of SW re-entry were analyzed during ventricular tachycardia (VT), induced by cross-field stimulation. Intercellular electrical coupling in the myocardial tissue was evaluated by the space constant. In separate experiments, AP recordings were made using the microelectrode technique from right ventricular papillary muscles of rabbit hearts. Ba(2+) (10-50 μM) caused a dose-dependent prolongation of VT cycle length and facilitated termination of VT in perfused hearts. Baseline VT was maintained by a stable rotor, where an SW rotated around an I-shaped functional block line (FBL). Ba(2+) at 10 μM prolonged I-shaped FBL and phase-singularity trajectory, whereas Ba(2+) at 50 μM transformed the SW rotation dynamics from a stable linear pattern to unstable circular/cycloidal meandering. The SW destabilization was not accompanied by SW breakup. Under constant pacing, Ba(2+) caused a dose-dependent prolongation of APs, and Ba(2+) at 50 μM decreased conduction velocity. In papillary muscles, Ba(2+) at 50 μM depolarized the resting membrane potential. The space constant was increased by 50 μM Ba(2+) Partial IK1 blockade destabilizes SW rotation dynamics through a combination of prolongation of the wave length, reduction of excitability, and enhancement of electrotonic interactions, which facilitates termination of ventricular tachyarrhythmias.
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.
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
1980-12-01
Sufficiently close to 0, the solution variety of a nonlinear relativistic wave equation-e.g., of the form squarevarphi + m(2)varphi + gvarphi(p) = 0-admits a canonical Lorentz-invariant hermitian structure, uniquely determined by the consideration that the action of the differential scattering transformation in each tangent space be unitary. Similar results apply to linear time-dependent equations or to equations in a curved asymptotically flat space-time. A close relation of the Riemannian structure to the determination of vacuum expectation values is developed and illustrated by an explicit determination of a perturbative 2-point function for the case of interaction arising from curvature. The theory underlying these developments is in part a generalization of that of M. G. Krein and collaborators concerning stability of differential equations in Hilbert space and in part a precise relation between the unitarization of given symplectic linear actions and their full probabilistic quantization. The unique causal structure in the infinite symplectic group is instrumental in these developments. PMID:16592923
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
An exact solution of the Jackiw-Rebbi equations for a fermion-monopole-Higgs system
NASA Astrophysics Data System (ADS)
Din, A. M.; Roy, S. M.
1983-09-01
We present an exact solution for arbitrary partial waves to the Jackiw-Rebbi equations for an isospinor fermion in the background of a non-abelian singular magnetic monopole and a Higgs field. The Higgs coupling produces a centrifugal barrier making the hamiltonian self-adjoint with ordinary boundary conditions at the origin. There are infinitely many bound states, each doubly degenerate. The scattering is charge conserving.
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)].
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.
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.
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.
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.
Partial wave analyses of J / ψ → γπ+π- and γπ0π0
NASA Astrophysics Data System (ADS)
Ablikim, M.; Bai, J. Z.; Ban, Y.; Bian, J. G.; Cai, X.; Chen, H. F.; Chen, H. S.; Chen, H. X.; Chen, J. C.; Chen, Jin; Chen, Y. B.; Chi, S. P.; Chu, Y. P.; Cui, X. Z.; Dai, Y. S.; Diao, L. Y.; Deng, Z. Y.; Dong, Q. F.; Du, S. X.; Fang, J.; Fang, S. S.; Fu, C. D.; Gao, C. S.; Gao, Y. N.; Gu, S. D.; Gu, Y. T.; Guo, Y. N.; Guo, Y. Q.; Guo, Z. J.; Harris, F. A.; He, K. L.; He, M.; Heng, Y. K.; Hu, H. M.; Hu, T.; Huang, G. S.; Huang, X. T.; Ji, X. B.; Jiang, X. S.; Jiang, X. Y.; Jiao, J. B.; Jin, D. P.; Jin, S.; Jin, Yi; Lai, Y. F.; Li, G.; Li, H. B.; Li, H. H.; Li, J.; Li, R. Y.; Li, S. M.; Li, W. D.; Li, W. G.; Li, X. L.; Li, X. N.; Li, X. Q.; Li, Y. L.; Liang, Y. F.; Liao, H. B.; Liu, B. J.; Liu, C. X.; Liu, F.; Liu, Fang; Liu, H. H.; Liu, H. M.; Liu, J.; Liu, J. B.; Liu, J. P.; Liu, Q.; Liu, R. G.; Liu, Z. A.; Lou, Y. C.; Lu, F.; Lu, G. R.; Lu, J. G.; Luo, C. L.; Ma, F. C.; Ma, H. L.; Ma, L. L.; Ma, Q. M.; Ma, X. B.; Mao, Z. P.; Mo, X. H.; Nie, J.; Olsen, S. L.; Peng, H. P.; Ping, R. G.; Qi, N. D.; Qin, H.; Qiu, J. F.; Ren, Z. Y.; Rong, G.; Shan, L. Y.; Shang, L.; Shen, C. P.; Shen, D. L.; Shen, X. Y.; Sheng, H. Y.; Sun, H. S.; Sun, J. F.; Sun, S. S.; Sun, Y. Z.; Sun, Z. J.; Tan, Z. Q.; Tang, X.; Tong, G. L.; Varner, G. S.; Wang, D. Y.; Wang, L.; Wang, L. L.; Wang, L. S.; Wang, M.; Wang, P.; Wang, P. L.; Wang, W. F.; Wang, Y. F.; Wang, Z.; Wang, Z. Y.; Wang, Zhe; Wang, Zheng; Wei, C. L.; Wei, D. H.; Wu, N.; Xia, X. M.; Xie, X. X.; Xu, G. F.; Xu, X. P.; Xu, Y.; Yan, M. L.; Yang, H. X.; Yang, Y. X.; Ye, M. H.; Ye, Y. X.; Yi, Z. Y.; Yu, G. W.; Yuan, C. Z.; Yuan, J. M.; Yuan, Y.; Zang, S. L.; Zeng, Y.; Zeng, Yu; Zhang, B. X.; Zhang, B. Y.; Zhang, C. C.; Zhang, D. H.; Zhang, H. Q.; Zhang, H. Y.; Zhang, J. W.; Zhang, J. Y.; Zhang, S. H.; Zhang, X. M.; Zhang, X. Y.; Zhang, Yiyun; Zhang, Z. P.; Zhao, D. X.; Zhao, J. W.; Zhao, M. G.; Zhao, P. P.; Zhao, W. R.; Zhao, Z. G.; Zheng, H. Q.; Zheng, J. P.; Zheng, Z. P.; Zhou, L.; Zhou, N. F.; Zhu, K. J.; Zhu, Q. M.; Zhu, Y. C.; Zhu, Y. S.; Zhu, Yingchun; Zhu, Z. A.; Zhuang, B. A.; Zhuang, X. A.; Zou, B. S.; BES Collaboration
2006-11-01
Results are presented on J / ψ radiative decays to π+π- and π0π0 based on a sample of 58M J / ψ events taken with the BES II detector. Partial wave analyses are carried out using the relativistic covariant tensor amplitude method in the 1.0 to 2.3GeV /c2 ππ mass range. There are conspicuous peaks due to the f2 (1270) and two 0++ states in the 1.45 and 1.75 GeV /c2 mass regions. The first 0++ state has a mass of 1466 ± 6 ± 20MeV /c2, a width of 108-11+14 ± 25MeV /c2, and a branching fraction B (J / ψ → γf0 (1500) → γπ+π-) = (0.67 ± 0.02 ± 0.30) ×10-4. Spin 0 is strongly preferred over spin 2. The second 0++ state peaks at 1765-3+4 ± 13MeV /c2 with a width of 145 ± 8 ± 69MeV /c2. If this 0++ is interpreted as coming from f0 (1710), the ratio of its branching fractions to ππ and KKbar is 0.41-0.17+0.11.
Partial-wave analysis of {pi}{sup -}{pi}{sup 0}{pi}{sup 0} events at 18 GeV/c
Brown, D. S.
1998-05-29
A partial-wave analysis has been performed on 170 K {pi}{sup -}{pi}{sup 0}{pi}{sup 0} events produced in the reaction {pi}{sup -}p{yields}p{pi}{sup -}{pi}{sup 0}{pi}{sup 0}, and the results of the mass-independent fits are presented. The objective was to confirm the existence of the {pi}(1800) and the exotic J{sup PC}=1{sup -+} object, reported by VES.
NASA Astrophysics Data System (ADS)
Guseinov, I. I.; Mamedov, B. A.; Ekenoğlu, A. S.
2006-08-01
A detailed study is undertaken, using various techniques, in deriving analytical formula of Franck-Condon overlap integrals and matrix elements of various functions of power (x), exponential (exp(-2cx)) and Gaussian (exp(-cx)) over displaced harmonic oscillator wave functions with arbitrary frequencies. The results suggested by previous experience with various algorithms are presented in mathematically compact form and consist of generalization. The relationships obtained are valid for the arbitrary values of parameters and the computation results are in good agreement with the literature. The numerical results illustrate clearly a further reduction in calculation times. Program summaryProgram name:FRANCK Catalogue identifier:ADXX_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXX_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Programming language:Mathematica 5.0 Computer:Pentium M 1.4 GHz Operating system:Mathematica 5.0 RAM:512 MB No. of lines in distributed program, including test data, etc.:825 No. of bytes in distributed program, including test data, etc.:16 344 Distribution format:tar.gz Nature of problem:The programs calculate the Franck-Condon factors and matrix elements over displaced harmonic oscillator wave functions with arbitrary quantum numbers (n,n), frequencies (a,a) and displacement (d) for the various functions of power (x), exponential (exp(-2cx)) and Gaussian (exp(-cx)). Solution method:The Franck-Condon factors and matrix elements are evaluated using binomial coefficients and basic integrals. Restrictions:The results obtained by the present programs show great numerical stability for arbitrary quantum numbers (n,n), frequencies (a,a) and displacement (d). Unusual features:None Running time:As an example, for the value of Franck-Condon Overlap Integral I(d;α,α)=0.004405001887372332 with n=3, n=2, a=4, a=3, d=2, the compilation time in a Pentium M 1.4 GHz computer is 0.18 s. Execution
NASA Astrophysics Data System (ADS)
Vitanov, Nikolay K.
2010-08-01
We search for traveling-wave solutions of the class of equations ∑p=1N1αp{∂pQ}/{∂tp}+∑q=1N2βq{∂qQ}/{∂xq}+∑m=1MμmQm=0 where αp,βq and μm are parameters. We obtain such solutions by the method of simplest equation for the cases when the simplest equation is the the equation of Bernoulli or the equation of Riccati. We modify the methodology of the simplest equation of Kudryashov as follows. Kudryashov uses the first step of the test for Painleve property in order to determine the size of the solution of the studied PDE. We divide the studied PDEs in two parts: part A which contains the derivatives, and part B which contains the rest of the equation. The application of the ansatz or the extended ansatz of Kudryashov, transforms part A and part B to two polynomials. We balance the highest powers of the polynomials for the parts A and B and, thus obtain a balance equation which depends on the kind of the used simplest equation. The balance equations are connected to nonlinear algebraic systems of relationships among the parameters of the equations and the parameters of the solution. On the basis of these systems, we obtain numerous solutions of the studied class of equations.
A partial-wave analysis of the (K +K -π-) system produced in π-p → K +K -π-p at 16 GeV/ c
NASA Astrophysics Data System (ADS)
Armstrong, T. A.; Baccari, B.; Bonesini, M.; Booth, P. S. L.; Brun, R.; Campbell, P. T.; Carroll, L. J.; Costa, G.; Donald, R. A.; Edwards, D. N.; Frame, D.; French, B. R.; Geer, S. H. P.; Girtler, P.; Ghidini, B.; Hughes, I. S.; Jackson, J. N.; Lynch, J. G.; Mandelli, L.; Minto, P. W.; Mitaroff, W. A.; Müller, K.; Otter, G.; Palano, A.; Perini, L.; Pinfold, J.; Range, W. H.; Richardson, J. A.; Rudolph, G.; Saleemi, F.; Schlütter, H.; Schmitz, W.; Scott, L.; Stewart, D. T.; Tamborini, M.; Thompson, A. S.; Turnbull, R. M.
1982-07-01
The reaction π-p → K +K -π- p at 16 GeV/ c was studied in the CERN OMEGA spectrometer and a partial-wave analysis (PWA) of the low-mass (K +K -π-) system (1.3-2.0 GeV) was performed. Only states in the unnatural spin-parity series produced by natural parity exchange are important and they approximately conserve t-channel helicity. The 1 +S K ∗overlineK wave dominates the low-mass (K +K -π-) region. We observe an enhancement in 2 -P K ∗overlineK wave at a mass of 1.7 GeV, consistent with the decay of the A 3 resonance.
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)
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.
NASA Astrophysics Data System (ADS)
Angelani, Luca
2015-12-01
Absorption problems of run-and-tumble particles, described by the telegrapher's equation, are analyzed in one space dimension considering partially reflecting boundaries. Exact expressions for the probability distribution function in the Laplace domain and for the mean time to absorption are given, discussing some interesting limits (Brownian and wave limit, large volume limit) and different case studies (semi-infinite segment, equal and symmetric boundaries, totally/partially reflecting boundaries).
Pietrzak, Robert H.; Goldstein, Risë B.; Southwick, Steven M.; Grant, Bridget F.
2011-01-01
Objective This study examined associations between lifetime trauma exposures, PTSD and partial PTSD, and past-year medical conditions in a nationally representative sample of U.S. adults. Methods Face-to-face interviews were conducted with 34,653 participants in the Wave 2 National Epidemiologic Survey on Alcohol and Related Conditions. Logistic regression analyses evaluated associations of trauma exposure, PTSD and partial PTSD with respondent-reported medical diagnoses. Results After adjustment for sociodemographic characteristics and comorbid Axis I and II disorders, respondents with full PTSD were more likely than traumatized respondents without full or partial PTSD (comparison group) to report diagnoses of diabetes mellitus, noncirrhotic liver disease, angina pectoris, tachycardia, hypercholesterolemia, other heart disease, stomach ulcer, HIV seropositivity, gastritis, and arthritis (odds ratios [ORs]=1.2-2.5). Respondents with partial PTSD were more likely than the comparison group to report past-year diagnoses of stomach ulcer, angina pectoris, tachycardia, and arthritis (ORs=1.3-1.6). Men with full and partial PTSD were more likely than controls to report diagnoses of hypertension (both ORs=1.6), and both men and women with PTSD (ORs=1.8 and 1.6, respectively), and men with partial PTSD (OR=2.0) were more likely to report gastritis. Total number of lifetime traumatic event types was associated with many assessed medical conditions (ORs=1.04-1.16), reducing the magnitudes and rendering non-significant some of the associations between PTSD status and medical conditions. Conclusions Greater lifetime trauma exposure and PTSD are associated with numerous medical conditions, many of which are stress-related and chronic, in U.S. adults. Partial PTSD is associated with intermediate odds of some of these conditions. PMID:21949429
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.
Isobar-model partial-wave analysis of πN-->ππN in the c.m. energy range 1320-1930 MeV
NASA Astrophysics Data System (ADS)
Manley, D. Mark; Arndt, Richard A.; Goradia, Yogesh; Teplitz, Vigdor L.
1984-09-01
We study the reactions πN-->ππN in the center-of-mass energy range 1320-1930 MeV within the framework of the isobar model. The present analysis includes over 30% more events than the most extensive previous analysis. Data for π-p-->π+π-n, π-p-->π0π-p, π+p-->π0π+p, and π+p-->π+π+n are simultaneously fitted assuming production of ɛ, ρ, Δ(P33) and N*(P11). The cross section for π-p-->π0π0n is predicted and found to be in good agreement with experiment. πN-->πN* amplitudes for I=12 are investigated for the first time. We confirm the existence of a significant πN* decay for the second P33 resonance and determine that πN* is the dominant inelastic channel for the P31 partial wave. The ρN decay of the G17 wave is observed for the first time. Evidence is found for unestablished resonances near 1900 MeV in the S11, P11, P13, and F15 partial waves. We also discuss evidence for a second F35 resonance. Signs of resonant amplitudes determined from this analysis are compared with results of previous analyses and with predictions from several models.
Partial-wave analysis of {pi}{sup {minus}}{pi}{sup 0}{pi}{sup 0} events at 18 GeV/c
Brown, D.S.
1998-05-01
A partial-wave analysis has been performed on 170 K {pi}{sup {minus}}{pi}{sup 0}{pi}{sup 0} events produced in the reaction {pi}{sup {minus}}p{r_arrow}p{pi}{sup {minus}}{pi}{sup 0}{pi}{sup 0}, and the results of the mass-independent fits are presented. The objective was to confirm the existence of the {pi}(1800) and the exotic J{sup PC}=1{sup {minus}+} object, reported by VES. {copyright} {ital 1998 American Institute of Physics.}
Lin, D.-H.
2004-05-01
Partial wave theory of a three dimensional scattering problem for an arbitrary short range potential and a nonlocal Aharonov-Bohm magnetic flux is established. The scattering process of a 'hard sphere'-like potential and the magnetic flux is examined. An anomalous total cross section is revealed at the specific quantized magnetic flux at low energy which helps explain the composite fermion and boson model in the fractional quantum Hall effect. Since the nonlocal quantum interference of magnetic flux on the charged particles is universal, the nonlocal effect is expected to appear in a quite general potential system and will be useful in understanding some other phenomena in mesoscopic physics.
Asymmetric inflation: Exact solutions
Buniy, Roman V.; Berera, Arjun; Kephart, Thomas W.
2006-03-15
We provide exact solutions to the Einstein equations when the universe contains vacuum energy plus a uniform arrangement of magnetic fields, strings, or domain walls. Such a universe has planar symmetry; i.e., it is homogeneous but not isotropic. Further exact solutions are obtained when dust is included and approximate solutions are found for w{ne}0 matter. These cosmologies also have planar symmetry. These results may eventually be used to explain some features in the Wilkinson Microwave Anisotropy Probe data. The magnetic field case is the easiest to motivate and has the highest possibility of yielding reliable constraints on observational cosmology.
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.
On exactly conservative integrators
Bowman, J.C.; Shadwick, B.A.; Morrison, P.J.
1997-06-01
Traditional explicit numerical discretizations of conservative systems generically predict artificial secular drifts of nonlinear invariants. These algorithms are based on polynomial functions of the time step. The authors discuss a general approach for developing explicit algorithms that conserve such invariants exactly. They illustrate the method by applying it to the truncated two-dimensional Euler equations.
Exact two-body solutions and quantum defect theory of two-dimensional dipolar quantum gas
NASA Astrophysics Data System (ADS)
Jie, Jianwen; Qi, Ran
2016-10-01
In this paper, we provide the two-body exact solutions of the two-dimensional (2D) Schrödinger equation with isotropic +/- 1/{r}3 interactions. An analytic quantum defect theory is constructed based on these solutions and it is applied to investigate the scattering properties as well as two-body bound states of an ultracold polar molecules confined in a quasi-2D geometry. Interestingly, we find that for the attractive case, the scattering resonance happens simultaneously in all partial waves, which has not been observed in other systems. The effect of this feature on the scattering phase shift across such resonances is also illustrated.
Exact Confidence Intervals in the Presence of Interference
Rigdon, Joseph; Hudgens, Michael G.
2015-01-01
For two-stage randomized experiments assuming partial interference, exact confidence intervals are proposed for treatment effects on a binary outcome. Empirical studies demonstrate the new intervals have narrower width than previously proposed exact intervals based on the Hoeffding inequality. PMID:26190877
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.
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
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)
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).
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
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.
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.
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.
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
Hur, Jin; Min, Hyunsoo
2008-06-15
Recently the partial-wave cutoff method was developed as a new calculational scheme for a functional determinant of quantum field theory in radial backgrounds. For the contribution given by an infinite sum of large partial waves, we derive explicitly radial-WKB series in the angular momentum cutoff for d=2, 3, 4, and 5 (d is the space-time dimension), which has uniform validity irrespectively of any specific values assumed for other parameters. Utilizing this series, precision evaluation of the renormalized functional determinant is possible with a relatively small number of low partial-wave contributions determined separately. We illustrate the power of this scheme in a numerically exact evaluation of the prefactor (expressed as a functional determinant) in the case of the false vacuum decay of 4D scalar field theory.
Exact solutions of forced Burgers equations with time variable coefficients
NASA Astrophysics Data System (ADS)
Büyükaşık, Şirin A.; Pashaev, Oktay K.
2013-07-01
In this paper, we consider a forced Burgers equation with time variable coefficients of the form Ut+(μ˙(t)/μ(t))U+UUx=(1/2μ(t))Uxx-ω2(t)x, and obtain an explicit solution of the general initial value problem in terms of a corresponding second order linear ordinary differential equation. Special exact solutions such as generalized shock and multi-shock waves, triangular wave, N-wave and rational type solutions are found and discussed. Then, we introduce forced Burgers equations with constant damping and an exponentially decaying diffusion coefficient as exactly solvable models. Different type of exact solutions are obtained for the critical, over and under damping cases, and their behavior is illustrated explicitly. In particular, the existence of inelastic type of collisions is observed by constructing multi-shock wave solutions, and for the rational type solutions the motion of the pole singularities is described.
A partial-wave analysis of the K -Φ system produced in the reaction K -p → K +K -K -p at 18.5 GeV/c
NASA Astrophysics Data System (ADS)
Armstrong, T.; Baubillier, M.; Beusch, W.; Bloodworth, I. J.; Bonesini, M.; Burns, A.; Calligarich, A.; Carney, J. N.; Cecchet, G.; Costa, G.; Dolfini, R.; Evangelista, C.; Ghidini, B.; Kinson, J. B.; Knudson, K.; Liguori, G.; Mandelli, L.; Mazzanti, M.; Navach, F.; Palano, A.; Perini, L.; Pons, Y.; Quercigh, E.; Strachman, Z.; Tamborini, M.; Teodoro, D.; Worsell, M. F.; Zito, G.; Zitoun, R.; Bari-Birmingham-CERN-Milan-Paris-Pavia Collaboration
1983-07-01
About 15 000 K -Φp events have been collected in the CERN Ω' spectrometer. A partial-wave decomposition of the K -Φ system is performed. The 1 +SO + wave is dominant. The 0 -P0 + and 2 -P0 + waves are important and show resonant behaviour at ˜ 1.83 GeV (Γ ˜ 0.25 GeV) and ˜ 1.73 GeV (Γ ˜ 0.22 GeV) respectively. The first one can be interpreted as the second radial excitation of the kaon while the second one can be identified as one of the two L mesons.
NASA Astrophysics Data System (ADS)
Cannoni, Mirco
2015-03-01
We show that the standard theory of thermal production and chemical decoupling of WIMPs is incomplete. The hypothesis that WIMPs are produced and decouple from a thermal bath implies that the rate equation the bath particles interacting with the WIMPs is an algebraic equation that constraints the actual WIMPs abundance to have a precise analytical form down to the temperature . The point , which coincides with the stationary point of the equation for the quantity , is where the maximum departure of the WIMPs abundance from the thermal value is reached. For each mass and total annihilation cross section , the temperature and the actual WIMPs abundance are exactly known. This value provides the true initial condition for the usual differential equation that have to be integrated in the interval . The matching of the two abundances at is continuous and differentiable. The dependence of the present relic abundance on the abundance at an intermediate temperature is an exact result. The exact theory suggests a new analytical approximation that furnishes the relic abundance accurate at the level of 1-2 % in the case of -wave and -wave scattering cross sections. We conclude the paper studying the evolution of the WIMPs chemical potential and the entropy production using methods of non-equilibrium thermodynamics.
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.
Exact vectorial law for axisymmetric MHD turbulence
NASA Astrophysics Data System (ADS)
Galtier, S.
2009-12-01
3D incompressible MHD turbulence is investigated under the assumptions of homogeneity and axisymmetry. We demonstrate that previous works of Chandrasekhar (1950) 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. We make the ansatz that the development of anisotropy implies an algebraic relation between the axial and the radial components of the separation vector and we derive an exact vectorial law which is parametrized by the intensity of anisotropy. The critical balance proposed by Goldreich & Sridhar (1995) is used to fix this parameter and to obtain a unique exact expression; the particular limits of correlations transverse and parallel to the mean field 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.
Exact Vectorial Law for Axisymmetric Magnetohydrodynamics Turbulence
NASA Astrophysics Data System (ADS)
Galtier, S.
2009-10-01
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 à la von Kármán-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 B0 . 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 & Sridhar is used to fix this parameter and to obtain a unique exact expression; the particular limits of correlations transverse and parallel to B0 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.
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)
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.
Andreev, Pavel A; Iqbal, Z
2016-03-01
We consider the separate spin evolution of electrons and positrons in electron-positron and electron-positron-ion plasmas. We consider the oblique propagating longitudinal waves in these systems. Working in a regime of high-density n(0) ∼ 10(27) cm(-3) and high-magnetic-field B(0)=10(10) G, we report the presence of the spin-electron acoustic waves and their dispersion dependencies. In electron-positron plasmas, similarly to the electron-ion plasmas, we find one spin-electron acoustic wave (SEAW) at the propagation parallel or perpendicular to the external field and two spin-electron acoustic waves at the oblique propagation. At the parallel or perpendicular propagation of the longitudinal waves in electron-positron-ion plasmas, we find four branches: the Langmuir wave, the positron-acoustic wave, and a pair of waves having spin nature, they are the SEAW and the wave discovered in this paper, called the spin-electron-positron acoustic wave (SEPAW). At the oblique propagation we find eight longitudinal waves: the Langmuir wave, the Trivelpiece--Gould wave, a pair of positron-acoustic waves, a pair of SEAWs, and a pair of SEPAWs. Thus, for the first time, we report the existence of the second positron-acoustic wave existing at the oblique propagation and the existence of SEPAWs.
Supersymmetric Ito equation: Bosonization and exact solutions
Ren Bo; Yu Jun; Lin Ji
2013-04-15
Based on the bosonization approach, the N=1 supersymmetric Ito (sIto) system is changed to a system of coupled bosonic equations. The approach can effectively avoid difficulties caused by intractable fermionic fields which are anticommuting. By solving the coupled bosonic equations, the traveling wave solutions of the sIto system are obtained with the mapping and deformation method. Some novel types of exact solutions for the supersymmetric system are constructed with the solutions and symmetries of the usual Ito equation. In the meanwhile, the similarity reduction solutions of the model are also studied with the Lie point symmetry theory.
Supersymmetric Ito equation: Bosonization and exact solutions
NASA Astrophysics Data System (ADS)
Ren, Bo; Lin, Ji; Yu, Jun
2013-04-01
Based on the bosonization approach, the N =1 N = 1 supersymmetric Ito (sIto) system is changed to a system of coupled bosonic equations. The approach can effectively avoid difficulties caused by intractable fermionic fields which are anticommuting. By solving the coupled bosonic equations, the traveling wave solutions of the sIto system are obtained with the mapping and deformation method. Some novel types of exact solutions for the supersymmetric system are constructed with the solutions and symmetries of the usual Ito equation. In the meanwhile, the similarity reduction solutions of the model are also studied with the Lie point symmetry theory.
Generating exact solutions to Einstein's equation using linearized approximations
NASA Astrophysics Data System (ADS)
Harte, Abraham I.; Vines, Justin
2016-10-01
We show that certain solutions to the linearized Einstein equation can—by the application of a particular type of linearized gauge transformation—be straightforwardly transformed into solutions of the exact Einstein equation. In cases with nontrivial matter content, the exact stress-energy tensor of the transformed metric has the same eigenvalues and eigenvectors as the linearized stress-energy tensor of the initial approximation. When our gauge exists, the tensorial structure of transformed metric perturbations identically eliminates all nonlinearities in Einstein's equation. As examples, we derive the exact Kerr and gravitational plane wave metrics from standard harmonic-gauge approximations.
Huang, Yi Ting; Spelke, Elizabeth; Snedeker, Jesse
2014-01-01
Number words are generally used to refer to the exact cardinal value of a set, but cognitive scientists disagree about their meanings. Although most psychological analyses presuppose that numbers have exact semantics (two means EXACTLY TWO), many linguistic accounts propose that numbers have lower-bounded semantics (AT LEAST TWO), and that speakers restrict their reference through a pragmatic inference (scalar implicature). We address this debate through studies of children who are in the process of acquiring the meanings of numbers. Adults and 2- and 3-year-olds were tested in a novel paradigm that teases apart semantic and pragmatic aspects of interpretation (the covered box task). Our findings establish that when scalar implicatures are cancelled in the critical trials of this task, both adults and children consistently give exact interpretations for number words. These results, in concert with recent work on real-time processing, provide the first unambiguous evidence that number words have exact semantics. PMID:25285053
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)
Saha Ray, S.
2016-09-01
In this article, the Jacobi elliptic function method viz. the mixed dn-sn method has been presented for finding the travelling wave solutions of the Davey-Stewartson equations. As a result, some solitary wave solutions and doubly periodic solutions are obtained in terms of Jacobi elliptic functions. Moreover, solitary wave solutions are obtained as simple limits of doubly periodic functions. These solutions can be useful to explain some physical phenomena, viz. evolution of a three-dimensional wave packet on water of finite depth. The proposed Jacobi elliptic function method is efficient, powerful and can be used in order to establish newer exact solutions for other kinds of nonlinear fractional partial differential equations arising in mathematical physics.
General Exact Solutions of the Harry—Dym Equation
NASA Astrophysics Data System (ADS)
Reza, Mokhtari
2011-02-01
The aim of this paper is to generate exact travelling wave solutions of the Harry—Dym equation through the methods of Adomian decomposition, He's variational iteration, direct integration, and power series. We show that the two later methods are more successful than the two former to obtain more solutions of the equation.
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.
Curved characteristics behind blast waves.
NASA Technical Reports Server (NTRS)
Laporte, O.; Chang, T. S.
1972-01-01
The behavior of nonisentropic flow behind a propagating blast wave is theoretically studied. Exact solutions, expressed in closed form in terms of elementary functions, are presented for three sets of curved characteristicseind a self-similar, strong blast wave.
Exact Lyapunov dimension of the universal attractor for the complex Ginzburg-Landau equation
Doering, C.R.; Gibbon, J.D.; Holm, D.D.; Nicolaenko, B.
1987-12-28
We present an exact analytic computation of the Lyapunov dimension of the universal attractor of the complex Ginzburg-Landau partial differential equation for a finite range of its parameter values. We obtain upper bounds on the attractor's dimension when the parameters do not permit an exact evaluation by our methods. The exact Lyapunov dimension agrees with an estimate of the number of degrees of freedom based on a simple linear stability analysis and mode-counting argument.
NASA Astrophysics Data System (ADS)
Kozhevnikov, V. A.; Sherman, S. G.
2008-11-01
The partial-wave inelasticity parameters of the amplitude for elastic pion-nucleon scattering are determined with the aid of the phenomenological amplitude for inelastic π N → ππ N processes in the energy range extending to the threshold for the production of two pions. The resulting inelasticity parameters are compared with their counterparts derived from modern partial-wave analyses. The largest inelastic-scattering cross section in the P11 wave is in excellent agreement with the analogous value from the analysis performed at the George Washington University in 2006. For other waves, however, the present results differ in the majority of cases from respective values given by partial-wave analyses (the distinctions are especially large for the isospin-3/2 amplitudes).
Quasinormal modes of charged scalars around dilaton black holes in 2+1 dimensions: Exact frequencies
Fernando, Sharmanthie
2008-06-15
We have studied the charged scalar perturbation around a dilaton black hole in 2+1 dimensions. The wave equations of a massless charged scalar field are shown to be exactly solvable in terms of hypergeometric functions. The quasinormal frequencies are computed exactly. The relation between the quasinormal frequencies and the charge of the black hole, charge of the scalar, and the temperature of the black hole are analyzed. The asymptotic form of the real part of the quasinormal frequencies is evaluated exactly.
Exact models for isotropic matter
NASA Astrophysics Data System (ADS)
Thirukkanesh, S.; Maharaj, S. D.
2006-04-01
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently, we can find an explicit exact solution to the Einstein-Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously, including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series, we show that the series terminate and there exist two linearly independent solutions. Consequently, it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.
Familial Sinistrals Avoid Exact Numbers
Sauerland, Uli; Gotzner, Nicole
2013-01-01
We report data from an internet questionnaire of sixty number trivia. Participants were asked for the number of cups in their house, the number of cities they know and 58 other quantities. We compare the answers of familial sinistrals – individuals who are left-handed themselves or have a left-handed close blood-relative – with those of pure familial dextrals – right-handed individuals who reported only having right-handed close blood-relatives. We show that familial sinistrals use rounder numbers than pure familial dextrals in the survey responses. Round numbers in the decimal system are those that are multiples of powers of 10 or of half or a quarter of a power of 10. Roundness is a gradient concept, e.g. 100 is rounder than 50 or 200. We show that very round number like 100 and 1000 are used with 25% greater likelihood by familial sinistrals than by pure familial dextrals, while pure familial dextrals are more likely to use less round numbers such as 25, 60, and 200. We then use Sigurd’s (1988, Language in Society) index of the roundness of a number and report that familial sinistrals’ responses are significantly rounder on average than those of pure familial dextrals. To explain the difference, we propose that the cognitive effort of using exact numbers is greater for the familial sinistral group because their language and number systems tend to be more distributed over both hemispheres of the brain. Our data support the view that exact and approximate quantities are processed by two separate cognitive systems. Specifically, our behavioral data corroborates the view that the evolutionarily older, approximate number system is present in both hemispheres of the brain, while the exact number system tends to be localized in only one hemisphere. PMID:23544052
Familial sinistrals avoid exact numbers.
Sauerland, Uli; Gotzner, Nicole
2013-01-01
We report data from an internet questionnaire of sixty number trivia. Participants were asked for the number of cups in their house, the number of cities they know and 58 other quantities. We compare the answers of familial sinistrals--individuals who are left-handed themselves or have a left-handed close blood-relative--with those of pure familial dextrals--right-handed individuals who reported only having right-handed close blood-relatives. We show that familial sinistrals use rounder numbers than pure familial dextrals in the survey responses. Round numbers in the decimal system are those that are multiples of powers of 10 or of half or a quarter of a power of 10. Roundness is a gradient concept, e.g. 100 is rounder than 50 or 200. We show that very round number like 100 and 1000 are used with 25% greater likelihood by familial sinistrals than by pure familial dextrals, while pure familial dextrals are more likely to use less round numbers such as 25, 60, and 200. We then use Sigurd's (1988, Language in Society) index of the roundness of a number and report that familial sinistrals' responses are significantly rounder on average than those of pure familial dextrals. To explain the difference, we propose that the cognitive effort of using exact numbers is greater for the familial sinistral group because their language and number systems tend to be more distributed over both hemispheres of the brain. Our data support the view that exact and approximate quantities are processed by two separate cognitive systems. Specifically, our behavioral data corroborates the view that the evolutionarily older, approximate number system is present in both hemispheres of the brain, while the exact number system tends to be localized in only one hemisphere.
NASA Astrophysics Data System (ADS)
Oberhardt, Tobias; Kim, Jin-Yeon; Qu, Jianmin; Jacobs, Laurence J.
2016-02-01
This research investigates the modeling of randomly distributed surface-breaking microcracks and the dependency of higher harmonic generation in Rayleigh surface waves on microcrack density. The microcrack model is based on micromechanical considerations of rough surface contact. An effective stress-strain relationship is derived to describe the nonlinear behavior of a single microcrack and implemented into a finite-element model via a hyperelastic constitutive law. Finite-element simulations of nonlinear wave propagation in a solid with distributed surface microcracks are performed for a range of microcrack densities. The evolution of fundamental and second harmonic amplitudes along the propagation distance is studied and the acoustic nonlinearity parameter is calculated. The results show that the nonlinearity parameter increases with crack density. While, for small crack densities (dilute concentration of microcracks) a proportionality between crack density and acoustic nonlinearity is observed, this is not valid for higher crack densities, as the microcracks start to interact.
MHD simple waves and the divergence wave
Webb, G. M.; Pogorelov, N. V.; Zank, G. P.
2010-03-25
In this paper we investigate magnetohydrodynamic (MHD) simple divergence waves in MHD, for models in which nablacentre dotBnot =0. These models are related to the eight wave Riemann solvers in numerical MHD, in which the eighth wave is the divergence wave associated with nablacentre dotBnot =0. For simple wave solutions, all physical variables (the gas density, pressure, fluid velocity, entropy, and magnetic field induction in the MHD case) depend on a single phase function phi. We consider the form of the MHD equations used by both Powell et al. and Janhunen. It is shown that the Janhunen version of the equations possesses fully nonlinear, exact simple wave solutions for the divergence wave, but no physically meaningful simple divergence wave solution exists for the Powell et al. system. We suggest that the 1D simple, divergence wave solution for the Janhunen system, may be useful for the testing and validation of numerical MHD codes.
Layden, B.; Cairns, Iver H.; Robinson, P. A.; Percival, D. J.
2012-07-15
The quadratic longitudinal response function describes the second-order nonlinear response of a plasma to electrostatic wave fields. An explicit expression for this function in the weak-turbulence regime requires the evaluation of velocity-space integrals involving the velocity distribution function and various resonant denominators. Previous calculations of the quadratic longitudinal response function were performed by approximating the resonant denominators to facilitate the integration. Here, we evaluate these integrals exactly for a non-relativistic collisionless unmagnetized isotropic Maxwellian plasma in terms of generalized plasma dispersion functions, and correct certain aspects of expressions previously derived for these functions. We show that in the appropriate limits the exact expression reduces to the approximate form used for interactions between two fast waves and one slow wave, such as the electrostatic decay of Langmuir waves into Langmuir waves and ion sound waves, and the scattering of Langmuir waves off thermal ions.
AESS: Accelerated Exact Stochastic Simulation
NASA Astrophysics Data System (ADS)
Jenkins, David D.; Peterson, Gregory D.
2011-12-01
The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution
Kao, Jim . E-mail: kao@lanl.gov; Flicker, Dawn; Ide, Kayo; Ghil, Michael
2006-05-20
This paper builds upon our recent data assimilation work with the extended Kalman filter (EKF) method [J. Kao, D. Flicker, R. Henninger, S. Frey, M. Ghil, K. Ide, Data assimilation with an extended Kalman filter for an impact-produced shock-wave study, J. Comp. Phys. 196 (2004) 705-723.]. The purpose is to test the capability of EKF in optimizing a model's physical parameters. The problem is to simulate the evolution of a shock produced through a high-speed flyer plate. In the earlier work, we have showed that the EKF allows one to estimate the evolving state of the shock wave from a single pressure measurement, assuming that all model parameters are known. In the present paper, we show that imperfectly known model parameters can also be estimated accordingly, along with the evolving model state, from the same single measurement. The model parameter optimization using the EKF can be achieved through a simple modification of the original EKF formalism by including the model parameters into an augmented state variable vector. While the regular state variables are governed by both deterministic and stochastic forcing mechanisms, the parameters are only subject to the latter. The optimally estimated model parameters are thus obtained through a unified assimilation operation. We show that improving the accuracy of the model parameters also improves the state estimate. The time variation of the optimized model parameters results from blending the data and the corresponding values generated from the model and lies within a small range, of less than 2%, from the parameter values of the original model. The solution computed with the optimized parameters performs considerably better and has a smaller total variance than its counterpart using the original time-constant parameters. These results indicate that the model parameters play a dominant role in the performance of the shock-wave hydrodynamic code at hand.
NASA Astrophysics Data System (ADS)
Park, Yongcheol; Yoo, Hyun Jae; Lee, Won Sang; Lee, Choon-Ki; Lee, Joohan; Park, Hadong; Kim, Jinseok; Kim, Yeadong
2015-12-01
Mt. Melbourne is a late Cenozoic intraplate volcano located ∼30 km northeast of Jang Bogo Station in Antarctica. The volcano is quiescent with fumarolic activity at the summit. To monitor volcanic activity and glacial movements near Jang Bogo Station, a seismic network was installed during the 2010-11 Antarctic summer field season. The network is maintained during the summer field season every year, and the number of stations has been increased. We used continuous seismic data recorded by the network and an Italian seismic station (TNV) at Mario Zucchelli Station to develop a 3-D P-wave velocity model for the Mt. Melbourne area based on the teleseismic P-wave tomographic method. The new 3-D model presented a relative velocity structure for the lower part of the crust and upper mantle between depths of 30 and 160 km and revealed the presence of two low-velocity anomalies beneath Mt. Melbourne and the Priestley Fault. The low-velocity anomaly beneath Mt. Melbourne may be caused by the edge flow of hot mantle material at the lithospheric step between the thick East Antarctic Craton and thin Ross Sea crust. The other low-velocity anomaly along the Priestley Fault may have been beneath Mt. Melbourne and moved to the southern tip of the Deep Freeze Range, where the crustal thickness is relatively thin. The anomaly was trapped on the fault line and laterally flowed along the fault line in the northwest direction.
2011-01-01
Introduction About 3% of people will be diagnosed with epilepsy during their lifetime, but about 70% of people with epilepsy eventually go into remission. Methods and outcomes We conducted a systematic review and aimed to answer the following clinical questions: What are the effects of starting antiepileptic drug treatment following a single seizure? What are the effects of drug monotherapy in people with partial epilepsy? What are the effects of additional drug treatments in people with drug-resistant partial epilepsy? What is the risk of relapse in people in remission when withdrawing antiepileptic drugs? What are the effects of behavioural and psychological treatments for people with epilepsy? What are the effects of surgery in people with drug-resistant temporal lobe epilepsy? We searched: Medline, Embase, The Cochrane Library, and other important databases up to July 2009 (Clinical Evidence reviews are updated periodically; please check our website for the most up-to-date version of this review). We included harms alerts from relevant organisations such as the US Food and Drug Administration (FDA) and the UK Medicines and Healthcare products Regulatory Agency (MHRA). Results We found 83 systematic reviews, RCTs, or observational studies that met our inclusion criteria. We performed a GRADE evaluation of the quality of evidence for interventions. Conclusions In this systematic review we present information relating to the effectiveness and safety of the following interventions: antiepileptic drugs after a single seizure; monotherapy for partial epilepsy using carbamazepine, gabapentin, lamotrigine, levetiracetam, phenobarbital, phenytoin, sodium valproate, or topiramate; addition of second-line drugs for drug-resistant partial epilepsy (allopurinol, eslicarbazepine, gabapentin, lacosamide, lamotrigine, levetiracetam, losigamone, oxcarbazepine, retigabine, tiagabine, topiramate, vigabatrin, or zonisamide); antiepileptic drug withdrawal for people with partial or
Periodic standing-wave approximation: Overview and three-dimensional scalar models
Andrade, Zeferino; Beetle, Christopher; Blinov, Alexey; Bromley, Benjamin; Burko, Lior M.; Cranor, Maria; Price, Richard H.; Owen, Robert
2004-09-15
The periodic standing-wave method for binary inspiral computes the exact numerical solution for periodic binary motion with standing gravitational waves, and uses it as an approximation to slow binary inspiral with outgoing waves. Important features of this method presented here are: (i) the mathematical nature of the 'mixed' partial differential equations to be solved (ii) the meaning of standing waves in the method (iii) computational difficulties, and (iv) the 'effective linearity' that ultimately justifies the approximation. The method is applied to three-dimensional nonlinear scalar model problems, and the numerical results are used to demonstrate extraction of the outgoing solution from the standing-wave solution, and the role of effective linearity.
NASA Astrophysics Data System (ADS)
Azbel, Mark Ya.
2005-07-01
Exact law of mortality dynamics in changing populations and environment is derived. It includes no explicit characteristics of animal- environment interactions (metabolism etc) which are a must for life; it is universal for all animals, from single cell yeast to humans, with their drastically different biology, evolutionary history, and complexity; it is rapidly (within few percent of life span) reversible. Such law is unique for live systems with their homeostatic self-adjustment to environment (cf. thermodynamics of liquids and glasses). The law which is valid for all live, and only live, systems is their specific natural law. Mortality is an instrument of natural selection and biological diversity. Its law, which is preserved in evolution of all species, is a conservation law of mortality, selection, evolution, biology. The law implies new kind of intrinsic mortality and adaptation which dominate in evolutionary unprecedented protected populations and, in contrast to species specific natural selection, proceed via universal stepwise rungs and reduce to universal cellular mechanism. The law demonstrates that intrinsic mortality and at least certain aspects of aging are disposable evolutionary byproducts, and directed genetic and/or biological changes may yield healthy and vital Methuselah lifespan. This is consistent with experiments. Universality implies that single cell yeast may provide a master key to the cellular mechanism of universal mortality, aging, selection, evolution, and its regulation in all animals. One may look for its manifestations in animal cells also, e.g., in their replicative senescence and cancer. Evolutionary origin and genetic nature of universality are suggested.
Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance.
Chen, Shihua; Grelu, Philippe; Soto-Crespo, J M
2014-01-01
Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves.
Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance.
Chen, Shihua; Grelu, Philippe; Soto-Crespo, J M
2014-01-01
Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves. PMID:24580164
NASA Astrophysics Data System (ADS)
Azbel‧, Mark Ya.
2005-08-01
The exact law of mortality dynamics in changing populations and environment is derived. It includes no explicit characteristics of animal-environment interactions (metabolism, etc.) which are a must for life; it is universal for all animals, from single-cell yeast to humans, with their drastically different biology, evolutionary history, and complexity; it is rapidly (within few percent of life span) reversible. Such a law is unique for live systems with their homeostatic self-adjustment to environment (cf. thermodynamics of liquids and glasses). The law which is valid for all live, and only live, systems is their specific natural law. Mortality is an instrument of natural selection and biological diversity. Its law, which is preserved in evolution of all species, is a conservation law of mortality, selection, evolution, biology. The law implies new kinds of intrinsic mortality and adaptation which dominate in evolutionary unprecedented protected populations and, in contrast to species-specific natural selection, proceed via universal stepwise rungs and reduce to universal cellular mechanism. The law demonstrates that intrinsic mortality and at least certain aspects of aging are disposable evolutionary byproducts, and directed genetic and/or biological changes may yield healthy and vital Methuselah lifespan. This is consistent with experiments. Universality implies that single-cell yeast may provide a master key to the cellular mechanism of universal mortality, aging, selection, evolution, and its regulation in all animals. One may look for its manifestations in animal cells also, e.g., in their replicative senescence and cancer. Evolutionary origin and genetic nature of universality are suggested.
Exact significance test for Markov order
NASA Astrophysics Data System (ADS)
Pethel, S. D.; Hahs, D. W.
2014-02-01
We describe an exact significance test of the null hypothesis that a Markov chain is nth order. The procedure utilizes surrogate data to yield an exact test statistic distribution valid for any sample size. Surrogate data are generated using a novel algorithm that guarantees, per shot, a uniform sampling from the set of sequences that exactly match the nth order properties of the observed data. Using the test, the Markov order of Tel Aviv rainfall data is examined.
The exact fundamental solution for the Benes tracking problem
NASA Astrophysics Data System (ADS)
Balaji, Bhashyam
2009-05-01
The universal continuous-discrete tracking problem requires the solution of a Fokker-Planck-Kolmogorov forward equation (FPKfe) for an arbitrary initial condition. Using results from quantum mechanics, the exact fundamental solution for the FPKfe is derived for the state model of arbitrary dimension with Benes drift that requires only the computation of elementary transcendental functions and standard linear algebra techniques- no ordinary or partial differential equations need to be solved. The measurement process may be an arbitrary, discrete-time nonlinear stochastic process, and the time step size can be arbitrary. Numerical examples are included, demonstrating its utility in practical implementation.
Exact parapositroniumlike solution to two-body Dirac equations
NASA Astrophysics Data System (ADS)
van Alstine, Peter; Crater, Horace
1986-09-01
Recently we used a supersymmetric version of Dirac's constraint mechanics to derive coupled Dirac equations for a quark and antiquark in mutual chromodynamiclike interaction. Here we investigate the properties of our equations for two spinning particles in mutual electromagneticlike interaction. In the chiral Dirac matrix representation we explicitly obtain a family of exact 16-component solutions with closed-form energy spectrum that agrees with that of parapositronium through order α4. We also find that various rearrangements of our Dirac equations simultaneously yield (for weak potentials) the relativistic wave equations of Todorov and Pilkuhn as well as (for weak potentials and slow motion) the semirelativistic interaction structure of Breit.
Exact solutions for modeling sound propagation through a combustion zone.
Sujith, R I
2001-10-01
Exact analytical solutions for one-dimensional sound propagation through a combustion zone, taking the effects of mean temperature gradient and oscillatory heat release into account, are presented in this paper. The wave equation is derived starting from the momentum and energy equations. Using appropriate transformations, solutions are derived for the case of an exponential mean temperature gradient in terms of Bessel functions. For the case of a linear mean temperature profile, solutions are derived in terms of confluent hypergeometric functions. Example calculations show that the accuracy in modeling combustion-acoustics interactions can be significantly increased by the use of these solutions.
Exact response functions within the time-dependent Gutzwiller approach
NASA Astrophysics Data System (ADS)
Bünemann, J.; Wasner, S.; Oelsen, E. v.; Seibold, G.
2015-02-01
We investigate the applicability of the two existing versions of a time-dependent Gutzwiller approach (TDGA) beyond the frequently used limit of infinite spatial dimensions. To this end, we study the two-particle response functions of a two-site Hubbard model where we can compare the exact results and those derived from the TDGA. It turns out that only the more recently introduced version of the TDGA can be combined with a diagrammatic approach which allows for the evaluation of Gutzwiller wave functions in finite dimensions. For this TDGA method, we derive the time-dependent Lagrangian for general single-band Hubbard models.
A class of exact classical solutions to string theory.
Coley, A A
2002-12-31
We show that the recently obtained class of spacetimes for which all of the scalar curvature invariants vanish (which can be regarded as generalizations of pp-wave spacetimes) are exact solutions in string theory to all perturbative orders in the string tension scale. As a result the spectrum of the theory can be explicitly obtained, and these spacetimes are expected to provide some hints for the study of superstrings on more general backgrounds. Since these Lorentzian spacetimes suffer no quantum corrections to all loop orders they may also offer insights into quantum gravity.
Effective photon mass and exact translating quantum relativistic structures
NASA Astrophysics Data System (ADS)
Haas, Fernando; Manrique, Marcos Antonio Albarracin
2016-04-01
Using a variation of the celebrated Volkov solution, the Klein-Gordon equation for a charged particle is reduced to a set of ordinary differential equations, exactly solvable in specific cases. The new quantum relativistic structures can reveal a localization in the radial direction perpendicular to the wave packet propagation, thanks to a non-vanishing scalar potential. The external electromagnetic field, the particle current density, and the charge density are determined. The stability analysis of the solutions is performed by means of numerical simulations. The results are useful for the description of a charged quantum test particle in the relativistic regime, provided spin effects are not decisive.
Exact Results in Frustrated Quantum Magnetism
NASA Astrophysics Data System (ADS)
Miyahara, Shin
Most of the exact results in frustrated spin systems have for a long time been regarded as of purely academic interest, being realized only due to the special geometry of the lattices concerned. However, recent developments in material design offer the genuine possibility of producing such exact states in real materials. In fact, the exact dimer singlet state of the two-dimensional Shastry-Sutherland model has already been found as the ground state of the quasi-two-dimensional material SrCu2(BO3)2. The cooperation between experimentalists and theorists in investigating this material has caused rapid development in the understanding of low-dimensional frustrated spin systems in general, due to the extreme utility of cases where the ground state is known exactly. This fact provides information essential to recognizing novel magnetic behavior in external magnetic fields, at finite temperatures, and in other regimes. In this chapter, we introduce spin-1 / 2 models which have an exact ground state, considering first exactly solvable spin-1 / 2 Heisenberg models, exemplified by the sawtooth-chain model, the Majumdar-Ghosh model, the two-dimensional Shastry-Sutherland model, and a frustrated ladder model. Such exact states can be realized due to special symmetries on geometrically frustrated lattices. As a second class of examples, we introduce also some exact ground states in spin-1/2 models with multiple-spin interactions.
EXACT2: the semantics of biomedical protocols
2014-01-01
Background The reliability and reproducibility of experimental procedures is a cornerstone of scientific practice. There is a pressing technological need for the better representation of biomedical protocols to enable other agents (human or machine) to better reproduce results. A framework that ensures that all information required for the replication of experimental protocols is essential to achieve reproducibility. Methods We have developed the ontology EXACT2 (EXperimental ACTions) that is designed to capture the full semantics of biomedical protocols required for their reproducibility. To construct EXACT2 we manually inspected hundreds of published and commercial biomedical protocols from several areas of biomedicine. After establishing a clear pattern for extracting the required information we utilized text-mining tools to translate the protocols into a machine amenable format. We have verified the utility of EXACT2 through the successful processing of previously 'unseen' (not used for the construction of EXACT2) protocols. Results The paper reports on a fundamentally new version EXACT2 that supports the semantically-defined representation of biomedical protocols. The ability of EXACT2 to capture the semantics of biomedical procedures was verified through a text mining use case. In this EXACT2 is used as a reference model for text mining tools to identify terms pertinent to experimental actions, and their properties, in biomedical protocols expressed in natural language. An EXACT2-based framework for the translation of biomedical protocols to a machine amenable format is proposed. Conclusions The EXACT2 ontology is sufficient to record, in a machine processable form, the essential information about biomedical protocols. EXACT2 defines explicit semantics of experimental actions, and can be used by various computer applications. It can serve as a reference model for for the translation of biomedical protocols in natural language into a semantically
Nonlinear evolution-type equations and their exact solutions using inverse variational methods
NASA Astrophysics Data System (ADS)
Kara, A. H.; Khalique, C. M.
2005-05-01
We present the role of invariants in obtaining exact solutions of differential equations. Firstly, conserved vectors of a partial differential equation (p.d.e.) allow us to obtain reduced forms of the p.d.e. for which some of the Lie point symmetries (in vector field form) are easily concluded and, therefore, provide a mechanism for further reduction. Secondly, invariants of reduced forms of a p.d.e. are obtainable from a variational principle even though the p.d.e. itself does not admit a Lagrangian. In this latter case, the reductions carry all the usual advantages regarding Noether symmetries and double reductions. The examples we consider are nonlinear evolution-type equations such as the Korteweg-deVries equation, but a detailed analysis is made on the Fisher equation (which describes reaction-diffusion waves in biology, inter alia). Other diffusion-type equations lend themselves well to the method we describe (e.g., the Fitzhugh Nagumo equation, which is briefly discussed). Some aspects of Painlevé properties are also suggested.
A class of reduced-order models in the theory of waves and stability
Sorokin, S. V.
2016-01-01
This paper presents a class of approximations to a type of wave field for which the dispersion relation is transcendental. The approximations have two defining characteristics: (i) they give the field shape exactly when the frequency and wavenumber lie on a grid of points in the (frequency, wavenumber) plane and (ii) the approximate dispersion relations are polynomials that pass exactly through points on this grid. Thus, the method is interpolatory in nature, but the interpolation takes place in (frequency, wavenumber) space, rather than in physical space. Full details are presented for a non-trivial example, that of antisymmetric elastic waves in a layer. The method is related to partial fraction expansions and barycentric representations of functions. An asymptotic analysis is presented, involving Stirling's approximation to the psi function, and a logarithmic correction to the polynomial dispersion relation. PMID:27118895
Exact Solutions and Conservation Laws for a New Integrable Equation
Gandarias, M. L.; Bruzon, M. S.
2010-09-30
In this work we study a generalization of an integrable equation proposed by Qiao and Liu from the point of view of the theory of symmetry reductions in partial differential equations. Among the solutions we obtain a travelling wave with decaying velocity and a smooth soliton solution. We determine the subclass of these equations which are quasi-self-adjoint and we get a nontrivial conservation law.
Vagov, A; Schomerus, H; Zalipaev, V V
2009-11-01
We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wave functions localized around unstable periodic orbits. The formalism applies to the description of scar states in fully or partially chaotic quantum systems, and also allows for the presence of smooth and sharp potentials, as well as magnetic fields. We argue that the separatrix wave function provides the largest contribution to the scars on a single wave function. This agrees with earlier results on the wave-function asymptotics and on the quantization condition of the scar states. Predictions of the ABL formalism are compared with the exact numerical solution for a strip resonator with a parabolic confinement potential and a magnetic field. PMID:20365055
Agakishiev, G.; Arnold, O.; Belver, D.; Belyaev, A.; Berger-Chen, J. C.; Blanco, A.; Böhmer, M.; Boyard, J. L.; Cabanelas, P.; Chernenko, S.; Dybczak, A.; Epple, E.; Fabbietti, L.; Fateev, O.; Finocchiaro, P.; Fonte, P.; Friese, J.; Fröhlich, I.; Galatyuk, T.; Garzón, J. A.; Gernhäuser, R.; Göbel, K.; Golubeva, M.; González-Díaz, D.; Guber, F.; Gumberidze, M.; Heinz, T.; Hennino, T.; Holzmann, R.; Ierusalimov, A.; Iori, I.; Ivashkin, A.; Jurkovic, M.; Kämpfer, B.; Karavicheva, T.; Koenig, I.; Koenig, W.; Kolb, B. W.; Kornakov, G.; Kotte, R.; Krása, A.; Krizek, F.; Krücken, R.; Kuc, H.; Kühn, W.; Kugler, A.; Kunz, T.; Kurepin, A.; Ladygin, V.; Lalik, R.; Lapidus, K.; Lebedev, A.; Lopes, L.; Lorenz, M.; Maier, L.; Mangiarotti, A.; Markert, J.; Metag, V.; Michel, J.; Müntz, C.; Münzer, R.; Naumann, L.; Pachmayer, Y. C.; Palka, M.; Parpottas, Y.; Pechenov, V.; Pechenova, O.; Pietraszko, J.; Przygoda, W.; Ramstein, B.; Reshetin, A.; Rustamov, A.; Sadovsky, A.; Salabura, P.; Schmah, A.; Schwab, E.; Siebenson, J.; Sobolev, Yu. G.; Spataro, S.; Spruck, B.; Ströbele, H.; Stroth, J.; Sturm, C.; Tarantola, A.; Teilab, K.; Tlusty, P.; Traxler, M.; Tsertos, H.; Vasiliev, T.; Wagner, V.; Weber, M.; Wendisch, C.; Wüstenfeld, J.; Yurevich, S.; Zanevsky, Y.; Sarantsev, A. V.
2015-01-26
Employing the Bonn–Gatchina partial wave analysis framework (PWA), we have analyzed HADES data of the reaction p(3.5GeV) + p → pK^{+}Λ. This reaction might contain information about the kaonic cluster “ppK^{-}” (with quantum numbers J^{P}=0^{-} and total isospin I =1/2) via its decay into pΛ. Due to interference effects in our coherent description of the data, a hypothetical K ¯NN (or, specifically “ppK^{-}”) cluster signal need not necessarily show up as a pronounced feature (e.g. a peak) in an invariant mass spectrum like pΛ. Our PWA analysis includes a variety of resonant and non-resonant intermediate states and delivers a good description of our data (various angular distributions and two-hadron invariant mass spectra) without a contribution of a K ¯NN cluster. At a confidence level of CL_{s}=95% such a cluster cannot contribute more than 2–12% to the total cross section with a pK^{+} Λ final state, which translates into a production cross-section between 0.7 μb and 4.2 μb, respectively. The range of the upper limit depends on the assumed cluster mass, width and production process.
Partial wave analysis of the reaction $\gamma p\to p\omega $ and the search for nucleon resonances
Williams, M.; Applegate, D.; Bellis, M.; Meyer, C. A.; Adhikari, K. P.; Anghinolfi, M.; Baghdasaryan, H.; Ball, J.; Battaglieri, M.; Bedlinskiy, I.; Berman, B. L.; Biselli, A. S.; Briscoe, W. J.; Brooks, W. K.; Burkert, V. D.; Careccia, S. L.; Carman, D. S.; Cole, P. L.; Collins, P.; Crede, V.; D’Angelo, A.; Daniel, A.; De Vita, R.; De Sanctis, E.; Deur, A.; Dey, B.; Dhamija, S.; Dickson, R.; Djalali, C.; Dodge, G. E.; Doughty, D.; Dugger, M.; Dupre, R.; Alaoui, A. El; Elouadrhiri, L.; Eugenio, P.; Fedotov, G.; Fegan, S.; Fradi, A.; Gabrielyan, M. Y.; Garçon, M.; Gilfoyle, G. P.; Giovanetti, K. L.; Girod, F. X.; Gohn, W.; Golovatch, E.; Gothe, R. W.; Griffioen, K. A.; Guidal, M.; Guler, N.; Guo, L.; Hafidi, K.; Hakobyan, H.; Hanretty, C.; Hassall, N.; Hicks, K.; Holtrop, M.; Ilieva, Y.; Ireland, D. G.; Ishkhanov, B. S.; Isupov, E. L.; Jawalkar, S. S.; Jo, H. S.; Johnstone, J. R.; Joo, K.; Keller, D.; Khandaker, M.; Khetarpal, P.; Kim, W.; Klein, A.; Klein, F. J.; Krahn, Z.; Kubarovsky, V.; Kuleshov, S. V.; Kuznetsov, V.; Livingston, K.; Lu, H. Y.; Mayer, M.; McAndrew, J.; McCracken, M. E.; McKinnon, B.; Mirazita, M.; Mokeev, V.; Moreno, B.; Moriya, K.; Morrison, B.; Munevar, E.; Nadel-Turonski, P.; Nepali, C. S.; Niccolai, S.; Niculescu, G.; Niculescu, I.; Niroula, M. R.; Niyazov, R. A.; Osipenko, M.; Ostrovidov, A. I.; Paris, M.; Park, K.; Park, S.; Pasyuk, E.; Pereira, S. Anefalos; Perrin, Y.; Pisano, S.; Pogorelko, O.; Pozdniakov, S.; Price, J. W.; Procureur, S.; Protopopescu, D.; Ricco, G.; Ripani, M.; Ritchie, B. G.; Rosner, G.; Rossi, P.; Sabatié, F.; Saini, M. S.; Salamanca, J.; Salgado, C.; Schott, D.; Schumacher, R. A.; Seraydaryan, H.; Sharabian, Y. G.; Smith, E. S.; Sober, D. I.; Sokhan, D.; Stepanyan, S. S.; Stoler, P.; Strakovsky, I. I.; Strauch, S.; Taiuti, M.; Tedeschi, D. J.; Tkachenko, S.; Ungaro, M.; Vineyard, M. F.; Voutier, E.; Watts, D. P.; Weygand, D. P.; Wood, M. H.; Zhang, J.; Zhao, B.
2009-12-30
We performed an event-based partial wave analysis (PWA) of the reaction γ p -> p ω on a high-statistics dataset obtained using the CLAS at Jefferson Lab for center-of-mass energies from threshold up to 2.4 GeV. This analysis benefits from access to the world's first high precision spin density matrix element measurements, available to the event-based PWA through the decay distribution of omega-> π^{+} π^{ -} π^{0}. The data confirm the dominance of the t-channel π^{0} exchange amplitude in the forward direction. The dominant resonance contributions are consistent with the previously identified states F[15](1680) and D[13](1700) near threshold, as well as the G[17](2190) at higher energies. Suggestive evidence for the presence of a J(P)=5/2^{+} state around 2 GeV, a "missing" state, has also been found. Evidence for other states is inconclusive.
A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations
Güner, Özkan; Cevikel, Adem C.
2014-01-01
We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions. PMID:24737972
A procedure to construct exact solutions of nonlinear fractional differential equations.
Güner, Özkan; Cevikel, Adem C
2014-01-01
We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.
EXACT Software Repository v 1.1
2007-01-07
The EXACT Software Repository contains a variety of software packages for describing, controlling, and analyzing computer experiments. The EXACT Python framework provides the experimentalist with convenient software tools to ease and organize the entire experimental process, including the description of factors and levels, the design of experiments, the control of experimental runs, the archiving of results, and analysis of results. The FAST package provides a Framework for Agile Software Testing. FAST manage the distributed executionmore » of EXACT, as well as summaries of test results.« less
EXACT Software Repository v 1.1
HART, WILLIAM; BERRY, JONATHAN; HEAPHY, ROBERT; PHILLIPS, CYNTHIA; CHAKERIAN, STEFAN
2007-01-07
The EXACT Software Repository contains a variety of software packages for describing, controlling, and analyzing computer experiments. The EXACT Python framework provides the experimentalist with convenient software tools to ease and organize the entire experimental process, including the description of factors and levels, the design of experiments, the control of experimental runs, the archiving of results, and analysis of results. The FAST package provides a Framework for Agile Software Testing. FAST manage the distributed execution of EXACT, as well as summaries of test results.
Exact optics - III. Schwarzschild's spectrograph camera revised
NASA Astrophysics Data System (ADS)
Willstrop, R. V.
2004-03-01
Karl Schwarzschild identified a system of two mirrors, each defined by conic sections, free of third-order spherical aberration, coma and astigmatism, and with a flat focal surface. He considered it impractical, because the field was too restricted. This system was rediscovered as a quadratic approximation to one of Lynden-Bell's `exact optics' designs which have wider fields. Thus the `exact optics' version has a moderate but useful field, with excellent definition, suitable for a spectrograph camera. The mirrors are strongly aspheric in both the Schwarzschild design and the exact optics version.
Exact coherent structures: from fluid turbulence to cardiac arrhythmias
NASA Astrophysics Data System (ADS)
Grigoriev, Roman; Marcotte, Christopher; Byrne, Gregory
2014-03-01
Ventricular fibrillation, a life threatening cardiac arrhythmia, is an example of spatiotemporally chaotic state dominated by multiple interacting spiral waves. Recent studies of weak fluid turbulence suggest that spatiotemporal chaos in general can be understood as a walk among exact unstable regular solutions (exact coherent states, ECS) of nonlinear evolution equations. Several classes of ECS are believed to play a dominant role; most typically these are equilibria and periodic orbits or relative equilibria and relative periodic orbits for systems with global continuous symmetries. Numerical methods originally developed in the context of fluid turbulence can also be applied to models of cardiac dynamics which possess translational and rotational symmetries and, indeed, allowed us to identify relative equilibria and periodic orbits describing isolated spirals with, respectively, fixed and drifting cores. In order to find regular solutions featuring multiple interacting spirals a new approach is required that takes into consideration the dynamics of slowly drifting cores associated with local, rather than global, symmetries. We describe how local symmetries can be reduced and more general types of ECS computed that dominate spiral wave chaos in models of cardiac tissue.
Exact simulation of polarized light reflectance by particle deposits
NASA Astrophysics Data System (ADS)
Ramezan Pour, B.; Mackowski, D. W.
2015-12-01
The use of polarimetric light reflection measurements as a means of identifying the physical and chemical characteristics of particulate materials obviously relies on an accurate model of predicting the effects of particle size, shape, concentration, and refractive index on polarized reflection. The research examines two methods for prediction of reflection from plane parallel layers of wavelength—sized particles. The first method is based on an exact superposition solution to Maxwell's time harmonic wave equations for a deposit of spherical particles that are exposed to a plane incident wave. We use a FORTRAN-90 implementation of this solution (the Multiple Sphere T Matrix (MSTM) code), coupled with parallel computational platforms, to directly simulate the reflection from particle layers. The second method examined is based upon the vector radiative transport equation (RTE). Mie theory is used in our RTE model to predict the extinction coefficient, albedo, and scattering phase function of the particles, and the solution of the RTE is obtained from adding—doubling method applied to a plane—parallel configuration. Our results show that the MSTM and RTE predictions of the Mueller matrix elements converge when particle volume fraction in the particle layer decreases below around five percent. At higher volume fractions the RTE can yield results that, depending on the particle size and refractive index, significantly depart from the exact predictions. The particle regimes which lead to dependent scattering effects, and the application of methods to correct the vector RTE for particle interaction, will be discussed.
Spin-wave modes of ferromagnetic films
NASA Astrophysics Data System (ADS)
Arias, R. E.
2016-10-01
The spin-wave modes of ferromagnetic films have been studied for a long time experimentally as well as theoretically, either in the magnetostatic approximation or also considering the exchange interaction. A theoretical method is presented that allows one to determine with ease the exact frequency dispersion relations of dipole-exchange modes under general conditions: an obliquely applied magnetic field, and surface boundary conditions that allow for partial pinning, which may be of different origins. The method is a generalization of Green's theorem to the problem of solving the linear dynamics of ferromagnetic spin-wave modes. Convolution integral equations for the magnetization and the magnetostatic potential of the modes are derived on the surfaces of the film. For the translation-invariant film these become simple local algebraic equations at each in-plane wave vector. Eigenfrequencies result from imposing a 6 ×6 determinant to be null, and spin-wave modes follow everywhere through solving linear 6 ×6 inhomogeneous systems. An interpretation of the results is that the Green's functions represent six independent plane-wave solutions to the equations of motion, with six associated complex perpendicular wave vectors: volume modes correspond to the cases in which two of these are purely real at a given frequency. Furthermore, the convolution extinction equations enforce the boundary conditions: this is possible at specific eigenfrequencies for a given in-plane wave vector. Magnetostatic modes may also be obtained in detail. At low frequencies and for some obliquely applied magnetic fields, magnetostatic and dipole-exchange volume modes may have forward or backward character depending on the frequency range.
George E. Valley, Jr. Prize Talk: Exact relations for Fermi gases with large scattering length
NASA Astrophysics Data System (ADS)
Tan, Shina
2011-05-01
Ultracold two-component atomic Fermi gases near broad Feshbach resonances have both strong interactions and relatively long life times, and the strong attractions between fermions lead to remarkable properties such as superfluidity at large percentages of the Fermi temperature. The interactions can often be described by a single parameter, the two-body s-wave scattering length, which determines how the many-body wave function behaves as two atoms get much closer than the average interparticle spacing. This short-range structure of the wave function leads to a number of exact relations among energy, momentum distribution, pressure, and various high-frequency and short-wave properties. All the relations involve a quantity called contact. The exact relations point to a number of independent determinations of the contact, which have been beautifully demonstrated experimentally as well as numerically. This work was supported, in part, by DOE Grant No. DE-FG02-00ER41132.
The EXACT description of biomedical protocols
Soldatova, Larisa N.; Aubrey, Wayne; King, Ross D.; Clare, Amanda
2008-01-01
Motivation: Many published manuscripts contain experiment protocols which are poorly described or deficient in information. This means that the published results are very hard or impossible to repeat. This problem is being made worse by the increasing complexity of high-throughput/automated methods. There is therefore a growing need to represent experiment protocols in an efficient and unambiguous way. Results: We have developed the Experiment ACTions (EXACT) ontology as the basis of a method of representing biological laboratory protocols. We provide example protocols that have been formalized using EXACT, and demonstrate the advantages and opportunities created by using this formalization. We argue that the use of EXACT will result in the publication of protocols with increased clarity and usefulness to the scientific community. Availability: The ontology, examples and code can be downloaded from http://www.aber.ac.uk/compsci/Research/bio/dss/EXACT/ Contact: Larisa Soldatova lss@aber.ac.uk PMID:18586727
Exact relativistic {beta} decay endpoint spectrum
Masood, S. S.; Nasri, S.; Schechter, J.; Tortola, M. A.; Valle, J. W. F.
2007-10-15
The exact relativistic form for the {beta} decay endpoint spectrum is derived and presented in a simple factorized form. We show that our exact formula can be well approximated to yield the endpoint form used in the fit method of the KATRIN Collaboration. We also discuss the three-neutrino case and how information from neutrino oscillation experiments may be useful in analyzing future {beta} decay endpoint experiments.
Effect of fracture compliance on wave propagation within a fluid-filled fracture.
Nakagawa, Seiji; Korneev, Valeri A
2014-06-01
Open and partially closed fractures can trap seismic waves. Waves propagating primarily within fluid in a fracture are sometimes called Krauklis waves, which are strongly dispersive at low frequencies. The behavior of Krauklis waves has previously been examined for an open, fluid-filled channel (fracture), but the impact of finite fracture compliance resulting from contacting asperities and porous fillings in the fracture (e.g., debris, proppants) has not been fully investigated. In this paper, a dispersion equation is derived for Krauklis wave propagation in a fracture with finite fracture compliance, using a modified linear-slip-interface model (seismic displacement-discontinuity model). The resulting equation is formally identical to the dispersion equation for the symmetric fracture interface wave, another type of guided wave along a fracture. The low-frequency solutions of the newly derived dispersion equations are in good agreement with the exact solutions available for an open fracture. The primary effect of finite fracture compliance on Krauklis wave propagation is to increase wave velocity and attenuation at low frequencies. These effects can be used to monitor changes in the mechanical properties of a fracture. PMID:24907784
Effect of fracture compliance on wave propagation within a fluid-filled fracture.
Nakagawa, Seiji; Korneev, Valeri A
2014-06-01
Open and partially closed fractures can trap seismic waves. Waves propagating primarily within fluid in a fracture are sometimes called Krauklis waves, which are strongly dispersive at low frequencies. The behavior of Krauklis waves has previously been examined for an open, fluid-filled channel (fracture), but the impact of finite fracture compliance resulting from contacting asperities and porous fillings in the fracture (e.g., debris, proppants) has not been fully investigated. In this paper, a dispersion equation is derived for Krauklis wave propagation in a fracture with finite fracture compliance, using a modified linear-slip-interface model (seismic displacement-discontinuity model). The resulting equation is formally identical to the dispersion equation for the symmetric fracture interface wave, another type of guided wave along a fracture. The low-frequency solutions of the newly derived dispersion equations are in good agreement with the exact solutions available for an open fracture. The primary effect of finite fracture compliance on Krauklis wave propagation is to increase wave velocity and attenuation at low frequencies. These effects can be used to monitor changes in the mechanical properties of a fracture.
Exact solution of a quantum forced time-dependent harmonic oscillator
NASA Technical Reports Server (NTRS)
Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN
1992-01-01
The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.
Exact Analytical Solution of the Klein-Gordon Equation in the Generalized Woods-Saxon Potential
NASA Astrophysics Data System (ADS)
Bayrak, O.; Sahin, D.
2015-09-01
The exact analytical solution of the Klein-Gordon equation for the spin-0 particles in the generalized Woods-Saxon potential is presented. The bound state energy eigenvalues and corresponding wave functions are obtained in the closed forms. The correlations between the potential parameters and energy eigenvalues are examined for π0 particles.
Exact solutions of Wick-type stochastic equations with variable coefficients
NASA Astrophysics Data System (ADS)
Kim, Hyunsoo; Sakthivel, Rathinasamy
In this paper, we consider the Wick-type stochastic generalized Boussinesq equation and Wick-type stochastic Kadomtsev-Petviashvili equation with variable coefficients. By employing the (GG)-expansion method with the aid of symbolic computation and Hermite transformation, we derive new exact travelling wave solutions, which mclude hyperbolic and trigonometric solutions for the considered equations.
The exact forces on classical nuclei in non-adiabatic charge transfer.
Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu; Min, Seung Kyu; Maitra, Neepa T; Gross, E K U
2015-02-28
The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packet in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect.
The exact forces on classical nuclei in non-adiabatic charge transfer.
Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu; Min, Seung Kyu; Maitra, Neepa T; Gross, E K U
2015-02-28
The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packet in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect. PMID:25725727
The exact forces on classical nuclei in non-adiabatic charge transfer
Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu; Min, Seung Kyu; Gross, E. K. U.; Maitra, Neepa T.
2015-02-28
The decomposition of electronic and nuclear motion presented in Abedi et al. [Phys. Rev. Lett. 105, 123002 (2010)] yields a time-dependent potential that drives the nuclear motion and fully accounts for the coupling to the electronic subsystem. Here, we show that propagation of an ensemble of independent classical nuclear trajectories on this exact potential yields dynamics that are essentially indistinguishable from the exact quantum dynamics for a model non-adiabatic charge transfer problem. We point out the importance of step and bump features in the exact potential that are critical in obtaining the correct splitting of the quasiclassical nuclear wave packet in space after it passes through an avoided crossing between two Born-Oppenheimer surfaces and analyze their structure. Finally, an analysis of the exact potentials in the context of trajectory surface hopping is presented, including preliminary investigations of velocity-adjustment and the force-induced decoherence effect.
Various Boussinesq solitary wave solutions
Yates, G.T.
1995-12-31
The generalized Boussinesq (gB) equations have been used to model nonlinear wave evolution over variable topography and wave interactions with structures. Like the KdV equation, the gB equations support a solitary wave solution which propagates without changing shape, and this solitary wave is often used as a primary test case for numerical studies of nonlinear waves using either the gB or other model equations. Nine different approximate solutions of the generalized Boussinesq equations are presented with simple closed form expressions for the wave elevation and wave speed. Each approximates the free propagation of a single solitary wave, and eight of these solutions are newly obtained. The author compares these solutions with the well known KdV solution, Rayleigh`s solution, Laitone`s higher order solution, and ``exact`` numerical integration of the gB equations. Existing experimental data on solitary wave shape and wave speed are compared with these models.
Classes of exact Einstein Maxwell solutions
NASA Astrophysics Data System (ADS)
Komathiraj, K.; Maharaj, S. D.
2007-12-01
We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.
Exact results on the ABJM Fermi gas
NASA Astrophysics Data System (ADS)
Hatsuda, Yasuyuki; Moriyama, Sanefumi; Okuyama, Kazumi
2012-10-01
We study the Fermi gas quantum mechanics associated to the ABJM matrix model. We develop a method to compute the grand partition function of the ABJM theory, and compute exactly the partition function Z( N) up to N = 9 with the Chern-Simons level k = 1. We find that the eigenvalue problem of this quantum mechanical system is reduced to the diagonalization of a certain Hankel matrix. In reducing the number of integrations by commuting coordinates and momenta, we find an exact relation concerning the grand partition function, which is interesting on its own right and very helpful for determining the partition function. We also study the TBA-type integral equations that allow us to compute the grand partition function numerically. Surprisingly, all of our exact partition functions are written in terms of polynomials of π -1 with rational coefficients.
Connecting exact coherent states to turbulent dynamics in channel flow
NASA Astrophysics Data System (ADS)
Park, Jae Sung; Graham, Michael D.
2015-11-01
The discovery of nonlinear traveling wave solutions to the Navier-Stokes equations or exact coherent states has greatly advanced the understanding of the nature of turbulent shear flows. These solutions are unstable saddle points in state space, while the time evolution of a turbulent flow is a dynamical trajectory wandering around them. In this regard, it is of interest to investigate how closely the turbulent trajectories approach these invariant states. Here, we present connections between turbulent trajectories and one intriguing solution family in channel flow. A state space visualization of turbulent trajectories is presented in a three-dimensional space. The lifetime of the trajectories is well represented by closeness to two distinct solutions resembling in many ways the active and hibernating phases of minimal channel turbulence (Xi & Graham PRL 2010). The connections are then examined by comparing mean profiles and flow structures. More importantly, the connections are confirmed by calculating the L2 distance between the trajectories and the traveling waves. Lastly, paths of an intermittent bursting phenomenon are identified in state space and the relationship between bursting paths and the traveling waves or hibernating turbulence is further discussed. This work was supported by the Air Force Office of Scientific Research through grant FA9550-15-1-0062 (Flow Interactions and Control Program).
Exactly solvable birth and death processes
Sasaki, Ryu
2009-10-15
Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable 'matrix' quantum mechanics, which is recently proposed by Odake and the author [S. Odake and R. Sasaki, J. Math. Phys. 49, 053503 (2008)]. The (q-) Askey scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of q{sup x} (with x being the population) corresponding to the q-Racah polynomial.
Exact solution of the robust knapsack problem☆
Monaci, Michele; Pferschy, Ulrich; Serafini, Paolo
2013-01-01
We consider an uncertain variant of the knapsack problem in which the weight of the items is not exactly known in advance, but belongs to a given interval, and an upper bound is imposed on the number of items whose weight differs from the expected one. For this problem, we provide a dynamic programming algorithm and present techniques aimed at reducing its space and time complexities. Finally, we computationally compare the performances of the proposed algorithm with those of different exact algorithms presented so far in the literature for robust optimization problems. PMID:24187428
Wave propagation in solids and fluids
Davis, J. L.
1988-01-01
The fundamental principles of mathematical analysis for wave phenomena in gases, solids, and liquids are presented in an introduction for scientists and engineers. Chapters are devoted to oscillatory phenomena, the physics of wave propagation, partial differential equations for wave propagation, transverse vibration of strings, water waves, and sound waves. Consideration is given to the dynamics of viscous and inviscid fluids, wave propagation in elastic media, and variational methods in wave phenomena. 41 refs.
Verbal Interference Suppresses Exact Numerical Representation
ERIC Educational Resources Information Center
Frank, Michael C.; Fedorenko, Evelina; Lai, Peter; Saxe, Rebecca; Gibson, Edward
2012-01-01
Language for number is an important case study of the relationship between language and cognition because the mechanisms of non-verbal numerical cognition are well-understood. When the Piraha (an Amazonian hunter-gatherer tribe who have no exact number words) are tested in non-verbal numerical tasks, they are able to perform one-to-one matching…
Exact Solutions to Time-dependent Mdps
NASA Technical Reports Server (NTRS)
Boyan, Justin A.; Littman, Michael L.
2000-01-01
We describe an extension of the Markov decision process model in which a continuous time dimension is included in the state space. This allows for the representation and exact solution of a wide range of problems in which transitions or rewards vary over time. We examine problems based on route planning with public transportation and telescope observation scheduling.
Exact fractional revival in spin chains
NASA Astrophysics Data System (ADS)
Genest, Vincent X.; Vinet, Luc; Zhedanov, Alexei
2016-09-01
The occurrence of fractional revival in quantum spin chains is examined. Analytic models where this phenomenon can be exhibited in exact solutions are provided. It is explained that spin chains with fractional revival can be obtained by isospectral deformations of spin chains with perfect state transfer.
Information entropy of conditionally exactly solvable potentials
Dutta, D.; Roy, P.
2011-03-15
We evaluate Shannon entropy for the position and momentum eigenstates of some conditionally exactly solvable potentials which are isospectral to harmonic oscillator and whose solutions are given in terms of exceptional orthogonal polynomials. The Bialynicki-Birula-Mycielski inequality has also been tested for a number of states.
Exact Abjm Partition Function from Tba
NASA Astrophysics Data System (ADS)
Putrov, Pavel; Yamazaki, Masahito
2012-11-01
We report on the exact computation of the S3 partition function of U(N)k × U(N)-k ABJM theory for k = 1, N = 1, …, 19. The result is a polynomial in π-1 with rational coefficients. As an application of our results, we numerically determine the coefficient of the membrane 1-instanton correction to the partition function.
Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions.
Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza
2016-08-12
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D-1. The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s-wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4π-periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary. PMID:27563986
Exact Solution of Quadratic Fermionic Hamiltonians for Arbitrary Boundary Conditions
NASA Astrophysics Data System (ADS)
Alase, Abhijeet; Cobanera, Emilio; Ortiz, Gerardo; Viola, Lorenza
2016-08-01
We present a procedure for exactly diagonalizing finite-range quadratic fermionic Hamiltonians with arbitrary boundary conditions in one of D dimensions, and periodic in the remaining D -1 . The key is a Hamiltonian-dependent separation of the bulk from the boundary. By combining information from the two, we identify a matrix function that fully characterizes the solutions, and may be used to construct an efficiently computable indicator of bulk-boundary correspondence. As an illustration, we show how our approach correctly describes the zero-energy Majorana modes of a time-reversal-invariant s -wave two-band superconductor in a Josephson ring configuration, and predicts that a fractional 4 π -periodic Josephson effect can only be observed in phases hosting an odd number of Majorana pairs per boundary.
Optimum intermediate fibers for reducing interconnection loss: exact solution.
Yablon, Andrew D; Sumetsky, M
2007-03-15
We derive an exact analytical solution for a transmission line of N single-mode intermediate optical fibers that minimize the interconnection loss between any two dissimilar fiber modes that are well described by that paraxial scalar wave equation. Our solution shows that N optimum intermediate fibers reduce the original interconnection loss by a factor of least 1/(N+1) and that the total interconnection loss is only a function of N and the original direct interconnection loss. Our solution is not restricted to axisymmetric fibers or mode fields and therefore could be useful for reducing the interconnection loss between microstructured optical fibers, between certain slab waveguides, or between fibers and optical sources or detectors.
Exact Relaxation in a Class of Nonequilibrium Quantum Lattice Systems
Cramer, M.; Eisert, J.; Dawson, C. M.; Osborne, T. J.
2008-01-25
A reasonable physical intuition in the study of interacting quantum systems says that, independent of the initial state, the system will tend to equilibrate. In this work we introduce an experimentally accessible setting where relaxation to a steady state is exact, namely, for the Bose-Hubbard model quenched from a Mott quantum phase to the free strong superfluid regime. We rigorously prove that the evolving state locally relaxes to a steady state with maximum entropy constrained by second moments--thus maximizing the entanglement. Remarkably, for this to be true, no time average is necessary. Our argument includes a central limit theorem and exploits the finite speed of information transfer. We also show that for all periodic initial configurations (charge density waves) the system relaxes locally, and identify experimentally accessible signatures in optical lattices as well as implications for the foundations of statistical mechanics.
New types of exact quasi-soliton solutions in metamaterials
NASA Astrophysics Data System (ADS)
Yang, Rongcao; Min, Xuemin; Tian, Jinping; Xue, Wenrui; Zhang, Wenmei
2016-02-01
We consider a generalized nonlinear Schrödinger equation describing the propagation of ultrashort pulses in metamaterials (MMs) and present three new types of exact bright, dark, bright-grey quasi-solitons with a free constant associated with their amplitudes, pulse widths and formation conditions. Based on the Drude model, we analyze the existence regions and characteristics of these quasi-solitons in MMs. The results show that these bright and dark (grey) quasi-solitons can exist in wider regions of MMs and their intensities and pulse widths can be adjusted by choosing a suitable free constant. Furthermore, we take the third type of quasi-soliton solution as an example to numerically discuss the stabilities under slight perturbations of the frequency and the initial pulse width. The obtained results are helpful in exploring more solitary waves in MMs and providing a new reference for experimental verification.
Time domain scattering of travelling wave radiance
NASA Astrophysics Data System (ADS)
Berger, Henry; Rand, Robert S.
2002-12-01
I present, apparently, a new description of radiative transfer problems in the time domain. It appears that for the first time a simple physical picture emerges of the underlying essence of scattered radiance when dealing with isotropic axially-symmetric scattering in nonconservative linear media as attenuated travelling waves was by analogy. The method used a new differential equation approach. Initially its accuracy in the frequency domain was demonstrated by applying it to a solved problem, where in the literature it is dealt with using the conventional 95-year-old integro-differential equation description. Confidence in the differential equation method was bolstered by showing how this new method produces the same analytical answer. The new technique converts the integro-differential equation formulation of radiative transfer into a "pure" differential equation formulation, consisting here in a mixture of ordinary and partial derivatives, and solves that. This paper analyzes the situation in the time domain using the differential equation description and again yields a travelling wave description. However, this time it is not simply by analogy that such a description is obtained. It is exact. This result of attenuated travelling waves was demonstrated in a prior paper by solving the integro-differential equation for the classic problem of axially-symmetric scalar isotropic scattering in a nonconservative linear medium. In this paper we revisit the problem, this time solving it by the differential equation method and obtain the identical result, once again confirming the method.
Fast numerical treatment of nonlinear wave equations by spectral methods
Skjaeraasen, Olaf; Robinson, P. A.; Newman, D. L.
2011-02-15
A method is presented that accelerates spectral methods for numerical solution of a broad class of nonlinear partial differential wave equations that are first order in time and that arise in plasma wave theory. The approach involves exact analytical treatment of the linear part of the wave evolution including growth and damping as well as dispersion. After introducing the method for general scalar and vector equations, we discuss and illustrate it in more detail in the context of the coupling of high- and low-frequency plasma wave modes, as modeled by the electrostatic and electromagnetic Zakharov equations in multiple dimensions. For computational efficiency, the method uses eigenvector decomposition, which is particularly advantageous when the wave damping is mode-dependent and anisotropic in wavenumber space. In this context, it is shown that the method can significantly speed up numerical integration relative to standard spectral or finite difference methods by allowing much longer time steps, especially in the limit in which the nonlinear Schroedinger equation applies.
Partial Dynamical Symmetry in Nuclear Systems
Escher, J E
2003-06-02
Partial dynamical symmetry (PDS) extends and complements the concepts of exact and dynamical symmetry. It allows one to remove undesired constraints from an algebraic theory, while preserving some of the useful aspects of a dynamical symmetry, and to study the effects of symmetry breaking in a controlled manner. An example of a PDS in an interacting fermion system is presented. The associated PDS Hamiltonians are closely related with a realistic quadrupole-quadrupole interaction and provide new insights into this important interaction.
A Series of Exact Solutions of (2+1)-Dimensional CDGKS Equation
NASA Astrophysics Data System (ADS)
Yang, Zong-Hang
2006-11-01
An algebraic method with symbolic computation is devised to uniformly construct a series of exact solutions of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawda equation. The solutions obtained in this paper include solitary wave solutions, rational solutions, triangular periodic solutions, Jacobi and Weierstrass doubly periodic solutions. Among them, the Jacobi periodic solutions exactly degenerate to the solutions at a certain limit condition. Compared with most existing tanh method, the method used here can give new and more general solutions. More importantly, this method provides a guideline to classify the various types of the solution according to some parameters.
Coherent diffractive imaging and partial coherence
NASA Astrophysics Data System (ADS)
Williams, Garth J.; Quiney, Harry M.; Peele, Andrew G.; Nugent, Keith A.
2007-03-01
We formulate coherent diffractive imaging in the framework of partially spatially coherent diffraction. We find that the reconstruction can be critically dependent on the degree of coherence in the illuminating field and that even a small departure from full coherence may invalidate the conventional assumption that a mapping exists between an exit surface wave of finite support and a far field diffraction pattern. We demonstrate that the introduction of sufficient phase curvature in the illumination can overcome the adverse effects of partial coherence.
Hidden algebra method (quasi-exact-solvability in quantum mechanics)
Turbiner, Alexander
1996-02-20
A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland N-body problems ass ociated with an existence of the hidden algebra slN is discussed extensively.
NASA Astrophysics Data System (ADS)
Chang, Kao-Hao; Tsaur, Deng-How; Wang, Jeen-Hwa
2014-12-01
A simplified mathematical model, composed of a semi-circular valley partially filled with an inclined alluvial layer under plane SH-wave incidence, is presented. To evaluate the site response theoretically, a rigorous series solution is derived via the region-matching technique. For angular wavefunctions constrained by an inclined free surface, the original form of Graf's addition formula is recast to arbitrarily shift the local coordinate system. The valley geometry, filling material, angle of incidence, and wave frequency are taken as significant parameters in exploring the site effect on ground motions. Also included are the frequency- and time-domain computations. Two canonical cases, the semi-circular vacant canyon and the fully filled semi-circular alluvial valley, with exact analytical solutions, and the partly horizontally filled case previously studied, are taken to be particular cases of the proposed general model. Steady-state results show that the peak amplitudes of motion may increase at low frequencies when the filling layer inclines to the illuminated region. At low-grazing incidence, the phenomenon of wave focusing becomes evident on the shadow side of the filling layer. Transient-state simulations elucidate how a sequence of surface waves travel on the topmost alluvium along opposite directions and interfere with multiple reflected waves within the filling layer.
Coriolis-coupled wave packet dynamics of H + HLi reaction.
Padmanaban, R; Mahapatra, S
2006-05-11
We investigated the effect of Coriolis coupling (CC) on the initial state-selected dynamics of H+HLi reaction by a time-dependent wave packet (WP) approach. Exact quantum scattering calculations were obtained by a WP propagation method based on the Chebyshev polynomial scheme and ab initio potential energy surface of the reacting system. Partial wave contributions up to the total angular momentum J=30 were found to be necessary for the scattering of HLi in its vibrational and rotational ground state up to a collision energy approximately 0.75 eV. For each J value, the projection quantum number K was varied from 0 to min (J, K(max)), with K(max)=8 until J=20 and K(max)=4 for further higher J values. This is because further higher values of K do not have much effect on the dynamics and also because one wishes to maintain the large computational overhead for each calculation within the affordable limit. The initial state-selected integral reaction cross sections and thermal rate constants were calculated by summing up the contributions from all partial waves. These were compared with our previous results on the title system, obtained within the centrifugal sudden and J-shifting approximations, to demonstrate the impact of CC on the dynamics of this system.
Representing exact number visually using mental abacus.
Frank, Michael C; Barner, David
2012-02-01
Mental abacus (MA) is a system for performing rapid and precise arithmetic by manipulating a mental representation of an abacus, a physical calculation device. Previous work has speculated that MA is based on visual imagery, suggesting that it might be a method of representing exact number nonlinguistically, but given the limitations on visual working memory, it is unknown how MA structures could be stored. We investigated the structure of the representations underlying MA in a group of children in India. Our results suggest that MA is represented in visual working memory by splitting the abacus into a series of columns, each of which is independently stored as a unit with its own detailed substructure. In addition, we show that the computations of practiced MA users (but not those of control participants) are relatively insensitive to verbal interference, consistent with the hypothesis that MA is a nonlinguistic format for exact numerical computation. PMID:21767040
Exact vectorial law for homogeneous rotating turbulence.
Galtier, Sébastien
2009-10-01
Three-dimensional hydrodynamic turbulence is investigated under the assumptions of homogeneity and weak axisymmetry. Following the kinematics developed by E. Lindborg [J. Fluid Mech. 302, 179 (1995)] we rewrite the von Kármán-Howarth equation in terms of measurable correlations and derive the exact relation associated with the flux conservation. This relation is then analyzed in the particular case of turbulence subject to solid-body rotation. 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 parametrized by the intensity of anisotropy. A simple dimensional analysis allows us to fix this parameter and find a unique expression.
Exact solution to fractional logistic equation
NASA Astrophysics Data System (ADS)
West, Bruce J.
2015-07-01
The logistic equation is one of the most familiar nonlinear differential equations in the biological and social sciences. Herein we provide an exact solution to an extension of this equation to incorporate memory through the use of fractional derivatives in time. The solution to the fractional logistic equation (FLE) is obtained using the Carleman embedding technique that allows the nonlinear equation to be replaced by an infinite-order set of linear equations, which we then solve exactly. The formal series expansion for the initial value solution of the FLE is shown to be expressed in terms of a series of weighted Mittag-Leffler functions that reduces to the well known analytic solution in the limit where the fractional index for the derivative approaches unity. The numerical integration to the FLE provides an excellent fit to the analytic solution. We propose this approach as a general technique for solving a class of nonlinear fractional differential equations.
Representing exact number visually using mental abacus.
Frank, Michael C; Barner, David
2012-02-01
Mental abacus (MA) is a system for performing rapid and precise arithmetic by manipulating a mental representation of an abacus, a physical calculation device. Previous work has speculated that MA is based on visual imagery, suggesting that it might be a method of representing exact number nonlinguistically, but given the limitations on visual working memory, it is unknown how MA structures could be stored. We investigated the structure of the representations underlying MA in a group of children in India. Our results suggest that MA is represented in visual working memory by splitting the abacus into a series of columns, each of which is independently stored as a unit with its own detailed substructure. In addition, we show that the computations of practiced MA users (but not those of control participants) are relatively insensitive to verbal interference, consistent with the hypothesis that MA is a nonlinguistic format for exact numerical computation.
Exact folded-band chaotic oscillator
NASA Astrophysics Data System (ADS)
Corron, Ned J.; Blakely, Jonathan N.
2012-06-01
An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.
On higher dimensional exact Courant algebroids
NASA Astrophysics Data System (ADS)
Rengifo, Camilo
2016-09-01
For a smooth manifold X we show an equivalence of categories between the category of OX♯ [ n ] -extensions of TX♯ and the category of higher-dimensional exact Courant algebroids on X. In addition, for any object in the category of R [ n ] dg-principal bundles over X♯ we construct its Atiyah algebroid which gives rise to an example of OX♯ [ n ] -extensions of TX♯.
Exact BPS bound for noncommutative baby Skyrmions
NASA Astrophysics Data System (ADS)
Domrin, Andrei; Lechtenfeld, Olaf; Linares, Román; Maceda, Marco
2013-11-01
The noncommutative baby Skyrme model is a Moyal deformation of the two-dimensional sigma model plus a Skyrme term, with a group-valued or Grassmannian target. Exact abelian solitonic solutions have been identified analytically in this model, with a singular commutative limit. Inside any given Grassmannian, we establish a BPS bound for the energy functional, which is saturated by these baby Skyrmions. This asserts their stability for unit charge, as we also test in second-order perturbation theory.
An exact solution for the Hawking effect in a dispersive fluid
NASA Astrophysics Data System (ADS)
Philbin, T. G.
2016-09-01
We consider the wave equation for sound in a moving fluid with a fourth-order anomalous dispersion relation. The velocity of the fluid is a linear function of position, giving two points in the flow where the fluid velocity matches the group velocity of low-frequency waves. We find the exact solution for wave propagation in the flow. The scattering shows amplification of classical waves, leading to spontaneous emission when the waves are quantized. In the dispersionless limit the system corresponds to a 1 +1 -dimensional black-hole or white-hole binary and there is a thermal spectrum of Hawking radiation from each horizon. Dispersion changes the scattering coefficients so that the quantum emission is no longer thermal. The scattering coefficients were previously obtained by Busch and Parentani in a study of dispersive fields in de Sitter space [Phys. Rev. D 86, 104033 (2012)]. Our results give further details of the wave propagation in this exactly solvable case, where our focus is on laboratory systems.
A hierarchical exact accelerated stochastic simulation algorithm
Orendorff, David; Mjolsness, Eric
2012-01-01
A new algorithm, “HiER-leap” (hierarchical exact reaction-leaping), is derived which improves on the computational properties of the ER-leap algorithm for exact accelerated simulation of stochastic chemical kinetics. Unlike ER-leap, HiER-leap utilizes a hierarchical or divide-and-conquer organization of reaction channels into tightly coupled “blocks” and is thereby able to speed up systems with many reaction channels. Like ER-leap, HiER-leap is based on the use of upper and lower bounds on the reaction propensities to define a rejection sampling algorithm with inexpensive early rejection and acceptance steps. But in HiER-leap, large portions of intra-block sampling may be done in parallel. An accept/reject step is used to synchronize across blocks. This method scales well when many reaction channels are present and has desirable asymptotic properties. The algorithm is exact, parallelizable and achieves a significant speedup over the stochastic simulation algorithm and ER-leap on certain problems. This algorithm offers a potentially important step towards efficient in silico modeling of entire organisms. PMID:23231214
Stochastic TDHF in an exactly solvable model
NASA Astrophysics Data System (ADS)
Lacombe, L.; Suraud, E.; Reinhard, P.-G.; Dinh, P. M.
2016-10-01
We apply in a schematic model a theory beyond mean-field, namely Stochastic Time-Dependent Hartree-Fock (STDHF), which includes dynamical electron-electron collisions on top of an incoherent ensemble of mean-field states by occasional 2-particle-2-hole (2 p 2 h) jumps. The model considered here is inspired by a Lipkin-Meshkov-Glick model of Ω particles distributed into two bands of energy and coupled by a two-body interaction. Such a model can be exactly solved (numerically though) for small Ω. It therefore allows a direct comparison of STDHF and the exact propagation. The systematic impact of the model parameters as the density of states, the excitation energy and the bandwidth is presented and discussed. The time evolution of the STDHF compares fairly well with the exact entropy, as soon as the excitation energy is sufficiently large to allow 2 p 2 h transitions. Limitations concerning low energy excitations and memory effects are also discussed.
Exact nonlinear excitations in double-degenerate plasmas
Akbari-Moghanjoughi, M.
2012-06-15
In this work, we use the conventional hydrodynamics formalism and incorporate the Chew-Goldberger-Low double-adiabatic theory to evaluate the nonlinear electrostatic ion excitations in double-degenerate (electron spin-orbit degenerate) magnetized quantum plasmas. Based on the Sagdeev pseudopotential method, an exact general pseudopotential is calculated which leads to the allowed Mach-number range criteria for such localized density structures in an anisotropic magnetized plasma. We employ the criteria on the Mach-number range for diverse magnetized quantum plasma with different equations of state. It is remarked that various plasma fractional parameters such as the system dimensionality, ion-temperature, relativistic-degeneracy, Zeeman-energy, and plasma composition are involved in the stability of an obliquely propagating nonlinear ion-acoustic wave in a double-degenerate quantum plasma. Current study is most appropriate for nonlinear wave analysis in dense astrophysical magnetized plasma environments such as white-dwarfs and neutron-star crusts where the strong magnetic fields can be present.
Freestyle Vs. Boolean: A Comparison of Partial and Exact Match Retrieval Systems.
ERIC Educational Resources Information Center
Paris, Lee Anne H.; Tibbo, Helen R.
1998-01-01
Compares results of traditional Boolean searching with those of Freestyle, LEXIS/NEXIS's natural language application. Study found that though the Boolean searches had better results more often, neither method demonstrated superior performance for every query, suggesting that different queries demand different techniques. Concludes that further…
Exact nonrelativistic polarizabilities of the hydrogen atom with the Lagrange-mesh method
NASA Astrophysics Data System (ADS)
Baye, Daniel
2012-12-01
Exact analytical expressions of the dipole polarizabilities of the nonrelativistic hydrogen atom in spherical coordinates are derived with the help of the Lagrange-mesh numerical method. This method can provide exact energies and wave functions for well-chosen conditions of calculation. Exact dipole polarizabilities are obtained after an unambiguous rounding up to at least principal quantum numbers around n=30. The scalar polarizability of any nl level is given by n4[4n2+14+7l(l+1)]/4 and its tensor polarizability is given by -n4[3n2-9+11l(l+1)]l/4(2l+3), which allows the calculation of the polarizability of any hydrogen state nlm.
Experiments on exactly computing non-linear energy transfer rate in MASNUM-WAM
NASA Astrophysics Data System (ADS)
Jiang, Xingjie; Wang, Daolong; Gao, Dalu; Zhang, Tingting
2016-07-01
The Webb-Resio-Tracy (WRT) method for exact computation of the non-linear energy transfer rate was implemented in MASNUM-WAM, which is a third-generation wave model solving the discrete spectral balance equation. In this paper, we describe the transformation of the spectral space in the original WRT method. Four numerical procedures were developed in which the acceleration techniques in the original WRT method, such as geometric scaling, pre-calculating, and grid-searching, are all reorganized. A series of numerical experiments including two simulations based on real data were performed. The availability of such implementation in both serial and parallel versions of the wave model was proved, and a comparison of computation times showed that some of the developed procedures provided good efficacy. With exact computation of non-linear energy transfer, MASNUM-WAM now can be used to perform numerical experiments for research purposes, which augurs well for further developments of the model.
Mitri, F. G.
2015-09-15
The standard Resonance Scattering Theory (RST) of plane waves is extended for the case of any two-dimensional (2D) arbitrarily-shaped monochromatic beam incident upon an elastic cylinder with arbitrary location using an exact methodology based on Graf’s translational addition theorem for the cylindrical wave functions. The analysis is exact as it does not require numerical integration procedures. The formulation is valid for any cylinder of finite size and material that is immersed in a nonviscous fluid. Partial-wave series expansions (PWSEs) for the incident, internal and scattered linear pressure fields are derived, and the analysis is further extended to obtain generalized expressions for the on-axis and off-axis acoustic radiation force components. The wave-fields are expressed using generalized PWSEs involving the beam-shape coefficients (BSCs) and the scattering coefficients of the cylinder. The off-axial BSCs are expressed analytically in terms of an infinite PWSE with emphasis on the translational offset distance d. Numerical computations are considered for a zeroth-order quasi-Gaussian beam chosen as an example to illustrate the analysis. Acoustic resonance scattering directivity diagrams are calculated by subtracting an appropriate background from the expression of the scattered pressure field. In addition, computations for the radiation force exerted on an elastic cylinder centered on the axis of wave propagation of the beam, and shifted off-axially are analyzed and discussed.
NASA Astrophysics Data System (ADS)
Mitri, F. G.
2015-09-01
The standard Resonance Scattering Theory (RST) of plane waves is extended for the case of any two-dimensional (2D) arbitrarily-shaped monochromatic beam incident upon an elastic cylinder with arbitrary location using an exact methodology based on Graf's translational addition theorem for the cylindrical wave functions. The analysis is exact as it does not require numerical integration procedures. The formulation is valid for any cylinder of finite size and material that is immersed in a nonviscous fluid. Partial-wave series expansions (PWSEs) for the incident, internal and scattered linear pressure fields are derived, and the analysis is further extended to obtain generalized expressions for the on-axis and off-axis acoustic radiation force components. The wave-fields are expressed using generalized PWSEs involving the beam-shape coefficients (BSCs) and the scattering coefficients of the cylinder. The off-axial BSCs are expressed analytically in terms of an infinite PWSE with emphasis on the translational offset distance d. Numerical computations are considered for a zeroth-order quasi-Gaussian beam chosen as an example to illustrate the analysis. Acoustic resonance scattering directivity diagrams are calculated by subtracting an appropriate background from the expression of the scattered pressure field. In addition, computations for the radiation force exerted on an elastic cylinder centered on the axis of wave propagation of the beam, and shifted off-axially are analyzed and discussed.
Exact solutions for steady reconnective annihilation revisited
NASA Astrophysics Data System (ADS)
Titov, Vyacheslav S.; Tassi, Emanuele; Hornig, Gunnar
2004-10-01
This work complements the previous studies on steady reconnective magnetic annihilation in three different geometries: the two-dimensional Cartesian and polar ones and the three-dimensional (3D) cylindrical one. A special class of diffusive solutions is found analytically in explicit form for all of the three geometries. In the 3D case it is extended to a much wider class of exact solutions describing reconnective magnetic annihilation at the separatrix spine line of a magnetic null point. One of the obtained solutions provides an explicit expression for the Craig-Fabling solution. It is also identified which of the steady flow regimes found are dynamically accessible.
Exactly soluble quantum wormhole in two dimensions
Kim, Won Tae; Son, Edwin J.; Yoon, Myung Seok
2004-11-15
We are presenting a quantum traversable wormhole in an exactly soluble two-dimensional model. This is different from previous works since the exotic negative energy that supports the wormhole is generated from the quantization of classical energy-momentum tensors. This explicit illustration shows the quantum-mechanical energy can be used as a candidate for the exotic source. As for the traversability, after a particle travels through the wormhole, the static initial wormhole geometry gets a back reaction which spoils the wormhole structure. However, it may still maintain the initial structure along with the appropriate boundary condition.
Exact solutions for network rewiring models
NASA Astrophysics Data System (ADS)
Evans, T. S.
2007-03-01
Evolving networks with a constant number of edges may be modelled using a rewiring process. These models are used to describe many real-world processes including the evolution of cultural artifacts such as family names, the evolution of gene variations, and the popularity of strategies in simple econophysics models such as the minority game. The model is closely related to Urn models used for glasses, quantum gravity and wealth distributions. The full mean field equation for the degree distribution is found and its exact solution and generating solution are given.
Exact and asymptotic distributions of LULU smoothers
NASA Astrophysics Data System (ADS)
Conradie, W. J.; de Wet, T.; Jankowitz, M.
2006-02-01
This paper considers a class of non-linear smoothers, called LULU smoothers, introduced by Rohwer in the late eighties in the mathematics literature, and since then investigated fairly extensively by a number of authors for its mathematical properties. They have been successfully applied in various engineering and scientific problems. However, to date their distribution theory has not received any attention in the literature. In this paper we derive their exact as well as asymptotic distributions and show their relationship to the upper order statistics.
Coherent states for exactly solvable potentials
Shreecharan, T.; Panigrahi, Prasanta K.; Banerji, J.
2004-01-01
A general algebraic procedure for constructing coherent states of a wide class of exactly solvable potentials, e.g., Morse and Poeschl-Teller, is given. The method, a priori, is potential independent and connects with earlier developed ones, including the oscillator-based approaches for coherent states and their generalizations. This approach can be straightforwardly extended to construct more general coherent states for the quantum-mechanical potential problems, such as the nonlinear coherent states for the oscillators. The time evolution properties of some of these coherent states show revival and fractional revival, as manifested in the autocorrelation functions, as well as, in the quantum carpet structures.
Exact teleparallel gravity of binary black holes
NASA Astrophysics Data System (ADS)
El Hanafy, W.; Nashed, G. G. L.
2016-02-01
An exact solution of two singularities in the teleparallel equivalent to general relativity theory has been obtained. A holographic visualization of the binary black holes (BBHs) space-time, due to the non vanishing torsion scalar field, has been given. The acceleration tensor of BBHs space-time has been calculated. The results identify the repulsive gravity zones of the BBHs field. The total conserved quantities of the BBHs has been evaluated. Possible gravitational radiation emission by the system has been calculated without assuming a weak field initial data.
Exact diagonalization of quantum-spin models
NASA Astrophysics Data System (ADS)
Lin, H. Q.
1990-10-01
We have developed a technique to replace hashing in implementing the Lanczös method for exact diagonalization of quantum-spin models that enables us to carry out numerical studies on substantially larger lattices than previously studied. We describe the algorithm in detail and present results for the ground-state energy, the first-excited-state energy, and the spin-spin correlations on various finite lattices for spins S=1/2, 1, 3/2, and 2. Results for an infinite system are obtained by extrapolation. We also discuss the generalization of our method to other models.
Implementing a Nonlocal Toffoli Gate Using Partially Entangled Qubit Pairs
NASA Astrophysics Data System (ADS)
Chen, Li-Bing; Lu, Hong
2011-11-01
We investigate the local implementation of a nonlocal quantum Toffoli gate via partially entangled states. Firstly, we show how the nonlocal Toffoli gate can be implemented with unit fidelity and a certain probability by employing two partially entangled qubit pairs as quantum channels. The quantum circuit that does this proposed implementation is built entirely of local single-level and two-level gates if the target node harness a three-level qudit as a catalyser. This enables the construction of this key nonlocal quantum gate with existing technology. Then, we put forward a scheme to realize deterministic and exact implementation of this nonlocal gate via more partially entangled pairs. In this scheme, the control nodes' local positive operator valued measurements (POVMs) lies at the heart. We construct the required POVMs. The fact that the deterministic and exact implementation of a nonlocal multi-qubit gate could be realized by using partially entangled qubit pairs and comparatively fewer resources cost is notable.
Photoelectron wave function in photoionization: plane wave or Coulomb wave?
Gozem, Samer; Gunina, Anastasia O; Ichino, Takatoshi; Osborn, David L; Stanton, John F; Krylov, Anna I
2015-11-19
The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectron wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. The results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion.
Photoelectron wave function in photoionization: plane wave or Coulomb wave?
Gozem, Samer; Gunina, Anastasia O; Ichino, Takatoshi; Osborn, David L; Stanton, John F; Krylov, Anna I
2015-11-19
The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectron wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. The results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion. PMID:26509428
... Jacksonian seizure; Seizure - partial (focal); Temporal lobe seizure; Epilepsy - partial seizures ... Abou-Khalil BW, Gallagher MJ, Macdonald RL. Epilepsies. In: Daroff ... Practice . 7th ed. Philadelphia, PA: Elsevier; 2016:chap 101. ...
Exactly separable Bohr Hamiltonian with the Killingbeck potential for triaxial nuclei
NASA Astrophysics Data System (ADS)
Neyazi, H.; Rajabi, A. A.; Hassanabadi, H.
2016-01-01
After pioneering work by Bohr, Mottelson and their numerous colleagues, the essential framework for understanding collective model is introduced. One of the applications of this framework is the study of shape phase transition, vibrational and rotational energy spectrum of nuclei. We consider the Bohr Hamiltonian and solve the beta and gamma part equation of it, by considering that reduced potential and wave function are exactly separable. In the beta part equation we consider the Killingbeck potential and derive the wave function and energy spectrum of it.
ALmost EXact boundary conditions for transient Schrödinger-Poisson system
NASA Astrophysics Data System (ADS)
Bian, Lei; Pang, Gang; Tang, Shaoqiang; Arnold, Anton
2016-05-01
For the Schrödinger-Poisson system, we propose an ALmost EXact (ALEX) boundary condition to treat accurately the numerical boundaries. Being local in both space and time, the ALEX boundary conditions are demonstrated to be effective in suppressing spurious numerical reflections. Together with the Crank-Nicolson scheme, we simulate a resonant tunneling diode. The algorithm produces numerical results in excellent agreement with those in Mennemann et al. [1], yet at a much reduced complexity. Primary peaks in wave function profile appear as a consequence of quantum resonance, and should be considered in selecting the cut-off wave number for numerical simulations.
On optimal system, exact solutions and conservation laws of the Broer-Kaup system
NASA Astrophysics Data System (ADS)
Zhao, Zhonglong; Han, Bo
2015-11-01
The Broer-Kaup system is an important physical model which is used to model the bi-directional propagation of long waves in shallow water. In this paper, Lie symmetry analysis is performed on the Broer-Kaup system. We get the Lie point symmetries and optimal system of one-dimensional subalgebras. Similarity reductions of the system are obtained based on optimal system of one-dimensional subalgebras. We present some exact solutions of the system, which include similarity solutions and travelling wave solutions. Furthermore, some conservation laws are generated via multipliers. The conservation laws associated with symmetries of this equation are constructed by utilizing the new conservation theorem.
Exact solution to the Schrödinger’s equation with pseudo-Gaussian potential
Iacob, Felix; Lute, Marina
2015-12-15
We consider the radial Schrödinger equation with the pseudo-Gaussian potential. By making an ansatz to the solution of the eigenvalue equation for the associate Hamiltonian, we arrive at the general exact eigenfunction. The values of energy levels for the bound states are calculated along with their corresponding normalized wave-functions. The case of positive energy levels, known as meta-stable states, is also discussed and the magnitude of transmission coefficient through the potential barrier is evaluated.
Topological and non-topological exact soliton solution of the power law KdV equation
NASA Astrophysics Data System (ADS)
Biswas, Anjan; Petković, Marko D.; Milović, Daniela
2010-11-01
This paper obtains the exact 1-soliton solution of the perturbed Korteweg-de Vries equation with power law nonlinearity. Both topological as well as non-topological soliton solutions are obtained. The solitary wave ansatz is used to carry out this integration. The domain restrictions are identified in the process and the parameter constraints are also obtained. Finally, the numerical simulations are implemented in the paper.
Waves in strong centrifugal fields: dissipationless gas
NASA Astrophysics Data System (ADS)
Bogovalov, S. V.; Kislov, V. A.; Tronin, I. V.
2015-04-01
Linear waves are investigated in a rotating gas under the condition of strong centrifugal acceleration of the order 106 g realized in gas centrifuges for separation of uranium isotopes. Sound waves split into three families of the waves under these conditions. Dispersion equations are obtained. The characteristics of the waves strongly differ from the conventional sound waves on polarization, velocity of propagation and distribution of energy of the waves in space for two families having frequencies above and below the frequency of the conventional sound waves. The energy of these waves is localized in rarefied region of the gas. The waves of the third family were not specified before. They propagate exactly along the rotational axis with the conventional sound velocity. These waves are polarized only along the rotational axis. Radial and azimuthal motions are not excited. Energy of the waves is concentrated near the wall of the rotor where the density of the gas is largest.
Inflationary potentials from the exact renormalisation group
NASA Astrophysics Data System (ADS)
Grozdanov, Sašo; Kraljić, David; Svanes, Eirik Eik
2016-08-01
We show that an inflationary slow-roll potential can be derived as an IR limit of the non-perturbative exact renormalisation group equation for a scalar field within the mean-field approximation. The result follows without having to specify a Lagrangian in the UV, which we take to be somewhere below the Planck scale to avoid discussing quantum gravity effects. We assume that the theory contains a scalar mode with suppressed coupling to other fields, and that higher derivative couplings are suppressed. In this framework the exact RG equation becomes a one-dimensional Schrödinger equation, which we solve. The effective IR potential is then dominated by the eigen-states of the RG Hamiltonian with the highest eigenvalues. We find that these potentials can generically give rise to slow-roll inflation, which is fully consistent with recent observations. As an example of how the proposed renormalisation group procedure works, we perform an explicit calculation in the ϕ4 theory in an appendix.
An exactly solvable model for quantum communications.
Smith, Graeme; Smolin, John A
2013-12-12
Information theory establishes the ultimate limits on performance for noisy communication systems. Accurate models of physical communication devices must include quantum effects, but these typically make the theory intractable. As a result, communication capacities--the maximum possible rates of data transmission--are not known, even for transmission between two users connected by an electromagnetic waveguide with Gaussian noise. Here we present an exactly solvable model of communication with a fully quantum electromagnetic field. This gives explicit expressions for all point-to-point capacities of noisy quantum channels, with implications for quantum key distribution and fibre-optic communications. We also develop a theory of quantum communication networks by solving some rudimentary models including broadcast and multiple-access channels. We compare the predictions of our model with the orthodox Gaussian model and in all cases find agreement to within a few bits. At high signal-to-noise ratios, our simple model captures the relevant physics while remaining amenable to exact solution. PMID:24240277
An exactly solvable model for quantum communications.
Smith, Graeme; Smolin, John A
2013-12-12
Information theory establishes the ultimate limits on performance for noisy communication systems. Accurate models of physical communication devices must include quantum effects, but these typically make the theory intractable. As a result, communication capacities--the maximum possible rates of data transmission--are not known, even for transmission between two users connected by an electromagnetic waveguide with Gaussian noise. Here we present an exactly solvable model of communication with a fully quantum electromagnetic field. This gives explicit expressions for all point-to-point capacities of noisy quantum channels, with implications for quantum key distribution and fibre-optic communications. We also develop a theory of quantum communication networks by solving some rudimentary models including broadcast and multiple-access channels. We compare the predictions of our model with the orthodox Gaussian model and in all cases find agreement to within a few bits. At high signal-to-noise ratios, our simple model captures the relevant physics while remaining amenable to exact solution.
Explicitly broken supersymmetry with exactly massless moduli
NASA Astrophysics Data System (ADS)
Dong, Xi; Freedman, Daniel Z.; Zhao, Yue
2016-06-01
The AdS/CFT correspondence is applied to an analogue of the little hierarchy problem in three-dimensional supersymmetric theories. The bulk is governed by a super-gravity theory in which a U(1) × U(1) R-symmetry is gauged by Chern-Simons fields. The bulk theory is deformed by a boundary term quadratic in the gauge fields. It breaks SUSY completely and sources an exactly marginal operator in the dual CFT. SUSY breaking is communicated by gauge interactions to bulk scalar fields and their spinor superpartners. The bulk-to-boundary propagator of the Chern-Simons fields is a total derivative with respect to the bulk coordinates. Integration by parts and the Ward identity permit evaluation of SUSY breaking effects to all orders in the strength of the deformation. The R-charges of scalars and spinors differ so large SUSY breaking mass shifts are generated. Masses of R-neutral particles such as scalar moduli are not shifted to any order in the deformation strength, despite the fact that they may couple to R-charged fields running in loops. We also obtain a universal deformation formula for correlation functions under an exactly marginal deformation by a product of holomorphic and anti-holomorphic U(1) currents.
Gap Filling as Exact Path Length Problem.
Salmela, Leena; Sahlin, Kristoffer; Mäkinen, Veli; Tomescu, Alexandru I
2016-05-01
One of the last steps in a genome assembly project is filling the gaps between consecutive contigs in the scaffolds. This problem can be naturally stated as finding an s-t path in a directed graph whose sum of arc costs belongs to a given range (the estimate on the gap length). Here s and t are any two contigs flanking a gap. This problem is known to be NP-hard in general. Here we derive a simpler dynamic programming solution than already known, pseudo-polynomial in the maximum value of the input range. We implemented various practical optimizations to it, and compared our exact gap-filling solution experimentally to popular gap-filling tools. Summing over all the bacterial assemblies considered in our experiments, we can in total fill 76% more gaps than the best previous tool, and the gaps filled by our method span 136% more sequence. Furthermore, the error level of the newly introduced sequence is comparable to that of the previous tools. The experiments also show that our exact approach does not easily scale to larger genomes, where the problem is in general difficult for all tools. PMID:26959081
Exact, zero-energy, square-integrable solutions of a model related to the Maxwell's fish-eye problem
Makowski, Adam J.
2009-12-15
A model, which admits normalizable wave functions of the Schroedinger equation at the energy of E = 0, is exactly solved and the solutions are compared to the corresponding classical trajectories. The wave functions are proved to be square-integrable for discrete (quantized) values of the coupling constant of the used potential. We also show that our model is a specific version of the well-known Maxwell's fish-eye. This is performed with the help of a suitably chosen conformal mapping.
21 CFR 874.3450 - Partial ossicular replacement prosthesis.
Code of Federal Regulations, 2013 CFR
2013-04-01
... (CONTINUED) MEDICAL DEVICES EAR, NOSE, AND THROAT DEVICES Prosthetic Devices § 874.3450 Partial ossicular... conduction of sound wave from the tympanic membrane to the inner ear. The device is made of materials such...
NASA Astrophysics Data System (ADS)
Villalba, Víctor M.; Catalá, Esteban Isasi
2002-10-01
We solve the Klein-Gordon and Dirac equations in an open cosmological universe with a partially horn topology in the presence of a time dependent magnetic field. Since the exact solution cannot be obtained explicitly for arbitrary time dependence of the field, we discuss the asymptotic behavior of the solutions with the help of the relativistic Hamilton-Jacobi equation.
Exact solution of the Isovector-Isoscalar pairing interaction
Errea, B.; Lerma, S.
2010-04-26
A Richardson-Gaudin exactly-solvable model is presented for an isovector-isoscalar pairing interaction. Exact results show the existence of quartet correlations at T = 0, that disappear at higher T where two condensates of identical particles coexist.
Travelling wave solutions for higher-order wave equations of kdv type (iii).
Li, Jibin; Rui, Weigou; Long, Yao; He, Bin
2006-01-01
By using the theory of planar dynamical systems to the travelling wave equation of a higher order nonlinear wave equations of KdV type, the existence of smooth solitary wave, kink wave and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions are proved. In different regions of the parametric space, the sufficient conditions to guarantee the existence of the above solutions are given. In some conditions, exact explicit parametric representations of these waves are obtain. PMID:20361813
Hidden algebra method (quasi-exact-solvability in quantum mechanics)
Turbiner, A. |
1996-02-01
A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland {ital N}-body problems ass ociated with an existence of the hidden algebra {ital sl}{sub {ital N}} is discussed extensively. {copyright} {ital 1996 American Institute of Physics.}
Weak-wave analysis of shock interaction with a slipstream
NASA Technical Reports Server (NTRS)
Barger, Raymond L.
1988-01-01
A weak wave analysis of shock interaction with a slipstream is presented. The theory is compared to that for the acoustic case and to the exact nonlinear analysis. Sample calculations indicate that the weak wave theory yields a good approximation to the exact solution when the shock waves are sufficiently weak that the associated entropy increase is negligible. A qualitative discussion of the case of counterflowing streams is also included.
Exact methods for self interacting neutrinos
Pehlivan, Y.; Balantekin, A. B.; Kajino, Toshitaka
2014-06-24
The effective many-body Hamiltonian which describes vacuum oscillations and self interactions of neutrinos in a two flavor mixing scheme under the single angle approximation has the same dynamical symmetries as the well known BCS pairing Hamiltonian. These dynamical symmetries manifest themselves in terms of a set of constants of motion and can be useful in formulating the collective oscillation modes in an intuitive way. In particular, we show that a neutrino spectral split can be simply viewed as an avoided level crossing between the eigenstates of a mean field Hamiltonian which includes a Lagrange multiplier in order to fix the value of an exact many-body constant of motion. We show that the same dynamical symmetries also exist in the three neutrino mixing scheme by explicitly writing down the corresponding constants of motion.
Exact iterative reconstruction for the interior problem
Zeng, Gengsheng L; Gullberg, Grant T
2010-01-01
There is a trend in single photon emission computed tomography (SPECT) that small and dedicated imaging systems are becoming popular. For example, many companies are developing small dedicated cardiac SPECT systems with different designs. These dedicated systems have a smaller field of view (FOV) than a full-size clinical system. Thus data truncation has become the norm rather than the exception in these systems. Therefore, it is important to develop region of interest (ROI) reconstruction algorithms using truncated data. This paper is a stepping stone toward this direction. This paper shows that the common generic iterative image reconstruction algorithms are able to exactly reconstruct the ROI under the conditions that the convex ROI is fully sampled and the image value in a sub-region within the ROI is known. If the ROI includes a sub-region that is outside the patient body, then the conditions can be easily satisfied. PMID:19741279
Exact formation of hairy planar black holes
NASA Astrophysics Data System (ADS)
Fan, Zhong-Ying; Chen, Bin
2016-04-01
We consider Einstein gravity minimally coupled to a scalar field with a given potential in general dimensions. We obtain large classes of static hairy planar black holes which are asymptotic to anti-de Sitter (AdS) space-times. In particular, for a special case μ =(n -2 )/2 , we obtain new classes of exact dynamical solutions describing black hole formation. We find there are two classes of collapse solutions. The first class of solutions describes the evolution start from AdS space-time with a naked singularity at the origin. The space-time is linearly unstable and evolves into stationary black hole states even under small perturbation. The second class of solutions describes the space-time spontaneously evolving from AdS vacua into stationary black hole states undergoing nonlinear instability. We also discuss the global properties of all these dynamical solutions.
Exactly isochoric deformations of soft solids
NASA Astrophysics Data System (ADS)
Biggins, John S.; Wei, Z.; Mahadevan, L.
2014-12-01
Many materials of contemporary interest, such as gels, biological tissues and elastomers, are easily deformed but essentially incompressible. Traditional linear theory of elasticity implements incompressibility only to first order and thus permits some volume changes, which become problematically large even at very small strains. Using a mixed coordinate transformation originally due to Gauss, we enforce the constraint of isochoric deformations exactly to develop a linear theory with perfect volume conservation that remains valid until strains become geometrically large. We demonstrate the utility of this approach by calculating the response of an infinite soft isochoric solid to a point force that leads to a nonlinear generalization of the Kelvin solution. Our approach naturally generalizes to a range of problems involving deformations of soft solids and interfaces in two-dimensional and axisymmetric geometries, which we exemplify by determining the solution to a distributed load that mimics muscular contraction within the bulk of a soft solid.
Complexified Path Integrals, Exact Saddles, and Supersymmetry
NASA Astrophysics Data System (ADS)
Behtash, Alireza; Dunne, Gerald V.; Schäfer, Thomas; Sulejmanpasic, Tin; Ünsal, Mithat
2016-01-01
In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semiclassical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex saddle points, even when the parameters in the action are real. We find new exact complex saddles, and show that without their contribution the semiclassical expansion is in conflict with basic properties such as the positive semidefiniteness of the spectrum, as well as constraints of supersymmetry. Generic saddles are not only complex, but also possibly multivalued and even singular. This is in contrast to instanton solutions, which are real, smooth, and single valued. The multivaluedness of the action can be interpreted as a hidden topological angle, quantized in units of π in supersymmetric theories. The general ideas also apply to nonsupersymmetric theories.
Exact solution of multilayered piezoelectric diaphragms.
Yao, Linquan; Lu, Li; Wang, Zhihong; Zhu, Weiguang; Dai, Ying
2003-10-01
This paper investigates dynamic behavior of multilayered piezoelectric diaphragms that are simplified as laminated plates. The validity of the dynamic analysis based on the simplified clamped multilayered plate model has first been studied using ANSYS finite element (FE)-codes. The simplified, clamped, multilayered plate model has been verified to be a reasonable one in comparison with the exact model. Subsequently, the frequency characteristics of clamped rectangular piezoelectric laminated plates were further analytically investigated. Using the classical laminated plate theory, mechanical, electrical, and electromechanical characteristics of the multilayered piezoelectric diaphragms were studied. For ease of calculation, the dimensionless method was adopted. Furthermore, numerical analysis was carried out using the Rayleigh-Ritz method. Influence of dimensions of the laminar diaphragm on nature frequencies also was studied. The thickness ratio of the PZT layer to the total thickness of the laminar diaphragm has been optimized to obtain the largest deflection.
Complexified Path Integrals, Exact Saddles, and Supersymmetry.
Behtash, Alireza; Dunne, Gerald V; Schäfer, Thomas; Sulejmanpasic, Tin; Ünsal, Mithat
2016-01-01
In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semiclassical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex saddle points, even when the parameters in the action are real. We find new exact complex saddles, and show that without their contribution the semiclassical expansion is in conflict with basic properties such as the positive semidefiniteness of the spectrum, as well as constraints of supersymmetry. Generic saddles are not only complex, but also possibly multivalued and even singular. This is in contrast to instanton solutions, which are real, smooth, and single valued. The multivaluedness of the action can be interpreted as a hidden topological angle, quantized in units of π in supersymmetric theories. The general ideas also apply to nonsupersymmetric theories. PMID:26799010
Exact Chi-Square and Fisher's Exact Probability Test for 3 by 2 Cross-Classification Tables.
ERIC Educational Resources Information Center
Berry, Kenneth J.; Mielke, Paul W., Jr.
1987-01-01
Subroutines to calculate exact chi square and Fisher's exact probability tests are presented for 3 by 2 cross-classification tables. A nondirectional probability value for each test is computed recursively. (Author/GDC)
NASA Technical Reports Server (NTRS)
Wilson, J. W.
1972-01-01
The exact nucleon-deuteron elastic single scattering integral was calculated numerically in order to evaluate errors in sticking factor approximations. A similar analysis made by using S wave separable potentials concluded that errors for these approximations were negligible except near backward angles where they were found to be about 10 percent.
NASA Astrophysics Data System (ADS)
Xu, Si-Liu; Liang, Jian-Chu; Yi, Lin
2010-01-01
The (1+1)-dimensional F-expansion technique and the homogeneous nonlinear balance principle have been generalized and applied for solving exact solutions to a general (3+1)-dimensional nonlinear Schrödinger equation (NLSE) with varying coefficients and a harmonica potential. We found that there exist two kinds of soliton solutions. The evolution features of exact solutions have been numerically studied. The (3+1)D soliton solutions may help us to understand the nonlinear wave propagation in the nonlinear media such as classical optical waves and the matter waves of the Bose-Einstein condensates.
Solution of the stochastic generalized shallow-water wave equation using RVT technique
NASA Astrophysics Data System (ADS)
Hussein, Abdallah; Selim, Mustafa M.
2015-12-01
In this paper, some exact solutions of the stochastic generalized nonlinear shallow-water wave (SGNSWW) equation are obtained. This equation is an important equation in fluid mechanics field. Opposite to what is usually assumed in the literature, the coefficients of the nonlinear terms in this stochastic nonlinear partial differential equation (SNLPDE) are considered to be random quantities. The random variable transformation (RVT) technique is combined with the modified extended-tanh function method (METFM) to get the stochastic solutions represented by the probability density functions (PDFs) of the solution processes in terms of the PDFs of the random coefficients. These solutions are illustrated graphically along the spacial and time dimensions at a certain wave speed.
Initial Value Problem Solution of Nonlinear Shallow Water-Wave Equations
Kanoglu, Utku; Synolakis, Costas
2006-10-06
The initial value problem solution of the nonlinear shallow water-wave equations is developed under initial waveforms with and without velocity. We present a solution method based on a hodograph-type transformation to reduce the nonlinear shallow water-wave equations into a second-order linear partial differential equation and we solve its initial value problem. The proposed solution method overcomes earlier limitation of small waveheights when the initial velocity is nonzero, and the definition of the initial conditions in the physical and transform spaces is consistent. Our solution not only allows for evaluation of differences in predictions when specifying an exact initial velocity based on nonlinear theory and its linear approximation, which has been controversial in geophysical practice, but also helps clarify the differences in runup observed during the 2004 and 2005 Sumatran tsunamigenic earthquakes.
Teaching Modeling with Partial Differential Equations: Several Successful Approaches
ERIC Educational Resources Information Center
Myers, Joseph; Trubatch, David; Winkel, Brian
2008-01-01
We discuss the introduction and teaching of partial differential equations (heat and wave equations) via modeling physical phenomena, using a new approach that encompasses constructing difference equations and implementing these in a spreadsheet, numerically solving the partial differential equations using the numerical differential equation…
Solitary waves in particle beams
Bisognano, J.J.
1996-07-01
Since space charge waves on a particle beam exhibit both dispersive and nonlinear character, solitary waves or solitons are possible. Dispersive, nonlinear wave propagation in high current beams is found to be similar to ion-acoustic waves in plasmas with an analogy between Debye screening and beam pipe shielding. Exact longitudinal solitary wave propagation is found for potentials associated with certain transverse distributions which fill the beam pipe. For weak dispersion, the waves satisfy the Korteweg-deVries (KdV) equation, but for strong dispersion they exhibit breaking. More physically realizable distributions which do not fill the beam pipe are investigated and shown to also satisfy a KdV equation for weak dispersion if averaging over rapid transverse motion is physically justified. Scaling laws are presented to explore likely parameter regimes where these phenomena may be observed experimentally.
Generation of a novel exactly solvable potential
NASA Astrophysics Data System (ADS)
Bougie, Jonathan; Gangopadhyaya, Asim; Mallow, Jeffry V.; Rasinariu, Constantin
2015-10-01
We report a new shape-invariant (SI) isospectral extension of the Morse potential. Previous investigations have shown that the list of "conventional" SI superpotentials that do not depend explicitly on Planck's constant ħ is complete. Additionally, a set of "extended" superpotentials has been identified, each containing a conventional superpotential as a kernel and additional ħ-dependent terms. We use the partial differential equations satisfied by all SI superpotentials to find a SI extension of Morse with novel properties. It has the same eigenenergies as Morse but different asymptotic limits, and does not conform to the standard generating structure for isospectral deformations.
Characteristics of pressure waves
NASA Technical Reports Server (NTRS)
1977-01-01
Air blast characteristics generated by most types of explosions are discussed. Data cover both negative and positive blast load phases and net transverse pressure as a function of time. The effects of partial or total confinement, atmospheric propagation, absorption of energy by ground shock or cratering, and transmission over irregular terrain on blast wave properties were also considered.
Effect of selection on ancestry: an exactly soluble case and its phenomenological generalization.
Brunet, E; Derrida, B; Mueller, A H; Munier, S
2007-10-01
We consider a family of models describing the evolution under selection of a population whose dynamics can be related to the propagation of noisy traveling waves. For one particular model that we shall call the exponential model, the properties of the traveling wave front can be calculated exactly, as well as the statistics of the genealogy of the population. One striking result is that, for this particular model, the genealogical trees have the same statistics as the trees of replicas in the Parisi mean-field theory of spin glasses. We also find that in the exponential model, the coalescence times along these trees grow like the logarithm of the population size. A phenomenological picture of the propagation of wave fronts that we introduced in a previous work, as well as our numerical data, suggest that these statistics remain valid for a larger class of models, while the coalescence times grow like the cube of the logarithm of the population size. PMID:17994933
Firpo, M.-C.; Leyvraz, F.; Attuel, G.
2006-12-15
Under the conditions of weak Langmuir turbulence, a self-consistent wave-particle Hamiltonian models the effective nonlinear interaction of a spectrum of M waves with N resonant out-of-equilibrium tail electrons. In order to address its intrinsically nonlinear time-asymptotic behavior, a Monte Carlo code was built to estimate its equilibrium statistical mechanics in both the canonical and microcanonical ensembles. First, the single wave model is considered in the cold beam-plasma instability and in the O'Neil setting for nonlinear Landau damping. O'Neil's threshold, which separates nonzero time-asymptotic wave amplitude states from zero ones, is associated with a second-order phase transition. These two studies provide both a testbed for the Monte Carlo canonical and microcanonical codes, with the comparison with exact canonical results, and an opportunity to propose quantitative results to longstanding issues in basic nonlinear plasma physics. Then, the properly speaking weak turbulence framework is considered through the case of a large spectrum of waves. Focusing on the small coupling limit as a benchmark for the statistical mechanics of weak Langmuir turbulence, it is shown that Monte Carlo microcanonical results fully agree with an exact microcanonical derivation. The wave spectrum is predicted to collapse towards small wavelengths together with the escape of initially resonant particles towards low bulk plasma thermal speeds. This study reveals the fundamental discrepancy between the long-time dynamics of single waves, which can support finite amplitude steady states, and of wave spectra, which cannot.
Exact solutions for extreme black hole magnetospheres
NASA Astrophysics Data System (ADS)
Lupsasca, Alexandru; Rodriguez, Maria J.
2015-07-01
We present new exact solutions of Force-Free Electrodynamics (FFE) in the Near-Horizon region of an Extremal Kerr black hole (NHEK) and offer a complete classifica-tion of the subset that form highest-weight representations of the spacetime's SL(2, ℝ)×U(1) isometry group. For a natural choice of spacetime embedding of this isometry group, the SL(2, ℝ) highest-weight conditions lead to stationary solutions with non-trivial angular de-pendence, as well as axisymmetry when the U(1)-charge vanishes. In addition, we unveil a hidden SL(2, ℂ) symmetry of the equations of FFE that stems from the action of a complex automorphism group, and enables us to generate an SL(2, ℂ) family of (generically time-dependent) solutions. We then obtain still more general solutions with less symmetry by appealing to a principle of linear superposition that holds for solutions with collinear cur-rents. This allows us to resum the highest-weight primaries and their SL(2, ℝ)-descendants.
Exact solutions to magnetized plasma flow
Wang, Zhehui; Barnes, Cris W.
2001-03-01
Exact analytic solutions for steady-state magnetized plasma flow (MPF) using ideal magnetohydrodynamics formalism are presented. Several cases are considered. When plasma flow is included, a finite plasma pressure gradient {nabla}p can be maintained in a force-free state JxB=0 by the velocity gradient. Both incompressible and compressible MPF examples are discussed for a Taylor-state spheromak B field. A new magnetized nozzle solution is given for compressible plasma when U{parallel}B. Transition from a magnetized nozzle to a magnetic nozzle is possible when the B field is strong enough. No physical nozzle would be needed in the magnetic nozzle case. Diverging-, drum- and nozzle-shaped MPF solutions when U{perpendicular}B are also given. The electric field is needed to balance the UxB term in Ohm's law. The electric field can be generated in the laboratory with the proposed conducting electrodes. If such electric fields also exist in stars and galaxies, such as through a dynamo process, then these solutions can be candidates to explain single and double jets.
Verbal interference suppresses exact numerical representation.
Frank, Michael C; Fedorenko, Evelina; Lai, Peter; Saxe, Rebecca; Gibson, Edward
2012-02-01
Language for number is an important case study of the relationship between language and cognition because the mechanisms of non-verbal numerical cognition are well-understood. When the Pirahã (an Amazonian hunter-gatherer tribe who have no exact number words) are tested in non-verbal numerical tasks, they are able to perform one-to-one matching tasks but make errors in more difficult tasks. Their pattern of errors suggests that they are using analog magnitude estimation, an evolutionarily- and developmentally-conserved mechanism for estimating quantities. Here we show that English-speaking participants rely on the same mechanisms when verbal number representations are unavailable due to verbal interference. Followup experiments demonstrate that the effects of verbal interference are primarily manifest during encoding of quantity information, and-using a new procedure for matching difficulty of interference tasks for individual participants-that the effects are restricted to verbal interference. These results are consistent with the hypothesis that number words are used online to encode, store, and manipulate numerical information. This linguistic strategy complements, rather than altering or replacing, non-verbal representations.
Exact solutions of the nonlinear Boltzmann equation
NASA Astrophysics Data System (ADS)
Ernst, Matthieu H.
1984-03-01
A review is given of research activities since 1976 on the nonlinear Boltzmann equation and related equations of Boltzmann type, in which several rediscoveries have been made and several conjectures have been disproved. Subjects are (i) the BKW solution of the Boltzmann equation for Maxwell molecules, first discovered by Krupp in 1967, and the Krook-Wu conjecture concerning the universal significance of the BKW solution for the large (v, t) behavior of the velocity distribution function f (v, t); (ii) moment equations and polynomial expansions of f (v, t); (iii) model Boltzmann equation for a spatially uniform system of very hard particles, that can be solved in closed form for general initial conditions; (iv) for Maxwell and non-Maxwell-type molecules there exist solutions of the nonlinear Boltzmann equation with algebraic decrease at υ→∞; connections with nonuniqueness and violation of conservation laws; (v) conjectured super- H-theorem and the BKW solution; (vi) exactly soluble one-dimensional Boltzmann equation with spatial dependence.
Transient myeloproliferative disorder with partial trisomy 21.
Takahashi, Takahide; Inoue, Akira; Yoshimoto, Junko; Kanamitsu, Kiichiro; Taki, Tomohiko; Imada, Masahide; Yamada, Mutsuko; Ninomiya, Shinsuke; Toki, Tsutomu; Terui, Kiminori; Ito, Etsuro; Shimada, Akira
2015-11-01
Myeloid malignancy with Down syndrome (ML-DS) is estimated to have a step-wise leukemogenesis including GATA1 mutation. Trisomy 21 is essential for ML-DS; however, we do not know exactly which gene or genes located on chromosome 21 are necessary for the ML-DS. We report a female infant with transient myeloproliferative disorder (TMD) and partial trisomy 21. SNP array analysis showed 10 Mb amplification of 21q22.12-21q22.3, which included DYRK1A, ERG, and ETS but not the RUNX1 gene. With two other reported TMD cases having partial trisomy 21, DYRK1A, ERG, and ETS were the most likely genes involved in collaboration with the GATA1 mutation. PMID:26138905
Nonlinear sharpening during superposition of surface waves
NASA Astrophysics Data System (ADS)
Chalikov, Dmitry; Babanin, Alexander V.
2016-08-01
Two-dimensional direct wave model is used for demonstration of the role of reversible interactions which probably is the main process leading to breaking. One-dimensional model was used for performing of thousands of exact short-term simulations of evolution of two superposed wave trains with different steepness, and wavenumbers were performed to investigate the effect of wave crests merging. Nonlinear sharpening of the merging crests is demonstrated. It is suggested that such effect may be responsible for appearance of the typical sharp crests of surface waves, as well as for wave breaking.
NASA Astrophysics Data System (ADS)
Sarwar, S.; Rashidi, M. M.
2016-07-01
This paper deals with the investigation of the analytical approximate solutions for two-term fractional-order diffusion, wave-diffusion, and telegraph equations. The fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], (1,2), and [1,2], respectively. In this paper, we extended optimal homotopy asymptotic method (OHAM) for two-term fractional-order wave-diffusion equations. Highly approximate solution is obtained in series form using this extended method. Approximate solution obtained by OHAM is compared with the exact solution. It is observed that OHAM is a prevailing and convergent method for the solutions of nonlinear-fractional-order time-dependent partial differential problems. The numerical results rendering that the applied method is explicit, effective, and easy to use, for handling more general fractional-order wave diffusion, diffusion, and telegraph problems.
Exact Approach to Inflationary Universe Models
NASA Astrophysics Data System (ADS)
del Campo, Sergio
In this chapter we introduce a study of inflationary universe models that are characterized by a single scalar inflation field . The study of these models is based on two dynamical equations: one corresponding to the Klein-Gordon equation for the inflaton field and the other to a generalized Friedmann equation. After describing the kinematics and dynamics of the models under the Hamilton-Jacobi scheme, we determine in some detail scalar density perturbations and relic gravitational waves. We also introduce the study of inflation under the hierarchy of the slow-roll parameters together with the flow equations. We apply this approach to the modified Friedmann equation that we call the Friedmann-Chern-Simons equation, characterized by F(H) = H^2- α H4, and the brane-world inflationary models expressed by the modified Friedmann equation.
Solitary and periodic wave solutions of the Majda-Biello system
NASA Astrophysics Data System (ADS)
Adem, Abdullahi Rashid
2016-05-01
In this paper, we present the exact solutions of the Majda-Biello system. This system describes the nonlinear interaction of long-wavelength equatorial Rossby waves and barotropic Rossby waves with a substantial midlatitude projection, in the presence of suitable horizontally and vertically sheared zonal mean flows. The methods used to construct the exact solutions are the Kudryashov method and Jacobi elliptic function method. These two methods yield solitary wave solutions and periodic wave solutions.
Transient response of lattice structures based on exact member theory
NASA Technical Reports Server (NTRS)
Anderson, Melvin S.
1989-01-01
The computer program BUNVIS-RG, which treats vibration and buckling of lattice structures using exact member stiffness matrices, has been extended to calculate the exact modal mass and stiffness quantities that can be used in a conventional transient response analysis based on modes. The exact nature of the development allows inclusion of local member response without introduction of any interior member nodes. Results are given for several problems in which significant interaction between local and global response occurs.
The Lockheed alternate partial polarizer universal filter
NASA Technical Reports Server (NTRS)
Title, A. M.
1976-01-01
A tunable birefringent filter using an alternate partial polarizer design has been built. The filter has a transmission of 38% in polarized light. Its full width at half maximum is .09A at 5500A. It is tunable from 4500 to 8500A by means of stepping motor actuated rotating half wave plates and polarizers. Wave length commands and thermal compensation commands are generated by a PPD 11/10 minicomputer. The alternate partial polarizer universal filter is compared with the universal birefringent filter and the design techniques, construction methods, and filter performance are discussed in some detail. Based on the experience of this filter some conclusions regarding the future of birefringent filters are elaborated.
NASA Astrophysics Data System (ADS)
Gurnett, Donald
2008-11-01
Although low-frequency radio waves of extra-terrestrial origin were known over a century ago, it wasn't until the beginning of the space era fifty years ago that the origin of these waves could be adequately investigated. Since then spacecraft-borne instruments have shown that space plasmas exhibit an almost bewildering variety of wave phenomena, sometimes referred to as the plasma wave zoo. In this talk I will focus on two types of waves that occur in the magnetospheres of the strongly magnetized planets. They are whistler mode emissions and cyclotron maser radiation. Whistler mode emissions are generated in the now famous plasma wave mode known as the whistler mode, and cyclotron maser radiation is emitted mainly in the right-hand polarized free space mode. Both involve a cyclotron resonant interaction and require a perpendicular anisotropy to achieve wave growth. However, the origin of the anisotropy is different in the two cases. Whistler mode emissions occur in planetary radiation belts and are driven by the loss-cone anisotropy imposed by the planet. The resulting waves play a major role in the scattering and loss of radiation belt electrons. In contrast, the cyclotron maser radiation is generated in the auroral regions where parallel electric fields accelerate down-going electrons to high energies. The wave growth is driven by the shell distribution that arises from a combination of the parallel electric field and the magnetic mirror force. The resulting radiation is extremely intense and can be detected at great distances as an escaping radio emission. Both the whistler mode emissions and the cyclotron maser radiation display an amazing amount of fine structure. This structure is thought to be due to nonlinear trapping of the resonant electrons. The exact nonlinear mechanisms involved are still a topic of current study.
The exact wavefunction factorization of a vibronic coupling system
Chiang, Ying-Chih; Klaiman, Shachar; Otto, Frank; Cederbaum, Lorenz S.
2014-02-07
We investigate the exact wavefunction as a single product of electronic and nuclear wavefunction for a model conical intersection system. Exact factorized spiky potentials and nodeless nuclear wavefunctions are found. The exact factorized potential preserves the symmetry breaking effect when the coupling mode is present. Additionally nodeless wavefunctions are found to be closely related to the adiabatic nuclear eigenfunctions. This phenomenon holds even for the regime where the non-adiabatic coupling is relevant, and sheds light on the relation between the exact wavefunction factorization and the adiabatic approximation.
From Bessel beam to complex-source-point cylindrical wave-function
Mitri, F.G.
2015-04-15
This investigation shows that a scalar Bessel beam can be transformed into the non-paraxial complex-source-point cylindrical wave (CSPCW). High-order CSPCW solutions, termed here high-order quasi-Gaussian cylindrical beams, which exactly satisfy the Helmholtz equation, are derived analytically. Moreover, partial-derivatives of the high-order CSPCW solutions satisfy the Helmholtz equation. In addition, the CSPCW solutions satisfy the nonrelativistic Schrödinger equation within standard quantum mechanics, thus, the results can be used in the description of elementary particle/matter motion and related applications in quantum scattering theory. Furthermore, the analysis is extended to the case of vector beams in which the components of the electromagnetic (EM) field are obtained based on different polarizations of the magnetic and electric vector potentials, which exactly satisfy Maxwell’s vectorial equations and Lorenz’ gauge condition. An attractive feature of the high-order solutions is the rigorous description of strongly focused (or strongly divergent) cylindrical wave-fields without any approximations, nor the need for numerical methods. Possible applications are in beam-forming design using high-aperture or collimated cylindrical laser/electron quasi-Gaussian beams in imaging microscopy, particle manipulation, optical tweezers, and the study of the scattering, and radiation forces on objects. - Highlights: • Bessel beam is transformed into the non-paraxial cylindrical complex-source-point. • Exact high-order tightly focused solutions are derived without any approximations. • The exact solutions also satisfy the nonrelativistic Schrödinger equation. • Electromagnetic beams are obtained as solutions of Maxwell’s vectorial equations. • Applications are in laser/electron beam imaging, tweezers, and radiation force.
Nonphotosensitive video game-induced partial seizures.
Takahashi, Y; Shigematsu, H; Kubota, H; Inoue, Y; Fujiwara, T; Yagi, K; Seino, M
1995-08-01
We report a 9-year-old boy with a ring 20 chromosome anomaly whose complex partial seizures (CPS), presumably of frontal lobe origin, were often induced by playing video games. Neither photosensitivity nor pattern sensitivity was observed. An intensive video-EEG investigation showed that video games as well as mental calculation elicited rhythmic runs of bilateral high-voltage slow waves, which eventually evolved into ictal discharges. This case suggests that higher brain functions can be involved in seizure induction.
NASA Astrophysics Data System (ADS)
Pantellini, Filippo; Griton, Léa
2016-10-01
The spatial structure of a steady state plasma flow is shaped by the standing modes with local phase velocity exactly opposite to the flow velocity. The general procedure of finding the wave vectors of all possible standing MHD modes in any given point of a stationary flow requires numerically solving an algebraic equation. We present the graphical procedure (already mentioned by some authors in the 1960's) along with the exact solution for the Alfvén mode and approximate analytic solutions for both fast and slow modes. The technique can be used to identify MHD modes in space and laboratory plasmas as well as in numerical simulations.
Quantifying Exact Motions Along Lineaments on Europa
NASA Technical Reports Server (NTRS)
Vetter, J. C.; Kattenhorn, S. A.
2005-01-01
Evaluating the precise motions along lineaments on the surface of Jupiter's icy moon, Europa, is a valuable tool for interpreting the development and history of lineaments of various morphologies. Such morphologies include strike-slip faults, dilational bands, ridges, and convergence zones. However, the exact mode of origin and kinematic behavior of these various lineaments are not obvious based on morphology alone. In fact, the apparent motions implied by displaced crosscut features can provide misleading indications of true motions along lineaments. Identifying the precise motions (combinations of sliding and opening/closing) is critical to the accurate characterization and interpretation of each of these lineament types. Lineaments of interest (i.e., those having displaced relatively older features in some manner) are identified on Galileo spacecraft images and measurements are made of the total offset, the separation, and relative orientations of crosscut features with respect to the lineament of interest. Specifically, by using these measured quantities and a series of trigonometric equations, the precise motions (i.e., dilation, convergence, strike-slip, or a combination of strike-slip and dilation or convergence) can be determined. These measurements are, however, limited by the resolution of the available images. This study focuses on motion analysis techniques for Europan lineaments and the precise characterization of fault-orthogonal and/or strike-slip motion along lineaments of varying morphologies. We highlight potential pitfalls of cursory analyses of motion indicators. For example, lineaments with obvious lateral offsets have typically been identified simply as strike-slip faults. This assumption may actually be incorrect, as fault-orthogonal motions may contribute to apparent lateral displacements (offsets or separations). Also, variability in the amount of fault motion along the trace length should theoretically be identifiable using the outlined
Twisted partially pure spinors
NASA Astrophysics Data System (ADS)
Herrera, Rafael; Tellez, Ivan
2016-08-01
Motivated by the relationship between orthogonal complex structures and pure spinors, we define twisted partially pure spinors in order to characterize spinorially subspaces of Euclidean space endowed with a complex structure.
Instability of Pollard's exact solution for geophysical ocean flows
NASA Astrophysics Data System (ADS)
Ionescu-Kruse, Delia
2016-08-01
In this paper we apply the short-wavelength perturbation method to derive instability criteria for the three-dimensional nonlinear Pollard geophysical waves. We show that these waves are linearly unstable when the wave steepness exceeds a certain threshold.
Exact supersymmetric massive and massless white holes
NASA Astrophysics Data System (ADS)
Kallosh, Renata; Linde, Andrei
1995-12-01
We study special points in the moduli space of vacua at which supersymmetric electric solutions of the heterotic string theory become massless. We concentrate on configurations for which the supersymmetric nonrenormalization theorem is valid. These are ten-dimensional supersymmetric string waves and generalized fundamental strings with SO(8) holonomy group. From these we find the four-dimensional spherically symmetric configurations which saturate the BPS bound, in particular, near the points of the vanishing ADM mass. The nontrivial massless supersymmetric states in this class exist only in the presence of non-Abelian vector fields. We also find a new class of supersymmetric massive solutions, closely related to the massless ones. A distinctive property of all these objects, either massless or massive, is the existence of gravitational repulsion. They reflect all particles with nonvanishing mass and/or angular momentum, and therefore they can be called white holes (repulsons), in contrast with black holes which tend to absorb particles of all kinds. If such objects can exist we will have the first realization of the universal gravitational force which repels all particles with the strength proportional to their mass and therefore can be associated with antigravity.
Coherent Backscattering by Polydisperse Discrete Random Media: Exact T-Matrix Results
NASA Technical Reports Server (NTRS)
Mishchenko, Michael I.; Dlugach, Janna M.; Mackowski, Daniel W.
2011-01-01
The numerically exact superposition T-matrix method is used to compute, for the first time to our knowledge, electromagnetic scattering by finite spherical volumes composed of polydisperse mixtures of spherical particles with different size parameters or different refractive indices. The backscattering patterns calculated in the far-field zone of the polydisperse multiparticle volumes reveal unequivocally the classical manifestations of the effect of weak localization of electromagnetic waves in discrete random media, thereby corroborating the universal interference nature of coherent backscattering. The polarization opposition effect is shown to be the least robust manifestation of weak localization fading away with increasing particle size parameter.
Two atoms in a double well: Exact solution with a Bethe ansatz
NASA Astrophysics Data System (ADS)
Liu, Yanxia; Zhang, Yunbo
2015-05-01
We propose to experimentally realize an odd-parity eigenstate |b > of two atoms in a double well. The occupation probability of this state shows evident dependence on the interaction, distinct from the result of two-mode model adopted in the Heidelberg experiment. The tunneling dynamics of two atoms starting from the NOON state with infinite barrier height can be derived from the exactly solved model of a δ -barrier split double well based on a Bethe ansatz type hypothesis of the wave functions. We find that the single-particle tunneling shifts between the probability of double occupancy in the same well and that of single occupancy in different wells.
Quasi-exact minus-quartic oscillators in strong-core regime
NASA Astrophysics Data System (ADS)
Znojil, Miloslav
2006-11-01
PT-symmetric potentials V(x)=-x+iBx+Cx+iDx+iF/x+G/x are quasi-exactly solvable, i.e., a specific choice of a small G=G=integer/4 is known to lead to wave functions ψ(x) in closed form at certain charges F=F and energies E=E. The existence of an alternative, simpler and non-numerical version of such a construction is announced here in the new dynamical regime of very large G→∞.
Lemeshko, Mikhail; Mustafa, Mustafa; Kais, Sabre; Friedrich, Bretislav
2011-04-15
By invoking supersymmetry, we found a condition under which the Stark-effect problem for a polar and polarizable molecule subject to nonresonant electric fields becomes exactly solvable for the |J-tilde=m,m> family of stretched states. The analytic expressions for the wave function and eigenenergy and other expectation values allow one to readily reverse-engineer the problem of finding the values of the interaction parameters required for creating quantum states with preordained characteristics. The method also allows the construction of families of isospectral potentials, realizable with combined fields.
Onural, Levent
2011-03-01
The diffraction relation between a plane and another plane that is both tilted and translated with respect to the first one is revisited. The derivation of the result becomes easier when the impulse function over a surface is used as a tool. Such an approach converts the original 2D problem to an intermediate 3D problem and thus allows utilization of easy-to-interpret Fourier transform properties due to rotation and translation. An exact solution for the scalar monochromatic propagating waves case when the propagation direction is restricted to be in the forward direction is presented. PMID:21383808
Exact null controllability of degenerate evolution equations with scalar control
Fedorov, Vladimir E; Shklyar, Benzion
2012-12-31
Necessary and sufficient conditions for the exact null controllability of a degenerate linear evolution equation with scalar control are obtained. These general results are used to examine the exact null controllability of the Dzektser equation in the theory of seepage. Bibliography: 13 titles.
Inference and Exact Numerical Representation in Early Language Development
ERIC Educational Resources Information Center
Barner, David; Bachrach, Asaf
2010-01-01
How do children as young as 2 years of age know that numerals, like "one," have exact interpretations, while quantifiers and words like "a" do not? Previous studies have argued that only numerals have exact lexical meanings. Children could not use scalar implicature to strengthen numeral meanings, it is argued, since they fail to do so for…
ERIC Educational Resources Information Center
DeClark, Tom
2000-01-01
Presents an activity on waves that addresses the state standards and benchmarks of Michigan. Demonstrates waves and studies wave's medium, motion, and frequency. The activity is designed to address different learning styles. (YDS)
A Well-Balanced Path-Integral f-Wave Method for Hyperbolic Problems with Source Terms.
Leveque, Randall J
2011-07-01
Systems of hyperbolic partial differential equations with source terms (balance laws) arise in many applications where it is important to compute accurate time-dependent solutions modeling small perturbations of equilibrium solutions in which the source terms balance the hyperbolic part. The f-wave version of the wave-propagation algorithm is one approach, but requires the use of a particular averaged value of the source terms at each cell interface in order to be "well balanced" and exactly maintain steady states. A general approach to choosing this average is developed using the theory of path conservative methods. A scalar advection equation with a decay or growth term is introduced as a model problem for numerical experiments.
An exact factorization perspective on quantum interferences in nonadiabatic dynamics.
Curchod, Basile F E; Agostini, Federica; Gross, E K U
2016-07-21
Nonadiabatic quantum interferences emerge whenever nuclear wavefunctions in different electronic states meet and interact in a nonadiabatic region. In this work, we analyze how nonadiabatic quantum interferences translate in the context of the exact factorization of the molecular wavefunction. In particular, we focus our attention on the shape of the time-dependent potential energy surface-the exact surface on which the nuclear dynamics takes place. We use a one-dimensional exactly solvable model to reproduce different conditions for quantum interferences, whose characteristic features already appear in one-dimension. The time-dependent potential energy surface develops complex features when strong interferences are present, in clear contrast to the observed behavior in simple nonadiabatic crossing cases. Nevertheless, independent classical trajectories propagated on the exact time-dependent potential energy surface reasonably conserve a distribution in configuration space that mimics one of the exact nuclear probability densities. PMID:27448870
An exact factorization perspective on quantum interferences in nonadiabatic dynamics
NASA Astrophysics Data System (ADS)
Curchod, Basile F. E.; Agostini, Federica; Gross, E. K. U.
2016-07-01
Nonadiabatic quantum interferences emerge whenever nuclear wavefunctions in different electronic states meet and interact in a nonadiabatic region. In this work, we analyze how nonadiabatic quantum interferences translate in the context of the exact factorization of the molecular wavefunction. In particular, we focus our attention on the shape of the time-dependent potential energy surface—the exact surface on which the nuclear dynamics takes place. We use a one-dimensional exactly solvable model to reproduce different conditions for quantum interferences, whose characteristic features already appear in one-dimension. The time-dependent potential energy surface develops complex features when strong interferences are present, in clear contrast to the observed behavior in simple nonadiabatic crossing cases. Nevertheless, independent classical trajectories propagated on the exact time-dependent potential energy surface reasonably conserve a distribution in configuration space that mimics one of the exact nuclear probability densities.
Conversion of borehole Stoneley waves to channel waves in coal
Johnson, P.A.; Albright, J.N.
1987-01-01
Evidence for the mode conversion of borehole Stoneley waves to stratigraphically guided channel waves was discovered in data from a crosswell acoustic experiment conducted between wells penetrating thin coal strata located near Rifle, Colorado. Traveltime moveout observations show that borehole Stoneley waves, excited by a transmitter positioned at substantial distances in one well above and below a coal stratum at 2025 m depth, underwent partial conversion to a channel wave propagating away from the well through the coal. In an adjacent well the channel wave was detected at receiver locations within the coal, and borehole Stoneley waves, arising from a second partial conversion of channel waves, were detected at locations above and below the coal. The observed channel wave is inferred to be the third-higher Rayleigh mode based on comparison of the measured group velocity with theoretically derived dispersion curves. The identification of the mode conversion between borehole and stratigraphically guided waves is significant because coal penetrated by multiple wells may be detected without placing an acoustic transmitter or receiver within the waveguide. 13 refs., 6 figs., 1 tab.
Large-amplitude waves in a gas disk. I. Stationary periodic waves
Abramyan, M.G.; Mikhailova, E.A.; Morozov, A.G.
1986-07-01
The exact nonlinear equation of short-wave perturbations of a rotating gas disk has been solved numerically. Nonlinear periodic waves whose amplitude for fixed propagation velocity is bounded above were obtained. The limiting value of the amplitude increases with increasing wave velocity. The results are used to estimate the parameters of the ''3-kpc arm'' and ''135-km/sec feature'' of the Galaxy and the fine structure of Saturn's rings.
NASA Astrophysics Data System (ADS)
Li, Jibin; Chen, Fengjuan
In this paper, we consider a model created by diffraction in periodic media. The study of the traveling wave solutions for this model derives a planar dynamical system with a singular straight line. 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, periodic peakon solutions, compactons, etc.) under different parameter conditions.
Electromagnetic wave scattering by Schwarzschild black holes.
Crispino, Luís C B; Dolan, Sam R; Oliveira, Ednilton S
2009-06-12
We analyze the scattering of a planar monochromatic electromagnetic wave incident upon a Schwarzschild black hole. We obtain accurate numerical results from the partial wave method for the electromagnetic scattering cross section and show that they are in excellent agreement with analytical approximations. The scattering of electromagnetic waves is compared with the scattering of scalar, spinor, and gravitational waves. We present a unified picture of the scattering of all massless fields for the first time. PMID:19658920
Layden, B.; Cairns, Iver H.; Robinson, P. A.
2013-08-15
Electrostatic decay of Langmuir waves into Langmuir and ion sound waves (L→L′+S) and scattering of Langmuir waves off thermal ions (L+i→L′+i′, also called “nonlinear Landau damping”) are important nonlinear weak-turbulence processes. The rates for these processes depend on the quadratic longitudinal response function α{sup (2)} (or, equivalently, the quadratic longitudinal susceptibility χ{sup (2)}), which describes the second-order response of a plasma to electrostatic wave fields. Previous calculations of these rates for an unmagnetized Maxwellian plasma have relied upon an approximate form for α{sup (2)} that is valid where two of the wave fields are fast (i.e., v{sub φ}=ω/k≫V{sub e} where ω is the angular frequency, k is the wavenumber, and V{sub e} is the electron thermal speed) and one is slow (v{sub φ}≪V{sub e}). Recently, an exact expression was derived for α{sup (2)} that is valid for any phase speeds of the three waves in an unmagnetized Maxwellian plasma. Here, this exact α{sup (2)} is applied to the calculation of the three-dimensional rates for electrostatic decay and scattering off thermal ions, and the resulting exact rates are compared with the approximate rates. The calculations are performed using previously derived three-dimensional rates for electrostatic decay given in terms of a general α{sup (2)}, and newly derived three-dimensional rates for scattering off thermal ions; the scattering rate is derived assuming a Maxwellian ion distribution, and both rates are derived assuming arc distributions for the wave spectra. For most space plasma conditions, the approximate rate is found to be accurate to better than 20%; however, for sufficiently low Langmuir phase speeds (v{sub φ}/V{sub e}≈3) appropriate to some spatial domains of the foreshock regions of planetary bow shocks and type II solar radio bursts, the use of the exact rate may be necessary for accurate calculations. The relative rates of electrostatic decay
NASA Astrophysics Data System (ADS)
Hayek, Mohamed
2016-04-01
This work develops a simple exact and explicit solution of the one-dimensional transient and nonlinear Richards' equation for soils in a special case of exponential water retention curve and power law hydraulic conductivity. The exact solution is obtained as traveling wave based on the approach proposed by Philip (1957, 1967) and adopted by Zlotnik et al. (2007). The obtained solution is novel, and it expresses explicitly the water content as function of the depth and time. It can be useful to model infiltration into semi-infinite soils with time-dependent boundary conditions and infiltration with constant boundary condition but space-dependent initial condition. A complete analytical inverse procedure based on the proposed analytical solution is presented which allows the estimation of hydraulic parameters. The proposed exact solution is also important for the verification of numerical schemes as well as for checking the implementation of time-dependent boundary conditions.
Variance Components: Partialled vs. Common.
ERIC Educational Resources Information Center
Curtis, Ervin W.
1985-01-01
A new approach to partialling components is used. Like conventional partialling, this approach orthogonalizes variables by partitioning the scores or observations. Unlike conventional partialling, it yields a common component and two unique components. (Author/GDC)
Methanol partial oxidation reformer
Ahmed, S.; Kumar, R.; Krumpelt, M.
1999-08-17
A partial oxidation reformer is described comprising a longitudinally extending chamber having a methanol, water and an air inlet and an outlet. An igniter mechanism is near the inlets for igniting a mixture of methanol and air, while a partial oxidation catalyst in the chamber is spaced from the inlets and converts methanol and oxygen to carbon dioxide and hydrogen. Controlling the oxygen to methanol mole ratio provides continuous slightly exothermic partial oxidation reactions of methanol and air producing hydrogen gas. The liquid is preferably injected in droplets having diameters less than 100 micrometers. The reformer is useful in a propulsion system for a vehicle which supplies a hydrogen-containing gas to the negative electrode of a fuel cell. 7 figs.
Methanol partial oxidation reformer
Ahmed, Shabbir; Kumar, Romesh; Krumpelt, Michael
1999-01-01
A partial oxidation reformer comprising a longitudinally extending chamber having a methanol, water and an air inlet and an outlet. An igniter mechanism is near the inlets for igniting a mixture of methanol and air, while a partial oxidation catalyst in the chamber is spaced from the inlets and converts methanol and oxygen to carbon dioxide and hydrogen. Controlling the oxygen to methanol mole ratio provides continuous slightly exothermic partial oxidation reactions of methanol and air producing hydrogen gas. The liquid is preferably injected in droplets having diameters less than 100 micrometers. The reformer is useful in a propulsion system for a vehicle which supplies a hydrogen-containing gas to the negative electrode of a fuel cell.
Methanol partial oxidation reformer
Ahmed, Shabbir; Kumar, Romesh; Krumpelt, Michael
2001-01-01
A partial oxidation reformer comprising a longitudinally extending chamber having a methanol, water and an air inlet and an outlet. An igniter mechanism is near the inlets for igniting a mixture of methanol and air, while a partial oxidation catalyst in the chamber is spaced from the inlets and converts methanol and oxygen to carbon dioxide and hydrogen. Controlling the oxygen to methanol mole ratio provides continuous slightly exothermic partial oxidation reactions of methanol and air producing hydrogen gas. The liquid is preferably injected in droplets having diameters less than 100 micrometers. The reformer is useful in a propulsion system for a vehicle which supplies a hydrogen-containing gas to the negative electrode of a fuel cell.
Methanol partial oxidation reformer
Ahmed, S.; Kumar, R.; Krumpelt, M.
1999-08-24
A partial oxidation reformer is described comprising a longitudinally extending chamber having a methanol, water and an air inlet and an outlet. An igniter mechanism is near the inlets for igniting a mixture of methanol and air, while a partial oxidation catalyst in the chamber is spaced from the inlets and converts methanol and oxygen to carbon dioxide and hydrogen. Controlling the oxygen to methanol mole ratio provides continuous slightly exothermic partial oxidation reactions of methanol and air producing hydrogen gas. The liquid is preferably injected in droplets having diameters less than 100 micrometers. The reformer is useful in a propulsion system for a vehicle which supplies a hydrogen-containing gas to the negative electrode of a fuel cell. 7 figs.
Oxygen partial pressure sensor
Dees, D.W.
1994-09-06
A method for detecting oxygen partial pressure and an oxygen partial pressure sensor are provided. The method for measuring oxygen partial pressure includes contacting oxygen to a solid oxide electrolyte and measuring the subsequent change in electrical conductivity of the solid oxide electrolyte. A solid oxide electrolyte is utilized that contacts both a porous electrode and a nonporous electrode. The electrical conductivity of the solid oxide electrolyte is affected when oxygen from an exhaust stream permeates through the porous electrode to establish an equilibrium of oxygen anions in the electrolyte, thereby displacing electrons throughout the electrolyte to form an electron gradient. By adapting the two electrodes to sense a voltage potential between them, the change in electrolyte conductivity due to oxygen presence can be measured. 1 fig.
Oxygen partial pressure sensor
Dees, Dennis W.
1994-01-01
A method for detecting oxygen partial pressure and an oxygen partial pressure sensor are provided. The method for measuring oxygen partial pressure includes contacting oxygen to a solid oxide electrolyte and measuring the subsequent change in electrical conductivity of the solid oxide electrolyte. A solid oxide electrolyte is utilized that contacts both a porous electrode and a nonporous electrode. The electrical conductivity of the solid oxide electrolyte is affected when oxygen from an exhaust stream permeates through the porous electrode to establish an equilibrium of oxygen anions in the electrolyte, thereby displacing electrons throughout the electrolyte to form an electron gradient. By adapting the two electrodes to sense a voltage potential between them, the change in electrolyte conductivity due to oxygen presence can be measured.
Symmetries, Integrability and Exact Solutions to the (2+1)-Dimensional Benney Types of Equations
NASA Astrophysics Data System (ADS)
Liu, Han-Ze; Xin, Xiang-Peng
2016-08-01
This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integrable condition of the equation is given. Then, the symmetry reductions and exact solutions to the (2+1)-dimensional nonlinear wave equations are presented. Especially, the shock wave solutions of the Benney equations are investigated by the symmetry reduction and trial function method. Supported by the National Natural Science Foundation of China under Grant Nos. 11171041 and 11505090, Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009, and the doctorial foundation of Liaocheng University under Grant No. 31805
Exact vortex solutions in a CP N Skyrme-Faddeev type model
NASA Astrophysics Data System (ADS)
Ferreira, L. A.; Klimas, P.
2010-10-01
We consider a four dimensional field theory with target space being CP N which constitutes a generalization of the usual Skyrme-Faddeev model defined on CP 1. We show that it possesses an integrable sector presenting an infinite number of local conservation laws, which are associated to the hidden symmetries of the zero curvature representation of the theory in loop space. We construct an infinite class of exact solutions for that integrable submodel where the fields are meromorphic functions of the combinations ( x 1 + ix 2) and x 3 + x 0 of the Cartesian coordinates of four dimensional Minkowski space-time. Among those solutions we have static vortices and also vortices with waves traveling along them with the speed of light. The energy per unity of length of the vortices show an interesting and intricate interaction among the vortices and waves.
In How Many Ways is the Approximate Number System Associated with Exact Calculation?
Pinheiro-Chagas, Pedro; Wood, Guilherme; Knops, André; Krinzinger, Helga; Lonnemann, Jan; Starling-Alves, Isabella; Willmes, Klaus; Haase, Vitor Geraldi
2014-01-01
The approximate number system (ANS) has been consistently found to be associated with math achievement. However, little is known about the interactions between the different instantiations of the ANS and in how many ways they are related to exact calculation. In a cross-sectional design, we investigated the relationship between three measures of ANS acuity (non-symbolic comparison, non-symbolic estimation and non-symbolic addition), their cross-sectional trajectories and specific contributions to exact calculation. Children with mathematical difficulties (MD) and typically achieving (TA) controls attending the first six years of formal schooling participated in the study. The MD group exhibited impairments in multiple instantiations of the ANS compared to their TA peers. The ANS acuity measured by all three tasks positively correlated with age in TA children, while no correlation was found between non-symbolic comparison and age in the MD group. The measures of ANS acuity significantly correlated with each other, reflecting at least in part a common numerosity code. Crucially, we found that non-symbolic estimation partially and non-symbolic addition fully mediated the effects of non-symbolic comparison in exact calculation. PMID:25409446
Sabuco, Juan; Sanjuán, Miguel A F; Yorke, James A
2012-12-01
Safe sets are a basic ingredient in the strategy of partial control of chaotic systems. Recently we have found an algorithm, the sculpting algorithm, which allows us to construct them, when they exist. Here we define another type of set, an asymptotic safe set, to which trajectories are attracted asymptotically when the partial control strategy is applied. We apply all these ideas to a specific example of a Duffing oscillator showing the geometry of these sets in phase space. The software for creating all the figures appearing in this paper is available as supplementary material. PMID:23278093
Application of monochromatic ocean wave forecasts to prediction of wave-induced currents
NASA Technical Reports Server (NTRS)
Poole, L. R.
1975-01-01
The use of monochromatic wind-wave forecasts in prediction of wind-wave-induced currents was assessed. Currents were computed for selected combinations of wind conditions by using a spectrum approach which was developed by using the Bretschneider wave spectrum for partially developed wind seas. These currents were compared with currents computed by using the significant and average monochromatic wave parameters related to the Bretschneider spectrum. Results indicate that forecasts of significant wave parameters can be used to predict surface wind-wave-induced currents. Conversion of these parameters to average wave parameters can furnish reasonable estimates of subsurface current values.
Stability of traveling waves of a diffusive susceptible-infective-removed (SIR) epidemic model
NASA Astrophysics Data System (ADS)
Li, Yan; Li, Wan-Tong; Yang, Yun-Rui
2016-04-01
This paper is concerned with the stability and uniqueness of traveling waves of a delayed diffusive susceptible-infective-removed (SIR) epidemic model. We first prove the exponential stability of traveling waves by using the weighted energy method, where the traveling waves are allowed to be non-monotone. Then we establish the exact asymptotic behavior of traveling waves at -∞ by using Ikehara's theorem. Finally, the uniqueness of traveling waves is proved by the stability result of traveling waves.
Comparison of exact solution with Eikonal approximation for elastic heavy ion scattering
NASA Technical Reports Server (NTRS)
Dubey, Rajendra R.; Khandelwal, Govind S.; Cucinotta, Francis A.; Maung, Khin Maung
1995-01-01
A first-order optical potential is used to calculate the total and absorption cross sections for nucleus-nucleus scattering. The differential cross section is calculated by using a partial-wave expansion of the Lippmann-Schwinger equation in momentum space. The results are compared with solutions in the Eikonal approximation for the equivalent potential and with experimental data in the energy range from 25A to 1000A MeV.
Dissociation between exact and approximate addition in developmental dyslexia.
Yang, Xiujie; Meng, Xiangzhi
2016-09-01
Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact. PMID:27310366
Compacton-like wave and kink-like wave solutions of the generalized KP-MEW (2, 2) equation
NASA Astrophysics Data System (ADS)
Li, Shaoyong; Song, Ming
2014-03-01
Using a bifurcation method and a numerical simulation approach of dynamical systems, we study the generalized KP-MEW(2, 2) equation (ut + (u2)x + (u2)xxt)x + uyy = 0. Two types of bounded traveling waves are found, that is, a compacton-like wave and a kink-like wave. The planar graphs of the compacton-like and kink-like waves are simulated using the software Maple. Exact implicit or parameter expressions of these solutions are given.
Exact-exchange time-dependent density-functional theory for static and dynamic polarizabilities
Hirata, So; Ivanov, Stanislav; Bartlett, Rodney J.; Grabowski, Ireneusz
2005-03-01
Time-dependent density-functional theory (TDDFT) employing the exact-exchange functional has been formulated on the basis of the optimized-effective-potential (OEP) method of Talman and Shadwick for second-order molecular properties and implemented into a Gaussian-basis-set, trial-vector algorithm. The only approximation involved, apart from the lack of correlation effects and the use of Gaussian-type basis functions, was the consistent use of the adiabatic approximation in the exchange kernel and in the linear response function. The static and dynamic polarizabilities and their anisotropy predicted by the TDDFT with exact exchange (TDOEP) agree accurately with the corresponding values from time-dependent Hartree-Fock theory, the exact-exchange counterpart in the wave function theory. The TDOEP is free from the nonphysical asymptotic decay of the exchange potential of most conventional density functionals or from any other manifestations of the incomplete cancellation of the self-interaction energy. The systematic overestimation of the absolute values and dispersion of polarizabilities that plagues most conventional TDDFT cannot be seen in the TDOEP.
A new fifth parameter for transverse isotropy II: partial derivatives
NASA Astrophysics Data System (ADS)
Kawakatsu, Hitoshi
2016-07-01
Kawakatsu et al. and Kawakatsu introduced a new fifth parameter, ηκ, to describe transverse isotropy (TI). Considering that ηκ characterizes the incidence angle dependence of body wave phase velocities for TI models, its relevance for body wave seismology is obvious. Here, we derive expressions for partial derivatives (sensitivity kernels) of surface wave phase velocity and normal mode eigenfrequency for the new set of five parameters. The partial derivative for ηκ is about twice as large as that for the conventional η, indicating that ηκ should be more readily resolved. While partial derivatives for S velocities are not so changed, those for P velocities are significantly modified; the sensitivity for anisotropic P velocities is greatly reduced. In contrary to the suggestion by Dziewonski & Anderson and Anderson & Dziewonski, there is not much control on the anisotropic P velocities. On the other hand, the significance of ηκ for long-period seismology has become clear.
Resonance Van Hove singularities in wave kinetics
NASA Astrophysics Data System (ADS)
Shi, Yi-Kang; Eyink, Gregory L.
2016-10-01
Wave kinetic theory has been developed to describe the statistical dynamics of weakly nonlinear, dispersive waves. However, we show that systems which are generally dispersive can have resonant sets of wave modes with identical group velocities, leading to a local breakdown of dispersivity. This shows up as a geometric singularity of the resonant manifold and possibly as an infinite phase measure in the collision integral. Such singularities occur widely for classical wave systems, including acoustical waves, Rossby waves, helical waves in rotating fluids, light waves in nonlinear optics and also in quantum transport, e.g. kinetics of electron-hole excitations (matter waves) in graphene. These singularities are the exact analogue of the critical points found by Van Hove in 1953 for phonon dispersion relations in crystals. The importance of these singularities in wave kinetics depends on the dimension of phase space D =(N - 2) d (d physical space dimension, N the number of waves in resonance) and the degree of degeneracy δ of the critical points. Following Van Hove, we show that non-degenerate singularities lead to finite phase measures for D > 2 but produce divergences when D ≤ 2 and possible breakdown of wave kinetics if the collision integral itself becomes too large (or even infinite). Similar divergences and possible breakdown can occur for degenerate singularities, when D - δ ≤ 2, as we find for several physical examples, including electron-hole kinetics in graphene. When the standard kinetic equation breaks down, then one must develop a new singular wave kinetics. We discuss approaches from pioneering 1971 work of Newell & Aucoin on multi-scale perturbation theory for acoustic waves and field-theoretic methods based on exact Schwinger-Dyson integral equations for the wave dynamics.
Fast and Exact Continuous Collision Detection with Bernstein Sign Classification
Tang, Min; Tong, Ruofeng; Wang, Zhendong; Manocha, Dinesh
2014-01-01
We present fast algorithms to perform accurate CCD queries between triangulated models. Our formulation uses properties of the Bernstein basis and Bézier curves and reduces the problem to evaluating signs of polynomials. We present a geometrically exact CCD algorithm based on the exact geometric computation paradigm to perform reliable Boolean collision queries. Our algorithm is more than an order of magnitude faster than prior exact algorithms. We evaluate its performance for cloth and FEM simulations on CPUs and GPUs, and highlight the benefits. PMID:25568589
The Quasi-Exactly Solvable Problems in Relativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
Liu, Li-Yan; Hao, Qing-Hai
2014-06-01
We study the quasi-exactly solvable problems in relativistic quantum mechanics. We consider the problems for the two-dimensional Klein—Gordon and Dirac equations with equal vector and scalar potentials, and try to find the general form of the quasi-exactly solvable potential. After obtaining the general form of the potential, we present several examples to give the specific forms. In the examples, we show for special parameters the harmonic potential plus Coulomb potential, Killingbeck potential and a quartic potential plus Cornell potential are quasi-exactly solvable potentials.
Logvinenko, Alexander D; Beattie, Lesley L
2011-01-01
It is widely believed that color can be decomposed into a small number of component colors. Particularly, each hue can be described as a combination of a restricted set of component hues. Methods, such as color naming and hue scaling, aim at describing color in terms of the relative amount of the component hues. However, there is no consensus on the nomenclature of component hues. Moreover, the very notion of hue (not to mention component hue) is usually defined verbally rather than perceptually. In this paper, we make an attempt to operationalize such a fundamental attribute of color as hue without the use of verbal terms. Specifically, we put forth a new method--partial hue-matching--that is based on judgments of whether two colors have some hue in common. It allows a set of component hues to be established objectively, without resorting to verbal definitions. Specifically, the largest sets of color stimuli, all of which partially match each other (referred to as chromaticity classes), can be derived from the observer's partial hue-matches. A chromaticity class proves to consist of all color stimuli that contain a particular component hue. Thus, the chromaticity classes fully define the set of component hues. Using samples of Munsell papers, a few experiments on partial hue-matching were carried out with twelve inexperienced normal trichromatic observers. The results reinforce the classical notion of four component hues (yellow, blue, red, and green). Black and white (but not gray) were also found to be component colors. PMID:21742961
... You will need to understand what surgery and recovery will be like. Partial knee arthroplasty may be a good choice if you have arthritis in only one side or part of the knee and: You are older, thin, and not very active. You do not ...
Acute renal injury after partial hepatectomy
Peres, Luis Alberto Batista; Bredt, Luis Cesar; Cipriani, Raphael Flavio Fachini
2016-01-01
Currently, partial hepatectomy is the treatment of choice for a wide variety of liver and biliary conditions. Among the possible complications of partial hepatectomy, acute kidney injury (AKI) should be considered as an important cause of increased morbidity and postoperative mortality. Difficulties in the data analysis related to postoperative AKI after liver resections are mainly due to the multiplicity of factors to be considered in the surgical patients, moreover, there is no consensus of the exact definition of AKI after liver resection in the literature, which hampers comparison and analysis of the scarce data published on the subject. Despite this multiplicity of risk factors for postoperative AKI after partial hepatectomy, there are main factors that clearly contribute to its occurrence. First factor relates to large blood losses with renal hypoperfusion during the operation, second factor relates to the occurrence of post-hepatectomy liver failure with consequent distributive circulatory changes and hepatorenal syndrome. Eventually, patients can have more than one factor contributing to post-operative AKI, and frequently these combinations of acute insults can be aggravated by sepsis or exposure to nephrotoxic drugs. PMID:27478539
Acute renal injury after partial hepatectomy.
Peres, Luis Alberto Batista; Bredt, Luis Cesar; Cipriani, Raphael Flavio Fachini
2016-07-28
Currently, partial hepatectomy is the treatment of choice for a wide variety of liver and biliary conditions. Among the possible complications of partial hepatectomy, acute kidney injury (AKI) should be considered as an important cause of increased morbidity and postoperative mortality. Difficulties in the data analysis related to postoperative AKI after liver resections are mainly due to the multiplicity of factors to be considered in the surgical patients, moreover, there is no consensus of the exact definition of AKI after liver resection in the literature, which hampers comparison and analysis of the scarce data published on the subject. Despite this multiplicity of risk factors for postoperative AKI after partial hepatectomy, there are main factors that clearly contribute to its occurrence. First factor relates to large blood losses with renal hypoperfusion during the operation, second factor relates to the occurrence of post-hepatectomy liver failure with consequent distributive circulatory changes and hepatorenal syndrome. Eventually, patients can have more than one factor contributing to post-operative AKI, and frequently these combinations of acute insults can be aggravated by sepsis or exposure to nephrotoxic drugs. PMID:27478539
Pan Xiaoyin; Slamet, Marlina; Sahni, Viraht
2010-04-15
We extend our prior work on the construction of variational wave functions {psi} that are functionals of functions {chi}:{psi}={psi}[{chi}] rather than simply being functions. In this manner, the space of variations is expanded over those of traditional variational wave functions. In this article we perform the constrained search over the functions {chi} chosen such that the functional {psi}[{chi}] satisfies simultaneously the constraints of normalization and the exact expectation value of an arbitrary single- or two-particle Hermitian operator, while also leading to a rigorous upper bound to the energy. As such the wave function functional is accurate not only in the region of space in which the principal contributions to the energy arise but also in the other region of the space represented by the Hermitian operator. To demonstrate the efficacy of these ideas, we apply such a constrained search to the ground state of the negative ion of atomic hydrogen H{sup -}, the helium atom He, and its positive ions Li{sup +} and Be{sup 2+}. The operators W whose expectations are obtained exactly are the sum of the single-particle operators W={Sigma}{sub i}r{sub i}{sup n},n=-2,-1,1,2, W={Sigma}{sub i{delta}}(r{sub i}), W=-(1/2){Sigma}{sub i{nabla}i}{sup 2}, and the two-particle operators W={Sigma}{sub n}u{sup n},n=-2,-1,1,2, where u=|r{sub i}-r{sub j}|. Comparisons with the method of Lagrangian multipliers and of other constructions of wave-function functionals are made. Finally, we present further insights into the construction of wave-function functionals by studying a previously proposed construction of functionals {psi}[{chi}] that lead to the exact expectation of arbitrary Hermitian operators. We discover that analogous to the solutions of the Schroedinger equation, there exist {psi}[{chi}] that are unphysical in that they lead to singular values for the expectations. We also explain the origin of the singularity.
Izard, Véronique; Streri, Arlette; Spelke, Elizabeth S
2014-07-01
Exact integer concepts are fundamental to a wide array of human activities, but their origins are obscure. Some have proposed that children are endowed with a system of natural number concepts, whereas others have argued that children construct these concepts by mastering verbal counting or other numeric symbols. This debate remains unresolved, because it is difficult to test children's mastery of the logic of integer concepts without using symbols to enumerate large sets, and the symbols themselves could be a source of difficulty for children. Here, we introduce a new method, focusing on large quantities and avoiding the use of words or other symbols for numbers, to study children's understanding of an essential property underlying integer concepts: the relation of exact numerical equality. Children aged 32-36 months, who possessed no symbols for exact numbers beyond 4, were given one-to-one correspondence cues to help them track a set of puppets, and their enumeration of the set was assessed by a non-verbal manual search task. Children used one-to-one correspondence relations to reconstruct exact quantities in sets of 5 or 6 objects, as long as the elements forming the sets remained the same individuals. In contrast, they failed to track exact quantities when one element was added, removed, or substituted for another. These results suggest an alternative to both nativist and symbol-based constructivist theories of the development of natural number concepts: Before learning symbols for exact numbers, children have a partial understanding of the properties of exact numbers.
Izard, Véronique; Streri, Arlette; Spelke, Elizabeth S.
2014-01-01
Exact integer concepts are fundamental to a wide array of human activities, but their origins are obscure. Some have proposed that children are endowed with a system of natural number concepts, whereas others have argued that children construct these concepts by mastering verbal counting or other numeric symbols. This debate remains unresolved, because it is difficult to test children’s mastery of the logic of integer concepts without using symbols to enumerate large sets, and the symbols themselves could be a source of difficulty for children. Here, we introduce a new method, focusing on large quantities and avoiding the use of words or other symbols for numbers, to study children’s understanding of an essential property underlying integer concepts: the relation of exact numerical equality. Children aged 32-36 months, who possessed no symbols for exact numbers beyond 4, were given one-to-one correspondence cues to help them track a set of puppets, and their enumeration of the set was assessed by a non-verbal manual search task. Children used one-to-one correspondence relations to reconstruct exact quantities in sets of 5 or 6 objects, as long as the elements forming the sets remained the same individuals. In contrast, they failed to track exact quantities when one element was added, removed, or substituted for another. These results suggest an alternative to both nativist and symbol-based constructivist theories of the development of natural number concepts: Before learning symbols for exact numbers, children have a partial understanding of the properties of exact numbers. PMID:24680885
Izard, Véronique; Streri, Arlette; Spelke, Elizabeth S
2014-07-01
Exact integer concepts are fundamental to a wide array of human activities, but their origins are obscure. Some have proposed that children are endowed with a system of natural number concepts, whereas others have argued that children construct these concepts by mastering verbal counting or other numeric symbols. This debate remains unresolved, because it is difficult to test children's mastery of the logic of integer concepts without using symbols to enumerate large sets, and the symbols themselves could be a source of difficulty for children. Here, we introduce a new method, focusing on large quantities and avoiding the use of words or other symbols for numbers, to study children's understanding of an essential property underlying integer concepts: the relation of exact numerical equality. Children aged 32-36 months, who possessed no symbols for exact numbers beyond 4, were given one-to-one correspondence cues to help them track a set of puppets, and their enumeration of the set was assessed by a non-verbal manual search task. Children used one-to-one correspondence relations to reconstruct exact quantities in sets of 5 or 6 objects, as long as the elements forming the sets remained the same individuals. In contrast, they failed to track exact quantities when one element was added, removed, or substituted for another. These results suggest an alternative to both nativist and symbol-based constructivist theories of the development of natural number concepts: Before learning symbols for exact numbers, children have a partial understanding of the properties of exact numbers. PMID:24680885
Inverse scattering transform analysis of rogue waves using local periodization procedure
Randoux, Stéphane; Suret, Pierre; El, Gennady
2016-01-01
The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra. PMID:27385164
Inverse scattering transform analysis of rogue waves using local periodization procedure
NASA Astrophysics Data System (ADS)
Randoux, Stéphane; Suret, Pierre; El, Gennady
2016-07-01
The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra.
Single-shot observation of optical rogue waves in integrable turbulence using time microscopy
Suret, Pierre; Koussaifi, Rebecca El; Tikan, Alexey; Evain, Clément; Randoux, Stéphane; Szwaj, Christophe; Bielawski, Serge
2016-01-01
Optical fibres are favourable tabletop laboratories to investigate both coherent and incoherent nonlinear waves. In particular, exact solutions of the one-dimensional nonlinear Schrödinger equation such as fundamental solitons or solitons on finite background can be generated by launching periodic, specifically designed coherent waves in optical fibres. It is an open fundamental question to know whether these coherent structures can emerge from the nonlinear propagation of random waves. However the typical sub-picosecond timescale prevented—up to now—time-resolved observations of the awaited dynamics. Here, we report temporal ‘snapshots' of random light using a specially designed ‘time-microscope'. Ultrafast structures having peak powers much larger than the average optical power are generated from the propagation of partially coherent waves in optical fibre and are recorded with 250 femtoseconds resolution. Our experiment demonstrates the central role played by ‘breather-like' structures such as the Peregrine soliton in the emergence of heavy-tailed statistics in integrable turbulence. PMID:27713416
Single-shot observation of optical rogue waves in integrable turbulence using time microscopy
NASA Astrophysics Data System (ADS)
Suret, Pierre; Koussaifi, Rebecca El; Tikan, Alexey; Evain, Clément; Randoux, Stéphane; Szwaj, Christophe; Bielawski, Serge
2016-10-01
Optical fibres are favourable tabletop laboratories to investigate both coherent and incoherent nonlinear waves. In particular, exact solutions of the one-dimensional nonlinear Schrödinger equation such as fundamental solitons or solitons on finite background can be generated by launching periodic, specifically designed coherent waves in optical fibres. It is an open fundamental question to know whether these coherent structures can emerge from the nonlinear propagation of random waves. However the typical sub-picosecond timescale prevented--up to now--time-resolved observations of the awaited dynamics. Here, we report temporal `snapshots' of random light using a specially designed `time-microscope'. Ultrafast structures having peak powers much larger than the average optical power are generated from the propagation of partially coherent waves in optical fibre and are recorded with 250 femtoseconds resolution. Our experiment demonstrates the central role played by `breather-like' structures such as the Peregrine soliton in the emergence of heavy-tailed statistics in integrable turbulence.
Linear superposition solutions to nonlinear wave equations
NASA Astrophysics Data System (ADS)
Liu, Yu
2012-11-01
The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed.
Nondiffracting accelerating wave packets of Maxwell's equations.
Kaminer, Ido; Bekenstein, Rivka; Nemirovsky, Jonathan; Segev, Mordechai
2012-04-20
We present the nondiffracting spatially accelerating solutions of the Maxwell equations. Such beams accelerate in a circular trajectory, thus generalizing the concept of Airy beams to the full domain of the wave equation. For both TE and TM polarizations, the beams exhibit shape-preserving bending which can have subwavelength features, and the Poynting vector of the main lobe displays a turn of more than 90°. We show that these accelerating beams are self-healing, analyze their properties, and find the new class of accelerating breathers: self-bending beams of periodically oscillating shapes. Finally, we emphasize that in their scalar form, these beams are the exact solutions for nondispersive accelerating wave packets of the most common wave equation describing time-harmonic waves. As such, this work has profound implications to many linear wave systems in nature, ranging from acoustic and elastic waves to surface waves in fluids and membranes. PMID:22680719
Extraordinary momentum and spin in evanescent waves.
Bliokh, Konstantin Y; Bekshaev, Aleksandr Y; Nori, Franco
2014-03-06
Momentum and spin represent fundamental dynamic properties of quantum particles and fields. In particular, propagating optical waves (photons) carry momentum and longitudinal spin determined by the wave vector and circular polarization, respectively. Here we show that exactly the opposite can be the case for evanescent optical waves. A single evanescent wave possesses a spin component, which is independent of the polarization and is orthogonal to the wave vector. Furthermore, such a wave carries a momentum component, which is determined by the circular polarization and is also orthogonal to the wave vector. We show that these extraordinary properties reveal a fundamental Belinfante's spin momentum, known in field theory and unobservable in propagating fields. We demonstrate that the transverse momentum and spin push and twist a probe Mie particle in an evanescent field. This allows the observation of 'impossible' properties of light and of a fundamental field-theory quantity, which was previously considered as 'virtual'.
Nondiffracting accelerating wave packets of Maxwell's equations.
Kaminer, Ido; Bekenstein, Rivka; Nemirovsky, Jonathan; Segev, Mordechai
2012-04-20
We present the nondiffracting spatially accelerating solutions of the Maxwell equations. Such beams accelerate in a circular trajectory, thus generalizing the concept of Airy beams to the full domain of the wave equation. For both TE and TM polarizations, the beams exhibit shape-preserving bending which can have subwavelength features, and the Poynting vector of the main lobe displays a turn of more than 90°. We show that these accelerating beams are self-healing, analyze their properties, and find the new class of accelerating breathers: self-bending beams of periodically oscillating shapes. Finally, we emphasize that in their scalar form, these beams are the exact solutions for nondispersive accelerating wave packets of the most common wave equation describing time-harmonic waves. As such, this work has profound implications to many linear wave systems in nature, ranging from acoustic and elastic waves to surface waves in fluids and membranes.
Whirling waves in Interference experiments
NASA Astrophysics Data System (ADS)
Sinha, Urbasi; Sawant, Rahul; Samuel, Joseph; Sinha, Aninda; Sinha, Supurna
2014-03-01
In a double slit interference experiment, the wave function at the screen with both slits open is not exactly the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well- known text books in quantum mechanics implicitly and/or explicitly use this assumption, the wave function hypothesis, which is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from non-classical paths in interference experiments which provide a measurable deviation from the wave function hypothesis. A direct experimental demonstration for the existence of these non-classical paths is hard. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence. I will also describe some ongoing experimental efforts towards testing our theoretical findings.
Target variability and exact signature reproduction requirements for Ka-band radar data
NASA Astrophysics Data System (ADS)
Giles, Robert H.; Kersey, William T.; McFarlin, M. Shane; Finley, Robbin; Neilson, H. J.; Nixon, William E.
2001-08-01
A variety of ATR algorithms have promise improved performance, not yet realized operationally. Typically, good results have been reported on data sets of limited size that have been tested in a laboratory environment, only to see the performance degrade when stressed with real-world target and environmental variability. To investigate exact signature reproduction requirements along with target and environment variability issues for stressing new ATR metrics, the U.S. Army's National Ground Intelligence Center (NGIC) and Targets Management Office (TMO) originated, sponsored, and directed a signature project plan to acquire multiple target full-polarimetric Ka-band radar signature data at Eglin AFB, as well as its submillimeter-wave compact radar range equivalent using high-fidelity exact 1/16th scale replicas fabricated by the ERADS program. To effectively understand signature reproduction requirements through the variability of multiple target RCS characteristics, TMO and NGIC sponsored researchers at U Mass Lowell's Submillimeter-Wave Technology Laboratory (STL) and Simulation Technologies (SimTech) to analyze the intra- class and inter-class variability of the full scale Ka-band turntable signature data. NGIC, TMO, STL and SimTech researchers then traveled to the location of the vehicles measured at Eglin AFB and conducted extensive documentation and mensuration on these vehicles. Using this information, ERADS built high fidelity, articulatable exact replicas for measurement in the NGIC's compact radar ranges. Signal processing software established by STL researchers in an NGIC directed signature study was used to execute an HRR and ISAR cross-correlation study of the field and scale-model signature data. The signature to signature variability quantified is presented, along with a description and examples of the signature analysis techniques exploited. This signature data is available from NGIC on request for Government Agencies and Government Contractors with an
Full and Partial Cloaking in Electromagnetic Scattering
NASA Astrophysics Data System (ADS)
Deng, Youjun; Liu, Hongyu; Uhlmann, Gunther
2016-08-01
In this paper, we consider two regularized transformation-optics cloaking schemes for electromagnetic (EM) waves. Both schemes are based on the blowup construction with the generating sets being, respectively, a generic curve and a planar subset. We derive sharp asymptotic estimates in assessing the cloaking performances of the two constructions in terms of the regularization parameters and the geometries of the cloaking devices. The first construction yields an approximate full-cloak, whereas the second construction yields an approximate partial-cloak. Moreover, by incorporating properly chosen conducting layers, both cloaking constructions are capable of nearly cloaking arbitrary EM contents. This work complements the existing results in Ammari et al. (SIAM J Appl Math 73:2055-2076, 2013), Bao and Liu (SIAM J Appl Math 74:724-742, 2014), Bao et al. (J Math Pure Appl (9) 101:716-733, 2014) on approximate EM cloaks with the generating set being a singular point, and it also extends Deng et al. (On regularized full- and partial-cloaks in acoustic scat- tering. Preprint, arXiv:1502.01174, 2015), Li et al. (Commun Math Phys, 335:671-712, 2015) on regularized full and partial cloaks for acoustic waves governed by the Helmholtz system to the more challenging EM case governed by the full Maxwell system.
Hard Times May Exact a Toll on Brain Health
... https://medlineplus.gov/news/fullstory_161283.html Hard Times May Exact a Toll on Brain Health Poverty ... a cause-and-effect relationship between hard economic times and brain health and aging. The findings were ...
Exact theory of intermediate phases in two dimensions
Delfino, Gesualdo Squarcini, Alessio
2014-03-15
We show how field theory yields the exact description of intermediate phases in the scaling limit of two-dimensional statistical systems at a first order phase transition point. The ability of a third phase to form an intermediate wetting layer or only isolated bubbles is explicitly related to the spectrum of excitations of the field theory. The order parameter profiles are determined and interface properties such as passage probabilities and internal structure are deduced from them. The theory is illustrated through the application to the q-state Potts model and the Ashkin–Teller model. The latter is shown to provide the first exact solution of a bulk wetting transition. -- Highlights: •Phase separation with appearance of a third phase is studied exactly. •Interfacial properties are derived from field theory. •Exact solution of bulk wetting transition is provided.
Exact geodesics and shortest paths on polyhedral surfaces.
Balasubramanian, Mukund; Polimeni, Jonathan R; Schwartz, Eric L
2009-06-01
We present two algorithms for computing distances along convex and non-convex polyhedral surfaces. The first algorithm computes exact minimal-geodesic distances and the second algorithm combines these distances to compute exact shortest-path distances along the surface. Both algorithms have been extended to compute the exact minimal-geodesic paths and shortest paths. These algorithms have been implemented and validated on surfaces for which the correct solutions are known, in order to verify the accuracy and to measure the run-time performance, which is cubic or less for each algorithm. The exact-distance computations carried out by these algorithms are feasible for large-scale surfaces containing tens of thousands of vertices, and are a necessary component of near-isometric surface flattening methods that accurately transform curved manifolds into flat representations.
Gravitational waves in ghost free bimetric gravity
Mohseni, Morteza
2012-11-01
We obtain a set of exact gravitational wave solutions for the ghost free bimetric theory of gravity. With a flat reference metric, the theory admits the vacuum Brinkmann plane wave solution for suitable choices of the coefficients of different terms in the interaction potential. An exact gravitational wave solution corresponding to a massive scalar mode is also admitted for arbitrary choice of the coefficients with the reference metric being proportional to the spacetime metric. The proportionality factor and the speed of the wave are calculated in terms of the parameters of the theory. We also show that a F(R) extension of the theory admits similar solutions but in general is plagued with ghost instabilities.
Rogue Waves and Modulational Instability
NASA Astrophysics Data System (ADS)
Zakharov, V. E.; Dyachenko, A.
2015-12-01
The most plausible cause of rogue wave formation in a deep ocean is development of modulational instability of quasimonochromatic wave trains. An adequate model for study of this phenomenon is the Euler equation for potential flow of incompressible fluid with free surface in 2-D geometry. Numerical integration of these equations confirms completely the conjecture of rogue wave formation from modulational instability but the procedure is time consuming for determination of rogue wave appearance probability for a given shape of wave energy spectrum. This program can be realized in framework of simpler model using replacement of the exact interaction Hamiltonian by more compact Hamiltonian. There is a family of such models. The popular one is the Nonlinear Schrodinger equation (NLSE). This model is completely integrable and suitable for numerical simulation but we consider that it is oversimplified. It misses such important phenomenon as wave breaking. Recently, we elaborated much more reliable model that describes wave breaking but is as suitable as NLSE from the point of numerical modeling. This model allows to perform massive numerical experiments and study statistics of rogue wave formation in details.
The implementation of holography in the plane wave matrix model
NASA Astrophysics Data System (ADS)
Mints, Aleksey Leonidovich
It is expected that at the core of nonperturbative theories of quantum gravity, such as M-theory, lies the realization of the holographic principle, in the sense that a holographic theory should contain one binary degree of freedom per Planck area. Present understanding of such theories requires the holographic encoding of bulk data in large matrices. Currently this mapping is poorly understood. The plane wave matrix model provides a laboratory for isolating aspects of this problem in a controlled setting. At large boosts, configurations of concentric membranes become superselection sectors, whose exact spectra are known. From the bulk point of view one expects product states of individual membranes to be contained within the full spectrum. However, for non-BPS states this inclusion relation is obscured by Gauss law constraints. Its validity rests on nontrivial relations in representation theory, which we identify and verify by explicit computation. Beyond the decoding and partial identification of selected states in large matrices, one would like to get a better understanding of the holographic state counting of these degrees of freedom, i.e., entropy. Contrary to the naive expectation of holography realized in terms of the covariant entropy bound, we present evidence that it is the Bekenstein entropy bound, which is related to area differences, that is manifest in the plane wave matrix model. If holography is implemented in this way, we predict crossover behavior at strong coupling when the energy exceeds N2 in units of the mass scale.
NASA Astrophysics Data System (ADS)
Nazarenko, Sergey
2015-07-01
Wave turbulence is the statistical mechanics of random waves with a broadband spectrum interacting via non-linearity. To understand its difference from non-random well-tuned coherent waves, one could compare the sound of thunder to a piece of classical music. Wave turbulence is surprisingly common and important in a great variety of physical settings, starting with the most familiar ocean waves to waves at quantum scales or to much longer waves in astrophysics. We will provide a basic overview of the wave turbulence ideas, approaches and main results emphasising the physics of the phenomena and using qualitative descriptions avoiding, whenever possible, involved mathematical derivations. In particular, dimensional analysis will be used for obtaining the key scaling solutions in wave turbulence - Kolmogorov-Zakharov (KZ) spectra.
Partially integrated exhaust manifold
Hayman, Alan W; Baker, Rodney E
2015-01-20
A partially integrated manifold assembly is disclosed which improves performance, reduces cost and provides efficient packaging of engine components. The partially integrated manifold assembly includes a first leg extending from a first port and terminating at a mounting flange for an exhaust gas control valve. Multiple additional legs (depending on the total number of cylinders) are integrally formed with the cylinder head assembly and extend from the ports of the associated cylinder and terminate at an exit port flange. These additional legs are longer than the first leg such that the exit port flange is spaced apart from the mounting flange. This configuration provides increased packaging space adjacent the first leg for any valving that may be required to control the direction and destination of exhaust flow in recirculation to an EGR valve or downstream to a catalytic converter.
Partially coherent ultrafast spectrography
Bourassin-Bouchet, C.; Couprie, M.-E.
2015-01-01
Modern ultrafast metrology relies on the postulate that the pulse to be measured is fully coherent, that is, that it can be completely described by its spectrum and spectral phase. However, synthesizing fully coherent pulses is not always possible in practice, especially in the domain of emerging ultrashort X-ray sources where temporal metrology is strongly needed. Here we demonstrate how frequency-resolved optical gating (FROG), the first and one of the most widespread techniques for pulse characterization, can be adapted to measure partially coherent pulses even down to the attosecond timescale. No modification of experimental apparatuses is required; only the processing of the measurement changes. To do so, we take our inspiration from other branches of physics where partial coherence is routinely dealt with, such as quantum optics and coherent diffractive imaging. This will have important and immediate applications, such as enabling the measurement of X-ray free-electron laser pulses despite timing jitter. PMID:25744080
Laparoscopic partial splenic resection.
Uranüs, S; Pfeifer, J; Schauer, C; Kronberger, L; Rabl, H; Ranftl, G; Hauser, H; Bahadori, K
1995-04-01
Twenty domestic pigs with an average weight of 30 kg were subjected to laparoscopic partial splenic resection with the aim of determining the feasibility, reliability, and safety of this procedure. Unlike the human spleen, the pig spleen is perpendicular to the body's long axis, and it is long and slender. The parenchyma was severed through the middle third, where the organ is thickest. An 18-mm trocar with a 60-mm Endopath linear cutter was used for the resection. The tissue was removed with a 33-mm trocar. The operation was successfully concluded in all animals. No capsule tears occurred as a result of applying the stapler. Optimal hemostasis was achieved on the resected edges in all animals. Although these findings cannot be extended to human surgery without reservations, we suggest that diagnostic partial resection and minor cyst resections are ideal initial indications for this minimally invasive approach.
Partially coherent ultrafast spectrography
NASA Astrophysics Data System (ADS)
Bourassin-Bouchet, C.; Couprie, M.-E.
2015-03-01
Modern ultrafast metrology relies on the postulate that the pulse to be measured is fully coherent, that is, that it can be completely described by its spectrum and spectral phase. However, synthesizing fully coherent pulses is not always possible in practice, especially in the domain of emerging ultrashort X-ray sources where temporal metrology is strongly needed. Here we demonstrate how frequency-resolved optical gating (FROG), the first and one of the most widespread techniques for pulse characterization, can be adapted to measure partially coherent pulses even down to the attosecond timescale. No modification of experimental apparatuses is required; only the processing of the measurement changes. To do so, we take our inspiration from other branches of physics where partial coherence is routinely dealt with, such as quantum optics and coherent diffractive imaging. This will have important and immediate applications, such as enabling the measurement of X-ray free-electron laser pulses despite timing jitter.
Mechanisms of wave transformation in finite-depth water
NASA Technical Reports Server (NTRS)
Shemdin, O. H.; Hsiao, S. V.; Carlson, H. E.; Hasselmann, K.; Schulze, K.
1980-01-01
Mechanisms of wave transformation in finite-depth water are investigated. The linear mechanisms examined are percolation, bottom motion, shoaling, and refraction. The nonlinear mechanisms examined are wave-wave interaction and bottom friction. New exact computations of the nonlinear transfer for finite-depth waves are presented for some directional wave spectra. These mechanisms are found to explain satisfactorily wave decay observations obtained at several sites with different bottom sediment properties. The decay rates at these sites are found to be dominated by different mechanisms which are determined by the bottom conditions. As an example, detailed calculations are presented for data obtained at the Jonswap site.
NASA Astrophysics Data System (ADS)
Bhat, R. B.; Mundkur, G.
1993-02-01
Vibration of rectangular plates is studied using a set of plate characteristic functions generated by reduction of the plate partial differential equation, and exactly solving the resulting ordinary differential equation. The plate characteristic functions are used as deflection shape functions in the Rayleigh-Ritz method to obtain the natural frequencies. Because the solution is exact in one direction, the results fall in between the exact values and those obtained with the straight forward Rayleigh-Ritz method, where the complete deflection shape is assumed initially. Results are provided for rectangular plates with combinations of clamped, simply supported and free edge conditions.
Algorithm refinement for stochastic partial differential equations.
Alexander, F. J.; Garcia, Alejandro L.,; Tartakovsky, D. M.
2001-01-01
A hybrid particle/continuum algorithm is formulated for Fickian diffusion in the fluctuating hydrodynamic limit. The particles are taken as independent random walkers; the fluctuating diffusion equation is solved by finite differences with deterministic and white-noise fluxes. At the interface between the particle and continuum computations the coupling is by flux matching, giving exact mass conservation. This methodology is an extension of Adaptive Mesh and Algorithm Refinement to stochastic partial differential equations. A variety of numerical experiments were performed for both steady and time-dependent scenarios. In all cases the mean and variance of density are captured correctly by the stochastic hybrid algorithm. For a non-stochastic version (i.e., using only deterministic continuum fluxes) the mean density is correct, but the variance is reduced except within the particle region, far from the interface. Extensions of the methodology to fluid mechanics applications are discussed.
Tapping of Love waves in an isotropic surface waveguide by surface-to-bulk wave transduction.
NASA Technical Reports Server (NTRS)
Tuan, H.-S.; Chang, C.-P.
1972-01-01
A theoretical study of tapping a Love wave in an isotropic microacoustic surface waveguide is given. The surface Love wave is tapped by partial transduction into a bulk wave at a discontinuity. It is shown that, by careful design of the discontinuity, the converted bulk wave power and the radiation pattern may be controlled. General formulas are derived for the calculation of these important characteristics from a relatively general surface contour deformation.
Norrman, Andreas; Setälä, Tero; Friberg, Ari T
2011-03-01
We consider partial spatial coherence and partial polarization of purely evanescent optical fields generated in total internal reflection at an interface of two dielectric (lossless) media. Making use of the electromagnetic degree of coherence, we show that, in such fields, the coherence length can be notably shorter than the light's vacuum wavelength, especially at a high-index-contrast interface. Physical explanation for this behavior, analogous to the generation of incoherent light in a multimode laser, is provided. We also analyze the degree of polarization by using a recent three-dimensional formulation and show that the field may be partially polarized at a subwavelength distance from the surface even though it is fully polarized farther away. The degree of polarization can assume values unattainable by beamlike fields, indicating that electromagnetic evanescent waves generally are genuine three-dimensional fields. The results can find applications in near-field optics and nanophotonics.
New Travelling Wave Solutions of Burgers Equation with Finite Transport Memory
NASA Astrophysics Data System (ADS)
Sakthivel, Rathinasamy; Chun, Changbum; Lee, Jonu
2010-09-01
The nonlinear evolution equations with finite memory have a wide range of applications in science and engineering. The Burgers equation with finite memory transport (time-delayed) describes convection-diffusion processes. In this paper, we establish the new solitary wave solutions for the time-delayed Burgers equation. The extended tanh method and the exp-function method have been employed to reveal these new solutions. Further, we have calculated the numerical solutions of the time-delayed Burgers equation with initial conditions by using the homotopy perturbation method (HPM). Our results show that the extended tanh and exp-function methods are very effective in finding exact solutions of the considered problem and HPM is very powerful in finding numerical solutions with good accuracy for nonlinear partial differential equations without any need of transformation or perturbation
Solitary waves in a nonintegrable Fermi-Pasta-Ulam chain
NASA Astrophysics Data System (ADS)
Truskinovsky, Lev; Vainchtein, Anna
2014-10-01
We present a family of exact solutions describing discrete solitary waves in a nonintegrable Fermi-Pasta-Ulam chain. The family is sufficiently rich to cover the whole spectrum of known behaviors from delocalized quasicontinuum waves moving with near-sonic velocities to highly localized anticontinuum excitations with only one particle moving at a time.
Midlatitude Rossby wave forcing of equatorial Kelvin waves
NASA Astrophysics Data System (ADS)
Biello, J. A.; Kiladis, G. N.; Back, A.
2015-12-01
Observations strongly suggest that convectively coupled Kelvin waves can be generated by extratropical wave activity. This mechanism is particularly efficient over Australia, where wave activity appears immediately after the extratropical Rossby waves propagate into the region during the Austral winter. This interaction occurs where the zonal wind is strongly sheared both in the meridional and vertical directions. In order to understand this phenomenon the authors study the linear primitive equations in the presence of barotropic and baroclinic shear and the dispersion characteristics of the sheared Matsuno modes are calculated. Depending on the shear strength, the waves are stable or unstable and can be categorized into three groups. First there are the classical Matsuno modes modified by shear. Second there are extratropical "free" Rossby waves. Third, there are Rossby waves meridionally confined to the shear layer - these latter modes can be unstable, or stable and part of the continuous spectrum. In examples where the zonal winds are barotropically and baroclinically stable, we show that a continuous spectrum of Rossby waves exists. If the zonal winds are strong enough, the Rossby waves in the continuous spectrum have an equatorial signature exactly like the Matsuno Kelvin wave - despite the fact that, in these examples, the Matsuno Kelvin wave also exists on its own and that all modes are stable. For stronger shears, these continuous spectrum modes become unstable. Although the appear similar to Sakai's Rossby/Kelvin instability, their existence arises from a completely different phenomenon. The Sakai instability requires the frequency of a stable equatorial Rossby mode to coincide with the stable Kelvin wave frequency in order for the two modes to create a stable/unstable pair. Our results show that unstable Rossby waves need only have their frequencies Doppler shifted to that of the Kelvin wave frequency by the underlying shear in order that they acquire a
NASA Astrophysics Data System (ADS)
Lake, Kayll
2010-12-01
The title immediately brings to mind a standard reference of almost the same title [1]. The authors are quick to point out the relationship between these two works: they are complementary. The purpose of this work is to explain what is known about a selection of exact solutions. As the authors state, it is often much easier to find a new solution of Einstein's equations than it is to understand it. Even at first glance it is very clear that great effort went into the production of this reference. The book is replete with beautifully detailed diagrams that reflect deep geometric intuition. In many parts of the text there are detailed calculations that are not readily available elsewhere. The book begins with a review of basic tools that allows the authors to set the notation. Then follows a discussion of Minkowski space with an emphasis on the conformal structure and applications such as simple cosmic strings. The next two chapters give an in-depth review of de Sitter space and then anti-de Sitter space. Both chapters contain a remarkable collection of useful diagrams. The standard model in cosmology these days is the ICDM model and whereas the chapter on the Friedmann-Lemaître-Robertson-Walker space-times contains much useful information, I found the discussion of the currently popular a representation rather too brief. After a brief but interesting excursion into electrovacuum, the authors consider the Schwarzschild space-time. This chapter does mention the Swiss cheese model but the discussion is too brief and certainly dated. Space-times related to Schwarzschild are covered in some detail and include not only the addition of charge and the cosmological constant but also the addition of radiation (the Vaidya solution). Just prior to a discussion of the Kerr space-time, static axially symmetric space-times are reviewed. Here one can find a very interesting discussion of the Curzon-Chazy space-time. The chapter on rotating black holes is rather brief and, for
DUSTYWAVE: Linear waves in gas and dust
NASA Astrophysics Data System (ADS)
Laibe, Guillaume; Price, Daniel J.
2016-02-01
Written in Fortran, DUSTYWAVE computes the exact solution for linear waves in a two-fluid mixture of gas and dust. The solutions are general with respect to both the dust-to-gas ratio and the amplitude of the drag coefficient.
Atmospheric Science Data Center
2013-04-19
article title: Gravity Waves Ripple over Marine Stratocumulus Clouds ... Imaging SpectroRadiometer (MISR), a fingerprint-like gravity wave feature occurs over a deck of marine stratocumulus clouds. Similar ... that occur when a pebble is thrown into a still pond, such "gravity waves" sometimes appear when the relatively stable and stratified air ...
Melancholia and partial insanity.
Jackson, S W
1983-04-01
In the medical literature of the eighteenth century melancholia came to be defined as partial insanity. Seventeenth-century English law introduced the term and influenced later forensic concerns about the concept. But the history of melancholia reveals a gradual development of such a concept of limited derangement associated with the delusions usually cited in accounts of this disease. In the early nineteenth century the relationship of melancholia and this concept weakened and was gradually abandoned, the content of the syndrome of melancholia was reduced, and out of this complex process emerged the notion of monomania.
Esthetic removable partial dentures.
Ancowitz, Stephen
2004-01-01
This article provides information regarding the many ways that removable partial dentures (RPDs) may be used to solve restorative problems in the esthetic zone without displaying metal components or conspicuous acrylic resin flanges. The esthetic zone is defined and described, as are methods for recording it. Six dental categories are presented that assist the dentist in choosing a variety of RPD design concepts that may be used to avoid metal display while still satisfying basic principles of RPDs. New materials that may be utilized for optimal esthetics are presented and techniques for contouring acrylic resin bases and tinting denture bases are described.
Exact-Differential Large-Scale Traffic Simulation
Hanai, Masatoshi; Suzumura, Toyotaro; Theodoropoulos, Georgios; Perumalla, Kalyan S
2015-01-01
Analyzing large-scale traffics by simulation needs repeating execution many times with various patterns of scenarios or parameters. Such repeating execution brings about big redundancy because the change from a prior scenario to a later scenario is very minor in most cases, for example, blocking only one of roads or changing the speed limit of several roads. In this paper, we propose a new redundancy reduction technique, called exact-differential simulation, which enables to simulate only changing scenarios in later execution while keeping exactly same results as in the case of whole simulation. The paper consists of two main efforts: (i) a key idea and algorithm of the exact-differential simulation, (ii) a method to build large-scale traffic simulation on the top of the exact-differential simulation. In experiments of Tokyo traffic simulation, the exact-differential simulation shows 7.26 times as much elapsed time improvement in average and 2.26 times improvement even in the worst case as the whole simulation.
Feshchenko, R M; Popov, A V
2013-11-01
We report an exact transparent boundary condition (TBC) on the surface of a rectangular cuboid for the three-dimensional (3D) time-dependent Schrödinger equation. It is obtained as a generalization of the well-known TBC for the 1D Schrödinger equation and of the exact TBC in the rectangular domain for the 3D parabolic wave equation, which we reported earlier. Like all other TBCs, it is nonlocal in time domain and relates the boundary transverse derivative of the wave function at any given time to the boundary values of the same wave function at all preceding times. We develop a discretization of this boundary condition for the implicit Crank-Nicolson finite difference scheme. Several numerical experiments demonstrate evolution of the wave function in free space as well as propagation through a number of 3D spherically symmetrical and asymmetrical barriers, and, finally, scattering off an asymmetrical 3D potential. The proposed boundary condition is simple and robust, and can be useful in computational quantum mechanics when an accurate numerical solution of the 3D Schrödinger equation is required. PMID:24329380
Experts' Understanding of Partial Derivatives Using the Partial Derivative Machine
ERIC Educational Resources Information Center
Roundy, David; Weber, Eric; Dray, Tevian; Bajracharya, Rabindra R.; Dorko, Allison; Smith, Emily M.; Manogue, Corinne A.
2015-01-01
Partial derivatives are used in a variety of different ways within physics. Thermodynamics, in particular, uses partial derivatives in ways that students often find especially confusing. We are at the beginning of a study of the teaching of partial derivatives, with a goal of better aligning the teaching of multivariable calculus with the needs of…
Nonlinear traveling wave solution for the MJO skeleton model
NASA Astrophysics Data System (ADS)
Chen, S.; Stechmann, S. N.
2014-12-01
Recently, a minimal dynamical model is presented for capturing MJO's fundamental features. The model is a nonlinear oscillator model for the MJO skeleton and it involves interactions between convection, moisture and circulation. I will present the exact nonlinear traveling wave solutions for the model based on its energy conservation. The exact nonlinear solution provides for an explicit comparison of features between linear and nonlinear waves such as dispersion relations and traveling wave speeds. Moreover, the nonlinear solutions, compared with the linear ones, produce a narrow region of active convection and a wider region of suppressed convection. These predictions offer nonlinear MJO features that could potentially be targets of observational investigations.
The Third Wave: A Position Paper.
ERIC Educational Resources Information Center
Dyrud, Marilyn A.
2000-01-01
Describes the Third Wave as an "information bomb... exploding in our midst, showering us with a shrapnel of images and drastically changing the way each of us perceives and acts upon our private world." Begins with a description of A. Toffler's Third Wave as an attempt to partially explain what is happening in higher education, especially distance…
Does the Wave Equation Really Work?
ERIC Educational Resources Information Center
Armstead, Donald C.; Karls, Michael A.
2006-01-01
The wave equation is a classic partial differential equation that one encounters in an introductory course on boundary value problems or mathematical physics, which can be used to describe the vertical displacement of a vibrating string. Using a video camera and Wave-in-Motion software to record displacement data from a vibrating string or spring,…
Exact Solutions of the Gardner Equation and their Applications to the Different Physical Plasmas
NASA Astrophysics Data System (ADS)
Daghan, D.; Donmez, O.
2016-06-01
Traveling wave solution of the Gardner equation is studied analytically by using the two dependent ( G '/ G,1/ G)-expansion and (1/ G ')-expansion methods and direct integration. The exact solutions of the Gardner equations are obtained. Our analytic solutions are applied to the unmagnetized four-component and dusty plasma systems consisting of hot protons and electrons to investigate dynamical features of the solitons and shock waves produced in these systems. A wide variety of parameters of the plasma is used, and the basic features of the Gardner solitons that are beyond the existing study in literature are found. It is observed that the analytic solutions from ( G '/ G,1/ G)-expansion and (1/ G ')-expansion methods only produce shock waves but the solitary waves are found from the analytic solutions derived from the direct integration. It is also noted that the superhot electrons and relative mass density of the electrons significantly effect the soliton's amplitude, width, and position. We have also numerically proved that the combination of every value of nomalized density μ 1 or temperature ratio σ 1 with the other sets of plasma parameters creates a region where the solutions have similar physical properties. The time-dependent behavior of the soliton is also studied, and a periodic motion of soliton along the phase variable η is found during the evolution. The investigations and the limits presented in this study may be helpful for studying and understanding the nonlinear properties of the solitary and shock waves seen in various physical and astrophysical plasma systems.
Periodic waves in fiber Bragg gratings
Chow, K. W.; Merhasin, Ilya M.; Malomed, Boris A.; Nakkeeran, K.; Senthilnathan, K.; Wai, P. K. A.
2008-02-15
We construct two families of exact periodic solutions to the standard model of fiber Bragg grating (FBG) with Kerr nonlinearity. The solutions are named ''sn'' and ''cn'' waves, according to the elliptic functions used in their analytical representation. The sn wave exists only inside the FBG's spectral bandgap, while waves of the cn type may only exist at negative frequencies ({omega}<0), both inside and outside the bandgap. In the long-wave limit, the sn and cn families recover, respectively, the ordinary gap solitons, and (unstable) antidark and dark solitons. Stability of the periodic solutions is checked by direct numerical simulations and, in the case of the sn family, also through the calculation of instability growth rates for small perturbations. Although, rigorously speaking, all periodic solutions are unstable, a subfamily of practically stable sn waves, with a sufficiently large spatial period and {omega}>0, is identified. However, the sn waves with {omega}<0, as well as all cn solutions, are strongly unstable.
Factorization and recomposition of molecular wave functions
NASA Astrophysics Data System (ADS)
Lefebvre, R.
2016-09-01
Some situations in the determination of molecular wave functions require to go beyond the Born-Oppenheimer (BO) approximation, with the wave function written as the product of an electronic wave function depending parametrically on the nuclear coordinates and a nuclear wave function. Such situations are usually treated by combining BO products. This form of the wave function leads to coupled equations which determine the nuclear factors of these products. There is another possibility: writing the exact molecular wave function as a single product having formally the same structure as a BO product. This approach has been at the origin of recent developments. We reconsider this problem with the aim of looking at the solutions of the coupled equations which determine the electronic factor of the factorization scheme. It is shown that these coupled equations can be reduced precisely to those encountered with the usual combination of diabatic BO products.
Forces and pressures in adsorbing partially directed walks
NASA Astrophysics Data System (ADS)
Janse van Rensburg, E. J.; Prellberg, T.
2016-05-01
Polymers in confined spaces lose conformational entropy. This induces a net repulsive entropic force on the walls of the confining space. A model for this phenomenon is a lattice walk between confining walls, and in this paper a model of an adsorbing partially directed walk is used. The walk is placed in a half square lattice {{{L}}}+2 with boundary \\partial {{{L}}}+2, and confined between two vertical parallel walls, which are vertical lines in the lattice, a distance w apart. The free energy of the walk is determined, as a function of w, for walks with endpoints in the confining walls and adsorbing in \\partial {{{L}}}+2. This gives the entropic force on the confining walls as a function of w. It is shown that there are zero force points in this model and the locations of these points are determined, in some cases exactly, and in other cases asymptotically.
Is Titan Partially Differentiated?
NASA Astrophysics Data System (ADS)
Mitri, G.; Pappalardo, R. T.; Stevenson, D. J.
2009-12-01
The recent measurement of the gravity coefficients from the Radio Doppler data of the Cassini spacecraft has improved our knowledge of the interior structure of Titan (Rappaport et al. 2008 AGU, P21A-1343). The measured gravity field of Titan is dominated by near hydrostatic quadrupole components. We have used the measured gravitational coefficients, thermal models and the hydrostatic equilibrium theory to derive Titan's interior structure. The axial moment of inertia gives us an indication of the degree of the interior differentiation. The inferred axial moment of inertia, calculated using the quadrupole gravitational coefficients and the Radau-Darwin approximation, indicates that Titan is partially differentiated. If Titan is partially differentiated then the interior must avoid melting of the ice during its evolution. This suggests a relatively late formation of Titan to avoid the presence of short-lived radioisotopes (Al-26). This also suggests the onset of convection after accretion to efficiently remove the heat from the interior. The outer layer is likely composed mainly of water in solid phase. Thermal modeling indicates that water could be present also in liquid phase forming a subsurface ocean between an outer ice I shell and a high pressure ice layer. Acknowledgments: This work was conducted at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.
Foulk, David M.; Galloway, Marc T.
2011-01-01
Partial triceps tendon disruptions are a rare injury that can lead to debilitating outcomes if misdiagnosed or managed inappropriately. The clinician should have a high index of suspicion when the mechanism involves a fall onto an outstretched arm and there is resultant elbow extension weakness along with pain and swelling. The most common location of rupture is at the tendon-osseous junction. This case report illustrates a partial triceps tendon disruption with involvement of, primarily, the medial head and the superficial expansion. Physical examination displayed weakness with resisted elbow extension in a flexed position over 90°. Radiographs revealed a tiny fleck of bone proximal to the olecranon, but this drastically underestimated the extent of injury upon surgical exploration. Magnetic resonance imaging is essential to ascertain the percentage involvement of the tendon; it can be used for patient education and subsequently to determine treatment recommendations. Although excellent at finding associated pathology, it may misjudge the size of the tear. As such, physicians must consider associated comorbidities and patient characteristics when formulating treatment plans. PMID:23016005
Universality in exact quantum state population dynamics and control
Wu, Lian-Ao; Segal, Dvira; Brumer, Paul; Egusquiza, Inigo L.
2010-09-15
We consider an exact population transition, defined as the probability of finding a state at a final time that is exactly equal to the probability of another state at the initial time. We prove that, given a Hamiltonian, there always exists a complete set of orthogonal states that can be employed as time-zero states for which this exact population transition occurs. The result is general: It holds for arbitrary systems, arbitrary pairs of initial and final states, and for any time interval. The proposition is illustrated with several analytic models. In particular, we demonstrate that in some cases, by tuning the control parameters, a complete transition might occur, where a target state, vacant at t=0, is fully populated at time {tau}.
Exact spectral elements for follower tension buckling by power series
NASA Astrophysics Data System (ADS)
Leung, A. Y. T.
2008-01-01
The spectral dynamic stiffness method using exact solutions of the governing equations as shape functions has been popular for vibration and dynamic stability analyses of framed structures consisting of uniform members. Since non-uniform members do not generally have closed form solutions, special cases only have been considered. However, exact solutions are still possible for generally non-uniform members using power series. The paper studies the exact dynamic stability of columns with distributed axial force by power series. Both uniform and distributed, compression and tension, and conservative and non-conservative axial forces are considered. Interaction diagrams of various kinds of axial loads on the natural frequencies including different intensities of the distributed loads and degree of tangency are given. Follower tension buckling is reported for the first time. It is found that the power series outperforms the dynamic stiffness method in terms of versatility in applications and numerical stability at the very low and high ends of the frequency spectrum.
An exact analysis of surface acoustic waves in a plate of functionally graded materials.
Gao, Liming; Wang, Ji; Zhong, Zheng; Du, Jianke
2009-12-01
Some traditional applications of structures and devices with homogeneous materials are being gradually replaced by functionally graded materials (FGM) with spatial variation of properties. The analysis of SAW propagating in FGM structures will be different primarily due to variations of material properties and resulting differential equations with variable coefficients. To provide an effective method and accurate results for the analysis of SAWs in FGM structures, we employed the Frobenius method as the only available method for a detailed analysis of SAW in materials with property variations in a linear pattern. Analytical examples are presented to demonstrate the effectiveness of the method and the effect of FGM on changes of surface displacements in SAW propagation.
A 1D exact treatment of shock waves within spectral methods in plane geometry
NASA Astrophysics Data System (ADS)
Bonazzola, Silvano; Marck, Jean-Alain
1991-12-01
A high-accuracy numerical technique is presented which employs two moving grids, respectively before and after the shock formation, to solve 1D Euler equations that are coupled with the transport equations for the entropy and the chemical abundances in cases with and without shock formation. Chebychev polynomial series are used to expand quantities on both sides of the matching point, and Rankine-Hugoniot conditions are used to ascertain the shock velocity after shock formation. Illustrative results are presented.
Exact maps in density functional theory for lattice models
NASA Astrophysics Data System (ADS)
Dimitrov, Tanja; Appel, Heiko; Fuks, Johanna I.; Rubio, Angel
2016-08-01
In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and graphically illustrate the complete exact density-to-wavefunction map that underly the Hohenberg-Kohn theorem in density functional theory. Having the explicit wavefunction-to-density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragments decreases and the correlation grows. We denominate this feature as intra-system steepening and discuss how it relates to the well-known inter-system derivative discontinuity. The inter-system derivative discontinuity is an exact concept for coupled subsystems with degenerate ground state. However, the coupling between subsystems as in charge transfer processes can lift the degeneracy. An important conclusion is that for such systems with a near-degenerate ground state, the corresponding cut along the particle number N of the exact density functionals is differentiable with a well-defined gradient near integer particle number.