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

Dubrovsky, V. G.; Topovsky, A. V.

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 ofmore » 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.« less

Anelastic sensitivity kernels with parsimonious storage for adjoint tomography and full waveform inversion

NASA Astrophysics Data System (ADS)

Komatitsch, Dimitri; Xie, Zhinan; Bozdaǧ, Ebru; Sales de Andrade, Elliott; Peter, Daniel; Liu, Qinya; Tromp, Jeroen

2016-09-01

We introduce a technique to compute exact anelastic sensitivity kernels in the time domain using parsimonious disk storage. The method is based on a reordering of the time loop of time-domain forward/adjoint wave propagation solvers combined with the use of a memory buffer. It avoids instabilities that occur when time-reversing dissipative wave propagation simulations. The total number of required time steps is unchanged compared to usual acoustic or elastic approaches. The cost is reduced by a factor of 4/3 compared to the case in which anelasticity is partially accounted for by accommodating the effects of physical dispersion. We validate our technique by performing a test in which we compare the Kα sensitivity kernel to the exact kernel obtained by saving the entire forward calculation. This benchmark confirms that our approach is also exact. We illustrate the importance of including full attenuation in the calculation of sensitivity kernels by showing significant differences with physical-dispersion-only kernels.

Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

Khater method for nonlinear Sharma Tasso-Olever (STO) equation of fractional order

NASA Astrophysics Data System (ADS)

Bibi, Sadaf; Mohyud-Din, Syed Tauseef; Khan, Umar; Ahmed, Naveed

In this work, we have implemented a direct method, known as Khater method to establish exact solutions of nonlinear partial differential equations of fractional order. Number of solutions provided by this method is greater than other traditional methods. Exact solutions of nonlinear fractional order Sharma Tasso-Olever (STO) equation are expressed in terms of kink, travelling wave, periodic and solitary wave solutions. Modified Riemann-Liouville derivative and Fractional complex transform have been used for compatibility with fractional order sense. Solutions have been graphically simulated for understanding the physical aspects and importance of the method. A comparative discussion between our established results and the results obtained by existing ones is also presented. Our results clearly reveal that the proposed method is an effective, powerful and straightforward technique to work out new solutions of various types of differential equations of non-integer order in the fields of applied sciences and engineering.

Exact master equation and non-Markovian decoherence dynamics of Majorana zero modes under gate-induced charge fluctuations

NASA Astrophysics Data System (ADS)

Lai, Hon-Lam; Yang, Pei-Yun; Huang, Yu-Wei; Zhang, Wei-Min

2018-02-01

In this paper, we use the exact master equation approach to investigate the decoherence dynamics of Majorana zero modes in the Kitaev model, a 1D p -wave spinless topological superconducting chain (TSC) that is disturbed by gate-induced charge fluctuations. The exact master equation is derived by extending Feynman-Vernon influence functional technique to fermionic open systems involving pairing excitations. We obtain the exact master equation for the zero-energy Bogoliubov quasiparticle (bogoliubon) in the TSC, and then transfer it into the master equation for the Majorana zero modes. Within this exact master equation formalism, we can describe in detail the non-Markovian decoherence dynamics of the zero-energy bogoliubon as well as Majorana zero modes under local perturbations. We find that at zero temperature, local charge fluctuations induce level broadening to one of the Majorana zero modes but there is an isolated peak (localized bound state) located at zero energy that partially protects the Majorana zero mode from decoherence. At finite temperatures, the zero-energy localized bound state does not precisely exist, but the coherence of the Majorana zero mode can still be partially but weakly protected, due to the sharp dip of the spectral density near the zero frequency. The decoherence will be enhanced as one increases the charge fluctuations and/or the temperature of the gate.

The exact solution of a four-body Coulomb problem

NASA Astrophysics Data System (ADS)

Ray, Hasi

2018-03-01

The elastic collision between two H-like atoms utilizing an ab initio static-exchange model (SEM) in the center of mass (CM) frame considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly, is studied thoroughly. A coupled-channel methodology in momentum space is used to solve Lippman-Schwinger equation following the integral approach. The new SEM code [Ray, Pramana 83, 907 (2014)] in which the Born-Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude using partial wave analysis, is utilized to study the s-, p-, d-wave elastic phase shifts and the corresponding partial cross sections. An augmented-Born approximation is used to include the contribution of higher partial waves more accurately to determine the total/integrated elastic cross sections. The effective range theory is used to determine the scattering lengths and effective ranges in the s-wave elastic scattering. The systems studied are Ps-Ps, Ps-Mu, Ps-H, Ps-D, Ps-T, Mu-Mu, Mu-H, Mu-D, Mu-T, H-H, H-D, H-T, D-D, D-T, T-T. The SEM includes the non-adiabatic short-range effects due to exchange. The MSEM code [Ray, Pramana 83, 907 (2014)] is used to study the effect of the long-range van der Waals interaction due to induced dipole polarizabilities of the atoms in H(1s)-H(1s) elastic collision. The dependence of scattering length on the reduced mass of the system and the dependence of scattering length on the strength of long-range van der Waals interaction that varies with the minimum interatomic distance are observed. Contribution to the Topical Issue "Low Energy Positron and Electron Interactions", edited by James Sullivan, Ron White, Michael Bromley, Ilya Fabrikant, and David Cassidy.

Whitham modulation theory for the two-dimensional Benjamin-Ono equation.

PubMed

Ablowitz, Mark; Biondini, Gino; Wang, Qiao

2017-09-01

Whitham modulation theory for the two-dimensional Benjamin-Ono (2DBO) equation is presented. A system of five quasilinear first-order partial differential equations is derived. The system describes modulations of the traveling wave solutions of the 2DBO equation. These equations are transformed to a singularity-free hydrodynamic-like system referred to here as the 2DBO-Whitham system. Exact reductions of this system are discussed, the formulation of initial value problems is considered, and the system is used to study the transverse stability of traveling wave solutions of the 2DBO equation.

On prototypical wave transmission across a junction of waveguides with honeycomb structure

NASA Astrophysics Data System (ADS)

Sharma, Basant Lal

2018-02-01

An exact expression for the scattering matrix associated with a junction generated by partial unzipping along the zigzag direction of armchair tubes is presented. The assumed simple, but representative, model, for scalar wave transmission can be interpreted in terms of the transport of the out-of-plane phonons in the ribbon-side vis-a-vis the radial phonons in the tubular-side of junction, based on the nearest-neighbor interactions between lattice sites. The exact solution for the `bondlength' in `broken' versus intact bonds can be constructed via a standard application of the Wiener-Hopf technique. The amplitude distribution of outgoing phonons, far away from the junction on either side of it, is obtained in closed form by the mode-matching method; eventually, this leads to the provision of the scattering matrix. As the main result of the paper, a succinct and closed form expression for the accompanying reflection and transmission coefficients is provided along with a detailed derivation using the Chebyshev polynomials. Applications of the analysis presented in this paper include linear wave transmission in nanotubes, nanoribbons, and monolayers of honeycomb lattices containing carbon-like units.

Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Vitanov, Nikolay K.; Dimitrova, Zlatinka I.

2018-03-01

We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

A Well-Balanced Path-Integral f-Wave Method for Hyperbolic Problems with Source Terms

PubMed Central

2014-01-01

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. PMID:24563581

Elastic Differential Cross Sections

NASA Technical Reports Server (NTRS)

Werneth, Charles M.; Maung, Khin M.; Ford, William P.; Norbury, John W.; Vera, Michael D.

2014-01-01

The eikonal, partial wave (PW) Lippmann-Schwinger, and three-dimensional Lippmann-Schwinger (LS3D) methods are compared for nuclear reactions that are relevant for space radiation applications. Numerical convergence of the eikonal method is readily achieved when exact formulas of the optical potential are used for light nuclei (A less than or equal to 16) and the momentum-space optical potential is used for heavier nuclei. The PW solution method is known to be numerically unstable for systems that require a large number of partial waves, and, as a result, the LS3D method is employed. The effect of relativistic kinematics is studied with the PW and LS3D methods and is compared to eikonal results. It is recommended that the LS3D method be used for high energy nucleon- nucleus reactions and nucleus-nucleus reactions at all energies because of its rapid numerical convergence and stability.

Nuclear Cross Sections for Space Radiation Applications

NASA Technical Reports Server (NTRS)

Werneth, C. M.; Maung, K. M.; Ford, W. P.; Norbury, J. W.; Vera, M. D.

2015-01-01

The eikonal, partial wave (PW) Lippmann-Schwinger, and three-dimensional Lippmann-Schwinger (LS3D) methods are compared for nuclear reactions that are relevant for space radiation applications. Numerical convergence of the eikonal method is readily achieved when exact formulas of the optical potential are used for light nuclei (A = 16) and the momentum-space optical potential is used for heavier nuclei. The PW solution method is known to be numerically unstable for systems that require a large number of partial waves, and, as a result, the LS3D method is employed. The effect of relativistic kinematics is studied with the PW and LS3D methods and is compared to eikonal results. It is recommended that the LS3D method be used for high energy nucleon-nucleus reactions and nucleus-nucleus reactions at all energies because of its rapid numerical convergence and stability for both non-relativistic and relativistic kinematics.

Diffraction of an Electromagnetic Wave on a Dielectric Rod in a Rectangular Waveguide. A Method of Partial Waveguide Filling

NASA Astrophysics Data System (ADS)

Zav'yalov, A. S.

2018-04-01

A variant of the method of partial waveguide filling is considered in which a sample is put into a waveguide through holes in wide waveguide walls at the distance equal to a quarter of the wavelength in the waveguide from a short-circuiter, and the total input impedance of the sample in the waveguide is directly measured. The equivalent circuit of the sample is found both without and with account of the hole. It is demonstrated that consideration of the edge effect makes it possible to obtain more exact values of the dielectric permittivity.

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.

Wigner functions for nonparaxial, arbitrarily polarized electromagnetic wave fields in free space.

PubMed

Alonso, Miguel A

2004-11-01

New representations are defined for describing electromagnetic wave fields in free space exactly in terms of rays for any wavelength, level of coherence or polarization, and numerical aperture, as long as there are no evanescent components. These representations correspond to tensors assigned to each ray such that the electric and magnetic energy densities, the Poynting vector, and the polarization properties of the field correspond to simple integrals involving these tensors for the rays that go through the specified point. For partially coherent fields, the ray-based approach provided by the new representations can reduce dramatically the computation times for the physical properties mentioned earlier.

Assessment of the further improved (G'/G)-expansion method and the extended tanh-method in probing exact solutions of nonlinear PDEs.

PubMed

Akbar, M Ali; Ali, Norhashidah Hj Mohd; Mohyud-Din, Syed Tauseef

2013-01-01

The (G'/G)-expansion method is one of the most direct and effective method for obtaining exact solutions of nonlinear partial differential equations (PDEs). In the present article, we construct the exact traveling wave solutions of nonlinear evolution equations in mathematical physics via the (2 + 1)-dimensional breaking soliton equation by using two methods: namely, a further improved (G'/G)-expansion method, where G(ξ) satisfies the auxiliary ordinary differential equation (ODE) [G'(ξ)](2) = p G (2)(ξ) + q G (4)(ξ) + r G (6)(ξ); p, q and r are constants and the well known extended tanh-function method. We demonstrate, nevertheless some of the exact solutions bring out by these two methods are analogous, but they are not one and the same. It is worth mentioning that the first method has not been exercised anybody previously which gives further exact solutions than the second one. PACS numbers 02.30.Jr, 05.45.Yv, 02.30.Ik.

Finite-size radiation force correction for inviscid spheres in standing waves.

PubMed

Marston, Philip L

2017-09-01

Yosioka and Kawasima gave a widely used approximation for the acoustic radiation force on small liquid spheres surrounded by an immiscible liquid in 1955. Considering the liquids to be inviscid with negligible thermal dissipation, in their approximation the force on the sphere is proportional to the sphere's volume and the levitation position in a vertical standing wave becomes independent of the size. The analysis given here introduces a small correction term proportional to the square of the sphere's radius relative to the aforementioned small-sphere force. The significance of this term also depends on the relative density and sound velocity of the sphere. The improved approximation is supported by comparison with the exact partial-wave-series based radiation force for ideal fluid spheres in ideal fluids.

Accurate quantum wave packet calculations for the F + HCl → Cl + HF reaction on the ground 1(2)A' potential energy surface.

PubMed

Bulut, Niyazi; Kłos, Jacek; Alexander, Millard H

2012-03-14

We present converged exact quantum wave packet calculations of reaction probabilities, integral cross sections, and thermal rate coefficients for the title reaction. Calculations have been carried out on the ground 1(2)A' global adiabatic potential energy surface of Deskevich et al. [J. Chem. Phys. 124, 224303 (2006)]. Converged wave packet reaction probabilities at selected values of the total angular momentum up to a partial wave of J = 140 with the HCl reagent initially selected in the v = 0, j = 0-16 rovibrational states have been obtained for the collision energy range from threshold up to 0.8 eV. The present calculations confirm an important enhancement of reactivity with rotational excitation of the HCl molecule. First, accurate integral cross sections and rate constants have been calculated and compared with the available experimental data.

The exact thermal rotational spectrum of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

NASA Technical Reports Server (NTRS)

Reimers, J. R.; Heller, E. J.

1985-01-01

The exact thermal rotational spectrum of a two-dimensional rigid rotor is obtained using Gaussian wave packet dynamics. The spectrum is obtained by propagating, without approximation, infinite sets of Gaussian wave packets. These sets are constructed so that collectively they have the correct periodicity, and indeed, are coherent states appropriate to this problem. Also, simple, almost classical, approximations to full wave packet dynamics are shown to give results which are either exact or very nearly exact. Advantages of the use of Gaussian wave packet dynamics over conventional linear response theory are discussed.

Single-shot observation of optical rogue waves in integrable turbulence using time microscopy

PubMed Central

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

Coriolis-coupled wave packet dynamics of H + HLi reaction.

PubMed

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.

Twisted gravitational waves

NASA Astrophysics Data System (ADS)

Bini, Donato; Chicone, Carmen; Mashhoon, Bahram

2018-03-01

In general relativity (GR), linearized gravitational waves propagating in empty Minkowski spacetime along a fixed spatial direction have the property that the wave front is the Euclidean plane. Beyond the linear regime, exact plane waves in GR have been studied theoretically for a long time and many exact vacuum solutions of the gravitational field equations are known that represent plane gravitational waves. These have parallel rays and uniform wave fronts. It turns out, however, that GR also admits exact solutions representing gravitational waves propagating along a fixed direction that are nonplanar. The wave front is then nonuniform and the bundle of rays is twisted. We find a class of solutions representing nonplanar unidirectional gravitational waves and study some of the properties of these twisted waves.

Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

Intermediate energy proton-deuteron elastic scattering

NASA Technical Reports Server (NTRS)

Wilson, J. W.

1973-01-01

A fully symmetrized multiple scattering series is considered for the description of proton-deuteron elastic scattering. An off-shell continuation of the experimentally known twobody amplitudes that retains the exchange symmeteries required for the calculation is presented. The one boson exchange terms of the two body amplitudes are evaluated exactly in this off-shell prescription. The first two terms of the multiple scattering series are calculated explicitly whereas multiple scattering effects are obtained as minimum variance estimates from the 146-MeV data of Postma and Wilson. The multiple scattering corrections indeed consist of low order partial waves as suggested by Sloan based on model studies with separable interactions. The Hamada-Johnston wave function is shown consistent with the data for internucleon distances greater than about 0.84 fm.

Evidence for unnatural-parity contributions to electron-impact ionization of laser-aligned atoms

DOE PAGES

Armstrong, Gregory S. J.; Colgan, James Patrick; Pindzola, M. S.; ...

2015-09-11

Recent measurements have examined the electron-impact ionization of excited-state laser-aligned Mg atoms. In this paper we show that the ionization cross section arising from the geometry where the aligned atom is perpendicular to the scattering plane directly probes the unnatural parity contributions to the ionization amplitude. The contributions from natural parity partial waves cancel exactly in this geometry. Our calculations resolve the discrepancy between the nonzero measured cross sections in this plane and the zero cross section predicted by distorted-wave approaches. Finally, we demonstrate that this is a general feature of ionization from p-state targets by additional studies of ionizationmore » from excited Ca and Na atoms.« less

Mathematical analysis of thermal diffusion shock waves

NASA Astrophysics Data System (ADS)

Gusev, Vitalyi; Craig, Walter; Livoti, Roberto; Danworaphong, Sorasak; Diebold, Gerald J.

2005-10-01

Thermal diffusion, also known as the Ludwig-Soret effect, refers to the separation of mixtures in a temperature gradient. For a binary mixture the time dependence of the change in concentration of each species is governed by a nonlinear partial differential equation in space and time. Here, an exact solution of the Ludwig-Soret equation without mass diffusion for a sinusoidal temperature field is given. The solution shows that counterpropagating shock waves are produced which slow and eventually come to a halt. Expressions are found for the shock time for two limiting values of the starting density fraction. The effects of diffusion on the development of the concentration profile in time and space are found by numerical integration of the nonlinear differential equation.

New solitary wave solutions of (3 + 1)-dimensional nonlinear extended Zakharov-Kuznetsov and modified KdV-Zakharov-Kuznetsov equations and their applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, A. R.; Arshad, M.; Wang, Jun

In this paper, new exact solitary wave, soliton and elliptic function solutions are constructed in various forms of three dimensional nonlinear partial differential equations (PDEs) in mathematical physics by utilizing modified extended direct algebraic method. Soliton solutions in different forms such as bell and anti-bell periodic, dark soliton, bright soliton, bright and dark solitary wave in periodic form etc are obtained, which have large applications in different branches of physics and other areas of applied sciences. The obtained solutions are also presented graphically. Furthermore, many other nonlinear evolution equations arising in mathematical physics and engineering can also be solved by this powerful, reliable and capable method. The nonlinear three dimensional extended Zakharov-Kuznetsov dynamica equation and (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation are selected to show the reliability and effectiveness of the current method.

The double polarization program of CBELSA/TAPS

NASA Astrophysics Data System (ADS)

Thiel, Annika

2014-06-01

The excitation spectrum of the proton consists of resonances with substancial width which are often strongly overlapping and are therefore difficult to disentangle. To determine the exact contributions and identify these resonances, a partial wave analysis solution has to be found. For a complete experiment, which leads to an unambiguous solution, several single and double polarization observables are needed. With the Crystal Barrel/TAPS experiment at ELSA, the measurement of double polarization observables in different reactions is possible by using a circularly or linearly polarized photon beam on a transversely or longitudinally polarized butanol target.

Finite Element Solution to the Helmholtz Equation with High Wave Number. Part 1. The h-Version of the FEM

DTIC Science & Technology

1993-11-01

4) between the exact solution and it’s best approximnation on the one and the FE-solution on the other hand. The determining equation for ti. & ielt ...Acknowledgement: The work of the first atitlhor wvas supported by Grant No 517 402 524 3 of the Gerinan Academic Exchange Service (l)AA[)). The work of thle second...methou, mn: A.K. Aziz (ed.), The mathematical foundations of tile finite element, method with applicai.4ons to partial differential equations, Academic

The exact eigenfunctions and eigenvalues of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

NASA Technical Reports Server (NTRS)

Reimers, J. R.; Heller, E. J.

1985-01-01

Exact eigenfunctions for a two-dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eigenstates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a posteriori justification of the De Leon-Heller spectral quantization method.

Quantum mechanical streamlines. I - Square potential barrier

NASA Technical Reports Server (NTRS)

Hirschfelder, J. O.; Christoph, A. C.; Palke, W. E.

1974-01-01

Exact numerical calculations are made for scattering of quantum mechanical particles hitting a square two-dimensional potential barrier (an exact analog of the Goos-Haenchen optical experiments). Quantum mechanical streamlines are plotted and found to be smooth and continuous, to have continuous first derivatives even through the classical forbidden region, and to form quantized vortices around each of the nodal points. A comparison is made between the present numerical calculations and the stationary wave approximation, and good agreement is found between both the Goos-Haenchen shifts and the reflection coefficients. The time-independent Schroedinger equation for real wavefunctions is reduced to solving a nonlinear first-order partial differential equation, leading to a generalization of the Prager-Hirschfelder perturbation scheme. Implications of the hydrodynamical formulation of quantum mechanics are discussed, and cases are cited where quantum and classical mechanical motions are identical.

New exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in multi-temperature electron plasmas

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Tian, Yu; Zeng, Zhi-Fang

2017-10-01

In this paper, we aim to introduce a new form of the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation for the long waves of small amplitude with slow dependence on the transverse coordinate. By using the Hirota's bilinear form and the extended homoclinic test approach, new exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation are presented. Moreover, the properties and characteristics for these new exact periodic solitary-wave solutions are discussed with some figures.

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents.

PubMed

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-04-08

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.

Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

PubMed Central

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

Exact finite difference schemes for the non-linear unidirectional wave equation

NASA Technical Reports Server (NTRS)

Mickens, R. E.

1985-01-01

Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.

On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.

PubMed

Yang, Xiao-Jun; Tenreiro Machado, J A; Baleanu, Dumitru; Cattani, Carlo

2016-08-01

This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.

On optimizing the treatment of exchange perturbations.

NASA Technical Reports Server (NTRS)

Hirschfelder, J. O.; Chipman, D. M.

1972-01-01

Most theories of exchange perturbations would give the exact energy and wave function if carried out to an infinite order. However, the different methods give different values for the second-order energy, and different values for E(1), the expectation value of the Hamiltonian corresponding to the zeroth- plus first-order wave function. In the presented paper, it is shown that the zeroth- plus first-order wave function obtained by optimizing the basic equation which is used in most exchange perturbation treatments is the exact wave function for the perturbation system and E(1) is the exact energy.

Electronic transport across a junction between armchair graphene nanotube and zigzag nanoribbon. Transmission in an armchair nanotube without a zigzag half-line of dimers

NASA Astrophysics Data System (ADS)

Sharma, Basant Lal

2018-05-01

Based on the well known nearest-neighbor tight-binding approximation for graphene, an exact expression for the electronic conductance across a zigzag nanoribbon/armchair nanotube junction is presented for non-interacting electrons. The junction results from the removal of a half-row of zigzag dimers in armchair nanotube, or equivalently by partial rolling of zigzag nanoribbon and insertion of a half-row of zigzag dimers in between. From the former point of view, a discrete form of Dirichlet condition is imposed on a zigzag half-line of dimers assuming the vanishing of wave function outside the physical structure. A closed form expression is provided for the reflection and transmission moduli for the outgoing wave modes for each given electronic wave mode incident from either side of the junction. It is demonstrated that such a contact junction between the nanotube and nanoribbon exhibits negligible backscattering, and the transmission has been found to be nearly ballistic. In contrast to the previously reported studies for partially unzipped carbon nanotubes (CNTs), using the same tight binding model, it is found that due to the "defect" there is certain amount of mixing between the electronic wave modes with even and odd reflection symmetries. But the junction remains a perfect valley filter for CNTs at certain energy ranges. Applications aside from the electronic case, include wave propagation in quasi-one-dimensional honeycomb structures of graphene-like constitution. The paper includes several numerical calculations, analytical derivations, and graphical results, which complement the provision of succinct closed form expressions.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H

2015-07-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

Separation of traveling and standing waves in a finite dispersive string with partial or continuous viscoelastic foundation

NASA Astrophysics Data System (ADS)

Cheng, Xiangle; Blanchard, Antoine; Tan, Chin An; Lu, Huancai; Bergman, Lawrence A.; McFarland, D. Michael; Vakakis, Alexander F.

2017-12-01

The free and forced vibrations of a linear string with a local spring-damper on a partial elastic foundation, as well as a linear string on a viscoelastic foundation conceptualized as a continuous distribution of springs and dampers, are studied in this paper. Exact, analytical results are obtained for the free and forced response to a harmonic excitation applied at one end of the string. Relations between mode complexity and energy confinement with the dispersion in the string system are examined for the steady-state forced vibration, and numerical methods are applied to simulate the transient evolution of energy propagation. Eigenvalue loci veering and normal mode localization are observed for weakly coupled subsystems, when the foundation stiffness is sufficiently large, for both the spatially symmetric and asymmetric systems. The forced vibration results show that nonproportional damping-induced mode complexity, for which there are co-existing regions of purely traveling waves and standing waves, is attainable for the dispersive string system. However, this wave transition phenomenon depends strongly on the location of the attached discrete spring-damper relative to the foundation and whether the excitation frequency Ω is above or below the cutoff frequency ωc. When Ω<ωc, the wave transition cannot be attained for a string on an elastic foundation, but is possible if the string is on a viscoelastic foundation. Although this study is primarily formulated for a harmonic boundary excitation at one end of the string, generalization of the mode complexity can be deduced for the steady-state forced response of the string-foundation system to synchronous end excitations and is confirmed numerically. This work represents a novel study to understand the wave transitions in a dispersive structural system and lays the groundwork for potentially effective passive vibration control strategies.

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

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.

2018-04-01

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

Acoustic scattering of a cylindrical quasi-Gaussian beam with arbitrary incidence focused on a rigid elliptical cylinder

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

Mitri, F. G., E-mail: F.G.Mitri@ieee.org

2015-11-14

Using the partial-wave series expansion method in cylindrical coordinates, a formal analytical solution for the acoustical scattering of a 2D cylindrical quasi-Gaussian beam with an arbitrary angle of incidence θ{sub i}, focused on a rigid elliptical cylinder in a non-viscous fluid, is developed. The cylindrical focused beam expression is an exact solution of the Helmholtz equation. The scattering coefficients for the elliptical cylinder are determined by forcing the expression of the total (incident + scattered) field to satisfy the Neumann boundary condition for a rigid immovable surface, and performing the product of matrices involving an inversion procedure. Computations for the matrices elementsmore » require a single numerical integration procedure for each partial-wave mode. Numerical results are performed with particular emphasis on the focusing properties of the incident beam and its angle of incidence with respect to the major axis a of the ellipse as well as the aspect ratio a/b where b is the minor axis (assuming a > b). The method is validated and verified against previous results obtained via the T-matrix for plane waves. The present analysis is the first to consider an acoustical beam on an elliptic cylinder of variable cross-section as opposed to plane waves of infinite extent. Other 2D non-spherical and Chebyshev surfaces are mentioned that may be examined throughout this analytical formalism assuming a small deformation parameter ε.« less

Study of coupled nonlinear partial differential equations for finding exact analytical solutions

PubMed Central

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

Some new traveling wave exact solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli equations.

PubMed

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.

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.

Inverse scattering transform analysis of rogue waves using local periodization procedure

PubMed Central

Randoux, Stéphane; Suret, Pierre; El, Gennady

2016-01-01

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

Rogue wave solutions for the infinite integrable nonlinear Schrödinger equation hierarchy.

PubMed

Ankiewicz, A; Akhmediev, N

2017-07-01

We present rogue wave solutions of the integrable nonlinear Schrödinger equation hierarchy with an infinite number of higher-order terms. The latter include higher-order dispersion and higher-order nonlinear terms. In particular, we derive the fundamental rogue wave solutions for all orders of the hierarchy, with exact expressions for velocities, phase, and "stretching factors" in the solutions. We also present several examples of exact solutions of second-order rogue waves, including rogue wave triplets.

Rogue periodic waves of the focusing nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Chen, Jinbing; Pelinovsky, Dmitry E.

2018-02-01

Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn. Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov-Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine's breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.

Rogue periodic waves of the focusing nonlinear Schrödinger equation.

PubMed

Chen, Jinbing; Pelinovsky, Dmitry E

2018-02-01

Rogue periodic waves stand for rogue waves on a periodic background. The nonlinear Schrödinger equation in the focusing case admits two families of periodic wave solutions expressed by the Jacobian elliptic functions dn and cn . Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov-Shabat spectral problem and the Darboux transformations. These exact solutions generalize the classical rogue wave (the so-called Peregrine's breather). The magnification factor of the rogue periodic waves is computed as a function of the elliptic modulus. Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.

Vestigial nematicity from spin and/or charge order in the cuprates

DOE PAGES

Nie, Laimei; Maharaj, Akash V.; Fradkin, Eduardo; ...

2017-08-01

Nematic order has manifested itself in a variety of materials in the cuprate family. We propose an effective field theory of a layered system with incommensurate, intertwined spin- and charge-density wave (SDW and CDW) orders, each of which consists of two components related by C4 rotations. Using a variational method (which is exact in a large N limit), we study the development of nematicity from partially melting those density waves by either increasing temperature or adding quenched disorder. As temperature decreases we first find a transition to a nematic phase, but depending on the range of parameters (e.g. doping concentration)more » the strongest fluctuations associated with this phase reflect either proximate SDW or CDW order. We also discuss the changes in parameters that can account for the differences in the SDW-CDW interplay between the (214) family and the other hole-doped cuprates.« less

Time-Harmonic Gaussian Beams: Exact Solutions of the Helmhotz Equation in Free Space

NASA Astrophysics Data System (ADS)

Kiselev, A. P.

2017-12-01

An exact solution of the Helmholtz equation u xx + u yy + u zz + k 2 u = 0 is presented, which describes propagation of monochromatic waves in the free space. The solution has the form of a superposition of plane waves with a specific weight function dependent on a certain free parameter a. If ka→∞, the solution is localized in the Gaussian manner in a vicinity of a certain straight line and asymptotically coincides with the famous approximate solution known as the fundamental mode of a paraxial Gaussian beam. The asymptotics of the aforementioned exact solution does not include a backward wave.

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.

Exact traveling-wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional Schrödinger equation with polynomial nonlinearity of arbitrary order.

PubMed

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. ©2011 American Physical Society

Peakompactons: Peaked compact nonlinear waves

DOE PAGES

Christov, Ivan C.; Kress, Tyler; Saxena, Avadh

2017-04-20

This paper is meant as an accessible introduction to/tutorial on the analytical construction and numerical simulation of a class of nonstandard solitary waves termed peakompactons. We present that these peaked compactly supported waves arise as solutions to nonlinear evolution equations from a hierarchy of nonlinearly dispersive Korteweg–de Vries-type models. Peakompactons, like the now-well-known compactons and unlike the soliton solutions of the Korteweg–de Vries equation, have finite support, i.e., they are of finite wavelength. However, unlike compactons, peakompactons are also peaked, i.e., a higher spatial derivative suffers a jump discontinuity at the wave’s crest. Here, we construct such solutions exactly bymore » reducing the governing partial differential equation to a nonlinear ordinary differential equation and employing a phase-plane analysis. Lastly, a simple, but reliable, finite-difference scheme is also designed and tested for the simulation of collisions of peakompactons. In addition to the peakompacton class of solutions, the general physical features of the so-called K #(n,m) hierarchy of nonlinearly dispersive Korteweg–de Vries-type models are discussed as well.« less

Non-autonomous matter-wave solitons in hybrid atomic-molecular Bose-Einstein condensates with tunable interactions and harmonic potential

NASA Astrophysics Data System (ADS)

Wang, Deng-Shan; Liu, Jiang; Wang, Lizhen

2018-03-01

In this paper, we investigate matter-wave solitons in hybrid atomic-molecular Bose-Einstein condensates with tunable interactions and external potentials. Three types of time-modulated harmonic potentials are considered and, for each of them, two groups of exact non-autonomous matter-wave soliton solutions of the coupled Gross-Pitaevskii equation are presented. Novel nonlinear structures of these non-autonomous matter-wave solitons are analyzed by displaying their density distributions. It is shown that the time-modulated nonlinearities and external potentials can support exact non-autonomous atomic-molecular matter-wave solitons.

The propagation of the shock wave from a strong explosion in a plane-parallel stratified medium: the Kompaneets approximation

NASA Astrophysics Data System (ADS)

Olano, C. A.

2009-11-01

Context: Using certain simplifications, Kompaneets derived a partial differential equation that states the local geometrical and kinematical conditions that each surface element of a shock wave, created by a point blast in a stratified gaseous medium, must satisfy. Kompaneets could solve his equation analytically for the case of a wave propagating in an exponentially stratified medium, obtaining the form of the shock front at progressive evolutionary stages. Complete analytical solutions of the Kompaneets equation for shock wave motion in further plane-parallel stratified media were not found, except for radially stratified media. Aims: We aim to analytically solve the Kompaneets equation for the motion of a shock wave in different plane-parallel stratified media that can reflect a wide variety of astrophysical contexts. We were particularly interested in solving the Kompaneets equation for a strong explosion in the interstellar medium of the Galactic disk, in which, due to intense winds and explosions of stars, gigantic gaseous structures known as superbubbles and supershells are formed. Methods: Using the Kompaneets approximation, we derived a pair of equations that we call adapted Kompaneets equations, that govern the propagation of a shock wave in a stratified medium and that permit us to obtain solutions in parametric form. The solutions provided by the system of adapted Kompaneets equations are equivalent to those of the Kompaneets equation. We solved the adapted Kompaneets equations for shock wave propagation in a generic stratified medium by means of a power-series method. Results: Using the series solution for a shock wave in a generic medium, we obtained the series solutions for four specific media whose respective density distributions in the direction perpendicular to the stratification plane are of an exponential, power-law type (one with exponent k=-1 and the other with k =-2) and a quadratic hyperbolic-secant. From these series solutions, we deduced exact solutions for the four media in terms of elemental functions. The exact solution for shock wave propagation in a medium of quadratic hyperbolic-secant density distribution is very appropriate to describe the growth of superbubbles in the Galactic disk. Member of the Carrera del Investigador Científico del CONICET, Argentina.

Condensates of p-wave pairs are exact solutions for rotating two-component Bose gases.

PubMed

Papenbrock, T; Reimann, S M; Kavoulakis, G M

2012-02-17

We derive exact analytical results for the wave functions and energies of harmonically trapped two-component Bose-Einstein condensates with weakly repulsive interactions under rotation. The isospin symmetric wave functions are universal and do not depend on the matrix elements of the two-body interaction. The comparison with the results from numerical diagonalization shows that the ground state and low-lying excitations consist of condensates of p-wave pairs for repulsive contact interactions, Coulomb interactions, and the repulsive interactions between aligned dipoles.

Rayleigh-Bloch waves trapped by a periodic perturbation: exact solutions

NASA Astrophysics Data System (ADS)

Merzon, A.; Zhevandrov, P.; Romero Rodríguez, M. I.; De la Paz Méndez, J. E.

2018-06-01

Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a small amplitude function which is periodic in one direction and of finite support in the other. These solutions are quasiperiodic along the structure and exponentially decay in the orthogonal direction. A simple formula for the dispersion relation of these waves is obtained.

Soliton interactions and the formation of solitonic patterns

NASA Astrophysics Data System (ADS)

Sears, Suzanne M.

From the stripes of a zebra, to the spirals of cream in a hot cup of coffee, we are surrounded by patterns in the natural world. But why are there patterns? Why drives their formation? In this thesis we study some of the diverse ways patterns can arise due to the interactions between solitary waves in nonlinear systems, sometimes starting from nothing more than random noise. What follows is a set of three studies. In the first, we show how a nonlinear system that supports solitons can be driven to generate exact (regular) Cantor set fractals. As an example, we use numerical simulations to demonstrate the formation of Cantor set fractals by temporal optical solitons. This fractal formation occurs in a cascade of nonlinear optical fibers through the dynamical evolution of a single input soliton. In the second study, we investigate pattern formation initiated by modulation instability in nonlinear partially coherent wave fronts and show that anisotropic noise and/or anisotropic correlation statistics can lead to ordered patterns such as grids and stripes. For the final study, we demonstrate the spontaneous clustering of solitons in partially coherent wavefronts during the final stages of pattern formation initiated by modulation instability and noise. Experimental observations are in agreement with theoretical predictions and are confirmed using numerical simulations.

A new class of exact solutions of the Klein-Gordon equation of a charged particle interacting with an electromagnetic plane wave in a medium

NASA Astrophysics Data System (ADS)

Varró, Sándor

2014-01-01

Exact solutions are presented of the Klein-Gordon equation of a charged particle moving in a transverse monochromatic plasmon wave of arbitrary high amplitude, which propagates in an underdense plasma. These solutions are expressed in terms of Ince polynomials, forming a doubly infinite set, parametrized by discrete momentum components of the charged particle’s de Broglie wave along the polarization vector and along the propagation direction of the plasmon radiation. The envelope of the exact wavefunctions describes a high-contrast periodic structure of the particle density on the plasma length scale, which may have relevance in novel particle acceleration mechanisms.

Large-amplitude hydromagnetic waves in collisionless relativistic plasma - Exact solution for the fast-mode magnetoacoustic wave

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.

Surface‐wave Green’s tensors in the near field

USGS Publications Warehouse

Haney, Matt; Nakahara, Hisashi

2014-01-01

We demonstrate the connection between theoretical expressions for the correlation of ambient noise Rayleigh and Love waves and the exact surface‐wave Green’s tensors for a point force. The surface‐wave Green’s tensors are well known in the far‐field limit. On the other hand, the imaginary part of the exact Green’s tensors, including near‐field effects, arises in correlation techniques such as the spatial autocorrelation (SPAC) method. Using the imaginary part of the exact Green’s tensors from the SPAC method, we find the associated real part using the Kramers–Kronig relations. The application of the Kramers–Kronig relations is not straightforward, however, because the causality properties of the different tensor components vary. In addition to the Green’s tensors for a point force, we also derive expressions for a general point moment tensor source.

Conservative, unconditionally stable discretization methods for Hamiltonian equations, applied to wave motion in lattice equations modeling protein molecules

NASA Astrophysics Data System (ADS)

LeMesurier, Brenton

2012-01-01

A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.

Exact solutions for (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation and coupled Klein-Gordon equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Islam, S M Rayhanul

2014-01-01

In this work, recently developed modified simple equation (MSE) method is applied to find exact traveling wave solutions of nonlinear evolution equations (NLEEs). To do so, we consider the (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and coupled Klein-Gordon (cKG) equations. Two classes of explicit exact solutions-hyperbolic and trigonometric solutions of the associated equations are characterized with some free parameters. Then these exact solutions correspond to solitary waves for particular values of the parameters. 02.30.Jr; 02.70.Wz; 05.45.Yv; 94.05.Fg.

How hairpin vortices emerge from exact invariant solutions

NASA Astrophysics Data System (ADS)

Schneider, Tobias M.; Farano, Mirko; de Palma, Pietro; Robinet, Jean-Christoph; Cherubini, Stefania

2017-11-01

Hairpin vortices are among the most commonly observed flow structures in wall-bounded shear flows. However, within the dynamical system approach to turbulence, those structures have not yet been described. They are not captured by known exact invariant solutions of the Navier-Stokes equations nor have other state-space structures supporting hairpins been identified. We show that hairpin structures are observed along an optimally growing trajectory leaving a well known exact traveling wave solution of plane Poiseuille flow. The perturbation triggering hairpins does not correspond to an unstable mode of the exact traveling wave but lies in the stable manifold where non-normality causes strong transient amplification.

General method of solving the Schroedinger equation of atoms and molecules

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

Nakatsuji, Hiroshi

2005-12-15

We propose a general method of solving the Schroedinger equation of atoms and molecules. We first construct the wave function having the exact structure, using the ICI (iterative configuration or complement interaction) method and then optimize the variables involved by the variational principle. Based on the scaled Schroedinger equation and related principles, we can avoid the singularity problem of atoms and molecules and formulate a general method of calculating the exact wave functions in an analytical expansion form. We choose initial function {psi}{sub 0} and scaling g function, and then the ICI method automatically generates the wave function that hasmore » the exact structure by using the Hamiltonian of the system. The Hamiltonian contains all the information of the system. The free ICI method provides a flexible and variationally favorable procedure of constructing the exact wave function. We explain the computational procedure of the analytical ICI method routinely performed in our laboratory. Simple examples are given using hydrogen atom for the nuclear singularity case, the Hooke's atom for the electron singularity case, and the helium atom for both cases.« less

Experimental Studies on Wave Interactions of Partially Perforated Wall under Obliquely Incident Waves

PubMed Central

Lee, Jong-In; Kim, Young-Taek; Shin, Sungwon

2014-01-01

This study presents wave height distribution in terms of stem wave evolution phenomena on partially perforated wall structures through three-dimensional laboratory experiments. The plain and partially perforated walls were tested to understand their effects on the stem wave evolution under the monochromatic and random wave cases with the various wave conditions, incident angle (from 10 to 40 degrees), and configurations of front and side walls. The partially perforated wall reduced the relative wave heights more effectively compared to the plain wall structure. Partially perforated walls with side walls showed a better performance in terms of wave height reduction compared to the structure without the side wall. Moreover, the relative wave heights along the wall were relatively small when the relative chamber width is large, within the range of the chamber width in this study. The wave spectra showed a frequency dependency of the wave energy dissipation. In most cases, the existence of side wall is a more important factor than the porosity of the front wall in terms of the wave height reduction even if the partially perforated wall was still effective compared to the plain wall. PMID:25254260

Experimental studies on wave interactions of partially perforated wall under obliquely incident waves.

PubMed

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.

An exact solution to the relativistic equation of motion of a charged particle driven by a linearly polarized electromagnetic wave

NASA Technical Reports Server (NTRS)

Shebalin, John V.

1988-01-01

An exact analytic solution is found for a basic electromagnetic wave-charged particle interaction by solving the nonlinear equations of motion. The particle position, velocity, and corresponding time are found to be explicit functions of the total phase of the wave. Particle position and velocity are thus implicit functions of time. Applications include describing the motion of a free electron driven by an intense laser beam..

Localized light waves: Paraxial and exact solutions of the wave equation (a review)

NASA Astrophysics Data System (ADS)

Kiselev, A. P.

2007-04-01

Simple explicit localized solutions are systematized over the whole space of a linear wave equation, which models the propagation of optical radiation in a linear approximation. Much attention has been paid to exact solutions (which date back to the Bateman findings) that describe wave beams (including Bessel-Gauss beams) and wave packets with a Gaussian localization with respect to the spatial variables and time. Their asymptotics with respect to free parameters and at large distances are presented. A similarity between these exact solutions and harmonic in time fields obtained in the paraxial approximation based on the Leontovich-Fock parabolic equation has been studied. Higher-order modes are considered systematically using the separation of variables method. The application of the Bateman solutions of the wave equation to the construction of solutions to equations with dispersion and nonlinearity and their use in wavelet analysis, as well as the summation of Gaussian beams, are discussed. In addition, solutions localized at infinity known as the Moses-Prosser “acoustic bullets”, as well as their harmonic in time counterparts, “ X waves”, waves from complex sources, etc., have been considered. Everywhere possible, the most elementary mathematical formalism is used.

Analysis of Multiple Contingency Tables by Exact Conditional Tests for Zero Partial Association.

ERIC Educational Resources Information Center

Kreiner, Svend

The tests for zero partial association in a multiple contingency table have gained new importance with the introduction of graphical models. It is shown how these may be performed as exact conditional tests, using as test criteria either the ordinary likelihood ratio, the standard x squared statistic, or any other appropriate statistics. A…

Exact ghost-free bigravitational waves

NASA Astrophysics Data System (ADS)

Ayón-Beato, Eloy; Higuita-Borja, Daniel; Méndez-Zavaleta, Julio A.; Velázquez-Rodríguez, Gerardo

2018-04-01

We study the propagation of exact gravitational waves in the ghost-free bimetric theory. Our focus is on type-N spacetimes compatible with the cosmological constants provided by the bigravity interaction potential, and particularly in the single class known by allowing at least a Killing symmetry: the AdS waves. They have the advantage of being represented by a generalized Kerr-Schild transformation from AdS spacetime. This entails a notorious simplification in bigravity by allowing to straightforwardly compute any power of its interaction square root matrix, opening the door to explore physically meaningful exact configurations. For these exact gravitational waves the complex dynamical structure of bigravity decomposes into elementary exact massless or massive excitations propagating on AdS. We use a complexified formulation of the Euler-Darboux equations to provide for the first time the general solutions to the massive version of the Siklos equation which rules the resulting AdS-wave dynamics, using an integral representation originally due to Poisson. Inspired by this progress, we tackle the subtle problem of how matter couples to bigravity and, more concretely, if this occurs through a composite metric, which is hard to handle in a general setting. Surprisingly, the Kerr-Schild ansatz brings again a huge simplification in how the related energy-momentum tensors are calculated. This allows us to explicitly characterize AdS waves supported by either a massless free scalar field or a wavefront-homogeneous Maxwell field. Considering the most general allowed Maxwell source instead is a highly nontrivial task, which we accomplish by again exploiting the complexified Euler-Darboux description and taking advantage of the classical Riemann method. In fact, this eventually allows us to find the most general configurations for any matter source.

Controlling rogue waves in inhomogeneous Bose-Einstein condensates.

PubMed

Loomba, Shally; Kaur, Harleen; Gupta, Rama; Kumar, C N; Raju, Thokala Soloman

2014-05-01

We present the exact rogue wave solutions of the quasi-one-dimensional inhomogeneous Gross-Pitaevskii equation by using similarity transformation. Then, by employing the exact analytical solutions we have studied the controllable behavior of rogue waves in the Bose-Einstein condensates context for the experimentally relevant systems. Additionally, we have also investigated the nonlinear tunneling of rogue waves through a conventional hyperbolic barrier and periodic barrier. We have found that, for the conventional nonlinearity barrier case, rogue waves are localized in space and time and get amplified near the barrier, while for the dispersion barrier case rogue waves are localized in space and propagating in time and their amplitude is reduced at the barrier location. In the case of the periodic barrier, the interesting dynamical features of rogue waves are obtained and analyzed analytically.

Exact Analytical Solutions for Elastodynamic Impact

DTIC Science & Technology

2015-11-30

corroborated by derivation of exact discrete solutions from recursive equations for the impact problems. 15. SUBJECT TERMS One-dimensional impact; Elastic...wave propagation; Laplace transform; Floor function; Discrete solutions 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18...impact Elastic wave propagation Laplace transform Floor function Discrete solutionsWe consider the one-dimensional impact problem in which a semi

Exact axisymmetric solutions of the Maxwell equations in a nonlinear nondispersive medium.

PubMed

Petrov, E Yu; Kudrin, A V

2010-05-14

The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of special importance and, at the same time, is an extremely complicated problem. It seems almost impossible to find a rigorous solution to such a problem even for any model of nonlinearity. We obtain the first exact solution of this type. We present a new method for deriving exact solutions of the Maxwell equations in a nonlinear medium without dispersion and give examples of the obtained solutions that describe propagation of cylindrical electromagnetic waves in a nonlinear nondispersive medium and free electromagnetic oscillations in a cylindrical cavity resonator filled with such a medium.

On the validity of the modified equation approach to the stability analysis of finite-difference methods

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1987-01-01

The validity of the modified equation stability analysis introduced by Warming and Hyett was investigated. It is shown that the procedure used in the derivation of the modified equation is flawed and generally leads to invalid results. Moreover, the interpretation of the modified equation as the exact partial differential equation solved by a finite-difference method generally cannot be justified even if spatial periodicity is assumed. For a two-level scheme, due to a series of mathematical quirks, the connection between the modified equation approach and the von Neuman method established by Warming and Hyett turns out to be correct despite its questionable original derivation. However, this connection is only partially valid for a scheme involving more than two time levels. In the von Neumann analysis, the complex error multiplication factor associated with a wave number generally has (L-1) roots for an L-level scheme. It is shown that the modified equation provides information about only one of these roots.

Gravitational waves in ghost free bimetric gravity

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

Mohseni, Morteza, E-mail: m-mohseni@pnu.ac.ir

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) extensionmore » of the theory admits similar solutions but in general is plagued with ghost instabilities.« less

Waves Generated by Asteroid Impacts and Their Hazard Consequences on The Shorelines

NASA Astrophysics Data System (ADS)

Ezzedine, S. M.; Miller, P. L.; Dearborn, D. S.

2014-12-01

We have performed numerical simulations of a hypothetical asteroid impact onto the ocean in support of an emergency preparedness, planning, and management exercise. We addressed the scenario from asteroid entry; to ocean impact (splash rim); to wave generation, propagation, and interaction with the shoreline. For the analysis we used GEODYN, a hydrocode, to simulate the impact and generate the source wave for the large-scale shallow water wave program, SWWP. Using state-of-the-art, high-performance computing codes we simulated three impact areas — two are located on the West Coast near Los Angeles's shoreline and the San Francisco Bay, respectively, and the third is located in the Gulf of Mexico, with a possible impact location between Texas and Florida. On account of uncertainty in the exact impact location within the asteroid risk corridor, we examined multiple possibilities for impact points within each area. Uncertainty in the asteroid impact location was then convolved and represented as uncertainty in the shoreline flooding zones. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, and partially funded by the Laboratory Directed Research and Development Program at LLNL under tracking code 12-ERD-005.

Pareto Joint Inversion of Love and Quasi Rayleigh's waves - synthetic study

NASA Astrophysics Data System (ADS)

Bogacz, Adrian; Dalton, David; Danek, Tomasz; Miernik, Katarzyna; Slawinski, Michael A.

2017-04-01

In this contribution the specific application of Pareto joint inversion in solving geophysical problem is presented. Pareto criterion combine with Particle Swarm Optimization were used to solve geophysical inverse problems for Love and Quasi Rayleigh's waves. Basic theory of forward problem calculation for chosen surface waves is described. To avoid computational problems some simplification were made. This operation allowed foster and more straightforward calculation without lost of solution generality. According to the solving scheme restrictions, considered model must have exact two layers, elastic isotropic surface layer and elastic isotropic half space with infinite thickness. The aim of the inversion is to obain elastic parameters and model geometry using dispersion data. In calculations different case were considered, such as different number of modes for different wave types and different frequencies. Created solutions are using OpenMP standard for parallel computing, which help in reduction of computational times. The results of experimental computations are presented and commented. This research was performed in the context of The Geomechanics Project supported by Husky Energy. Also, this research was partially supported by the Natural Sciences and Engineering Research Council of Canada, grant 238416-2013, and by the Polish National Science Center under contract No. DEC-2013/11/B/ST10/0472.

Traveling waves in Hall-magnetohydrodynamics and the ion-acoustic shock structure

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

Hagstrom, George I.; Hameiri, Eliezer

Hall-magnetohydrodynamics (HMHD) is a mixed hyperbolic-parabolic partial differential equation that describes the dynamics of an ideal two fluid plasma with massless electrons. We study the only shock wave family that exists in this system (the other discontinuities being contact discontinuities and not shocks). We study planar traveling wave solutions and we find solutions with discontinuities in the hydrodynamic variables, which arise due to the presence of real characteristics in Hall-MHD. We introduce a small viscosity into the equations and use the method of matched asymptotic expansions to show that solutions with a discontinuity satisfying the Rankine-Hugoniot conditions and also anmore » entropy condition have continuous shock structures. The lowest order inner equations reduce to the compressible Navier-Stokes equations, plus an equation which implies the constancy of the magnetic field inside the shock structure. We are able to show that the current is discontinuous across the shock, even as the magnetic field is continuous, and that the lowest order outer equations, which are the equations for traveling waves in inviscid Hall-MHD, are exactly integrable. We show that the inner and outer solutions match, which allows us to construct a family of uniformly valid continuous composite solutions that become discontinuous when the diffusivity vanishes.« less

Exact treatment of the Jaynes-Cummings model under the action of an external classical field

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

Abdalla, M. Sebawe, E-mail: m.sebaweh@physics.org; Khalil, E.M.; Mathematics Department, College of Science, Taibah University, Al-MaDinah

2011-09-15

We consider the usual Jaynes-Cummings model (JCM), in the presence of an external classical field. Under a certain canonical transformation for the Pauli operators, the system is transformed into the usual JCM. Using the equations of motion in the Heisenberg picture, exact solutions for the time-dependent dynamical operators are obtained. In order to calculate the expectation values of these operators, the wave function has been constructed. It has been shown that the classical field augments the atomic frequency {omega}{sub 0} and mixes the original atomic states. Changes of squeezing from one quadrature to another is also observed for a strongmore » value of the coupling parameter of the classical field. Furthermore, the system in this case displays partial entanglement and the state of the field losses its purity. - Highlights: > The time-dependent JCM, in the presence of the classical field, is still one of the essential problems in the quantum optics. > A new approach is applied through a certain canonical transformation. > The classical field augments the atomic frequency {omega}{sub 0} and mixes the original atomic states.« less

On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Putkaradze, Vakhtang

2015-08-01

We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We first derive the equations of motion directly, by using an Euler-Poincaré variational principle. We then justify this derivation with a more general theory elucidating the interesting mathematical concepts appearing in this problem, such as partial left (elastic) and right (fluid) invariance of the system, with the added holonomic constraint (volume). We analyze the fully nonlinear behavior of the model when the axis of the tube remains straight. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross section. Finally, we derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions.

Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

NASA Astrophysics Data System (ADS)

Rahmatullah; Ellahi, Rahmat; Mohyud-Din, Syed Tauseef; Khan, Umar

2018-03-01

We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses.

Turbulence regeneration in pipe flow at moderate Reynolds numbers.

PubMed

Hof, Björn; van Doorne, Casimir W H; Westerweel, Jerry; Nieuwstadt, Frans T M

2005-11-18

We present the results of an experimental investigation into the nature and structure of turbulent pipe flow at moderate Reynolds numbers. A turbulence regeneration mechanism is identified which sustains a symmetric traveling wave within the flow. The periodicity of the mechanism allows comparison to the wavelength of numerically observed exact traveling wave solutions and close agreement is found. The advection speed of the upstream turbulence laminar interface in the experimental flow is observed to form a lower bound on the phase velocities of the exact traveling wave solutions. Overall our observations suggest that the dynamics of the turbulent flow at moderate Reynolds numbers are governed by unstable nonlinear traveling waves.

Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G'/G)-expansion method.

PubMed

Alam, Md Nur; Akbar, M Ali

2013-01-01

The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.

On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Masood Khalique, Chaudry

2018-05-01

In this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.

Localization of massless Dirac particles via spatial modulations of the Fermi velocity

NASA Astrophysics Data System (ADS)

Downing, C. A.; Portnoi, M. E.

2017-08-01

The electrons found in Dirac materials are notorious for being difficult to manipulate due to the Klein phenomenon and absence of backscattering. Here we investigate how spatial modulations of the Fermi velocity in two-dimensional Dirac materials can give rise to localization effects, with either full (zero-dimensional) confinement or partial (one-dimensional) confinement possible depending on the geometry of the velocity modulation. We present several exactly solvable models illustrating the nature of the bound states which arise, revealing how the gradient of the Fermi velocity is crucial for determining fundamental properties of the bound states such as the zero-point energy. We discuss the implications for guiding electronic waves in few-mode waveguides formed by Fermi velocity modulation.

Networked dynamical systems with linear coupling: synchronisation patterns, coherence and other behaviours.

PubMed

Judd, Kevin

2013-12-01

Many physical and biochemical systems are well modelled as a network of identical non-linear dynamical elements with linear coupling between them. An important question is how network structure affects chaotic dynamics, for example, by patterns of synchronisation and coherence. It is shown that small networks can be characterised precisely into patterns of exact synchronisation and large networks characterised by partial synchronisation at the local and global scale. Exact synchronisation modes are explained using tools of symmetry groups and invariance, and partial synchronisation is explained by finite-time shadowing of exact synchronisation modes.

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…

On the exact solutions of high order wave equations of KdV type (I)

NASA Astrophysics Data System (ADS)

Bulut, Hasan; Pandir, Yusuf; Baskonus, Haci Mehmet

2014-12-01

In this paper, by means of a proper transformation and symbolic computation, we study high order wave equations of KdV type (I). We obtained classification of exact solutions that contain soliton, rational, trigonometric and elliptic function solutions by using the extended trial equation method. As a result, the motivation of this paper is to utilize the extended trial equation method to explore new solutions of high order wave equation of KdV type (I). This method is confirmed by applying it to this kind of selected nonlinear equations.

Towards an exact factorization of the molecular wave function

NASA Astrophysics Data System (ADS)

Parashar, Shubham; Sajeev, Y.; Ghosh, Swapan K.

2015-10-01

An exact single-product factorisation of the molecular wave function for the timedependent Schrödinger equation is investigated by using an ansatz involving a phase factor. By using the Frenkel variational method, we obtain the Schrödinger equations for the electronic and nuclear wave functions. The concept of a potential energy surface (PES) is retained by introducing a modified Hamiltonian as suggested earlier by Cederbaum. The parameter ω in the phase factor is chosen such that the equations of motion retain the physically appealing Born- Oppenheimer-like form, and is therefore unique.

Solutions of the cylindrical nonlinear Maxwell equations.

PubMed

Xiong, Hao; Si, Liu-Gang; Ding, Chunling; Lü, Xin-You; Yang, Xiaoxue; Wu, Ying

2012-01-01

Cylindrical nonlinear optics is a burgeoning research area which describes cylindrical electromagnetic wave propagation in nonlinear media. Finding new exact solutions for different types of nonlinearity and inhomogeneity to describe cylindrical electromagnetic wave propagation is of great interest and meaningful for theory and application. This paper gives exact solutions for the cylindrical nonlinear Maxwell equations and presents an interesting connection between the exact solutions for different cylindrical nonlinear Maxwell equations. We also provide some examples and discussion to show the application of the results we obtained. Our results provide the basis for solving complex systems of nonlinearity and inhomogeneity with simple systems.

Exact traveling soliton solutions for the generalized Benjamin-Bona-Mahony equation

NASA Astrophysics Data System (ADS)

Boudoue Hubert, Malwe; Kudryashov, Nikolai A.; Justin, Mibaile; Abbagari, Souleymanou; Betchewe, Gambo; Doka, Serge Y.

2018-03-01

In this paper, we investigate the generalized Benjamin-Bona-Mahony equation which better describes long waves with arbitrary power-law nonlinearity. As a result, we obtain exact travelling wave soliton solutions, such as anti-kink soliton solution, bright soliton solution, dark soliton solution and periodic solution. These solutions have many free parameters such that they may be used to simulate many experimental situations. The main contribution, in this work, is to not apply the computer codes for construction of exact solutions and not consider the integration constants as zero, because they give all variants for solutions.

Nodal surfaces and interdimensional degeneracies

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

Loos, Pierre-François, E-mail: pf.loos@anu.edu.au; Bressanini, Dario, E-mail: dario.bressanini@uninsubria.it

2015-06-07

The aim of this paper is to shed light on the topology and properties of the nodes (i.e., the zeros of the wave function) in electronic systems. Using the “electrons on a sphere” model, we study the nodes of two-, three-, and four-electron systems in various ferromagnetic configurations (sp, p{sup 2}, sd, pd, p{sup 3}, sp{sup 2}, and sp{sup 3}). In some particular cases (sp, p{sup 2}, sd, pd, and p{sup 3}), we rigorously prove that the non-interacting wave function has the same nodes as the exact (yet unknown) wave function. The number of atomic and molecular systems for whichmore » the exact nodes are known analytically is very limited and we show here that this peculiar feature can be attributed to interdimensional degeneracies. Although we have not been able to prove it rigorously, we conjecture that the nodes of the non-interacting wave function for the sp{sup 3} configuration are exact.« less

Bright, dark and W-shaped solitons with extended nonlinear Schrödinger's equation for odd and even higher-order terms

NASA Astrophysics Data System (ADS)

Bendahmane, Issam; Triki, Houria; Biswas, Anjan; Saleh Alshomrani, Ali; Zhou, Qin; Moshokoa, Seithuti P.; Belic, Milivoj

2018-02-01

We present solitary wave solutions of an extended nonlinear Schrödinger equation with higher-order odd (third-order) and even (fourth-order) terms by using an ansatz method. The including high-order dispersion terms have significant physical applications in fiber optics, the Heisenberg spin chain, and ocean waves. Exact envelope solutions comprise bright, dark and W-shaped solitary waves, illustrating the potentially rich set of solitary wave solutions of the extended model. Furthermore, we investigate the properties of these solitary waves in nonlinear and dispersive media. Moreover, specific constraints on the system parameters for the existence of these structures are discussed exactly. The results show that the higher-order dispersion and nonlinear effects play a crucial role for the formation and properties of propagating waves.

The extended Einstein-Maxwell-aether-axion model: Exact solutions for axionically controlled pp-wave aether modes

NASA Astrophysics Data System (ADS)

Balakin, Alexander B.

2018-03-01

The extended Einstein-Maxwell-aether-axion model describes internal interactions inside the system, which contains gravitational, electromagnetic fields, the dynamic unit vector field describing the velocity of an aether, and the pseudoscalar field associated with the axionic dark matter. The specific feature of this model is that the axion field controls the dynamics of the aether through the guiding functions incorporated into Jacobson’s constitutive tensor. Depending on the state of the axion field, these guiding functions can control and switch on or switch off the influence of acceleration, shear, vorticity and expansion of the aether flow on the state of physical system as a whole. We obtain new exact solutions, which possess the pp-wave symmetry, and indicate them by the term pp-wave aether modes in contrast to the pure pp-waves, which cannot propagate in this field conglomerate. These exact solutions describe a specific dynamic state of the pseudoscalar field, which corresponds to one of the minima of the axion potential and switches off the influence of shear and expansion of the aether flow; the model does not impose restrictions on Jacobson’s coupling constants and on the axion mass. Properties of these new exact solutions are discussed.

Nucleon-nucleon interactions from dispersion relations: Elastic partial waves

NASA Astrophysics Data System (ADS)

Albaladejo, M.; Oller, J. A.

2011-11-01

We consider nucleon-nucleon (NN) interactions from chiral effective field theory. In this work we restrict ourselves to the elastic NN scattering. We apply the N/D method to calculate the NN partial waves taking as input the one-pion exchange discontinuity along the left-hand cut. This discontinuity is amenable to a chiral power counting as discussed by Lacour, Oller, and Meißner [Ann. Phys. (NY)APNYA60003-491610.1016/j.aop.2010.06.012 326, 241 (2011)], with one-pion exchange as its leading order contribution. The resulting linear integral equation for a partial wave with orbital angular momentum ℓ≥2 is solved in the presence of ℓ-1 constraints, so as to guarantee the right behavior of the D- and higher partial waves near threshold. The calculated NN partial waves are based on dispersion relations and are independent of regulator. This method can also be applied to higher orders in the calculation of the discontinuity along the left-hand cut and extended to triplet coupled partial waves.

Waveguide effect under 'antiguiding' conditions in graded anisotropic media.

PubMed

Kozlov, A V; Mozhaev, V G; Zyryanova, A V

2010-02-24

A new wave confinement effect is predicted in graded crystals with a concave slowness surface under conditions of growth of the phase velocity with decreasing distance from the waveguide axis. This finding overturns the common notion about the guiding and 'antiguiding' profiles of wave velocity in inhomogeneous media. The waveguide effect found is elucidated by means of ray analysis and particular exact wave solutions. The exact solution obtained for localized flexural waves in thin plates of graded cubic and tetragonal crystals confirms the predicted effect. Since this solution is substantially different with respect to the existence conditions from all others yet reported, and it cannot be deduced from the previously known results, the predicted waves can be classified as a new type of waveguide mode in graded anisotropic media. Although the concrete calculations are given in the article for acoustic waves, its general predictions are expected to be valid for waves of various natures, including spin, plasma, and optical waves.

Transfer matrix approach to the persistent current in quantum rings: Application to hybrid normal-superconducting rings

NASA Astrophysics Data System (ADS)

Nava, Andrea; Giuliano, Rosa; Campagnano, Gabriele; Giuliano, Domenico

2016-11-01

Using the properties of the transfer matrix of one-dimensional quantum mechanical systems, we derive an exact formula for the persistent current across a quantum mechanical ring pierced by a magnetic flux Φ as a single integral of a known function of the system's parameters. Our approach provides exact results at zero temperature, which can be readily extended to a finite temperature T . We apply our technique to exactly compute the persistent current through p -wave and s -wave superconducting-normal hybrid rings, deriving full plots of the current as a function of the applied flux at various system's scales. Doing so, we recover at once a number of effects such as the crossover in the current periodicity on increasing the size of the ring and the signature of the topological phase transition in the p -wave case. In the limit of a large ring size, resorting to a systematic expansion in inverse powers of the ring length, we derive exact analytic closed-form formulas, applicable to a number of cases of physical interest.

A Gaussian wave packet phase-space representation of quantum canonical statistics

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

Coughtrie, David J.; Tew, David P.

2015-07-28

We present a mapping of quantum canonical statistical averages onto a phase-space average over thawed Gaussian wave-packet (GWP) parameters, which is exact for harmonic systems at all temperatures. The mapping invokes an effective potential surface, experienced by the wave packets, and a temperature-dependent phase-space integrand, to correctly transition from the GWP average at low temperature to classical statistics at high temperature. Numerical tests on weakly and strongly anharmonic model systems demonstrate that thermal averages of the system energy and geometric properties are accurate to within 1% of the exact quantum values at all temperatures.

A numerical comparison with an exact solution for the transient response of a cylinder immersed in a fluid. [computer simulated underwater tests to determine transient response of a submerged cylindrical shell

NASA Technical Reports Server (NTRS)

Giltrud, M. E.; Lucas, D. S.

1979-01-01

The transient response of an elastic cylindrical shell immersed in an acoustic media that is engulfed by a plane wave is determined numerically. The method applies to the USA-STAGS code which utilizes the finite element method for the structural analysis and the doubly asymptotic approximation for the fluid-structure interaction. The calculations are compared to an exact analysis for two separate loading cases: a plane step wave and an exponentially decaying plane wave.

Interference effects in phased beam tracing using exact half-space solutions.

PubMed

Boucher, Matthew A; Pluymers, Bert; Desmet, Wim

2016-12-01

Geometrical acoustics provides a correct solution to the wave equation for rectangular rooms with rigid boundaries and is an accurate approximation at high frequencies with nearly hard walls. When interference effects are important, phased geometrical acoustics is employed in order to account for phase shifts due to propagation and reflection. Error increases, however, with more absorption, complex impedance values, grazing incidence, smaller volumes and lower frequencies. Replacing the plane wave reflection coefficient with a spherical one reduces the error but results in slower convergence. Frequency-dependent stopping criteria are then applied to avoid calculating higher order reflections for frequencies that have already converged. Exact half-space solutions are used to derive two additional spherical wave reflection coefficients: (i) the Sommerfeld integral, consisting of a plane wave decomposition of a point source and (ii) a line of image sources located at complex coordinates. Phased beam tracing using exact half-space solutions agrees well with the finite element method for rectangular rooms with absorbing boundaries, at low frequencies and for rooms with different aspect ratios. Results are accurate even for long source-to-receiver distances. Finally, the crossover frequency between the plane and spherical wave reflection coefficients is discussed.

Harbingers and latecomers - the order of appearance of exact coherent structures in plane Poiseuille flow

NASA Astrophysics Data System (ADS)

Zammert, Stefan; Eckhardt, Bruno

2017-02-01

The transition to turbulence in plane Poiseuille flow (PPF) is connected with the presence of exact coherent structures. We here discuss a variety of different structures that are relevant for the transition, compare the critical Reynolds numbers and optimal wavelengths for their appearance, and explore the differences between flows operating at constant mass flux or at constant pressure drop. The Reynolds numbers quoted here are based on the mean flow velocity and refer to constant mass flux. Reynolds numbers based on constant pressure drop are always higher. The Tollmien-Schlichting (TS) waves bifurcate subcritically from the laminar profile at Re = 5772 at wavelength 6.16 and reach down to Re = 2610 at a different optimal wave length of 4.65. Their streamwise localised counter part bifurcates at the even lower value Re = 2334. Three-dimensional exact solutions appear at much lower Reynolds numbers. We describe one exact solutions that has a critical Reynolds number of 316. Streamwise localised versions of this state require higher Reynolds numbers, with the lowest bifurcation occurring near Re = 1018. The analysis shows that the various branches of TS-waves cannot be connected with transition observed near Re ≈ 1000 and that the exact coherent structures related to downstream vortices come in at lower Reynolds numbers and prepare for the transition.

Quantum Chemistry on Quantum Computers: A Polynomial-Time Quantum Algorithm for Constructing the Wave Functions of Open-Shell Molecules.

PubMed

Sugisaki, Kenji; Yamamoto, Satoru; Nakazawa, Shigeaki; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Takui, Takeji

2016-08-18

Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum. The proposed quantum algorithm enables us to prepare the wave function consisting of an exponential number of Slater determinants only by a polynomial number of quantum operations.

Analysis of dispersion and attenuation of surface waves in poroelastic media in the exploration-seismic frequency band

USGS Publications Warehouse

Zhang, Y.; Xu, Y.; Xia, J.

2011-01-01

We analyse dispersion and attenuation of surface waves at free surfaces of possible vacuum/poroelastic media: permeable-'open pore', impermeable-'closed pore' and partially permeable boundaries, which have not been previously reported in detail by researchers, under different surface-permeable, viscous-damping, elastic and fluid-flowing conditions. Our discussion is focused on their characteristics in the exploration-seismic frequency band (a few through 200 Hz) for near-surface applications. We find two surface-wave modes exist, R1 waves for all conditions, and R2 waves for closed-pore and partially permeable conditions. For R1 waves, velocities disperse most under partially permeable conditions and least under the open-pore condition. High-coupling damping coefficients move the main dispersion frequency range to high frequencies. There is an f1 frequency dependence as a constant-Q model for attenuation at high frequencies. R1 waves for the open pore are most sensitive to elastic modulus variation, but least sensitive to tortuosities variation. R1 waves for partially permeable surface radiate as non-physical waves (Im(k) < 0) at low frequencies. For R2 waves, velocities are slightly lower than the bulk slow P2 waves. At low frequencies, both velocity and attenuation are diffusive of f1/2 frequency dependence, as P2 waves. It is found that for partially permeable surfaces, the attenuation displays -f1 frequency dependence as frequency increasing. High surface permeability, low-coupling damping coefficients, low Poisson's ratios, and low tortuosities increase the slope of the -f1 dependence. When the attenuation coefficients reach 0, R2 waves for partially permeable surface begin to radiate as non-physical waves. ?? 2011 The Authors Geophysical Journal International ?? 2011 RAS.

Exact relativistic expressions for wave refraction in a generally moving fluid.

PubMed

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.

Wave propagation model of heat conduction and group speed

NASA Astrophysics Data System (ADS)

Zhang, Long; Zhang, Xiaomin; Peng, Song

2018-03-01

In view of the finite relaxation model of non-Fourier's law, the Cattaneo and Vernotte (CV) model and Fourier's law are presented in this work for comparing wave propagation modes. Independent variable translation is applied to solve the partial differential equation. Results show that the general form of the time spatial distribution of temperature for the three media comprises two solutions: those corresponding to the positive and negative logarithmic heating rates. The former shows that a group of heat waves whose spatial distribution follows the exponential function law propagates at a group speed; the speed of propagation is related to the logarithmic heating rate. The total speed of all the possible heat waves can be combined to form the group speed of the wave propagation. The latter indicates that the spatial distribution of temperature, which follows the exponential function law, decays with time. These features show that propagation accelerates when heated and decelerates when cooled. For the model media that follow Fourier's law and correspond to the positive heat rate of heat conduction, the propagation mode is also considered the propagation of a group of heat waves because the group speed has no upper bound. For the finite relaxation model with non-Fourier media, the interval of group speed is bounded and the maximum speed can be obtained when the logarithmic heating rate is exactly the reciprocal of relaxation time. And for the CV model with a non-Fourier medium, the interval of group speed is also bounded and the maximum value can be obtained when the logarithmic heating rate is infinite.

An Efficient Approximation of the Coronal Heating Rate for use in Global Sun-Heliosphere Simulations

NASA Astrophysics Data System (ADS)

Cranmer, Steven R.

2010-02-01

The origins of the hot solar corona and the supersonically expanding solar wind are still the subject of debate. A key obstacle in the way of producing realistic simulations of the Sun-heliosphere system is the lack of a physically motivated way of specifying the coronal heating rate. Recent one-dimensional models have been found to reproduce many observed features of the solar wind by assuming the energy comes from Alfvén waves that are partially reflected, then dissipated by magnetohydrodynamic turbulence. However, the nonlocal physics of wave reflection has made it difficult to apply these processes to more sophisticated (three-dimensional) models. This paper presents a set of robust approximations to the solutions of the linear Alfvén wave reflection equations. A key ingredient of the turbulent heating rate is the ratio of inward-to-outward wave power, and the approximations developed here allow this to be written explicitly in terms of local plasma properties at any given location. The coronal heating also depends on the frequency spectrum of Alfvén waves in the open-field corona, which has not yet been measured directly. A model-based assumption is used here for the spectrum, but the results of future measurements can be incorporated easily. The resulting expression for the coronal heating rate is self-contained, computationally efficient, and applicable directly to global models of the corona and heliosphere. This paper tests and validates the approximations by comparing the results to exact solutions of the wave transport equations in several cases relevant to the fast and slow solar wind.

Kuramoto model of coupled oscillators with positive and negative coupling parameters: an example of conformist and contrarian oscillators.

PubMed

Hong, Hyunsuk; Strogatz, Steven H

2011-02-04

We consider a generalization of the Kuramoto model in which the oscillators are coupled to the mean field with random signs. Oscillators with positive coupling are "conformists"; they are attracted to the mean field and tend to synchronize with it. Oscillators with negative coupling are "contrarians"; they are repelled by the mean field and prefer a phase diametrically opposed to it. The model is simple and exactly solvable, yet some of its behavior is surprising. Along with the stationary states one might have expected (a desynchronized state, and a partially-synchronized state, with conformists and contrarians locked in antiphase), it also displays a traveling wave, in which the mean field oscillates at a frequency different from the population's mean natural frequency.

On the comparison of perturbation-iteration algorithm and residual power series method to solve fractional Zakharov-Kuznetsov equation

NASA Astrophysics Data System (ADS)

Şenol, Mehmet; Alquran, Marwan; Kasmaei, Hamed Daei

2018-06-01

In this paper, we present analytic-approximate solution of time-fractional Zakharov-Kuznetsov equation. This model demonstrates the behavior of weakly nonlinear ion acoustic waves in a plasma bearing cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Basic definitions of fractional derivatives are described in the Caputo sense. Perturbation-iteration algorithm (PIA) and residual power series method (RPSM) are applied to solve this equation with success. The convergence analysis is also presented for both methods. Numerical results are given and then they are compared with the exact solutions. Comparison of the results reveal that both methods are competitive, powerful, reliable, simple to use and ready to apply to wide range of fractional partial differential equations.

Bifurcations of solitary wave solutions for (two and three)-dimensional nonlinear partial differential equation in quantum and magnetized plasma by using two different methods

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-06-01

In this research, we study new two techniques that called the extended simple equation method and the novel (G‧/G) -expansion method. The extended simple equation method depend on the auxiliary equation (dϕ/dξ = α + λϕ + μϕ2) which has three ways for solving depends on the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (α = 0) this auxiliary equation reduces to Bernoulli equation and when (α ≠ 0, λ ≠ 0, μ ≠ 0) we the general solutions of this auxiliary equation while the novel (G‧/G) -expansion method depends also on similar auxiliary equation (G‧/G)‧ = μ + λ(G‧/G) + (v - 1)(G‧/G) 2 which depend also on the value of (λ2 - 4 (v - 1) μ) and the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (μ = 0) this auxiliary equation reduces to Bernoulli equation and when (λ2 ≠ 4 (v - 1) μ) we the general solutions of this auxiliary equation. This show how both of these auxiliary equation are special cases of Riccati equation. We apply these methods on two dimensional nonlinear Kadomtsev-Petviashvili Burgers equation in quantum plasma and three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. We obtain the exact traveling wave solutions of these important models and under special condition on the parameters, we get solitary traveling wave solutions. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions.

A highly accurate finite-difference method with minimum dispersion error for solving the Helmholtz equation

NASA Astrophysics Data System (ADS)

Wu, Zedong; Alkhalifah, Tariq

2018-07-01

Numerical simulation of the acoustic wave equation in either isotropic or anisotropic media is crucial to seismic modeling, imaging and inversion. Actually, it represents the core computation cost of these highly advanced seismic processing methods. However, the conventional finite-difference method suffers from severe numerical dispersion errors and S-wave artifacts when solving the acoustic wave equation for anisotropic media. We propose a method to obtain the finite-difference coefficients by comparing its numerical dispersion with the exact form. We find the optimal finite difference coefficients that share the dispersion characteristics of the exact equation with minimal dispersion error. The method is extended to solve the acoustic wave equation in transversely isotropic (TI) media without S-wave artifacts. Numerical examples show that the method is highly accurate and efficient.

Exact result in strong wave turbulence of thin elastic plates

NASA Astrophysics Data System (ADS)

Düring, Gustavo; Krstulovic, Giorgio

2018-02-01

An exact result concerning the energy transfers between nonlinear waves of a thin elastic plate is derived. Following Kolmogorov's original ideas in hydrodynamical turbulence, but applied to the Föppl-von Kármán equation for thin plates, the corresponding Kármán-Howarth-Monin relation and an equivalent of the 4/5 -Kolmogorov's law is derived. A third-order structure function involving increments of the amplitude, velocity, and the Airy stress function of a plate, is proven to be equal to -ɛ ℓ , where ℓ is a length scale in the inertial range at which the increments are evaluated and ɛ the energy dissipation rate. Numerical data confirm this law. In addition, a useful definition of the energy fluxes in Fourier space is introduced and proven numerically to be flat in the inertial range. The exact results derived in this Rapid Communication are valid for both weak and strong wave turbulence. They could be used as a theoretical benchmark of new wave-turbulence theories and to develop further analogies with hydrodynamical turbulence.

A procedure to construct exact solutions of nonlinear fractional differential equations.

PubMed

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.

Görtler instability of the axisymmetric boundary layer along a cone

NASA Astrophysics Data System (ADS)

ITOH, Nobutake

2014-10-01

Exact partial differential equations are derived to describe Görtler instability, caused by a weakly concave wall, of axisymmetric boundary layers with similar velocity profiles that are decomposed into a sequence of ordinary differential systems on the assumption that the solution can be expanded into inverse powers of local Reynolds number. The leading terms of the series solution are determined by solving a non-parallel version of Görtler’s eigenvalue problem and lead to a neutral stability curve and finite values of critical Görtler number and wave number for stationary and longitudinal vortices. Higher-order terms of the series solution indicate Reynolds-number dependence of Görtler instability and a limited validity of Görtler’s approximation based on the leading terms only. The present formulation is simply applicable to two-dimensional boundary layers of similar profiles, and critical Görtler number and wave number of the Blasius boundary layer on a flat plate are given by G2c = 1.23 and β2c = 0.288, respectively, if the momentum thickness is chosen as the reference length.

Propagation of large-amplitude waves on dielectric liquid sheets in a tangential electric field: exact solutions in three-dimensional geometry.

PubMed

Zubarev, Nikolay M; Zubareva, Olga V

2010-10-01

Nonlinear waves on sheets of dielectric liquid in the presence of an external tangential electric field are studied theoretically. It is shown that waves of arbitrary shape in three-dimensional geometry can propagate along (or against) the electric field direction without distortion, i.e., the equations of motion admit a wide class of exact traveling wave solutions. This unusual situation occurs for nonconducting ideal liquids with high dielectric constants in the case of a sufficiently strong field strength. Governing equations for evolution of plane symmetric waves on fluid sheets are derived using conformal variables. A dispersion relation for the evolution of small perturbations of the traveling wave solutions is obtained. It follows from this relation that, regardless of the wave shape, the amplitudes of small-scale perturbations do not increase with time and, hence, the traveling waves are stable. We also study the interaction of counterpropagating symmetric waves with small but finite amplitudes. The corresponding solution of the equations of motion describes the nonlinear superposition of the oppositely directed waves. The results obtained are applicable for the description of long waves on fluid sheets in a horizontal magnetic field.

A generalized simplest equation method and its application to the Boussinesq-Burgers equation.

PubMed

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.

A Generalized Simplest Equation Method and Its Application to the Boussinesq-Burgers Equation

PubMed Central

Sudao, Bilige; Wang, Xiaomin

2015-01-01

In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method. PMID:25973605

Correlated electron-nuclear dynamics with conditional wave functions.

PubMed

Albareda, Guillermo; Appel, Heiko; Franco, Ignacio; Abedi, Ali; Rubio, Angel

2014-08-22

The molecular Schrödinger equation is rewritten in terms of nonunitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear) trajectories. This scheme is exact and does not rely on the tracing out of degrees of freedom. Hence, the use of trajectory-based statistical techniques can be exploited to circumvent the calculation of the computationally demanding Born-Oppenheimer potential-energy surfaces and nonadiabatic coupling elements. The concept of the potential-energy surface is restored by establishing a formal connection with the exact factorization of the full wave function. This connection is used to gain insight from a simplified form of the exact propagation scheme.

Exact closed-form solutions of a fully nonlinear asymptotic two-fluid model

NASA Astrophysics Data System (ADS)

Cheviakov, Alexei F.

2018-05-01

A fully nonlinear model of Choi and Camassa (1999) describing one-dimensional incompressible dynamics of two non-mixing fluids in a horizontal channel, under a shallow water approximation, is considered. An equivalence transformation is presented, leading to a special dimensionless form of the system, involving a single dimensionless constant physical parameter, as opposed to five parameters present in the original model. A first-order dimensionless ordinary differential equation describing traveling wave solutions is analyzed. Several multi-parameter families of physically meaningful exact closed-form solutions of the two-fluid model are derived, corresponding to periodic, solitary, and kink-type bidirectional traveling waves; specific examples are given, and properties of the exact solutions are analyzed.

Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation

NASA Technical Reports Server (NTRS)

Karney, C. F. F.

1977-01-01

Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.

The memory effect for plane gravitational waves

NASA Astrophysics Data System (ADS)

Zhang, P.-M.; Duval, C.; Gibbons, G. W.; Horvathy, P. A.

2017-09-01

We give an account of the gravitational memory effect in the presence of the exact plane wave solution of Einstein's vacuum equations. This allows an elementary but exact description of the soft gravitons and how their presence may be detected by observing the motion of freely falling particles. The theorem of Bondi and Pirani on caustics (for which we present a new proof) implies that the asymptotic relative velocity is constant but not zero, in contradiction with the permanent displacement claimed by Zel'dovich and Polnarev. A non-vanishing asymptotic relative velocity might be used to detect gravitational waves through the "velocity memory effect", considered by Braginsky, Thorne, Grishchuk, and Polnarev.

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.

Explicit Solutions and Bifurcations for a Class of Generalized Boussinesq Wave Equation

NASA Astrophysics Data System (ADS)

Ma, Zhi-Min; Sun, Yu-Huai; Liu, Fu-Sheng

2013-03-01

In this paper, the generalized Boussinesq wave equation utt — uxx + a(um)xx + buxxxx = 0 is investigated by using the bifurcation theory and the method of phase portraits analysis. Under the different parameter conditions, the exact explicit parametric representations for solitary wave solutions and periodic wave solutions are obtained.

A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

PubMed Central

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

Class of exactly solvable scattering potentials in two dimensions, entangled-state pair generation, and a grazing-angle resonance effect

NASA Astrophysics Data System (ADS)

Loran, Farhang; Mostafazadeh, Ali

2017-12-01

We provide an exact solution of the scattering problem for the potentials of the form v (x ,y ) =χa(x ) [v0(x ) +v1(x ) ei α y] , where χa(x ) :=1 for x ∈[0 ,a ] , χa(x ) :=0 for x ∉[0 ,a ] , vj(x ) are real or complex-valued functions, χa(x ) v0(x ) is an exactly solvable scattering potential in one dimension, and α is a positive real parameter. If α exceeds the wave number k of the incident wave, the scattered wave does not depend on the choice of v1(x ) . In particular, v (x ,y ) is invisible if v0(x ) =0 and k <α . For k >α and v1(x ) ≠0 , the scattered wave consists of a finite number of coherent plane-wave pairs ψn± with wave vector: kn=(±√{k2-[nα ] 2 },n α ) , where n =0 ,1 ,2 ,...

Effects of partial sleep deprivation on slow waves during non-rapid eye movement sleep: A high density EEG investigation.

PubMed

Plante, David T; Goldstein, Michael R; Cook, Jesse D; Smith, Richard; Riedner, Brady A; Rumble, Meredith E; Jelenchick, Lauren; Roth, Andrea; Tononi, Giulio; Benca, Ruth M; Peterson, Michael J

2016-02-01

Changes in slow waves during non-rapid eye movement (NREM) sleep in response to acute total sleep deprivation are well-established measures of sleep homeostasis. This investigation utilized high-density electroencephalography (hdEEG) to examine topographic changes in slow waves during repeated partial sleep deprivation. Twenty-four participants underwent a 6-day sleep restriction protocol. Spectral and period-amplitude analyses of sleep hdEEG data were used to examine changes in slow wave energy, count, amplitude, and slope relative to baseline. Changes in slow wave energy were dependent on the quantity of NREM sleep utilized for analysis, with widespread increases during sleep restriction and recovery when comparing data from the first portion of the sleep period, but restricted to recovery sleep if the entire sleep episode was considered. Period-amplitude analysis was less dependent on the quantity of NREM sleep utilized, and demonstrated topographic changes in the count, amplitude, and distribution of slow waves, with frontal increases in slow wave amplitude, numbers of high-amplitude waves, and amplitude/slopes of low amplitude waves resulting from partial sleep deprivation. Topographic changes in slow waves occur across the course of partial sleep restriction and recovery. These results demonstrate a homeostatic response to partial sleep loss in humans. Copyright © 2015 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

General Notions on Macroscopic Theory of Waves in Plasmas; NOTIONS GENERALES SUR LA THEORIE MACROSCOPIQUE DES ONDES DANS LES PLASMAS

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

Allis, W.P.; Delcroix, J.L.

1963-01-01

The propagation of monochromatic plane waves in an indefinite plasma is treated in the hydrodynamic theory of two fluids. Plasmas with isotropic pressure and waves obeying exact adiabaticity are considered. (D.C.W.)

Nondiffracting wave beams in non-Hermitian Glauber-Fock lattice

NASA Astrophysics Data System (ADS)

Oztas, Z.

2018-05-01

We theoretically study non-Hermitian Glauber-Fock lattice with nonuniform hopping. We show how to engineer this lattice to get nondiffracting wave beams and find an exact analytical solution to nondiffracting localized waves. The exceptional points in the energy spectrum are also analyzed.

Characterization of the reference wave in a compact digital holographic camera.

PubMed

Park, I S; Middleton, R J C; Coggrave, C R; Ruiz, P D; Coupland, J M

2018-01-01

A hologram is a recording of the interference between an unknown object wave and a coherent reference wave. Providing the object and reference waves are sufficiently separated in some region of space and the reference beam is known, a high-fidelity reconstruction of the object wave is possible. In traditional optical holography, high-quality reconstruction is achieved by careful reillumination of the holographic plate with the exact same reference wave that was used at the recording stage. To reconstruct high-quality digital holograms the exact parameters of the reference wave must be known mathematically. This paper discusses a technique that obtains the mathematical parameters that characterize a strongly divergent reference wave that originates from a fiber source in a new compact digital holographic camera. This is a lensless design that is similar in principle to a Fourier hologram, but because of the large numerical aperture, the usual paraxial approximations cannot be applied and the Fourier relationship is inexact. To characterize the reference wave, recordings of quasi-planar object waves are made at various angles of incidence using a Dammann grating. An optimization process is then used to find the reference wave that reconstructs a stigmatic image of the object wave regardless of the angle of incidence.

Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

NASA Astrophysics Data System (ADS)

Liu, Ping; Wang, Ya-Xiong; Ren, Bo; Li, Jin-Hua

2016-12-01

Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. Supported by the National Natural Science Foundation of China under Grant Nos. 11305031 and 11305106, and Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No. Yq2013205

SH3BP1-induced Rac-Wave2 pathway activation regulates cervical cancer cell migration, invasion, and chemoresistance to cisplatin.

PubMed

Wang, Jingjing; Feng, Yeqian; Chen, Xishan; Du, Zheng; Jiang, Shaijun; Ma, Shuyun; Zou, Wen

2018-02-01

Cervical cancer still remains the fourth most common cancer, affecting women worldwide with large geographic variations in cervical cancer incidence and mortality rates. SH3-domain binding protein-1 (SH3BP1) specifically inactivating Rac1 and its target Wave2 is required for cell motility, thus regarded as an essential regulator of cancer cell metastasis. However, the exact effects and molecular mechanisms of SH3BP1 in cervical cancer progression are still unknown. The present study is aimed to investigate the mechanism of SH3BP1 in regulation of cervical cancer cell metastasis and chemoresistance. In the present study, we demonstrated a high SH3BP1 expression in cervical cancer tissues; a higher SH3BP1 expression is also correlated with a shorter overall survival of patients with cervical cancer. Further, we revealed that SH3BP1 overexpression promoted the invasion, migration, and chemoresistance of cervical cancer cell through increasing Rac1 activity and Wave2 protein level. The promotive effect of SH3BP1 could be partially reversed by a Rac1 inhibitor, NSC 23766. In cisplatin-resistant cervical cancer tissues, SH3BP1, Rac1, and Wave2 mRNA expression was significantly up-regulated compared to that of the cisplatin-sensitive cervical cancer tissues. Taken together, SH3BP1/Rac1/Wave2 pathway may potentially act as an effective therapeutic target combined with traditional cisplatin-based chemotherapy for cervical cancer. © 2017 Wiley Periodicals, Inc.

Exact traveling wave solutions for system of nonlinear evolution equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H

2016-01-01

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.

Twisted rogue-wave pairs in the Sasa-Satsuma equation.

PubMed

Chen, Shihua

2013-08-01

Exact explicit rogue wave solutions of the Sasa-Satsuma equation are obtained by use of a Darboux transformation. In addition to the double-peak structure and an analog of the Peregrine soliton, the rogue wave can exhibit an intriguing twisted rogue-wave pair that involves four well-defined zero-amplitude points. This exotic structure may enrich our understanding on the nature of rogue waves.

Observations of running penumbral waves.

NASA Technical Reports Server (NTRS)

Zirin, H.; Stein, A.

1972-01-01

Quiet sunspots with well-developed penumbrae show running intensity waves with period running around 300 sec. The waves appear connected with umbral flashes of exactly half the period. Waves are concentric, regular, with velocity constant around 10 km/sec. They are probably sound waves and show intensity fluctuation in H alpha centerline or wing of 10 to 20%. The energy is tiny compared to the heat deficit of the umbra.

Amplitude reconstruction from complete photoproduction experiments and truncated partial-wave expansions

NASA Astrophysics Data System (ADS)

Workman, R. L.; Tiator, L.; Wunderlich, Y.; Döring, M.; Haberzettl, H.

2017-01-01

We compare the methods of amplitude reconstruction, for a complete experiment and a truncated partial-wave analysis, applied to the photoproduction of pseudoscalar mesons. The approach is pedagogical, showing in detail how the amplitude reconstruction (observables measured at a single energy and angle) is related to a truncated partial-wave analysis (observables measured at a single energy and a number of angles).

Amplitude reconstruction from complete photoproduction experiments and truncated partial-wave expansions

DOE PAGES

Workman, R. L.; Tiator, L.; Wunderlich, Y.; ...

2017-01-19

Here, we compare the methods of amplitude reconstruction, for a complete experiment and a truncated partial-wave analysis, applied to the photoproduction of pseudoscalar mesons. The approach is pedagogical, showing in detail how the amplitude reconstruction (observables measured at a single energy and angle) is related to a truncated partial-wave analysis (observables measured at a single energy and a number of angles).

Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs

NASA Astrophysics Data System (ADS)

Vitanov, Nikolay K.

2011-03-01

We discuss the class of equations ∑i,j=0mAij(u){∂iu}/{∂ti}∂+∑k,l=0nBkl(u){∂ku}/{∂xk}∂=C(u) where Aij( u), Bkl( u) and C( u) are functions of u( x, t) as follows: (i) Aij, Bkl and C are polynomials of u; or (ii) Aij, Bkl and C can be reduced to polynomials of u by means of Taylor series for small values of u. For these two cases the above-mentioned class of equations consists of nonlinear PDEs with polynomial nonlinearities. We show that the modified method of simplest equation is powerful tool for obtaining exact traveling-wave solution of this class of equations. The balance equations for the sub-class of traveling-wave solutions of the investigated class of equations are obtained. We illustrate the method by obtaining exact traveling-wave solutions (i) of the Swift-Hohenberg equation and (ii) of the generalized Rayleigh equation for the cases when the extended tanh-equation or the equations of Bernoulli and Riccati are used as simplest equations.

New trial wave function for the nuclear cluster structure of nuclei

NASA Astrophysics Data System (ADS)

Zhou, Bo

2018-04-01

A new trial wave function is proposed for nuclear cluster physics, in which an exact solution to the long-standing center-of-mass problem is given. In the new approach, the widths of the single-nucleon Gaussian wave packets and the widths of the relative Gaussian wave functions describing correlations of nucleons or clusters are treated as variables in the explicit intrinsic wave function of the nuclear system. As an example, this new wave function was applied to study the typical {^{20}Ne} (α+{{^{16}}O}) cluster system. By removing exactly the spurious center-of-mass effect in a very simple way, the energy curve of {^{20}Ne} was obtained by variational calculations with the width of the α cluster, the width of the {{^{16}}O} cluster, and the size parameter of the nucleus. These are considered the three crucial variational variables in describing the {^{20}Ne} (α+{{^{16}}O}) cluster system. This shows that the new wave function can be a very interesting new tool for studying many-body and cluster effects in nuclear physics.

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2010-01-29

... Partially Exclusive Licensing of U.S. Provisional Patent Application Concerning Blast Wave Sensor AGENCY... ``Blast Wave Sensor,'' filed January 4, 2010. The United States Government, as represented by the... wave sensors and their use to detect blast induced pressure changes, and, in particular, a blast wave...

A low-dispersion, exactly energy-charge-conserving semi-implicit relativistic particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, Guangye; Luis, Chacon; Bird, Robert; Stark, David; Yin, Lin; Albright, Brian

2017-10-01

Leap-frog based explicit algorithms, either ``energy-conserving'' or ``momentum-conserving'', do not conserve energy discretely. Time-centered fully implicit algorithms can conserve discrete energy exactly, but introduce large dispersion errors in the light-wave modes, regardless of timestep sizes. This can lead to intolerable simulation errors where highly accurate light propagation is needed (e.g. laser-plasma interactions, LPI). In this study, we selectively combine the leap-frog and Crank-Nicolson methods to produce a low-dispersion, exactly energy-and-charge-conserving PIC algorithm. Specifically, we employ the leap-frog method for Maxwell equations, and the Crank-Nicolson method for particle equations. Such an algorithm admits exact global energy conservation, exact local charge conservation, and preserves the dispersion properties of the leap-frog method for the light wave. The algorithm has been implemented in a code named iVPIC, based on the VPIC code developed at LANL. We will present numerical results that demonstrate the properties of the scheme with sample test problems (e.g. Weibel instability run for 107 timesteps, and LPI applications.

Wave interactions in a three-dimensional attachment line boundary layer

NASA Technical Reports Server (NTRS)

Hall, Philip; Mackerrell, Sharon O.

1988-01-01

The 3-D boundary layer on a swept wing can support different types of hydrodynamic instability. Attention is focused on the so-called spanwise contamination problem, which occurs when the attachment line boundary layer on the leading edge becomes unstable to Tollmien-Schlichting waves. In order to gain insight into the interactions important in that problem, a simplified basic state is considered. This simplified flow corresponds to the swept attachment line boundary layer on an infinite flat plate. The basic flow here is an exact solution of the Navier-Stokes equations and its stability to 2-D waves propagating along the attachment can be considered exactly at finite Reynolds number. This has been done in the linear and weakly nonlinear regimes. The corresponding problem is studied for oblique waves and their interaction with 2-D waves is investigated. In fact, oblique modes cannot be described exactly at finite Reynolds number so it is necessary to make a high Reynolds number approximation and use triple deck theory. It is shown that there are two types of oblique wave which, if excited, cause the destabilization of the 2-D mode and the breakdown of the disturbed flow at a finite distance from the leading edge. First, a low frequency mode related to the viscous stationary crossflow mode is a possible cause of breakdown. Second, a class of oblique wave with frequency comparable with that of the 2-D mode is another cause of breakdown. It is shown that the relative importance of the modes depends on the distance from the attachment line.

Gaussian and Airy wave packets of massive particles with orbital angular momentum

NASA Astrophysics Data System (ADS)

Karlovets, Dmitry V.

2015-01-01

While wave-packet solutions for relativistic wave equations are oftentimes thought to be approximate (paraxial), we demonstrate, by employing a null-plane- (light-cone-) variable formalism, that there is a family of such solutions that are exact. A scalar Gaussian wave packet in the transverse plane is generalized so that it acquires a well-defined z component of the orbital angular momentum (OAM), while it may not acquire a typical "doughnut" spatial profile. Such quantum states and beams, in contrast to the Bessel states, may have an azimuthal-angle-dependent probability density and finite uncertainty of the OAM, which is determined by the packet's width. We construct a well-normalized Airy wave packet, which can be interpreted as a one-particle state for a relativistic massive boson, show that its center moves along the same quasiclassical straight path, and, which is more important, spreads with time and distance exactly as a Gaussian wave packet does, in accordance with the uncertainty principle. It is explained that this fact does not contradict the well-known "nonspreading" feature of the Airy beams. While the effective OAM for such states is zero, its uncertainty (or the beam's OAM bandwidth) is found to be finite, and it depends on the packet's parameters. A link between exact solutions for the Klein-Gordon equation in the null-plane-variable formalism and the approximate ones in the usual approach is indicated; generalizations of these states for a boson in the external field of a plane electromagnetic wave are also presented.

Causal properties of nonlinear gravitational waves in modified gravity

NASA Astrophysics Data System (ADS)

Suvorov, Arthur George; Melatos, Andrew

2017-09-01

Some exact, nonlinear, vacuum gravitational wave solutions are derived for certain polynomial f (R ) gravities. We show that the boundaries of the gravitational domain of dependence, associated with events in polynomial f (R ) gravity, are not null as they are in general relativity. The implication is that electromagnetic and gravitational causality separate into distinct notions in modified gravity, which may have observable astrophysical consequences. The linear theory predicts that tachyonic instabilities occur, when the quadratic coefficient a2 of the Taylor expansion of f (R ) is negative, while the exact, nonlinear, cylindrical wave solutions presented here can be superluminal for all values of a2. Anisotropic solutions are found, whose wave fronts trace out time- or spacelike hypersurfaces with complicated geometric properties. We show that the solutions exist in f (R ) theories that are consistent with Solar System and pulsar timing experiments.

Trial wave functions for a composite Fermi liquid on a torus

NASA Astrophysics Data System (ADS)

Fremling, M.; Moran, N.; Slingerland, J. K.; Simon, S. H.

2018-01-01

We study the two-dimensional electron gas in a magnetic field at filling fraction ν =1/2 . At this filling the system is in a gapless state which can be interpreted as a Fermi liquid of composite fermions. We construct trial wave functions for the system on a torus, based on this idea, and numerically compare these to exact wave functions for small systems found by exact diagonalization. We find that the trial wave functions give an excellent description of the ground state of the system, as well as its charged excitations, in all momentum sectors. We analyze the dispersion of the composite fermions and the Berry phase associated with dragging a single fermion around the Fermi surface and comment on the implications of our results for the current debate on whether composite fermions are Dirac fermions.

Propagation of arbitrary initial wave packets in a quantum parametric oscillator: Instability zones for higher order moments

NASA Astrophysics Data System (ADS)

Biswas, Subhadip; Chattopadhyay, Rohitashwa; Bhattacharjee, Jayanta K.

2018-05-01

We consider the dynamics of a particle in a parametric oscillator with a view to exploring any quantum feature of the initial wave packet that shows divergent (in time) behaviour for parameter values where the classical motion dynamics of the mean position is bounded. We use Ehrenfest's theorem to explore the dynamics of nth order moment which reduces exactly to a linear non autonomous differential equation of order n + 1. It is found that while the width and skewness of the packet is unbounded exactly in the zones where the classical motion is unbounded, the kurtosis of an initially non-gaussian wave packet can become infinitely large in certain additional zones. This implies that the shape of the wave packet can change drastically with time in these zones.

Evolution of nonlinear waves in a blood-filled artery with an aneurysm

NASA Astrophysics Data System (ADS)

Nikolova, E. V.; Jordanov, I. P.; Dimitrova, Z. I.; Vitanov, N. K.

2017-10-01

We discuss propagation of traveling waves in a blood-filled hyper-elastic artery with a local dilatation (an aneurysm). The processes in the injured artery are modeled by an equation of the motion of the arterial wall and by equations of the motion of the fluid (the blood). Taking into account the specific arterial geometry and applying the reductive perturbation method in long-wave approximation we reduce the model equations to a version of the perturbed Korteweg-de Vries kind equation with variable coefficients. Exact traveling-wave solutions of this equation are obtained by the modified method of simplest equation where the differential equation of Abel is used as a simplest equation. A particular case of the obtained exact solution is numerically simulated and discussed from the point of view of arterial disease mechanics.

Colliding impulsive gravitational waves

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

Nutku, Y.; Halil, M.

1977-11-28

We formulate the problem of colliding plane gravitational waves with two polarizations as the harmonic mappings of Riemannian manifolds and construct an exact solution of the vacuum Einstein field equations describing the interaction of colliding impulsive gravitational waves which in the limit of collinear polarization reduces to the solution of Khan and Penrose.

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.

Nodal-line dynamics via exact polynomial solutions for coherent waves traversing aberrated imaging systems.

PubMed

Paganin, David M; Beltran, Mario A; Petersen, Timothy C

2018-03-01

We obtain exact polynomial solutions for two-dimensional coherent complex scalar fields propagating through arbitrary aberrated shift-invariant linear imaging systems. These solutions are used to model nodal-line dynamics of coherent fields output by such systems.

Comparison of two leading uniform theories of edge diffraction with the exact uniform asymptotic solution

NASA Technical Reports Server (NTRS)

Boersma, J.; Rahmat-Samii, Y.

1980-01-01

The diffraction of an arbitrary cylindrical wave by a half-plane has been treated by Rahmat-Samii and Mittra who used a spectral domain approach. In this paper, their exact solution for the total field is expressed in terms of a new integral representation. For large wave number k, two rigorous procedures are described for the exact uniform asymptotic expansion of the total field solution. The uniform expansions obtained are valid in the entire space, including transition regions around the shadow boundaries. The final results are compared with the formulations of two leading uniform theories of edge diffraction, namely, the uniform asymptotic theory and the uniform theory of diffraction. Some unique observations and conclusions are made in relating the two theories.

Exact solutions for the source-excited cylindrical electromagnetic waves in a nonlinear nondispersive medium.

PubMed

Es'kin, V A; Kudrin, A V; Petrov, E Yu

2011-06-01

The behavior of electromagnetic fields in nonlinear media has been a topical problem since the discovery of materials with a nonlinearity of electromagnetic properties. The problem of finding exact solutions for the source-excited nonlinear waves in curvilinear coordinates has been regarded as unsolvable for a long time. In this work, we present the first solution of this type for a cylindrically symmetric field excited by a pulsed current filament in a nondispersive medium that is simultaneously inhomogeneous and nonlinear. Assuming that the medium has a power-law permittivity profile in the linear regime and lacks a center of inversion, we derive an exact solution for the electromagnetic field excited by a current filament in such a medium and discuss the properties of this solution.

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

Scherrer, Arne; UMR 8640 ENS-CNRS-UPMC, Département de Chimie, 24 rue Lhomond, École Normale Supérieure, 75005 Paris; UPMC Université Paris 06, 4, Place Jussieu, 75005 Paris

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 canmore » 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.« less

Correlations of π N partial waves for multireaction analyses

DOE PAGES

Doring, M.; Revier, J.; Ronchen, D.; ...

2016-06-15

In the search for missing baryonic resonances, many analyses include data from a variety of pion- and photon-induced reactions. For elastic πN scattering, however, usually the partial waves of the SAID (Scattering Analysis Interactive Database) or other groups are fitted, instead of data. We provide the partial-wave covariance matrices needed to perform correlated χ 2 fits, in which the obtained χ 2 equals the actual χ 2 up to nonlinear and normalization corrections. For any analysis relying on partial waves extracted from elastic pion scattering, this is a prerequisite to assess the significance of resonance signals and to assign anymore » uncertainty on results. Lastly, the influence of systematic errors is also considered.« less

On approximating guided waves in plates with thin anisotropic coatings by means of effective boundary conditions

PubMed

Niklasson; Datta; Dunn

2000-09-01

In this paper, effective boundary conditions for elastic wave propagation in plates with thin coatings are derived. These effective boundary conditions are used to obtain an approximate dispersion relation for guided waves in an isotropic plate with thin anisotropic coating layers. The accuracy of the effective boundary conditions is investigated numerically by comparison with exact solutions for two different material systems. The systems considered consist of a metallic core with thin superconducting coatings. It is shown that for wavelengths long compared to the coating thickness there is excellent agreement between the approximate and exact solutions for both systems. Furthermore, numerical results presented might be used to characterize coating properties by ultrasonic techniques.

Efficient Calculation of Exact Exchange Within the Quantum Espresso Software Package

NASA Astrophysics Data System (ADS)

Barnes, Taylor; Kurth, Thorsten; Carrier, Pierre; Wichmann, Nathan; Prendergast, David; Kent, Paul; Deslippe, Jack

Accurate simulation of condensed matter at the nanoscale requires careful treatment of the exchange interaction between electrons. In the context of plane-wave DFT, these interactions are typically represented through the use of approximate functionals. Greater accuracy can often be obtained through the use of functionals that incorporate some fraction of exact exchange; however, evaluation of the exact exchange potential is often prohibitively expensive. We present an improved algorithm for the parallel computation of exact exchange in Quantum Espresso, an open-source software package for plane-wave DFT simulation. Through the use of aggressive load balancing and on-the-fly transformation of internal data structures, our code exhibits speedups of approximately an order of magnitude for practical calculations. Additional optimizations are presented targeting the many-core Intel Xeon-Phi ``Knights Landing'' architecture, which largely powers NERSC's new Cori system. We demonstrate the successful application of the code to difficult problems, including simulation of water at a platinum interface and computation of the X-ray absorption spectra of transition metal oxides.

Anomalous diffusion associated with nonlinear fractional derivative fokker-planck-like equation: exact time-dependent solutions

PubMed

Bologna; Tsallis; Grigolini

2000-08-01

We consider the d=1 nonlinear Fokker-Planck-like equation with fractional derivatives ( partial differential/ partial differentialt)P(x,t)=D( partial differential(gamma)/ partial differentialx(gamma))[P(x,t)](nu). Exact time-dependent solutions are found for nu=(2-gamma)/(1+gamma)(-infinity

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.

Pseudopotential Method for Higher Partial Wave Scattering

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

Idziaszek, Zbigniew; Centrum Fizyki Teoretycznej, Polska Akademia Nauk, 02-668 Warsaw; 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.

Modulation instability, Fermi-Pasta-Ulam recurrence, rogue waves, nonlinear phase shift, and exact solutions of the Ablowitz-Ladik equation.

PubMed

Akhmediev, Nail; Ankiewicz, Adrian

2011-04-01

We study modulation instability (MI) of the discrete constant-background wave of the Ablowitz-Ladik (A-L) equation. We derive exact solutions of the A-L equation which are nonlinear continuations of MI at longer times. These periodic solutions comprise a family of two-parameter solutions with an arbitrary background field and a frequency of initial perturbation. The solutions are recurrent, since they return the field state to the original constant background solution after the process of nonlinear evolution has passed. These solutions can be considered as a complete resolution of the Fermi-Pasta-Ulam paradox for the A-L system. One remarkable consequence of the recurrent evolution is the nonlinear phase shift gained by the constant background wave after the process. A particular case of this family is the rational solution of the first-order or fundamental rogue wave.

Testing the Perey effect

DOE PAGES

Titus, L. J.; Nunes, Filomena M.

2014-03-12

Here, the effects of non-local potentials have historically been approximately included by applying a correction factor to the solution of the corresponding equation for the local equivalent interaction. This is usually referred to as the Perey correction factor. In this work we investigate the validity of the Perey correction factor for single-channel bound and scattering states, as well as in transfer (p, d) cross sections. Method: We solve the scattering and bound state equations for non-local interactions of the Perey-Buck type, through an iterative method. Using the distorted wave Born approximation, we construct the T-matrix for (p,d) on 17O, 41Ca,more » 49Ca, 127Sn, 133Sn, and 209Pb at 20 and 50 MeV. As a result, we found that for bound states, the Perey corrected wave function resulting from the local equation agreed well with that from the non-local equation in the interior region, but discrepancies were found in the surface and peripheral regions. Overall, the Perey correction factor was adequate for scattering states, with the exception of a few partial waves corresponding to the grazing impact parameters. These differences proved to be important for transfer reactions. In conclusion, the Perey correction factor does offer an improvement over taking a direct local equivalent solution. However, if the desired accuracy is to be better than 10%, the exact solution of the non-local equation should be pursued.« less

On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and shocks

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.

A connection between the maximum displacements of rogue waves and the dynamics of poles in the complex plane.

PubMed

Liu, T Y; Chiu, T L; Clarkson, P A; Chow, K W

2017-09-01

Rogue waves of evolution systems are displacements which are localized in both space and time. The locations of the points of maximum displacements of the wave profiles may correlate with the trajectories of the poles of the exact solutions from the perspective of complex variables through analytic continuation. More precisely, the location of the maximum height of the rogue wave in laboratory coordinates (real space and time) is conjectured to be equal to the real part of the pole of the exact solution, if the spatial coordinate is allowed to be complex. This feature can be verified readily for the Peregrine breather (lowest order rogue wave) of the nonlinear Schrödinger equation. This connection is further demonstrated numerically here for more complicated scenarios, namely the second order rogue wave of the Boussinesq equation (for bidirectional long waves in shallow water), an asymmetric second order rogue wave for the nonlinear Schrödinger equation (as evolution system for slowly varying wave packets), and a symmetric second order rogue wave of coupled Schrödinger systems. Furthermore, the maximum displacements in physical space occur at a time instant where the trajectories of the poles in the complex plane reverse directions. This property is conjectured to hold for many other systems, and will help to determine the maximum amplitudes of rogue waves.

A connection between the maximum displacements of rogue waves and the dynamics of poles in the complex plane

NASA Astrophysics Data System (ADS)

Liu, T. Y.; Chiu, T. L.; Clarkson, P. A.; Chow, K. W.

2017-09-01

Rogue waves of evolution systems are displacements which are localized in both space and time. The locations of the points of maximum displacements of the wave profiles may correlate with the trajectories of the poles of the exact solutions from the perspective of complex variables through analytic continuation. More precisely, the location of the maximum height of the rogue wave in laboratory coordinates (real space and time) is conjectured to be equal to the real part of the pole of the exact solution, if the spatial coordinate is allowed to be complex. This feature can be verified readily for the Peregrine breather (lowest order rogue wave) of the nonlinear Schrödinger equation. This connection is further demonstrated numerically here for more complicated scenarios, namely the second order rogue wave of the Boussinesq equation (for bidirectional long waves in shallow water), an asymmetric second order rogue wave for the nonlinear Schrödinger equation (as evolution system for slowly varying wave packets), and a symmetric second order rogue wave of coupled Schrödinger systems. Furthermore, the maximum displacements in physical space occur at a time instant where the trajectories of the poles in the complex plane reverse directions. This property is conjectured to hold for many other systems, and will help to determine the maximum amplitudes of rogue waves.

Breakup fusion theory of nuclear reactions

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

Mastroleo, R.C.

1987-01-01

Continuum spectra of particles emitted in incomplete fusion reactions are one of the major interests in current nuclear reaction studies. Based on an idea of the so-called breakup fusion (BF) reaction, several authors derived closed formulas for the singles cross section of the particles that are emitted. There have been presented, however, two conflicting cross section formulas for the same BF reaction. For convenience, we shall call one of them the IAV (Ichimura, Austern and Vincent) and the other UT (Udagawa and Tamura) cross section formulas. In this work, the formulation of the UT cross section formula (prior-form) is presented,more » and the post-form version of the IAV cross section formula is evaluted for a few {alpha}- and d-induced reactions based on the exact finite range method. It is shown that the values thus calculated are larger by an order of magnitude as compared with the experimental cross sections for the {alpha}-induced reactions, while they are comparable with the experimental cross sections for the d-induced reactions. A possible origin of why such a large cross section is resulted in the case of {alpha}-induced reactions is also discussed. Polarization of the residual compound nucleus produced in breakup fusion reactions are calculated and compared with experiments. It is shown that the polarization is rather sensitive to the deflection angles of the strongly absortive partial waves and to obtain a good fit with the experimental data a l-dependent potential in the incident channel is needed in order to stress the lower partial waves.« less

Applications of He's semi-inverse method, ITEM and GGM to the Davey-Stewartson equation

NASA Astrophysics Data System (ADS)

Zinati, Reza Farshbaf; Manafian, Jalil

2017-04-01

We investigate the Davey-Stewartson (DS) equation. Travelling wave solutions were found. In this paper, we demonstrate the effectiveness of the analytical methods, namely, He's semi-inverse variational principle method (SIVPM), the improved tan(φ/2)-expansion method (ITEM) and generalized G'/G-expansion method (GGM) for seeking more exact solutions via the DS equation. These methods are direct, concise and simple to implement compared to other existing methods. The exact solutions containing four types solutions have been achieved. The results demonstrate that the aforementioned methods are more efficient than the Ansatz method applied by Mirzazadeh (2015). Abundant exact travelling wave solutions including solitons, kink, periodic and rational solutions have been found by the improved tan(φ/2)-expansion and generalized G'/G-expansion methods. By He's semi-inverse variational principle we have obtained dark and bright soliton wave solutions. Also, the obtained semi-inverse variational principle has profound implications in physical understandings. These solutions might play important role in engineering and physics fields. Moreover, by using Matlab, some graphical simulations were done to see the behavior of these solutions.

How Accurately Does the Free Complement Wave Function of a Helium Atom Satisfy the Schroedinger Equation?

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

Nakashima, Hiroyuki; Nakatsuji, Hiroshi

2008-12-12

The local energy defined by H{psi}/{psi} must be equal to the exact energy E at any coordinate of an atom or molecule, as long as the {psi} under consideration is exact. The discrepancy from E of this quantity is a stringent test of the accuracy of the calculated wave function. The H-square error for a normalized {psi}, defined by {sigma}{sup 2}{identical_to}<{psi}|(H-E){sup 2}|{psi}>, is also a severe test of the accuracy. Using these quantities, we have examined the accuracy of our wave function of a helium atom calculated using the free complement method that was developed to solve the Schroedinger equation.more » Together with the variational upper bound, the lower bound of the exact energy calculated using a modified Temple's formula ensured the definitely correct value of the helium fixed-nucleus ground state energy to be -2.903 724 377 034 119 598 311 159 245 194 4 a.u., which is correct to 32 digits.« less

Exact analytic solution of position-dependent mass Schrödinger equation

NASA Astrophysics Data System (ADS)

Rajbongshi, Hangshadhar

2018-03-01

Exact analytic solution of position-dependent mass Schrödinger equation is generated by using extended transformation, a method of mapping a known system into a new system equipped with energy eigenvalues and corresponding wave functions. First order transformation is performed on D-dimensional radial Schrödinger equation with constant mass by taking trigonometric Pöschl-Teller potential as known system. The exactly solvable potentials with position-dependent mass generated for different choices of mass functions through first order transformation are also taken as known systems in the second order transformation performed on D-dimensional radial position-dependent mass Schrödinger equation. The solutions are fitted for "Zhu and Kroemer" ordering of ambiguity. All the wave functions corresponding to nonzero energy eigenvalues are normalizable. The new findings are that the normalizability condition of the wave functions remains independent of mass functions, and some of the generated potentials show a family relationship among themselves where power law potentials also get related to non-power law potentials and vice versa through the transformation.

An all-fiber partial discharge monitoring system based on both intrinsic fiber optic interferometry sensor and fluorescent fiber

NASA Astrophysics Data System (ADS)

Yin, Zelin; Zhang, Ruirui; Tong, Jie; Chen, Xi

2013-12-01

Partial discharges (PDs) are an electrical phenomenon that occurs within a transformer whenever the voltage stress is sufficient to produce ionization in voids or inclusions within a solid dielectric, at conductor/dielectric interfaces, or in bubbles within liquid dielectrics such as oil; high-frequency transient current discharges will then appear repeatedly and will progressively deteriorate the insulation, ultimately leading to breakdown. Fiber sensor has great potential on the partial discharge detection in high-voltage equipment for its immunity to electromagnetic interference and it can take direct measurement in the high voltage equipment. The energy released in PDs produces a number of effects, resulting in flash, chemical and structural changes and electromagnetic emissions and so on. Acoustic PD detection is based on the mechanical pressure wave emitted from the discharge and fluorescent fiber PD detection is based on the emitted light produced by ionization, excitation and recombination processes during the discharge. Both of the two methods have the shortage of weak anti-interference capacity in the physical environment, like thunder or other sound source. In order to avoid the false report, an all-fiber combined PD detection system of the two methods is developed in this paper. In the system the fluorescent fiber PD sensor is considered as a reference signal, three F-P based PD detection sensors are used to both monitor the PD intensity and calculate the exact position of the discharge source. Considering the wave band of the F-P cavity and the fluorescent probe are quite different, the reflection spectrum of the F-P cavity is in the infrared region, however the fluorescent probe is about 600nm to 700nm, thus the F-P sensor and fluorescent fiber probe can be connected in one fiber and the reflection light can be detected by two different detectors without mutual interference. The all-fiber partial discharge monitoring system not only can detect the PDs but also can ensure the position of the PD source and is of great anti-interference capacity in harsh environment.

Two-dimensional solitary waves and periodic waves on coupled nonlinear electrical transmission lines

NASA Astrophysics Data System (ADS)

Wang, Heng; Zheng, Shuhua

2017-06-01

By using the dynamical system approach, the exact travelling wave solutions for a system of coupled nonlinear electrical transmission lines are studied. Based on this method, the bifurcations of phase portraits of a dynamical system are given. The two-dimensional solitary wave solutions and periodic wave solutions on coupled nonlinear transmission lines are obtained. With the aid of Maple, the numerical simulations are conducted for solitary wave solutions and periodic wave solutions to the model equation. The results presented in this paper improve upon previous studies.

Direct Calculation of the Scattering Amplitude Without Partial Wave Decomposition. III; Inclusion of Correlation Effects

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.

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition. 2; Inclusion of Exchange

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.

The Effect of Dynamic Wetting on the Stability of a Gas-Liquid Interface Subjected to Vertical Oscillations

NASA Astrophysics Data System (ADS)

Kraynik, Andrew M.; Romero, Louis; Torczynski, John R.; Brooks, Carlton F.; O'Hern, Timothy J.; Jepson, Richard A.; Benavides, Gilbert L.

2009-11-01

The stability of an interface in a container partially filled with silicone oil and subjected to gravity and vertical oscillations has been examined theoretically and computationally. An exact theory for the onset of a parametric instability producing Faraday-like waves was developed for arbitrary liquid viscosity, stress-free walls, and deep two-dimensional or axisymmetric containers. Finite-element simulations for stress-free walls are in excellent agreement with the theory, which predicts instability in discrete frequency bands. These simpler calculations are a departure point for examining the more realistic problem, which involves no-slip at the walls and dynamic wetting modeled with a Blake condition. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Inclusion of electron correlation for the target wave function in low- to intermediate-energy e-N2 scattering

NASA Technical Reports Server (NTRS)

Weatherford, C. A.; Brown, F. B.; Temkin, A.

1987-01-01

In a recent calculation, an exact exchange method was developed for use in the partial-differential-equation approach to electron-molecule scattering and was applied to e-N2 scattering in the fixed-nuclei approximation with an adiabatic polarization potential at low energies (0-10 eV). Integrated elastic cross sections were calculated and found to be lower than experiment at energies both below and above the Pi(g) resonance. It was speculated at that time that improved experimental agreement could be obtained if a correlated target representation were used in place of the uncorrelated one. The present paper implements this suggestion and demonstrates the improved agreement. These calculations are also extended to higher energies (0-30 eV) so asd to include the Sigma(u) resonance. Some discrepancies among the experiments and between experiment and the various calculations at very low energy are noted.

Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance.

PubMed

Chen, Shihua; Grelu, Philippe; Soto-Crespo, J M

2014-01-01

Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves.

Exact time-dependent nonlinear dispersive wave solutions in compressible magnetized plasmas exhibiting collapse.

PubMed

Chakrabarti, Nikhil; Maity, Chandan; Schamel, Hans

2011-04-08

Compressional waves in a magnetized plasma of arbitrary resistivity are treated with the lagrangian fluid approach. An exact nonlinear solution with a nontrivial space and time dependence is obtained with boundary conditions as in Harris' current sheet. The solution shows competition among hydrodynamic convection, magnetic field diffusion, and dispersion. This results in a collapse of density and the magnetic field in the absence of dispersion. The dispersion effects arrest the collapse of density but not of the magnetic field. A possible application is in the early stage of magnetic star formation.

Exact periodic cross-kink wave solutions for the new (2+1)-dimensional KdV equation in fluid flows and plasma physics.

PubMed

Liu, Jian-Guo; Du, Jian-Qiang; Zeng, Zhi-Fang; Ai, Guo-Ping

2016-10-01

The Korteweg-de Vries (KdV)-type models have been shown to describe many important physical situations such as fluid flows, plasma physics, and solid state physics. In this paper, a new (2 + 1)-dimensional KdV equation is discussed. Based on the Hirota's bilinear form and a generalized three-wave approach, we obtain new exact solutions for the new (2 + 1)-dimensional KdV equation. With the help of symbolic computation, the properties for some new solutions are presented with some figures.

The big bang as a higher-dimensional shock wave

NASA Astrophysics Data System (ADS)

Wesson, P. S.; Liu, H.; Seahra, S. S.

2000-06-01

We give an exact solution of the five-dimensional field equations which describes a shock wave moving in time and the extra (Kaluza-Klein) coordinate. The matter in four-dimensional spacetime is a cosmology with good physical properties. The solution suggests to us that the 4D big bang was a 5D shock wave.

Effect of Gravity Waves from Small Islands in the Southern Ocean on the Southern Hemisphere Atmospheric Circulation

NASA Technical Reports Server (NTRS)

Garfinkel, C. I.; Oman, L. D.

2018-01-01

The effect of small islands in the Southern Ocean on the atmospheric circulation in the Southern Hemisphere is considered with a series of simulations using the NASA Goddard Earth Observing System Chemistry-Climate Model in which the gravity wave stress generated by these islands is increased to resemble observed values. The enhanced gravity wave drag leads to a 2 K warming of the springtime polar stratosphere, partially ameliorating biases in this region. Resolved wave drag declines in the stratospheric region in which the added orographic gravity waves deposit their momentum, such that changes in gravity waves are partially compensated by changes in resolved waves, though resolved wave drag increases further poleward. The orographic drag from these islands has impacts for surface climate, as biases in tropospheric jet position are also partially ameliorated. These results suggest that these small islands are likely contributing to the missing drag near 60 degrees S in the upper stratosphere evident in many data assimilation products.

Lorentz-Abraham-Dirac versus Landau-Lifshitz radiation friction force in the ultrarelativistic electron interaction with electromagnetic wave (exact solutions).

PubMed

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.

Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations.

PubMed

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.

Lorentz-Abraham-Dirac versus Landau-Lifshitz radiation friction force in the ultrarelativistic electron interaction with electromagnetic wave (exact solutions)

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

Bulanov, Sergei V.; Esirkepov, Timur Zh.; Kando, Masaki

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 themore » nonlinear problems of charged particle motion in the time-varying electromagnetic field is used.« less

Factors Influencing Army Accessions.

DTIC Science & Technology

1982-12-01

partial autocorrelations were examined for significant lags or a recognizable pattern such as a damped exponential or a sine wave. The TSP prugrams...decreasing function indicating nonstation- *arity or a very long sine wave where only a small portion of the wave is plotted. The partial...plot of the raw data appeared (Appendix E-1) to be either the middle of a long sine wave or a linearly decreasing function. This pattern is recognized

Propagation of thickness-twist waves in a piezoelectric ceramic plate with unattached electrodes.

PubMed

Qian, Zheng-Hua; Kishimoto, Kikuo; Yang, Jiashi

2009-06-01

We analyze the propagation of thickness-twist waves in an unbounded piezoelectric ceramic plate with air gaps between the plate surfaces and two electrodes. These waves are also called anti-plane or shear-horizontal waves with one displacement component only. An exact solution is obtained from the equations of the linear theory of piezoelectricity. Dispersion relations of the waves are obtained and plotted. Results show that the wave frequency or speed is sensitive to the air gap thickness. This effect can be used to manipulate the behavior of the waves and has implications in acoustic wave devices.

The formation mechanism of defects, spiral wave in the network of neurons.

PubMed

Wu, Xinyi; Ma, Jun

2013-01-01

A regular network of neurons is constructed by using the Morris-Lecar (ML) neuron with the ion channels being considered, and the potential mechnism of the formation of a spiral wave is investigated in detail. Several spiral waves are initiated by blocking the target wave with artificial defects and/or partial blocking (poisoning) in ion channels. Furthermore, possible conditions for spiral wave formation and the effect of partial channel blocking are discussed completely. Our results are summarized as follows. 1) The emergence of a target wave depends on the transmembrane currents with diversity, which mapped from the external forcing current and this kind of diversity is associated with spatial heterogeneity in the media. 2) Distinct spiral wave could be induced to occupy the network when the target wave is broken by partially blocking the ion channels of a fraction of neurons (local poisoned area), and these generated spiral waves are similar with the spiral waves induced by artificial defects. It is confirmed that partial channel blocking of some neurons in the network could play a similar role in breaking a target wave as do artificial defects; 3) Channel noise and additive Gaussian white noise are also considered, and it is confirmed that spiral waves are also induced in the network in the presence of noise. According to the results mentioned above, we conclude that appropriate poisoning in ion channels of neurons in the network acts as 'defects' on the evolution of the spatiotemporal pattern, and accounts for the emergence of a spiral wave in the network of neurons. These results could be helpful to understand the potential cause of the formation and development of spiral waves in the cortex of a neuronal system.

The Formation Mechanism of Defects, Spiral Wave in the Network of Neurons

PubMed Central

Wu, Xinyi; Ma, Jun

2013-01-01

A regular network of neurons is constructed by using the Morris-Lecar (ML) neuron with the ion channels being considered, and the potential mechnism of the formation of a spiral wave is investigated in detail. Several spiral waves are initiated by blocking the target wave with artificial defects and/or partial blocking (poisoning) in ion channels. Furthermore, possible conditions for spiral wave formation and the effect of partial channel blocking are discussed completely. Our results are summarized as follows. 1) The emergence of a target wave depends on the transmembrane currents with diversity, which mapped from the external forcing current and this kind of diversity is associated with spatial heterogeneity in the media. 2) Distinct spiral wave could be induced to occupy the network when the target wave is broken by partially blocking the ion channels of a fraction of neurons (local poisoned area), and these generated spiral waves are similar with the spiral waves induced by artificial defects. It is confirmed that partial channel blocking of some neurons in the network could play a similar role in breaking a target wave as do artificial defects; 3) Channel noise and additive Gaussian white noise are also considered, and it is confirmed that spiral waves are also induced in the network in the presence of noise. According to the results mentioned above, we conclude that appropriate poisoning in ion channels of neurons in the network acts as ‘defects’ on the evolution of the spatiotemporal pattern, and accounts for the emergence of a spiral wave in the network of neurons. These results could be helpful to understand the potential cause of the formation and development of spiral waves in the cortex of a neuronal system. PMID:23383179

Connection between angle-dependent phase ambiguities and the uniqueness of the partial-wave decomposition

NASA Astrophysics Data System (ADS)

Švarc, A.; Wunderlich, Y.; Osmanović, H.; Hadžimehmedović, M.; Omerović, R.; Stahov, J.; Kashevarov, V.; Nikonov, K.; Ostrick, M.; Tiator, L.; Workman, R.

2018-05-01

Unconstrained partial -wave amplitudes, obtained at discrete energies from fits to complete sets of eight independent observables, may be used to reconstruct reaction amplitudes. These partial-wave amplitudes do not vary smoothly with energy and are in principle nonunique. We demonstrate how this behavior can be ascribed to the continuum ambiguity. Starting from the spinless scattering case, we show how an unknown overall phase, depending on energy and angle, mixes the structures seen in the associated partial-wave amplitudes. This process is illustrated using a simple toy model. We then apply these principles to pseudoscalar meson photoproduction, showing how the above effect can be removed through a phase rotation, allowing a consistent comparison with model amplitudes. The effect of this phase ambiguity is also considered for Legendre expansions of experimental observables.

Exact solutions for a type of electron pairing model with spin-orbit interactions and Zeeman coupling.

PubMed

Liu, Jia; Han, Qiang; Shao, L B; Wang, Z D

2011-07-08

A type of electron pairing model with spin-orbit interactions or Zeeman coupling is solved exactly in the framework of the Richardson ansatz. Based on the exact solutions for the case with spin-orbit interactions, it is shown rigorously that the pairing symmetry is of the p + ip wave and the ground state possesses time-reversal symmetry, regardless of the strength of the pairing interaction. Intriguingly, how Majorana fermions can emerge in the system is also elaborated. Exact results are illustrated for two systems, respectively, with spin-orbit interactions and Zeeman coupling.

Experimental observation of water saturation effects on shear wave splitting in synthetic rock with fractures aligned at oblique angles

NASA Astrophysics Data System (ADS)

Amalokwu, Kelvin; Chapman, Mark; Best, Angus I.; Sothcott, Jeremy; Minshull, Timothy A.; Li, Xiang-Yang

2015-01-01

Fractured rocks are known to exhibit seismic anisotropy and shear wave splitting (SWS). SWS is commonly used for fractured rock characterization and has been shown to be sensitive to fluid type. The presence of partial liquid/gas saturation is also known to affect the elastic properties of rocks. The combined effect of both fractures and partial liquid/gas saturation is still unknown. Using synthetic, silica-cemented sandstones with aligned penny-shaped voids, we conducted laboratory ultrasonic experiments to investigate the effect fractures aligned at an oblique angle to wave propagation would have on SWS under partial liquid/gas saturation conditions. The result for the fractured rock shows a saturation dependence which can be explained by combining a fractured rock model and a partial saturation model. At high to full water saturation values, SWS decreases as a result of the fluid bulk modulus effect on the quasi-shear wave. This bulk modulus effect is frequency dependent as a result of wave-induced fluid flow mechanisms, which would in turn lead to frequency dependent SWS. This result suggests the possible use of SWS for discriminating between full liquid saturation and partial liquid/gas saturation.

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.

Dispersive solitary wave solutions of Kadomtsev-Petviashvili and modified Kadomtsev-Petviashvili dynamical equations in unmagnetized dust plasma

NASA Astrophysics Data System (ADS)

Seadawy, A. R.; El-Rashidy, K.

2018-03-01

The Kadomtsev-Petviashvili (KP) and modified KP equations are two of the most universal models in nonlinear wave theory, which arises as a reduction of system with quadratic nonlinearity which admit weakly dispersive waves. The generalized extended tanh method and the F-expansion method are used to derive exact solitary waves solutions of KP and modified KP equations. The region of solutions are displayed graphically.

Wave-function functionals

NASA Astrophysics Data System (ADS)

Pan, Xiao-Yin; Slamet, Marlina; Sahni, Viraht

2010-04-01

We extend our prior work on the construction of variational wave functions ψ that are functionals of functions χ:ψ=ψ[χ] 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 χ chosen such that the functional ψ[χ] 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-, the helium atom He, and its positive ions Li+ and Be2+. The operators W whose expectations are obtained exactly are the sum of the single-particle operators W=∑irin,n=-2,-1,1,2, W=∑iδ(ri), W=-(1)/(2)∑i∇i2, and the two-particle operators W=∑nun,n=-2,-1,1,2, where u=|ri-rj|. 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 ψ[χ] that lead to the exact expectation of arbitrary Hermitian operators. We discover that analogous to the solutions of the Schrödinger equation, there exist ψ[χ] that are unphysical in that they lead to singular values for the expectations. We also explain the origin of the singularity.

Faddeev calculation for ^9_ΛBe hypernucleus

NASA Astrophysics Data System (ADS)

Suslov, Vladimir; Filikhin, Igor; Vlahovic, Branislav

2003-04-01

Faddeev calculations are performed for the ^9_ΛBe hypernucleus in terms of α's and Λ clusters using various Λα potential models. The main goal of our calculations is to estimate higher partial waves contribution in binding energy of ^9_ΛBe ground state (1/2^+) and particularly contribution from the high partial waves of the Λα pair. Phenomenological Ali-Bodmer potential is employed for description of the αα interaction. This potential has s, d and g - waves components. For a Λα potential both form and parameters are uncertain, because Λα interaction data are limited by the experimental value of binding energy of the ^5_ΛHe hypernucleus, which is considered as the bound s-wave state of the Λα system. The binding energy of the ^9_ΛBe is calculated for two different cases. First the s-wave Λα potential acting in all partial waves in the Λα subsystem is used. Second, a recent more realistic Λα potential model including the s and p-partial components from work [1] is employed. We compared these models and discussed validity of the s-wave approximation for calculation of ^9_ΛBe hypernucleus. This work was partially supported by Department of Defenses through the grant No.DAAD 19-01-1-0795. The work of V.M.S and I.N.F was supported by the RFFI under Grant No. 02-02-16562. References: [1] K.S. Myint, S. Shinmura and Y. Akaishi, nucl-th/0209090.

Nonparaxial wave beams and packets with general astigmatism

NASA Astrophysics Data System (ADS)

Kiselev, A. P.; Plachenov, A. B.; Chamorro-Posada, P.

2012-04-01

We present exact solutions of the wave equation involving an arbitrary wave form with a phase closely similar to the general astigmatic phase of paraxial wave optics. Special choices of the wave form allow general astigmatic beamlike and pulselike waves with a Gaussian-type unrestricted localization in space and time. These solutions are generalizations of the known Bateman-type waves obtained from the connection existing between beamlike solutions of the paraxial parabolic equation and relatively undistorted wave solutions of the wave equation. As a technical tool, we present a full description of parametrizations of 2×2 symmetric matrices with positive imaginary part, which arise in the theory of Gaussian beams.

Partial-wave analysis of nucleon-nucleon elastic scattering data

DOE PAGES

Workman, Ron L.; Briscoe, William J.; Strakovsky, Igor I.

2016-12-19

Energy-dependent and single-energy fits to the existing nucleon-nucleon database have been updated to incorporate recent measurements. The fits cover a region from threshold to 3 GeV, in the laboratory kinetic energy, for proton-proton scattering, with an upper limit of 1.3 GeV for neutron-proton scattering. Experiments carried out at the COSY-WASA and COSY-ANKE facilities have had a significant impact on the partial-wave solutions. Lastly, results are discussed in terms of both partial-wave and direct reconstruction amplitudes.

Effects of partial slip boundary condition and radiation on the heat and mass transfer of MHD-nanofluid flow

NASA Astrophysics Data System (ADS)

Abd Elazem, Nader Y.; Ebaid, Abdelhalim

2017-12-01

In this paper, the effect of partial slip boundary condition on the heat and mass transfer of the Cu-water and Ag-water nanofluids over a stretching sheet in the presence of magnetic field and radiation. Such partial slip boundary condition has attracted much attention due to its wide applications in industry and chemical engineering. The flow is basically governing by a system of partial differential equations which are reduced to a system of ordinary differential equations. This system has been exactly solved, where exact analytical expression has been obtained for the fluid velocity in terms of exponential function, while the temperature distribution, and the nanoparticles concentration are expressed in terms of the generalized incomplete gamma function. In addition, explicit formulae are also derived from the rates of heat transfer and mass transfer. The effects of the permanent parameters on the skin friction, heat transfer coefficient, rate of mass transfer, velocity, the temperature profile, and concentration profile have been discussed through tables and graphs.

The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method.

PubMed

Gai, Litao; Bilige, Sudao; Jie, Yingmo

2016-01-01

In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.

Quantum recurrence and fractional dynamic localization in ac-driven perfect state transfer Hamiltonians

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

Longhi, Stefano, E-mail: stefano.longhi@fisi.polimi.it

Quantum recurrence and dynamic localization are investigated in a class of ac-driven tight-binding Hamiltonians, the Krawtchouk quantum chain, which in the undriven case provides a paradigmatic Hamiltonian model that realizes perfect quantum state transfer and mirror inversion. The equivalence between the ac-driven single-particle Krawtchouk Hamiltonian H{sup -hat} (t) and the non-interacting ac-driven bosonic junction Hamiltonian enables to determine in a closed form the quasi energy spectrum of H{sup -hat} (t) and the conditions for exact wave packet reconstruction (dynamic localization). In particular, we show that quantum recurrence, which is predicted by the general quantum recurrence theorem, is exact for themore » Krawtchouk quantum chain in a dense range of the driving amplitude. Exact quantum recurrence provides perfect wave packet reconstruction at a frequency which is fractional than the driving frequency, a phenomenon that can be referred to as fractional dynamic localization.« less

Scattering of plane evanescent waves by buried cylinders: Modeling the coupling to guided waves and resonances

NASA Astrophysics Data System (ADS)

Marston, Philip L.

2003-04-01

The coupling of sound to buried targets can be associated with acoustic evanescent waves when the sea bottom is smooth. To understand the excitation of guided waves on buried fluid cylinders and shells by acoustic evanescent waves and the associated target resonances, the two-dimensional partial wave series for the scattering is found for normal incidence in an unbounded medium. The shell formulation uses the simplifications of thin-shell dynamics. The expansion of the incident wave becomes a double summation with products of modified and ordinary Bessel functions [P. L. Marston, J. Acoust. Soc. Am. 111, 2378 (2002)]. Unlike the case of an ordinary incident wave, the counterpropagating partial waves of the same angular order have unequal magnitudes when the incident wave is evanescent. This is a consequence of the exponential dependence of the incident wave amplitude on depth. Some consequences of this imbalance of partial-wave amplitudes are given by modifying previous ray theory for the scattering [P. L. Marston and N. H. Sun, J. Acoust. Soc. Am. 97, 777-783 (1995)]. The exponential dependence of the scattering on the location of a scatterer was previously demonstrated in air [T. J. Matula and P. L. Marston, J. Acoust. Soc. Am. 93, 1192-1195 (1993)].

A numerical study of nonlinear waves in a transcritical flow of stratified fluid past an obstacle

NASA Astrophysics Data System (ADS)

Hanazaki, Hideshi

1992-10-01

A numerical study of the flow of stratified fluid past an obstacle in a horizontal channel is described. Upstream advancing of waves near critically (resonance) appears in the case of ordinary two-layer flow, in which case the flow is described well by the solution of the forced extended Korteweg-de Vries (KdV) equation which has a cubic nonlinear term. It is shown theoretically that the upstream waves in the general two-layer flow cannot be well described by the forced KdV equation except when the wave amplitude is very small. The critical-level flow is also governed by the forced extended KdV equation. However, because of the smallness of the coefficient of the quadratic nonlinear term, the bore cannot propagate upstream at exact resonance. The results for the linearly stratified Boussinesq flow show good agreement with the solution of the Grimshaw and Yi (1991) equation, at least for exact resonance.

Ultrarelativistic boost of a black hole in the magnetic universe of Levi-Civita-Bertotti-Robinson

NASA Astrophysics Data System (ADS)

Ortaggio, Marcello; Astorino, Marco

2018-05-01

We consider an exact Einstein-Maxwell solution constructed by Alekseev and Garcia, which describes a Schwarzschild black hole immersed in the magnetic universe of Levi-Civita, Bertotti, and Robinson (LCBR). After reviewing the basic properties of this spacetime, we study the ultrarelativistic limit in which the black hole is boosted to the speed of light, while sending its mass to 0. This results in a nonexpanding impulsive wave traveling in the LCBR universe. The wave front is a 2-sphere carrying two null point particles at its poles—a remnant of the structure of the original static spacetime. It is also shown that the obtained line element belongs to the Kundt class of spacetimes, and the relation with the known family of exact gravitational waves of finite duration propagating in the LCBR background is clarified. In the limit of a vanishing electromagnetic field, one point particle is pushed away to infinity and the single-particle Aichelburg-Sexl p p -wave propagating in Minkowski space is recovered.

Relativistic optical model on the basis of the Moscow potential and lower phase shifts for nucleon-nucleon scattering at laboratory energies of up to 3 GeV

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

Knyr, V. A.; Neudatchin, V. G.; Khokhlov, N. A.

Data of a partial-wave analysis of nucleon-nucleon scattering at energies of up to E{sub lab} = 3 GeV (lower partial waves) and the properties of the deuteron are described within the relativistic optical model based on deep attractive quasipotentials involving forbidden states (as exemplified by the Moscow potential). Partial-wave potentials are derived by the inverse-scattering-problem method based on the Marchenko equation by using present-day data from the partial-wave analysis of nucleon-nucleon scattering at energies of up to 3 GeV. Channel coupling is taken into account. The imaginary parts of the potentials are deduced from the phase equation of the variable-phasemore » approach. The general situation around the manifestation of quark effects in nucleon-nucleon interaction is discussed.« less

Approximating the Helium Wavefunction in Positronium-Helium Scattering

NASA Technical Reports Server (NTRS)

DiRienzi, Joseph; Drachman, Richard J.

2003-01-01

In the Kohn variational treatment of the positronium- hydrogen scattering problem the scattering wave function is approximated by an expansion in some appropriate basis set, but the target and projectile wave functions are known exactly. In the positronium-helium case, however, a difficulty immediately arises in that the wave function of the helium target atom is not known exactly, and there are several ways to deal with the associated eigenvalue in formulating the variational scattering equations to be solved. In this work we will use the Kohn variational principle in the static exchange approximation to d e t e e the zero-energy scattering length for the Ps-He system, using a suite of approximate target functions. The results we obtain will be compared with each other and with corresponding values found by other approximation techniques.

Soliton and periodic solutions for time-dependent coefficient non-linear equation

NASA Astrophysics Data System (ADS)

Guner, Ozkan

2016-01-01

In this article, we establish exact solutions for the generalized (3+1)-dimensional variable coefficient Kadomtsev-Petviashvili (GVCKP) equation. Using solitary wave ansatz in terms of ? functions and the modified sine-cosine method, we find exact analytical bright soliton solutions and exact periodic solutions for the considered model. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. The effectiveness and reliability of the method are shown by its application to the GVCKP equation.

Exact solution for a non-Markovian dissipative quantum dynamics.

PubMed

Ferialdi, Luca; Bassi, Angelo

2012-04-27

We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.

An exact solution for effects of topography on free Rayleigh waves

USGS Publications Warehouse

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 quantization of Einstein-Rosen waves coupled to massless scalar matter.

PubMed

Barbero G, J Fernando; Garay, Iñaki; Villaseñor, Eduardo J S

2005-07-29

We show in this Letter that gravity coupled to a massless scalar field with full cylindrical symmetry can be exactly quantized by an extension of the techniques used in the quantization of Einstein-Rosen waves. This system provides a useful test bed to discuss a number of issues in quantum general relativity, such as the emergence of the classical metric, microcausality, and large quantum gravity effects. It may also provide an appropriate framework to study gravitational critical phenomena from a quantum point of view, issues related to black hole evaporation, and the consistent definition of test fields and particles in quantum gravity.

Nonlinear low-frequency electrostatic wave dynamics in a two-dimensional quantum plasma

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

Ghosh, Samiran, E-mail: sran_g@yahoo.com; Chakrabarti, Nikhil, E-mail: nikhil.chakrabarti@saha.ac.in

2016-08-15

The problem of two-dimensional arbitrary amplitude low-frequency electrostatic oscillation in a quasi-neutral quantum plasma is solved exactly by elementary means. In such quantum plasmas we have treated electrons quantum mechanically and ions classically. The exact analytical solution of the nonlinear system exhibits the formation of dark and black solitons. Numerical simulation also predicts the possible periodic solution of the nonlinear system. Nonlinear analysis reveals that the system does have a bifurcation at a critical Mach number that depends on the angle of propagation of the wave. The small-amplitude limit leads to the formation of weakly nonlinear Kadomstev–Petviashvili solitons.

New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.

PubMed

Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum

2014-01-01

In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.

Wave packet and statistical quantum calculations for the He + NeH⁺ → HeH⁺ + Ne reaction on the ground electronic state.

PubMed

Koner, Debasish; Barrios, Lizandra; González-Lezana, Tomás; Panda, Aditya N

2014-09-21

A real wave packet based time-dependent method and a statistical quantum method have been used to study the He + NeH(+) (v, j) reaction with the reactant in various ro-vibrational states, on a recently calculated ab initio ground state potential energy surface. Both the wave packet and statistical quantum calculations were carried out within the centrifugal sudden approximation as well as using the exact Hamiltonian. Quantum reaction probabilities exhibit dense oscillatory pattern for smaller total angular momentum values, which is a signature of resonances in a complex forming mechanism for the title reaction. Significant differences, found between exact and approximate quantum reaction cross sections, highlight the importance of inclusion of Coriolis coupling in the calculations. Statistical results are in fairly good agreement with the exact quantum results, for ground ro-vibrational states of the reactant. Vibrational excitation greatly enhances the reaction cross sections, whereas rotational excitation has relatively small effect on the reaction. The nature of the reaction cross section curves is dependent on the initial vibrational state of the reactant and is typical of a late barrier type potential energy profile.

Surface wave scattering from sharp lateral discontinuities

NASA Astrophysics Data System (ADS)

Pollitz, Fred F.

1994-11-01

The problem of surface wave scattering is re-explored, with quasi-degenerate normal mode coupling as the starting point. For coupling among specified spheroidal and toroidal mode dispersion branches, a set of coupled wave equations is derived in the frequency domain for first-arriving Rayleigh and Love waves. The solutions to these coupled wave equations using linear perturbation theory are surface integrals over the unit sphere covering the lateral distribution of perturbations in Earth structure. For isotropic structural perturbations and surface topographic perturbations, these solutions agree with the Born scattering theory previously obtained by Snieder and Romanowicz. By transforming these surface integrals into line integrals along the boundaries of the heterogeneous regions in the case of sharp discontinuities, and by using uniformly valid Green's functions, it is possible to extend the solution to the case of multiple scattering interactions. The proposed method allows the relatively rapid calculation of exact second order scattered wavefield potentials for scattering by sharp discontinuities, and it has many advantages not realized in earlier treatments. It employs a spherical Earth geometry, uses no far field approximation, and implicitly contains backward as well as forward scattering. Comparisons of asymptotic scattering and an exact solution with single scattering and multiple scattering integral formulations show that the phase perturbation predicted by geometrical optics breaks down for scatterers less than about six wavelengths in diameter, and second-order scattering predicts well both the amplitude and phase pattern of the exact wavefield for sufficiently small scatterers, less than about three wavelengths in diameter for anomalies of a few percent.

Tsunami Wave Run-up on a Vertical Wall in Tidal Environment

NASA Astrophysics Data System (ADS)

Didenkulova, Ira; Pelinovsky, Efim

2018-04-01

We solve analytically a nonlinear problem of shallow water theory for the tsunami wave run-up on a vertical wall in tidal environment. Shown that the tide can be considered static in the process of tsunami wave run-up. In this approximation, it is possible to obtain the exact solution for the run-up height as a function of the incident wave height. This allows us to investigate the tide influence on the run-up characteristics.

Penetration and screening of perpendicularly launched electromagnetic waves through bounded supercritical plasma confined in multicusp magnetic field

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

Dey, Indranuj; Bhattacharjee, Sudeep

2011-02-15

The question of electromagnetic wave penetration and screening by a bounded supercritical ({omega}{sub p}>{omega} with {omega}{sub p} and {omega} being the electron-plasma and wave frequencies, respectively) plasma confined in a minimum B multicusp field, for waves launched in the k perpendicular B{sub o} mode, is addressed through experiments and numerical simulations. The scale length of radial plasma nonuniformity (|n{sub e}/({partial_derivative}n{sub e}/{partial_derivative}r)|) and magnetostatic field (B{sub o}) inhomogeneity (|B{sub o}/({partial_derivative}B{sub o}/{partial_derivative}r)|) are much smaller than the free space ({lambda}{sub o}) and guided wavelengths ({lambda}{sub g}). Contrary to predictions of plane wave dispersion theory and the Clemow-Mullaly-Allis (CMA) diagram, for a boundedmore » plasma a finite propagation occurs through the central plasma regions where {alpha}{sub p}{sup 2}={omega}{sub p}{sup 2}/{omega}{sup 2}{>=}1 and {beta}{sub c}{sup 2}={omega}{sub ce}{sup 2}/{omega}{sup 2}<<1({approx}10{sup -4}), with {omega}{sub ce} being the electron cyclotron frequency. Wave screening, as predicted by the plane wave model, does not remain valid due to phase mixing and superposition of reflected waves from the conducting boundary, leading to the formation of electromagnetic standing wave modes. The waves are found to satisfy a modified upper hybrid resonance (UHR) relation in the minimum B field and are damped at the local electron cyclotron resonance (ECR) location.« less

Stressful Events and Other Predictors of Remission from Drug Dependence in the United States: Longitudinal Results from a National Survey

PubMed Central

McCabe, Sean Esteban; Cranford, James A.; Boyd, Carol J.

2016-01-01

This study examined stressful life events and other predictors associated with remission from DSM-IV drug dependence involving cannabis, cocaine, hallucinogens, heroin, inhalants, non-heroin opioids, sedatives, stimulants, tranquilizers, or other drugs. Waves 1 and 2 of the National Epidemiologic Survey on Alcohol and Related Conditions were used to examine the prevalence and predictors of past-year remission status. Among U.S. adults with previous (i.e., prior-to-past-year) drug dependence (n = 921) at baseline (Wave 1), the prevalence of past-year remission status at Wave 1 was: abstinence (60.5%), asymptomatic drug use (18.8%), partial remission (7.1%), and still drug dependent (13.5%). Similarly, the prevalence of past-year remission status three years after baseline at Wave 2 was: abstinence (69.1%), asymptomatic drug use (15.5%), partial remission (8.4%), and still drug dependent (7.0%). Remission three years after baseline at Wave 2 was much more likely among formerly drug dependent U.S. adults who abstained from drug use at baseline (Wave 1) relative to those who reported asymptomatic drug use, partial remission, or remained drug dependent. Design-based weighted multinomial logistic regression analysis showed that relative to abstinence, past-year stressful events at baseline (Wave 1) predicted higher odds of partial remission and drug dependence at both Waves 1 and 2. This is the first national study to examine the potential role of stressful life events associated with remission from drug dependence. Although the majority of those who reported previous drug dependence transitioned to full remission, a sizeable percentage were either still drug dependent or in partial remission. Higher levels of stressful life events appear to create barriers for remission and should remain a focus for relapse prevention programs. PMID:27776676

A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Ghanbari, Behzad; Inc, Mustafa

2018-04-01

The present paper suggests a novel technique to acquire exact solutions of nonlinear partial differential equations. The main idea of the method is to generalize the exponential rational function method. In order to examine the ability of the method, we consider the resonant nonlinear Schrödinger equation (R-NLSE). Many variants of exact soliton solutions for the equation are derived by the proposed method. Physical interpretations of some obtained solutions is also included. One can easily conclude that the new proposed method is very efficient and finds the exact solutions of the equation in a relatively easy way.

Closed solutions to a differential-difference equation and an associated plate solidification problem.

PubMed

Layeni, Olawanle P; Akinola, Adegbola P; Johnson, Jesse V

2016-01-01

Two distinct and novel formalisms for deriving exact closed solutions of a class of variable-coefficient differential-difference equations arising from a plate solidification problem are introduced. Thereupon, exact closed traveling wave and similarity solutions to the plate solidification problem are obtained for some special cases of time-varying plate surface temperature.

Time-periodic solutions of the Benjamin-Ono equation

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

Ambrose , D.M.; Wilkening, Jon

2008-04-01

We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which, in the case of the Benjamin-Ono equation, are the mean, a spatial phase, a temporal phase and the real part of one ofmore » the Fourier modes at t = 0. We use our method to study global paths of non-trivial time-periodic solutions connecting stationary and traveling waves of the Benjamin-Ono equation. As a starting guess for each path, we compute periodic solutions of the linearized problem by solving an infinite dimensional eigenvalue problem in closed form. We then use our numerical method to continue these solutions beyond the realm of linear theory until another traveling wave is reached (or until the solution blows up). By experimentation with data fitting, we identify the analytical form of the solutions on the path connecting the one-hump stationary solution to the two-hump traveling wave. We then derive exact formulas for these solutions by explicitly solving the system of ODE's governing the evolution of solitons using the ansatz suggested by the numerical simulations.« less

Influences of periodic mechanical deformation on pinned spiral waves

NASA Astrophysics Data System (ADS)

Chen, Jiang-Xing; Peng, Liang; Zheng, Qiang; Zhao, Ye-Hua; Ying, He-Ping

2014-09-01

In a generic model of excitable media, we study the behavior of spiral waves interacting with obstacles and their dynamics under the influences of simple periodic mechanical deformation (PMD). Depending on the characteristics of the obstacles, i.e., size and excitability, the rotation of a pinned spiral wave shows different scenarios, e.g., embedding into or anchoring on an obstacle. Three different drift phenomena induced by PMD are observed: scattering on small partial-excitable obstacles, meander-induced unpinning on big partial-excitable obstacles, and drifting around small unexcitable obstacles. Their underlying mechanisms are discussed. The dependence of the threshold amplitude of PMD on the characteristics of the obstacles to successfully remove pinned spiral waves on big partial-excitable obstacles is studied.

Description of an α-cluster tail in 8Be and 20Ne: Delocalization of the α cluster by quantum penetration

NASA Astrophysics Data System (ADS)

Kanada-En'yo, Yoshiko

2014-10-01

We analyze the α-cluster wave functions in cluster states of ^8Be and ^{20}Ne by comparing the exact relative wave function obtained by the generator coordinate method (GCM) with various types of trial functions. For the trial functions, we adopt the fixed range shifted Gaussian of the Brink-Bloch (BB) wave function, the spherical Gaussian with the adjustable range parameter of the spherical Tohsaki-Horiuchi-Schuck-Röpke (sTHSR), the deformed Gaussian of the deformed THSR (dTHSR), and a function with the Yukawa tail (YT). The quality of the description of the exact wave function with a trial function is judged by the squared overlap between the trial function and the GCM wave function. A better result is obtained with the sTHSR wave function than the BB wave function, and further improvement can be made with the dTHSR wave function because these wave functions can describe the outer tail better. The YT wave function gives almost an equal quality to or even better quality than the dTHSR wave function, indicating that the outer tail of α-cluster states is characterized by the Yukawa-like tail rather than the Gaussian tail. In weakly bound α-cluster states with small α separation energy and the low centrifugal and Coulomb barriers, the outer tail part is the slowly damping function described well by the quantum penetration through the effective barrier. This outer tail characterizes the almost zero-energy free α gas behavior, i.e., the delocalization of the cluster.

The Dynamics and Evolution of Poles and Rogue Waves for Nonlinear Schrödinger Equations*

NASA Astrophysics Data System (ADS)

Chiu, Tin Lok; Liu, Tian Yang; Chan, Hiu Ning; Wing Chow, Kwok

2017-09-01

Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of these rogue waves are correlated with the movement of poles of the exact solutions extended to the complex plane through analytic continuation. Such links are shown to be surprisingly precise for the first order rogue wave of the nonlinear Schrödinger (NLS) and the derivative NLS equations. A computational study on the second order rogue waves of the NLS equation also displays remarkable agreements.

Alfven wave cyclotron resonance heating

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

White, R.B.; Yosikawa, S.; Oberman, C.

1981-02-01

The resonance absorption of fast Alfven waves at the proton ctclotron resonance of a predominately deuterium plasma is investigated. An approximate dispersion relation is derived, valid in the vicinity of the resonance, which permits an exact calculation of transmission and reflection coefficients. For reasonable plasma parameters significant linear resonance absorption is found.

Application of the Parabolic Approximation to Predict Acoustical Propagation in the Ocean.

ERIC Educational Resources Information Center

McDaniel, Suzanne T.

1979-01-01

A simplified derivation of the parabolic approximation to the acoustical wave equation is presented. Exact solutions to this approximate equation are compared with solutions to the wave equation to demonstrate the applicability of this method to the study of underwater sound propagation. (Author/BB)

Partial transpose of random quantum states: Exact formulas and meanders

NASA Astrophysics Data System (ADS)

Fukuda, Motohisa; Śniady, Piotr

2013-04-01

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.

Excitations of breathers and rogue wave in the Heisenberg spin chain

NASA Astrophysics Data System (ADS)

Qi, Jian-Wen; Duan, Liang; Yang, Zhan-Ying; Yang, Wen-Li

2018-01-01

We study the excitations of breathers and rogue wave in a classical Heisenberg spin chain with twist interaction, which is governed by a fourth-order integrable nonlinear Schrödinger equation. The dynamics of these waves have been extracted from an exact solution. In particular, the corresponding existence conditions based on the parameters of perturbation wave number K, magnon number N, background wave vector ks and amplitude c are presented explicitly. Furthermore, the characteristics of magnetic moment distribution corresponding to these nonlinear waves are also investigated in detail. Finally, we discussed the state transition of three types nonlinear localized waves under the different excitation conditions.

Angular-momentum couplings in ultra-long-range giant dipole molecules

NASA Astrophysics Data System (ADS)

Stielow, Thomas; Scheel, Stefan; Kurz, Markus

2018-02-01

In this article we extend the theory of ultra-long-range giant dipole molecules, formed by an atom in a giant dipole state and a ground-state alkali-metal atom, by angular-momentum couplings known from recent works on Rydberg molecules. In addition to s -wave scattering, the next higher order of p -wave scattering in the Fermi pseudopotential describing the binding mechanism is considered. Furthermore, the singlet and triplet channels of the scattering interaction as well as angular-momentum couplings such as hyperfine interaction and Zeeman interactions are included. Within the framework of Born-Oppenheimer theory, potential energy surfaces are calculated in both first-order perturbation theory and exact diagonalization. Besides the known pure triplet states, mixed-spin character states are obtained, opening up a whole new landscape of molecular potentials. We determine exact binding energies and wave functions of the nuclear rotational and vibrational motion numerically from the various potential energy surfaces.

Physiological breakdown of Jeffrey six constant nanofluid flow in an endoscope with nonuniform wall

NASA Astrophysics Data System (ADS)

Nadeem, S.; Shaheen, A.; Hussain, S.

2015-12-01

This paper analyse the endoscopic effects of peristaltic nanofluid flow of Jeffrey six-constant fluid model in the presence of magnetohydrodynamics flow. The current problem is modeled in the cylindrical coordinate system and exact solutions are managed (where possible) under low Reynolds number and long wave length approximation. The influence of emerging parameters on temperature and velocity profile are discussed graphically. The velocity equation is solved analytically by utilizing the homotopy perturbation technique strongly, while the exact solutions are computed from temperature equation. The obtained expressions for velocity , concentration and temperature is sketched during graphs and the collision of assorted parameters is evaluate for transform peristaltic waves. The solution depend on thermophoresis number Nt, local nanoparticles Grashof number Gr, and Brownian motion number Nb. The obtained expressions for the velocity, temperature, and nanoparticles concentration profiles are plotted and the impact of various physical parameters are investigated for different peristaltic waves.

Rarefaction acceleration in magnetized gamma-ray burst jets

NASA Astrophysics Data System (ADS)

Sapountzis, Konstantinos; Vlahakis, Nektarios

2013-09-01

Relativistic jets associated with long/soft gamma-ray bursts are formed and initially propagate in the interior of the progenitor star. Because of the subsequent loss of their external pressure support after they cross the stellar surface, these flows can be modelled as moving around a corner. A strong steady-state rarefaction wave is formed, and the sideways expansion is accompanied by a rarefaction acceleration. We investigate the efficiency and the general characteristics of this mechanism by integrating the steady-state, special relativistic, magnetohydrodynamic equations, using a special set of partial exact solutions in planar geometry (r self-similar with respect to the `corner'). We also derive analytical approximate scalings in the ultrarelativistic cold/magnetized, and hydrodynamic limits. The mechanism is more effective in magnetized than in purely hydrodynamic flows. It substantially increases the Lorentz factor without much affecting the opening of the jet; the resulting values of their product can be much greater than unity, allowing for possible breaks in the afterglow light curves. These findings are similar to the ones from numerical simulations of axisymmetric jets by Komissarov et al. and Tchekhovskoy et al., although in our approach we describe the rarefaction as a steady-state simple wave and self-consistently calculate the opening of the jet that corresponds to zero external pressure.

Acoustic radiation force of a Bessel beam on a porous sphere.

PubMed

Azarpeyvand, Mahdi

2012-06-01

The possibility of using acoustic Bessel beams to produce an axial pulling force on porous particles is examined in an exact manner. The mathematical model utilizes the appropriate partial-wave expansion method in spherical coordinates, while Biot's model is used to describe the wave motion within the poroelastic medium. Of particular interest here is to examine the feasibility of using Bessel beams for (a) acoustic manipulation of fine porous particles and (b) suppression of particle resonances. To verify the viability of the technique, the radiation force and scattering form-function are calculated for aluminum and silica foams at various porosities. Inspection of the results has shown that acoustic manipulation of low porosity (<0.3) spheres is similar to that of solid elastic spheres, but this behavior significantly changes at higher porosities. Results have also shown a strong correlation between the backscattered form-function and the regions of negative radiation force. It has also been observed that the high-order resonances of the particle can be effectively suppressed by choosing the beam conical angle such that the acoustic contribution from that particular mode vanishes. This investigation may be helpful in the development of acoustic tweezers for manipulation of micro-porous drug delivery carrier and contrast agents.

Causal dissipation and shock profiles in the relativistic fluid dynamics of pure radiation.

PubMed

Freistühler, Heinrich; Temple, Blake

2014-06-08

CURRENT THEORIES OF DISSIPATION IN THE RELATIVISTIC REGIME SUFFER FROM ONE OF TWO DEFICITS: either their dissipation is not causal or no profiles for strong shock waves exist. This paper proposes a relativistic Navier-Stokes-Fourier-type viscosity and heat conduction tensor such that the resulting second-order system of partial differential equations for the fluid dynamics of pure radiation is symmetric hyperbolic. This system has causal dissipation as well as the property that all shock waves of arbitrary strength have smooth profiles. Entropy production is positive both on gradients near those of solutions to the dissipation-free equations and on gradients of shock profiles. This shows that the new dissipation stress tensor complies to leading order with the principles of thermodynamics. Whether higher order modifications of the ansatz are required to obtain full compatibility with the second law far from the zero-dissipation equilibrium is left to further investigations. The system has exactly three a priori free parameters χ , η , ζ , corresponding physically to heat conductivity, shear viscosity and bulk viscosity. If the bulk viscosity is zero (as is stated in the literature) and the total stress-energy tensor is trace free, the entire viscosity and heat conduction tensor is determined to within a constant factor.

Causal dissipation and shock profiles in the relativistic fluid dynamics of pure radiation

PubMed Central

Freistühler, Heinrich; Temple, Blake

2014-01-01

Current theories of dissipation in the relativistic regime suffer from one of two deficits: either their dissipation is not causal or no profiles for strong shock waves exist. This paper proposes a relativistic Navier–Stokes–Fourier-type viscosity and heat conduction tensor such that the resulting second-order system of partial differential equations for the fluid dynamics of pure radiation is symmetric hyperbolic. This system has causal dissipation as well as the property that all shock waves of arbitrary strength have smooth profiles. Entropy production is positive both on gradients near those of solutions to the dissipation-free equations and on gradients of shock profiles. This shows that the new dissipation stress tensor complies to leading order with the principles of thermodynamics. Whether higher order modifications of the ansatz are required to obtain full compatibility with the second law far from the zero-dissipation equilibrium is left to further investigations. The system has exactly three a priori free parameters χ,η,ζ, corresponding physically to heat conductivity, shear viscosity and bulk viscosity. If the bulk viscosity is zero (as is stated in the literature) and the total stress–energy tensor is trace free, the entire viscosity and heat conduction tensor is determined to within a constant factor. PMID:24910526

Focusing of noncircular self-similar shock waves.

PubMed

Betelu, S I; Aronson, D G

2001-08-13

We study the focusing of noncircular shock waves in a perfect gas. We construct an explicit self-similar solution by combining three convergent plane waves with regular shock reflections between them. We then show, with a numerical Riemann solver, that there are initial conditions with smooth shocks whose intermediate asymptotic stage is described by the exact solution. Unlike the focusing of circular shocks, our self-similar shocks have bounded energy density.

The mu-derivative and its applications to finding exact solutions of the Cahn-Hilliard, Korteveg-de Vries, and Burgers equations.

PubMed

Mitlin, Vlad

2005-10-15

A new transformation termed the mu-derivative is introduced. Applying it to the Cahn-Hilliard equation yields dynamical exact solutions. It is shown that the mu-transformed Cahn-Hilliard equation can be presented in a separable form. This transformation also yields dynamical exact solutions and separable forms for other nonlinear models such as the modified Korteveg-de Vries and the Burgers equations. The general structure of a nonlinear partial differential equation that becomes separable upon applying the mu-derivative is described.

Theoretical and lidar studies of the density response of the mesospheric sodium layer to gravity wave perturbations

NASA Technical Reports Server (NTRS)

Shelton, J. D.; Gardner, C. S.

1981-01-01

The density response of atmospheric layers to gravity waves is developed in two forms, an exact solution and a perturbation series solution. The degree of nonlinearity in the layer density response is described by the series solution whereas the exact solution gives insight into the nature of the responses. Density perturbation in an atmospheric layer are shown to be substantially greater than the atmospheric density perturbation associated with the propagation of a gravity wave. Because of the density gradients present in atmospheric layers, interesting effects were observed such as a phase reversal in the linear layer response which occurs near the layer peak. Once the layer response is understood, the sodium layer can be used as a tracer of atmospheric wave motions. A two dimensional digital signal processing technique was developed. Both spatial and temporal filtering are utilized to enhance the resolution by decreasing shot noise by more han 10 dB. Many of the features associated with a layer density response to gravity waves were observed in high resolution density profiles of the mesospheric sodium layer. These include nonlinearities as well as the phase reversal in the linear layer response.

Exact theory of freeze-out

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.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations.

PubMed

Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio

2014-10-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.

A note on improved F-expansion method combined with Riccati equation applied to nonlinear evolution equations

PubMed Central

Islam, Md. Shafiqul; Khan, Kamruzzaman; Akbar, M. Ali; Mastroberardino, Antonio

2014-01-01

The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin–Bona–Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering. PMID:26064530

Some new exact solitary wave solutions of the van der Waals model arising in nature

NASA Astrophysics Data System (ADS)

Bibi, Sadaf; Ahmed, Naveed; Khan, Umar; Mohyud-Din, Syed Tauseef

2018-06-01

This work proposes two well-known methods, namely, Exponential rational function method (ERFM) and Generalized Kudryashov method (GKM) to seek new exact solutions of the van der Waals normal form for the fluidized granular matter, linked with natural phenomena and industrial applications. New soliton solutions such as kink, periodic and solitary wave solutions are established coupled with 2D and 3D graphical patterns for clarity of physical features. Our comparison reveals that the said methods excel several existing methods. The worked-out solutions show that the suggested methods are simple and reliable as compared to many other approaches which tackle nonlinear equations stemming from applied sciences.

Exact and approximate solutions to the oblique shock equations for real-time applications

NASA Technical Reports Server (NTRS)

Hartley, T. T.; Brandis, R.; Mossayebi, F.

1991-01-01

The derivation of exact solutions for determining the characteristics of an oblique shock wave in a supersonic flow is investigated. Specifically, an explicit expression for the oblique shock angle in terms of the free stream Mach number, the centerbody deflection angle, and the ratio of the specific heats, is derived. A simpler approximate solution is obtained and compared to the exact solution. The primary objectives of obtaining these solutions is to provide a fast algorithm that can run in a real time environment.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

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

Meek, Garrett A.; Levine, Benjamin G., E-mail: levine@chemistry.msu.edu

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplingsmore » at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.« less

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

NASA Astrophysics Data System (ADS)

Meek, Garrett A.; Levine, Benjamin G.

2016-05-01

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.

PubMed

Meek, Garrett A; Levine, Benjamin G

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

DOE PAGES

Colangelo, Gilberto; Hoferichter, Martin; Procura, Massimiliano; ...

2017-04-27

In our third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon (g - 2) μ, including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of γ*γ* → ππ. We validate the formalism extensively using the pion-box contribution, defined by two-pion intermediate states with a pion-pole left-hand cut, and demonstrate how the full known result is reproduced when resumming the partial waves. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, amore » $$π-box\\atop{μ}$$ =-15.9(2) × 10 -11. As an application of the partial-wave formalism, we present a first calculation of ππ-rescattering effects in HLbL scattering, with γ*γ* → ππ helicity partial waves constructed dispersively using ππ phase shifts derived from the inverse-amplitude method. In this way, the isospin-0 part of our calculation can be interpreted as the contribution of the f0(500) to HLbL scattering in (g - 2) μ. We also argue that the contribution due to charged-pion rescattering implements corrections related to the corresponding pion polarizability and show that these are moderate. Our final result for the sum of pion-box contribution and its S-wave rescattering corrections reads a$$π-box\\atop{μ}$$ + a$$ππ, π-pole LHC\\atop{μ, J=0}$$ = -24(1) × 10 -11.« less

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

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

Colangelo, Gilberto; Hoferichter, Martin; Procura, Massimiliano

In our third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon (g - 2) μ, including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of γ*γ* → ππ. We validate the formalism extensively using the pion-box contribution, defined by two-pion intermediate states with a pion-pole left-hand cut, and demonstrate how the full known result is reproduced when resumming the partial waves. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, amore » $$π-box\\atop{μ}$$ =-15.9(2) × 10 -11. As an application of the partial-wave formalism, we present a first calculation of ππ-rescattering effects in HLbL scattering, with γ*γ* → ππ helicity partial waves constructed dispersively using ππ phase shifts derived from the inverse-amplitude method. In this way, the isospin-0 part of our calculation can be interpreted as the contribution of the f0(500) to HLbL scattering in (g - 2) μ. We also argue that the contribution due to charged-pion rescattering implements corrections related to the corresponding pion polarizability and show that these are moderate. Our final result for the sum of pion-box contribution and its S-wave rescattering corrections reads a$$π-box\\atop{μ}$$ + a$$ππ, π-pole LHC\\atop{μ, J=0}$$ = -24(1) × 10 -11.« less

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

NASA Astrophysics Data System (ADS)

Zhi, L.; Gu, H.

2017-12-01

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion has a better applicability. It doesn't need some assumptions and can estimate more parameters simultaneously. Meanwhile, by using the generalized linear method, the inversion is easily realized and its calculation amount is small. We use the Marmousi model to generate synthetic seismic records to test and analyze the influence of random noise. Without noise, all estimation results are relatively accurate. With the increase of noise, P-wave velocity change and oil saturation change are stable and less affected by noise. S-wave velocity change is most affected by noise. Finally we use the actual field data of time-lapse seismic prospecting to process and the results can prove the availability and feasibility of our method in actual situation.

Period of vibration of axially vibrating truly nonlinear rod

NASA Astrophysics Data System (ADS)

Cveticanin, L.

2016-07-01

In this paper the axial vibration of a muscle whose fibers are parallel to the direction of muscle compression is investigated. The model is a clamped-free rod with a strongly nonlinear elastic property. Axial vibration is described by a nonlinear partial differential equation. A solution of the equation is constructed for special initial conditions by using the method of separation of variables. The partial differential equation is separated into two uncoupled strongly nonlinear second order differential equations. Both equations, with displacement function and with time function are exactly determined. Exact solutions are given in the form of inverse incomplete and inverse complete Beta function. Using boundary and initial conditions, the frequency of vibration is obtained. It has to be mentioned that the determined frequency represents the exact analytic description for the axially vibrating truly nonlinear clamped-free rod. The procedure suggested in this paper is applied for calculation of the frequency of the longissimus dorsi muscle of a cow. The influence of elasticity order and elasticity coefficient on the frequency property is tested.

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.

Caudal Regression Syndrome with Partial Agenesis of the Corpus callosum and Partial Lobar Holoprosencephaly

PubMed Central

Hashami, Hilal Al; Bataclan, Maria F; Mathew, Mariam; Krishnan, Lalitha

2010-01-01

Caudal regression syndrome is a rare fetal condition of diabetic pregnancy. Although the exact mechanism is not known, hyperglycaemia during embryogenesis seems to act as a teratogen. Independently, caudal regression syndrome (CRS), agenesis of the corpus callosum (ACC) and partial lobar holoprosencephaly (HPE) have been reported in infants of diabetic mothers. To our knowledge, a combination of all these three conditions has not been reported so far. PMID:21509087

Caudal Regression Syndrome with Partial Agenesis of the Corpus callosum and Partial Lobar Holoprosencephaly: Case report.

PubMed

Hashami, Hilal Al; Bataclan, Maria F; Mathew, Mariam; Krishnan, Lalitha

2010-04-01

Caudal regression syndrome is a rare fetal condition of diabetic pregnancy. Although the exact mechanism is not known, hyperglycaemia during embryogenesis seems to act as a teratogen. Independently, caudal regression syndrome (CRS), agenesis of the corpus callosum (ACC) and partial lobar holoprosencephaly (HPE) have been reported in infants of diabetic mothers. To our knowledge, a combination of all these three conditions has not been reported so far.

Two-body Schrödinger wave functions in a plane-wave basis via separation of dimensions

NASA Astrophysics Data System (ADS)

Jerke, Jonathan; Poirier, Bill

2018-03-01

Using a combination of ideas, the ground and several excited electronic states of the helium atom and the hydrogen molecule are computed to chemical accuracy—i.e., to within 1-2 mhartree or better. The basic strategy is very different from the standard electronic structure approach in that the full two-electron six-dimensional (6D) problem is tackled directly, rather than starting from a single-electron Hartree-Fock approximation. Electron correlation is thus treated exactly, even though computational requirements remain modest. The method also allows for exact wave functions to be computed, as well as energy levels. From the full-dimensional 6D wave functions computed here, radial distribution functions and radial correlation functions are extracted—as well as a 2D probability density function exhibiting antisymmetry for a single Cartesian component. These calculations support a more recent interpretation of Hund's rule, which states that the lower energy of the higher spin-multiplicity states is actually due to reduced screening, rather than reduced electron-electron repulsion. Prospects for larger systems and/or electron dynamics applications appear promising.

Composite fermion basis for two-component Bose gases

NASA Astrophysics Data System (ADS)

Meyer, Marius; Liabotro, Ola

The composite fermion (CF) construction is known to produce wave functions that are not necessarily orthogonal, or even linearly independent, after projection. While usually not a practical issue in the quantum Hall regime, we have previously shown that it presents a technical challenge for rotating Bose gases with low angular momentum. These are systems where the CF approach yield surprisingly good approximations to the exact eigenstates of weak short-range interactions, and so solving the problem of linearly dependent wave functions is of interest. It can also be useful for studying CF excitations for fermions. Here we present several ways of constructing a basis for the space of ``simple CF states'' for two-component rotating Bose gases in the lowest Landau level, and prove that they all give a basis. Using the basis, we study the structure of the lowest-lying state using so-called restricted wave functions. We also examine the scaling of the overlap between the exact and CF wave functions at the maximal possible angular momentum for simple states. This work was financially supported by the Research Council of Norway.

Nonstationary magnetosonic wave dynamics in plasmas exhibiting collapse.

PubMed

Chakrabarti, Nikhil; Maity, Chandan; Schamel, Hans

2013-08-01

In a Lagrangian fluid approach, an explicit method has been presented previously to obtain an exact nonstationary magnetosonic-type wave solution in compressible magnetized plasmas of arbitrary resistivity showing competition among hydrodynamic convection, magnetic field diffusion, and dispersion [Chakrabarti et al., Phys. Rev. Lett. 106, 145003 (2011)]. The purpose of the present work is twofold: it serves (i) to describe the physical and mathematical background of the involved magnetosonic wave dynamics in more detail, as proposed by our original Letter, and (ii) to present an alternative approach, which utilizes the Lagrangian mass variable as a new spatial coordinate [Schamel, Phys. Rep. 392, 279 (2004)]. The obtained exact nonlinear wave solutions confirm the correctness of our previous results, indicating a collapse of the magnetic field irrespective of the presence of dispersion and resistivity. The mean plasma density, on the other hand, is less singular, showing collapse only when dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas, and they are expected to be of special importance in the astrophysical context of magnetic star formation.

Two-body Schrödinger wave functions in a plane-wave basis via separation of dimensions.

PubMed

Jerke, Jonathan; Poirier, Bill

2018-03-14

Using a combination of ideas, the ground and several excited electronic states of the helium atom and the hydrogen molecule are computed to chemical accuracy-i.e., to within 1-2 mhartree or better. The basic strategy is very different from the standard electronic structure approach in that the full two-electron six-dimensional (6D) problem is tackled directly, rather than starting from a single-electron Hartree-Fock approximation. Electron correlation is thus treated exactly, even though computational requirements remain modest. The method also allows for exact wave functions to be computed, as well as energy levels. From the full-dimensional 6D wave functions computed here, radial distribution functions and radial correlation functions are extracted-as well as a 2D probability density function exhibiting antisymmetry for a single Cartesian component. These calculations support a more recent interpretation of Hund's rule, which states that the lower energy of the higher spin-multiplicity states is actually due to reduced screening, rather than reduced electron-electron repulsion. Prospects for larger systems and/or electron dynamics applications appear promising.

The {sech}( {\\hat{ξ }} ) -Type Profiles: A Swiss-Army Knife for Exact Analytical Modeling of Thermal Diffusion and Wave Propagation in Graded Media

NASA Astrophysics Data System (ADS)

Krapez, J.-C.

2018-07-01

This work deals with the exact analytical modeling of transfer phenomena in heterogeneous materials exhibiting one-dimensional continuous variations of their properties. Regarding heat transfer, it has recently been shown that by applying a Liouville transformation and multiple Darboux transformations, infinite sequences of solvable profiles of thermal effusivity can be constructed together with the associated temperature (exact) solutions, all in closed-form expressions (vs. the diffusion-time variable and with a growing number of parameters). In addition, a particular class of profiles, the so-called {sech}( {\\hat{ξ }} ) -type profiles, exhibit high agility and at the same time parsimony. In this paper we delve further into the description of these solvable profiles and their properties. Most importantly, their quadrupole formulation is provided, enabling smooth synthetic profiles of effusivity of arbitrary complexity to be built, and allowing the corresponding temperature dynamic response to be obtained very easily thereafter. Examples are given with increasing variability of the effusivity and an increasing number of elementary profiles. These highly flexible profiles are equally relevant to providing an exact analytical solution to wave propagation problems in 1D graded media (i.e., Maxwell's equations, the acoustic equation, the telegraph equation, etc.). From now on, whether it be for diffusion-like or wave-like problems, when the leading properties present (possibly piecewise-) continuously heterogeneous profiles, the classical staircase model can be advantageously replaced by a "high-level" quadrupole model consisting of one or more {sech}( {\\hat{ξ }} ) -type profiles, which makes the latter a true Swiss-Army knife for analytical modeling.

Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium

PubMed Central

Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying

2015-01-01

A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066

High-order rogue waves in vector nonlinear Schrödinger equations.

PubMed

Ling, Liming; Guo, Boling; Zhao, Li-Chen

2014-04-01

We study the dynamics of high-order rogue waves (RWs) in two-component coupled nonlinear Schrödinger equations. We find that four fundamental rogue waves can emerge from second-order vector RWs in the coupled system, in contrast to the high-order ones in single-component systems. The distribution shape can be quadrilateral, triangle, and line structures by varying the proper initial excitations given by the exact analytical solutions. The distribution pattern for vector RWs is more abundant than that for scalar rogue waves. Possibilities to observe these new patterns for rogue waves are discussed for a nonlinear fiber.

Can a pure vector gravitational wave mimic a pure tensor one?

NASA Astrophysics Data System (ADS)

Allen, Bruce

2018-06-01

In the general theory of relativity, gravitational waves have two possible polarizations, which are transverse and traceless with helicity ±2 . Some alternative theories contain additional helicity 0 and helicity ±1 polarization modes. Here, we consider a hypothetical "pure vector" theory in which gravitational waves have only two possible polarizations, with helicity ±1 . We show that if these polarizations are allowed to rotate as the wave propagates, then for certain source locations on the sky, the strain outputs of three ideal interferometric gravitational wave detectors can exactly reproduce the strain outputs predicted by general relativity.

Electromagnetic or other directed energy pulse launcher

DOEpatents

Ziolkowski, Richard W.

1990-01-01

The physical realization of new solutions of wave propagation equations, such as Maxwell's equations and the scaler wave equation, produces localized pulses of wave energy such as electromagnetic or acoustic energy which propagate over long distances without divergence. The pulses are produced by driving each element of an array of radiating sources with a particular drive function so that the resultant localized packet of energy closely approximates the exact solutions and behaves the same.

Observation of 1-D time dependent non-propagating laser plasma structures using fluid and PIC codes

NASA Astrophysics Data System (ADS)

Verma, Deepa; Bera, Ratan Kumar; Kumar, Atul; Patel, Bhavesh; Das, Amita

2017-12-01

The manuscript reports the observation of time dependent localized and non-propagating structures in the coupled laser plasma system through 1-D fluid and Particle-In-Cell (PIC) simulations. It is reported that such structures form spontaneously as a result of collision amongst certain exact solitonic solutions. They are seen to survive as coherent entities for a long time up to several hundreds of plasma periods. Furthermore, it is shown that such time dependence can also be artificially recreated by significantly disturbing the delicate balance between the radiation and the density fields required for the exact non-propagating solution obtained by Esirkepov et al., JETP 68(1), 36-41 (1998). The ensuing time evolution is an interesting interplay between kinetic and field energies of the system. The electrostatic plasma oscillations are coupled with oscillations in the electromagnetic field. The inhomogeneity of the background and the relativistic nature, however, invariably produces large amplitude density perturbations leading to its wave breaking. In the fluid simulations, the signature of wave breaking can be discerned by a drop in the total energy which evidently gets lost to the grid. The PIC simulations are observed to closely follow the fluid simulations till the point of wave breaking. However, the total energy in the case of PIC simulations is seen to remain conserved throughout the simulations. At the wave breaking, the particles are observed to acquire thermal kinetic energy in the case of PIC. Interestingly, even after wave breaking, compact coherent structures with trapped radiation inside high-density peaks continue to exist both in PIC and fluid simulations. Although the time evolution does not exactly match in the two simulations as it does prior to the process of wave breaking, the time-dependent features exhibited by the remnant structures are characteristically similar.

Bianchi class A models in Sàez-Ballester's theory

NASA Astrophysics Data System (ADS)

Socorro, J.; Espinoza-García, Abraham

2012-08-01

We apply the Sàez-Ballester (SB) theory to Bianchi class A models, with a barotropic perfect fluid in a stiff matter epoch. We obtain exact classical solutions à la Hamilton for Bianchi type I, II and VIh=-1 models. We also find exact quantum solutions to all Bianchi Class A models employing a particular ansatz for the wave function of the universe.

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

NASA Astrophysics Data System (ADS)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

A Study of Supersonic Surface Sources: The Ffowcs Williams-Hawkings Equation and the Kirchhoff Formula

NASA Technical Reports Server (NTRS)

Farassat, F.; Brentner, Kenneth S.; Dunn, M. H.

2004-01-01

In this paper we address the mathematical problem of noise generation from high speed moving surfaces. The problem we are solving is the linear wave equation with sources on a moving surface. The Ffowcs Williams-Hawkings (FW-H) equation as well as the govern- ing equation for deriving the Kirchhoff formula for moving surfaces are both this type of partial differential equation. We give a new exact solution of this problem here in closed form which is valid for subsonic and supersonic motion of the surface but it is particularly suitable for supersonically moving surfaces. This new solution is the simplest of all high speed formulations of Langley and is denoted formulation 4 following the tradition of numbering of our major results for the prediction of the noise of rotating blades. We show that for a smooth surface moving at supersonic speed, our solution has only removable singularities. Thus it can be used for numerical work.

Numerical solution to generalized Burgers'-Fisher equation using Exp-function method hybridized with heuristic computation.

PubMed

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems.

Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation

PubMed Central

Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Malik, Aqdas Naveed; Haq, Ihsanul

2015-01-01

In this paper, a new heuristic scheme for the approximate solution of the generalized Burgers'-Fisher equation is proposed. The scheme is based on the hybridization of Exp-function method with nature inspired algorithm. The given nonlinear partial differential equation (NPDE) through substitution is converted into a nonlinear ordinary differential equation (NODE). The travelling wave solution is approximated by the Exp-function method with unknown parameters. The unknown parameters are estimated by transforming the NODE into an equivalent global error minimization problem by using a fitness function. The popular genetic algorithm (GA) is used to solve the minimization problem, and to achieve the unknown parameters. The proposed scheme is successfully implemented to solve the generalized Burgers'-Fisher equation. The comparison of numerical results with the exact solutions, and the solutions obtained using some traditional methods, including adomian decomposition method (ADM), homotopy perturbation method (HPM), and optimal homotopy asymptotic method (OHAM), show that the suggested scheme is fairly accurate and viable for solving such problems. PMID:25811858

Spatial and temporal compact equations for water waves

NASA Astrophysics Data System (ADS)

Dyachenko, Alexander; Kachulin, Dmitriy; Zakharov, Vladimir

2016-04-01

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

Confinement-induced p-wave resonances from s-wave interactions

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

Nishida, Yusuke; Tan, Shina; School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332

2010-12-15

We show that a purely s-wave interaction in three dimensions (3D) can induce higher partial-wave resonances in mixed dimensions. We develop two-body scattering theories in all three cases of 0D-3D, 1D-3D, and 2D-3D mixtures and determine the positions of higher partial-wave resonances in terms of the 3D s-wave scattering length assuming a harmonic confinement potential. We also compute the low-energy scattering parameters in the p-wave channel (scattering volume and effective momentum) that are necessary for the low-energy effective theory of the p-wave resonance. We point out that some of the resonances observed in the Florence group experiment [Phys. Rev. Lett.more » 104, 153202 (2010)] can be interpreted as the p-wave resonances in the 2D-3D mixed dimensions. Our study paves the way for a variety of physics, such as Anderson localization of matter waves under p-wave resonant scatterers.« less

Acoustic radiation force expansions in terms of partial wave phase shifts for scattering: Applications

NASA Astrophysics Data System (ADS)

Marston, Philip L.; Zhang, Likun

2016-11-01

When evaluating radiation forces on spheres in soundfields (with or without orbital-angular momentum) the interpretation of analytical results is greatly simplified by retaining the use of s-function notation for partial-wave coefficients imported into acoustics from quantum scattering theory in the 1970s. This facilitates easy interpretation of various efficiency factors. For situations in which dissipation is negligible, each partial-wave s-function becomes characterized by a single parameter: a phase shift allowing for all possible situations. These phase shifts are associated with scattering by plane traveling waves and the incident wavefield of interest is separately parameterized. (When considering outcomes, the method of fabricating symmetric objects having a desirable set of phase shifts becomes a separate issue.) The existence of negative radiation force "islands" for beams reported in 2006 by Marston is manifested. This approach and consideration of conservation theorems illustrate the unphysical nature of various claims made by other researchers. This approach is also directly relevant to objects in standing waves. Supported by ONR.

26 CFR 1.669(b)-1A - Tax on distribution.

Code of Federal Regulations, 2010 CFR

2010-04-01

... section (the “exact” method), or (2) The tax computed under paragraph (c) of this section (the “short-cut..., the method used in the return shall be accepted as the method that produces the lesser tax. The... tax imposed by section 668(a)(2). (b) Computation of partial tax by the exact method. The partial tax...

Acoustic attraction, repulsion and radiation force cancellation on a pair of rigid particles with arbitrary cross-sections in 2D: Circular cylinders example

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2017-11-01

The acoustic radiation forces arising on a pair of sound impenetrable cylindrical particles of arbitrary cross-sections are derived. Plane progressive, standing or quasi-standing waves with an arbitrary incidence angle are considered. Multiple scattering effects are described using the multipole expansion formalism and the addition theorem of cylindrical wave functions. An effective incident acoustic field on a particular object is determined, and used with the scattered field to derive closed-form analytical expressions for the radiation force vector components. The mathematical expressions for the radiation force components are exact, and have been formulated in partial-wave series expansions in cylindrical coordinates involving the angle of incidence, the reflection coefficient forming the progressive or the (quasi)standing wave field, the addition theorem, and the expansion coefficients. Numerical examples illustrate the analysis for two rigid circular cross-sections immersed in a non-viscous fluid. Computations for the dimensionless radiation force functions are performed with emphasis on varying the angle of incidence, the interparticle distance, the sizes of the particles as well as the characteristics of the incident field. Depending on the interparticle distance and angle of incidence, one of the particles yields neutrality; it experiences no force and becomes unresponsive (i.e., ;invisible;) to the linear momentum transfer of the effective incident field due to multiple scattering cancellation effects. Moreover, attractive or repulsive forces between the two particles may arise depending on the interparticle distance, the angle of incidence and size parameters of the particles. This study provides a complete analytical method and computations for the axial and transverse radiation force components in multiple acoustic scattering encompassing the cases of plane progressive, standing or quasi-standing waves of arbitrary incidence by a pair of scatterers. Potential applications concern the prediction of the forces used in acoustically-engineered metamaterials with reconfigurable periodicities, cloaking devices, and liquid crystals to name a few examples.

Ambiguities in model-independent partial-wave analysis

NASA Astrophysics Data System (ADS)

Krinner, F.; Greenwald, D.; Ryabchikov, D.; Grube, B.; Paul, S.

2018-06-01

Partial-wave analysis is an important tool for analyzing large data sets in hadronic decays of light and heavy mesons. It commonly relies on the isobar model, which assumes multihadron final states originate from successive two-body decays of well-known undisturbed intermediate states. Recently, analyses of heavy-meson decays and diffractively produced states have attempted to overcome the strong model dependences of the isobar model. These analyses have overlooked that model-independent, or freed-isobar, partial-wave analysis can introduce mathematical ambiguities in results. We show how these ambiguities arise and present general techniques for identifying their presence and for correcting for them. We demonstrate these techniques with specific examples in both heavy-meson decay and pion-proton scattering.

Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers

NASA Astrophysics Data System (ADS)

Javeed, Shumaila; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru

2018-06-01

The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.

Exact Lyapunov exponent of the harmonic magnon modes of one-dimensional Heisenberg-Mattis spin glasses

NASA Astrophysics Data System (ADS)

Sepehrinia, Reza; Niry, M. D.; Bozorg, B.; Tabar, M. Reza Rahimi; Sahimi, Muhammad

2008-03-01

A mapping is developed between the linearized equation of motion for the dynamics of the transverse modes at T=0 of the Heisenberg-Mattis model of one-dimensional (1D) spin glasses and the (discretized) random wave equation. The mapping is used to derive an exact expression for the Lyapunov exponent (LE) of the magnon modes of spin glasses and to show that it follows anomalous scaling at low magnon frequencies. In addition, through numerical simulations, the differences between the LE and the density of states of the wave equation in a discrete 1D model of randomly disordered media (those with a finite correlation length) and that of continuous media (with a zero correlation length) are demonstrated and emphasized.

Recovery time in quantum dynamics of wave packets

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

Strekalov, M. L., E-mail: strekalov@kinetics.nsc.ru

2017-01-15

A wave packet formed by a linear superposition of bound states with an arbitrary energy spectrum returns arbitrarily close to the initial state after a quite long time. A method in which quantum recovery times are calculated exactly is developed. In particular, an exact analytic expression is derived for the recovery time in the limiting case of a two-level system. In the general case, the reciprocal recovery time is proportional to the Gauss distribution that depends on two parameters (mean value and variance of the return probability). The dependence of the recovery time on the mean excitation level of themore » system is established. The recovery time is the longest for the maximal excitation level.« less

On optimizing the treatment of exchange perturbations

NASA Technical Reports Server (NTRS)

Hirschfelder, J. O.; Chipman, D. M.

1972-01-01

A method using the zeroth plus first order wave functions, obtained by optimizing the basic equation used in exchange perturbation treatments, is utilized in an attempt to determine the exact energy and wave function in the exchange process. Attempts to determine the first order perturbation solution by optimizing the sum of the first and second order energies were unsuccessful.

An Exact Algebraic Evaluation of Path-Length Difference for Two-Source Interference

ERIC Educational Resources Information Center

Hopper, Seth; Howell, John

2006-01-01

When studying wave interference, one often wants to know the difference in path length for two waves arriving at a common point P but coming from adjacent sources. For example, in many contexts interference maxima occur where this path-length difference is an integer multiple of the wavelength. The standard approximation for the path-length…

Acoustic Models of Optical Mirrors

ERIC Educational Resources Information Center

Mayer, V. V.; Varaksina, E. I.

2014-01-01

Students form a more exact idea of the action of optical mirrors if they can observe the wave field being formed during reflection. For this purpose it is possible to organize model experiments with flexural waves propagating in thin elastic plates. The direct and round edges of the plates are used as models of plane, convex and concave mirrors.…

Lie symmetry analysis, exact solutions and conservation laws for the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-06-01

In this work, we investigate the Lie symmetry analysis, exact solutions and conservation laws (Cls) to the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGDK) equation with Riemann-Liouville (RL) derivative. The time fractional CDGDK is reduced to nonlinear ordinary differential equation (ODE) of fractional order. New exact traveling wave solutions for the time fractional CDGDK are obtained by fractional sub-equation method. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. Ibragimov's nonlocal conservation method is applied to construct Cls for time fractional CDGDK.

Are There Optical Solitary Wave Solutions in Linear Media with Group Velocity Dispersion?

NASA Technical Reports Server (NTRS)

Li, Zhonghao; Zhou, Guosheng

1996-01-01

A generalized exact optical bright solitary wave solution in a three dimensional dispersive linear medium is presented. The most interesting property of the solution is that it can exist in the normal group-velocity-dispersion (GVD) region. In addition, another peculiar feature is that it may achieve a condition of 'zero-dispersion' to the media so that a solitary wave of arbitrarily small amplitude may be propagated with no dependence on is pulse width.

Updated analysis of NN elastic scattering to 3 GeV

NASA Astrophysics Data System (ADS)

Arndt, R. A.; Briscoe, W. J.; Strakovsky, I. I.; Workman, R. L.

2007-08-01

A partial-wave analysis of NN elastic scattering data has been updated to include a number of recent measurements. Experiments carried out at the Cooler Synchrotron (COSY) by the EDDA Collaboration have had a significant impact above 1 GeV. Results are discussed in terms of the partial-wave and direct-reconstruction amplitudes.

Laser backscattered from partially convex targets of large sizes in random media for E-wave polarization.

PubMed

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.

Resonances in the optical response of a slab with time-periodic dielectric function {epsilon}(t)

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

Zurita-Sanchez, Jorge R.; Halevi, P.

2010-05-15

We demonstrate that the optical response of a periodically modulated dynamic slab exhibits infinite resonances for frequencies {omega}=({Omega}/2)(2l+1), namely, odd multiples of one-half of the modulating frequency {Omega} of the dielectric function {epsilon}(t). These frequencies coincide partially with the usual condition of parametric amplification. However, the resonances occur only for certain normalized slab thicknesses L{sub R}. These resonances follow from detailed numerical studies based on our recent paper [Zurita-Sanchez, Halevi, and Cervantes-Gonzalez, Phys. Rev. A 79, 053821 (2009)]. As the thickness L nearly matches a resonance thickness L{sub R}, the amplitudes of counterpropagating modes in the slab obey a conditionmore » implying that both have the same modulus and their phases match a condition related to L{sub R} and the bulk wave vectors. When this condition is met, the electric field profile inside the slab is a superposition of standing waves with odd and even symmetries, and the reflection and transmission coefficients can reach great values and become infinite at exact resonance. Numerical simulations of the optical response are shown for a sinusoidal {epsilon}(t) with either moderate or strong modulation. As expected, as the modulation strength increases, higher-order harmonics {omega}-n{Omega} (n=0,{+-}1,{+-}2,...) become more noticeable, and short-wavelength bulk modes contribute significantly. However, we found that, regardless of the excitation frequency {omega}=({Omega}/2)(2l+1), the dominant spectral component of the generated fields is {Omega}/2. Also, as the excitation frequency increases, the parity of the standing waves is conserved.« less

Born approximation for scattering by evanescent waves: Comparison with exact scattering by an infinite fluid cylinder

NASA Astrophysics Data System (ADS)

Marston, Philip L.

2004-05-01

In some situations, evanescent waves can be an important component of the acoustic field within the sea bottom. For this reason (as well as to advance the understanding of scattering processes) it can be helpful to examine the modifications to scattering theory resulting from evanescence. Modifications to ray theory were examined in a prior approximation [P. L. Marston, J. Acoust. Soc. Am. 113, 2320 (2003)]. The new research concerns the modifications to the low-frequency Born approximation and confirmation by comparison with the exact two-dimensional scattering by a fluid cylinder. In the case of a circular cylinder having the same density as the surroundings but having a compressibility contrast with the surroundings, the Born approximation with a nonevanescent incident wave gives only monopole scattering. When the cylinder has a density contrast and the same compressibility as the surroundings the regular Born approximation gives only dipole scattering (with the dipole oriented along to the incident wavevector). In both cases when the Born approximation is modified to include the evanescence of the incident wave, an additional dipole scattering term is evident. In each case the new dipole is oriented along to the decay axis of the evanescent wave. [Research supported by ONR.

Improved optical filter

NASA Technical Reports Server (NTRS)

Title, A. M.

1978-01-01

Filter includes partial polarizer between birefrigent elements. Plastic film on partial polarizer compensates for any polarization rotation by partial polarizer. Two quarter-wave plates change incident, linearly polarized light into elliptically polarized light.

On mass transport in porosity waves

NASA Astrophysics Data System (ADS)

Jordan, Jacob S.; Hesse, Marc A.; Rudge, John F.

2018-03-01

Porosity waves arise naturally from the equations describing fluid migration in ductile rocks. Here, we show that higher-dimensional porosity waves can transport mass and therefore preserve geochemical signatures, at least partially. Fluid focusing into these high porosity waves leads to recirculation in their center. This recirculating fluid is separated from the background flow field by a circular dividing streamline and transported with the phase velocity of the porosity wave. Unlike models for one-dimensional chromatography in geological porous media, tracer transport in higher-dimensional porosity waves does not produce chromatographic separations between relatively incompatible elements due to the circular flow pattern. This may allow melt that originated from the partial melting of fertile heterogeneities or fluid produced during metamorphism to retain distinct geochemical signatures as they rise buoyantly towards the surface.

Theory of dissociative tunneling ionization

NASA Astrophysics Data System (ADS)

Svensmark, Jens; Tolstikhin, Oleg I.; Madsen, Lars Bojer

2016-05-01

We present a theoretical study of the dissociative tunneling ionization process. Analytic expressions for the nuclear kinetic energy distribution of the ionization rates are derived. A particularly simple expression for the spectrum is found by using the Born-Oppenheimer (BO) approximation in conjunction with the reflection principle. These spectra are compared to exact non-BO ab initio spectra obtained through model calculations with a quantum mechanical treatment of both the electronic and nuclear degrees of freedom. In the regime where the BO approximation is applicable, imaging of the BO nuclear wave function is demonstrated to be possible through reverse use of the reflection principle, when accounting appropriately for the electronic ionization rate. A qualitative difference between the exact and BO wave functions in the asymptotic region of large electronic distances is shown. Additionally, the behavior of the wave function across the turning line is seen to be reminiscent of light refraction. For weak fields, where the BO approximation does not apply, the weak-field asymptotic theory describes the spectrum accurately.

Bosonized Supersymmetric Sawada-Kotera Equations: Symmetries and Exact Solutions

NASA Astrophysics Data System (ADS)

Liu, Ping; Zeng, Bao-Qing; Liu, Li-Ming

2015-04-01

The Bosonized Supersymmetric Sawada-Kotera (BSSK) system is constructed by applying bosonization method to a Supersymmetric Sawada-Kotera system in this paper. The symmetries on the BSSK equations are researched and the calculation shows that the BSSK equations are invariant under the scaling transformations, the space-time translations and Galilean boosts. The one-parameter invariant subgroups and the corresponding invariant solutions are researched for the BSSK equations. Four types of reduction equations and similarity solutions are proposed. Period Cnoidal wave solutions, dark solitary wave solutions and bright solitary wave solutions of the BSSK equations are demonstrated and some evolution curves of the exact solutions are figured out. Supported by the National Natural Science Foundation of China under Grant No. 11305031, the Natural Science Foundation of Guangdong Province under Grant No. S2013010011546, the Science and Technology Project Foundation of Zhongshan under Grant Nos. 2013A3FC0264 and 2013A3FC0334, and Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No. Yq2013205

Time-Accurate, Unstructured-Mesh Navier-Stokes Computations with the Space-Time CESE Method

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan

2006-01-01

Application of the newly emerged space-time conservation element solution element (CESE) method to compressible Navier-Stokes equations is studied. In contrast to Euler equations solvers, several issues such as boundary conditions, numerical dissipation, and grid stiffness warrant systematic investigations and validations. Non-reflecting boundary conditions applied at the truncated boundary are also investigated from the stand point of acoustic wave propagation. Validations of the numerical solutions are performed by comparing with exact solutions for steady-state as well as time-accurate viscous flow problems. The test cases cover a broad speed regime for problems ranging from acoustic wave propagation to 3D hypersonic configurations. Model problems pertinent to hypersonic configurations demonstrate the effectiveness of the CESE method in treating flows with shocks, unsteady waves, and separations. Good agreement with exact solutions suggests that the space-time CESE method provides a viable alternative for time-accurate Navier-Stokes calculations of a broad range of problems.

High-order rogue waves of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Liu, Wei

2017-10-01

High-order rogue wave solutions of the Benjamin-Ono equation and the nonlocal nonlinear Schrödinger equation are derived by employing the bilinear method, which are expressed by simple polynomials. Typical dynamics of these high-order rogue waves are studied by analytical and graphical ways. For the Benjamin-Ono equation, there are two types of rogue waves, namely, bright rogue waves and dark rogue waves. In particular, the fundamental rogue wave pattern is different from the usual fundamental rogue wave patterns in other soliton equations. For the nonlocal nonlinear Schrödinger equation, the exact explicit rogue wave solutions up to the second order are presented. Typical rogue wave patterns such as Peregrine-type, triple and fundamental rogue waves are put forward. These high-order rogue wave patterns have not been shown before in the nonlocal Schrödinger equation.

Semiconductor Quantum Electron Wave Transport, Diffraction, and Interference: Analysis, Device, and Measurement.

NASA Astrophysics Data System (ADS)

Henderson, Gregory Newell

Semiconductor device dimensions are rapidly approaching a fundamental limit where drift-diffusion equations and the depletion approximation are no longer valid. In this regime, quantum effects can dominate device response. To increase further device density and speed, new devices must be designed that use these phenomena to positive advantage. In addition, quantum effects provide opportunities for a new class of devices which can perform functions previously unattainable with "conventional" semiconductor devices. This thesis has described research in the analysis of electron wave effects in semiconductors and the development of methods for the design, fabrication, and characterization of quantum devices based on these effects. First, an exact set of quantitative analogies are presented which allow the use of well understood optical design and analysis tools for the development of electron wave semiconductor devices. Motivated by these analogies, methods are presented for modeling electron wave grating diffraction using both an exact rigorous coupled-wave analysis and approximate analyses which are useful for grating design. Example electron wave grating switch and multiplexer designs are presented. In analogy to thin-film optics, the design and analysis of electron wave Fabry-Perot interference filters are also discussed. An innovative technique has been developed for testing these (and other) electron wave structures using Ballistic Electron Emission Microscopy (BEEM). This technique uses a liquid-helium temperature scanning tunneling microscope (STM) to perform spectroscopy of the electron transmittance as a function of electron energy. Experimental results show that BEEM can resolve even weak quantum effects, such as the reflectivity of a single interface between materials. Finally, methods are discussed for incorporating asymmetric electron wave Fabry-Perot filters into optoelectronic devices. Theoretical and experimental results show that such structures could be the basis for a new type of electrically pumped mid - to far-infrared semiconductor laser.

Exact solutions of a hierarchy of mixing speeds models

NASA Astrophysics Data System (ADS)

Cornille, H.; Platkowski, T.

1992-07-01

This paper presents several new aspects of discrete kinetic theory (DKT). First a hierarchy of d-dimensional (d=1,2,3) models is proposed with (2d+3) velocities and three moduli speeds: 0, 2, and a third one that can be arbitrary. It is assumed that the particles at rest have an internal energy which, for microscopic collisions, supplies for the loss of the kinetic energy. In a more general way than usual, collisions are allowed that mix particles with different speeds. Second, for the (1+1)-dimensional restriction of the systems of PDE for these models which have two independent quadratic collision terms we construct different exact solutions. The usual types of exact solutions are studied: periodic solutions and shock wave solutions obtained from the standard linearization of the scalar Riccati equations called Riccatian shock waves. Then other types of solutions of the coupled Riccati equations are found called non-Riccatian shock waves and they are compared with the previous ones. The main new result is that, between the upstream and downstream states, these new solutions are not necessarily monotonous. Further, for the shock problem, a two-dimensional dynamical system of ODE is solved numerically with limit values corresponding to the upstream and downstream states. As a by-product of this study two new linearizations for the Riccati coupled equations with two functions are proposed.

Scattering of plane evanescent waves by cylindrical shells and wave vector coupling conditions for exciting flexural waves

NASA Astrophysics Data System (ADS)

Marston, Philip L.

2002-05-01

The coupling of sound to buried targets can be associated with acoustic evanescent waves when the sea bottom is smooth. To understand the excitation of flexural waves on buried shells by acoustic evanescent waves, the partial wave series for the scattering is found for cylindrical shells at normal incidence in an unbounded medium. The formulation uses the simplifications of thin-shell dynamics. In the case of ordinary waves incident on a shell, a ray formulation is available to describe the coupling to subsonic flexural waves [P. L. Marston and N. H. Sun, J. Acoust. Soc. Am. 97, 777-783 (1995)]. When the incident wave is evanescent, the distance between propagating plane wavefronts is smaller than the ordinary acoustical wavelength at the same frequency and the coupling condition for the excitation of flexural waves on shells or plates is modified. Instead of matching the flexural wave number with the propagating part of the acoustic wave number only at the coincidence frequency, a second low-frequency wave number matching condition is found for highly evanescent waves. Numerical evaluation of the modified partial-wave-series appropriate for an evanescent wave is used to investigate the low-frequency coupling of evanescent waves with flexural wave resonances of shells.

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II: Inclusion of Exchange

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.

Partial tooth gear bearings

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.

An Analytical Model of Periodic Waves in Shallow Water,

DTIC Science & Technology

1984-07-01

the KP equation , "f’ + 6f +x + 3 f 0 (1.8) "’ S(t o x yy describes their evolution if they are weakly two-dimensional ( Kadomtsev & Petviashvili ...directions. Both short-crested and long-crested waves are available from the model. Every wave pattern is an exact solution of the Kadomtsev - Petviashvili ...vol. 9, pp 65-66 Kadomtsev , B. B. & V. I. Petviashvili , 1970, Soy. Phys. Doklady, vol. 15, pp 539-541 Korteweg, D. J. & G. de~ries, 1895, Phil Mag

Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials.

PubMed

Kourakis, I; Shukla, P K

2005-07-01

We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained.

Corrigendum to “A new hyperbolic auxiliary function method and exact solutions of the mBBM equation” [Commun Nonlinear Sci Numer Simul 2010;15:135-138

NASA Astrophysics Data System (ADS)

Layeni, Olawanle P.; Akinola, Ade P.

2010-09-01

The symbols w and ω were abused in article [1]. Replacing ξ + ω with ξ throughout the article (that is in Eqs. (5) and (13)-(23)) and afterwards taking w and ω to denote the (same) frequency of the traveling wave(s) set this right.

A note on sound radiation from distributed sources

NASA Technical Reports Server (NTRS)

Levine, H.

1979-01-01

The power output from a normally vibrating strip radiator is expressed in alternative general forms, one of these being chosen to refine and correct some particular estimates given by Heckl for different numerical ratios of strip width to wave length. An exact and explicit calculation is effected for sinusoidal velocity profiles when the strip width equals an integer number of half wave lengths.

Making Optical-Fiber Chemical Detectors More Sensitive

NASA Technical Reports Server (NTRS)

Rogowski, Robert S.; Egalon, Claudio O.

1993-01-01

Calculations based on exact theory of optical fiber shown how to increase optical efficiency and sensitivity of active-cladding step-index-profile optical-fiber fluorosensor using evanescent wave coupling. Optical-fiber fluorosensor contains molecules fluorescing when illuminated by suitable light in presence of analyte. Fluorescence coupled into and launched along core by evanescent-wave interaction. Efficiency increases with difference in refractive indices.

Second-order numerical solution of time-dependent, first-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Shah, Patricia L.; Hardin, Jay

1995-01-01

A finite difference scheme is developed to find an approximate solution of two similar hyperbolic equations, namely a first-order plane wave and spherical wave problem. Finite difference approximations are made for both the space and time derivatives. The result is a conditionally stable equation yielding an exact solution when the Courant number is set to one.

A first-order k-space model for elastic wave propagation in heterogeneous media.

PubMed

Firouzi, K; Cox, B T; Treeby, B E; Saffari, N

2012-09-01

A pseudospectral model of linear elastic wave propagation is described based on the first order stress-velocity equations of elastodynamics. k-space adjustments to the spectral gradient calculations are derived from the dyadic Green's function solution to the second-order elastic wave equation and used to (a) ensure the solution is exact for homogeneous wave propagation for timesteps of arbitrarily large size, and (b) also allows larger time steps without loss of accuracy in heterogeneous media. The formulation in k-space allows the wavefield to be split easily into compressional and shear parts. A perfectly matched layer (PML) absorbing boundary condition was developed to effectively impose a radiation condition on the wavefield. The staggered grid, which is essential for accurate simulations, is described, along with other practical details of the implementation. The model is verified through comparison with exact solutions for canonical examples and further examples are given to show the efficiency of the method for practical problems. The efficiency of the model is by virtue of the reduced point-per-wavelength requirement, the use of the fast Fourier transform (FFT) to calculate the gradients in k space, and larger time steps made possible by the k-space adjustments.

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

Inclusion of exact exchange in the noniterative partial-differential-equation method of electron-molecule scattering - Application to e-N2

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.

Mathieu Progressive Waves

NASA Astrophysics Data System (ADS)

Andrei, B. Utkin

2011-10-01

A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal curvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type.

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

NASA Astrophysics Data System (ADS)

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

2004-04-01

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

The transmission or scattering of elastic waves by an inhomogeneity of simple geometry: A comparison of theories

NASA Technical Reports Server (NTRS)

Sheu, Y. C.; Fu, L. S.

1983-01-01

The extended method of equivalent inclusions is applied to study the specific wave problems: (1) the transmission of elastic waves in an infinite medium containing a layer of inhomogeneity, and (2) the scattering of elastic waves in an infinite medium containing a perfect spherical inhomogeneity. Eigenstrains are expanded as a geometric series and a method of integration based on the inhomogeneous Helmholtz operator is adopted. This study compares results, obtained by using limited number of terms in the eigenstrain expansion, with exact solutions for the layer problem and that for a perfect sphere.

Traveling waves in actin dynamics and cell motility

PubMed Central

Allard, Jun; Mogilner, Alex

2012-01-01

Much of current understanding of cell motility arose from studying steady treadmilling of actin arrays. Recently, there have been a growing number of observations of a more complex, non-steady, actin behavior, including self-organized waves. It is becoming clear that these waves result from activation and inhibition feedbacks in actin dynamics acting on different scales, but the exact molecular nature of these feedbacks and respective roles of biomechanics and biochemistry are still unclear. Here, we review recent advances achieved in experimental and theoretical studies of actin waves and discuss mechanisms and physiological significance of wavy protrusions. PMID:22985541

Analytical time-domain Green’s functions for power-law media

PubMed Central

Kelly, James F.; McGough, Robert J.; Meerschaert, Mark M.

2008-01-01

Frequency-dependent loss and dispersion are typically modeled with a power-law attenuation coefficient, where the power-law exponent ranges from 0 to 2. To facilitate analytical solution, a fractional partial differential equation is derived that exactly describes power-law attenuation and the Szabo wave equation [“Time domain wave-equations for lossy media obeying a frequency power-law,” J. Acoust. Soc. Am. 96, 491–500 (1994)] is an approximation to this equation. This paper derives analytical time-domain Green’s functions in power-law media for exponents in this range. To construct solutions, stable law probability distributions are utilized. For exponents equal to 0, 1∕3, 1∕2, 2∕3, 3∕2, and 2, the Green’s function is expressed in terms of Dirac delta, exponential, Airy, hypergeometric, and Gaussian functions. For exponents strictly less than 1, the Green’s functions are expressed as Fox functions and are causal. For exponents greater than or equal than 1, the Green’s functions are expressed as Fox and Wright functions and are noncausal. However, numerical computations demonstrate that for observation points only one wavelength from the radiating source, the Green’s function is effectively causal for power-law exponents greater than or equal to 1. The analytical time-domain Green’s function is numerically verified against the material impulse response function, and the results demonstrate excellent agreement. PMID:19045774

Study of the exact analytical solution of the equation of longitudinal waves in a liquid with account of its relaxation properties

NASA Astrophysics Data System (ADS)

Kudinov, I. V.; Kudinov, V. A.

2013-09-01

A mathematical model of elastic vibrations of an incompressible liquid has been developed based on the hypothesis on the finite velocity of propagation of field potentials in this liquid. A hyperbolic equation of vibrations of such a liquid with account of its relaxation properties has been obtained. An exact analytical solution of this equation has been found and investigated in detail.

New envelope solitons for Gerdjikov-Ivanov model in nonlinear fiber optics

NASA Astrophysics Data System (ADS)

Triki, Houria; Alqahtani, Rubayyi T.; Zhou, Qin; Biswas, Anjan

2017-11-01

Exact soliton solutions in a class of derivative nonlinear Schrödinger equations including a pure quintic nonlinearity are investigated. By means of the coupled amplitude-phase formulation, we derive a nonlinear differential equation describing the evolution of the wave amplitude in the non-Kerr quintic media. The resulting amplitude equation is then solved to get exact analytical chirped bright, kink, antikink, and singular soliton solutions for the model. It is also shown that the nonlinear chirp associated with these solitons is crucially dependent on the wave intensity and related to self-steepening and group velocity dispersion parameters. Parametric conditions on physical parameters for the existence of chirped solitons are also presented. These localized structures exist due to a balance among quintic nonlinearity, group velocity dispersion, and self-steepening effects.

Exact exchange-correlation potentials of singlet two-electron systems

NASA Astrophysics Data System (ADS)

Ryabinkin, Ilya G.; Ospadov, Egor; Staroverov, Viktor N.

2017-10-01

We suggest a non-iterative analytic method for constructing the exchange-correlation potential, v XC ( r ) , of any singlet ground-state two-electron system. The method is based on a convenient formula for v XC ( r ) in terms of quantities determined only by the system's electronic wave function, exact or approximate, and is essentially different from the Kohn-Sham inversion technique. When applied to Gaussian-basis-set wave functions, the method yields finite-basis-set approximations to the corresponding basis-set-limit v XC ( r ) , whereas the Kohn-Sham inversion produces physically inappropriate (oscillatory and divergent) potentials. The effectiveness of the procedure is demonstrated by computing accurate exchange-correlation potentials of several two-electron systems (helium isoelectronic series, H2, H3 + ) using common ab initio methods and Gaussian basis sets.

Theory of electron-impact ionization of atoms

NASA Astrophysics Data System (ADS)

Kadyrov, A. S.; Mukhamedzhanov, A. M.; Stelbovics, A. T.; Bray, I.

2004-12-01

The existing formulations of electron-impact ionization of a hydrogenic target suffer from a number of formal problems including an ambiguous and phase-divergent definition of the ionization amplitude. An alternative formulation of the theory is given. An integral representation for the ionization amplitude which is free of ambiguity and divergence problems is derived and is shown to have four alternative, but equivalent, forms well suited for practical calculations. The extension to amplitudes of all possible scattering processes taking place in an arbitrary three-body system follows. A well-defined conventional post form of the breakup amplitude valid for arbitrary potentials including the long-range Coulomb interaction is given. Practical approaches are based on partial-wave expansions, so the formulation is also recast in terms of partial waves and partial-wave expansions of the asymptotic wave functions are presented. In particular, expansions of the asymptotic forms of the total scattering wave function, developed from both the initial and the final state, for electron-impact ionization of hydrogen are given. Finally, the utility of the present formulation is demonstrated on some well-known model problems.

Simple iterative construction of the optimized effective potential for orbital functionals, including exact exchange.

PubMed

Kümmel, Stephan; Perdew, John P

2003-01-31

For exchange-correlation functionals that depend explicitly on the Kohn-Sham orbitals, the potential V(xcsigma)(r) must be obtained as the solution of the optimized effective potential (OEP) integral equation. This is very demanding and has limited the use of orbital functionals. We demonstrate that instead the OEP can be obtained iteratively by solving the partial differential equations for the orbital shifts that exactify the Krieger-Li-Iafrate approximation. Unoccupied orbitals do not need to be calculated. Accuracy and efficiency of the method are shown for atoms and clusters using the exact-exchange energy. Counterintuitive asymptotic limits of the exact OEP are presented.

Pushing, pulling and electromagnetic radiation force cloaking by a pair of conducting cylindrical particles

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2018-02-01

The present analysis shows that two conducting cylindrical particles illuminated by an axially-polarized electric field of plane progressive waves at arbitrary incidence will attract, repel or become totally cloaked (i.e., invisible to the transfer of linear momentum carried by the incident waves), depending on their sizes, the interparticle distance as well as the angle of incidence of the incident field. Based on the rigorous multipole expansion method and the translational addition theorem of cylindrical wave functions, the electromagnetic (EM) radiation forces arising from multiple scattering effects between a pair of perfectly conducting cylindrical particles of circular cross-sections are derived and computed. An effective incident field on a particular particle is determined first, and used subsequently with its corresponding scattered field to derive the closed-form analytical expressions for the radiation force vector components. The mathematical expressions for the EM radiation force components (i.e. longitudinal and transverse) are exact, and have been formulated in partial-wave series expansions in cylindrical coordinates involving the angle of incidence, the interparticle distance and the expansion coefficients. Numerical examples illustrate the analysis for two perfectly conducting circular cylinders in a homogeneous nonmagnetic medium of wave propagation. The computations for the dimensionless radiation force functions are performed with particular emphasis on varying the angle of incidence, the interparticle distance, and the sizes of the particles. Depending on the interparticle distance and angle of incidence, the cylinders yield total neutrality (or invisibility); they experience no force and become unresponsive to the transfer of the EM linear momentum due to multiple scattering cancellation effects. Moreover, pushing or pulling EM forces between the two cylinders arise depending on the interparticle distance, the angle of incidence and their size parameters. This study provides a complete analytical method and computations for the longitudinal and transverse radiation force components in the multiple scattering of EM plane progressive waves with potential applications in particle manipulation, optically-engineered metamaterials with reconfigurable periodicities and cloaking devices to name a few examples.

An exact solution of the van der Waals interaction between two ground-state hydrogen atoms

NASA Astrophysics Data System (ADS)

Koga, Toshikatsu; Matsumoto, Shinya

1985-06-01

A momentum space treatment shows that perturbation equations for the H(1s)-H(1s) van der Waals interaction can be exactly solved in their Schrödinger forms without invoking any variational methods. Using the Fock transformation, which projects the momentum vector of an electron from the three-dimensional hyperplane onto the four-dimensional hypersphere, we solve the third order integral-type perturbation equation with respect to the reciprocal of the internuclear distance R. An exact third order wave function is found as a linear combination of infinite number of four-dimensional spherical harmonics. The result allows us to evaluate the exact dispersion energy E6R-6, which is completely determined by the first three coefficients of the above linear combination.

Shear waves in inhomogeneous, compressible fluids in a gravity field.

PubMed

Godin, Oleg A

2014-03-01

While elastic solids support compressional and shear waves, waves in ideal compressible fluids are usually thought of as compressional waves. Here, a class of acoustic-gravity waves is studied in which the dilatation is identically zero, and the pressure and density remain constant in each fluid particle. These shear waves are described by an exact analytic solution of linearized hydrodynamics equations in inhomogeneous, quiescent, inviscid, compressible fluids with piecewise continuous parameters in a uniform gravity field. It is demonstrated that the shear acoustic-gravity waves also can be supported by moving fluids as well as quiescent, viscous fluids with and without thermal conductivity. Excitation of a shear-wave normal mode by a point source and the normal mode distortion in realistic environmental models are considered. The shear acoustic-gravity waves are likely to play a significant role in coupling wave processes in the ocean and atmosphere.

TM surface wave diffraction by a truncated dielectric slab recessed in a perfectly conducting surface. [considering flush mounted space shuttle antenna

NASA Technical Reports Server (NTRS)

Pathak, P. H.; Kouyoumjian, R. G.

1974-01-01

The diffraction of a TM sub o surface wave by a terminated dielectric slab which is flush mounted in a perfectly conducting surface is studied. The incident surface wave gives rise to waves reflected and diffracted by the termination; these reflected and diffracted fields may be expressed in terms of the geometrical theory of diffraction by introducing surface wave reflection and diffraction coefficients which are associated with the termination. In this investigation, the surface wave reflection and diffraction coefficients have been deduced from a formally exact solution to this canonical problem. The solution is obtained by a combination of the generalized scattering matrix technique and function theoretic methods.

Nonlinear helicons bearing multi-scale structures

NASA Astrophysics Data System (ADS)

Abdelhamid, Hamdi M.; Yoshida, Zensho

2017-02-01

The helicon waves exhibit varying characters depending on plasma parameters, geometry, and wave numbers. Here, we elucidate an intrinsic multi-scale property embodied by the combination of the dispersive effect and nonlinearity. The extended magnetohydrodynamics model (exMHD) is capable of describing a wide range of parameter space. By using the underlying Hamiltonian structure of exMHD, we construct an exact nonlinear solution, which turns out to be a combination of two distinct modes, the helicon and Trivelpiece-Gould (TG) waves. In the regime of relatively low frequency or high density, however, the combination is made of the TG mode and an ion cyclotron wave (slow wave). The energy partition between these modes is determined by the helicities carried by the wave fields.

Note: A novel method for generating multichannel quasi-square-wave pulses.

PubMed

Mao, C; Zou, X; Wang, X

2015-08-01

A 21-channel quasi-square-wave nanosecond pulse generator was constructed. The generator consists of a high-voltage square-wave pulser and a channel divider. Using an electromagnetic relay as a switch and a 50-Ω polyethylene cable as a pulse forming line, the high-voltage pulser produces a 10-ns square-wave pulse of 1070 V. With a specially designed resistor-cable network, the channel divider divides the high-voltage square-wave pulse into 21 identical 10-ns quasi-square-wave pulses of 51 V, exactly equal to 1070 V/21. The generator can operate not only in a simultaneous mode but also in a delay mode if the cables in the channel divider are different in length.

Generic short-time propagation of sharp-boundaries wave packets

NASA Astrophysics Data System (ADS)

Granot, E.; Marchewka, A.

2005-11-01

A general solution to the "shutter" problem is presented. The propagation of an arbitrary initially bounded wave function is investigated, and the general solution for any such function is formulated. It is shown that the exact solution can be written as an expression that depends only on the values of the function (and its derivatives) at the boundaries. In particular, it is shown that at short times (t << 2mx2/hbar, where x is the distance to the boundaries) the wave function propagation depends only on the wave function's values (or its derivatives) at the boundaries of the region. Finally, we generalize these findings to a non-singular wave function (i.e., for wave packets with finite-width boundaries) and suggest an experimental verification.

Wave velocity characteristic for Kenaf natural fibre under impact damage

NASA Astrophysics Data System (ADS)

Zaleha, M.; Mahzan, S.; Fitri, Muhamad; Kamarudin, K. A.; Eliza, Y.; Tobi, A. L. Mohd

2017-01-01

This paper aims to determining the wave velocity characteristics for kenaf fibre reinforced composite (KFC) and it includes both experimental and simulation results. Lead zirconate titanate (PZT) sensor were proposed to be positioned to corresponding locations on the panel. In order to demonstrate the wave velocity, an impacts was introduced onto the panel. It is based on a classical sensor triangulation methodology, combines with experimental strain wave velocity analysis. Then the simulation was designed to replicate panel used in the experimental impacts test. This simulation was carried out using ABAQUS. It was shown that the wave velocity propagates faster in the finite element simulation. Although the experimental strain wave velocity and finite element simulation results do not match exactly, the shape of both waves is similar.

Exp-function method for solving fractional partial differential equations.

PubMed

Zheng, Bin

2013-01-01

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

On mass transport in magmatic porosity waves

NASA Astrophysics Data System (ADS)

Jordan, J.; Hesse, M. A.; Rudge, J. F.

2017-12-01

Geochemical analyses of oceanic basalts indicate the mantle is lithologically heterogenous and subject to partial melting. Here we show that porosity waves-which arise naturally in models of buoyancy driven melt migration-transport mass and preserve geochemical signatures, at least partially. Prior studies of tracer transport in one dimensional porosity waves conclude that porosity waves do not transfer mass. However, it is well known that one-dimensional porosity waves are unstable in two and three dimensions and break up into sets of cylindrical or spherical porosity waves. We show that tracer transport in higher dimensional porosity waves is dramatically different than in one dimension. Lateral melt focusing into these high porosity regions leads to melt recirculating in the center of the wave. Melt focusing and recirculation are not resolvable in one dimension where no sustained transport is observed in numerical experiments of solitary porosity waves. In two and three dimensions, the recirculating melt is separated from the background melt-flow field by a circular or spherical dividing streamline and transported with the phase velocity of the porosity wave. The amount of melt focusing that occurs within any given porosity wave, and thus, the extent of the dividing streamline, and resultant volume of transported melt is extremely sensitive to the selection of porosity-permeability and porosity-rheology relationships. Therefore, we present a regime diagram spanning common parameterizations that illustrates the minimum amplitude and phase velocity required for a solitary porosity wave to transport mass as a function of material properties and common parameters used in magma dynamics and mid-ocean ridge models. The realization that solitary waves are capable of sustaining melt transport may require the reinterpretation of previous studies. For example, transport in porosity waves may allow melts that originated from the partial melting of fertile heterogeneities to retain their incompatible trace element signatures as they rise through the mantle. Porosity waves may also provide a mechanism for mixing melts derived from heterogeneities with ambient melts derived from different depths in the mantle.

A scalable method for computing quadruplet wave-wave interactions

NASA Astrophysics Data System (ADS)

Van Vledder, Gerbrant

2017-04-01

Non-linear four-wave interactions are a key physical process in the evolution of wind generated ocean waves. The present generation operational wave models use the Discrete Interaction Approximation (DIA), but it accuracy is poor. It is now generally acknowledged that the DIA should be replaced with a more accurate method to improve predicted spectral shapes and derived parameters. The search for such a method is challenging as one should find a balance between accuracy and computational requirements. Such a method is presented here in the form of a scalable and adaptive method that can mimic both the time consuming exact Snl4 approach and the fast but inaccurate DIA, and everything in between. The method provides an elegant approach to improve the DIA, not by including more arbitrarily shaped wave number configurations, but by a mathematically consistent reduction of an exact method, viz. the WRT method. The adaptiveness is to adapt the abscissa of the locus integrand in relation to the magnitude of the known terms. The adaptiveness is extended to the highest level of the WRT method to select interacting wavenumber configurations in a hierarchical way in relation to their importance. This adaptiveness results in a speed-up of one to three orders of magnitude depending on the measure of accuracy. This definition of accuracy should not be expressed in terms of the quality of the transfer integral for academic spectra but rather in terms of wave model performance in a dynamic run. This has consequences for the balance between the required accuracy and the computational workload for evaluating these interactions. The performance of the scalable method on different scales is illustrated with results from academic spectra, simple growth curves to more complicated field cases using a 3G-wave model.

Nonlinear waves of a nonlocal modified KdV equation in the atmospheric and oceanic dynamical system

NASA Astrophysics Data System (ADS)

Tang, Xiao-yan; Liang, Zu-feng; Hao, Xia-zhi

2018-07-01

A new general nonlocal modified KdV equation is derived from the nonlinear inviscid dissipative and equivalent barotropic vorticity equation in a β-plane. The nonlocal property is manifested in the shifted parity and delayed time reversal symmetries. Exact solutions of the nonlocal modified KdV equation are obtained including periodic waves, kink waves, solitary waves, kink- and/or anti-kink-cnoidal periodic wave interaction solutions, which can be utilized to describe various two-place and time-delayed correlated events. As an illustration, a special approximate solution is applied to theoretically capture the salient features of two correlated dipole blocking events in atmospheric dynamical systems.

Low-frequency fluid waves in fractures and pipes

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

Korneev, Valeri

2010-09-01

Low-frequency analytical solutions have been obtained for phase velocities of symmetrical fluid waves within both an infinite fracture and a pipe filled with a viscous fluid. Three different fluid wave regimes can exist in such objects, depending on the various combinations of parameters, such as fluid density, fluid viscosity, walls shear modulus, channel thickness, and frequency. Equations for velocities of all these regimes have explicit forms and are verified by comparisons with the exact solutions. The dominant role of fractures in rock permeability at field scales and the strong amplitude and frequency effects of Stoneley guided waves suggest the importancemore » of including these wave effects into poroelastic theories.« less

Waves and instabilities in an anisotropic universe

NASA Astrophysics Data System (ADS)

Papadopoulos, D.; Vlahos, L.; Esposito, F. P.

2002-01-01

The excitation of low frequency plasma waves in an expanding anisotropic cosmological model that contains a magnetic field frozen into the matter and pointing in the longitudinal direction is discussed. Using the exact equations governing finite-amplitude wave propagation in hydromagnetic media within the framework of the general theory of relativity, we show that a spectrum of magnetized sound waves will be excited and form large-scale ``damped oscillations'' in the expanding universe. The characteristic frequency of the excited waves is slightly shifted away from the sound frequency and the shift depends on the strength of the primordial magnetic field. This magnetic field dependent shift may have an effect on the acoustic peaks of the CMB.

Beta value coupled wave theory for nonslanted reflection gratings.

PubMed

Neipp, Cristian; Francés, Jorge; Gallego, Sergi; Bleda, Sergio; Martínez, Francisco Javier; Pascual, Inmaculada; Beléndez, Augusto

2014-01-01

We present a modified coupled wave theory to describe the properties of nonslanted reflection volume diffraction gratings. The method is based on the beta value coupled wave theory, which will be corrected by using appropriate boundary conditions. The use of this correction allows predicting the efficiency of the reflected order for nonslanted reflection gratings embedded in two media with different refractive indices. The results obtained by using this method will be compared to those obtained using a matrix method, which gives exact solutions in terms of Mathieu functions, and also to Kogelnik's coupled wave theory. As will be demonstrated, the technique presented in this paper means a significant improvement over Kogelnik's coupled wave theory.

Beta Value Coupled Wave Theory for Nonslanted Reflection Gratings

PubMed Central

Neipp, Cristian; Francés, Jorge; Gallego, Sergi; Bleda, Sergio; Martínez, Francisco Javier; Pascual, Inmaculada; Beléndez, Augusto

2014-01-01

We present a modified coupled wave theory to describe the properties of nonslanted reflection volume diffraction gratings. The method is based on the beta value coupled wave theory, which will be corrected by using appropriate boundary conditions. The use of this correction allows predicting the efficiency of the reflected order for nonslanted reflection gratings embedded in two media with different refractive indices. The results obtained by using this method will be compared to those obtained using a matrix method, which gives exact solutions in terms of Mathieu functions, and also to Kogelnik's coupled wave theory. As will be demonstrated, the technique presented in this paper means a significant improvement over Kogelnik's coupled wave theory. PMID:24723811

The Aharonov-Bohm effect and Tonomura et al. experiments: Rigorous results

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

Ballesteros, Miguel; Weder, Ricardo

The Aharonov-Bohm effect is a fundamental issue in physics. It describes the physically important electromagnetic quantities in quantum mechanics. Its experimental verification constitutes a test of the theory of quantum mechanics itself. The remarkable experiments of Tonomura et al. ['Observation of Aharonov-Bohm effect by electron holography', Phys. Rev. Lett 48, 1443 (1982) and 'Evidence for Aharonov-Bohm effect with magnetic field completely shielded from electron wave', Phys. Rev. Lett 56, 792 (1986)] are widely considered as the only experimental evidence of the physical existence of the Aharonov-Bohm effect. Here we give the first rigorous proof that the classical ansatz of Aharonovmore » and Bohm of 1959 ['Significance of electromagnetic potentials in the quantum theory', Phys. Rev. 115, 485 (1959)], that was tested by Tonomura et al., is a good approximation to the exact solution to the Schroedinger equation. This also proves that the electron, that is, represented by the exact solution, is not accelerated, in agreement with the recent experiment of Caprez et al. in 2007 ['Macroscopic test of the Aharonov-Bohm effect', Phys. Rev. Lett. 99, 210401 (2007)], that shows that the results of the Tonomura et al. experiments can not be explained by the action of a force. Under the assumption that the incoming free electron is a Gaussian wave packet, we estimate the exact solution to the Schroedinger equation for all times. We provide a rigorous, quantitative error bound for the difference in norm between the exact solution and the Aharonov-Bohm Ansatz. Our bound is uniform in time. We also prove that on the Gaussian asymptotic state the scattering operator is given by a constant phase shift, up to a quantitative error bound that we provide. Our results show that for intermediate size electron wave packets, smaller than the ones used in the Tonomura et al. experiments, quantum mechanics predicts the results observed by Tonomura et al. with an error bound smaller than 10{sup -99}. It would be quite interesting to perform experiments with electron wave packets of intermediate size. Furthermore, we provide a physical interpretation of our error bound.« less

Comment on "Collision of plane gravitational waves without singularities"

NASA Astrophysics Data System (ADS)

Nutku, Y.

1981-08-01

An incorrect paper was published by B. J. Stoyanov carrying the title above. Here we shall point out a coordinate transformation whereby "the new exact solution" of his paper is recognized as a Kasner universe. Further, we shall show that Stoyanov's interpretation of the Kasner solution as colliding plane gravitational waves runs into the difficulty that the Einstein field equations are not satisfied everywhere.

Comment on ''Collision of plane gravitational waves without singularities''

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

Nutku, Y.

1981-08-15

An incorrect paper was published by B. J. Stoyanov carrying the title above. Here we shall point out a coordinate transformation whereby ''the new exact solution'' of his paper is recognized as a Kasner universe. Further, we shall show that Stoyanov's interpretation of the Kasner solution as colliding plane gravitational waves runs into the difficulty that the Einstein field equations are not satisfied everywhere.

Bifurcation of rupture path by linear and cubic damping force

NASA Astrophysics Data System (ADS)

Dennis L. C., C.; Chew X., Y.; Lee Y., C.

2014-06-01

Bifurcation of rupture path is studied for the effect of linear and cubic damping. Momentum equation with Rayleigh factor was transformed into ordinary differential form. Bernoulli differential equation was obtained and solved by the separation of variables. Analytical or exact solutions yielded the bifurcation was visible at imaginary part when the wave was non dispersive. For the dispersive wave, bifurcation of rupture path was invisible.

A Numerical and Theoretical Study of Seismic Wave Diffraction in Complex Geologic Structure

DTIC Science & Technology

1989-04-14

element methods for analyzing linear and nonlinear seismic effects in the surficial geologies relevant to several Air Force missions. The second...exact solution evaluated here indicates that edge-diffracted seismic wave fields calculated by discrete numerical methods probably exhibits significant...study is to demonstrate and validate some discrete numerical methods essential for analyzing linear and nonlinear seismic effects in the surficial

Many-body Green’s function theory for electron-phonon interactions: Ground state properties of the Holstein dimer

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

Säkkinen, Niko; Leeuwen, Robert van; Peng, Yang

2015-12-21

We study ground-state properties of a two-site, two-electron Holstein model describing two molecules coupled indirectly via electron-phonon interaction by using both exact diagonalization and self-consistent diagrammatic many-body perturbation theory. The Hartree and self-consistent Born approximations used in the present work are studied at different levels of self-consistency. The governing equations are shown to exhibit multiple solutions when the electron-phonon interaction is sufficiently strong, whereas at smaller interactions, only a single solution is found. The additional solutions at larger electron-phonon couplings correspond to symmetry-broken states with inhomogeneous electron densities. A comparison to exact results indicates that this symmetry breaking is stronglymore » correlated with the formation of a bipolaron state in which the two electrons prefer to reside on the same molecule. The results further show that the Hartree and partially self-consistent Born solutions obtained by enforcing symmetry do not compare well with exact energetics, while the fully self-consistent Born approximation improves the qualitative and quantitative agreement with exact results in the same symmetric case. This together with a presented natural occupation number analysis supports the conclusion that the fully self-consistent approximation describes partially the bipolaron crossover. These results contribute to better understanding how these approximations cope with the strong localizing effect of the electron-phonon interaction.« less

The generation and propagation of internal gravity waves in a rotating fluid

NASA Technical Reports Server (NTRS)

Maxworthy, T.; Chabert Dhieres, G.; Didelle, H.

1984-01-01

The present investigation is concerned with an extension of a study conducted bu Maxworthy (1979) on internal wave generation by barotropic tidal flow over bottom topography. A short series of experiments was carried out during a limited time period on a large (14-m diameter) rotating table. It was attempted to obtain, in particular, information regarding the plan form of the waves, the exact character of the flow over the obstacle, and the evolution of the waves. The main basin was a dammed section of a long free surface water tunnel. The obstacle was towed back and forth by a wire harness connected to an electronically controlled hydraulic piston, the stroke and period of which could be independently varied. Attention is given to the evolution of the wave crests, the formation of solitary wave groups the evolution of the three-dimensional wave field wave shapes, the wave amplitudes, and particle motion.

Analytical approach for the fractional differential equations by using the extended tanh method

NASA Astrophysics Data System (ADS)

Pandir, Yusuf; Yildirim, Ayse

2018-07-01

In this study, we consider analytical solutions of space-time fractional derivative foam drainage equation, the nonlinear Korteweg-de Vries equation with time and space-fractional derivatives and time-fractional reaction-diffusion equation by using the extended tanh method. The fractional derivatives are defined in the modified Riemann-Liouville context. As a result, various exact analytical solutions consisting of trigonometric function solutions, kink-shaped soliton solutions and new exact solitary wave solutions are obtained.

Relationship of scattering phase shifts to special radiation force conditions for spheres in axisymmetric wave-fields.

PubMed

Marston, Philip L; Zhang, Likun

2017-05-01

When investigating the radiation forces on spheres in complicated wave-fields, the interpretation of analytical results can be simplified by retaining the s-function notation and associated phase shifts imported into acoustics from quantum scattering theory. For situations in which dissipation is negligible, as taken to be the case in the present investigation, there is an additional simplification in that partial-wave phase shifts become real numbers that vanish when the partial-wave index becomes large and when the wave-number-sphere-radius product vanishes. By restricting attention to monopole and dipole phase shifts, transitions in the axial radiation force for axisymmetric wave-fields are found to be related to wave-field parameters for traveling and standing Bessel wave-fields by considering the ratio of the phase shifts. For traveling waves, the special force conditions concern negative forces while for standing waves, the special force conditions concern vanishing radiation forces. An intermediate step involves considering the functional dependence on phase shifts. An appendix gives an approximation for zero-force plane standing wave conditions. Connections with early investigations of acoustic levitation are mentioned and some complications associated with viscosity are briefly noted.

Scattering of acoustic evanescent waves by circular cylinders: Partial wave series solution

NASA Astrophysics Data System (ADS)

Marston, Philip L.

2002-05-01

Evanescent acoustical waves occur in a variety of situations such as when sound is incident on a fluid interface beyond the critical angle and when flexural waves on a plate are subsonic with respect to the surrounding fluid. The scattering by circular cylinders at normal incidence was calculated to give insight into the consequences on the scattering of the evanescence of the incident wave. To analyze the scattering, it is necessary to express the incident wave using a modified expansion involving cylindrical functions. For plane evanescent waves, the expansion becomes a double summation with products of modified and ordinary Bessel functions. The resulting modified series is found for the scattering by a fluid cylinder in an unbounded medium. The perfectly soft and rigid cases are also examined. Unlike the case of an ordinary incident wave, the counterpropagating partial waves of the same angular order have unequal magnitudes when the incident wave is evanescent. This is a consequence of the exponential dependence of the incident wave amplitude on the transverse coordinate. The associated exponential dependence of the scattering on the location of a scatterer was previously demonstrated [T. J. Matula and P. L. Marston, J. Acoust. Soc. Am. 93, 1192-1195 (1993)].

Explaining the Relationship Between Sexually Explicit Internet Material and Casual Sex: A Two-Step Mediation Model.

PubMed

Vandenbosch, Laura; van Oosten, Johanna M F

2018-07-01

Despite increasing interest in the implications of adolescents' use of sexually explicit Internet material (SEIM), we still know little about the relationship between SEIM use and adolescents' casual sexual activities. Based on a three-wave online panel survey study among Dutch adolescents (N = 1079; 53.1% boys; 93.5% with an exclusively heterosexual orientation; M age  = 15.11; SD = 1.39), we found that watching SEIM predicted engagement in casual sex over time. In turn, casual sexual activities partially predicted adolescents' use of SEIM. A two-step mediation model was tested to explain the relationship between watching SEIM and casual sex. It was partially confirmed. First, watching SEIM predicted adolescents' perceptions of SEIM as a relevant information source from Wave 2 to Wave 3, but not from Wave 1 to Wave 2. Next, such perceived utility of SEIM was positively related to stronger instrumental attitudes toward sex and thus their views about sex as a core instrument for sexual gratification. Lastly, adolescents' instrumental attitudes toward sex predicted adolescents' engagement in casual sex activities consistently across waves. Partial support emerged for a reciprocal relationship between watching SEIM and perceived utility. We did not find a reverse relationship between casual sex activities and instrumental attitudes toward sex. No significant gender differences emerged.

Smoking policy change at a homeless shelter: attitudes and effects.

PubMed

Businelle, Michael S; Poonawalla, Insiya B; Kendzor, Darla E; Rios, Debra M; Cuate, Erica L; Savoy, Elaine J; Ma, Ping; Baggett, Travis P; Reingle, Jennifer; Reitzel, Lorraine R

2015-01-01

Homeless adults are exposed to more smokers and smoke in response to environmental tobacco cues more than other socioeconomically disadvantaged groups. Addressing the culture of smoking in homeless shelters through policy initiatives may support cessation and improve health in this vulnerable and understudied population. This study examined support for and expected/actual effects of a smoking ban at a homeless shelter. A 2-wave cross-sectional study with an embedded cohort was conducted in the summer of 2013 two weeks before (wave 1) and two months after (wave 2) a partial outdoor smoking ban was implemented. A total of 394 homeless adults were surveyed (i.e., wave 1 [n=155]; wave 2 [n=150]; and 89 additional participants completed both waves). On average, participants were 43 years old, primarily African American (63%), male (72%), and had been homeless for the previous 12 months (median). Most participants were smokers (76%) smoking 12 cigarettes per day on average. Most participants supported the creation of a large smoke-free zone on the shelter campus, but there was less support for a shelter-wide smoking ban. Average cigarettes smoked per day did not differ between study waves. However, participants who completed both study waves experienced a reduction in expired carbon monoxide at wave 2 (W1=18.2 vs. W2=15.8 parts per million, p=.02). Expected effects of the partial ban were similar to actual effects. Partial outdoor smoking bans may be well supported by homeless shelter residents and may have a positive impact on shelter resident health. Copyright © 2014 Elsevier Ltd. All rights reserved.

Standard map in magnetized relativistic systems: fixed points and regular acceleration.

PubMed

de Sousa, M C; Steffens, F M; Pakter, R; Rizzato, F B

2010-08-01

We investigate the concept of a standard map for the interaction of relativistic particles and electrostatic waves of arbitrary amplitudes, under the action of external magnetic fields. The map is adequate for physical settings where waves and particles interact impulsively, and allows for a series of analytical result to be exactly obtained. Unlike the traditional form of the standard map, the present map is nonlinear in the wave amplitude and displays a series of peculiar properties. Among these properties we discuss the relation involving fixed points of the maps and accelerator regimes.

Seismo-Electromagnetic Emissions Related to Seismic Waves can Trigger TLEs

NASA Astrophysics Data System (ADS)

Sorokin, Leonid V.

2009-04-01

This paper deals with the rare high intensity electromagnetic pulses associated with earthquakes, whose spectrum signature differs from that of atmospherics produced by lightning discharges. On the basis of actual data records, cases of the generation of anomalous seismo-electromagnetic emissions are described. These natural sub-millisecond electromagnetic pulses were associated with the passage of seismic waves from earthquakes to Moscow, the place where the electromagnetic field observations were made. Space-time coupling has been revealed between exact seismic waves from the earthquakes, lightning triggering and Transient Luminous Events triggering.

Time's arrow: A numerical experiment

NASA Astrophysics Data System (ADS)

Fowles, G. Richard

1994-04-01

The dependence of time's arrow on initial conditions is illustrated by a numerical example in which plane waves produced by an initial pressure pulse are followed as they are multiply reflected at internal interfaces of a layered medium. Wave interactions at interfaces are shown to be analogous to the retarded and advanced waves of point sources. The model is linear and the calculation is exact and demonstrably time reversible; nevertheless the results show most of the features expected of a macroscopically irreversible system, including the approach to the Maxwell-Boltzmann distribution, ergodicity, and concomitant entropy increase.

Identical Collision Terms/Solutions of Kinetic Eqn. and Explanation of Damping of Waves in Plasmas and Solids Known by Different Names

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

Sharma, S. K.

2010-11-23

In this paper we show that identical collision terms are known by different names in gaseous plasmas and solids. Method used by plasma physicists and the one used by solid state physicists to solve Kinetic equation are also exactly same but they are also known by different names. In fact the physical explanation of damping of plasma Waves given by plasma physicists is quite similar to that given by solid state physicists to explain the absorption of acoustic waves in solids.

Analytical studies on the Benney-Luke equation in mathematical physics

NASA Astrophysics Data System (ADS)

Islam, S. M. Rayhanul; Khan, Kamruzzaman; Woadud, K. M. Abdul Al

2018-04-01

The enhanced (G‧/G)-expansion method presents wide applicability to handling nonlinear wave equations. In this article, we find the new exact traveling wave solutions of the Benney-Luke equation by using the enhanced (G‧/G)-expansion method. This method is a useful, reliable, and concise method to easily solve the nonlinear evaluation equations (NLEEs). The traveling wave solutions have expressed in term of the hyperbolic and trigonometric functions. We also have plotted the 2D and 3D graphics of some analytical solutions obtained in this paper.

Potential clinical applications of photoacoustics

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

Rosencwaig, A.

1982-09-01

Photoacoustic spectroscopy offers the opportunity for extending the exact science of noninvasive spectral analysis to intact medical substances such as tissues. Thermal-wave imaging offers the potential for microscopic imaging of thermal features in biological matter.

Surface wave energy absorption by a partially submerged bio-inspired canopy.

PubMed

Nové-Josserand, C; Castro Hebrero, F; Petit, L-M; Megill, W M; Godoy-Diana, R; Thiria, B

2018-03-27

Aquatic plants are known to protect coastlines and riverbeds from erosion by damping waves and fluid flow. These flexible structures absorb the fluid-borne energy of an incoming fluid by deforming mechanically. In this paper we focus on the mechanisms involved in these fluid-elasticity interactions, as an efficient energy harvesting system, using an experimental canopy model in a wave tank. We study an array of partially-submerged flexible structures that are subjected to the action of a surface wave field, investigating in particular the role of spacing between the elements of the array on the ability of our system to absorb energy from the flow. The energy absorption potential of the canopy model is examined using global wave height measurements for the wave field and local measurements of the elastic energy based on the kinematics of each element of the canopy. We study different canopy arrays and show in particular that flexibility improves wave damping by around 40%, for which half is potentially harvestable.

Multi-fluid Approach to High-frequency Waves in Plasmas. III. Nonlinear Regime and Plasma Heating

NASA Astrophysics Data System (ADS)

Martínez-Gómez, David; Soler, Roberto; Terradas, Jaume

2018-03-01

The multi-fluid modeling of high-frequency waves in partially ionized plasmas has shown that the behavior of magnetohydrodynamic waves in the linear regime is heavily influenced by the collisional interaction between the different species that form the plasma. Here, we go beyond linear theory and study large-amplitude waves in partially ionized plasmas using a nonlinear multi-fluid code. It is known that in fully ionized plasmas, nonlinear Alfvén waves generate density and pressure perturbations. Those nonlinear effects are more pronounced for standing oscillations than for propagating waves. By means of numerical simulations and analytical approximations, we examine how the collisional interaction between ions and neutrals affects the nonlinear evolution. The friction due to collisions dissipates a fraction of the wave energy, which is transformed into heat and consequently raises the temperature of the plasma. As an application, we investigate frictional heating in a plasma with physical conditions akin to those in a quiescent solar prominence.

Radiation from a current filament driven by a traveling wave

NASA Technical Reports Server (NTRS)

Levine, D. M.; Meneghini, R.

1976-01-01

Solutions are presented for the electromagnetic fields radiated by an arbitrarily oriented current filament located above a perfectly conducting ground plane and excited by a traveling current wave. Both an approximate solution, valid in the fraunhofer region of the filament and predicting the radiation terms in the fields, and an exact solution, which predicts both near and far field components of the electromagnetic fields, are presented. Both solutions apply to current waveforms which propagate along the channel but are valid regardless of the actual waveshape. The exact solution is valid only for waves which propagate at the speed of light, and the approximate solution is formulated for arbitrary velocity of propagation. The spectrum-magnitude of the fourier transform-of the radiated fields is computed by assuming a compound exponential model for the current waveform. The effects of channel orientation and length, as well as velocity of propagation of the current waveform and location of the observer, are discussed. It is shown that both velocity of propagation and an effective channel length are important in determining the shape of the spectrum.

Reorientational versus Kerr dark and gray solitary waves using modulation theory.

PubMed

Assanto, Gaetano; Marchant, T R; Minzoni, Antonmaria A; Smyth, Noel F

2011-12-01

We develop a modulation theory model based on a Lagrangian formulation to investigate the evolution of dark and gray optical spatial solitary waves for both the defocusing nonlinear Schrödinger (NLS) equation and the nematicon equations describing nonlinear beams, nematicons, in self-defocusing nematic liquid crystals. Since it has an exact soliton solution, the defocusing NLS equation is used as a test bed for the modulation theory applied to the nematicon equations, which have no exact solitary wave solution. We find that the evolution of dark and gray NLS solitons, as well as nematicons, is entirely driven by the emission of diffractive radiation, in contrast to the evolution of bright NLS solitons and bright nematicons. Moreover, the steady nematicon profile is nonmonotonic due to the long-range nonlocality associated with the perturbation of the optic axis. Excellent agreement is obtained with numerical solutions of both the defocusing NLS and nematicon equations. The comparisons for the nematicon solutions raise a number of subtle issues relating to the definition and measurement of the width of a dark or gray nematicon.

The exact rogue wave recurrence in the NLS periodic setting via matched asymptotic expansions, for 1 and 2 unstable modes

NASA Astrophysics Data System (ADS)

Grinevich, P. G.; Santini, P. M.

2018-04-01

The focusing Nonlinear Schrödinger (NLS) equation is the simplest universal model describing the modulation instability (MI) of quasi monochromatic waves in weakly nonlinear media, the main physical mechanism for the generation of rogue (anomalous) waves (RWs) in Nature. In this paper we investigate the x-periodic Cauchy problem for NLS for a generic periodic initial perturbation of the unstable constant background solution, in the case of N = 1 , 2 unstable modes. We use matched asymptotic expansion techniques to show that the solution of this problem describes an exact deterministic alternate recurrence of linear and nonlinear stages of MI, and that the nonlinear RW stages are described by the N-breather solution of Akhmediev type, whose parameters, different at each RW appearance, are always given in terms of the initial data through elementary functions. This paper is motivated by a preceding work of the authors in which a different approach, the finite gap method, was used to investigate periodic Cauchy problems giving rise to RW recurrence.

Analytical treatment of particle motion in circularly polarized slab-mode wave fields

NASA Astrophysics Data System (ADS)

Schreiner, Cedric; Vainio, Rami; Spanier, Felix

2018-02-01

Wave-particle interaction is a key process in particle diffusion in collisionless plasmas. We look into the interaction of single plasma waves with individual particles and discuss under which circumstances this is a chaotic process, leading to diffusion. We derive the equations of motion for a particle in the fields of a magnetostatic, circularly polarized, monochromatic wave and show that no chaotic particle motion can arise under such circumstances. A novel and exact analytic solution for the equations is presented. Additional plasma waves lead to a breakdown of the analytic solution and chaotic particle trajectories become possible. We demonstrate this effect by considering a linearly polarized, monochromatic wave, which can be seen as the superposition of two circularly polarized waves. Test particle simulations are provided to illustrate and expand our analytical considerations.

Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation.

PubMed

Hu, Xiao-Rui; Lou, Sen-Yue; Chen, Yong

2012-05-01

In nonlinear science, it is very difficult to find exact interaction solutions among solitons and other kinds of complicated waves such as cnoidal waves and Painlevé waves. Actually, even if for the most well-known prototypical models such as the Kortewet-de Vries (KdV) equation and the Kadomtsev-Petviashvili (KP) equation, this kind of problem has not yet been solved. In this paper, the explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetries which are related to Darboux transformation for the well-known KdV equation. The same approach also yields some other types of interaction solutions among different types of solutions such as solitary waves, rational solutions, Bessel function solutions, and/or general Painlevé II solutions.

Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-12-01

In this study, we presented the problem formulations of models for internal solitary waves in a stratified shear flow with a free surface. The nonlinear higher order of extended KdV equations for the free surface displacement is generated. We derived the coefficients of the nonlinear higher-order extended KdV equation in terms of integrals of the modal function for the linear long-wave theory. The wave amplitude potential and the fluid pressure of the extended KdV equation in the form of solitary-wave solutions are deduced. We discussed and analyzed the stability of the obtained solutions and the movement role of the waves by making graphs of the exact solutions.

Time dependent wave envelope finite difference analysis of sound propagation

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1984-01-01

A transient finite difference wave envelope formulation is presented for sound propagation, without steady flow. Before the finite difference equations are formulated, the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction. This transformation reduces the required number of grid points by an order of magnitude. Physically, the transformed pressure represents the amplitude of the conventional sound wave. The derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements. To illustrate the method, example solutions are presented for sound propagation in a straight hard wall duct and in a two dimensional straight soft wall duct. The numerical results are in good agreement with exact analytical results.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves.

PubMed

Tsitoura, F; Gietz, U; Chabchoub, A; Hoffmann, N

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Effects of the Kelvin-Helmholtz surface instability on supersonic jets

NASA Technical Reports Server (NTRS)

Hardee, P. E.

1982-01-01

An exact numerical calculation is provided for of linear growth and phase velocity of Kelvin-Helmholtz unstable wave modes on a supersonic jet of cylindrical cross section. An expression for the maximally unstable wavenumber of each wave mode is found. Provided a sharp velocity discontinuity exists all wave modes are unstable. A combination of rapid jet expansion and velocity shear across a jet can effectively stabilize all wave modes. The more likely case of slow jet expansion and of velocity shear at the jet surface allows wave modes with maximally unstable wavelength longer than or on the order of the jet radius to grow. The relative energy in different wave modes and effect on the jet is investigated. Energy input into a jet resulting from surface instability is discussed.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves

NASA Astrophysics Data System (ADS)

Tsitoura, F.; Gietz, U.; Chabchoub, A.; Hoffmann, N.

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II

NASA Technical Reports Server (NTRS)

Shertzer, J.; Temkin, A.

2003-01-01

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE) can be reduced to a 2d partial differential equation (pde), and was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation. The resultant equation can be reduced to a pair of coupled pde's, to which the finite element method can still be applied. The resultant scattering amplitudes, both singlet and triplet, as a function of angle can be calculated for various energies. The results are in excellent agreement with converged partial wave results.

Water saturation effects on P-wave anisotropy in synthetic sandstone with aligned fractures

NASA Astrophysics Data System (ADS)

Amalokwu, Kelvin; Chapman, Mark; Best, Angus I.; Minshull, Timothy A.; Li, Xiang-Yang

2015-08-01

The seismic properties of rocks are known to be sensitive to partial liquid or gas saturation, and to aligned fractures. P-wave anisotropy is widely used for fracture characterization and is known to be sensitive to the saturating fluid. However, studies combining the effect of multiphase saturation and aligned fractures are limited even though such conditions are common in the subsurface. An understanding of the effects of partial liquid or gas saturation on P-wave anisotropy could help improve seismic characterization of fractured, gas bearing reservoirs. Using octagonal-shaped synthetic sandstone samples, one containing aligned penny-shaped fractures and the other without fractures, we examined the influence of water saturation on P-wave anisotropy in fractured rocks. In the fractured rock, the saturation related stiffening effect at higher water saturation values is larger in the direction across the fractures than along the fractures. Consequently, the anisotropy parameter `ε' decreases as a result of this fluid stiffening effect. These effects are frequency dependent as a result of wave-induced fluid flow mechanisms. Our observations can be explained by combining a frequency-dependent fractured rock model and a frequency-dependent partial saturation model.

Rotational superradiant scattering in a vortex flow

NASA Astrophysics Data System (ADS)

Torres, Theo; Patrick, Sam; Coutant, Antonin; Richartz, Maurício; Tedford, Edmund W.; Weinfurtner, Silke

2017-09-01

When an incident wave scatters off of an obstacle, it is partially reflected and partially transmitted. In theory, if the obstacle is rotating, waves can be amplified in the process, extracting energy from the scatterer. Here we describe in detail the first laboratory detection of this phenomenon, known as superradiance. We observed that waves propagating on the surface of water can be amplified after being scattered by a draining vortex. The maximum amplification measured was 14% +/- 8%, obtained for 3.70 Hz waves, in a 6.25-cm-deep fluid, consistent with the superradiant scattering caused by rapid rotation. We expect our experimental findings to be relevant to black-hole physics, since shallow water waves scattering on a draining fluid constitute an analogue of a black hole, as well as to hydrodynamics, due to the close relation to over-reflection instabilities.

Exact time-dependent solutions for a self-regulating gene.

PubMed

Ramos, A F; Innocentini, G C P; Hornos, J E M

2011-06-01

The exact time-dependent solution for the stochastic equations governing the behavior of a binary self-regulating gene is presented. Using the generating function technique to rephrase the master equations in terms of partial differential equations, we show that the model is totally integrable and the analytical solutions are the celebrated confluent Heun functions. Self-regulation plays a major role in the control of gene expression, and it is remarkable that such a microscopic model is completely integrable in terms of well-known complex functions.

Analytical solution for boundary heat fluxes from a radiating rectangular medium

NASA Technical Reports Server (NTRS)

Siegel, R.

1991-01-01

Reference is made to the work of Shah (1979) which demonstrated the possibility of partially integrating the radiative equations analytically to obtain an 'exact' solution. Shah's solution was given as a double integration of the modified Bessel function of order zero. Here, it is shown that the 'exact' solution for a rectangular region radiating to cold black walls can be conveniently derived, and expressed in simple form, by using an integral function, Sn, analogous to the exponential integral function appearing in plane-layer solutions.

Worldline approach to helicity flip in plane waves

NASA Astrophysics Data System (ADS)

Ilderton, Anton; Torgrimsson, Greger

2016-04-01

We apply worldline methods to the study of vacuum polarization effects in plane wave backgrounds, in both scalar and spinor QED. We calculate helicity-flip probabilities to one loop order and treated exactly in the background field, and provide a toolkit of methods for use in investigations of higher-order processes. We also discuss the connections between the worldline, S-matrix, and lightfront approaches to vacuum polarization effects.

Propagation phenomena in monostable integro-differential equations: Acceleration or not?

NASA Astrophysics Data System (ADS)

Alfaro, Matthieu; Coville, Jérôme

2017-11-01

We consider the homogeneous integro-differential equation ∂t u = J * u - u + f (u) with a monostable nonlinearity f. Our interest is twofold: we investigate the existence/nonexistence of travelling waves, and the propagation properties of the Cauchy problem. When the dispersion kernel J is exponentially bounded, travelling waves are known to exist and solutions of the Cauchy problem typically propagate at a constant speed [7,10,11,22,26,27]. On the other hand, when the dispersion kernel J has heavy tails and the nonlinearity f is nondegenerate, i.e. f‧ (0) > 0, travelling waves do not exist and solutions of the Cauchy problem propagate by accelerating [14,20,27]. For a general monostable nonlinearity, a dichotomy between these two types of propagation behaviour is still not known. The originality of our work is to provide such dichotomy by studying the interplay between the tails of the dispersion kernel and the Allee effect induced by the degeneracy of f, i.e. f‧ (0) = 0. First, for algebraic decaying kernels, we prove the exact separation between existence and nonexistence of travelling waves. This in turn provides the exact separation between nonacceleration and acceleration in the Cauchy problem. In the latter case, we provide a first estimate of the position of the level sets of the solution.

A mechanism of wave drag reduction in the thermal energy deposition experiments

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

Markhotok, A., E-mail: amarhotk@phys.washington.edu

2015-06-15

Many experimental studies report reduced wave drag when thermal energy is deposited in the supersonic flow upstream of a body. Though a large amount of research on this topic has been accumulated, the exact mechanism of the drag reduction is still unknown. This paper is to fill the gap in the understanding connecting multiple stages of the observed phenomena with a single mechanism. The proposed model provides an insight on the origin of the chain of subsequent transformations in the flow leading to the reduction in wave drag, such as typical deformations of the front, changes in the gas pressuremore » and density in front of the body, the odd shapes of the deflection signals, and the shock wave extinction in the plasma area. The results of numerical simulation based on the model are presented for three types of plasma parameter distribution. The spherical and cylindrical geometry has been used to match the data with the experimental observations. The results demonstrate full ability of the model to exactly explain all the features observed in the drag reduction experiments. Analytical expressions used in the model allow separating out a number of adjustment parameters that can be used to optimize thermal energy input and thus achieve fundamentally lower drag values than that of conventional approaches.« less

Exact Solution of a Two-Species Quantum Dimer Model for Pseudogap Metals

NASA Astrophysics Data System (ADS)

Feldmeier, Johannes; Huber, Sebastian; Punk, Matthias

2018-05-01

We present an exact ground state solution of a quantum dimer model introduced by Punk, Allais, and Sachdev [Quantum dimer model for the pseudogap metal, Proc. Natl. Acad. Sci. U.S.A. 112, 9552 (2015)., 10.1073/pnas.1512206112], which features ordinary bosonic spin-singlet dimers as well as fermionic dimers that can be viewed as bound states of spinons and holons in a hole-doped resonating valence bond liquid. Interestingly, this model captures several essential properties of the metallic pseudogap phase in high-Tc cuprate superconductors. We identify a line in parameter space where the exact ground state wave functions can be constructed at an arbitrary density of fermionic dimers. At this exactly solvable line the ground state has a huge degeneracy, which can be interpreted as a flat band of fermionic excitations. Perturbing around the exactly solvable line, this degeneracy is lifted and the ground state is a fractionalized Fermi liquid with a small pocket Fermi surface in the low doping limit.

Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis

ERIC Educational Resources Information Center

Jeffrey, Alan

1971-01-01

The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)

Geometric transformations of optical orbital angular momentum spatial modes

NASA Astrophysics Data System (ADS)

He, Rui; An, Xin

2018-02-01

With the aid of the bosonic mode conversions in two different coordinate frames, we show that (1) the coordinate eigenstate is exactly the EPR entangled state representation, and (2) the Laguerre-Gaussian (LG) mode is exactly the wave function of the common eigenvector of the orbital angular momentum and the total photon number operator. Moreover, by using the conversion of the bosonic modes, theWigner representation of the LG mode can be obtained directly. It provides an alternative to the method of Simon and Agarwal.

Exact solution to the Schrödinger’s equation with pseudo-Gaussian potential

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

Iacob, Felix, E-mail: felix@physics.uvt.ro; Lute, Marina, E-mail: marina.lute@upt.ro

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.

Reciprocal links among differential parenting, perceived partiality, and self-worth: a three-wave longitudinal study.

PubMed

Shebloski, Barbara; Conger, Katherine J; Widaman, Keith F

2005-12-01

This study examined reciprocal links between parental differential treatment, siblings' perception of partiality, and self-worth with 3 waves of data from 384 adolescent sibling dyads. Results suggest that birth-order status was significantly associated with self-worth and perception of maternal and paternal differential treatment. There was a consistent across-time effect of self-worth on perception of parental partiality for later born siblings, but not earlier born siblings, and a consistent effect of differential treatment on perception of partiality for earlier born but not later born siblings. The results contribute new insight into the associations between perception of differential parenting and adolescents' adjustment and the role of birth order. Copyright 2006 APA, all rights reserved).

A Rosetta Stone Relating Conventions In Photo-Meson Partial Wave Analyses

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

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.

Effect of H-wave polarization on laser radar detection of partially convex targets in random media.

PubMed

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.

Collision effects on propagation characteristics of electromagnetic waves in a sub-wavelength plasma slab of partially ionized dense plasmas

NASA Astrophysics Data System (ADS)

Bowen, LI; Zhibin, WANG; Qiuyue, NIE; Xiaogang, WANG; Fanrong, KONG; Zhenyu, WANG

2018-01-01

Intensive collisions between electrons and neutral particles in partially ionized plasmas generated in atmospheric/sub-atmospheric pressure environments can sufficiently affect the propagation characteristics of electromagnetic waves, particularly in the sub-wavelength regime. To investigate the collisional effect in such plasmas, we introduce a simplified plasma slab model with a thickness on the order of the wavelength of the incident electromagnetic wave. The scattering matrix method (SMM) is applied to solve the wave equation in the plasma slab with significant nonuniformity. Results show that the collisions between the electrons and the neutral particles, as well as the incident angle and the plasma thickness, can disturb the transmission and reduce reflection significantly.

Functional Coordination of WAVE and WASP in C. elegans Neuroblast Migration.

PubMed

Zhu, Zhiwen; Chai, Yongping; Jiang, Yuxiang; Li, Wenjing; Hu, Huifang; Li, Wei; Wu, Jia-Wei; Wang, Zhi-Xin; Huang, Shanjin; Ou, Guangshuo

2016-10-24

Directional cell migration is critical for metazoan development. We define two molecular pathways that activate the Arp2/3 complex during neuroblast migration in Caenorhabditis elegans. The transmembrane protein MIG-13/Lrp12 is linked to the Arp2/3 nucleation-promoting factors WAVE or WASP through direct interactions with ABL-1 or SEM-5/Grb2, respectively. WAVE mutations partially impaired F-actin organization and decelerated cell migration, and WASP mutations did not inhibit cell migration but enhanced migration defects in WAVE-deficient cells. Purified SEM-5 and MIG-2 synergistically stimulated the F-actin branching activity of WASP-Arp2/3 in vitro. In GFP knockin animals, WAVE and WASP were largely organized into separate clusters at the leading edge, and the amount of WASP was less than WAVE but could be elevated by WAVE mutations. Our results indicate that the MIG-13-WAVE pathway provides the major force for directional cell motility, whereas MIG-13-WASP partially compensates for its loss, underscoring their coordinated activities in facilitating robust cell migration. Copyright © 2016 Elsevier Inc. All rights reserved.

Spontaneous emergence of rogue waves in partially coherent waves: A quantitative experimental comparison between hydrodynamics and optics

NASA Astrophysics Data System (ADS)

El Koussaifi, R.; Tikan, A.; Toffoli, A.; Randoux, S.; Suret, P.; Onorato, M.

2018-01-01

Rogue waves are extreme and rare fluctuations of the wave field that have been discussed in many physical systems. Their presence substantially influences the statistical properties of a partially coherent wave field, i.e., a wave field characterized by a finite band spectrum with random Fourier phases. Their understanding is fundamental for the design of ships and offshore platforms. In many meteorological conditions waves in the ocean are characterized by the so-called Joint North Sea Wave Project (JONSWAP) spectrum. Here we compare two unique experimental results: the first one has been performed in a 270 m wave tank and the other in optical fibers. In both cases, waves characterized by a JONSWAP spectrum and random Fourier phases have been launched at the input of the experimental device. The quantitative comparison, based on an appropriate scaling of the two experiments, shows a very good agreement between the statistics in hydrodynamics and optics. Spontaneous emergence of heavy tails in the probability density function of the wave amplitude is observed in both systems. The results demonstrate the universal features of rogue waves and provide a fundamental and explicit bridge between two important fields of research. Numerical simulations are also compared with experimental results.

Spontaneous emergence of rogue waves in partially coherent waves: A quantitative experimental comparison between hydrodynamics and optics.

PubMed

El Koussaifi, R; Tikan, A; Toffoli, A; Randoux, S; Suret, P; Onorato, M

2018-01-01

Rogue waves are extreme and rare fluctuations of the wave field that have been discussed in many physical systems. Their presence substantially influences the statistical properties of a partially coherent wave field, i.e., a wave field characterized by a finite band spectrum with random Fourier phases. Their understanding is fundamental for the design of ships and offshore platforms. In many meteorological conditions waves in the ocean are characterized by the so-called Joint North Sea Wave Project (JONSWAP) spectrum. Here we compare two unique experimental results: the first one has been performed in a 270 m wave tank and the other in optical fibers. In both cases, waves characterized by a JONSWAP spectrum and random Fourier phases have been launched at the input of the experimental device. The quantitative comparison, based on an appropriate scaling of the two experiments, shows a very good agreement between the statistics in hydrodynamics and optics. Spontaneous emergence of heavy tails in the probability density function of the wave amplitude is observed in both systems. The results demonstrate the universal features of rogue waves and provide a fundamental and explicit bridge between two important fields of research. Numerical simulations are also compared with experimental results.

Nonlinear Binormal Flow of Vortex Filaments

NASA Astrophysics Data System (ADS)

Strong, Scott; Carr, Lincoln

2015-11-01

With the current advances in vortex imaging of Bose-Einstein condensates occurring at the Universities of Arizona, São Paulo and Cambridge, interest in vortex filament dynamics is experiencing a resurgence. Recent simulations, Salman (2013), depict dissipative mechanisms resulting from vortex ring emissions and Kelvin wave generation associated with vortex self-intersections. As the local induction approximation fails to capture reconnection events, it lacks a similar dissipative mechanism. On the other hand, Strong&Carr (2012) showed that the exact representation of the velocity field induced by a curved segment of vortex contains higher-order corrections expressed in powers of curvature. This nonlinear binormal flow can be transformed, Hasimoto (1972), into a fully nonlinear equation of Schrödinger type. Continued transformation, Madelung (1926), reveals that the filament's square curvature obeys a quasilinear scalar conservation law with source term. This implies a broader range of filament dynamics than is possible with the integrable linear binormal flow. In this talk we show the affect higher-order corrections have on filament dynamics and discuss physical scales for which they may be witnessed in future experiments. Partially supported by NSF.

Two-photon absorption induced stimulated Rayleigh-Bragg scattering

NASA Astrophysics Data System (ADS)

He, Guang S.; Prasad, Paras N.

2005-01-01

A frequency-unshifted and backward stimulated scattering can be efficiently generated in one-photon-absorption free but two-photon absorbing materials. Using a number of novel two-photon absorbing dye solutions as the scattering media and nanosecond pulsed laser as the pump beams, a highly directional backward stimulated scattering at the exact pump wavelength can be readily observed once the pump intensity is higher than a certain threshold level. The spectral and spatial structures as well as the temporal behavior and optical phase-conjugation property of this new type of backward stimulated scattering have been experimentally studied. This stimulated scattering phenomenon can be explained by using a model of two-photon-excitation enhanced standing-wave Bragg grating initially formed by the strong forward pump beam and much weaker backward Rayleigh scattering beam; the partial reflection of the pump beam from this grating provides an positive feedback to the initial backward Rayleigh scattering beam without suffering linear attenuation influence. Comparing to other known stimulated (Raman, Brillouin, Rayleigh-wing, and Kerr) scattering effects, the stimulated Rayleigh-Bragg scattering exhibits the advantages of no frequency-shift, low pump threshold, and low spectral linewidth requirement.

5-D interpolation with wave-front attributes

NASA Astrophysics Data System (ADS)

Xie, Yujiang; Gajewski, Dirk

2017-11-01

Most 5-D interpolation and regularization techniques reconstruct the missing data in the frequency domain by using mathematical transforms. An alternative type of interpolation methods uses wave-front attributes, that is, quantities with a specific physical meaning like the angle of emergence and wave-front curvatures. In these attributes structural information of subsurface features like dip and strike of a reflector are included. These wave-front attributes work on 5-D data space (e.g. common-midpoint coordinates in x and y, offset, azimuth and time), leading to a 5-D interpolation technique. Since the process is based on stacking next to the interpolation a pre-stack data enhancement is achieved, improving the signal-to-noise ratio (S/N) of interpolated and recorded traces. The wave-front attributes are determined in a data-driven fashion, for example, with the Common Reflection Surface (CRS method). As one of the wave-front-attribute-based interpolation techniques, the 3-D partial CRS method was proposed to enhance the quality of 3-D pre-stack data with low S/N. In the past work on 3-D partial stacks, two potential problems were still unsolved. For high-quality wave-front attributes, we suggest a global optimization strategy instead of the so far used pragmatic search approach. In previous works, the interpolation of 3-D data was performed along a specific azimuth which is acceptable for narrow azimuth acquisition but does not exploit the potential of wide-, rich- or full-azimuth acquisitions. The conventional 3-D partial CRS method is improved in this work and we call it as a wave-front-attribute-based 5-D interpolation (5-D WABI) as the two problems mentioned above are addressed. Data examples demonstrate the improved performance by the 5-D WABI method when compared with the conventional 3-D partial CRS approach. A comparison of the rank-reduction-based 5-D seismic interpolation technique with the proposed 5-D WABI method is given. The comparison reveals that there are significant advantages for steep dipping events using the 5-D WABI method when compared to the rank-reduction-based 5-D interpolation technique. Diffraction tails substantially benefit from this improved performance of the partial CRS stacking approach while the CPU time is comparable to the CPU time consumed by the rank-reduction-based method.

Soliton-cnoidal interactional wave solutions for the reduced Maxwell-Bloch equations

NASA Astrophysics Data System (ADS)

Huang, Li-Li; Qiao, Zhi-Jun; Chen, Yong

2018-02-01

Based on nonlocal symmetry method, localized excitations and interactional solutions are investigated for the reduced Maxwell-Bloch equations. The nonlocal symmetries of the reduced Maxwell-Bloch equations are obtained by the truncated Painleve expansion approach and the Mobious invariant property. The nonlocal symmetries are localized to a prolonged system by introducing suitable auxiliary dependent variables. The extended system can be closed and a novel Lie point symmetry system is constructed. By solving the initial value problems, a new type of finite symmetry transformations is obtained to derive periodic waves, Ma breathers and breathers travelling on the background of periodic line waves. Then rich exact interactional solutions are derived between solitary waves and other waves including cnoidal waves, rational waves, Painleve waves, and periodic waves through similarity reductions. In particular, several new types of localized excitations including rogue waves are found, which stem from the arbitrary function generated in the process of similarity reduction. By computer numerical simulation, the dynamics of these localized excitations and interactional solutions are discussed, which exhibit meaningful structures.

Coarse-grained forms for equations describing the microscopic motion of particles in a fluid.

PubMed

Das, Shankar P; Yoshimori, Akira

2013-10-01

Exact equations of motion for the microscopically defined collective density ρ(x,t) and the momentum density ĝ(x,t) of a fluid have been obtained in the past starting from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse-grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.

Interactions of solitary waves and compression/expansion waves in core-annular flows

NASA Astrophysics Data System (ADS)

Maiden, Michelle; Anderson, Dalton; El, Gennady; Franco, Nevil; Hoefer, Mark

2017-11-01

The nonlinear hydrodynamics of an initial step leads to the formation of rarefaction waves and dispersive shock waves in dispersive media. Another hallmark of these media is the soliton, a localized traveling wave whose speed is amplitude dependent. Although compression/expansion waves and solitons have been well-studied individually, there has been no mathematical description of their interaction. In this talk, the interaction of solitons and shock/rarefaction waves for interfacial waves in viscous, miscible core-annular flows are modeled mathematically and explored experimentally. If the interior fluid is continuously injected, a deformable conduit forms whose interfacial dynamics are well-described by a scalar, dispersive nonlinear partial differential equation. The main focus is on interactions of solitons with dispersive shock waves and rarefaction waves. Theory predicts that a soliton can either be transmitted through or trapped by the extended hydrodynamic state. The notion of reciprocity is introduced whereby a soliton interacts with a shock wave in a reciprocal or dual fashion as with the rarefaction. Soliton reciprocity, trapping, and transmission are observed experimentally and are found to agree with the modulation theory and numerical simulations. This work was partially supported by NSF CAREER DMS-1255422 (M.A.H.) and NSF GRFP (M.D.M.).

Tailoring of the partial magnonic gap in three-dimensional magnetoferritin-based magnonic crystals

NASA Astrophysics Data System (ADS)

Mamica, S.

2013-07-01

We investigate theoretically the use of magnetoferritin nanoparticles, self-assembled in the protein crystallization process, as the basis for the realization of 3D magnonic crystals in which the interparticle space is filled with a ferromagnetic material. Using the plane wave method we study the dependence of the width of the partial band gap and its central frequency on the total magnetic moment of the magnetoferritin core and the lattice constant of the magnetoferritin crystal. We show that by adjusting the combination of these two parameters the partial gap can be tailored in a wide frequency range and shifted to sub-terahertz frequencies. Moreover, the difference in the width of the partial gap for spin waves propagating in planes parallel and perpendicular to the external field allows for switching on and off the partial magnonic gap by changing the direction of the applied field.

Modeling of matter-wave solitons in a nonlinear inductor-capacitor network through a Gross-Pitaevskii equation with time-dependent linear potential

NASA Astrophysics Data System (ADS)

Kengne, E.; Lakhssassi, A.; Liu, W. M.

2017-08-01

A lossless nonlinear L C transmission network is considered. With the use of the reductive perturbation method in the semidiscrete limit, we show that the dynamics of matter-wave solitons in the network can be modeled by a one-dimensional Gross-Pitaevskii (GP) equation with a time-dependent linear potential in the presence of a chemical potential. An explicit expression for the growth rate of a purely growing modulational instability (MI) is presented and analyzed. We find that the potential parameter of the GP equation of the system does not affect the different regions of the MI. Neglecting the chemical potential in the GP equation, we derive exact analytical solutions which describe the propagation of both bright and dark solitary waves on continuous-wave (cw) backgrounds. Using the found exact analytical solutions of the GP equation, we investigate numerically the transmission of both bright and dark solitary voltage signals in the network. Our numerical studies show that the amplitude of a bright solitary voltage signal and the depth of a dark solitary voltage signal as well as their width, their motion, and their behavior depend on (i) the propagation frequencies, (ii) the potential parameter, and (iii) the amplitude of the cw background. The GP equation derived in this paper with a time-dependent linear potential opens up different ideas that may be of considerable theoretical interest for the management of matter-wave solitons in nonlinear L C transmission networks.

Representation of the exact relativistic electronic Hamiltonian within the regular approximation

NASA Astrophysics Data System (ADS)

Filatov, Michael; Cremer, Dieter

2003-12-01

The exact relativistic Hamiltonian for electronic states is expanded in terms of energy-independent linear operators within the regular approximation. An effective relativistic Hamiltonian has been obtained, which yields in lowest order directly the infinite-order regular approximation (IORA) rather than the zeroth-order regular approximation method. Further perturbational expansion of the exact relativistic electronic energy utilizing the effective Hamiltonian leads to new methods based on ordinary (IORAn) or double [IORAn(2)] perturbation theory (n: order of expansion), which provide improved energies in atomic calculations. Energies calculated with IORA4 and IORA3(2) are accurate up to c-20. Furthermore, IORA is improved by using the IORA wave function to calculate the Rayleigh quotient, which, if minimized, leads to the exact relativistic energy. The outstanding performance of this new IORA method coined scaled IORA is documented in atomic and molecular calculations.

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

Agostini, Federica; Abedi, Ali; Suzuki, Yasumitsu

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 packetmore » 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.« less

Exact semiclassical expansions for one-dimensional quantum oscillators

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

Delabaere, E.; Dillinger, H.; Pham, F.

1997-12-01

A set of rules is given for dealing with WKB expansions in the one-dimensional analytic case, whereby such expansions are not considered as approximations but as exact encodings of wave functions, thus allowing for analytic continuation with respect to whichever parameters the potential function depends on, with an exact control of small exponential effects. These rules, which include also the case when there are double turning points, are illustrated on various examples, and applied to the study of bound state or resonance spectra. In the case of simple oscillators, it is thus shown that the Rayleigh{endash}Schr{umlt o}dinger series is Borelmore » resummable, yielding the exact energy levels. In the case of the symmetrical anharmonic oscillator, one gets a simple and rigorous justification of the Zinn-Justin quantization condition, and of its solution in terms of {open_quotes}multi-instanton expansions.{close_quotes} {copyright} {ital 1997 American Institute of Physics.}« less

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).

Determining the dominant partial wave contributions from angular distributions of single- and double-polarization observables in pseudoscalar meson photoproduction

NASA Astrophysics Data System (ADS)

Wunderlich, Y.; Afzal, F.; Thiel, A.; Beck, R.

2017-05-01

This work presents a simple method to determine the significant partial wave contributions to experimentally determined observables in pseudoscalar meson photoproduction. First, fits to angular distributions are presented and the maximum orbital angular momentum Lmax needed to achieve a good fit is determined. Then, recent polarization measurements for γ p → π0 p from ELSA, GRAAL, JLab and MAMI are investigated according to the proposed method. This method allows us to project high-spin partial wave contributions to any observable as long as the measurement has the necessary statistical accuracy. We show, that high precision and large angular coverage in the polarization data are needed in order to be sensitive to high-spin resonance states and thereby also for the finding of small resonance contributions. This task can be achieved via interference of these resonances with the well-known states. For the channel γ p → π0 p, those are the N(1680)5/2+ and Δ(1950)7/2+, contributing to the F-waves.

Turbulence in the Ott-Antonsen equation for arrays of coupled phase oscillators

NASA Astrophysics Data System (ADS)

Wolfrum, M.; Gurevich, S. V.; Omel'chenko, O. E.

2016-02-01

In this paper we study the transition to synchrony in an one-dimensional array of oscillators with non-local coupling. For its description in the continuum limit of a large number of phase oscillators, we use a corresponding Ott-Antonsen equation, which is an integro-differential equation for the evolution of the macroscopic profiles of the local mean field. Recently, it was reported that in the spatially extended case at the synchronisation threshold there appear partially coherent plane waves with different wave numbers, which are organised in the well-known Eckhaus scenario. In this paper, we show that for Kuramoto-Sakaguchi phase oscillators the phase lag parameter in the interaction function can induce a Benjamin-Feir-type instability of the partially coherent plane waves. The emerging collective macroscopic chaos appears as an intermediate stage between complete incoherence and stable partially coherent plane waves. We give an analytic treatment of the Benjamin-Feir instability and its onset in a codimension-two bifurcation in the Ott-Antonsen equation as well as a numerical study of the transition from phase turbulence to amplitude turbulence inside the Benjamin-Feir unstable region.

Analytic computation of energy derivatives - Relationships among partial derivatives of a variationally determined function

NASA Technical Reports Server (NTRS)

King, H. F.; Komornicki, A.

1986-01-01

Formulas are presented relating Taylor series expansion coefficients of three functions of several variables, the energy of the trial wave function (W), the energy computed using the optimized variational wave function (E), and the response function (lambda), under certain conditions. Partial derivatives of lambda are obtained through solution of a recursive system of linear equations, and solution through order n yields derivatives of E through order 2n + 1, extending Puley's application of Wigner's 2n + 1 rule to partial derivatives in couple perturbation theory. An examination of numerical accuracy shows that the usual two-term second derivative formula is less stable than an alternative four-term formula, and that previous claims that energy derivatives are stationary properties of the wave function are fallacious. The results have application to quantum theoretical methods for the computation of derivative properties such as infrared frequencies and intensities.

Power counting in peripheral partial waves: The singlet channels

NASA Astrophysics Data System (ADS)

Valderrama, M. Pavón; Sánchez, M. Sánchez; Yang, C.-J.; Long, Bingwei; Carbonell, J.; van Kolck, U.

2017-05-01

We analyze the power counting of the peripheral singlet partial waves in nucleon-nucleon scattering. In agreement with conventional wisdom, we find that pion exchanges are perturbative in the peripheral singlets. We quantify from the effective field theory perspective the well-known suppression induced by the centrifugal barrier in the pion-exchange interactions. By exploring perturbation theory up to fourth order, we find that the one-pion-exchange potential in these channels is demoted from leading to subleading order by a given power of the expansion parameter that grows with the orbital angular momentum. We discuss the implications of these demotions for few-body calculations: though higher partial waves have been known for a long time to be irrelevant in these calculations (and are hence ignored), here we explain how to systematize the procedure in a way that is compatible with the effective field theory expansion.

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…

Kinetic energy and angular momentum of free particles in the gyratonic pp-waves space-times

NASA Astrophysics Data System (ADS)

Maluf, J. W.; da Rocha-Neto, J. F.; Ulhoa, S. C.; Carneiro, F. L.

2018-06-01

Gyratonic pp-waves are exact solutions of Einstein’s equations that represent non-linear gravitational waves endowed with angular momentum. We consider gyratonic pp-waves that travel in the z direction and whose time dependence on the variable is given by Gaussians, so that the waves represent short bursts of gravitational radiation propagating in the z direction. We evaluate numerically the geodesics and velocities of free particles in the space-time of these waves, and find that after the passage of the waves both the kinetic energy and the angular momentum per unit mass of the particles are changed. Therefore there is a transfer of energy and angular momentum between the gravitational field and the free particles, so that the final values of the energy and angular momentum of the free particles may be smaller or larger in magnitude than the initial values.

Stability: Conservation laws, Painlevé analysis and exact solutions for S-KP equation in coupled dusty plasma

NASA Astrophysics Data System (ADS)

EL-Kalaawy, O. H.; Moawad, S. M.; Wael, Shrouk

The propagation of nonlinear waves in unmagnetized strongly coupled dusty plasma with Boltzmann distributed electrons, iso-nonthermal distributed ions and negatively charged dust grains is considered. The basic set of fluid equations is reduced to the Schamel Kadomtsev-Petviashvili (S-KP) equation by using the reductive perturbation method. The variational principle and conservation laws of S-KP equation are obtained. It is shown that the S-KP equation is non-integrable using Painlevé analysis. A set of new exact solutions are obtained by auto-Bäcklund transformations. The stability analysis is discussed for the existence of dust acoustic solitary waves (DASWs) and it is found that the physical parameters have strong effects on the stability criterion. In additional to, the electric field and the true Mach number of this solution are investigated. Finally, we will study the physical meanings of solutions.

(p,q) deformations and (p,q)-vector coherent states of the Jaynes-Cummings model in the rotating wave approximation

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

Ben Geloun, Joseph; Govaerts, Jan; Hounkonnou, M. Norbert

2007-03-15

Classes of (p,q) deformations of the Jaynes-Cummings model in the rotating wave approximation are considered. Diagonalization of the Hamiltonian is performed exactly, leading to useful spectral decompositions of a series of relevant operators. The latter include ladder operators acting between adjacent energy eigenstates within two separate infinite discrete towers, except for a singleton state. These ladder operators allow for the construction of (p,q)-deformed vector coherent states. Using (p,q) arithmetics, explicit and exact solutions to the associated moment problem are displayed, providing new classes of coherent states for such models. Finally, in the limit of decoupled spin sectors, our analysis translatesmore » into (p,q) deformations of the supersymmetric harmonic oscillator, such that the two supersymmetric sectors get intertwined through the action of the ladder operators as well as in the associated coherent states.« less

New exact solutions of the Dirac and Klein-Gordon equations of a charged particle propagating in a strong laser field in an underdense plasma

NASA Astrophysics Data System (ADS)

Varró, Sándor

2014-03-01

Exact solutions are presented of the Dirac and Klein-Gordon equations of a charged particle propagating in a classical monochromatic electromagnetic plane wave in a medium of index of refraction nm<1. In the Dirac case the solutions are expressed in terms of new complex polynomials, and in the Klein-Gordon case the found solutions are expressed in terms of Ince polynomials. In each case they form a doubly infinite set, labeled by two integer quantum numbers. These integer numbers represent quantized momentum components of the charged particle along the polarization vector and along the propagation direction of the electromagnetic radiation. Since this radiation may represent a plasmon wave of arbitrary high amplitude, propagating in an underdense plasma, the solutions obtained may have relevance in describing possible quantum features of novel acceleration mechanisms.

Cosmology on a cosmic ring

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

Niedermann, Florian; Schneider, Robert, E-mail: florian.niedermann@physik.lmu.de, E-mail: robert.bob.schneider@physik.uni-muenchen.de

We derive the modified Friedmann equations for a generalization of the Dvali-Gabadadze-Porrati (DGP) model in which the brane has one additional compact dimension. The main new feature is the emission of gravitational waves into the bulk. We study two classes of solutions: first, if the compact dimension is stabilized, the waves vanish and one exactly recovers DGP cosmology. However, a stabilization by means of physical matter is not possible for a tension-dominated brane, thus implying a late time modification of 4D cosmology different from DGP. Second, for a freely expanding compact direction, we find exact attractor solutions with zero 4Dmore » Hubble parameter despite the presence of a 4D cosmological constant. The model hence constitutes an explicit example of dynamical degravitation at the full nonlinear level. Without stabilization, however, there is no 4D regime and the model is ruled out observationally, as we demonstrate explicitly by comparing to supernova data.« less

Nonlinearity Domination in Hassellmann Equation as a Reason for Alternative Framework of its Numerical Simulation

DTIC Science & Technology

2014-09-30

nonlinear Schrodinger equation. It is well known that dark solitons are exact solutions of such equation. In the present paper it has been shown that gray...Reason for Alternative Framework of its Numerical Simulation Vladimir Zakharov, Andrei Pushkarev Waves and Solitons LLC 1719 W. Marlette Ave...situation; study of the implications of modulational instability on solitons , rogue waves and air-surface interaction. APPROACH Numerical methods

Wave Functions for Time-Dependent Dirac Equation under GUP

NASA Astrophysics Data System (ADS)

Zhang, Meng-Yao; Long, Chao-Yun; Long, Zheng-Wen

2018-04-01

In this work, the time-dependent Dirac equation is investigated under generalized uncertainty principle (GUP) framework. It is possible to construct the exact solutions of Dirac equation when the time-dependent potentials satisfied the proper conditions. In (1+1) dimensions, the analytical wave functions of the Dirac equation under GUP have been obtained for the two kinds time-dependent potentials. Supported by the National Natural Science Foundation of China under Grant No. 11565009

Wave propagation in a multilayered laminated cross-ply composite plate

NASA Technical Reports Server (NTRS)

Shah, A. H.; Datta, S. K.; Karunasena, W.

1991-01-01

Dispersion of guided waves in a cross-ply laminated plate has been studied here using a stiffness method and an exact method. It is shown that the number of laminae strongly influences the dispersion behavior. Further, it is found that when the number of laminae is sufficiently large, then the dispersion behavior can be predicted by treating the plate as homogeneous with six stiffness constants obtained by using an effective modulus method.

Endogenous Crisis Waves: Stochastic Model with Synchronized Collective Behavior

NASA Astrophysics Data System (ADS)

Gualdi, Stanislao; Bouchaud, Jean-Philippe; Cencetti, Giulia; Tarzia, Marco; Zamponi, Francesco

2015-02-01

We propose a simple framework to understand commonly observed crisis waves in macroeconomic agent-based models, which is also relevant to a variety of other physical or biological situations where synchronization occurs. We compute exactly the phase diagram of the model and the location of the synchronization transition in parameter space. Many modifications and extensions can be studied, confirming that the synchronization transition is extremely robust against various sources of noise or imperfections.

Pure quasi-P-wave calculation in transversely isotropic media using a hybrid method

NASA Astrophysics Data System (ADS)

Wu, Zedong; Liu, Hongwei; Alkhalifah, Tariq

2018-07-01

The acoustic approximation for anisotropic media is widely used in current industry imaging and inversion algorithms mainly because Pwaves constitute the majority of the energy recorded in seismic exploration. The resulting acoustic formulae tend to be simpler, resulting in more efficient implementations, and depend on fewer medium parameters. However, conventional solutions of the acoustic wave equation with higher-order derivatives suffer from shear wave artefacts. Thus, we derive a new acoustic wave equation for wave propagation in transversely isotropic (TI) media, which is based on a partially separable approximation of the dispersion relation for TI media and free of shear wave artefacts. Even though our resulting equation is not a partial differential equation, it is still a linear equation. Thus, we propose to implement this equation efficiently by combining the finite difference approximation with spectral evaluation of the space-independent parts. The resulting algorithm provides solutions without the constraint ɛ ≥ δ. Numerical tests demonstrate the effectiveness of the approach.

Impulsive spherical gravitational waves

NASA Astrophysics Data System (ADS)

Aliev, A. N.; Nutku, Y.

2001-03-01

Penrose's identification with warp provides the general framework for constructing the continuous form of impulsive gravitational wave metrics. We present the two-component spinor formalism for the derivation of the full family of impulsive spherical gravitational wave metrics which brings out the power in identification with warp and leads to the simplest derivation of exact solutions. These solutions of the Einstein vacuum field equations are obtained by cutting Minkowski space into two pieces along a null cone and re-identifying them with warp which is given by an arbitrary nonlinear holomorphic transformation. Using two-component spinor techniques we construct a new metric describing an impulsive spherical gravitational wave where the vertex of the null cone lies on a worldline with constant acceleration.

Optical Kerr Spatiotemporal Dark-Lump Dynamics of Hydrodynamic Origin

NASA Astrophysics Data System (ADS)

Baronio, Fabio; Wabnitz, Stefan; Kodama, Yuji

2016-04-01

There is considerable fundamental and applicative interest in obtaining nondiffractive and nondispersive spatiotemporal localized wave packets propagating in optical cubic nonlinear or Kerr media. Here, we analytically predict the existence of a novel family of spatiotemporal dark lump solitary wave solutions of the (2 +1 )D nonlinear Schrödinger equation. Dark lumps represent multidimensional holes of light on a continuous wave background. We analytically derive the dark lumps from the hydrodynamic exact soliton solutions of the (2 +1 )D shallow water Kadomtsev-Petviashvili model, inheriting their complex interaction properties. This finding opens a novel path for the excitation and control of optical spatiotemporal waveforms of hydrodynamic footprint and multidimensional optical extreme wave phenomena.

Extended nonlinear Schrödinger equation with higher-order odd and even terms and its rogue wave solutions.

PubMed

Ankiewicz, Adrian; Wang, Yan; Wabnitz, Stefan; Akhmediev, Nail

2014-01-01

We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian-Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.

Optical Kerr Spatiotemporal Dark-Lump Dynamics of Hydrodynamic Origin.

PubMed

Baronio, Fabio; Wabnitz, Stefan; Kodama, Yuji

2016-04-29

There is considerable fundamental and applicative interest in obtaining nondiffractive and nondispersive spatiotemporal localized wave packets propagating in optical cubic nonlinear or Kerr media. Here, we analytically predict the existence of a novel family of spatiotemporal dark lump solitary wave solutions of the (2+1)D nonlinear Schrödinger equation. Dark lumps represent multidimensional holes of light on a continuous wave background. We analytically derive the dark lumps from the hydrodynamic exact soliton solutions of the (2+1)D shallow water Kadomtsev-Petviashvili model, inheriting their complex interaction properties. This finding opens a novel path for the excitation and control of optical spatiotemporal waveforms of hydrodynamic footprint and multidimensional optical extreme wave phenomena.

Formation of rarefaction waves in origami-based metamaterials

NASA Astrophysics Data System (ADS)

Yasuda, H.; Chong, C.; Charalampidis, E. G.; Kevrekidis, P. G.; Yang, J.

2016-04-01

We investigate the nonlinear wave dynamics of origami-based metamaterials composed of Tachi-Miura polyhedron (TMP) unit cells. These cells exhibit strain softening behavior under compression, which can be tuned by modifying their geometrical configurations or initial folded conditions. We assemble these TMP cells into a cluster of origami-based metamaterials, and we theoretically model and numerically analyze their wave transmission mechanism under external impact. Numerical simulations show that origami-based metamaterials can provide a prototypical platform for the formation of nonlinear coherent structures in the form of rarefaction waves, which feature a tensile wavefront upon the application of compression to the system. We also demonstrate the existence of numerically exact traveling rarefaction waves in an effective lumped-mass model. Origami-based metamaterials can be highly useful for mitigating shock waves, potentially enabling a wide variety of engineering applications.

Contributions of aortic pulse wave velocity and backward wave pressure to variations in left ventricular mass are independent of each other.

PubMed

Bello, Hamza; Norton, Gavin R; Ballim, Imraan; Libhaber, Carlos D; Sareli, Pinhas; Woodiwiss, Angela J

2017-05-01

Aortic pulse wave velocity (PWV) and backward waves, as determined from wave separation analysis, predict cardiovascular events beyond brachial blood pressure. However, the extent to which these aortic hemodynamic variables contribute independent of each other is uncertain. In 749 randomly selected participants of African ancestry, we therefore assessed the extent to which relationships between aortic PWV or backward wave pressures (Pb) (and hence central aortic pulse pressure [PPc]) and left ventricular mass index (LVMI) occur independent of each other. Aortic PWV, PPc, forward wave pressure (Pf), and Pb were determined using radial applanation tonometry and SphygmoCor software and LVMI using echocardiography; 44.5% of participants had an increased left ventricular mass indexed to height 1.7 . With adjustments for age, brachial systolic blood pressure or PP, and additional confounders, PPc and Pb, but not Pf, were independently related to LVMI and left ventricular hypertrophy (LVH) in both men and women. However, PWV was independently associated with LVMI in women (partial r = 0.16, P < .001), but not in men (partial r = 0.03), and PWV was independently associated with LVH in women (P < .05), but not in men (P = .07). With PWV and Pb included in the same multivariate regression models, PWV (partial r = 0.14, P < .005) and Pb (partial r = 0.10, P < .05) contributed to a similar extent to variations in LVMI in women. In addition, with PWV and Pb included in the same multivariate regression models, PWV (P < .05) and Pb (P < .02) contributed to LVH in women. In conclusion, aortic PWV and Pb (and hence pulse pressure) although both associated with LVMI and LVH produce effects which are independent of each other. Copyright © 2017 American Society of Hypertension. Published by Elsevier Inc. All rights reserved.

{omega} meson production in pp collisions with a polarized beam

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

Balasubramanyam, J.; Venkataraya,; Ramachandran, G.

2008-07-15

Model independent formulas are derived for the beam analyzing power A{sub y} and beam to meson spin transfers in pp{yields}pp{omega}, taking into consideration all six threshold partial wave amplitudes f{sub 1},...,f{sub 6} covering the Ss, Sp, and Ps channels. It is shown that the lowest three partial wave amplitudes f{sub 1},f{sub 2},f{sub 3} can be determined empirically without any discrete ambiguities. Partial information with regard to the amplitudes f{sub 4},f{sub 5},f{sub 6} covering the Ps channel may be extracted, if the measurements are carried through at the double differential level.

White-light parametric instabilities in plasmas.

PubMed

Santos, J E; Silva, L O; Bingham, R

2007-06-08

Parametric instabilities driven by partially coherent radiation in plasmas are described by a generalized statistical Wigner-Moyal set of equations, formally equivalent to the full wave equation, coupled to the plasma fluid equations. A generalized dispersion relation for stimulated Raman scattering driven by a partially coherent pump field is derived, revealing a growth rate dependence, with the coherence width sigma of the radiation field, scaling with 1/sigma for backscattering (three-wave process), and with 1/sigma1/2 for direct forward scattering (four-wave process). Our results demonstrate the possibility to control the growth rates of these instabilities by properly using broadband pump radiation fields.

Magnetohydrodynamic motion of a two-fluid plasma

DOE PAGES

Burby, Joshua W.

2017-07-21

Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, asmore » well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.« less

Magnetohydrodynamic motion of a two-fluid plasma

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

Burby, Joshua W.

Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, asmore » well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.« less

Layering, interface and edge effects in multi-layered composite medium

NASA Technical Reports Server (NTRS)

Datta, S. K.; Shah, A. H.; Karunesena, W.

1990-01-01

Guided waves in a cross-ply laminated plate are studied. Because of the complexity of the exact dispersion equation that governs the wave propagation in a multi-layered fiber-reinforced plate, a stiffness method that can be applied to any number of layers is presented. It is shown that, for a sufficiently large number of layers, the plate can be modeled as a homogeneous anisotropic plate. Also studied is the reflection of guided waves from the edge of a multilayered plate. These results are quite different than in the case of a single homogeneous plate.

Higher-order vector discrete rogue-wave states in the coupled Ablowitz-Ladik equations: Exact solutions and stability.

PubMed

Wen, Xiao-Yong; Yan, Zhenya; Malomed, Boris A

2016-12-01

An integrable system of two-component nonlinear Ablowitz-Ladik equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, the perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.

Evolution of wave function in a dissipative system

NASA Technical Reports Server (NTRS)

Yu, Li-Hua; Sun, Chang-Pu

1994-01-01

For a dissipative system with Ohmic friction, we obtain a simple and exact solution for the wave function of the system plus the bath. It is described by the direct product in two independent Hilbert space. One of them is described by an effective Hamiltonian, the other represents the effect of the bath, i.e., the Brownian motion, thus clarifying the structure of the wave function of the system whose energy is dissipated by its interaction with the bath. No path integral technology is needed in this treatment. The derivation of the Weisskopf-Wigner line width theory follows easily.

Accurate expansion of cylindrical paraxial waves for its straightforward implementation in electromagnetic scattering

NASA Astrophysics Data System (ADS)

Naserpour, Mahin; Zapata-Rodríguez, Carlos J.

2018-01-01

The evaluation of vector wave fields can be accurately performed by means of diffraction integrals, differential equations and also series expansions. In this paper, a Bessel series expansion which basis relies on the exact solution of the Helmholtz equation in cylindrical coordinates is theoretically developed for the straightforward yet accurate description of low-numerical-aperture focal waves. The validity of this approach is confirmed by explicit application to Gaussian beams and apertured focused fields in the paraxial regime. Finally we discuss how our procedure can be favorably implemented in scattering problems.

Exact Solutions to Several Nonlinear Cases of Generalized Grad-Shafranov Equation for Ideal Magnetohydrodynamic Flows in Axisymmetric Domain

NASA Astrophysics Data System (ADS)

Adem, Abdullahi Rashid; Moawad, Salah M.

2018-05-01

In this paper, the steady-state equations of ideal magnetohydrodynamic incompressible flows in axisymmetric domains are investigated. These flows are governed by a second-order elliptic partial differential equation as a type of generalized Grad-Shafranov equation. The problem of finding exact equilibria to the full governing equations in the presence of incompressible mass flows is considered. Two different types of constraints on position variables are presented to construct exact solution classes for several nonlinear cases of the governing equations. Some of the obtained results are checked for their applications to magnetic confinement plasma. Besides, they cover many previous configurations and include new considerations about the nonlinearity of magnetic flux stream variables.

Time-local equation for exact time-dependent optimized effective potential in time-dependent density functional theory

NASA Astrophysics Data System (ADS)

Liao, Sheng-Lun; Ho, Tak-San; Rabitz, Herschel; Chu, Shih-I.

2017-04-01

Solving and analyzing the exact time-dependent optimized effective potential (TDOEP) integral equation has been a longstanding challenge due to its highly nonlinear and nonlocal nature. To meet the challenge, we derive an exact time-local TDOEP equation that admits a unique real-time solution in terms of time-dependent Kohn-Sham orbitals and effective memory orbitals. For illustration, the dipole evolution dynamics of a one-dimension-model chain of hydrogen atoms is numerically evaluated and examined to demonstrate the utility of the proposed time-local formulation. Importantly, it is shown that the zero-force theorem, violated by the time-dependent Krieger-Li-Iafrate approximation, is fulfilled in the current TDOEP framework. This work was partially supported by DOE.

Coulomb wave functions in momentum space

DOE PAGES

Eremenko, V.; Upadhyay, N. J.; Thompson, I. J.; ...

2015-10-15

We present an algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space. The arguments are the Sommerfeld parameter η, the angular momentum l, the asymptotic momentum q and the 'running' momentum p, where both momenta are real. Since the partial-wave Coulomb functions exhibit singular behavior when p → q, different representations of the Legendre functions of the 2nd kind need to be implemented in computing the functions for the values of p close to the singularity and far away from it. The code for the momentum-space Coulomb wave functions is applicable for values of vertical bar eta vertical barmore » in the range of 10 -1 to 10, and thus is particularly suited for momentum space calculations of nuclear reactions.« less

Strongly interacting high-partial-wave Bose gas

NASA Astrophysics Data System (ADS)

Yao, Juan; Qi, Ran; Zhang, Pengfei

2018-04-01

Motivated by recent experimental progress, we make an investigation of p - and d -wave resonant Bose gas. An explanation of the Nozières and Schmitt-Rink (NSR) scheme in terms of two-channel model is provided. Different from the s -wave case, high-partial-wave interaction supports a quasibound state in the weak-coupling regime. Within the NSR approximation, we study the equation of state, critical temperature, and particle population distributions. We clarify the effect of the quasibound state on the phase diagram and the dimer production. A multicritical point where normal phase, atomic superfluid phase, and molecular superfluid phase meet is predicted within the phase diagram. We also show the occurrence of a resonant conversion between solitary atoms and dimers when temperature kBT approximates the quasibound energy.

Rogue waves in the multicomponent Mel'nikov system and multicomponent Schrödinger-Boussinesq system

NASA Astrophysics Data System (ADS)

Sun, Baonan; Lian, Zhan

2018-02-01

By virtue of the bilinear method and the KP hierarchy reduction technique, exact explicit rational solutions of the multicomponent Mel'nikov equation and the multicomponent Schrödinger-Boussinesq equation are constructed, which contain multicomponent short waves and single-component long wave. For the multicomponent Mel'nikov equation, the fundamental rational solutions possess two different behaviours: lump and rogue wave. It is shown that the fundamental (simplest) rogue waves are line localised waves which arise from the constant background with a line profile and then disappear into the constant background again. The fundamental line rogue waves can be classified into three: bright, intermediate and dark line rogue waves. Two subclasses of non-fundamental rogue waves, i.e., multirogue waves and higher-order rogue waves are discussed. The multirogue waves describe interaction of several fundamental line rogue waves, in which interesting wave patterns appear in the intermediate time. Higher-order rogue waves exhibit dynamic behaviours that the wave structures start from lump and then retreat back to it. Moreover, by taking the parameter constraints further, general higher-order rogue wave solutions for the multicomponent Schrödinger-Boussinesq system are generated.

Plateau Waves of Intracranial Pressure and Partial Pressure of Cerebral Oxygen.

PubMed

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.

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

On the motion of a quantum particle in the spinning cosmic string space–time

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

Hassanabadi, H., E-mail: h.hasanabadi@shahroodut.ac.ir; Afshardoost, A.; Zarrinkamar, S.

2015-05-15

We analyze the energy spectrum and the wave function of a particle subjected to magnetic field in the spinning cosmic string space–time and investigate the influence of the spinning reference frame and topological defect on the system. To do this we solve Schrödinger equation in the spinning cosmic string background. In our work, instead of using an approximation in the calculations, we use the quasi-exact ansatz approach which gives the exact solutions for some primary levels. - Highlights: • Solving the Schrödinger equation in the spinning cosmic string space time. • Proposing a quasi-exact analytical solution to the general formmore » of the corresponding equation. • Generalizing the previous works.« less

Perturbed Coulomb Potentials in the Klein-Gordon Equation: Quasi-Exact Solution

NASA Astrophysics Data System (ADS)

Baradaran, M.; Panahi, H.

2018-05-01

Using the Lie algebraic approach, we present the quasi-exact solutions of the relativistic Klein-Gordon equation for perturbed Coulomb potentials namely the Cornell potential, the Kratzer potential and the Killingbeck potential. We calculate the general exact expressions for the energies, corresponding wave functions and the allowed values of the parameters of the potential within the representation space of sl(2) Lie algebra. In addition, we show that the considered equations can be transformed into the Heun's differential equations and then we reproduce the results using the associated special functions. Also, we study the special case of the Coulomb potential and show that in the non-relativistic limit, the solution of the Klein-Gordon equation converges to that of Schrödinger equation.

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

NASA Astrophysics Data System (ADS)

Zhi, Longxiao; Gu, Hanming

2018-03-01

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor series expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain the P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion doesn't need certain assumptions and can estimate more parameters simultaneously. It has a better applicability. Meanwhile, by using the generalized linear method, the inversion is easily implemented and its calculation cost is small. We use the theoretical model to generate synthetic seismic records to test and analyze the influence of random noise. The results can prove the availability and anti-noise-interference ability of our method. We also apply the inversion to actual field data and prove the feasibility of our method in actual situation.

Teaching graphical simulations of Fourier series expansion of some periodic waves using spreadsheets

NASA Astrophysics Data System (ADS)

Singh, Iqbal; Kaur, Bikramjeet

2018-05-01

The present article demonstrates a way of programming using an Excel spreadsheet to teach Fourier series expansion in school/colleges without the knowledge of any typical programming language. By using this, a student learns to approximate partial sum of the n terms of Fourier series for some periodic signals such as square wave, saw tooth wave, half wave rectifier and full wave rectifier signals.

New classes of solutions in the coupled PT symmetric nonlocal nonlinear Schrödinger equations with four wave mixing

NASA Astrophysics Data System (ADS)

Vinayagam, P. S.; Radha, R.; Al Khawaja, U.; Ling, Liming

2018-06-01

We investigate generalized nonlocal coupled nonlinear Schorödinger equation containing Self-Phase Modulation, Cross-Phase Modulation and four wave mixing involving nonlocal interaction. By means of Darboux transformation we obtained a family of exact breathers and solitons including the Peregrine soliton, Kuznetsov-Ma breather, Akhmediev breather along with all kinds of soliton-soliton and breather-soltion interactions. We analyze and emphasize the impact of the four-wave mixing on the nature and interaction of the solutions. We found that the presence of four wave mixing converts a two-soliton solution into an Akhmediev breather. In particular, the inclusion of four wave mixing results in the generation of a new solutions which is spatially and temporally periodic called "Soliton (Breather) lattice".

Measurements of Mode Converted Ion Cyclotron Wave with Phase Contrast Imaging in Alcator C-Mod and Comparisons with Synthetic PCI Simulations in TORIC

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

Tsujii, N.; Porkolab, M.; Edlund, E. M.

2009-11-26

Mode converted ion cyclotron wave (ICW) has been observed with phase contrast imaging (PCI) in D-{sup 3}He plasmas in Alcator C-Mod. The measurements were carried out with the optical heterodyne technique using acousto-optic modulators which modulate the CO2 laser beam intensity near the ion cyclotron frequency. With recently improved calibration of the PCI system using a calibrated sound wave source, the measurements have been compared with the full-wave code TORIC, as interpreted by a synthetic diagnostic. Because of the line-integrated nature of the PCI signal, the predictions are sensitive to the exact wave field pattern. The simulations are found tomore » be in qualitative agreement with the measurements.« less

Immersion angle dependence of the resonant-frequency shift of the quartz crystal microbalance in a liquid: effects of longitudinal wave.

PubMed

Yoshimoto, Minoru; Kobirata, Satoshi; Aizawa, Hideo; Kurosawa, Shigeru

2007-06-19

We investigated the effects of the longitudinal wave on the immersion angle dependence of the resonant-frequency shift, deltaF, of the quartz crystal microbalance, QCM. In order to study exactly the effects, we employed the three types of cells: normal cell, cell with the glass beads and cell with sponge. The longitudinal wave exists in the normal cell. On the other hand, both the cell with the glass beads and the cell with sponge eliminate the longitudinal wave. As results, we have found that the tendencies of deltaF are the same in the three types of cells. That is, we conclude that the longitudinal wave does not have effects on the immersion angle dependence of deltaF.

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.

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

Workman, Ron L.; Briscoe, William J.; Strakovsky, Igor I.

Energy-dependent and single-energy fits to the existing nucleon-nucleon database have been updated to incorporate recent measurements. The fits cover a region from threshold to 3 GeV, in the laboratory kinetic energy, for proton-proton scattering, with an upper limit of 1.3 GeV for neutron-proton scattering. Experiments carried out at the COSY-WASA and COSY-ANKE facilities have had a significant impact on the partial-wave solutions. Lastly, results are discussed in terms of both partial-wave and direct reconstruction amplitudes.

a Partial Wave Analysis of the Reaction Negative Pion Proton ---> Positive Pion Negative Pion Neutral Pion Neutron at 8.45 Gev/c.

NASA Astrophysics Data System (ADS)

Dankowych, John Alexander

1980-06-01

We have performed an isobar model partial wave analysis (PWA) of a high statistics sample of the reaction (pi)('-)p (,(--->)) (pi)('+)(pi)('-)(pi)('0)n at 8.45 GeV/c. We present strong evidence for the existence of the unnatural parity, isoscalar (H) and isovector (A(,1)) axial-vector mesons. The intensity distributions show significant structure while the forward phase motion relative to the isospin-2 axial-vector partial wave is consistent with that expected for Breit-Wigner resonances. The A(,1) production is mainly via M = 1, natural parity exchange while the H is produced mainly in M = 0, natural parity exchange. From a Deck model fit we obtain for the A(,1) a mass of 1241 (+OR-) 80 MeV and a width of 380 (+OR-) 100 MeV; for the H we obtain a mass of 1194 (+OR-) 55 MeV and a width of 320 (+OR-) 50 MeV. In nucleon spin flip we have evidence for an isovector, pseudoscalar resonance ((pi)') under the A(,2). The natural parity states : the (omega)(IJP = 01-), the A(,2) (IJP = 12+) and the (omega)(,g )(IJP = 03-) are strong features of the data. In the IJP = 01- partial wave thre is more cross-section than that expected for just the (omega)(783) tail.

Dissipative instability in a partially ionised prominence plasma slab

NASA Astrophysics Data System (ADS)

Ballai, I.; Pintér, B.; Oliver, R.; Alexandrou, M.

2017-07-01

Aims: We aim to investigate the nature of dissipative instability appearing in a prominence planar thread filled with partially ionised plasma in the incompressible limit. The importance of partial ionisation is investigated in terms of the ionisation factor and the wavelength of sausage and kink waves propagating in the slab. Methods: In order to highlight the role of partial ionisation, we have constructed models describing various situations we can meet in solar prominence fine structure. Matching the solutions for the transversal component of the velocity and total pressure at the interfaces between the prominence slab and surrounding plasmas, we derived a dispersion relation whose imaginary part describes the evolution of the instability. Results were obtained in the limit of weak dissipation. We have investigated the appearance of instabilities in prominence dark plumes using single and two-fluid approximations. Results: Using simple analytical methods, we show that dissipative instabilities appear for flow speeds that are less than the Kelvin-Helmholtz instability threshold. The onset of instability is determined by the equilibrium flow strength, the ionisation factor of the plasma, the wavelength of waves and the ion-neutral collisional rate. For a given wavelength and for ionisation degrees closer to a neutral gas, the propagating waves become unstable for a narrow band of flow speeds, meaning that neutrals have a stabilising effect. Our results show that the partially ionised plasma describing prominence dark plumes becomes unstable only in a two-fluid (charged particles-neutrals) model, that is for periods that are smaller than the ion-neutral collision time. Conclusions: The present study improves our understanding of the complexity of dynamical processes and stability of solar prominences and the role partial ionisation in destabilising the plasma. We showed the necessity of two-fluid approximation when discussing the nature of instabilities: waves in a single fluid approximation show a great deal of stability. Our results clearly show that the problem of partial ionisation introduces new aspects of plasma stability with consequences on the evolution of partially ionised plasmas and solar prominences, in particular.

An asymptotically exact reduced PDE model for the magnetorotational instability: derivation and numerical simulations

NASA Astrophysics Data System (ADS)

Jamroz, Ben; Julien, Keith; Knobloch, Edgar

2008-12-01

Taking advantage of disparate spatio-temporal scales relevant to astrophysics and laboratory experiments, we derive asymptotically exact reduced partial differential equation models for the magnetorotational instability. These models extend recent single-mode formulations leading to saturation in the presence of weak dissipation, and are characterized by a back-reaction on the imposed shear. Numerical simulations performed for a broad class of initial conditions indicate an initial phase of growth dominated by the optimal (fastest growing) magnetorotational instability fingering mode, followed by a vertical coarsening to a box-filling mode.

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.

Accuracy & Computational Considerations for Wide--Angle One--way Seismic Propagators and Multiple Scattering by Invariant Embedding

NASA Astrophysics Data System (ADS)

Thomson, C. J.

2004-12-01

Pseudodifferential operators (PSDOs) yield in principle exact one--way seismic wave equations, which are attractive both conceptually and for their promise of computational efficiency. The one--way operators can be extended to include multiple--scattering effects, again in principle exactly. In practice approximations must be made and, as an example, the variable--wavespeed Helmholtz equation for scalar waves in two space dimensions is here factorized to give the one--way wave equation. This simple case permits clear identification of a sequence of physically reasonable approximations to be used when the mathematically exact PSDO one--way equation is implemented on a computer. As intuition suggests, these approximations hinge on the medium gradients in the direction transverse to the main propagation direction. A key point is that narrow--angle approximations are to be avoided in the interests of accuracy. Another key consideration stems from the fact that the so--called ``standard--ordering'' PSDO indicates how lateral interpolation of the velocity structure can significantly reduce computational costs associated with the Fourier or plane--wave synthesis lying at the heart of the calculations. The decision on whether a slow or a fast Fourier transform code should be used rests upon how many lateral model parameters are truly distinct. A third important point is that the PSDO theory shows what approximations are necessary in order to generate an exponential one--way propagator for the laterally varying case, representing the intuitive extension of classical integral--transform solutions for a laterally homogeneous medium. This exponential propagator suggests the use of larger discrete step sizes, and it can also be used to approach phase--screen like approximations (though the latter are not the main interest here). Numerical comparisons with finite--difference solutions will be presented in order to assess the approximations being made and to gain an understanding of computation time differences. The ideas described extend to the three--dimensional, generally anisotropic case and to multiple scattering by invariant embedding.

Analytical study of exact solutions of the nonlinear Korteweg-de Vries equation with space-time fractional derivatives

NASA Astrophysics Data System (ADS)

Liu, Jiangen; Zhang, Yufeng

2018-01-01

This paper gives an analytical study of dynamic behavior of the exact solutions of nonlinear Korteweg-de Vries equation with space-time local fractional derivatives. By using the improved (G‧ G )-expansion method, the explicit traveling wave solutions including periodic solutions, dark soliton solutions, soliton solutions and soliton-like solutions, are obtained for the first time. They can better help us further understand the physical phenomena and provide a strong basis. Meanwhile, some solutions are presented through 3D-graphs.

A class of exact classical solutions to string theory.

PubMed

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.

Maslov indices, Poisson brackets, and singular differential forms

NASA Astrophysics Data System (ADS)

Esterlis, I.; Haggard, H. M.; Hedeman, A.; Littlejohn, R. G.

2014-06-01

Maslov indices are integers that appear in semiclassical wave functions and quantization conditions. They are often notoriously difficult to compute. We present methods of computing the Maslov index that rely only on typically elementary Poisson brackets and simple linear algebra. We also present a singular differential form, whose integral along a curve gives the Maslov index of that curve. The form is closed but not exact, and transforms by an exact differential under canonical transformations. We illustrate the method with the 6j-symbol, which is important in angular-momentum theory and in quantum gravity.

High Resolution WENO Simulation of 3D Detonation Waves

DTIC Science & Technology

2012-02-27

pocket behind the detonation front was not observed in their results because the rotating transverse detonation completely consumed the unburned gas. Dou...three-dimensional detonations We add source terms (functions of x, y, z and t) to the PDE system so that the following functions are exact solutions to... detonation rotates counter-clockwise, opposite to that in [48]. It can be seen that, the triple lines and transverse waves collide with the walls, and strong

USSR and Eastern Europe Scientific Abstracts- Physics - Number 45

DTIC Science & Technology

1978-10-02

compound, a function of the angle between the electrical vector of the ’ light wave and the optical c-axis of the crystal. Heterodiodes have first...of naturally radioactive U, Th and K in a 1-liter sample. USSR A VECTOR MESON IN A QUANTUM ELECTROMAGNETIC FIELD Moscow TEORETICHESKAYA I...arbitrary spin in a classical plane electromagnetic field are used to find the exact wave function of a vector meson in the quantum field of a linearly

Exact wave packet dynamics of singlet fission in unsubstituted and substituted polyene chains within long-range interacting models

NASA Astrophysics Data System (ADS)

Prodhan, Suryoday; Ramasesha, S.

2017-08-01

Singlet fission (SF) is a potential pathway for significant enhancement of efficiency in organic solar cells (OSC). In this paper, we study singlet fission in a pair of polyene molecules in two different stacking arrangements employing exact many-body wave packet dynamics. In the noninteracting model, the SF yield is absent. The individual molecules are treated within Hubbard and Pariser-Parr-Pople (PPP) models and the interaction between them involves transfer terms, intersite electron repulsions, and site-charge-bond-charge repulsion terms. Initial wave packet is constructed from excited singlet state of one molecule and ground state of the other. Time development of this wave packet under the influence of intermolecular interactions is followed within the Schrödinger picture by an efficient predictor-corrector scheme. In unsubstituted Hubbard and PPP chains, 2 1A excited singlet state leads to significant SF yield while the 1 1B state gives negligible fission yield. On substitution by donor-acceptor groups of moderate strength, the lowest excited state will have sufficient 2 1A character and hence results in significant SF yield. Because of rapid internal conversion, the nature of the lowest excited singlet will determine the SF contribution to OSC efficiency. Furthermore, we find the fission yield depends considerably on the stacking arrangement of the polyene molecules.

Solitary traveling wave solutions of pressure equation of bubbly liquids with examination for viscosity and heat transfer

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-03-01

In this research, we investigate one of the most popular model in nature and also industrial which is the pressure equation of bubbly liquids with examination for viscosity and heat transfer which has many application in nature and engineering. Understanding the physical meaning of exact and solitary traveling wave solutions for this equation gives the researchers in this field a great clear vision of the pressure waves in a mixture liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer and also dynamics of contrast agents in the blood flow at ultrasonic researches. To achieve our goal, we apply three different methods which are extended tanh-function method, extended simple equation method and a new auxiliary equation method on this equation. We obtained exact and solitary traveling wave solutions and we also discuss the similarity and difference between these three method and make a comparison between results that we obtained with another results that obtained with the different researchers using different methods. All of these results and discussion explained the fact that our new auxiliary equation method is considered to be the most general, powerful and the most result-oriented. These kinds of solutions and discussion allow for the understanding of the phenomenon and its intrinsic properties as well as the ease of way of application and its applicability to other phenomena.

Hairpin exact coherent states in channel flow

NASA Astrophysics Data System (ADS)

Graham, Michael; Shekar, Ashwin

2017-11-01

Questions remain over the role of hairpin vortices in fully developed turbulent flows. Studies have shown that hairpins play a role in the dynamics away from the wall but the question still persists if they play any part in (near wall) fully developed turbulent dynamics. In addition, the robustness of the hairpin vortex regeneration mechanism is still under investigation. Recent studies have shown the existence of nonlinear traveling wave solutions to the Navier-Stokes equations, also known as exact coherent states (ECS), that capture many aspects of near-wall turbulent structures. Previously discovered ECS in channel flow have a quasi-streamwise vortex structure, with no indication of hairpin formation. Here we present a family of traveling wave solutions for channel flow that displays hairpin vortices. They have a streamwise vortex-streak structure near the wall with a spatially localized hairpin head near the channel centerline, attached to and sustained by the near wall structures. This family of solutions emerges through a transcritical bifurcation from a branch of traveling wave solutions with y and z reflectional symmetry. We also look into the instabilities that lead to the development of hairpins also explore its connection to turbulent dynamics.

Time reversal for photoacoustic tomography based on the wave equation of Nachman, Smith, and Waag

NASA Astrophysics Data System (ADS)

Kowar, Richard

2014-02-01

One goal of photoacoustic tomography (PAT) is to estimate an initial pressure function φ from pressure data measured at a boundary surrounding the object of interest. This paper is concerned with a time reversal method for PAT that is based on the dissipative wave equation of Nachman, Smith, and Waag [J. Acoust. Soc. Am. 88, 1584 (1990), 10.1121/1.400317]. This equation is a correction of the thermoviscous wave equation such that its solution has a finite wave front speed and, in contrast, it can model several relaxation processes. In this sense, it is more accurate than the thermoviscous wave equation. For simplicity, we focus on the case of one relaxation process. We derive an exact formula for the time reversal image I, which depends on the relaxation time τ1 and the compressibility κ1 of the dissipative medium, and show I (τ1,κ1)→φ for κ1→0. This implies that I =φ holds in the dissipation-free case and that I is similar to φ for sufficiently small compressibility κ1. Moreover, we show for tissue similar to water that the small wave number approximation I0 of the time reversal image satisfies I0=η0*xφ with accent="true">η̂0(|k|)≈const. for |k|≪1/c0τ1, where φ denotes the initial pressure function. For such tissue, our theoretical analysis and numerical simulations show that the time reversal image I is very similar to the initial pressure function φ and that a resolution of σ ≈0.036mm is feasible (for exact measurement data).

The epigenetics of obesity

USDA-ARS?s Scientific Manuscript database

Maternal nutrition at the time of conception and during pregnancy is considered a factor for individual differences in having obesity. The mechanisms underlying this association are likely partially epigenetic in nature, but pinning down the exact nature, location, and timing of these changes remain...

The K-π+ S-wave from the D+→K-π+π+ decay

NASA Astrophysics Data System (ADS)

FOCUS Collaboration; Link, J. M.; Yager, P. M.; Anjos, J. C.; Bediaga, I.; Castromonte, C.; Machado, A. A.; Magnin, J.; Massafferri, A.; de Miranda, J. M.; Pepe, I. M.; Polycarpo, E.; Dos Reis, A. C.; Carrillo, S.; Cuautle, E.; Sánchez-Hernández, A.; Uribe, C.; Vázquez, F.; Agostino, L.; Cinquini, L.; Cumalat, J. P.; Frisullo, V.; O'Reilly, B.; Segoni, I.; Stenson, K.; Butler, J. N.; Cheung, H. W. K.; Chiodini, G.; Gaines, I.; Garbincius, P. H.; Garren, L. A.; Gottschalk, E.; Kasper, P. H.; Kreymer, A. E.; Kutschke, R.; Wang, M.; Benussi, L.; Bianco, S.; Fabbri, F. L.; Zallo, A.; Casimiro, E.; Reyes, M.; Cawlfield, C.; Kim, D. Y.; Rahimi, A.; Wiss, J.; Gardner, R.; Kryemadhi, A.; Chung, Y. S.; Kang, J. S.; Ko, B. R.; Kwak, J. W.; Lee, K. B.; Cho, K.; Park, H.; Alimonti, G.; Barberis, S.; Boschini, M.; Cerutti, A.; D'Angelo, P.; Dicorato, M.; Dini, P.; Edera, L.; Erba, S.; Inzani, P.; Leveraro, F.; Malvezzi, S.; Menasce, D.; Mezzadri, M.; Moroni, L.; Pedrini, D.; Pontoglio, C.; Prelz, F.; Rovere, M.; Sala, S.; Davenport, T. F.; Arena, V.; Boca, G.; Bonomi, G.; Gianini, G.; Liguori, G.; Pegna, D. Lopes; Merlo, M. M.; Pantea, D.; Ratti, S. P.; Riccardi, C.; Vitulo, P.; Göbel, C.; Otalora, J.; Hernandez, H.; Lopez, A. M.; Mendez, H.; Paris, A.; Quinones, J.; Ramirez, J. E.; Zhang, Y.; Wilson, J. R.; Handler, T.; Mitchell, R.; Engh, D.; Hosack, M.; Johns, W. E.; Luiggi, E.; Moore, J. E.; Nehring, M.; Sheldon, P. D.; Vaandering, E. W.; Webster, M.; Sheaff, M.

2009-10-01

Using data from FOCUS (E831) experiment at Fermilab, we present a model independent partial-wave analysis of the K-π+ S-wave amplitude from the decay D+→K-π+π+. The S-wave is a generic complex function to be determined directly from the data fit. The P- and D-waves are parameterized by a sum of Breit-Wigner amplitudes. The measurement of the S-wave amplitude covers the whole elastic range of the K-π+ system.

Weierstrass traveling wave solutions for dissipative Benjamin, Bona, and Mahony (BBM) equation

NASA Astrophysics Data System (ADS)

Mancas, Stefan C.; Spradlin, Greg; Khanal, Harihar

2013-08-01

In this paper the effect of a small dissipation on waves is included to find exact solutions to the modified Benjamin, Bona, and Mahony (BBM) equation by viscosity. Using Lyapunov functions and dynamical systems theory, we prove that when viscosity is added to the BBM equation, in certain regions there still exist bounded traveling wave solutions in the form of solitary waves, periodic, and elliptic functions. By using the canonical form of Abel equation, the polynomial Appell invariant makes the equation integrable in terms of Weierstrass ℘ functions. We will use a general formalism based on Ince's transformation to write the general solution of dissipative BBM in terms of ℘ functions, from which all the other known solutions can be obtained via simplifying assumptions. Using ODE (ordinary differential equations) analysis we show that the traveling wave speed is a bifurcation parameter that makes transition between different classes of waves.

Method and apparatus for generating motor current spectra to enhance motor system fault detection

DOEpatents

Linehan, Daniel J.; Bunch, Stanley L.; Lyster, Carl T.

1995-01-01

A method and circuitry for sampling periodic amplitude modulations in a nonstationary periodic carrier wave to determine frequencies in the amplitude modulations. The method and circuit are described in terms of an improved motor current signature analysis. The method insures that the sampled data set contains an exact whole number of carrier wave cycles by defining the rate at which samples of motor current data are collected. The circuitry insures that a sampled data set containing stationary carrier waves is recreated from the analog motor current signal containing nonstationary carrier waves by conditioning the actual sampling rate to adjust with the frequency variations in the carrier wave. After the sampled data is transformed to the frequency domain via the Discrete Fourier Transform, the frequency distribution in the discrete spectra of those components due to the carrier wave and its harmonics will be minimized so that signals of interest are more easily analyzed.

Formation of rarefaction waves in origami-based metamaterials

DOE PAGES

Yasuda, H.; Chong, C.; Charalampidis, E. G.; ...

2016-04-15

Here, we investigate the nonlinear wave dynamics of origami-based metamaterials composed of Tachi-Miura polyhedron (TMP) unit cells. These cells exhibit strain softening behavior under compression, which can be tuned by modifying their geometrical configurations or initial folded conditions. We assemble these TMP cells into a cluster of origami-based metamaterials, and we theoretically model and numerically analyze their wave transmission mechanism under external impact. Numerical simulations show that origami-based metamaterials can provide a prototypical platform for the formation of nonlinear coherent structures in the form of rarefaction waves, which feature a tensile wavefront upon the application of compression to the system.more » We also demonstrate the existence of numerically exact traveling rarefaction waves in an effective lumped-mass model. Origami-based metamaterials can be highly useful for mitigating shock waves, potentially enabling a wide variety of engineering applications.« less

Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation

NASA Astrophysics Data System (ADS)

Ak, Turgut; Aydemir, Tugba; Saha, Asit; Kara, Abdul Hamid

2018-06-01

Propagation of nonlinear shock waves for the generalised Oskolkov equation and dynamic motions of the perturbed Oskolkov equation are investigated. Employing the unified method, a collection of exact shock wave solutions for the generalised Oskolkov equations is presented. Collocation finite element method is applied to the generalised Oskolkov equation for checking the accuracy of the proposed method by two test problems including the motion of shock wave and evolution of waves with Gaussian and undular bore initial conditions. Considering an external periodic perturbation, the dynamic motions of the perturbed generalised Oskolkov equation are studied depending on the system parameters with the help of phase portrait and time series plot. The perturbed generalised Oskolkov equation exhibits period-3, quasiperiodic and chaotic motions for some special values of the system parameters, whereas the generalised Oskolkov equation presents shock waves in the absence of external periodic perturbation.

Standing spin-wave mode structure and linewidth in partially disordered hexagonal arrays of perpendicularly magnetized sub-micron Permalloy discs

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

Ross, N., E-mail: rossn2282@gmail.com; Kostylev, M., E-mail: mikhail.kostylev@uwa.edu.au; Stamps, R. L.

2014-09-21

Standing spin wave mode frequencies and linewidths in partially disordered perpendicular magnetized arrays of sub-micron Permalloy discs are measured using broadband ferromagnetic resonance and compared to analytical results from a single, isolated disc. The measured mode structure qualitatively reproduces the structure expected from the theory. Fitted demagnetizing parameters decrease with increasing array disorder. The frequency difference between the first and second radial modes is found to be higher in the measured array systems than predicted by theory for an isolated disc. The relative frequencies between successive spin wave modes are unaffected by reduction of the long-range ordering of discs inmore » the array. An increase in standing spin wave resonance linewidth at low applied magnetic fields is observed and grows more severe with increased array disorder.« less

Calculation of total electron excitation cross-sections and partial electron ionization cross-sections for the elements. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Green, T. J.

1973-01-01

Computer programs were used to calculate the total electron excitation cross-section for atoms and the partial ionization cross-section. The approximations to the scattering amplitude used are as follows: (1) Born, Bethe, and Modified Bethe for non-exchange excitation; (2) Ochkur for exchange excitation; and (3) Coulomb-Born of non-exchange ionization. The amplitudes are related to the differential cross-sections which are integrated to give the total excitation (or partial ionization) cross-section for the collision. The atomic wave functions used are Hartree-Fock-Slater functions for bound states and the coulomb wave function for the continuum. The programs are presented and the results are examined.

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.

Disentangling the dynamical origin of P11 nucleon resonances.

PubMed

Suzuki, N; Juliá-Díaz, B; Kamano, H; Lee, T-S H; Matsuyama, A; Sato, T

2010-01-29

We show that two almost degenerate poles near the piDelta threshold and the next higher mass pole in the P11 partial wave of piN scattering evolve from a single bare state through its coupling with piN, etaN, and pipiN reaction channels. This finding provides new information on understanding the dynamical origins of the Roper N{*}(1440) and N{*}(1710) resonances listed by Particle Data Group. Our results for the resonance poles in other piN partial waves are also presented.

S-matrix method for the numerical determination of bound states.

NASA Technical Reports Server (NTRS)

Bhatia, A. K.; Madan, R. N.

1973-01-01

A rapid numerical technique for the determination of bound states of a partial-wave-projected Schroedinger equation is presented. First, one needs to integrate the equation only outwards as in the scattering case, and second, the number of trials necessary to determine the eigenenergy and the corresponding eigenfunction is considerably less than in the usual method. As a nontrivial example of the technique, bound states are calculated in the exchange approximation for the e-/He+ system and l equals 1 partial wave.

On the origin of heavy-tail statistics in equations of the Nonlinear Schrödinger type

NASA Astrophysics Data System (ADS)

Onorato, Miguel; Proment, Davide; El, Gennady; Randoux, Stephane; Suret, Pierre

2016-09-01

We study the formation of extreme events in incoherent systems described by the Nonlinear Schrödinger type of equations. We consider an exact identity that relates the evolution of the normalized fourth-order moment of the probability density function of the wave envelope to the rate of change of the width of the Fourier spectrum of the wave field. We show that, given an initial condition characterized by some distribution of the wave envelope, an increase of the spectral bandwidth in the focusing/defocusing regime leads to an increase/decrease of the probability of formation of rogue waves. Extensive numerical simulations in 1D+1 and 2D+1 are also performed to confirm the results.

Theoretical and experimental evidence of non-symmetric doubly localized rogue waves.

PubMed

He, Jingsong; Guo, Lijuan; Zhang, Yongshuai; Chabchoub, Amin

2014-11-08

We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water.

Theoretical and experimental evidence of non-symmetric doubly localized rogue waves

PubMed Central

He, Jingsong; Guo, Lijuan; Zhang, Yongshuai; Chabchoub, Amin

2014-01-01

We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water. PMID:25383023

FAST TRACK COMMUNICATION: Soliton solutions of the KP equation with V-shape initial waves

NASA Astrophysics Data System (ADS)

Kodama, Y.; Oikawa, M.; Tsuji, H.

2009-08-01

We consider the initial value problems of the Kadomtsev-Petviashvili (KP) equation for symmetric V-shape initial waves consisting of two semi-infinite line solitons with the same amplitude. Those are particularly important for studies of large amplitude waves such as tsunami in shallow water. Numerical simulations show that the solutions of the initial value problem approach asymptotically to certain exact solutions of the KP equation found recently in [1]. We then use a chord diagram to explain the asymptotic result. This provides an analytical method to study asymptotic behavior for the initial value problem of the KP equation. We also demonstrate a real experiment of shallow water waves which may represent the solution discussed in this communication.

Exact semi-separation of variables in waveguides with non-planar boundaries

NASA Astrophysics Data System (ADS)

Athanassoulis, G. A.; Papoutsellis, Ch. E.

2017-05-01

Series expansions of unknown fields Φ =∑φn Zn in elongated waveguides are commonly used in acoustics, optics, geophysics, water waves and other applications, in the context of coupled-mode theories (CMTs). The transverse functions Zn are determined by solving local Sturm-Liouville problems (reference waveguides). In most cases, the boundary conditions assigned to Zn cannot be compatible with the physical boundary conditions of Φ, leading to slowly convergent series, and rendering CMTs mild-slope approximations. In the present paper, the heuristic approach introduced in Athanassoulis & Belibassakis (Athanassoulis & Belibassakis 1999 J. Fluid Mech. 389, 275-301) is generalized and justified. It is proved that an appropriately enhanced series expansion becomes an exact, rapidly convergent representation of the field Φ, valid for any smooth, non-planar boundaries and any smooth enough Φ. This series expansion can be differentiated termwise everywhere in the domain, including the boundaries, implementing an exact semi-separation of variables for non-separable domains. The efficiency of the method is illustrated by solving a boundary value problem for the Laplace equation, and computing the corresponding Dirichlet-to-Neumann operator, involved in Hamiltonian equations for nonlinear water waves. The present method provides accurate results with only a few modes for quite general domains. Extensions to general waveguides are also discussed.

Erratum: Nonlinear Dirac equation solitary waves in external fields [Phys. Rev. E 86, 046602 (2012)

DOE PAGES

Mertens, Franz G.; Quintero, Niurka R.; Cooper, Fred; ...

2016-05-10

In Sec. IV of our original paper, we assumed a particular conservation law Eq. (4.6), which was true in the absence of external potentials, to derive some particular potentials for which we obtained solutions to the nonlinear Dirac equation (NLDE). Because the conservation law of Eq. (4.6) for the component T 11 of the energy-momentum tensor is not true in the presence of these external potentials, the solutions we found do not satisfy the NLDEs in the presence of these potentials. Thus all the equations from Eq. (4.6) through Eq. (4.44) are not correct, since the exact solutions that followedmore » in that section presumed Eq. (4.6) was true. Also Eqs. (A3)–(A5) are a restatement of Eq. (4.6) and also are not correct. These latter equations are also not used in Sec. V and beyond. The rest of our original paper (starting with Sec. V) was not concerned with exact solutions, rather it was concerned with how the exact solitary-wave solutions to the NLDE in the absence of an external potential responded to being in the presence of various external potentials. This Erratum corrects this mistake.« less

New Optical Field Generated by Partial Tracing Over Two-Mode Squeezing-Rotating Entangled Vacuum State ^{{*}}

NASA Astrophysics Data System (ADS)

Ren, Gang; Du, Jian-ming; Zhang, Wen-Hai

2018-05-01

Based on the two-mode squeezing-rotating entangled vacuum state (Fan and Fan in Commun Theor Phys 33:701-704, 2000), we obtained a new quantum state by using partial tracing method. This new state can be considered as a real chaotic field. We also studied its squeezing properties and quantum statistical properties by giving the analytic results and exact numerical results. It was established that the rotation angle's parameter plays an important role in this new optical field.

Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Aziz, Taha; Fatima, Aeeman; Khalique, Chaudry Masood

2018-03-01

The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

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,…

Single-Layer Plasmonic Metasurface Half-Wave Plates with Wavelength-Independent Polarization Conversion Angle

DOE PAGES

Liu, Zhaocheng; Li, Zhancheng; Liu, Zhe; ...

2017-06-30

Manipulation of polarization state is of great fundamental importance and plays a crucial role in modern photonic applications such as optical communication, imaging, and sensing. Metamaterials and metasurfaces have attracted increasing interest in this area because they facilitate designer optical response through engineering the composite subwavelength structures. In this paper, we propose a general methods of designing half-wave plate and demonstrate in the near-infrared wavelength range an optically thin plasmonic metasurface half-wave plates that rotate the polarization direction of the linearly polarized incident light with a high degree of linear polarization. Finally, the half-wave plate functionality is realized through arrangingmore » the orientation of the nanoantennas to form an appropriate spatial distribution profile, which behave exactly as in classical half-wave plates but over in a wavelength-independent way.« less

Wave-packet continuum-discretization approach to ion-atom collisions including rearrangement: Application to differential ionization in proton-hydrogen scattering

NASA Astrophysics Data System (ADS)

Abdurakhmanov, I. B.; Bailey, J. J.; Kadyrov, A. S.; Bray, I.

2018-03-01

In this work, we develop a wave-packet continuum-discretization approach to ion-atom collisions that includes rearrangement processes. The total scattering wave function is expanded using a two-center basis built from wave-packet pseudostates. The exact three-body Schrödinger equation is converted into coupled-channel differential equations for time-dependent expansion coefficients. In the asymptotic region these time-dependent coefficients represent transition amplitudes for all processes including elastic scattering, excitation, ionization, and electron capture. The wave-packet continuum-discretization approach is ideal for differential ionization studies as it allows one to generate pseudostates with arbitrary energies and distribution. The approach is used to calculate the double differential cross section for ionization in proton collisions with atomic hydrogen. Overall good agreement with experiment is obtained for all considered cases.

Nonlinear modes of the tensor Dirac equation and CPT violation

NASA Technical Reports Server (NTRS)

Reifler, Frank J.; Morris, Randall D.

1993-01-01

Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.

Time-Reversal Generation of Rogue Waves

NASA Astrophysics Data System (ADS)

Chabchoub, Amin; Fink, Mathias

2014-03-01

The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized in both time and space is considered to provide appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space. The potential applications of this time-reversal approach include remote sensing and motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates, and plasma, where the wave motion dynamics is governed by the NLS.

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

Yasuda, H.; Chong, C.; Charalampidis, E. G.

Here, we investigate the nonlinear wave dynamics of origami-based metamaterials composed of Tachi-Miura polyhedron (TMP) unit cells. These cells exhibit strain softening behavior under compression, which can be tuned by modifying their geometrical configurations or initial folded conditions. We assemble these TMP cells into a cluster of origami-based metamaterials, and we theoretically model and numerically analyze their wave transmission mechanism under external impact. Numerical simulations show that origami-based metamaterials can provide a prototypical platform for the formation of nonlinear coherent structures in the form of rarefaction waves, which feature a tensile wavefront upon the application of compression to the system.more » We also demonstrate the existence of numerically exact traveling rarefaction waves in an effective lumped-mass model. Origami-based metamaterials can be highly useful for mitigating shock waves, potentially enabling a wide variety of engineering applications.« less

Sound-turbulence interaction in transonic boundary layers

NASA Astrophysics Data System (ADS)

Lelostec, Ludovic; Scalo, Carlo; Lele, Sanjiva

2014-11-01

Acoustic wave scattering in a transonic boundary layer is investigated through a novel approach. Instead of simulating directly the interaction of an incoming oblique acoustic wave with a turbulent boundary layer, suitable Dirichlet conditions are imposed at the wall to reproduce only the reflected wave resulting from the interaction of the incident wave with the boundary layer. The method is first validated using the laminar boundary layer profiles in a parallel flow approximation. For this scattering problem an exact inviscid solution can be found in the frequency domain which requires numerical solution of an ODE. The Dirichlet conditions are imposed in a high-fidelity unstructured compressible flow solver for Large Eddy Simulation (LES), CharLESx. The acoustic field of the reflected wave is then solved and the interaction between the boundary layer and sound scattering can be studied.

Spin waves in rings of classical magnetic dipoles

NASA Astrophysics Data System (ADS)

Schmidt, Heinz-Jürgen; Schröder, Christian; Luban, Marshall

2017-03-01

We theoretically and numerically investigate spin waves that occur in systems of classical magnetic dipoles that are arranged at the vertices of a regular polygon and interact solely via their magnetic fields. There are certain limiting cases that can be analyzed in detail. One case is that of spin waves as infinitesimal excitations from the system’s ground state, where the dispersion relation can be determined analytically. The frequencies of these infinitesimal spin waves are compared with the peaks of the Fourier transform of the thermal expectation value of the autocorrelation function calculated by Monte Carlo simulations. In the special case of vanishing wave number an exact solution of the equations of motion is possible describing synchronized oscillations with finite amplitudes. Finally, the limiting case of a dipole chain with N\\longrightarrow ∞ is investigated and completely solved.

On the design of wave digital filters with low sensitivity properties.

NASA Technical Reports Server (NTRS)

Renner, K.; Gupta, S. C.

1973-01-01

The wave digital filter patterned after doubly terminated maximum available power (MAP) networks by means of the Richard's transformation has been shown to have low-coefficient-sensitivity properties. This paper examines the exact nature of the relationship between the wave-digital-filter structure and the MAP networks and how the sensitivity property arises, which permits implementation of the digital structure with a lower coefficient word length than that possible with the conventional structures. The proper design procedure is specified and the nature of the unique complementary outputs is discussed. Finally, an example is considered which illustrates the design, the conversion techniques, and the low sensitivity properties.

Some examples of exact and approximate solutions in small particle scattering - A progress report

NASA Technical Reports Server (NTRS)

Greenberg, J. M.

1974-01-01

The formulation of basic equations from which the scattering of radiation by a localized variation in a medium is discussed. These equations are developed in both the differential and the integral form. Primary interest is in the scattering of electromagnetic waves for which the solution of the vector wave equation with appropriate boundary conditions must be considered. Scalar scattering by an infinite homogeneous isotropic circular cylinder, and scattering of electromagnetic waves by infinite circular cylinders are treated, and the case of the finite circular cylinder is considered. A procedure is given for obtaining angular scattering distributions from spheroids.

Front acceleration by dynamic selection in Fisher population waves

NASA Astrophysics Data System (ADS)

Bénichou, O.; Calvez, V.; Meunier, N.; Voituriez, R.

2012-10-01

We introduce a minimal model of population range expansion in which the phenotypes of individuals present no selective advantage and differ only in their diffusion rate. We show that such neutral phenotypic variability (i.e., that does not modify the growth rate) alone can yield phenotype segregation at the front edge, even in absence of genetic noise, and significantly impact the dynamical properties of the expansion wave. We present an exact asymptotic traveling wave solution and show analytically that phenotype segregation accelerates the front propagation. The results are compatible with field observations such as invasions of cane toads in Australia or bush crickets in Britain.

Gravitational waves from rotating and precessing rigid bodies. 2: General solutions and computationally useful formulae

NASA Technical Reports Server (NTRS)

Zimmerman, M.

1979-01-01

The classical mechanics results for free precession which are needed in order to calculate the weak field, slow-motion, quadrupole-moment gravitational waves are reviewed. Within that formalism, algorithms are given for computing the exact gravitational power radiated and waveforms produced by arbitrary rigid-body freely-precessing sources. The dominant terms are presented in series expansions of the waveforms for the case of an almost spherical object precessing with a small wobble angle. These series expansions, which retain the precise frequency dependence of the waves, may be useful for gravitational astronomers when freely-precessing sources begin to be observed.

Dissipative nonlinear waves in a gravitating quantum fluid

NASA Astrophysics Data System (ADS)

Sahu, Biswajit; Sinha, Anjana; Roychoudhury, Rajkumar

2018-02-01

Nonlinear wave propagation is studied in a dissipative, self-gravitating Bose-Einstein condensate, starting from the Gross-Pitaevskii equation. In the absence of an exact analytical result, approximate methods like the linear analysis and perturbative approach are applied. The linear dispersion relation puts a restriction on the permissible range of the dissipation parameter. The waves get damped due to dissipation. The small amplitude analysis using reductive perturbation technique is found to yield a modified form of KdV equation, which is solved both analytically as well as numerically. Interestingly, the analytical and numerical plots match excellently with each other, in the realm of weak dissipation.

Influence of two-stream relativistic electron beam parameters on the space-charge wave with broad frequency spectrum formation

NASA Astrophysics Data System (ADS)

Alexander, LYSENKO; Iurii, VOLK

2018-03-01

We developed a cubic non-linear theory describing the dynamics of the multiharmonic space-charge wave (SCW), with harmonics frequencies smaller than the two-stream instability critical frequency, with different relativistic electron beam (REB) parameters. The self-consistent differential equation system for multiharmonic SCW harmonic amplitudes was elaborated in a cubic non-linear approximation. This system considers plural three-wave parametric resonant interactions between wave harmonics and the two-stream instability effect. Different REB parameters such as the input angle with respect to focusing magnetic field, the average relativistic factor value, difference of partial relativistic factors, and plasma frequency of partial beams were investigated regarding their influence on the frequency spectrum width and multiharmonic SCW saturation levels. We suggested ways in which the multiharmonic SCW frequency spectrum widths could be increased in order to use them in multiharmonic two-stream superheterodyne free-electron lasers, with the main purpose of forming a powerful multiharmonic electromagnetic wave.