Molecular wave function and effective adiabatic potentials calculated by extended multi-configuration time-dependent Hartree-Fock method

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

Kato, Tsuyoshi; Ide, Yoshihiro; Yamanouchi, Kaoru

We first calculate the ground-state molecular wave function of 1D model H{sub 2} molecule by solving the coupled equations of motion formulated in the extended multi-configuration time-dependent Hartree-Fock (MCTDHF) method by the imaginary time propagation. From the comparisons with the results obtained by the Born-Huang (BH) expansion method as well as with the exact wave function, we observe that the memory size required in the extended MCTDHF method is about two orders of magnitude smaller than in the BH expansion method to achieve the same accuracy for the total energy. Second, in order to provide a theoretical means to understandmore » dynamical behavior of the wave function, we propose to define effective adiabatic potential functions and compare them with the conventional adiabatic electronic potentials, although the notion of the adiabatic potentials is not used in the extended MCTDHF approach. From the comparison, we conclude that by calculating the effective potentials we may be able to predict the energy differences among electronic states even for a time-dependent system, e.g., time-dependent excitation energies, which would be difficult to be estimated within the BH expansion approach.« less

Modification of 2-D Time-Domain Shallow Water Wave Equation using Asymptotic Expansion Method

NASA Astrophysics Data System (ADS)

Khairuman, Teuku; Nasruddin, MN; Tulus; Ramli, Marwan

2018-01-01

Generally, research on the tsunami wave propagation model can be conducted by using a linear model of shallow water theory, where a non-linear side on high order is ignored. In line with research on the investigation of the tsunami waves, the Boussinesq equation model underwent a change aimed to obtain an improved quality of the dispersion relation and non-linearity by increasing the order to be higher. To solve non-linear sides at high order is used a asymptotic expansion method. This method can be used to solve non linear partial differential equations. In the present work, we found that this method needs much computational time and memory with the increase of the number of elements.

Second-Order Perturbation Theory for Generalized Active Space Self-Consistent-Field Wave Functions.

PubMed

Ma, Dongxia; Li Manni, Giovanni; Olsen, Jeppe; Gagliardi, Laura

2016-07-12

A multireference second-order perturbation theory approach based on the generalized active space self-consistent-field (GASSCF) wave function is presented. Compared with the complete active space (CAS) and restricted active space (RAS) wave functions, GAS wave functions are more flexible and can employ larger active spaces and/or different truncations of the configuration interaction expansion. With GASSCF, one can explore chemical systems that are not affordable with either CASSCF or RASSCF. Perturbation theory to second order on top of GAS wave functions (GASPT2) has been implemented to recover the remaining electron correlation. The method has been benchmarked by computing the chromium dimer ground-state potential energy curve. These calculations show that GASPT2 gives results similar to CASPT2 even with a configuration interaction expansion much smaller than the corresponding CAS expansion.

Photonic band structures solved by a plane-wave-based transfer-matrix method.

PubMed

Li, Zhi-Yuan; Lin, Lan-Lan

2003-04-01

Transfer-matrix methods adopting a plane-wave basis have been routinely used to calculate the scattering of electromagnetic waves by general multilayer gratings and photonic crystal slabs. In this paper we show that this technique, when combined with Bloch's theorem, can be extended to solve the photonic band structure for 2D and 3D photonic crystal structures. Three different eigensolution schemes to solve the traditional band diagrams along high-symmetry lines in the first Brillouin zone of the crystal are discussed. Optimal rules for the Fourier expansion over the dielectric function and electromagnetic fields with discontinuities occurring at the boundary of different material domains have been employed to accelerate the convergence of numerical computation. Application of this method to an important class of 3D layer-by-layer photonic crystals reveals the superior convergency of this different approach over the conventional plane-wave expansion method.

Resonant frequency method for bearing ball inspection

DOEpatents

Khuri-Yakub, B. T.; Hsieh, Chung-Kao

1993-01-01

The present invention provides for an inspection system and method for detecting defects in test objects which includes means for generating expansion inducing energy focused upon the test object at a first location, such expansion being allowed to contract, thereby causing pressure wave within and on the surface of the test object. Such expansion inducing energy may be provided by, for example, a laser beam or ultrasonic energy. At a second location, the amplitudes and phases of the acoustic waves are detected and the resonant frequencies' quality factors are calculated and compared to predetermined quality factor data, such comparison providing information of whether the test object contains a defect. The inspection system and method also includes means for mounting the bearing ball for inspection.

Resonant frequency method for bearing ball inspection

DOEpatents

Khuri-Yakub, B.T.; Chungkao Hsieh.

1993-11-02

The present invention provides for an inspection system and method for detecting defects in test objects which includes means for generating expansion inducing energy focused upon the test object at a first location, such expansion being allowed to contract, thereby causing pressure wave within and on the surface of the test object. Such expansion inducing energy may be provided by, for example, a laser beam or ultrasonic energy. At a second location, the amplitudes and phases of the acoustic waves are detected and the resonant frequencies' quality factors are calculated and compared to predetermined quality factor data, such comparison providing information of whether the test object contains a defect. The inspection system and method also includes means for mounting the bearing ball for inspection. 5 figures.

Method and Apparatus for Determining Changes in Intracranial Pressure Utilizing Measurement of the Circumferential Expansion or Contraction of a Patient's Skull

NASA Technical Reports Server (NTRS)

Yos, William T. (Inventor); Cantrell, John H., Jr. (Inventor)

2004-01-01

A method and apparatus for measuring changes in intracranial pressure (ICP) utilizing the variation of the surface wave propagation parameters of the patient's skull to determine the change in ICP. In one embodiment, the method comprises the steps of transmitting an ultrasonic bulk compressional wave onto the surface of the skull at a predetermined angle with respect to the skull so as to produce a surface wave, receiving the surface wave at an angle with respect tn the skull which is substantially the same as the predetermined angle and at a location that is a predetermined distance from where the ultrasonic bulk compressional wave was transmitted upon the skull, determining the retardation or advancement in phase of the received surface wave with respect to a reference phase, and processing the determined retardation or advancement in phase to determine circumferential expansion or contraction of the skull and utilizing the determined circumferential change to determine the change in intracranial pressure.

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

Exact soliton of (2 + 1)-dimensional fractional Schrödinger equation

NASA Astrophysics Data System (ADS)

Rizvi, S. T. R.; Ali, K.; Bashir, S.; Younis, M.; Ashraf, R.; Ahmad, M. O.

2017-07-01

The nonlinear fractional Schrödinger equation is the basic equation of fractional quantum mechanics introduced by Nick Laskin in 2002. We apply three tools to solve this mathematical-physical model. First, we find the solitary wave solutions including the trigonometric traveling wave solutions, bell and kink shape solitons using the F-expansion and Improve F-expansion method. We also obtain the soliton solution, singular soliton solutions, rational function solution and elliptic integral function solutions, with the help of the extended trial equation method.

Modeling transversely isotropic, viscoelastic, incompressible tissue-like materials with application in ultrasound shear wave elastography

NASA Astrophysics Data System (ADS)

Qiang, Bo; Brigham, John C.; Aristizabal, Sara; Greenleaf, James F.; Zhang, Xiaoming; Urban, Matthew W.

2015-02-01

In this paper, we propose a method to model the shear wave propagation in transversely isotropic, viscoelastic and incompressible media. The targeted application is ultrasound-based shear wave elastography for viscoelasticity measurements in anisotropic tissues such as the kidney and skeletal muscles. The proposed model predicts that if the viscoelastic parameters both across and along fiber directions can be characterized as a Voigt material, then the spatial phase velocity at any angle is also governed by a Voigt material model. Further, with the aid of Taylor expansions, it is shown that the spatial group velocity at any angle is close to a Voigt type for weakly attenuative materials within a certain bandwidth. The model is implemented in a finite element code by a time domain explicit integration scheme and shear wave simulations are conducted. The results of the simulations are analyzed to extract the shear wave elasticity and viscosity for both the spatial phase and group velocities. The estimated values match well with theoretical predictions. The proposed theory is further verified by an ex vivo tissue experiment measured in a porcine skeletal muscle by an ultrasound shear wave elastography method. The applicability of the Taylor expansion to analyze the spatial velocities is also discussed. We demonstrate that the approximations from the Taylor expansions are subject to errors when the viscosities across or along the fiber directions are large or the maximum frequency considered is beyond the bandwidth defined by radii of convergence of the Taylor expansions.

The Effect of Area Variation on Wave Rotor Elements

NASA Technical Reports Server (NTRS)

Wilson, Jack

1997-01-01

The effect of varying the cross-sectional flow area of the passages of a wave rotor is examined by means of the method of characteristics. An idealized expansion wave, an idealized inlet port, and an idealized compression stage are considered. It is found that area variation does not have a very significant effect on the expansion wave, nor on the compression stage. For the expansion wave, increasing the passage area in the flow direction has the same effect as a diffuser, so that the flow emerges at a lower velocity than it would for the constant area case. This could be advantageous. The inlet is strongly affected by the area variation, as it changes the strength of the hammer shock wave, thereby changing the pressure behind it. In this case, reduction in the passage area in the flow direction leads to increased pressure. However, this result is dependent on the assumption that the inlet conditions remain constant with area variation. This may not be the case.

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.

Clinical scale rapid expansion of lymphocytes for adoptive cell transfer therapy in the WAVE® bioreactor

PubMed Central

2012-01-01

Background To simplify clinical scale lymphocyte expansions, we investigated the use of the WAVE®, a closed system bioreactor that utilizes active perfusion to generate high cell numbers in minimal volumes. Methods We have developed an optimized rapid expansion protocol for the WAVE bioreactor that produces clinically relevant numbers of cells for our adoptive cell transfer clinical protocols. Results TIL and genetically modified PBL were rapidly expanded to clinically relevant scales in both static bags and the WAVE bioreactor. Both bioreactors produced comparable numbers of cells; however the cultures generated in the WAVE bioreactor had a higher percentage of CD4+ cells and had a less activated phenotype. Conclusions The WAVE bioreactor simplifies the process of rapidly expanding tumor reactive lymphocytes under GMP conditions, and provides an alternate approach to cell generation for ACT protocols. PMID:22475724

Nonlocal symmetry and explicit solutions from the CRE method of the Boussinesq equation

NASA Astrophysics Data System (ADS)

Zhao, Zhonglong; Han, Bo

2018-04-01

In this paper, we analyze the integrability of the Boussinesq equation by using the truncated Painlevé expansion and the CRE method. Based on the truncated Painlevé expansion, the nonlocal symmetry and Bäcklund transformation of this equation are obtained. A prolonged system is introduced to localize the nonlocal symmetry to the local Lie point symmetry. It is proved that the Boussinesq equation is CRE solvable. The two-solitary-wave fusion solutions, single soliton solutions and soliton-cnoidal wave solutions are presented by means of the Bäcklund transformations.

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

Inversion of residual stress profiles from ultrasonic Rayleigh wave dispersion data

NASA Astrophysics Data System (ADS)

Mora, P.; Spies, M.

2018-05-01

We investigate theoretically and with synthetic data the performance of several inversion methods to infer a residual stress state from ultrasonic surface wave dispersion data. We show that this particular problem may reveal in relevant materials undesired behaviors for some methods that could be reliably applied to infer other properties. We focus on two methods, one based on a Taylor-expansion, and another one based on a piecewise linear expansion regularized by a singular value decomposition. We explain the instabilities of the Taylor-based method by highlighting singularities in the series of coefficients. At the same time, we show that the other method can successfully provide performances which only weakly depend on the material.

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.

Effects of nonuniform Mach-number entrance on scramjet nozzle flowfield and performance

NASA Astrophysics Data System (ADS)

Zhang, Pu; Xu, Jinglei; Quan, Zhibin; Mo, Jianwei

2016-12-01

Considering the non-uniformities of nozzle entrance influenced by the upstream, the effects of nonuniform Mach-number coupled with shock and expansion-wave on the flowfield and performances of single expansion ramp nozzle (SERN) are numerically studied using Reynolds-Averaged Navier-Stokes equations. The adopted Reynolds-averaged Navier-Stokes methodology is validated by comparing the numerical results with the cold experimental data, and the average method used in this paper is discussed. Uniform and nonuniform facility nozzles are designed to generate different Mach-number profile for the inlet of SERN, which is direct-connected with different facility nozzle, and the whole flowfield is simulated. Because of the coupling of shock and expansion-wave, flow direction of nonuniform SERN entrance is distorted. Compared with Mach contour of uniform case, the line is more curved for coupling shock-wave entrance (SWE) case, and flatter for the coupling expansion-wave entrance (EWE) case. Wall pressure distribution of SWE case appears rising region, whereas decreases like stairs of EWE case. The numerical results reveal that the coupled shock and expansion-wave play significant roles on nozzle performances. Compared with the SERN performances of uniform entrance case at the same work conditions, the thrust of nonuniform entrance cases reduces by 3-6%, pitch moment decreases by 2.5-7%. The negative lift presents an incremental trend with EWE while the situation is the opposite with SWE. These results confirm that considering the entrance flow parameter nonuniformities of a scramjet nozzle coupled with shock or expansion-wave from the upstream is necessary.

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.

Lamb wave scattering by a surface-breaking crack in a plate

NASA Technical Reports Server (NTRS)

Datta, S. K.; Al-Nassar, Y.; Shah, A. H.

1991-01-01

An NDE method based on finite-element representation and modal expansion has been developed for solving the scattering of Lamb waves in an elastic plate waveguide. This method is very powerful for handling discontinuities of arbitrary shape, weldments of different orientations, canted cracks, etc. The advantage of the method is that it can be used to study the scattering of Lamb waves in anisotropic elastic plates and in multilayered plates as well.

CTE method and interaction solutions for the Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Ren, Bo

2017-02-01

The consistent tanh expansion method is applied to the Kadomtsev-Petviashvili equation. The interaction solutions among one soliton and other types of solitary waves, such as multiple resonant soliton solutions and cnoidal waves, are explicitly given. Some special concrete interaction solutions are discussed both in analytical and graphical ways.

The generalized scattering coefficient method for plane wave scattering in layered structures

NASA Astrophysics Data System (ADS)

Liu, Yu; Li, Chao; Wang, Huai-Yu; Zhou, Yun-Song

2017-02-01

The generalized scattering coefficient (GSC) method is pedagogically derived and employed to study the scattering of plane waves in homogeneous and inhomogeneous layered structures. The numerical stabilities and accuracies of this method and other commonly used numerical methods are discussed and compared. For homogeneous layered structures, concise scattering formulas with clear physical interpretations and strong numerical stability are obtained by introducing the GSCs. For inhomogeneous layered structures, three numerical methods are employed: the staircase approximation method, the power series expansion method, and the differential equation based on the GSCs. We investigate the accuracies and convergence behaviors of these methods by comparing their predictions to the exact results. The conclusions are as follows. The staircase approximation method has a slow convergence in spite of its simple and intuitive implementation, and a fine stratification within the inhomogeneous layer is required for obtaining accurate results. The expansion method results are sensitive to the expansion order, and the treatment becomes very complicated for relatively complex configurations, which restricts its applicability. By contrast, the GSC-based differential equation possesses a simple implementation while providing fast and accurate results.

The compression and expansion waves of the forward and backward flows: an in-vitro arterial model.

PubMed

Feng, J; Khir, A W

2008-05-01

Although the propagation of arterial waves of forward flows has been studied before, that of backward flows has not been thoroughly investigated. The aim of this research is to investigate the propagation of the compression and expansion waves of backward flows in terms of wave speed and dissipation, in flexible tubes. The aim is also to compare the propagation of these waves with those of forward flows. A piston pump generated a flow waveform in the shape of approximately half-sinusoid, in flexible tubes (12 mm and 16 mm diameter). The pump produced flow in either the forward or the backward direction by moving the piston forward, in a 'pushing action' or backward, in a 'pulling action', using a graphite brushes d.c. motor. Pressure and flow were measured at intervals of 5 cm along each tube and wave speed was determined using the PU-loop method. The simultaneous measurements of diameter were also taken at the same position of the pressure and flow in the 16 mm tube. Wave intensity analysis was used to determine the magnitude of the pressure and velocity waveforms and wave intensity in the forward and backward directions. Under the same initial experimental conditions, wave speed was higher during the pulling action (backward flow) than during the pushing action (forward flow). The amplitudes of pressure and velocity in the pulling action were significantly higher than those in the pushing action. The tube diameter was approximately 20 per cent smaller in the pulling action than in the pushing action in the 16 mm tube. The compression and expansion waves resulting from the pushing and pulling actions dissipated exponentially along the travelling distance, and their dissipation was greater in the smaller than in the larger tubes. Local wave speed in flexible tubes is flow direction- and wave nature-dependent and is greater with expansion than with compression waves. Wave dissipation has an inverse relationship with the vessel diameter, and dissipation of the expansion wave of the pulling action was greater than that of the pushing action.

Exact Solutions for the Integrable Sixth-Order Drinfeld-Sokolov-Satsuma-Hirota System by the Analytical Methods.

PubMed

Manafian Heris, Jalil; Lakestani, Mehrdad

2014-01-01

We establish exact solutions including periodic wave and solitary wave solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota system. We employ this system by using a generalized (G'/G)-expansion and the generalized tanh-coth methods. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that these methods, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.

Acoustic Interaction Forces and Torques Acting on Suspended Spheres in an Ideal Fluid.

PubMed

Lopes, J Henrique; Azarpeyvand, Mahdi; Silva, Glauber T

2016-01-01

In this paper, the acoustic interaction forces and torques exerted by an arbitrary time-harmonic wave on a set of N objects suspended in an inviscid fluid are theoretically analyzed. We utilize the partial-wave expansion method with translational addition theorem and re-expansion of multipole series to solve the related multiple scattering problem. We show that the acoustic interaction force and torque can be obtained using the farfield radiation force and torque formulas. To exemplify the method, we calculate the interaction forces exerted by an external traveling and standing plane wave on an arrangement of two and three olive-oil droplets in water. The droplets' radii are comparable to the wavelength (i.e., Mie scattering regime). The results show that the acoustic interaction forces present an oscillatory spatial distribution which follows the pattern formed by interference between the external and rescattered waves. In addition, acoustic interaction torques arise on the absorbing droplets whenever a nonsymmetric wavefront is formed by the external and rescattered waves' interference.

A class of traveling wave solutions for space-time fractional biological population model in mathematical physics

NASA Astrophysics Data System (ADS)

Akram, Ghazala; Batool, Fiza

2017-10-01

The (G'/G)-expansion method is utilized for a reliable treatment of space-time fractional biological population model. The method has been applied in the sense of the Jumarie's modified Riemann-Liouville derivative. Three classes of exact traveling wave solutions, hyperbolic, trigonometric and rational solutions of the associated equation are characterized with some free parameters. A generalized fractional complex transform is applied to convert the fractional equations to ordinary differential equations which subsequently resulted in number of exact solutions. It should be mentioned that the (G'/G)-expansion method is very effective and convenient for solving nonlinear partial differential equations of fractional order whose balancing number is a negative integer.

Nonlocal Symmetries, Conservation Laws and Interaction Solutions of the Generalised Dispersive Modified Benjamin-Bona-Mahony Equation

NASA Astrophysics Data System (ADS)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Wang, Xiu-Bin; Zhang, Tian-Tian

2018-05-01

We consider the generalised dispersive modified Benjamin-Bona-Mahony equation, which describes an approximation status for long surface wave existed in the non-linear dispersive media. By employing the truncated Painlevé expansion method, we derive its non-local symmetry and Bäcklund transformation. The non-local symmetry is localised by a new variable, which provides the corresponding non-local symmetry group and similarity reductions. Moreover, a direct method can be provided to construct a kind of finite symmetry transformation via the classic Lie point symmetry of the normal prolonged system. Finally, we find that the equation is a consistent Riccati expansion solvable system. With the help of the Jacobi elliptic function, we get its interaction solutions between solitary waves and cnoidal periodic waves.

Self-force calculations with matched expansions and quasinormal mode sums

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

Casals, Marc; Dolan, Sam; Ottewill, Adrian C.

2009-06-15

Accurate modeling of gravitational wave emission by extreme-mass ratio inspirals is essential for their detection by the LISA mission. A leading perturbative approach involves the calculation of the self-force acting upon the smaller orbital body. In this work, we present the first application of the Poisson-Wiseman-Anderson method of 'matched expansions' to compute the self-force acting on a point particle moving in a curved spacetime. The method employs two expansions for the Green function, which are, respectively, valid in the 'quasilocal' and 'distant past' regimes, and which may be matched together within the normal neighborhood. We perform our calculation in amore » static region of the spherically symmetric Nariai spacetime (dS{sub 2}xS{sup 2}), in which scalar-field perturbations are governed by a radial equation with a Poeschl-Teller potential (frequently used as an approximation to the Schwarzschild radial potential) whose solutions are known in closed form. The key new ingredients in our study are (i) very high order quasilocal expansions and (ii) expansion of the distant past Green function in quasinormal modes. In combination, these tools enable a detailed study of the properties of the scalar-field Green function. We demonstrate that the Green function is singular whenever x and x{sup '} are connected by a null geodesic, and apply asymptotic methods to determine the structure of the Green function near the null wave front. We show that the singular part of the Green function undergoes a transition each time the null wave front passes through a caustic point, following a repeating fourfold sequence {delta}({sigma}), 1/{pi}{sigma}, -{delta}({sigma}), -1/{pi}{sigma}, etc., where {sigma} is Synge's world function. The matched-expansion method provides insight into the nonlocal properties of the self-force. We show that the self-force generated by the segment of the worldline lying outside the normal neighborhood is not negligible. We apply the matched-expansion method to compute the scalar self-force acting on a static particle on the Nariai spacetime, and validate against an alternative method, obtaining agreement to six decimal places. We conclude with a discussion of the implications for wave propagation and self-force calculations. On black hole spacetimes, any expansion of the Green function in quasinormal modes must be augmented by a branch-cut integral. Nevertheless, we expect the Green function in Schwarzschild spacetime to inherit certain key features, such as a fourfold singular structure manifesting itself through the asymptotic behavior of quasinormal modes. In this way, the Nariai spacetime provides a fertile testing ground for developing insight into the nonlocal part of the self-force on black hole spacetimes.« less

Variational treatment of electron-polyatomic-molecule scattering calculations using adaptive overset grids

NASA Astrophysics Data System (ADS)

Greenman, Loren; Lucchese, Robert R.; McCurdy, C. William

2017-11-01

The complex Kohn variational method for electron-polyatomic-molecule scattering is formulated using an overset-grid representation of the scattering wave function. The overset grid consists of a central grid and multiple dense atom-centered subgrids that allow the simultaneous spherical expansions of the wave function about multiple centers. Scattering boundary conditions are enforced by using a basis formed by the repeated application of the free-particle Green's function and potential Ĝ0+V ̂ on the overset grid in a Born-Arnoldi solution of the working equations. The theory is shown to be equivalent to a specific Padé approximant to the T matrix and has rapid convergence properties, in both the number of numerical basis functions employed and the number of partial waves employed in the spherical expansions. The method is demonstrated in calculations on methane and CF4 in the static-exchange approximation and compared in detail with calculations performed with the numerical Schwinger variational approach based on single-center expansions. An efficient procedure for operating with the free-particle Green's function and exchange operators (to which no approximation is made) is also described.

Multiple scattering and stop band characteristics of flexural waves on a thin plate with circular holes

NASA Astrophysics Data System (ADS)

Wang, Zuowei; Biwa, Shiro

2018-03-01

A numerical procedure is proposed for the multiple scattering analysis of flexural waves on a thin plate with circular holes based on the Kirchhoff plate theory. The numerical procedure utilizes the wave function expansion of the exciting as well as scattered fields, and the boundary conditions at the periphery of holes are incorporated as the relations between the expansion coefficients of exciting and scattered fields. A set of linear algebraic equations with respect to the wave expansion coefficients of the exciting field alone is established by the numerical collocation method. To demonstrate the applicability of the procedure, the stop band characteristics of flexural waves are analyzed for different arrangements and concentrations of circular holes on a steel plate. The energy transmission spectra of flexural waves are shown to capture the detailed features of the stop band formation of regular and random arrangements of holes. The increase of the concentration of holes is found to shift the dips of the energy transmission spectra toward higher frequencies as well as deepen them. The hexagonal hole arrangement can form a much broader stop band than the square hole arrangement for flexural wave transmission. It is also demonstrated that random arrangements of holes make the transmission spectrum more complicated.

A semi-analytical method for near-trapped mode and fictitious frequencies of multiple scattering by an array of elliptical cylinders in water waves

NASA Astrophysics Data System (ADS)

Chen, Jeng-Tzong; Lee, Jia-Wei

2013-09-01

In this paper, we focus on the water wave scattering by an array of four elliptical cylinders. The null-field boundary integral equation method (BIEM) is used in conjunction with degenerate kernels and eigenfunctions expansion. The closed-form fundamental solution is expressed in terms of the degenerate kernel containing the Mathieu and the modified Mathieu functions in the elliptical coordinates. Boundary densities are represented by using the eigenfunction expansion. To avoid using the addition theorem to translate the Mathieu functions, the present approach can solve the water wave problem containing multiple elliptical cylinders in a semi-analytical manner by introducing the adaptive observer system. Regarding water wave problems, the phenomena of numerical instability of fictitious frequencies may appear when the BIEM/boundary element method (BEM) is used. Besides, the near-trapped mode for an array of four identical elliptical cylinders is observed in a special layout. Both physical (near-trapped mode) and mathematical (fictitious frequency) resonances simultaneously appear in the present paper for a water wave problem by an array of four identical elliptical cylinders. Two regularization techniques, the combined Helmholtz interior integral equation formulation (CHIEF) method and the Burton and Miller approach, are adopted to alleviate the numerical resonance due to fictitious frequency.

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…

The fifth-order partial differential equation for the description of the α + β Fermi-Pasta-Ulam model

NASA Astrophysics Data System (ADS)

Kudryashov, Nikolay A.; Volkov, Alexandr K.

2017-01-01

We study a new nonlinear partial differential equation of the fifth order for the description of perturbations in the Fermi-Pasta-Ulam mass chain. This fifth-order equation is an expansion of the Gardner equation for the description of the Fermi-Pasta-Ulam model. We use the potential of interaction between neighbouring masses with both quadratic and cubic terms. The equation is derived using the continuous limit. Unlike the previous works, we take into account higher order terms in the Taylor series expansions. We investigate the equation using the Painlevé approach. We show that the equation does not pass the Painlevé test and can not be integrated by the inverse scattering transform. We use the logistic function method and the Laurent expansion method to find travelling wave solutions of the fifth-order equation. We use the pseudospectral method for the numerical simulation of wave processes, described by the equation.

Propagation of thickness shear waves in a periodically corrugated quartz crystal plate and its application exploration in acoustic wave filters.

PubMed

Li, Peng; Cheng, Li

2017-05-01

The propagation of thickness shear waves in a periodically corrugated quartz crystal plate is investigated in the present paper using a power series expansion technique. In the proposed simulation model, an equivalent continuity of shear stress moment is introduced as an approximation to handle sectional interfaces with abrupt thickness changes. The Bloch theory is applied to simulate the band structures for three different thickness variation patterns. It is shown that the power series expansion method exhibits good convergence and accuracy, in agreement with results by finite element method (FEM). A broad stop band can be obtained in the power transmission spectra owing to the trapped thickness shear modes excited by the thickness variation, whose physical mechanism is totally different from the well-known Bragg scattering effect and is insensitive to the structural periodicity. Based on the observed energy trapping phenomenon, an acoustic wave filter is proposed in a quartz plate with sectional decreasing thickness, which inhibits wave propagation in different regions. Copyright © 2017 Elsevier B.V. All rights reserved.

Explicit and exact nontraveling wave solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation

NASA Astrophysics Data System (ADS)

Yuan, Na

2018-04-01

With the aid of the symbolic computation, we present an improved ( G ‧ / G ) -expansion method, which can be applied to seek more types of exact solutions for certain nonlinear evolution equations. In illustration, we choose the (3 + 1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation to demonstrate the validity and advantages of the method. As a result, abundant explicit and exact nontraveling wave solutions are obtained including two solitary waves solutions, nontraveling wave solutions and dromion soliton solutions. Some particular localized excitations and the interactions between two solitary waves are researched. The method can be also applied to other nonlinear partial differential equations.

Influence of the nozzle angle on refrigeration performance of a gas wave refrigerator

NASA Astrophysics Data System (ADS)

Liu, P.; Zhu, Y.; Wang, H.; Zhu, C.; Zou, J.; Wu, J.; Hu, D.

2017-05-01

A gas wave refrigerator (GWR) is a novel refrigerating device that refrigerates a medium by shock waves and expansion waves generated by gas pressure energy. In a typical GWR, the injection energy losses between the nozzle and the expansion tube are essential factors which influence the refrigeration efficiency. In this study, numerical simulations are used to analyze the underlying mechanism of the injection energy losses. The results of simulations show that the vortex loss, mixing energy loss, and oblique shock wave reflection loss are the main factors contributing to the injection energy losses in the expansion tube. Furthermore, the jet angle of the gas is found to dominate the injection energy losses. Therefore, the optimum jet angle is theoretically calculated based on the velocity triangle method. The value of the optimum jet angle is found to be 4^{circ }, 8^{circ }, and 12^{circ } when the refrigeration efficiency is the first-order, second-order, and third-order maximum value over all working ranges of jet frequency, respectively. Finally, a series of experiments are conducted with the jet angle ranging from -4^{circ } to 12^{circ } at a constant expansion ratio. The results indicate the optimal jet angle obtained by the experiments is in good agreement with the calculated value. The isentropic refrigeration efficiency increased by about 4 % after the jet angle was optimized.

Convergent close-coupling approach to positron scattering on He+★

NASA Astrophysics Data System (ADS)

Rawlins, Charlie M.; Kadyrov, Alisher S.; Bray, Igor

2018-05-01

A close-coupling method is used to generate electron-loss and total scattering cross sections for the first three partial waves with both a single-centre and two-centre expansion of the scattering wave function for positron scattering on He +. The two expansions are consistent with each other above the ionisation threshold verifying newly-developed positronium-formation matrix elements. Below the positronium-formation threshold both the single- and two-centre results agree with the elastic-scattering cross sections generated from the phase shifts reported in previous calculations.

Denoising in digital speckle pattern interferometry using wave atoms.

PubMed

Federico, Alejandro; Kaufmann, Guillermo H

2007-05-15

We present an effective method for speckle noise removal in digital speckle pattern interferometry, which is based on a wave-atom thresholding technique. Wave atoms are a variant of 2D wavelet packets with a parabolic scaling relation and improve the sparse representation of fringe patterns when compared with traditional expansions. The performance of the denoising method is analyzed by using computer-simulated fringes, and the results are compared with those produced by wavelet and curvelet thresholding techniques. An application of the proposed method to reduce speckle noise in experimental data is also presented.

Travelling wave solutions and conservation laws for the Korteweg-de Vries-Bejamin-Bona-Mahony equation

NASA Astrophysics Data System (ADS)

Simbanefayi, Innocent; Khalique, Chaudry Masood

2018-03-01

In this work we study the Korteweg-de Vries-Benjamin-Bona-Mahony (KdV-BBM) equation, which describes the two-way propagation of waves. Using Lie symmetry method together with Jacobi elliptic function expansion and Kudryashov methods we construct its travelling wave solutions. Also, we derive conservation laws of the KdV-BBM equation using the variational derivative approach. In this method, we begin by computing second-order multipliers for the KdV-BBM equation followed by a derivation of the respective conservation laws for each multiplier.

A wideband fast multipole boundary element method for half-space/plane-symmetric acoustic wave problems

NASA Astrophysics Data System (ADS)

Zheng, Chang-Jun; Chen, Hai-Bo; Chen, Lei-Lei

2013-04-01

This paper presents a novel wideband fast multipole boundary element approach to 3D half-space/plane-symmetric acoustic wave problems. The half-space fundamental solution is employed in the boundary integral equations so that the tree structure required in the fast multipole algorithm is constructed for the boundary elements in the real domain only. Moreover, a set of symmetric relations between the multipole expansion coefficients of the real and image domains are derived, and the half-space fundamental solution is modified for the purpose of applying such relations to avoid calculating, translating and saving the multipole/local expansion coefficients of the image domain. The wideband adaptive multilevel fast multipole algorithm associated with the iterative solver GMRES is employed so that the present method is accurate and efficient for both lowand high-frequency acoustic wave problems. As for exterior acoustic problems, the Burton-Miller method is adopted to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method. Details on the implementation of the present method are described, and numerical examples are given to demonstrate its accuracy and efficiency.

A plane wave generation method by wave number domain point focusing.

PubMed

Chang, Ji-Ho; Choi, Jung-Woo; Kim, Yang-Hann

2010-11-01

A method for generation of a wave-field that is a plane wave is described. This method uses an array of loudspeakers phased so that the field in the wave-number domain is nearly concentrated at a point, this point being at the wave-number vector of the desired plane wave. The method described here for such a wave-number concentration makes use of an expansion in spherical harmonics, and requires a relatively small number of measurement points for a good approximate achievement of a plane wave. The measurement points are on a spherical surface surrounding the array of loudspeakers. The input signals for the individual loudspeakers can be derived without a matrix inversion or without explicit assumptions about the loudspeakers. The mathematical development involves spherical harmonics and three-dimensional Fourier transforms. Some numerical examples are given, with various assumptions concerning the nature of the loudspeakers, that support the premise that the method described in the present paper may be useful in applications.

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.

Soliton and quasi-periodic wave solutions for b-type Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Singh, Manjit; Gupta, R. K.

2017-11-01

In this paper, truncated Laurent expansion is used to obtain the bilinear equation of a nonlinear evolution equation. As an application of Hirota's method, multisoliton solutions are constructed from the bilinear equation. Extending the application of Hirota's method and employing multidimensional Riemann theta function, one and two-periodic wave solutions are also obtained in a straightforward manner. The asymptotic behavior of one and two-periodic wave solutions under small amplitude limits is presented, and their relations with soliton solutions are also demonstrated.

Generalized moments expansion applied to the two-dimensional S= 1 /2 Heisenberg model

NASA Astrophysics Data System (ADS)

Mancini, Jay D.; Murawski, Robert K.; Fessatidis, Vassilios; Bowen, Samuel P.

2005-12-01

In this work we derive a generalized moments expansion (GMX), to third order, of which the well-established connected moments expansion and the alternate moments expansion are shown to be special cases. We discuss the benefits of the GMX with respect to the avoidance of singularities which are known to plague such moments methods. We then apply the GMX estimates for the ground-state energy for the two-dimensional S=1/2 Heisenberg square lattice and compare these results to those of both spin-wave theory and the linked-cluster expansion.

Expansion shock waves in regularized shallow-water theory

NASA Astrophysics Data System (ADS)

El, Gennady A.; Hoefer, Mark A.; Shearer, Michael

2016-05-01

We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularized shallow-water equations that include the Benjamin-Bona-Mahony and Boussinesq equations. An expansion shock exhibits divergent characteristics, thereby contravening the classical Lax entropy condition. The persistence of the expansion shock in initial value problems is analysed and justified using matched asymptotic expansions and numerical simulations. The expansion shock's existence is traced to the presence of a non-local dispersive term in the governing equation. We establish the algebraic decay of the shock as it is gradually eroded by a simple wave on either side. More generally, we observe a robustness of the expansion shock in the presence of weak dissipation and in simulations of asymmetric initial conditions where a train of solitary waves is shed from one side of the shock.

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.

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).

Applicability of the polynomial chaos expansion method for personalization of a cardiovascular pulse wave propagation model.

PubMed

Huberts, W; Donders, W P; Delhaas, T; van de Vosse, F N

2014-12-01

Patient-specific modeling requires model personalization, which can be achieved in an efficient manner by parameter fixing and parameter prioritization. An efficient variance-based method is using generalized polynomial chaos expansion (gPCE), but it has not been applied in the context of model personalization, nor has it ever been compared with standard variance-based methods for models with many parameters. In this work, we apply the gPCE method to a previously reported pulse wave propagation model and compare the conclusions for model personalization with that of a reference analysis performed with Saltelli's efficient Monte Carlo method. We furthermore differentiate two approaches for obtaining the expansion coefficients: one based on spectral projection (gPCE-P) and one based on least squares regression (gPCE-R). It was found that in general the gPCE yields similar conclusions as the reference analysis but at much lower cost, as long as the polynomial metamodel does not contain unnecessary high order terms. Furthermore, the gPCE-R approach generally yielded better results than gPCE-P. The weak performance of the gPCE-P can be attributed to the assessment of the expansion coefficients using the Smolyak algorithm, which might be hampered by the high number of model parameters and/or by possible non-smoothness in the output space. Copyright © 2014 John Wiley & Sons, Ltd.

Interfacial wave theory for dendritic structure of a growing needle crystal. I - Local instability mechanism. II - Wave-emission mechanism at the turning point

NASA Technical Reports Server (NTRS)

Xu, Jian-Jun

1989-01-01

The complicated dendritic structure of a growing needle crystal is studied on the basis of global interfacial wave theory. The local dispersion relation for normal modes is derived in a paraboloidal coordinate system using the multiple-variable-expansion method. It is shown that the global solution in a dendrite growth process incorporates the morphological instability factor and the traveling wave factor.

Expansion shock waves in regularized shallow-water theory

PubMed Central

El, Gennady A.; Shearer, Michael

2016-01-01

We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularized shallow-water equations that include the Benjamin–Bona–Mahony and Boussinesq equations. An expansion shock exhibits divergent characteristics, thereby contravening the classical Lax entropy condition. The persistence of the expansion shock in initial value problems is analysed and justified using matched asymptotic expansions and numerical simulations. The expansion shock's existence is traced to the presence of a non-local dispersive term in the governing equation. We establish the algebraic decay of the shock as it is gradually eroded by a simple wave on either side. More generally, we observe a robustness of the expansion shock in the presence of weak dissipation and in simulations of asymmetric initial conditions where a train of solitary waves is shed from one side of the shock. PMID:27279780

Spherical-wave expansions of piston-radiator fields.

PubMed

Wittmann, R C; Yaghjian, A D

1991-09-01

Simple spherical-wave expansions of the continuous-wave fields of a circular piston radiator in a rigid baffle are derived. These expansions are valid throughout the illuminated half-space and are useful for efficient numerical computation in the near-field region. Multipole coefficients are given by closed-form expressions which can be evaluated recursively.

Separable Ernst-Shakin-Thaler expansions of local potentials

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

Bund, G.W.

The boundary condition Ernst-Shakin-Thaler method, introduced previously to generate separable expansions of local potentials of finite range, is applied to the study of the triplet s-wave Malfliet-Tjon potential. The effect of varying the radius where the boundary condition is applied on the T matrix is analyzed. Further, we compare the convergence of the n-d scattering cross sections in the quartet state below the breakup threshold for expansions corresponding to two different boundaries.

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

NASA Astrophysics Data System (ADS)

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

2013-03-01

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

Wake-shock interaction at a Mach number of 6

NASA Technical Reports Server (NTRS)

Walsh, M. J.

1978-01-01

Measurements of mean pitot pressure, static pressure, and total temperature were made in the two dimensional turbulent mixing region of a wake downstream of an interaction with a shock-expansion wave system. The results indicated that: (1) the shock increased the mixing, and (2) the expansion field that followed the shock decreased the turbulent mixing. The overall effect of the shock-expansion wave interaction was dependent on the orientation of the expansion wave with respect to the intersecting shock wave. These data could be used to validate nonequilibrium turbulence modeling and numerical solution of the time averaged Navier-Stokes equations.

Two dimensional fully nonlinear numerical wave tank based on the BEM

NASA Astrophysics Data System (ADS)

Sun, Zhe; Pang, Yongjie; Li, Hongwei

2012-12-01

The development of a two dimensional numerical wave tank (NWT) with a rocker or piston type wavemaker based on the high order boundary element method (BEM) and mixed Eulerian-Lagrangian (MEL) is examined. The cauchy principle value (CPV) integral is calculated by a special Gauss type quadrature and a change of variable. In addition the explicit truncated Taylor expansion formula is employed in the time-stepping process. A modified double nodes method is assumed to tackle the corner problem, as well as the damping zone technique is used to absorb the propagation of the free surface wave at the end of the tank. A variety of waves are generated by the NWT, for example; a monochromatic wave, solitary wave and irregular wave. The results confirm the NWT model is efficient and stable.

Symplectic semiclassical wave packet dynamics II: non-Gaussian states

NASA Astrophysics Data System (ADS)

Ohsawa, Tomoki

2018-05-01

We generalize our earlier work on the symplectic/Hamiltonian formulation of the dynamics of the Gaussian wave packet to non-Gaussian semiclassical wave packets. We find the symplectic forms and asymptotic expansions of the Hamiltonians associated with these semiclassical wave packets, and obtain Hamiltonian systems governing their dynamics. Numerical experiments demonstrate that the dynamics give a very good approximation to the short-time dynamics of the expectation values computed by a method based on Egorov’s theorem or the initial value representation.

Derivative expansion of wave function equivalent potentials

NASA Astrophysics Data System (ADS)

Sugiura, Takuya; Ishii, Noriyoshi; Oka, Makoto

2017-04-01

Properties of the wave function equivalent potentials introduced by the HAL QCD collaboration are studied in a nonrelativistic coupled-channel model. The derivative expansion is generalized, and then applied to the energy-independent and nonlocal potentials. The expansion coefficients are determined from analytic solutions to the Nambu-Bethe-Salpeter wave functions. The scattering phase shifts computed from these potentials are compared with the exact values to examine the convergence of the expansion. It is confirmed that the generalized derivative expansion converges in terms of the scattering phase shift rather than the functional structure of the non-local potentials. It is also found that the convergence can be improved by tuning either the choice of interpolating fields or expansion scale in the generalized derivative expansion.

Application of hyperspherical harmonics expansion method to the low-lying bound S-states of exotic two-muon three-body systems

NASA Astrophysics Data System (ADS)

Khan, Md. Abdul

2014-09-01

In this paper, energies of the low-lying bound S-states (L = 0) of exotic three-body systems, consisting a nuclear core of charge +Ze (Z being atomic number of the core) and two negatively charged valence muons, have been calculated by hyperspherical harmonics expansion method (HHEM). The three-body Schrödinger equation is solved assuming purely Coulomb interaction among the binary pairs of the three-body systems XZ+μ-μ- for Z = 1 to 54. Convergence pattern of the energies have been checked with respect to the increasing number of partial waves Λmax. For available computer facilities, calculations are feasible up to Λmax = 28 partial waves, however, calculation for still higher partial waves have been achieved through an appropriate extrapolation scheme. The dependence of bound state energies has been checked against increasing nuclear charge Z and finally, the calculated energies have been compared with the ones of the literature.

Mode Identification of High-Amplitude Pressure Waves in Liquid Rocket Engines

NASA Astrophysics Data System (ADS)

EBRAHIMI, R.; MAZAHERI, K.; GHAFOURIAN, A.

2000-01-01

Identification of existing instability modes from experimental pressure measurements of rocket engines is difficult, specially when steep waves are present. Actual pressure waves are often non-linear and include steep shocks followed by gradual expansions. It is generally believed that interaction of these non-linear waves is difficult to analyze. A method of mode identification is introduced. After presumption of constituent modes, they are superposed by using a standard finite difference scheme for solution of the classical wave equation. Waves are numerically produced at each end of the combustion tube with different wavelengths, amplitudes, and phases with respect to each other. Pressure amplitude histories and phase diagrams along the tube are computed. To determine the validity of the presented method for steep non-linear waves, the Euler equations are numerically solved for non-linear waves, and negligible interactions between these waves are observed. To show the applicability of this method, other's experimental results in which modes were identified are used. Results indicate that this simple method can be used in analyzing complicated pressure signal measurements.

Finite-amplitude, pulsed, ultrasonic beams

NASA Astrophysics Data System (ADS)

Coulouvrat, François; Frøysa, Kjell-Eivind

An analytical, approximate solution of the inviscid KZK equation for a nonlinear pulsed sound beam radiated by an acoustic source with a Gaussian velocity distribution, is obtained by means of the renormalization method. This method involves two steps. First, the transient, weakly nonlinear field is computed. However, because of cumulative nonlinear effects, that expansion is non-uniform and breaks down at some distance away from the source. So, in order to extend its validity, it is re-written in a new frame of co-ordinates, better suited to following the nonlinear distorsion of the wave profile. Basically, the nonlinear coordinate transform introduces additional terms in the expansion, which are chosen so as to counterbalance the non-uniform ones. Special care is devoted to the treatment of shock waves. Finally, comparisons with the results of a finite-difference scheme turn out favorable, and show the efficiency of the method for a rather large range of parameters.

Seismic tomography of northeastern Tibetan Plateau from body wave arrival times and surface wave dispersion data

NASA Astrophysics Data System (ADS)

Fang, H.; Yao, H.; Zhang, H.

2017-12-01

Reliable crustal and upper mantle structure is important to understand expansion of material from the Tibetan plateau to its northeastern margin. Previous studies have used either ambient noise tomography or body wave traveltime tomography to obtain the crustal velocity models in northeastern Tibetan Plateau. However, clear differences appear in these models obtained using different datasets. Here we propose to jointly invert local and teleseismic body wave arrival times and surface wave dispersion data from ambient noise cross correlation to obtain a unified P and S wavespeed model of the crust and upper mantle in NE Tibetan Plateau. Following Fang et al. (2016), we adopt the direct inversion strategy for surface wave data (Fang et al., 2015), which eliminates the need to construct the phase/group velocity maps and allows the straightforward incorporation of surface wave dispersion data into the body wave inversion framework. For body wave data including both local and teleseismic arrival times, we use the fast marching method (Rawlinson et al., 2004) in order to trace multiple seismic phases simultaneously. The joint inversion method takes advantage of the complementary strengths of different data types, with local body wave data constraining more on the P than S wavespeed in the crust, surface wave data most sensitive to S wavespeed in the crust and upper mantle, teleseismic body wave data resolving the upper mantle structure. A series of synthetic tests will be used to show the robustness and superiority of the joint inversion method. Besides, the inverted model will be validated by waveform simulation and comparison with other studies, like receiver function imaging. The resultant P and S wavespeed models, as well as the derived Vp/Vs model, will be essential to understand the regional tectonics of the northeastern Tibetan Plateau, and to address the related geodynamic questions of the Tibetan Plateau formation and expansion.

Compact terahertz wave polarization beam splitter using photonic crystal.

PubMed

Mo, Guo-Qiang; Li, Jiu-Sheng

2016-09-01

Electromagnetic polarization conveys valuable information for signal processing. Manipulation of a terahertz wave polarization state exhibits tremendous potential in developing applications of terahertz science and technology. We propose an approach to efficiently split transverse-electric and transverse-magnetic polarized terahertz waves into different propagation directions over the frequency range from 0.9998 to 1.0007 THz. Both the plane wave expansion method and the finite-difference time-domain method are used to calculate and analyze the transmission characteristics of the proposed device. The present device is very compact and the total size is 1.02  mm×0.99  mm. This polarization beam splitter performance indicates that the structure has a potential application for forthcoming terahertz-wave integrated circuit fields.

Lamb waves in phononic crystal slabs with square or rectangular symmetries

NASA Astrophysics Data System (ADS)

Brunet, Thomas; Vasseur, Jérôme; Bonello, Bernard; Djafari-Rouhani, Bahram; Hladky-Hennion, Anne-Christine

2008-08-01

We report on both numerical and experimental results showing the occurrence of band gaps for Lamb waves propagating in phononic crystal plates. The structures are made of centered rectangular and square arrays of holes drilled in a silicon plate. A supercell plane wave expansion method is used to calculate the band structures and to predict the position and the magnitude of the gaps. The band structures of phononic crystal slabs are then measured using a laser ultrasonic technique. Lamb waves in the megahertz range and with wave vectors ranging over more than the first two reduced Brillouin zones are investigated.

Auxiliary-field-based trial wave functions in quantum Monte Carlo calculations

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

Chang, Chia -Chen; Rubenstein, Brenda M.; Morales, Miguel A.

2016-12-19

Quantum Monte Carlo (QMC) algorithms have long relied on Jastrow factors to incorporate dynamic correlation into trial wave functions. While Jastrow-type wave functions have been widely employed in real-space algorithms, they have seen limited use in second-quantized QMC methods, particularly in projection methods that involve a stochastic evolution of the wave function in imaginary time. Here we propose a scheme for generating Jastrow-type correlated trial wave functions for auxiliary-field QMC methods. The method is based on decoupling the two-body Jastrow into one-body projectors coupled to auxiliary fields, which then operate on a single determinant to produce a multideterminant trial wavemore » function. We demonstrate that intelligent sampling of the most significant determinants in this expansion can produce compact trial wave functions that reduce errors in the calculated energies. Lastly, our technique may be readily generalized to accommodate a wide range of two-body Jastrow factors and applied to a variety of model and chemical systems.« less

An original method for characterizing internal waves

NASA Astrophysics Data System (ADS)

Casagrande, Gaëlle; Varnas, Alex Warn; Folégot, Thomas; Stéphan, Yann

This study consisted in the characterization of internal waves in the south of the Strait of Messina (Italy). The observational data consisted in thermistor string profiles from the Coastal Ocean Acoustic Changes at High frequencies (COACH06) sea trial. An empirical orthogonal function analysis is applied to the data. The first two spatial empirical modes represent over 99% of the variability, and their corresponding time-dependent expansion coefficients take higher absolute values during internal wave events. In order to check how the expansion coefficients vary during an internal wave event, their time derivative, called here changing rates, are computed. It shows that each wave of an internal wave train is characterized by a double oscillation of the changing rates. At the front of the wave, both changing rates increase in absolute value with opposite sign, and then decrease to become null at the maximum amplitude of the wave. At the rear of the wave, the changing rates describe another period, again with opposite sign. This double oscillation can be used as a detector of internal waves, but it can also give information on the width of the wave, by measuring the length of the oscillation, as this information may sometimes be hard to read straight out of the data. When plotting the changing rates one versus another, the resulting scatter diagram puts on a butterfly shape that illustrates well this behaviour.

Unconditionally stable WLP-FDTD method for the modeling of electromagnetic wave propagation in gyrotropic materials.

PubMed

Li, Zheng-Wei; Xi, Xiao-Li; Zhang, Jin-Sheng; Liu, Jiang-fan

2015-12-14

The unconditional stable finite-difference time-domain (FDTD) method based on field expansion with weighted Laguerre polynomials (WLPs) is applied to model electromagnetic wave propagation in gyrotropic materials. The conventional Yee cell is modified to have the tightly coupled current density components located at the same spatial position. The perfectly matched layer (PML) is formulated in a stretched-coordinate (SC) system with the complex-frequency-shifted (CFS) factor to achieve good absorption performance. Numerical examples are shown to validate the accuracy and efficiency of the proposed method.

Scattering of antiplane shear waves by a circular cylinder in a traction-free plate

PubMed

Wang; Ying; Li

2000-09-01

Following a well-established formula used by many researchers, the scattering of an anti-plane shear wave by an infinite elastic cylinder of arbitrary relative radius centered in a traction-free two-dimensional isotropic plate has been examined. The plate is divided into three regions by introducing two imaginary planes located symmetrically away from the surface of the cylinder and perpendicular to surfaces of the plate. The wave field is expanded into cylinder wave modes in the central bounded region containing the cylinder, while the fields in the other two outer regions are expanded into plate wave modes. A system of equations determining the expansion coefficients is obtained according to the traction-free boundary conditions on the plate walls and the stress and displacement continuity conditions across the imaginary planes. By taking an appropriate finite number of terms of the infinite expansion series and a few selected points on the two properly chosen virtual planes and the surfaces of the plate through convergence and precision tests, a matrix equation to numerically evaluate the expansion coefficients is found. The method of how to choose the locations of the imaginary planes and the terms of the expansion series as well as the points on each respective boundary is given in Sec. III in detail. Curves of the reflection and transmission coefficients against the relative radius of the cylinder in welded and slip or cracked interfacial conditions are shown. Analysis on the contrast variations of the reflection and transmission coefficients for a cylinder in bonded and debonded interfacial situations is made. The relative errors estimated by the deviation of the numerical results from the principle of the conservation of energy are found to be less than 2%.

Truncated Painlevé expansion: Tanh-traveling wave solutions and reduction of sine-Poisson equation to a quadrature for stationary and nonstationary three-dimensional collisionless cold plasma

NASA Astrophysics Data System (ADS)

Ibrahim, R. S.; El-Kalaawy, O. H.

2006-10-01

The relativistic nonlinear self-consistent equations for a collisionless cold plasma with stationary ions [R. S. Ibrahim, IMA J. Appl. Math. 68, 523 (2003)] are extended to 3 and 3+1 dimensions. The resulting system of equations is reduced to the sine-Poisson equation. The truncated Painlevé expansion and reduction of the partial differential equation to a quadrature problem (RQ method) are described and applied to obtain the traveling wave solutions of the sine-Poisson equation for stationary and nonstationary equations in 3 and 3+1 dimensions describing the charge-density equilibrium configuration model.

Comparative study of the expansion dynamics of laser-driven plasma and shock wave in in-air and underwater ablation regimes

NASA Astrophysics Data System (ADS)

Nguyen, Thao T. P.; Tanabe, Rie; Ito, Yoshiro

2018-03-01

We compared the expansion characteristics of the plasma plumes and shock waves generated in laser-induced shock process between the two ablation regimes: in air and under water. The observation was made from the initial moment when the laser pulse hit the target until 1.5 μs. The shock processes were driven by focusing a single laser pulse (1064 nm, FWHM = 13 ns) onto the surface of epoxy-resin blocks using a 40-mm focal length lens. The estimated laser intensity at the target plane is approximate to 9 ×109Wcm-2 . We used the fast-imaging technique to observe the expansion of the plasma plume and a custom-designed time-resolved photoelasticity imaging technique to observe the propagation of shock waves with the time resolution of nanoseconds. We found that at the same intensity of the laser beam, the plasma expansion during the laser pulse follows different mechanisms: the plasma plume that grows in air follows a radiation-wave model while a detonation-wave model can explain the expansion of the plasma plume induced in water. The ideal blast wave theory can be used to predict the decay of the shock wave in air but is not appropriate to describe the decay of the shock wave induced under water.

Analytical approximation and numerical simulations for periodic travelling water waves

NASA Astrophysics Data System (ADS)

Kalimeris, Konstantinos

2017-12-01

We present recent analytical and numerical results for two-dimensional periodic travelling water waves with constant vorticity. The analytical approach is based on novel asymptotic expansions. We obtain numerical results in two different ways: the first is based on the solution of a constrained optimization problem, and the second is realized as a numerical continuation algorithm. Both methods are applied on some examples of non-constant vorticity. This article is part of the theme issue 'Nonlinear water waves'.

A novel approach for solitary wave solutions of the generalized fractional Zakharov-Kuznetsov equation

NASA Astrophysics Data System (ADS)

Batool, Fiza; Akram, Ghazala

2018-01-01

In this article the solitary wave solutions of generalized fractional Zakharov-Kuznetsov (GZK) equation which appear in the electrical transmission line model are investigated. The (G'/G)-expansion method is used to obtain the solitary solutions of fractional GZK equation via local fractional derivative. Three classes of solutions, hyperbolic, trigonometric and rational wave solutions of the associated equation are characterized with some free parameters. The obtained solutions reveal that the proposed technique is effective and powerful.

Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.; Kumar, Dipankar; Chakrabarty, Anuz Kumar

2018-05-01

The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.

Instability of a planar expansion wave.

PubMed

Velikovich, A L; Zalesak, S T; Metzler, N; Wouchuk, J G

2005-10-01

An expansion wave is produced when an incident shock wave interacts with a surface separating a fluid from a vacuum. Such an interaction starts the feedout process that transfers perturbations from the rippled inner (rear) to the outer (front) surface of a target in inertial confinement fusion. Being essentially a standing sonic wave superimposed on a centered expansion wave, a rippled expansion wave in an ideal gas, like a rippled shock wave, typically produces decaying oscillations of all fluid variables. Its behavior, however, is different at large and small values of the adiabatic exponent gamma. At gamma > 3, the mass modulation amplitude delta(m) in a rippled expansion wave exhibits a power-law growth with time alpha(t)beta, where beta = (gamma - 3)/(gamma - 1). This is the only example of a hydrodynamic instability whose law of growth, dependent on the equation of state, is expressed in a closed analytical form. The growth is shown to be driven by a physical mechanism similar to that of a classical Richtmyer-Meshkov instability. In the opposite extreme gamma - 1 < 1, delta(m) exhibits oscillatory growth, approximately linear with time, until it reaches its peak value approximately (gamma - 1)(-1/2), and then starts to decrease. The mechanism driving the growth is the same as that of Vishniac's instability of a blast wave in a gas with low . Exact analytical expressions for the growth rates are derived for both cases and favorably compared to hydrodynamic simulation results.

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.

A convergent series expansion for hyperbolic systems of conservation laws

NASA Technical Reports Server (NTRS)

Harabetian, E.

1985-01-01

The discontinuities piecewise analytic initial value problem for a wide class of conservation laws is considered which includes the full three-dimensional Euler equations. The initial interaction at an arbitrary curved surface is resolved in time by a convergent series. Among other features the solution exhibits shock, contact, and expansion waves as well as sound waves propagating on characteristic surfaces. The expansion waves correspond to he one-dimensional rarefactions but have a more complicated structure. The sound waves are generated in place of zero strength shocks, and they are caused by mismatches in derivatives.

Propagation of elastic wave in nanoporous material with distributed cylindrical nanoholes

NASA Astrophysics Data System (ADS)

Qiang, FangWei; Wei, PeiJun; Liu, XiQiang

2013-08-01

The effective propagation constants of plane longitudinal and shear waves in nanoporous material with random distributed parallel cylindrical nanoholes are studied. The surface elastic theory is used to consider the surface stress effects and to derive the nontraditional boundary condition on the surface of nanoholes. The plane wave expansion method is used to obtain the scattering waves from the single nanohole. The multiple scattering effects are taken into consideration by summing the scattered waves from all scatterers and performing the configuration averaging of random distributed scatterers. The effective propagation constants of coherent waves along with the associated dynamic effective elastic modulus are numerically evaluated. The influences of surface stress are discussed based on the numerical results.

Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation.

PubMed

Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus

2014-01-01

Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.

Evaluation of dual flow thrust vectored nozzles with exhaust stream impingement. MS Thesis Final Technical Report, Oct. 1990 - Jul. 1991

NASA Technical Reports Server (NTRS)

Carpenter, Thomas W.

1991-01-01

The main objective of this project was to predict the expansion wave/oblique shock wave structure in an under-expanded jet expanding from a convergent nozzle. The shock structure was predicted by combining the calculated curvature of the free pressure boundary with principles and governing equations relating to oblique shock wave and expansion wave interaction. The procedure was then continued until the shock pattern repeated itself. A mathematical model was then formulated and written in FORTRAN to calculate the oblique shock/expansion wave structure within the jet. In order to study shock waves in expanding jets, Schlieren photography, a form of flow visualization, was employed. Thirty-six Schlieren photographs of jets from both a straight and 15 degree nozzle were taken. An iterative procedure was developed to calculate the shock structure within the jet and predict the non-dimensional values of Prandtl primary wavelength (w/rn), distance to Mach Disc (Ld) and Mach Disc radius (rd). These values were then compared to measurements taken from Schlieren photographs and experimental results. The results agreed closely to measurements from Schlieren photographs and previously obtained data. This method provides excellent results for pressure ratios below that at which a Mach Disc first forms. Calculated values of non-dimensional distance to the Mach Disc (Ld) agreed closely to values measured from Schlieren photographs and published data. The calculated values of non-dimensional Mach Disc radius (rd), however, deviated from published data by as much as 25 percent at certain pressure ratios.

Two dimensional cylindrical fast magnetoacoustic solitary waves in a dust plasma

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

Liu Haifeng; Wang Shiqing; Engineering and Technical College of Chengdu University of Technology, Leshan 614000

2011-04-15

The nonlinear fast magnetoacoustic solitary waves in a dust plasma with the combined effects of bounded cylindrical geometry and transverse perturbation are investigated in a new equation. In this regard, cylindrical Kadomtsev-Petviashvili (CKP) equation is derived using the small amplitude perturbation expansion method. Under a suitable coordinate transformation, the CKP equation can be solved analytically. It is shown that the dust cylindrical fast magnetoacoustic solitary waves can exist in the CKP equation. The present investigation may have relevance in the study of nonlinear electromagnetic soliton waves both in laboratory and astrophysical plasmas.

Sauter-Schwinger pair creation dynamically assisted by a plane wave

NASA Astrophysics Data System (ADS)

Torgrimsson, Greger; Schneider, Christian; Schützhold, Ralf

2018-05-01

We study electron-positron pair creation by a strong and constant electric field superimposed with a weaker transversal plane wave which is incident perpendicularly (or under some angle). Comparing the fully nonperturbative approach based on the world-line instanton method with a perturbative expansion into powers of the strength of the weaker plane wave, we find good agreement—provided that the latter is carried out to sufficiently high orders. As usual for the dynamically assisted Sauter-Schwinger effect, the additional plane wave induces an exponential enhancement of the pair-creation probability if the combined Keldysh parameter exceeds a certain threshold.

Numerical Study of Interaction of a Vortical Density Inhomogeneity with Shock and Expansion Waves

NASA Technical Reports Server (NTRS)

Povitsky, A.; Ofengeim, D.

1998-01-01

We studied the interaction of a vortical density inhomogeneity (VDI) with shock and expansion waves. We call the VDI the region of concentrated vorticity (vortex) with a density different from that of ambiance. Non-parallel directions of the density gradient normal to the VDI surface and the pressure gradient across a shock wave results in an additional vorticity. The roll-up of the initial round VDI towards a non-symmetrical shape is studied numerically. Numerical modeling of this interaction is performed by a 2-D Euler code. The use of an adaptive unstructured numerical grid makes it possible to obtain high accuracy and capture regions of induced vorticity with a moderate overall number of mesh points. For the validation of the code, the computational results are compared with available experimental results and good agreement is obtained. The interaction of the VDI with a propagating shock wave is studied for a range of initial and induced circulations and obtained flow patterns are presented. The splitting of the VDI develops into the formation of a non-symmetrical vortex pair and not in a set of vortices. A method for the analytical computation of an overall induced circulation Gamma(sub 1) as a result of the interaction of a moving VDI with a number of waves is proposed. Simplified, approximated, expressions for Gamma(sub 1) are derived and their accuracy is discussed. The splitting of the VDI passing through the Prandtl-Meyer expansion wave is studied numerically. The obtained VDI patterns are compared to those for the interaction of the VDI with a propagating shock wave for the same values of initial and induced circulations. These patterns have similar shapes for corresponding time moments.

The Formation and Early Evolution of a Coronal Mass Ejection and its Associated Shock Wave on 2014 January 8

NASA Astrophysics Data System (ADS)

Wan, Linfeng; Cheng, Xin; Shi, Tong; Su, Wei; Ding, M. D.

2016-08-01

In this paper, we study the formation and early evolution of a limb coronal mass ejection (CME) and its associated shock wave that occurred on 2014 January 8. The extreme ultraviolet (EUV) images provided by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory disclose that the CME first appears as a bubble-like structure. Subsequently, its expansion forms the CME and causes a quasi-circular EUV wave. Interestingly, both the CME and the wave front are clearly visible at all of the AIA EUV passbands. Through a detailed kinematical analysis, it is found that the expansion of the CME undergoes two phases: a first phase with a strong but transient lateral over-expansion followed by a second phase with a self-similar expansion. The temporal evolution of the expansion velocity coincides very well with the variation of the 25-50 keV hard X-ray flux of the associated flare, which indicates that magnetic reconnection most likely plays an important role in driving the expansion. Moreover, we find that, when the velocity of the CME reaches ˜600 km s-1, the EUV wave starts to evolve into a shock wave, which is evidenced by the appearance of a type II radio burst. The shock’s formation height is estimated to be ˜0.2 R sun, which is much lower than the height derived previously. Finally, we also study the thermal properties of the CME and the EUV wave. We find that the plasma in the CME leading front and the wave front has a temperature of ˜2 MK, while that in the CME core region and the flare region has a much higher temperature of ≥8 MK.

Research on the mechanics of underwater supersonic gas jets

NASA Astrophysics Data System (ADS)

Shi, Honghui; Wang, Boyi; Dai, Zhenqing

2010-03-01

An experimental research was carried out to study the fluid mechanics of underwater supersonic gas jets. High pressure air was injected into a water tank through converging-diverging nozzles (Laval nozzles). The jets were operated at different conditions of over-, full- and under-expansions. The jet sequences were visualized using a CCD camera. It was found that the injection of supersonic air jets into water is always accompanied by strong flow oscillation, which is related to the phenomenon of shock waves feedback in the gas phase. The shock wave feedback is different from the acoustic feedback when a supersonic gas jet discharges into open air, which causes screech tone. It is a process that the shock waves enclosed in the gas pocket induce a periodic pressure with large amplitude variation in the gas jet. Consequently, the periodic pressure causes the jet oscillation including the large amplitude expansion. Detailed pressure measurements were also conducted to verify the shock wave feedback phenomenon. Three kinds of measuring methods were used, i.e., pressure probe submerged in water, pressure measurements from the side and front walls of the nozzle devices respectively. The results measured by these methods are in a good agreement. They show that every oscillation of the jets causes a sudden increase of pressure and the average frequency of the shock wave feedback is about 5-10 Hz.

A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations

NASA Astrophysics Data System (ADS)

Bhrawy, A. H.; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.

2015-07-01

In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave equations with damping. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional integrals, described in the Riemann-Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations in the unknown expansion coefficients of the sought-for spectral approximations. The validity and effectiveness of the method are demonstrated by solving five numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions more easier.

Effect of viscosity on the wave propagation: Experimental determination of compression and expansion pulse wave velocity in fluid-fill elastic tube.

PubMed

Stojadinović, Bojana; Tenne, Tamar; Zikich, Dragoslav; Rajković, Nemanja; Milošević, Nebojša; Lazović, Biljana; Žikić, Dejan

2015-11-26

The velocity by which the disturbance travels through the medium is the wave velocity. Pulse wave velocity is one of the main parameters in hemodynamics. The study of wave propagation through the fluid-fill elastic tube is of great importance for the proper biophysical understanding of the nature of blood flow through of cardiovascular system. The effect of viscosity on the pulse wave velocity is generally ignored. In this paper we present the results of experimental measurements of pulse wave velocity (PWV) of compression and expansion waves in elastic tube. The solutions with different density and viscosity were used in the experiment. Biophysical model of the circulatory flow is designed to perform measurements. Experimental results show that the PWV of the expansion waves is higher than the compression waves during the same experimental conditions. It was found that the change in viscosity causes a change of PWV for both waves. We found a relationship between PWV, fluid density and viscosity. Copyright © 2015 Elsevier Ltd. All rights reserved.

Oblique wave trapping by vertical permeable membrane barriers located near a wall

NASA Astrophysics Data System (ADS)

Koley, Santanu; Sahoo, Trilochan

2017-12-01

The effectiveness of a vertical partial flexible porous membrane wave barrier located near a rigid vertical impermeable seawall for trapping obliquely incident surface gravity waves are analyzed in water of uniform depth under the assumption of linear water wave theory and small amplitude membrane barrier response. From the general formulation of the submerged membrane barrier, results for bottom-standing and surface-piercing barriers are computed and analyzed in special cases. Using the eigenfunction expansion method, the boundary-value problems are converted into series relations and then the required unknowns are obtained using the least squares approximation method. Various physical quantities of interests like reflection coefficient, wave energy dissipation, wave forces acting on the membrane barrier and the seawall are computed and analyzed for different values of the wave and structural parameters. The study will be useful in the design of the membrane wave barrier for the creation of tranquility zone in the lee side of the barrier to protect the seawall.

Microscopic Lagrangian description of warm plasmas. I - Linear wave propagation. II - Nonlinear wave interactions

NASA Technical Reports Server (NTRS)

Kim, H.; Crawford, F. W.

1977-01-01

It is pointed out that the conventional iterative analysis of nonlinear plasma wave phenomena, which involves a direct use of Maxwell's equations and the equations describing the particle dynamics, leads to formidable theoretical and algebraic complexities, especially for warm plasmas. As an effective alternative, the Lagrangian method may be applied. It is shown how this method may be used in the microscopic description of small-signal wave propagation and in the study of nonlinear wave interactions. The linear theory is developed for an infinite, homogeneous, collisionless, warm magnetoplasma. A summary is presented of a perturbation expansion scheme described by Galloway and Kim (1971), and Lagrangians to third order in perturbation are considered. Attention is given to the averaged-Lagrangian density, the action-transfer and coupled-mode equations, and the general solution of the coupled-mode equations.

Compact four-channel terahertz demultiplexer based on directional coupling photonic crystal

NASA Astrophysics Data System (ADS)

Jiu-Sheng, Li; Han, Liu; Le, Zhang

2015-09-01

Electromagnetic polarization conveys valuable information for signal processing. Manipulation of terahertz wavelength demultiplexer exhibits tremendous potential in developing application of terahertz science and technology. We propose an approach to separate efficiently four frequencies terahertz waves based on three cascaded directional coupling two-dimensional photonic crystal waveguides. Both plane wave expansion method and finite-difference time-domain method are used to calculate and analyze the characteristics of the proposed device. The simulation results show that the designed terahertz wavelength demultiplexer can split four different wavelengths of terahertz wave into different propagation directions with high transmittance and low crosstalk. The present device is very compact and the total size is 6.8×10.6 mm2. This enables the terahertz wavelength demultiplexer to be used in terahertz wave system and terahertz wave integrated circuit fields.

Exhaust Nozzle Plume Effects on Sonic Boom Test Results for Isolated Nozzles

NASA Technical Reports Server (NTRS)

Castner, Raymond S.

2011-01-01

Reducing or eliminating the operational restrictions of supersonic aircraft over populated areas has led to extensive research at NASA. Restrictions were due to the disturbance of the sonic boom, caused by the coalescence of shock waves formed off the aircraft. Recent work has been performed to reduce the magnitude of the sonic boom N-wave generated by airplane components with focus on shock waves caused by the exhaust nozzle plume. Previous Computational Fluid Dynamics (CFD) analysis showed how the shock wave formed at the nozzle lip interacts with the nozzle boat-tail expansion wave. An experiment was conducted in the 1- by 1-ft Supersonic Wind Tunnel at the NASA Glenn Research Center to validate the computational study. Results demonstrated how the nozzle lip shock moved with increasing nozzle pressure ratio (NPR) and reduced the nozzle boat-tail expansion, causing a favorable change in the observed pressure signature. Experimental results were presented for comparison to the CFD results. The strong nozzle lip shock at high values of NPR intersected the nozzle boat-tail expansion and suppressed the expansion wave. Based on these results, it may be feasible to reduce the boat-tail expansion for a future supersonic aircraft with under-expanded nozzle exhaust flow by modifying nozzle pressure or nozzle divergent section geometry.

Optical soliton solutions for the higher-order dispersive cubic-quintic nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

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

2017-12-01

In this paper, we analyze new optical soliton solutions to the higher-order dispersive cubic-quintic nonlinear Schrödinger equation (NLSE) using three integration schemes. The schemes used in this paper are modified tanh-coth (MTC), extended Jacobi elliptic function expansion (EJEF), and two variable (G‧ / G , 1 / G) -expansion methods. We obtain new solutions that to the best of our knowledge do not exist previously. The obtained solutions includes bright, dark, combined bright-dark, singular as well as periodic waves solitons. The obtained solutions may be used to explain and understand the physical nature of the wave spreads in the most dispersive optical medium. Some interesting figures for the physical interpretation of the obtained solutions are also presented.

Acoustic waves in shock tunnels and expansion tubes

NASA Technical Reports Server (NTRS)

Paull, A.; Stalker, R. J.

1992-01-01

It is shown that disturbances in shock and expansion tubes can be modelled as lateral acoustic waves. The ratio of sound speed across the driver-test gas interface is shown to govern the quantity of noise in the test gas. Frequency 'focusing' which is fundamental to centered unsteady expansions is discussed and displayed in centerline pitot pressure measurements.

Accurate double many-body expansion potential energy surface for the 2(1)A' state of N2O.

PubMed

Li, Jing; Varandas, António J C

2014-08-28

An accurate double many-body expansion potential energy surface is reported for the 2(1)A' state of N2O. The new double many-body expansion (DMBE) form has been fitted to a wealth of ab initio points that have been calculated at the multi-reference configuration interaction level using the full-valence-complete-active-space wave function as reference and the cc-pVQZ basis set, and subsequently corrected semiempirically via double many-body expansion-scaled external correlation method to extrapolate the calculated energies to the limit of a complete basis set and, most importantly, the limit of an infinite configuration interaction expansion. The topographical features of the novel potential energy surface are then examined in detail and compared with corresponding attributes of other potential functions available in the literature. Exploratory trajectories have also been run on this DMBE form with the quasiclassical trajectory method, with the thermal rate constant so determined at room temperature significantly enhancing agreement with experimental data.

Hydroelastic analysis of surface wave interaction with concentric porous and flexible cylinder systems

NASA Astrophysics Data System (ADS)

Mandal, S.; Datta, N.; Sahoo, T.

2013-10-01

The present study deals with the hydroelastic analysis of gravity wave interaction with concentric porous and flexible cylinder systems, in which the inner cylinder is rigid and the outer cylinder is porous and flexible. The problems are analyzed in finite water depth under the assumption of small amplitude water wave theory and structural response. The cylinder configurations in the present study are namely (a) surface-piercing truncated cylinders, (b) bottom-touching truncated cylinders and (c) complete submerged cylinders extended from free surface to bottom. As special cases of the concentric cylinder system, wave diffraction by (i) porous flexible cylinder and (ii) flexible floating cage with rigid bottom are analyzed. The scattering potentials are evaluated using Fourier-Bessel series expansion method and the least square approximation method. The convergence of the double series is tested numerically to determine the number of terms in the Fourier-Bessel series expansion. The effects of porosity and flexibility of the outer cylinder, in attenuating the hydrodynamic forces and dynamic overturning moments, are analyzed for various cylinder configurations and wave characteristics. A parametric study with respect to wave frequency, ratios of inner-to-outer cylinder radii, annular spacing between the two cylinders and porosities is done. In order to understand the flow distribution around the cylinders, contour plots are provided. The findings of the present study are likely to be of immense help in the design of various types of marine structures which can withstand the wave loads of varied nature in the marine environment. The theory can be easily extended to deal with a large class of problems associated with acoustic wave interaction with flexible porous structures.

Modeling guided wave excitation in plates with surface mounted piezoelectric elements: coupled physics and normal mode expansion

NASA Astrophysics Data System (ADS)

Ren, Baiyang; Lissenden, Cliff J.

2018-04-01

Guided waves have been extensively studied and widely used for structural health monitoring because of their large volumetric coverage and good sensitivity to defects. Effectively and preferentially exciting a desired wave mode having good sensitivity to a certain defect is of great practical importance. Piezoelectric discs and plates are the most common types of surface-mounted transducers for guided wave excitation and reception. Their geometry strongly influences the proportioning between excited modes as well as the total power of the excited modes. It is highly desirable to predominantly excite the selected mode while the total transduction power is maximized. In this work, a fully coupled multi-physics finite element analysis, which incorporates the driving circuit, the piezoelectric element and the wave guide, is combined with the normal mode expansion method to study both the mode tuning and total wave power. The excitation of circular crested waves in an aluminum plate with circular piezoelectric discs is numerically studied for different disc and adhesive thicknesses. Additionally, the excitation of plane waves in an aluminum plate, using a stripe piezoelectric element is studied both numerically and experimentally. It is difficult to achieve predominant single mode excitation as well as maximum power transmission simultaneously, especially for higher order modes. However, guidelines for designing the geometry of piezoelectric elements for optimal mode excitation are recommended.

Progressive wave expansions and open boundary problems

NASA Technical Reports Server (NTRS)

Hagstrom, T.; Hariharan, S. I.

1995-01-01

In this paper we construct progressive wave expansions and asymptotic boundary conditions for wave-like equations in exterior domains, including applications to electromagnetics, compressible flows and aero-acoustics. The development of the conditions will be discussed in two parts. The first part will include derivations of asymptotic conditions based on the well-known progressive wave expansions for the two-dimensional wave equations. A key feature in the derivations is that the resulting family of boundary conditions involves a single derivative in the direction normal to the open boundary. These conditions are easy to implement and an application in electromagnetics will be presented. The second part of the paper will discuss the theory for hyperbolic systems in two dimensions. Here, the focus will be to obtain the expansions in a general way and to use them to derive a class of boundary conditions that involve only time derivatives or time and tangential derivatives. Maxwell's equations and the compressible Euler equations are used as examples. Simulations with the linearized Euler equations are presented to validate the theory.

Phase-shift parametrization and extraction of asymptotic normalization constants from elastic-scattering data

NASA Astrophysics Data System (ADS)

Ramírez Suárez, O. L.; Sparenberg, J.-M.

2017-09-01

We introduce a simplified effective-range function for charged nuclei, related to the modified K matrix but differing from it in several respects. Negative-energy zeros of this function correspond to bound states. Positive-energy zeros correspond to resonances and "echo poles" appearing in elastic-scattering phase-shifts, while its poles correspond to multiple-of-π phase shifts. Padé expansions of this function allow one to parametrize phase shifts on large energy ranges and to calculate resonance and bound-state properties in a very simple way, independently of any potential model. The method is first tested on a d -wave 12C+α potential model. It is shown to lead to a correct estimate of the subthreshold-bound-state asymptotic normalization constant (ANC) starting from the elastic-scattering phase shifts only. Next, the 12C+α experimental p -wave and d -wave phase shifts are analyzed. For the d wave, the relatively large error bars on the phase shifts do not allow one to improve the ANC estimate with respect to existing methods. For the p wave, a value agreeing with the 12C(6Li,d )16O transfer-reaction measurement and with the recent remeasurement of the 16Nβ -delayed α decay is obtained, with improved accuracy. However, the method displays two difficulties: the results are sensitive to the Padé-expansion order and the simplest fits correspond to an imaginary ANC, i.e., to a negative-energy "echo pole," the physical meaning of which is still debatable.

Wave energy patterns of counterpulsation: a novel approach with wave intensity analysis.

PubMed

Lu, Pong-Jeu; Yang, Chi-Fu Jeffrey; Wu, Meng-Yu; Hung, Chun-Hao; Chan, Ming-Yao; Hsu, Tzu-Cheng

2011-11-01

In counterpulsation, diastolic augmentation increases coronary blood flow and systolic unloading reduces left ventricular afterload. We present a new approach with wave intensity analysis to revisit and explain counterpulsation principles. In an acute porcine model, a standard intra-aortic balloon pump was placed in descending aorta in 4 pigs. We measured pressure and velocity with probes in left anterior descending artery and aorta during and without intra-aortic balloon pump assistance. Wave intensities of aortic and left coronary waves were derived from pressure and flow measurements with synchronization correction. We identified predominating waves in counterpulsation. In the aorta, during diastolic augmentation, intra-aortic balloon inflation generated a backward compression wave, with a "pushing" effect toward the aortic root that translated to a forward compression wave into coronary circulation. During systolic unloading, intra-aortic balloon pump deflation generated a backward expansion wave that "sucked" blood from left coronary bed into the aorta. While this backward expansion wave translated to reduced left ventricular afterload, the "sucking" effect resulted in left coronary blood steal, as demonstrated by a forward expansion wave in left anterior descending coronary flow. The waves were sensitive to inflation and deflation timing, with just 25 ms delay from standard deflation timing leading to weaker forward expansion wave and less coronary regurgitation. Intra-aortic balloon pumps generate backward-traveling waves that predominantly drive aortic and coronary blood flow during counterpulsation. Wave intensity analysis of arterial circulations may provide a mechanism to explain diastolic augmentation and systolic unloading of intra-aortic balloon pump counterpulsation. Copyright © 2011 The American Association for Thoracic Surgery. Published by Mosby, Inc. All rights reserved.

Periodic wave, breather wave and travelling wave solutions of a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation in fluids or plasmas

NASA Astrophysics Data System (ADS)

Hu, Wen-Qiang; Gao, Yi-Tian; Jia, Shu-Liang; Huang, Qian-Min; Lan, Zhong-Zhou

2016-11-01

In this paper, a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation is investigated, which has been presented as a model for the shallow water wave in fluids or the electrostatic wave potential in plasmas. By virtue of the binary Bell polynomials, the bilinear form of this equation is obtained. With the aid of the bilinear form, N -soliton solutions are obtained by the Hirota method, periodic wave solutions are constructed via the Riemann theta function, and breather wave solutions are obtained according to the extended homoclinic test approach. Travelling waves are constructed by the polynomial expansion method as well. Then, the relations between soliton solutions and periodic wave solutions are strictly established, which implies the asymptotic behaviors of the periodic waves under a limited procedure. Furthermore, we obtain some new solutions of this equation by the standard extended homoclinic test approach. Finally, we give a generalized form of this equation, and find that similar analytical solutions can be obtained from the generalized equation with arbitrary coefficients.

Closed form solutions of two time fractional nonlinear wave equations

NASA Astrophysics Data System (ADS)

Akbar, M. Ali; Ali, Norhashidah Hj. Mohd.; Roy, Ripan

2018-06-01

In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G‧ / G) -expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics.

Cigar-shaped quarkonia under strong magnetic field

NASA Astrophysics Data System (ADS)

Suzuki, Kei; Yoshida, Tetsuya

2016-03-01

Heavy quarkonia in a homogeneous magnetic field are analyzed by using a potential model with constituent quarks. To obtain anisotropic wave functions and corresponding eigenvalues, the cylindrical Gaussian expansion method is applied, where the anisotropic wave functions are expanded by a Gaussian basis in the cylindrical coordinates. Deformation of the wave functions and the mass shifts of the S-wave heavy quarkonia (ηc, J /ψ , ηc(2 S ), ψ (2 S ) and bottomonia) are examined for the wide range of external magnetic field. The spatial structure of the wave functions changes drastically as adjacent energy levels cross each other. Possible observables in heavy-ion collision experiments and future lattice QCD simulations are also discussed.

Traveling wave and exact solutions for the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity

NASA Astrophysics Data System (ADS)

Akram, Ghazala; Mahak, Nadia

2018-06-01

The nonlinear Schrödinger equation (NLSE) with the aid of three order dispersion terms is investigated to find the exact solutions via the extended (G'/G2)-expansion method and the first integral method. Many exact traveling wave solutions, such as trigonometric, hyperbolic, rational, soliton and complex function solutions, are characterized with some free parameters of the problem studied. It is corroborated that the proposed techniques are manageable, straightforward and powerful tools to find the exact solutions of nonlinear partial differential equations (PDEs). Some figures are plotted to describe the propagation of traveling wave solutions expressed by the hyperbolic functions, trigonometric functions and rational functions.

Breathers, quasi-periodic and travelling waves for a generalized ?-dimensional Yu-Toda-Sasa-Fukayama equation in fluids

NASA Astrophysics Data System (ADS)

Hu, Wen-Qiang; Gao, Yi-Tian; Zhao, Chen; Jia, Shu-Liang; Lan, Zhong-Zhou

2017-07-01

Under investigation in this paper is a generalized ?-dimensional Yu-Toda-Sasa-Fukayama equation for the interfacial wave in a two-layer fluid or the elastic quasi-plane wave in a liquid lattice. By virtue of the binary Bell polynomials, bilinear form of this equation is obtained. With the help of the bilinear form, N-soliton solutions are obtained via the Hirota method, and a bilinear Bäcklund transformation is derived to verify the integrability. Homoclinic breather waves are obtained according to the homoclinic test approach, which is not only the space-periodic breather but also the time-periodic breather via the graphic analysis. Via the Riemann theta function, quasi one-periodic waves are constructed, which can be viewed as a superposition of the overlapping solitary waves, placed one period apart. Finally, soliton-like, periodical triangle-type, rational-type and solitary bell-type travelling waves are obtained by means of the polynomial expansion method.

Optimal variable-grid finite-difference modeling for porous media

NASA Astrophysics Data System (ADS)

Liu, Xinxin; Yin, Xingyao; Li, Haishan

2014-12-01

Numerical modeling of poroelastic waves by the finite-difference (FD) method is more expensive than that of acoustic or elastic waves. To improve the accuracy and computational efficiency of seismic modeling, variable-grid FD methods have been developed. In this paper, we derived optimal staggered-grid finite difference schemes with variable grid-spacing and time-step for seismic modeling in porous media. FD operators with small grid-spacing and time-step are adopted for low-velocity or small-scale geological bodies, while FD operators with big grid-spacing and time-step are adopted for high-velocity or large-scale regions. The dispersion relations of FD schemes were derived based on the plane wave theory, then the FD coefficients were obtained using the Taylor expansion. Dispersion analysis and modeling results demonstrated that the proposed method has higher accuracy with lower computational cost for poroelastic wave simulation in heterogeneous reservoirs.

Expansion Under Climate Change: The Genetic Consequences.

PubMed

Garnier, Jimmy; Lewis, Mark A

2016-11-01

Range expansion and range shifts are crucial population responses to climate change. Genetic consequences are not well understood but are clearly coupled to ecological dynamics that, in turn, are driven by shifting climate conditions. We model a population with a deterministic reaction-diffusion model coupled to a heterogeneous environment that develops in time due to climate change. We decompose the resulting travelling wave solution into neutral genetic components to analyse the spatio-temporal dynamics of its genetic structure. Our analysis shows that range expansions and range shifts under slow climate change preserve genetic diversity. This is because slow climate change creates range boundaries that promote spatial mixing of genetic components. Mathematically, the mixing leads to so-called pushed travelling wave solutions. This mixing phenomenon is not seen in spatially homogeneous environments, where range expansion reduces genetic diversity through gene surfing arising from pulled travelling wave solutions. However, the preservation of diversity is diminished when climate change occurs too quickly. Using diversity indices, we show that fast expansions and range shifts erode genetic diversity more than slow range expansions and range shifts. Our study provides analytical insight into the dynamics of travelling wave solutions in heterogeneous environments.

Numerical investigation of over expanded flow behavior in a single expansion ramp nozzle

NASA Astrophysics Data System (ADS)

Mousavi, Seyed Mahmood; Pourabidi, Reza; Goshtasbi-Rad, Ebrahim

2018-05-01

The single expansion ramp nozzle is severely over-expanded when the vehicle is at low speed, which hinders its ability to provide optimal configurations for combined cycle engines. The over-expansion leads to flow separation as a result of shock wave/boundary-layer interaction. Flow separation, and the presence of shocks themselves, result in a performance loss in the single expansion ramp nozzle, leading to reduced thrust and increased pressure losses. In the present work, the unsteady two dimensional compressible flow in an over expanded single expansion ramp nozzle has been investigated using finite volume code. To achieve this purpose, the Reynolds stress turbulence model and full multigrid initialization, in addition to the Smirnov's method for examining the errors accumulation, have been employed and the results are compared with available experimental data. The results show that the numerical code is capable of predicting the experimental data with high accuracy. Afterward, the effect of discontinuity jump in wall temperature as well as the length of straight ramp on flow behavior have been studied. It is concluded that variations in wall temperature and length of straight ramp change the shock wave boundary layer interaction, shock structure, shock strength as well as the distance between Lambda shocks.

Generalized framework for testing gravity with gravitational-wave propagation. II. Constraints on Horndeski theory

NASA Astrophysics Data System (ADS)

Arai, Shun; Nishizawa, Atsushi

2018-05-01

Gravitational waves (GW) are generally affected by modification of a gravity theory during propagation at cosmological distances. We numerically perform a quantitative analysis on Horndeski theory at the cosmological scale to constrain the Horndeski theory by GW observations in a model-independent way. We formulate a parametrization for a numerical simulation based on the Monte Carlo method and obtain the classification of the models that agrees with cosmic accelerating expansion within observational errors of the Hubble parameter. As a result, we find that a large group of the models in the Horndeski theory that mimic cosmic expansion of the Λ CDM model can be excluded from the simultaneous detection of a GW and its electromagnetic transient counterpart. Based on our result and the latest detection of GW170817 and GRB170817A, we conclude that the subclass of Horndeski theory including arbitrary functions G4 and G5 can hardly explain cosmic accelerating expansion without fine-tuning.

A new equation in two dimensional fast magnetoacoustic shock waves in electron-positron-ion plasmas

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

Masood, W.; Jehan, Nusrat; Mirza, Arshad M.

2010-03-15

Nonlinear properties of the two dimensional fast magnetoacoustic waves are studied in a three-component plasma comprising of electrons, positrons, and ions. In this regard, Kadomtsev-Petviashvili-Burger (KPB) equation is derived using the small amplitude perturbation expansion method. Under the condition that the electron and positron inertia are ignored, Burger-Kadomtsev-Petviashvili (Burger-KP) for a fast magnetoacoustic wave is derived for the first time, to the best of author's knowledge. The solutions of both KPB and Burger-KP equations are obtained using the tangent hyperbolic method. The effects of positron concentration, kinematic viscosity, and plasma beta are explored both for the KPB and the Burger-KPmore » shock waves and the differences between the two are highlighted. The present investigation may have relevance in the study of nonlinear electromagnetic shock waves both in laboratory and astrophysical plasmas.« less

Lie symmetry analysis, Bäcklund transformations, and exact solutions of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system

NASA Astrophysics Data System (ADS)

Zhao, Zhonglong; Han, Bo

2017-10-01

In this paper, the Lie symmetry analysis method is employed to investigate the Lie point symmetries and the one-parameter transformation groups of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system. By using Ibragimov's method, the optimal system of one-dimensional subalgebras of this system is constructed. Truncated Painlevé analysis is used for deriving the Bäcklund transformation. The method of constructing lump-type solutions of integrable equations by means of Bäcklund transformation is first presented. Meanwhile, the lump-type solutions of the (2 + 1)-dimensional Boiti-Leon-Pempinelli system are obtained. The lump-type wave is one kind of rogue wave. The fusion-type N-solitary wave solutions are also constructed. In addition, this system is integrable in terms of the consistent Riccati expansion method.

[Physical and mechanical properties of the thermosetting resin for crown and bridge cured by micro-wave heating].

PubMed

Kaneko, K

1989-09-01

A heating method using micro-waves was utilized to obtain strong thermosetting resin for crown and bridge. The physical and mechanical properties of the thermosetting resin were examined. The resin was cured in a shorter time by the micro-waves heating method than by the conventional heat curing method and the working time was reduced markedly. The base resins of the thermosetting resin for crown and bridge for the micro-waves heating method were 2 PA and diluent 3 G. A compounding volume of 30 wt% for diluent 3 G was considered good the results of compressive strength, bending strength and diametral tensile strength. Grams of 200-230 of the filler compounded to the base resins of 2 PA-3 G system provided optimal compressive strength, bending strength and diametral tensile strength. A filler gram of 230 provided optimal hardness and curing shrinkage rate, the coefficient of thermal expansion became smaller with the increase of the compounding volume of the filler. The trial thermosetting resin for crown and bridge formed by the micro-waves heating method was not inferior to the conventional resin by the heat curing method or the light curing method.

Monitoring Changes in Hepatic Venous Velocities Flow after a Fluid Challenge Can Identify Shock Patients Who Lack Fluid Responsiveness

PubMed Central

Du, Wei; Wang, Xiao-Ting; Long, Yun; Liu, Da-Wei

2017-01-01

Background: Evaluating the hemodynamic status and predicting fluid responsiveness are important in critical ultrasound assessment of shock patients. Transthoracic echocardiography with noninvasive diagnostic parameters allows the assessment of volume responsiveness. This study aimed to assess the hemodynamic changes in the liver and systemic hemodynamic changes during fluid challenge and during passive leg raising (PLR) by measuring hepatic venous flow (HVF) velocity. Methods: This is an open-label study in a tertiary teaching hospital. Shock patients with hypoperfusion who required fluid challenge were selected for the study. Patients <18 years old and those with contraindications to PLR were excluded from the study. Baseline values were measured, PLR tests were performed, and 500 ml of saline was infused over 30 min. Parameters associated with cardiac output (CO) in the left ventricular outflow tract were measured using the Doppler method. In addition, HVF velocity and right ventricular function parameters were determined. Results: Middle hepatic venous (MHV) S-wave velocity was positively correlated in all patients with CO at baseline (r = 0.706, P < 0.01) and after volume expansion (r = 0.524, P = 0.003). CO was also significantly correlated with MHV S-wave velocity in responders (r = 0.608, P < 0.01). During PLR, however, hepatic venous S-wave velocity did not correlate with CO. For the parameter ΔMHV D (increase in change in MHV D-wave velocity after volume expansion), defined as (MHV DafterVE − MHV DBaseline)/MHV DBaseline × 100%, >21% indicated no fluid responsiveness, with a sensitivity of 100%, a specificity of 71.2%, and an area under the receiver operating characteristic curve of 0.918. Conclusions: During fluid expansion, hepatic venous S-wave velocity can be used to monitor CO, whether or not it is increasing. ΔMHV D ≥21% indicated a lack of fluid responsiveness, thus helping to decide when to stop infusions. PMID:28485321

Intrinsic acoustical cross sections in the multiple scattering by a pair of rigid cylindrical particles in 2D

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2017-08-01

The multiple scattering effects occurring between two scatterers are described based upon the multipole expansion formalism as well as the addition theorem of cylindrical wave functions. An original approach is presented in which an effective incident acoustic field on a particular object, which includes both the primary and re-scattered waves from the other particle is determined first, and then used with the scattered field to derive closed-form analytical expressions for the inherent (i.e. intrinsic) cross-sections based on the far-field scattering. This method does not introduce any approximation in the calculation of the intrinsic cross-sections since the procedure is reduced to the one-body problem. The mathematical expressions for the intrinsic cross-sections are formulated in partial-wave series expansions (PWSEs) in cylindrical coordinates involving the angle of incidence, the addition theorem for the cylindrical wave functions, and the expansion coefficients of the scatterers. Numerical examples illustrate the analysis for two rigid circular cylindrical cross-sections with different radii immersed in a non-viscous fluid. Computations for the dimensionless extrinsic and intrinsic extinction cross-section factors are evaluated with particular emphasis on varying the angle of incidence, the interparticle distance, as well as the sizes of the particles. A symmetric behavior is observed for the dimensionless extrinsic extinction cross-section, while asymmetry arises for the intrinsic extinction cross-section of each particle with respect to the angle of incidence. The present analysis provides a complete analytical and computational method for the prediction of the intrinsic (local) scattering, absorption and extinction cross-sections in the multiple acoustic scatterings of plane progressive waves of arbitrary incidence by a pair of scatterers. The results and computational analyses can be used as a priori information for future applications to guide the direct or inverse characterization of multiple scattering systems in acoustically-engineered metamaterials, cloaking devices, particle dynamics, levitation, manipulation and handling, and other areas.

Interaction of grid generated turbulence with expansion waves

NASA Astrophysics Data System (ADS)

Xanthos, Savvas Steliou

2004-11-01

The interaction of traveling expansion waves with grid-generated turbulence was investigated in a large-scale shock tube research facility. The incident shock and the induced flow behind it passed through a rectangular grid, which generated a nearly homogeneous and nearly isotropic turbulent flow. As the shock wave exited the open end of the shock tube, a system of expansion waves was generated which traveled upstream and interacted with the grid-generated turbulence. The Mach number of the incoming flows investigated was about 0.3 hence interactions are considered as interactions with an almost incompressible flow. Mild interactions with expansion waves, which generated expansion ratios of the order of 1.8, were achieved in the present investigations. In that respect the compressibility effects started to become important during the interaction. A custom designed vorticity probe was used to measure for the first time the rate-of-strain, the rate-of-rotation and the velocity-gradient tensors in several of the present flows. Custom made x-hotwire probes were initially used to measure the flow quantities simultaneously at different locations inside the flow field. Although the strength of the generated expansion waves was mild, S = 6U6x EW = 50 to 100 s-1, the effect on damping fluctuations of turbulence was clear. Vorticity fluctuations were reduced dramatically more than velocity or pressure fluctuations. Attenuation of longitudinal velocity fluctuations has been observed in all experiments. It appears that the attenuation increases in interactions with higher Reynolds number. The data of velocity fluctuations in the lateral directions show no consistent behavior change or some minor attenuation through the interaction. The present results clearly show that in most of the cases, attenuation occurs at large xM distances where length scales of the incoming flow are high and turbulence intensities are low. Thus large in size eddies with low velocity fluctuations are affected the most by the interaction with the expansion waves. Spectral analysis indicated that spectral energy is shifted after the interaction to lower wave numbers suggesting that the typical length scales of turbulence are increased after the interaction.

THE FORMATION AND EARLY EVOLUTION OF A CORONAL MASS EJECTION AND ITS ASSOCIATED SHOCK WAVE ON 2014 JANUARY 8

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

Wan Linfeng; Cheng, Xin; Shi, Tong

2016-08-01

In this paper, we study the formation and early evolution of a limb coronal mass ejection (CME) and its associated shock wave that occurred on 2014 January 8. The extreme ultraviolet (EUV) images provided by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory disclose that the CME first appears as a bubble-like structure. Subsequently, its expansion forms the CME and causes a quasi-circular EUV wave. Interestingly, both the CME and the wave front are clearly visible at all of the AIA EUV passbands. Through a detailed kinematical analysis, it is found that the expansion of the CMEmore » undergoes two phases: a first phase with a strong but transient lateral over-expansion followed by a second phase with a self-similar expansion. The temporal evolution of the expansion velocity coincides very well with the variation of the 25–50 keV hard X-ray flux of the associated flare, which indicates that magnetic reconnection most likely plays an important role in driving the expansion. Moreover, we find that, when the velocity of the CME reaches ∼600 km s{sup −1}, the EUV wave starts to evolve into a shock wave, which is evidenced by the appearance of a type II radio burst. The shock’s formation height is estimated to be ∼0.2 R {sub sun}, which is much lower than the height derived previously. Finally, we also study the thermal properties of the CME and the EUV wave. We find that the plasma in the CME leading front and the wave front has a temperature of ∼2 MK, while that in the CME core region and the flare region has a much higher temperature of ≥8 MK.« less

Teaching Graphical Simulations of Fourier Series Expansion of Some Periodic Waves Using Spreadsheets

ERIC Educational Resources Information Center

Singh, Iqbal; Kaur, Bikramjeet

2018-01-01

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,…

Solution of Linearized Drift Kinetic Equations in Neoclassical Transport Theory by the Method of Matched Asymptotic Expansions

NASA Astrophysics Data System (ADS)

Wong, S. K.; Chan, V. S.; Hinton, F. L.

2001-10-01

The classic solution of the linearized drift kinetic equations in neoclassical transport theory for large-aspect-ratio tokamak flux-surfaces relies on the variational principle and the choice of ``localized" distribution functions as trialfunctions.(M.N. Rosenbluth, et al., Phys. Fluids 15) (1972) 116. Somewhat unclear in this approach are the nature and the origin of the ``localization" and whether the results obtained represent the exact leading terms in an asymptotic expansion int he inverse aspect ratio. Using the method of matched asymptotic expansions, we were able to derive the leading approximations to the distribution functions and demonstrated the asymptotic exactness of the existing results. The method is also applied to the calculation of angular momentum transport(M.N. Rosenbluth, et al., Plasma Phys. and Contr. Nucl. Fusion Research, 1970, Vol. 1 (IAEA, Vienna, 1971) p. 495.) and the current driven by electron cyclotron waves.

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

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.

In situ measurement of plasma and shock wave properties inside laser-drilled metal holes

NASA Astrophysics Data System (ADS)

Brajdic, Mihael; Hermans, Martin; Horn, Alexander; Kelbassa, Ingomar

2008-10-01

High-speed imaging of shock wave and plasma dynamics is a commonly used diagnostic method for monitoring processes during laser material treatment. It is used for processes such as laser ablation, cutting, keyhole welding and drilling. Diagnosis of laser drilling is typically adopted above the material surface because lateral process monitoring with optical diagnostic methods inside the laser-drilled hole is not possible due to the hole walls. A novel method is presented to investigate plasma and shock wave properties during the laser drilling inside a confined environment such as a laser-drilled hole. With a novel sample preparation and the use of high-speed imaging combined with spectroscopy, a time and spatial resolved monitoring of plasma and shock wave dynamics is realized. Optical emission of plasma and shock waves during drilling of stainless steel with ns-pulsed laser radiation is monitored and analysed. Spatial distributions and velocities of shock waves and of plasma are determined inside the holes. Spectroscopy is accomplished during the expansion of the plasma inside the drilled hole allowing for the determination of electron densities.

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.

Coronary wave energy: a novel predictor of functional recovery after myocardial infarction.

PubMed

De Silva, Kalpa; Foster, Paul; Guilcher, Antoine; Bandara, Asela; Jogiya, Roy; Lockie, Tim; Chowiencyzk, Phil; Nagel, Eike; Marber, Michael; Redwood, Simon; Plein, Sven; Perera, Divaka

2013-04-01

Revascularization after acute coronary syndromes provides prognostic benefit, provided that the subtended myocardium is viable. The microcirculation and contractility of the subtended myocardium affect propagation of coronary flow, which can be characterized by wave intensity analysis. The study objective was to determine in acute coronary syndromes whether early wave intensity analysis-derived microcirculatory (backward) expansion wave energy predicts late viability, defined by functional recovery. Thirty-one patients (58±11 years) were enrolled after non-ST elevation myocardial infarction. Regional left ventricular function and late-gadolinium enhancement were assessed by cardiac magnetic resonance imaging, before and 3 months after revascularization. The backward-traveling (microcirculatory) expansion wave was derived from wave intensity analysis of phasic coronary pressure and velocity in the infarct-related artery, whereas mean values were used to calculate hyperemic microvascular resistance. Twelve-hour troponin T, left ventricular ejection fraction, and percentage late-gadolinium enhancement mass were 1.35±1.21 µg/L, 56±11%, and 8.4±6.0%, respectively. The infarct-related artery backward-traveling (microcirculatory) expansion wave was inversely correlated with late-gadolinium enhancement infarct mass (r=-0.81; P<0.0001) and strongly predicted regional left ventricular recovery (r=0.68; P=0.001). By receiver operating characteristic analysis, a backward-traveling (microcirculatory) expansion wave threshold of 2.8 W m(-2) s(-2)×10(5) predicted functional recovery with sensitivity and specificity of 0.91 and 0.82 (AUC 0.88). Hyperemic microvascular resistance correlated with late-gadolinium enhancement mass (r=0.48; P=0.03) but not left ventricular recovery (r=-0.34; P=0.07). The microcirculation-derived backward expansion wave is a new index that correlates with the magnitude and location of infarction, which may allow for the prediction of functional myocardial recovery. Coronary wave intensity analysis may facilitate myocardial viability assessment during cardiac catheterization.

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.

1982-01-01

The extended method of equivalent inclusion developed is applied to study the specific wave problems of the transmission of elastic waves in an infinite medium containing a layer of inhomogeneity, and of the scattering of elastic waves in an infinite medium containing a perfect spherical inhomogeneity. The eigenstrains are expanded as a geometric series and the method of integration for the inhomogeneous Helmholtz operator given by Fu and Mura is adopted. The results obtained by using a limited number of terms in the eigenstrain expansion are compared with exact solutions for the layer problem and for a perfect sphere. Two parameters are singled out for this comparison: the ratio of elastic moduli, and the ratio of the mass densities. General trends for three different situations are shown.

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.

The SEM description of interaction of a transient electromagnetic wave with an object

NASA Technical Reports Server (NTRS)

Pearson, L. W.; Wilton, D. R.

1980-01-01

The singularity expansion method (SEM), proposed as a means for determining and representing the transient surface current density induced on a scatterer by a transient electromagnetic wave is described. The resulting mathematical description of the transient surface current on the object is discussed. The data required to represent the electromagnetic scattering properties of a given object are examined. Experimental methods which were developed for the determination of the SEM description are discussed. The feasibility of characterizing the surface current induced on aircraft flying in proximity to a lightning stroke by way of SEM is examined.

Characteristics of a liquid-crystal-filled composite lattice terahertz bandgap fiber

NASA Astrophysics Data System (ADS)

Bai, Jinjun; Ge, Meilan; Wang, Shasha; Yang, Yanan; Li, Yong; Chang, Shengjiang

2018-07-01

A new type of terahertz fiber is presented based on composite lattice photonic crystal bandgap. The cladding is filled selectively with the nematic liquid crystal 5CB which is sensitive to the electric field. The terahertz wave can be modulated by using the electric field to control the orientation of liquid crystal molecules. The plane wave expansion method and the finite element method are employed to theoretically analyze bandgap characteristics, polarization characteristics, energy fraction and material absorption loss. The results show that this fiber structure can be used as tunable terahertz polarization controller.

Charge-transfer excited states: Seeking a balanced and efficient wave function ansatz in variational Monte Carlo

DOE PAGES

Blunt, Nick S.; Neuscamman, Eric

2017-11-16

We present a simple and efficient wave function ansatz for the treatment of excited charge-transfer states in real-space quantum Monte Carlo methods. Using the recently-introduced variation-after-response method, this ansatz allows a crucial orbital optimization step to be performed beyond a configuration interaction singles expansion, while only requiring calculation of two Slater determinant objects. As a result, we demonstrate this ansatz for the illustrative example of the stretched LiF molecule, for a range of excited states of formaldehyde, and finally for the more challenging ethylene-tetrafluoroethylene molecule.

A Generalized Fast Frequency Sweep Algorithm for Coupled Circuit-EM Simulations

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

Rockway, J D; Champagne, N J; Sharpe, R M

2004-01-14

Frequency domain techniques are popular for analyzing electromagnetics (EM) and coupled circuit-EM problems. These techniques, such as the method of moments (MoM) and the finite element method (FEM), are used to determine the response of the EM portion of the problem at a single frequency. Since only one frequency is solved at a time, it may take a long time to calculate the parameters for wideband devices. In this paper, a fast frequency sweep based on the Asymptotic Wave Expansion (AWE) method is developed and applied to generalized mixed circuit-EM problems. The AWE method, which was originally developed for lumped-loadmore » circuit simulations, has recently been shown to be effective at quasi-static and low frequency full-wave simulations. Here it is applied to a full-wave MoM solver, capable of solving for metals, dielectrics, and coupled circuit-EM problems.« less

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.

Shock-Strength Determination With Seeded and Seedless Laser Methods

NASA Technical Reports Server (NTRS)

Herring, G. C.; Meyers, James F.

2008-01-01

Two nonintrusive laser diagnostics were independently used to demonstrate the measurement of time-averaged and spatially-resolved pressure change across a twodimensional (2-D) shock wave. The first method is Doppler global velocimetry (DGV) which uses water seeding and generates 2-D maps of 3-orthogonal components of velocity. A DGV-measured change in flow direction behind an oblique shock provides an indirect determination of pressure jump across the shock, when used with the known incoming Mach number and ideal shock relations (or Prandtl-Meyer flow equations for an expansion fan). This approach was demonstrated at Mach 2 on 2-D shocks and expansions generated from a flat plate at angles-of-attack approx. equals -2.4deg and +0.6deg, respectively. This technique also works for temperature jump (as well as pressure) and for normal shocks (as well as oblique). The second method, laser-induced thermal acoustics (LITA), is a seedless approach that was used to generate 1-D spatial profiles of streamwise Mach number, sound speed, pressure, and temperature across the same shock waves. Excellent agreement was obtained between the DGV and LITA methods, suggesting that either technique is viable for noninvasive shock-strength measurements.

A Supersonic Tunnel for Laser and Flow-Seeding Techniques

NASA Technical Reports Server (NTRS)

Bruckner, Robert J.; Lepicovsky, Jan

1994-01-01

A supersonic wind tunnel with flow conditions of 3 lbm/s (1.5 kg/s) at a free-stream Mach number of 2.5 was designed and tested to provide an arena for future development work on laser measurement and flow-seeding techniques. The hybrid supersonic nozzle design that was used incorporated the rapid expansion method of propulsive nozzles while it maintained the uniform, disturbance-free flow required in supersonic wind tunnels. A viscous analysis was performed on the tunnel to determine the boundary layer growth characteristics along the flowpath. Appropriate corrections were then made to the contour of the nozzle. Axial pressure distributions were measured and Mach number distributions were calculated based on three independent data reduction methods. A complete uncertainty analysis was performed on the precision error of each method. Complex shock-wave patterns were generated in the flow field by wedges mounted near the roof and floor of the tunnel. The most stable shock structure was determined experimentally by the use of a focusing schlieren system and a novel, laser based dynamic shock position sensor. Three potential measurement regions for future laser and flow-seeding studies were created in the shock structure: deceleration through an oblique shock wave of 50 degrees, strong deceleration through a normal shock wave, and acceleration through a supersonic expansion fan containing 25 degrees of flow turning.

a 2d Model of Ultrasonic Testing for Cracks Near a Nonplanar Surface

NASA Astrophysics Data System (ADS)

Westlund, Jonathan; Boström, Anders

2010-02-01

2D P-SV elastic wave scattering by a crack near a non-planar surface is investigated. The wave scattering problem is solved in the frequency domain using a combination of the boundary element method (BEM) for the back surface displacement and a Fourier series expansion of the crack opening displacement (COD). The model accounts for the action of the transmitting and receiving ultrasonic contact probes, and the time traces are obtained by applying an inverse temporal Fourier transform.

Scattering of Lamb waves in a composite plate

NASA Technical Reports Server (NTRS)

Bratton, Robert; Datta, Subhendu; Shah, Arvind

1991-01-01

A combined analytical and finite element technique is developed to gain a better understanding of the scattering of elastic waves by defects. This hybrid method is capable of predicting scattered displacements from arbitrary shaped defects as well as inclusions of different material. The continuity of traction and displacements at the boundaries of the two areas provided the necessary equations to find the nodal displacements and expansion coefficients. Results clearly illustrate the influence of increasing crack depth on the scattered signal.

Composite scheme using localized relaxation with non-standard finite difference method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Kumar, Vivek; Raghurama Rao, S. V.

2008-04-01

Non-standard finite difference methods (NSFDM) introduced by Mickens [ Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791-797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250-2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235-276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter ( λ) is chosen locally on the three point stencil of grid which makes the proposed method more efficient. This composite scheme overcomes the problem of unphysical expansion shocks and captures the shock waves with an accuracy better than the upwind relaxation scheme, as demonstrated by the test cases, together with comparisons with popular numerical methods like Roe scheme and ENO schemes.

On the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_1^\\alpha ({T^N})

NASA Astrophysics Data System (ADS)

Ahmedov, Anvarjon; Materneh, Ehab; Zainuddin, Hishamuddin

2017-09-01

The relevance of waves in quantum mechanics naturally implies that the decomposition of arbitrary wave packets in terms of monochromatic waves plays an important role in applications of the theory. When eigenfunction expansions does not converge, then the expansions of the functions with certain smoothness should be considered. Such functions gained prominence primarily through their application in quantum mechanics. In this work we study the almost everywhere convergence of the eigenfunction expansions from Liouville classes L_p^α ({T^N}), related to the self-adjoint extension of the Laplace operator in torus TN . The sufficient conditions for summability is obtained using the modified Poisson formula. Isomorphism properties of the elliptic differential operators is applied in order to obtain estimation for the Fourier series of the functions from the classes of Liouville L_p^α .

Subwavelength and directional control of flexural waves in zone-folding induced topological plates

NASA Astrophysics Data System (ADS)

Chaunsali, Rajesh; Chen, Chun-Wei; Yang, Jinkyu

2018-02-01

Inspired by the quantum spin Hall effect shown by topological insulators, we propose a plate structure that can be used to demonstrate the pseudospin Hall effect for flexural waves. The system consists of a thin plate with periodically arranged resonators mounted on its top surface. We extend a technique based on the plane-wave expansion method to identify a double Dirac cone emerging due to the zone-folding in frequency band structures. This particular design allows us to move the double Dirac cone to a lower frequency than the resonating frequency of local resonators. We then manipulate the pattern of local resonators to open subwavelength Bragg band gaps that are topologically distinct. Building on this method, we verify numerically that a waveguide at an interface between two topologically distinct resonating plate structures can be used for guiding low-frequency, spin-dependent one-way flexural waves along a desired path with bends.

Analysis of a dual-reflector antenna system using physical optics and digital computers

NASA Technical Reports Server (NTRS)

Schmidt, R. F.

1972-01-01

The application of physical-optics diffraction theory to a deployable dual-reflector geometry is discussed. The methods employed are not restricted to the Conical-Gregorian antenna, but apply in a general way to dual and even multiple reflector systems. Complex vector wave methods are used in the Fresnel and Fraunhofer regions of the reflectors. Field amplitude, phase, polarization data, and time average Poynting vectors are obtained via an IBM 360/91 digital computer. Focal region characteristics are plotted with the aid of a CalComp plotter. Comparison between the GSFC Huygens wavelet approach, JPL measurements, and JPL computer results based on the near field spherical wave expansion method are made wherever possible.

Free iterative-complement-interaction calculations of the hydrogen molecule

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

Kurokawa, Yusaku; Nakashima, Hiroyuki; Nakatsuji, Hiroshi

2005-12-15

The free iterative-complement-interaction (ICI) method based on the scaled Schroedinger equation proposed previously has been applied to the calculations of very accurate wave functions of the hydrogen molecule in an analytical expansion form. All the variables were determined with the variational principle by calculating the necessary integrals analytically. The initial wave function and the scaling function were changes to see the effects on the convergence speed of the ICI calculations. The free ICI wave functions that were generated automatically were different from the existing wave functions, and this difference was shown to be physically important. The best wave function reportedmore » in this paper seems to be the best worldwide in the literature from the variational point of view. The quality of the wave function was examined by calculating the nuclear and electron cusps.« less

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.

Toward the detection of gravitational waves under non-Gaussian noises I. Locally optimal statistic.

PubMed

Yokoyama, Jun'ichi

2014-01-01

After reviewing the standard hypothesis test and the matched filter technique to identify gravitational waves under Gaussian noises, we introduce two methods to deal with non-Gaussian stationary noises. We formulate the likelihood ratio function under weakly non-Gaussian noises through the Edgeworth expansion and strongly non-Gaussian noises in terms of a new method we call Gaussian mapping where the observed marginal distribution and the two-body correlation function are fully taken into account. We then apply these two approaches to Student's t-distribution which has a larger tails than Gaussian. It is shown that while both methods work well in the case the non-Gaussianity is small, only the latter method works well for highly non-Gaussian case.

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.

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.

Two-scale homogenization to determine effective parameters of thin metallic-structured films

PubMed Central

Marigo, Jean-Jacques

2016-01-01

We present a homogenization method based on matched asymptotic expansion technique to derive effective transmission conditions of thin structured films. The method leads unambiguously to effective parameters of the interface which define jump conditions or boundary conditions at an equivalent zero thickness interface. The homogenized interface model is presented in the context of electromagnetic waves for metallic inclusions associated with Neumann or Dirichlet boundary conditions for transverse electric or transverse magnetic wave polarization. By comparison with full-wave simulations, the model is shown to be valid for thin interfaces up to thicknesses close to the wavelength. We also compare our effective conditions with the two-sided impedance conditions obtained in transmission line theory and to the so-called generalized sheet transition conditions. PMID:27616916

Analytical solution for the transient wave propagation of a buried cylindrical P-wave line source in a semi-infinite elastic medium with a fluid surface layer

NASA Astrophysics Data System (ADS)

Shan, Zhendong; Ling, Daosheng

2018-02-01

This article develops an analytical solution for the transient wave propagation of a cylindrical P-wave line source in a semi-infinite elastic solid with a fluid layer. The analytical solution is presented in a simple closed form in which each term represents a transient physical wave. The Scholte equation is derived, through which the Scholte wave velocity can be determined. The Scholte wave is the wave that propagates along the interface between the fluid and solid. To develop the analytical solution, the wave fields in the fluid and solid are defined, their analytical solutions in the Laplace domain are derived using the boundary and interface conditions, and the solutions are then decomposed into series form according to the power series expansion method. Each item of the series solution has a clear physical meaning and represents a transient wave path. Finally, by applying Cagniard's method and the convolution theorem, the analytical solutions are transformed into the time domain. Numerical examples are provided to illustrate some interesting features in the fluid layer, the interface and the semi-infinite solid. When the P-wave velocity in the fluid is higher than that in the solid, two head waves in the solid, one head wave in the fluid and a Scholte wave at the interface are observed for the cylindrical P-wave line source.

Experimental and calculative estimation of femtosecond laser induced-impulsive force in culture medium solution with motion analysis of polymer micro-beads

NASA Astrophysics Data System (ADS)

Yamakawa, Takeshi; Maruyama, Akihiro; Uedan, Hirohisa; Iino, Takanori; Hosokawa, Yoichiroh

2015-03-01

A new methodology to estimate the dynamics of femtosecond laser-induced impulsive force generated into water under microscope was developed. In this method, the position shift of the bead in water before and after the femtosecond laser irradiation was investigated experimentally and compared with motion equation assuming stress wave propagation with expansion and collapse the cavitation bubble. In the process of the comparison, parameters of force and time of the stress wave were determined. From these results, dynamics of propagations of shock and stress waves, cavitation bubble generation, and these actions to micro-objects were speculated.

Band structure analysis of leaky Bloch waves in 2D phononic crystal plates.

PubMed

Mazzotti, Matteo; Miniaci, Marco; Bartoli, Ivan

2017-02-01

A hybrid Finite Element-Plane Wave Expansion method is presented for the band structure analysis of phononic crystal plates with two dimensional lattice that are in contact with acoustic half-spaces. The method enables the computation of both real (propagative) and imaginary (attenuation) components of the Bloch wavenumber at any given frequency. Three numerical applications are presented: a benchmark dispersion analysis for an oil-loaded Titanium isotropic plate, the band structure analysis of a water-loaded Tungsten slab with square cylindrical cavities and a phononic crystal plate composed of Aurum cylinders embedded in an epoxy matrix. Copyright © 2016 Elsevier B.V. All rights reserved.

Optical NOR logic gate design on square lattice photonic crystal platform

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

D’souza, Nirmala Maria, E-mail: nirmala@cukerala.ac.in; Mathew, Vincent, E-mail: vincent@cukerala.ac.in

We numerically demonstrate a new configuration of all-optical NOR logic gate with square lattice photonic crystal (PhC) waveguide using finite difference time domain (FDTD) method. The logic operations are based on interference effect of optical waves. We have determined the operating frequency range by calculating the band structure for a perfectly periodic PhC using plane wave expansion (PWE) method. Response time of this logic gate is 1.98 ps and it can be operated with speed about 513 GB/s. The proposed device consists of four linear waveguides and a square ring resonator waveguides on PhC platform.

A high-order perturbation of surfaces method for scattering of linear waves by periodic multiply layered gratings in two and three dimensions

NASA Astrophysics Data System (ADS)

Hong, Youngjoon; Nicholls, David P.

2017-09-01

The capability to rapidly and robustly simulate the scattering of linear waves by periodic, multiply layered media in two and three dimensions is crucial in many engineering applications. In this regard, we present a High-Order Perturbation of Surfaces method for linear wave scattering in a multiply layered periodic medium to find an accurate numerical solution of the governing Helmholtz equations. For this we truncate the bi-infinite computational domain to a finite one with artificial boundaries, above and below the structure, and enforce transparent boundary conditions there via Dirichlet-Neumann Operators. This is followed by a Transformed Field Expansion resulting in a Fourier collocation, Legendre-Galerkin, Taylor series method for solving the problem in a transformed set of coordinates. Assorted numerical simulations display the spectral convergence of the proposed algorithm.

Separated-pair independent particle model and the generalized Brillouin theorem: ab initio calculations on the dissociation of polyatomic molecules

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

Sundberg, Kenneth Randall

1976-01-01

A method is developed to optimize the separated-pair independent particle (SPIP) wave function; it is a special case of the separated-pair theory obtained by using two-term natural expansions of the geminals. The orbitals are optimized by a theory based on the generalized Brillouin theorem and iterative configuration interaction (CI) calculations in the space of the SPIP function and its single excitations. The geminal expansion coefficients are optimized by serial 2 x 2 CI calculations. Formulas are derived for the matrix elements. An algorithm to implement the method is presented, and the work needed to evaluate the molecular integrals is discussed.

Abundant closed form solutions of the conformable time fractional Sawada-Kotera-Ito equation using (G‧ / G) -expansion method

NASA Astrophysics Data System (ADS)

Al-Shawba, Altaf Abdulkarem; Gepreel, K. A.; Abdullah, F. A.; Azmi, A.

2018-06-01

In current study, we use the (G‧ / G) -expansion method to construct the closed form solutions of the seventh order time fractional Sawada-Kotera-Ito (TFSKI) equation based on conformable fractional derivative. As a result, trigonometric, hyperbolic and rational functions solutions with arbitrary constants are obtained. When the arbitrary constants are taken some special values, the periodic and soliton solutions are obtained from the travelling wave solutions. The obtained solutions are new and not found elsewhere. The effect of the fractional order on some of these solutions are represented graphically to illustrate the behavior of the exact solutions when the parameter take some special choose.

The pattern space factor and quality factor of cylindrical source antennas

NASA Astrophysics Data System (ADS)

Jarem, John M.

1982-09-01

For the first time the quality factor of cylindrical source antennas is derived by a plane wave expansion. The evanescent energy (and therefore the quality factor) as defined by a plane wave expansion is shown to be different from Collin and Rothschild's [IEEE Trans. Antennas Propagation AP-12, 23 (1964)] quality factor.

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.

Sound field reconstruction within an entire cavity by plane wave expansions using a spherical microphone array.

PubMed

Wang, Yan; Chen, Kean

2017-10-01

A spherical microphone array has proved effective in reconstructing an enclosed sound field by a superposition of spherical wave functions in Fourier domain. It allows successful reconstructions surrounding the array, but the accuracy will be degraded at a distance. In order to extend the effective reconstruction to the entire cavity, a plane-wave basis in space domain is used owing to its non-decaying propagating characteristic and compared with the conventional spherical wave function method in a low frequency sound field within a cylindrical cavity. The sensitivity to measurement noise, the effects of the numbers of plane waves, and measurement positions are discussed. Simulations show that under the same measurement conditions, the plane wave function method is superior in terms of reconstruction accuracy and data processing efficiency, that is, the entire sound field imaging can be achieved by only one time calculation instead of translations of local sets of coefficients with respect to every measurement position into a global one. An experiment was conducted inside an aircraft cabin mock-up for validation. Additionally, this method provides an alternative possibility to recover the coefficients of high order spherical wave functions in a global coordinate system without coordinate translations with respect to local origins.

Gene surfing in expanding populations.

PubMed

Hallatschek, Oskar; Nelson, David R

2008-02-01

Large scale genomic surveys are partly motivated by the idea that the neutral genetic variation of a population may be used to reconstruct its migration history. However, our ability to trace back the colonization pathways of a species from their genetic footprints is limited by our understanding of the genetic consequences of a range expansion. Here, we study, by means of simulations and analytical methods, the neutral dynamics of gene frequencies in an asexual population undergoing a continual range expansion in one dimension. During such a colonization period, lineages can fix at the wave front by means of a "surfing" mechanism [Edmonds, C.A., Lillie, A.S., Cavalli-Sforza, L.L., 2004. Mutations arising in the wave front of an expanding population. Proc. Natl. Acad. Sci. 101, 975-979]. We quantify this phenomenon in terms of (i) the spatial distribution of lineages that reach fixation and, closely related, (ii) the continual loss of genetic diversity (heterozygosity) at the wave front, characterizing the approach to fixation. Our stochastic simulations show that an effective population size can be assigned to the wave that controls the (observable) gradient in heterozygosity left behind the colonization process. This effective population size is markedly higher in the presence of cooperation between individuals ("pushed waves") than when individuals proliferate independently ("pulled waves"), and increases only sub-linearly with deme size. To explain these and other findings, we develop a versatile analytical approach, based on the physics of reaction-diffusion systems, that yields simple predictions for any deterministic population dynamics. Our analytical theory compares well with the simulation results for pushed waves, but is less accurate in the case of pulled waves when stochastic fluctuations in the tip of the wave are important.

Asymptotic expansions and solitons of the Camassa-Holm - nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Mylonas, I. K.; Ward, C. B.; Kevrekidis, P. G.; Rothos, V. M.; Frantzeskakis, D. J.

2017-12-01

We study a deformation of the defocusing nonlinear Schrödinger (NLS) equation, the defocusing Camassa-Holm NLS, hereafter referred to as CH-NLS equation. We use asymptotic multiscale expansion methods to reduce this model to a Boussinesq-like equation, which is then subsequently approximated by two Korteweg-de Vries (KdV) equations for left- and right-traveling waves. We use the soliton solution of the KdV equation to construct approximate solutions of the CH-NLS system. It is shown that these solutions may have the form of either dark or antidark solitons, namely dips or humps on top of a stable continuous-wave background. We also use numerical simulations to investigate the validity of the asymptotic solutions, study their evolution, and their head-on collisions. It is shown that small-amplitude dark and antidark solitons undergo quasi-elastic collisions.

An optimal implicit staggered-grid finite-difference scheme based on the modified Taylor-series expansion with minimax approximation method for elastic modeling

NASA Astrophysics Data System (ADS)

Yang, Lei; Yan, Hongyong; Liu, Hong

2017-03-01

Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.

Cylindrical ion-acoustic solitary waves in electronegative plasmas with superthermal electrons

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

Eslami, Parvin; Mottaghizadeh, Marzieh

2012-06-15

By using the standard reductive perturbation technique, a three-dimensional cylindrical Kadomtsev-Petviashvili equation (CKPE), which governs the dynamics of ion acoustic solitary waves (IASWs), is derived for small but finite amplitude ion-acoustic waves in cylindrical geometry in a collisionless unmagnetized plasma with kappa distributed electrons, thermal positrons, and cold ions. The generalized expansion method is used to solve analytically the CKPE. The existence regions of localized pulses are investigated. It is found that the solution of the CKPE supports only compressive solitary waves. Furthermore, the effects of superthermal electrons, the ratio of the electron temperature to positron temperature, the ratio ofmore » the positron density to electron density and direction cosine of the wave propagation on the profiles of the amplitudes, and widths of the solitary structures are examined numerically. It is shown these parameters play a vital role in the formation of ion acoustic solitary waves.« less

Effect of anisotropic dust pressure and superthermal electrons on propagation and stability of dust acoustic solitary waves

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

Bashir, M. F., E-mail: frazbashir@yahoo.com; Behery, E. E., E-mail: eebehery@gmail.com; Department of Physics, Faculty of Science, Damietta University, P.O. 34517, New Damietta

2015-06-15

Employing the reductive perturbation technique, Zakharov–Kuznetzov (ZK) equation is derived for dust acoustic (DA) solitary waves in a magnetized plasma which consists the effects of dust anisotropic pressure, arbitrary charged dust particles, Boltzmann distributed ions, and Kappa distributed superthermal electrons. The ZK solitary wave solution is obtained. Using the small-k expansion method, the stability analysis for DA solitary waves is also discussed. The effects of the dust pressure anisotropy and the electron superthermality on the basic characteristics of DA waves as well as on the three-dimensional instability criterion are highlighted. It is found that the DA solitary wave is rarefactivemore » (compressive) for negative (positive) dust. In addition, the growth rate of instability increases rapidly as the superthermal spectral index of electrons increases with either positive or negative dust grains. A brief discussion for possible applications is included.« less

Gravitational Radiation with a Positive Cosmological Constant

NASA Astrophysics Data System (ADS)

Bonga, Beatrice

Gravitational radiation is well-understood in spacetimes that are asymptotically flat. However, our Universe is currently expanding at an accelerated rate, which is best described by including a positive cosmological constant, Lambda, in Einstein's equations. Consequently, no matter how far one recedes from sources generating gravitational waves, spacetime curvature never dies and is not asymptotically flat. This dissertation provides first steps to incorporate Lambda in the study of gravitational radiation by analyzing linearized gravitational waves on a de Sitter background. Since the asymptotic structure of de Sitter is very different from that of Minkowski spacetime, many conceptual and technical difficulties arise. The limit Lambda → 0 can be discontinuous: Although energy carried by gravitational waves is always positive in Minkowski spacetime, it can be arbitrarily negative in de Sitter spacetime. Additionally, many of the standard techniques, including 1/r expansions, are no longer applicable. We generalize Einstein's celebrated quadrupole formula describing the power radiated on a flat background to de Sitter spacetime. Even a tiny Lambda brings in qualitatively new features such as contributions from pressure quadrupole moments. Nonetheless, corrections induced by Lambda are O(√Lambda tc) with tc the characteristic time scale of the source and are negligible for current gravitational wave observatories. We demonstrate this explicitly for a binary system in a circular orbit. Radiative modes are encoded in the transverse-traceless part of the spatial components of a gravitational perturbation. When Lambda = 0, one typically extracts these modes in the wave zone by projecting the gravitational perturbation onto the two-sphere orthogonal to the radial direction. We show that this method for waves emitted by spatially compact sources on Minkowski spacetime generically does not yield the transverse-traceless modes; not even infinitely far away. However, the difference between the transverse-traceless and projected modes is non-dynamical and disappears from all physical observables. When one is interested in 'Coulombic' information not captured by the radiative modes, the projection method does not suffice. This is, for example, important for angular momentum carried by gravitational waves. This result relies on Bondi-type expansions for asymptotically flat spacetimes. Therefore, the projection method is not applicable to de Sitter spacetimes.

Boby-Vortex Interaction, Sound Generation and Destructive Interference

NASA Technical Reports Server (NTRS)

Kao, Hsiao C.

2000-01-01

It is generally recognized that interaction of vortices with downstream blades is a major source of noise production. To analyze this problem numerically, a two-dimensional model of inviscid flow together with the method of matched asymptotic expansions is proposed. The method of matched asymptotic expansions is used to match the inner region of incompressible flow to the outer region of compressible flow. Because of incompressibility, relatively simple numerical methods are available to treat multiple vortices and multiple bodies of arbitrary shape. Disturbances from vortices and bodies propagate outward as sound waves. Due to their interactions, either constructive or destructive interference may result. When it is destructive, the combined sound intensity can be reduced, sometimes substantially. In addition, an analytical solution to sound generation by the cascade-vonex interaction is given.

The effective propagation constants of SH wave in composites reinforced by dispersive parallel nanofibers

NASA Astrophysics Data System (ADS)

Qiang, FangWei; Wei, PeiJun; Li, Li

2012-07-01

In the present paper, the effective propagation constants of elastic SH waves in composites with randomly distributed parallel cylindrical nanofibers are studied. The surface stress effects are considered based on the surface elasticity theory and non-classical interfacial conditions between the nanofiber and the host are derived. The scattering waves from individual nanofibers embedded in an infinite elastic host are obtained by the plane wave expansion method. The scattering waves from all fibers are summed up to obtain the multiple scattering waves. The interactions among random dispersive nanofibers are taken into account by the effective field approximation. The effective propagation constants are obtained by the configurational average of the multiple scattering waves. The effective speed and attenuation of the averaged wave and the associated dynamical effective shear modulus of composites are numerically calculated. Based on the numerical results, the size effects of the nanofibers on the effective propagation constants and the effective modulus are discussed.

Extended quantum jump description of vibronic two-dimensional spectroscopy

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

Albert, Julian; Falge, Mirjam; Keß, Martin

2015-06-07

We calculate two-dimensional (2D) vibronic spectra for a model system involving two electronic molecular states. The influence of a bath is simulated using a quantum-jump approach. We use a method introduced by Makarov and Metiu [J. Chem. Phys. 111, 10126 (1999)] which includes an explicit treatment of dephasing. In this way it is possible to characterize the influence of dissipation and dephasing on the 2D-spectra, using a wave function based method. The latter scales with the number of stochastic runs and the number of system eigenstates included in the expansion of the wave-packets to be propagated with the stochastic methodmore » and provides an efficient method for the calculation of the 2D-spectra.« less

A synoptic and dynamical characterization of wave-train and blocking cold surge over East Asia

NASA Astrophysics Data System (ADS)

Park, Tae-Won; Ho, Chang-Hoi; Deng, Yi

2014-08-01

Through an agglomerative hierarchical clustering method, cold surges over East Asia are classified into two distinct types based on the spatial pattern of the geopotential height anomalies at 300 hPa. One is the wave-train type that is associated with developing large-scale waves across the Eurasian continent. The other is the blocking type whose occurrence accompanies subarctic blocking. During the wave-train cold surge, growing baroclinic waves induce a southeastward expansion of the Siberian High and strong northerly winds over East Asia. Blocking cold surge, on the other hand, is associated with a southward expansion of the Siberian High and northeasterly winds inherent to a height dipole consisting of the subarctic blocking and the East Asian coastal trough. The blocking cold surge tends to be more intense and last longer compared to the wave-train type. The wave-train cold surge is associated with the formation of a negative upper tropospheric height anomaly southeast of Greenland approximately 12 days before the surge occurrence. Further analysis of isentropic potential vorticity reveals that this height anomaly could originate from the lower stratosphere over the North Atlantic. Cold surge of the blocking type occurs with an amplifying positive geopotential and a negative potential vorticity anomaly over the Arctic and the northern Eurasia in stratosphere. These anomalies resemble the stratospheric signature of a negative phase of the Arctic Oscillation. This stratospheric feature is further demonstrated by the observation that the blocking type cold surge occurs more often when the Arctic Oscillation is in its negative phase.

The investigation of trapped thickness shear modes in a contoured AT-cut quartz plate using the power series expansion technique

NASA Astrophysics Data System (ADS)

Li, Peng; Jin, Feng

2018-01-01

The dynamic model about the anti-plane vibration of a contoured quartz plate with thickness changing continuously is established by ignoring the effect of small elastic constant c 56. The governing equation is solved using the power series expansion technique, and the trapped thickness shear modes caused by bulge thickness are revealed. Theoretically, the proposed method is more general, which can be capable of handling various thickness profiles defined mathematically. After the convergence of the series is demonstrated and the correctness is numerically validated with the aid of finite element method results, systematic parametric studies are subsequently carried out to quantify the effects of the geometry parameter upon the trapped modes, including resonant frequency and mode shape. After that, the band structures of thickness shear waves propagation in a periodically contoured quartz plate, as well as the power transmission spectra, are obtained based on the power series expansion technique. It is revealed that broad stop bands below cut-off frequency exist owing to the trapped modes excited by the geometry inhomogeneity, which has little relationship with the structural periodicity, and its physical mechanism is different from the Bragg scattering effect. The outcome is widely applicable, and can be utilized to provide theoretical and practical guidance for the design and manufacturing of quartz resonators and wave filters.

Toward the detection of gravitational waves under non-Gaussian noises I. Locally optimal statistic

PubMed Central

YOKOYAMA, Jun’ichi

2014-01-01

After reviewing the standard hypothesis test and the matched filter technique to identify gravitational waves under Gaussian noises, we introduce two methods to deal with non-Gaussian stationary noises. We formulate the likelihood ratio function under weakly non-Gaussian noises through the Edgeworth expansion and strongly non-Gaussian noises in terms of a new method we call Gaussian mapping where the observed marginal distribution and the two-body correlation function are fully taken into account. We then apply these two approaches to Student’s t-distribution which has a larger tails than Gaussian. It is shown that while both methods work well in the case the non-Gaussianity is small, only the latter method works well for highly non-Gaussian case. PMID:25504231

The FLAME-slab method for electromagnetic wave scattering in aperiodic slabs

NASA Astrophysics Data System (ADS)

Mansha, Shampy; Tsukerman, Igor; Chong, Y. D.

2017-12-01

The proposed numerical method, "FLAME-slab," solves electromagnetic wave scattering problems for aperiodic slab structures by exploiting short-range regularities in these structures. The computational procedure involves special difference schemes with high accuracy even on coarse grids. These schemes are based on Trefftz approximations, utilizing functions that locally satisfy the governing differential equations, as is done in the Flexible Local Approximation Method (FLAME). Radiation boundary conditions are implemented via Fourier expansions in the air surrounding the slab. When applied to ensembles of slab structures with identical short-range features, such as amorphous or quasicrystalline lattices, the method is significantly more efficient, both in runtime and in memory consumption, than traditional approaches. This efficiency is due to the fact that the Trefftz functions need to be computed only once for the whole ensemble.

Determination of two-stroke engine exhaust noise by the method of characteristics

NASA Technical Reports Server (NTRS)

Jones, A. D.; Brown, G. L.

1981-01-01

A computational technique was developed for the method of characteristics solution of a one-dimensional flow in a duct as applied to the wave action in an engine exhaust system. By using the method, it was possible to compute the unsteady flow in both straight pipe and tuned expansion chamber exhaust systems as matched to the flow from the cylinder of a small two-stroke engine. The radiated exhaust noise was then determined by assuming monopole radiation from the tailpipe outlet. Very good agreement with experiment on an operation engine was achieved in the calculation of both the third octave radiated noise and the associated pressure cycles at several locations in the different exhaust systems. Of particular interest is the significance of nonlinear behavior which results in wave steepening and shock wave formation. The method computes the precise paths on the x-t plane of a finite number of C(sub +), C(sub -) and P characteristics, thereby obtaining high accuracy in determining the tailpipe outlet velocity and the radiated noise.

Determination of two-stroke engine exhaust noise by the method of characteristics

NASA Astrophysics Data System (ADS)

Jones, A. D.; Brown, G. L.

1981-06-01

A computational technique was developed for the method of characteristics solution of a one-dimensional flow in a duct as applied to the wave action in an engine exhaust system. By using the method, it was possible to compute the unsteady flow in both straight pipe and tuned expansion chamber exhaust systems as matched to the flow from the cylinder of a small two-stroke engine. The radiated exhaust noise was then determined by assuming monopole radiation from the tailpipe outlet. Very good agreement with experiment on an operation engine was achieved in the calculation of both the third octave radiated noise and the associated pressure cycles at several locations in the different exhaust systems. Of particular interest is the significance of nonlinear behavior which results in wave steepening and shock wave formation. The method computes the precise paths on the x-t plane of a finite number of C(sub +), C(sub -) and P characteristics, thereby obtaining high accuracy in determining the tailpipe outlet velocity and the radiated noise.

Rigorous coupled wave analysis of acousto-optics with relativistic considerations.

PubMed

Xia, Guoqiang; Zheng, Weijian; Lei, Zhenggang; Zhang, Ruolan

2015-09-01

A relativistic analysis of acousto-optics is presented, and a rigorous coupled wave analysis is generalized for the diffraction of the acousto-optical effect. An acoustic wave generates a grating with temporally and spatially modulated permittivity, hindering direct applications of the rigorous coupled wave analysis for the acousto-optical effect. In a reference frame which moves with the acoustic wave, the grating is static, the medium moves, and the coupled wave equations for the static grating may be derived. Floquet's theorem is then applied to cast these equations into an eigenproblem. Using a Lorentz transformation, the electromagnetic fields in the grating region are transformed to the lab frame where the medium is at rest, and relativistic Doppler frequency shifts are introduced into various diffraction orders. In the lab frame, the boundary conditions are considered and the diffraction efficiencies of various orders are determined. This method is rigorous and general, and the plane waves in the resulting expansion satisfy the dispersion relation of the medium and are propagation modes. Properties of various Bragg diffractions are results, rather than preconditions, of this method. Simulations of an acousto-optical tunable filter made by paratellurite, TeO(2), are given as examples.

Focusing of Finite-Amplitude Cylindrical and Spherical Sound Waves in a Viscous and Heat-Conducting Medium. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Chu, T.

1971-01-01

The focusing of acoustic pulses is studied analytically by considering the region of study in three parts: the converging, interaction and diverging regions. First, the linear problem of a pulse of infinitesimal amplitude is studied. For the spherical case, the expected phase change as a result of focusing is verified. The nonlinear case of finite-amplitude pulses leads to the development of M-waves, as determined by applying the method of matched-asymptotic expansions to Burges equation.

Obliquely propagating low frequency electromagnetic shock waves in two dimensional quantum magnetoplasmas

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

Masood, W.

2009-04-15

Linear and nonlinear propagation characteristics of low frequency magnetoacoustic waves in quantum magnetoplasmas are studied employing the quantum magnetohydrodynamic model. In this regard, a quantum Kadomtsev-Petviashvili-Burgers (KPB) equation is derived using the small amplitude expansion method. The dissipation is introduced by taking into account the kinematic viscosity among the plasma constituents. Furthermore, the solution of KPB equation is presented using the tangent hyperbolic (tanh) method. The variation in the fast and slow magnetoacoustic shock profiles with the quantum Bohm potential via increasing number density, obliqueness angle {theta}, magnetic field, and the resistivity are also investigated. It is observed that themore » aforementioned plasma parameters significantly modify the propagation characteristics of nonlinear magnetoacoustic shock waves in quantum magnetoplasmas. The relevance of the present investigation with regard to dense astrophysical environments is also pointed out.« less

A class of reduced-order models in the theory of waves and stability.

PubMed

Chapman, C J; Sorokin, S V

2016-02-01

This paper presents a class of approximations to a type of wave field for which the dispersion relation is transcendental. The approximations have two defining characteristics: (i) they give the field shape exactly when the frequency and wavenumber lie on a grid of points in the (frequency, wavenumber) plane and (ii) the approximate dispersion relations are polynomials that pass exactly through points on this grid. Thus, the method is interpolatory in nature, but the interpolation takes place in (frequency, wavenumber) space, rather than in physical space. Full details are presented for a non-trivial example, that of antisymmetric elastic waves in a layer. The method is related to partial fraction expansions and barycentric representations of functions. An asymptotic analysis is presented, involving Stirling's approximation to the psi function, and a logarithmic correction to the polynomial dispersion relation.

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.

Suppression of large intraluminal bubble expansion in shock wave lithotripsy without compromising stone comminution: Methodology and in vitro experiments

NASA Astrophysics Data System (ADS)

Zhong, Pei; Zhou, Yufeng

2001-12-01

To reduce the potential of vascular injury without compromising the stone comminution capability of a Dornier HM-3 lithotripter, we have devised a method to suppress intraluminal bubble expansion via in situ pulse superposition. A thin shell ellipsoidal reflector insert was designed and fabricated to fit snugly into the original reflector of an HM-3 lithotripter. The inner surface of the reflector insert shares the same first focus with the original HM-3 reflector, but has its second focus located 5 mm proximal to the generator than that of the HM-3 reflector. With this modification, the original lithotripter shock wave is partitioned into a leading lithotripter pulse (peak positive pressure of 46 MPa and positive pulse duration of 1 μs at 24 kV) and an ensuing second compressive wave of 10 MPa peak pressure and 2 μs pulse duration, separated from each other by about 4 μs. Superposition of the two waves leads to a selective truncation of the trailing tensile component of the lithotripter shock wave, and consequently, a reduction in the maximum bubble expansion up to 41% compared to that produced by the original reflector. The pulse amplitude and -6 dB beam width of the leading lithotripter shock wave from the upgraded reflector at 24 kV are comparable to that produced by the original HM-3 reflector at 20 kV. At the lithotripter focus, while only about 30 shocks are needed to cause a rupture of a blood vessel phantom made of cellulose hollow fiber (i.d.=0.2 mm) using the original HM-3 reflector at 20 kV, no rupture could be produced after 200 shocks using the upgraded reflector at 24 kV. On the other hand, after 100 shocks the upgraded reflector at 24 kV can achieve a stone comminution efficiency of 22%, which is better than the 18% efficiency produced by the original reflector at 20 kV (p=0.043). All together, it has been shown in vitro that the upgraded reflector can produce satisfactory stone comminution while significantly reducing the potential for vessel rupture in shock wave lithotripsy.

Stochastic series expansion simulation of the t -V model

NASA Astrophysics Data System (ADS)

Wang, Lei; Liu, Ye-Hua; Troyer, Matthias

2016-04-01

We present an algorithm for the efficient simulation of the half-filled spinless t -V model on bipartite lattices, which combines the stochastic series expansion method with determinantal quantum Monte Carlo techniques widely used in fermionic simulations. The algorithm scales linearly in the inverse temperature, cubically with the system size, and is free from the time-discretization error. We use it to map out the finite-temperature phase diagram of the spinless t -V model on the honeycomb lattice and observe a suppression of the critical temperature of the charge-density-wave phase in the vicinity of a fermionic quantum critical point.

Vibrational and Thermal Properties of Oxyanionic Crystals

NASA Astrophysics Data System (ADS)

Korabel'nikov, D. V.

2018-03-01

The vibrational and thermal properties of dolomite and alkali chlorates and perchlorates were studied in the gradient approximation of density functional theory using the method of a linear combination of atomic orbitals (LCAO). Long-wave vibration frequencies, IR and Raman spectra, and mode Gruneisen parameters were calculated. Equation-of-state parameters, thermodynamic potentials, entropy, heat capacity, and thermal expansion coefficient were also determined. The thermal expansion coefficient of dolomite was established to be much lower than for chlorates and perchlorates. The temperature dependence of the heat capacity at T > 200 K was shown to be generally governed by intramolecular vibrations.

Nonlocal Symmetries, Consistent Riccati Expansion, and Analytical Solutions of the Variant Boussinesq System

NASA Astrophysics Data System (ADS)

Feng, Lian-Li; Tian, Shou-Fu; Zhang, Tian-Tian; Zhou, Jun

2017-07-01

Under investigation in this paper is the variant Boussinesq system, which describes the propagation of surface long wave towards two directions in a certain deep trough. With the help of the truncated Painlevé expansion, we construct its nonlocal symmetry, Bäcklund transformation, and Schwarzian form, respectively. The nonlocal symmetries can be localised to provide the corresponding nonlocal group, and finite symmetry transformations and similarity reductions are computed. Furthermore, we verify that the variant Boussinesq system is solvable via the consistent Riccati expansion (CRE). By considering the consistent tan-function expansion (CTE), which is a special form of CRE, the interaction solutions between soliton and cnoidal periodic wave are explicitly studied.

Two dimensional electrostatic shock waves in relativistic electron positron ion plasmas

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

Masood, W.; Rizvi, H.

2010-05-15

Ion-acoustic shock waves (IASWs) are studied in an unmagnetized plasma consisting of electrons, positrons and hot ions. In this regard, Kadomtsev-Petviashvili-Burgers (KPB) equation is derived using the small amplitude perturbation expansion method. The dependence of the IASWs on various plasma parameters is numerically investigated. It is observed that ratio of ion to electron temperature, kinematic viscosity, positron concentration, and the relativistic ion streaming velocity affect the structure of the IASW. Limiting case of the KPB equation is also discussed. Stability of KPB equation is also presented. The present investigation may have relevance in the study of electrostatic shock waves inmore » relativistic electron-positron-ion plasmas.« less

Comparison of femtosecond laser ablation of aluminum in water and in air by time-resolved optical diagnosis.

PubMed

Hu, Haofeng; Liu, Tiegen; Zhai, Hongchen

2015-01-26

The dynamic process of material ejection and shock wave evolution during one single femtosecond laser pulse ablation of aluminum target in water and air is experimentally investigated by employing pump-probe technique. Shadowgraphs and digital holograms with high temporal resolution are recorded, which intuitively reveal the characteristics of femtosecond laser ablation in the water-confined environment. The experimental result indicates that the liquid significantly restrict the diffusion of the ejected material, and it has a considerable effect on the attenuation of the shock wave. In addition, the expansion Mach wave generated by the ultrasonic expansion of the shock wave is observed.

Vibration isolation in a free-piston driven expansion tube facility

NASA Astrophysics Data System (ADS)

Gildfind, D. E.; Jacobs, P. A.; Morgan, R. G.

2013-09-01

The stress waves produced by rapid piston deceleration are a fundamental feature of free-piston driven expansion tubes, and wave propagation has to be considered in the design process. For lower enthalpy test conditions, these waves can traverse the tube ahead of critical flow processes, severely interfering with static pressure measurements of the passing flow. This paper details a new device which decouples the driven tube from the free-piston driver, and thus prevents transmission of stress waves. Following successful incorporation of the concept in the smaller X2 facility, it has now been applied to the larger X3 facility, and results for both facilities are presented.

PROTON HEATING BY PICK-UP ION DRIVEN CYCLOTRON WAVES IN THE OUTER HELIOSPHERE: HYBRID EXPANDING BOX SIMULATIONS

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

Hellinger, Petr; Trávníček, Pavel M., E-mail: petr.hellinger@asu.cas.cz

Using a one-dimensional hybrid expanding box model, we investigate properties of the solar wind in the outer heliosphere. We assume a proton–electron plasma with a strictly transverse ambient magnetic field and, aside from the expansion, we take into account the influence of a continuous injection of cold pick-up protons through the charge-exchange process between the solar wind protons and hydrogen of interstellar origin. The injected cold pick-up protons form a ring distribution function, which rapidly becomes unstable, and generate Alfvén cyclotron waves. The Alfvén cyclotron waves scatter pick-up protons to a spherical shell distribution function that thickens over that timemore » owing to the expansion-driven cooling. The Alfvén cyclotron waves heat solar wind protons in the perpendicular direction (with respect to the ambient magnetic field) through cyclotron resonance. At later times, the Alfvén cyclotron waves become parametrically unstable and the generated ion-acoustic waves heat protons in the parallel direction through Landau resonance. The resulting heating of the solar wind protons is efficient on the expansion timescale.« less

Transport of phase space densities through tetrahedral meshes using discrete flow mapping

NASA Astrophysics Data System (ADS)

Bajars, Janis; Chappell, David J.; Søndergaard, Niels; Tanner, Gregor

2017-01-01

Discrete flow mapping was recently introduced as an efficient ray based method determining wave energy distributions in complex built up structures. Wave energy densities are transported along ray trajectories through polygonal mesh elements using a finite dimensional approximation of a ray transfer operator. In this way the method can be viewed as a smoothed ray tracing method defined over meshed surfaces. Many applications require the resolution of wave energy distributions in three-dimensional domains, such as in room acoustics, underwater acoustics and for electromagnetic cavity problems. In this work we extend discrete flow mapping to three-dimensional domains by propagating wave energy densities through tetrahedral meshes. The geometric simplicity of the tetrahedral mesh elements is utilised to efficiently compute the ray transfer operator using a mixture of analytic and spectrally accurate numerical integration. The important issue of how to choose a suitable basis approximation in phase space whilst maintaining a reasonable computational cost is addressed via low order local approximations on tetrahedral faces in the position coordinate and high order orthogonal polynomial expansions in momentum space.

Design of an optomechanical filter based on solid/solid phoxonic crystals

NASA Astrophysics Data System (ADS)

Moradi, Pedram; Bahrami, Ali

2018-03-01

We simulate a phoxonic crystal which shows complete phononic and TM-polarized photonic bandgaps. The constituent materials are tungsten and polymethyl methacrylate, and we obtained these bandgaps with a filling factor of only 28%, which is very compatible with the fabrication method. A cavity was then defined that selects narrow passbands of optical and elastic waves. In order to maximize the quality factor, a defect rod is added in the output waveguide. The final structure filters an optical wavelength of 840 nm (with corresponding frequency of 357 THz) and an elastic frequency of 3.6703 GHz. Simulations are done by using finite element, plane wave expansion, and finite difference time domain methods.

Shock wave polarizations and optical metrics in the Born and the Born–Infeld electrodynamics

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

Minz, Christoph, E-mail: christoph.minz@alumni.tu-berlin.de; Borzeszkowski, Horst-Heino von, E-mail: borzeszk@mailbox.tu-berlin.de; Chrobok, Thoralf, E-mail: tchrobok@mailbox.tu-berlin.de

We analyze the behavior of shock waves in nonlinear theories of electrodynamics. For this, by use of generalized Hadamard step functions of increasing order, the electromagnetic potential is developed in a series expansion near the shock wave front. This brings about a corresponding expansion of the respective electromagnetic field equations which allows for deriving relations that determine the jump coefficients in the expansion series of the potential. We compute the components of a suitable gauge-normalized version of the jump coefficients given for a prescribed tetrad compatible with the shock front foliation. The solution of the first-order jump relations shows that,more » in contrast to linear Maxwell’s electrodynamics, in general the propagation of shock waves in nonlinear theories is governed by optical metrics and polarization conditions describing the propagation of two differently polarized waves (leading to a possible appearance of birefringence). In detail, shock waves are analyzed in the Born and Born–Infeld theories verifying that the Born–Infeld model exhibits no birefringence and the Born model does. The obtained results are compared to those ones found in literature. New results for the polarization of the two different waves are derived for Born-type electrodynamics.« less

Rogue Wave Modes for the Long Wave-Short Wave Resonance and the Derivative Nonlinear Schrödinger Models

NASA Astrophysics Data System (ADS)

Chan, Hiu Ning; Chow, Kwok Wing; Kedziora, David Jacob; Grimshaw, Roger Hamilton James; Ding, Edwin

2014-11-01

Rogue waves are unexpectedly large displacements of the water surface and will obviously pose threat to maritime activities. Recently, the formation of rogue waves is correlated with the onset of modulation instabilities of plane waves of the system. The long wave-short wave resonance and the derivative nonlinear Schrödinger models are considered. They are relevant in a two-layer fluid and a fourth order perturbation expansion of free surface waves respectively. Analytical solutions of rogue wave modes for the two models are derived by the Hirota bilinear method. Properties and amplitudes of these rogue wave modes are investigated. Conditions for modulation instability of the plane waves are shown to be precisely the requirements for the occurrence of rogue waves. In contrast with the nonlinear Schrödinger equation, rogue wave modes for the derivative nonlinear Schrödinger model exist even if the dispersion and cubic nonlinearity are of the opposite signs, provided that a sufficiently strong self-steepening nonlinearity is present. Extensions to the coupled case (multiple waveguides) will be discussed. This work is partially supported by the Research Grants Council General Research Fund Contract HKU 711713E.

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.

A modified symplectic PRK scheme for seismic wave modeling

NASA Astrophysics Data System (ADS)

Liu, Shaolin; Yang, Dinghui; Ma, Jian

2017-02-01

A new scheme for the temporal discretization of the seismic wave equation is constructed based on symplectic geometric theory and a modified strategy. The ordinary differential equation in terms of time, which is obtained after spatial discretization via the spectral-element method, is transformed into a Hamiltonian system. A symplectic partitioned Runge-Kutta (PRK) scheme is used to solve the Hamiltonian system. A term related to the multiplication of the spatial discretization operator with the seismic wave velocity vector is added into the symplectic PRK scheme to create a modified symplectic PRK scheme. The symplectic coefficients of the new scheme are determined via Taylor series expansion. The positive coefficients of the scheme indicate that its long-term computational capability is more powerful than that of conventional symplectic schemes. An exhaustive theoretical analysis reveals that the new scheme is highly stable and has low numerical dispersion. The results of three numerical experiments demonstrate the high efficiency of this method for seismic wave modeling.

Hydrodynamic analysis and shape optimization for vertical axisymmetric wave energy converters

NASA Astrophysics Data System (ADS)

Zhang, Wan-chao; Liu, Heng-xu; Zhang, Liang; Zhang, Xue-wei

2016-12-01

The absorber is known to be vertical axisymmetric for a single-point wave energy converter (WEC). The shape of the wetted surface usually has a great influence on the absorber's hydrodynamic characteristics which are closely linked with the wave power conversion ability. For complex wetted surface, the hydrodynamic coefficients have been predicted traditionally by hydrodynamic software based on the BEM. However, for a systematic study of various parameters and geometries, they are too multifarious to generate so many models and data grids. This paper examines a semi-analytical method of decomposing the complex axisymmetric boundary into several ring-shaped and stepped surfaces based on the boundary discretization method (BDM) which overcomes the previous difficulties. In such case, by using the linear wave theory based on eigenfunction expansion matching method, the expressions of velocity potential in each domain, the added mass, radiation damping and wave excitation forces of the oscillating absorbers are obtained. The good astringency of the hydrodynamic coefficients and wave forces are obtained for various geometries when the discrete number reaches a certain value. The captured wave power for a same given draught and displacement for various geometries are calculated and compared. Numerical results show that the geometrical shape has great effect on the wave conversion performance of the absorber. For absorbers with the same outer radius and draught or displacement, the cylindrical type shows fantastic wave energy conversion ability at some given frequencies, while in the random sea wave, the parabolic and conical ones have better stabilization and applicability in wave power conversion.

Surface acoustic waves in acoustic superlattice lithium niobate coated with a waveguide layer

NASA Astrophysics Data System (ADS)

Yang, G. Y.; Du, J. K.; Huang, B.; Jin, Y. A.; Xu, M. H.

2017-04-01

The effects of the waveguide layer on the band structure of Rayleigh waves are studied in this work based on a one-dimensional acoustic superlattice lithium niobate substrate coated with a waveguide layer. The present phononic structure is formed by the periodic domain-inverted single crystal that is the Z-cut lithium niobate substrate with a waveguide layer on the upper surface. The plane wave expansion method (PWE) is adopted to determine the band gap behavior of the phononic structure and validated by the finite element method (FEM). The FEM is also used to investigate the transmission of Rayleigh waves in the phononic structure with the interdigital transducers by means of the commercial package COMSOL. The results show that, although there is a homogeneous waveguide layer on the surface, the band gap of Rayleigh waves still exist. It is also found that increasing the thickness of the waveguide layer, the band width narrows and the band structure shifts to lower frequency. The present approach can be taken as an efficient tool in designing of phononic structures with waveguide layer.

Jupiters North Equatorial Belt Expansion and Thermal Wave Activity Ahead of Junos Arrival.

NASA Technical Reports Server (NTRS)

Fletcher, L. N.; Orton, G. S.; Sinclair, J. A.; Donnelly, P.; Melin, H.; Rogers, J. H.; Greathouse, T. K.; Kasaba, Y.; Fujiyoshi, T.; Sato, T. M.;

Effect of filling factor on photonic bandgap of chalcogenide photonic crystal

NASA Astrophysics Data System (ADS)

Singh, Rajpal; Suthar, B.; Bhargava, A.

2018-05-01

In the present work, the photonic band structure of 1-D chalcogenide photonic crystal of As2S3/air multilayered structure is calculated using the plane wave expansion method. The study is extended to investigate the effect of filling factor on the photonic bandgap. The increase of bandgap is explained in the study.

Modal Ring Method for the Scattering of Electromagnetic Waves

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1993-01-01

The modal ring method for electromagnetic scattering from perfectly electric conducting (PEC) symmetrical bodies is presented. The scattering body is represented by a line of finite elements (triangular) on its outer surface. The infinite computational region surrounding the body is represented analytically by an eigenfunction expansion. The modal ring method effectively reduces the two dimensional scattering problem to a one-dimensional problem similar to the method of moments. The modal element method is capable of handling very high frequency scattering because it has a highly banded solution matrix.

Evolving Waves and Turbulence in the Outer Corona and Inner Heliosphere: The Accelerating Expanding Box

NASA Astrophysics Data System (ADS)

Tenerani, Anna; Velli, Marco

2017-07-01

Alfvénic fluctuations in the solar wind display many properties reflecting an ongoing nonlinear cascade, e.g., a well-defined spectrum in frequency, together with some characteristics more commonly associated with the linear propagation of waves from the Sun, such as the variation of fluctuation amplitude with distance, dominated by solar wind expansion effects. Therefore, both nonlinearities and expansion must be included simultaneously in any successful model of solar wind turbulence evolution. Because of the disparate spatial scales involved, direct numerical simulations of turbulence in the solar wind represent an arduous task, especially if one wants to go beyond the incompressible approximation. Indeed, most simulations neglect solar wind expansion effects entirely. Here we develop a numerical model to simulate turbulent fluctuations from the outer corona to 1 au and beyond, including the sub-Alfvénic corona. The accelerating expanding box (AEB) extends the validity of previous expanding box models by taking into account both the acceleration of the solar wind and the inhomogeneity of background density and magnetic field. Our method incorporates a background accelerating wind within a magnetic field that naturally follows the Parker spiral evolution using a two-scale analysis in which the macroscopic spatial effect coupling fluctuations with background gradients becomes a time-dependent coupling term in a homogeneous box. In this paper we describe the AEB model in detail and discuss its main properties, illustrating its validity by studying Alfvén wave propagation across the Alfvén critical point.

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.

Space Propulsion and Power

DTIC Science & Technology

2013-03-08

crystals with tunable band gaps possible Refractive index N is imaginary - Bulk Electromagnetic waves cannot propogate But surface plasmons...Directional wave radiation through plasmon resonances Directional wave guiding through mid-band defect wave localization Distribution A: Approved for... acoustic damping, shear- layer instability (PERTURBATION EXPANSION EXAMPLE) classical wave equation for combustion instability: model

Unconventional pairing symmetry of interacting Dirac fermions on a π -flux lattice

NASA Astrophysics Data System (ADS)

Guo, Huaiming; Khatami, Ehsan; Wang, Yao; Devereaux, Thomas P.; Singh, Rajiv R. P.; Scalettar, Richard T.

2018-04-01

The pairing symmetry of interacting Dirac fermions on the π -flux lattice is studied with the determinant quantum Monte Carlo and numerical linked-cluster expansion methods. The s*- (i.e., extended s -) and d -wave pairing symmetries, which are distinct in the conventional square lattice, are degenerate under the Landau gauge. We demonstrate that the dominant pairing channel at strong interactions is an unconventional d s* -wave phase consisting of alternating stripes of s*- and d -wave phases. A complementary mean-field analysis shows that while the s*- and d -wave symmetries individually have nodes in the energy spectrum, the d s* channel is fully gapped. The results represent a new realization of pairing in Dirac systems, connected to the problem of chiral d -wave pairing on the honeycomb lattice, which might be more readily accessed by cold-atom experiments.

Unconventional pairing symmetry of interacting Dirac fermions on a π -flux lattice

DOE PAGES

Guo, Huaiming; Khatami, Ehsan; Wang, Yao; ...

2018-04-20

The pairing symmetry of interacting Dirac fermions on the π-flux lattice is studied with the determinant quantum Monte Carlo and numerical linked-cluster expansion methods. The s*- (i.e., extended s-) and d-wave pairing symmetries, which are distinct in the conventional square lattice, are degenerate under the Landau gauge. We demonstrate that the dominant pairing channel at strong interactions is an unconventional ds*-wave phase consisting of alternating stripes of s*- and d-wave phases. A complementary mean-field analysis shows that while the s*- and d-wave symmetries individually have nodes in the energy spectrum, the ds* channel is fully gapped. The results represent amore » new realization of pairing in Dirac systems, connected to the problem of chiral d-wave pairing on the honeycomb lattice, which might be more readily accessed by cold-atom experiments.« less

Quantitative evaluation of the mechanical strength of titanium/composite bonding using laser-generated shock waves

NASA Astrophysics Data System (ADS)

Ducousso, M.; Bardy, S.; Rouchausse, Y.; Bergara, T.; Jenson, F.; Berthe, L.; Videau, L.; Cuvillier, N.

2018-03-01

Intense acoustic shock waves were applied to evaluate the mechanical strength of structural epoxy bonds between a TA6V4 titanium alloy and a 3D woven carbon/epoxy composite material. Two bond types with different mechanical strengths were obtained from two different adhesive reticulations, at 50% and 90% of conversion, resulting in longitudinal static strengths of 10 and 39 MPa and transverse strengths of 15 and 35 MPa, respectively. The GPa shock waves were generated using ns-scale intense laser pulses and reaction principles to a confined plasma expansion. Simulations taking into account the laser-matter interaction, plasma relaxation, and non-linear shock wave propagation were conducted to aid interpretation of the experiments. Good correlations were obtained between the experiments and the simulation and between different measurement methods of the mechanical strength (normalized tests vs laser-generated shock waves). Such results open the door toward certification of structural bonding.

Quasilinear theory of plasma turbulence. Origins, ideas, and evolution of the method

NASA Astrophysics Data System (ADS)

Bakunin, O. G.

2018-01-01

The quasilinear method of describing weak plasma turbulence is one of the most important elements of current plasma physics research. Today, this method is not only a tool for solving individual problems but a full-fledged theory of general physical interest. The author's objective is to show how the early ideas of describing the wave-particle interactions in a plasma have evolved as a result of the rapid expansion of the research interests of turbulence and turbulent transport theorists.

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.

A Simple Way of Modeling the Expansion of the Universe: What Does Light Tell Us?

ERIC Educational Resources Information Center

Coban, Gul Unal; Sengoren, Serap Kaya

2011-01-01

The purpose of this activity is to model the expansion of the universe by investigating the behavior of water waves. It is designed for students in the upper grades of physics and physical science who are learning about the wave nature of light and are ready to discover such important questions about science. The article explains first the Doppler…

Variation of Time Domain Failure Probabilities of Jack-up with Wave Return Periods

NASA Astrophysics Data System (ADS)

Idris, Ahmad; Harahap, Indra S. H.; Ali, Montassir Osman Ahmed

2018-04-01

This study evaluated failure probabilities of jack up units on the framework of time dependent reliability analysis using uncertainty from different sea states representing different return period of the design wave. Surface elevation for each sea state was represented by Karhunen-Loeve expansion method using the eigenfunctions of prolate spheroidal wave functions in order to obtain the wave load. The stochastic wave load was propagated on a simplified jack up model developed in commercial software to obtain the structural response due to the wave loading. Analysis of the stochastic response to determine the failure probability in excessive deck displacement in the framework of time dependent reliability analysis was performed by developing Matlab codes in a personal computer. Results from the study indicated that the failure probability increases with increase in the severity of the sea state representing a longer return period. Although the results obtained are in agreement with the results of a study of similar jack up model using time independent method at higher values of maximum allowable deck displacement, it is in contrast at lower values of the criteria where the study reported that failure probability decreases with increase in the severity of the sea state.

Inclusive breakup calculations in angular momentum basis: Application to 7Li+58Ni

NASA Astrophysics Data System (ADS)

Lei, Jin

2018-03-01

The angular momentum basis method is introduced to solve the inclusive breakup problem within the model proposed by Ichimura, Austern, and Vincent [Phys. Rev. C 32, 431 (1985), 10.1103/PhysRevC.32.431]. This method is based on the geometric transformation between different Jacobi coordinates, in which the particle spins can be included in a natural and efficient way. To test the validity of this partial wave expansion method, a benchmark calculation is done comparing with the one given by Lei and Moro [Phys. Rev. C 92, 044616 (2015), 10.1103/PhysRevC.92.044616]. In addition, using the distorted-wave Born approximation version of the IAV model, applications to 7Li+58Ni reactions at energies around Coulomb barrier are presented and compared with available data.

State-vector formalism and the Legendre polynomial solution for modelling guided waves in anisotropic plates

NASA Astrophysics Data System (ADS)

Zheng, Mingfang; He, Cunfu; Lu, Yan; Wu, Bin

2018-01-01

We presented a numerical method to solve phase dispersion curve in general anisotropic plates. This approach involves an exact solution to the problem in the form of the Legendre polynomial of multiple integrals, which we substituted into the state-vector formalism. In order to improve the efficiency of the proposed method, we made a special effort to demonstrate the analytical methodology. Furthermore, we analyzed the algebraic symmetries of the matrices in the state-vector formalism for anisotropic plates. The basic feature of the proposed method was the expansion of field quantities by Legendre polynomials. The Legendre polynomial method avoid to solve the transcendental dispersion equation, which can only be solved numerically. This state-vector formalism combined with Legendre polynomial expansion distinguished the adjacent dispersion mode clearly, even when the modes were very close. We then illustrated the theoretical solutions of the dispersion curves by this method for isotropic and anisotropic plates. Finally, we compared the proposed method with the global matrix method (GMM), which shows excellent agreement.

New exact solutions for a discrete electrical lattice using the analytical methods

NASA Astrophysics Data System (ADS)

Manafian, Jalil; Lakestani, Mehrdad

2018-03-01

This paper retrieves soliton solutions to an equation in nonlinear electrical transmission lines using the semi-inverse variational principle method (SIVPM), the \\exp(-Ω(ξ)) -expansion method (EEM) and the improved tan(φ/2) -expansion method (ITEM), with the aid of the symbolic computation package Maple. As a result, the SIVPM, EEM and ITEM methods are successfully employed and some new exact solitary wave solutions are acquired in terms of kink-singular soliton solution, hyperbolic solution, trigonometric solution, dark and bright soliton solutions. All solutions have been verified back into their corresponding equations with the aid of the Maple package program. We depicted the physical explanation of the extracted solutions with the choice of different parameters by plotting some 2D and 3D illustrations. Finally, we show that the used methods are robust and more efficient than other methods. More importantly, the solutions found in this work can have significant applications in telecommunication systems where solitons are used to codify data.

The Space-Time Conservation Element and Solution Element Method-A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws. 2; Numerical Simulation of Shock Waves and Contact Discontinuities

NASA Technical Reports Server (NTRS)

Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung

1998-01-01

Without resorting to special treatment for each individual test case, the 1D and 2D CE/SE shock-capturing schemes described previously (in Part I) are used to simulate flows involving phenomena such as shock waves, contact discontinuities, expansion waves and their interactions. Five 1D and six 2D problems are considered to examine the capability and robustness of these schemes. Despite their simple logical structures and low computational cost (for the 2D CE/SE shock-capturing scheme, the CPU time is about 2 micro-secs per mesh point per marching step on a Cray C90 machine), the numerical results, when compared with experimental data, exact solutions or numerical solutions by other methods, indicate that these schemes can accurately resolve shock and contact discontinuities consistently.

The Formation and Early Evolution of a CME and the Associated Shock on 2014 January 8

NASA Astrophysics Data System (ADS)

Wan, Linfeng; Cheng, Xin; Shi, Tong; Su, Wei; Ding, Mingde

2017-08-01

We study the formation and early evolution of a limb coronal mass ejection (CME) and its associated shock wave that occurred on 2014 January 8. The extreme ultraviolet (EUV) images provided by AIA on board \\textit{Solar Dynamics Observatory} disclose that the CME first appears as a bubble-like structure. Subsequently, its expansion forms the CME and causes a quasi-circular EUV wave. Both the CME and the wave front are clearly visible at all of the AIA EUV passbands. Through a detailed kinematical analysis, it is found that the expansion of the CME undergoes two phases: a first phase with a strong but transient lateral over-expansion followed by a second phase with a self-similar expansion. The temporal evolution of the expansion velocity coincides very well with the variation of the 25--50 keV hard X-ray (HXR) flux of the associated flare, which indicates that magnetic reconnection most likely plays an important role in driving the expansion. Moreover, we find that, when the velocity of the CME reaches $\\sim$600 km s$^{-1}$, the EUV wave starts to evolve into a shock wave, which is evidenced by the appearance of a type II radio burst. Interestingly, we also notice an unusual solar radio signal at $\\sim$4 GHz that is similar to the pattern of a type II radio burst but drifts to higher frequencies at a rate of $\\sim$0.3 MHz per second during about 7 minutes. Its derived density is $\\sim$5$\\times$10$^{10}$ cm$^{-3}$ and increases slowly with time. Joint imaging observations of HXR and EUV help to locate the loop-top region and calculate its thermal proprieties, including slowly increasing densities ($\\sim$5$\\times$10$^{10}$ cm$^{-3}$) and temperatures ($\\sim$14 MK). The similar results obtained from two different ways above imply the possibility of this scenario: plasma blobs that are ejected along the current sheet via magnetic reconnection collide with underlying flare loops that are undergoing chromospheric evaporation. Finally, we also study the thermal properties of the CME and the EUV wave. We find that the plasma in the CME leading front and the wave front has a temperature of $\\sim$2 MK, while that in the CME core region and the flare region has a much higher temperature of $\\ge$8 MK.

Simulations of wave propagation and disorder in 3D non-close-packed colloidal photonic crystals with low refractive index contrast.

PubMed

Glushko, O; Meisels, R; Kuchar, F

2010-03-29

The plane-wave expansion method (PWEM), the multiple-scattering method (MSM) and the 3D finite-difference time-domain method (FDTD) are applied for simulations of propagation of electromagnetic waves through 3D colloidal photonic crystals. The system investigated is not a "usual" artificial opal with close-packed fcc lattice but a dilute bcc structure which occurs due to long-range repulsive interaction between electrically charged colloidal particles during the growth process. The basic optical properties of non-close-packed colloidal PhCs are explored by examining the band structure and reflection spectra for a bcc lattice of silica spheres in an aqueous medium. Finite size effects and correspondence between the Bragg model, band structure and reflection spectra are discussed. The effects of size, positional and missing-spheres disorder are investigated. In addition, by analyzing the results of experimental work we show that the fabricated structures have reduced plane-to-plane distance probably due to the effect of gravity during growth.

Detecting Rhythms in Time Series with RAIN

PubMed Central

Thaben, Paul F.; Westermark, Pål O.

2014-01-01

A fundamental problem in research on biological rhythms is that of detecting and assessing the significance of rhythms in large sets of data. Classic methods based on Fourier theory are often hampered by the complex and unpredictable characteristics of experimental and biological noise. Robust nonparametric methods are available but are limited to specific wave forms. We present RAIN, a robust nonparametric method for the detection of rhythms of prespecified periods in biological data that can detect arbitrary wave forms. When applied to measurements of the circadian transcriptome and proteome of mouse liver, the sets of transcripts and proteins with rhythmic abundances were significantly expanded due to the increased detection power, when we controlled for false discovery. Validation against independent data confirmed the quality of these results. The large expansion of the circadian mouse liver transcriptomes and proteomes reflected the prevalence of nonsymmetric wave forms and led to new conclusions about function. RAIN was implemented as a freely available software package for R/Bioconductor and is presently also available as a web interface. PMID:25326247

Electromagnetic and scalar diffraction by a right-angled wedge with a uniform surface impedance

NASA Technical Reports Server (NTRS)

Hwang, Y. M.

1974-01-01

The diffraction of an electromagnetic wave by a perfectly-conducting right-angled wedge with one surface covered by a dielectric slab or absorber is considered. The effect of the coated surface is approximated by a uniform surface impedance. The solution of the normally incident electromagnetic problem is facilitated by introducing two scalar fields which satisfy a mixed boundary condition on one surface of the wedge and a Neumann of Dirichlet boundary condition on the other. A functional transformation is employed to simplify the boundary conditions so that eigenfunction expansions can be obtained for the resulting Green's functions. The eigenfunction expansions are transformed into the integral representations which then are evaluated asymptotically by the modified Pauli-Clemmow method of steepest descent. A far zone approximation is made to obtain the scattered field from which the diffraction coefficient is found for scalar plane, cylindrical or sperical wave incident on the edge. With the introduction of a ray-fixed coordinate system, the dyadic diffraction coefficient for plane or cylindrical EM waves normally indicent on the edge is reduced to the sum of two dyads which can be written alternatively as a 2 X 2 diagonal matrix.

Collective pulsatile expansion and swirls in proliferating tumor tissue

NASA Astrophysics Data System (ADS)

Yang, Taeseok Daniel; Kim, Hyun; Yoon, Changhyeong; Baek, Seung-Kuk; Lee, Kyoung J.

2016-10-01

Understanding the dynamics of expanding biological tissues is essential to a wide range of phenomena in morphogenesis, wound healing and tumor proliferation. Increasing evidence suggests that many of the relevant phenomena originate from complex collective dynamics, inherently nonlinear, of constituent cells that are physically active. Here, we investigate thin disk layers of proliferating, cohesive, monoclonal tumor cells and report the discovery of macroscopic, periodic, soliton-like mechanical waves with which cells are collectively ratcheting, as in the traveling-wave chemotaxis of dictyostelium discodium amoeba cells. The relevant length-scale of the waves is remarkably large (∼1 mm), compared to the thickness of a mono-layer tissue (∼ 10 μ {{m}}). During the tissue expansion, the waves are found to repeat several times with a quite well defined period of approximately 4 h. Our analyses suggest that the waves are initiated by the leading edge that actively pulls the tissue in the outward direction, while the cells within the bulk tissue do not seem to generate a strong self-propulsion. Subsequently, we demonstrate that a simple mathematical model chain of nonlinear springs that are constantly pulled in the outward direction at the leading edge recapitulates the observed phenomena well. As the areal cell density becomes too high, the tissue expansion stalls and the periodic traveling waves yield to multiple swirling vortices. Cancer cells are known to possess a broad spectrum of migration mechanisms. Yet, our finding has established a new unusual mode of tumor tissue expansion, and it may be equally applicable for many different expanding thin layers of cell tissues.

Amplification of seismic waves beneath active volcanoes

NASA Astrophysics Data System (ADS)

Navon, O.; Lensky, N. G.; Collier, L.; Neuberg, J.; Lyakhovsky, V.

2003-04-01

Long-period (LP) seismic events are typical for many volcanoes and are attributed to energy leaking from waves traveling along the conduit - country-rock interface. While the wave propagation is well understood, their actual trigger mechanism and their energy source are not. Here we test the hypothesis that energy may be supplied by volatile-release from a supersaturated melt. If bubbles are initially in equilibrium with the melt in the conduit, and the melt is suddenly decompressed, the transfer of volatiles from the supersaturated melt into the bubbles transforms stored potential energy into expansion work. For example, small dome collapse, opening of a crack or a displacement along the brittle part of the conduit may decompress the magma by a few bars and create the needed supersaturation. This energy is released over the timescale of accelerated expansion, which is longer than a typical LP event. Following decompression, when the transfer of volatiles into bubbles is fast enough, expansion accelerates and the bulk viscosity of the bubbly magma is negative (Lensky et al., 2002). New calculations show that under such conditions a sinusoidal P-wave is amplified. We note that seismic waves created by tectonic earthquakes that are not associated with net decompression, do not lead to net release of volatiles or to net expansion. In this case, the bulk viscosity is positive and waves traveling through the magma should attenuate. The proposed model explains how weak seismic signals may be amplified as they travel through a conduit that contains supersaturated bubbly magma. It provides the general framework for amplifying volcanic seismicity such as long-period events.

CRE Solvability, Nonlocal Symmetry and Exact Interaction Solutions of the Fifth-Order Modified Korteweg-de Vries Equation

NASA Astrophysics Data System (ADS)

Cheng, Wen-Guang; Qiu, De-Qin; Yu, Bo

2017-06-01

This paper is concerned with the fifth-order modified Korteweg-de Vries (fmKdV) equation. It is proved that the fmKdV equation is consistent Riccati expansion (CRE) solvable. Three special form of soliton-cnoidal wave interaction solutions are discussed analytically and shown graphically. Furthermore, based on the consistent tanh expansion (CTE) method, the nonlocal symmetry related to the consistent tanh expansion (CTE) is investigated, we also give the relationship between this kind of nonlocal symmetry and the residual symmetry which can be obtained with the truncated Painlevé method. We further study the spectral function symmetry and derive the Lax pair of the fmKdV equation. The residual symmetry can be localized to the Lie point symmetry of an enlarged system and the corresponding finite transformation group is computed. Supported by National Natural Science Foundation of China under Grant No. 11505090, and Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009

An improved wave rotor refrigerator using an outside gas flow for recycling the expansion work

NASA Astrophysics Data System (ADS)

Zhao, J.; Hu, D.

2017-03-01

To overcome the bottleneck of traditional gas wave refrigeration, an improved wave rotor refrigerator (WRR) cycle has been proposed, in which the expansion work was recycled during the process of refrigeration. Thermodynamic analysis of the two cycles shows that the refrigeration efficiency of the improved WRR cycle has been greatly increased compared with the traditional WRR. The performance of an improved WRR was investigated by adjusting the major operational parameters, such as the rotational speed of the wave rotor, port size, and inflow overpressure. The experimental results show that pressure loss can be reduced by nearly 40 % in this improved refrigeration system. Meanwhile, a two-dimensional numerical simulation was performed to understand the wave interactions that take place inside the rotor channels.

ISCFD Nagoya 1989 - International Symposium on Computational Fluid Dynamics, 3rd, Nagoya, Japan, Aug. 28-31, 1989, Technical Papers

NASA Astrophysics Data System (ADS)

Recent advances in computational fluid dynamics are discussed in reviews and reports. Topics addressed include large-scale LESs for turbulent pipe and channel flows, numerical solutions of the Euler and Navier-Stokes equations on parallel computers, multigrid methods for steady high-Reynolds-number flow past sudden expansions, finite-volume methods on unstructured grids, supersonic wake flow on a blunt body, a grid-characteristic method for multidimensional gas dynamics, and CIC numerical simulation of a wave boundary layer. Consideration is given to vortex simulations of confined two-dimensional jets, supersonic viscous shear layers, spectral methods for compressible flows, shock-wave refraction at air/water interfaces, oscillatory flow in a two-dimensional collapsible channel, the growth of randomness in a spatially developing wake, and an efficient simplex algorithm for the finite-difference and dynamic linear-programming method in optimal potential control.

Accelerated Cartesian expansion (ACE) based framework for the rapid evaluation of diffusion, lossy wave, and Klein-Gordon potentials

DOE PAGES

Baczewski, Andrew David; Vikram, Melapudi; Shanker, Balasubramaniam; ...

2010-08-27

Diffusion, lossy wave, and Klein–Gordon equations find numerous applications in practical problems across a range of diverse disciplines. The temporal dependence of all three Green’s functions are characterized by an infinite tail. This implies that the cost complexity of the spatio-temporal convolutions, associated with evaluating the potentials, scales as O(N s 2N t 2), where N s and N t are the number of spatial and temporal degrees of freedom, respectively. In this paper, we discuss two new methods to rapidly evaluate these spatio-temporal convolutions by exploiting their block-Toeplitz nature within the framework of accelerated Cartesian expansions (ACE). The firstmore » scheme identifies a convolution relation in time amongst ACE harmonics and the fast Fourier transform (FFT) is used for efficient evaluation of these convolutions. The second method exploits the rank deficiency of the ACE translation operators with respect to time and develops a recursive numerical compression scheme for the efficient representation and evaluation of temporal convolutions. It is shown that the cost of both methods scales as O(N sN tlog 2N t). Furthermore, several numerical results are presented for the diffusion equation to validate the accuracy and efficacy of the fast algorithms developed here.« less

Pump-probe imaging of the fs-ps-ns dynamics during femtosecond laser Bessel beam drilling in PMMA.

PubMed

Yu, Yanwu; Jiang, Lan; Cao, Qiang; Xia, Bo; Wang, Qingsong; Lu, Yongfeng

2015-12-14

A pump-probe shadowgraph imaging technique was used to reveal the femtosecond-picosecond-nanosecond multitimescale fundamentals of high-quality, high-aspect-ratio (up to 287:1) microhole drilling in poly-methyl-meth-acrylate (PMMA) by a single-shot femtosecond laser Bessel beam. The propagation of Bessel beam in PMMA (at 1.98 × 10⁸ m/s) and it induced cylindrical pressure wave expansion (at 3000-3950 m/s in radius) were observed during drilling processes. Also, it was unexpectedly found that the expansion of the cylindrical pressure wave in PMMA showed a linear relation with time and was insensitive to the laser energy fluctuation, quite different from the case in air. It was assumed that the energy insensitivity was due to the anisotropy of wave expansion in PMMA and the ambient air.

Detonative propagation and accelerative expansion of the Crab Nebula shock front.

PubMed

Gao, Yang; Law, Chung K

2011-10-21

The accelerative expansion of the Crab Nebula's outer envelope is a mystery in dynamics, as a conventional expanding blast wave decelerates when bumping into the surrounding interstellar medium. Here we show that the strong relativistic pulsar wind bumping into its surrounding nebula induces energy-generating processes and initiates a detonation wave that propagates outward to form the current outer edge, namely, the shock front, of the nebula. The resulting detonation wave, with a reactive downstream, then provides the needed power to maintain propagation of the shock front. Furthermore, relaxation of the curvature-induced reduction of the propagation velocity from the initial state of formation to the asymptotic, planar state of Chapman-Jouguet propagation explains the observed accelerative expansion. Potential richness in incorporating reactive fronts in the description of various astronomical phenomena is expected. © 2011 American Physical Society

2D instabilities of surface gravity waves on a linear shear current

NASA Astrophysics Data System (ADS)

Francius, Marc; Kharif, Christian

2016-04-01

Periodic 2D surface water waves propagating steadily on a rotational current have been studied by many authors (see [1] and references therein). Although the recent important theoretical developments have confirmed that periodic waves can exist over flows with arbitrary vorticity, their stability and their nonlinear evolution have not been much studied extensively so far. In fact, even in the rather simple case of uniform vorticity (linear shear), few papers have been published on the effect of a vertical shear current on the side-band instability of a uniform wave train over finite depth. In most of these studies [2-5], asymptotic expansions and multiple scales method have been used to obtain envelope evolution equations, which allow eventually to formulate a condition of (linear) instability to long modulational perturbations. It is noted here that this instability is often referred in the literature as the Benjamin-Feir or modulational instability. In the present study, we consider the linear stability of finite amplitude two-dimensional, periodic water waves propagating steadily on the free surface of a fluid with constant vorticity and finite depth. First, the steadily propagating surface waves are computed with steepness up to very close to the highest, using a Fourier series expansions and a collocation method, which constitutes a simple extension of Fenton's method [6] to the cases with a linear shear current. Then, the linear stability of these permanent waves to infinitesimal 2D perturbations is developed from the fully nonlinear equations in the framework of normal modes analysis. This linear stability analysis is an extension of [7] to the case of waves in the presence of a linear shear current and permits the determination of the dominant instability as a function of depth and vorticity for a given steepness. The numerical results are used to assess the accuracy of the vor-NLS equation derived in [5] for the characteristics of modulational instabilities due to resonant four-wave interactions, as well as to study the influence of vorticity and nonlinearity on the characteristics of linear instabilities due to resonant five-wave and six-wave interactions. Depending on the dimensionless depth, superharmonic instabilities due to five-wave interactions can become dominant with increasing positive vorticiy. Acknowledgments: This work was supported by the Direction Générale de l'Armement and funded by the ANR project n°. ANR-13-ASTR-0007. References [1] A. Constantin, Two-dimensionality of gravity water flows of constant non-zero vorticity beneath a surface wave train, Eur. J. Mech. B/Fluids, 2011, 30, 12-16. [2] R. S. Johnson, On the modulation of water waves on shear flows, Proc. Royal Soc. Lond. A., 1976, 347, 537-546. [3] M. Oikawa, K. Chow, D. J. Benney, The propagation of nonlinear wave packets in a shear flow with a free surface, Stud. Appl. Math., 1987, 76, 69-92. [4] A. I Baumstein, Modulation of gravity waves with shear in water, Stud. Appl. Math., 1998, 100, 365-90. [5] R. Thomas, C. Kharif, M. Manna, A nonlinear Schrödinger equation for water waves on finite depth with constant vorticity, Phys. Fluids, 2012, 24, 127102. [6] M. M Rienecker, J. D Fenton, A Fourier approximation method for steady water waves , J. Fluid Mech., 1981, 104, 119-137 [7] M. Francius, C. Kharif, Three-dimensional instabilities of periodic gravity waves in shallow water, J. Fluid Mech., 2006, 561, 417-437

General high-order breathers and rogue waves in the (3 + 1) -dimensional KP-Boussinesq equation

NASA Astrophysics Data System (ADS)

Sun, Baonan; Wazwaz, Abdul-Majid

2018-11-01

In this work, we investigate the (3 + 1) -dimensional KP-Boussinesq equation, which can be used to describe the nonlinear dynamic behavior in scientific and engineering applications. We derive general high-order soliton solutions by using the Hirota's bilinear method combined with the perturbation expansion technique. We also obtain periodic solutions comprising of high-order breathers, periodic line waves, and mixed solutions consisting of breathers and periodic line waves upon selecting particular parameter constraints of the obtained soliton solutions. Furthermore, smooth rational solutions are generated by taking a long wave limit of the soliton solutions. These smooth rational solutions include high-order rogue waves, high-order lumps, and hybrid solutions consisting of lumps and line rogue waves. To better understand the dynamical behaviors of these solutions, we discuss some illustrative graphical analyses. It is expected that our results can enrich the dynamical behavior of the (3 + 1) -dimensional nonlinear evolution equations of other forms.

Complexiton and solitary wave solutions of the coupled nonlinear Maccari’s system using two integration schemes

NASA Astrophysics Data System (ADS)

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

2018-01-01

In this paper, we consider a coupled nonlinear Maccari’s system (CNMS) which describes the motion of isolated waves localized in a small part of space. There are some integration tools that are adopted to retrieve the solitary wave solutions. They are the modified F-Expansion and the generalized projective Riccati equation methods. Topological, non-topological, complexiton, singular and trigonometric function solutions are derived. A comparison between the results in this paper and the well-known results in the literature is also given. The derived structures of the obtained solutions offer a rich platform to study the nonlinear CNMS. Numerical simulation of the obtained solutions are presented with interesting figures showing the physical meaning of the solutions.

Nonuniform Expansion of the Youngest Galactic Supernova Remnant G1.9+0.3

NASA Technical Reports Server (NTRS)

Borkowski, Kazimierz J.; Reynolds, Stephen P.; Green, David A.; Hwang, Una; Petre, Robert; Krishnamurthy, Kalyani; Willett, Rebecca

2014-01-01

We report measurements of the X-ray expansion of the youngest Galactic supernova remnant, G1.9+0.3, using Chandra observations in 2007, 2009, and 2011. The measured rates strongly deviate from uniform expansion, decreasing radially by about 60 along the X-ray bright SE-NW axis from 0.84 plus or minus 0.06% yr(exp -1) to 0.52% plus or minus 0.03 yr(exp -1). This corresponds to undecelerated ages of 120-190 yr, confirming the young age of G1.9+0.3 and implying a significant deceleration of the blast wave. The synchrotron-dominated X-ray emission brightens at a rate of 1.9% plus or minus 0.4% yr(exp -1). We identify bright outer and inner rims with the blast wave and reverse shock, respectively. Sharp density gradients in either the ejecta or ambient medium are required to produce the sudden deceleration of the reverse shock or the blast wave implied by the large spread in expansion ages. The blast wave could have been decelerated recently by an encounter with a modest density discontinuity in the ambient medium, such as may be found at a wind termination shock, requiring strong mass loss in the progenitor.

Stellar winds driven by Alfven waves

NASA Technical Reports Server (NTRS)

Belcher, J. W.; Olbert, S.

1973-01-01

Models of stellar winds were considered in which the dynamic expansion of a corona is driven by Alfven waves propagating outward along radial magnetic field lines. In the presence of Alfven waves, a coronal expansion can exist for a broad range of reference conditions which would, in the absence of waves, lead to static configurations. Wind models in which the acceleration mechanism is due to Alfven waves alone and exhibit lower mass fluxes and higher energies per particle are compared to wind models in which the acceleration is due to thermal processes. For example, winds driven by Alfven waves exhibit streaming velocities at infinity which may vary between the escape velocity at the coronal base and the geometrical mean of the escape velocity and the speed of light. Upper and lower limits were derived for the allowed energy fluxes and mass fluxes associated with these winds.

A combined analytical and numerical analysis of the flow-acoustic coupling in a cavity-pipe system

NASA Astrophysics Data System (ADS)

Langthjem, Mikael A.; Nakano, Masami

2018-05-01

The generation of sound by flow through a closed, cylindrical cavity (expansion chamber) accommodated with a long tailpipe is investigated analytically and numerically. The sound generation is due to self-sustained flow oscillations in the cavity. These oscillations may, in turn, generate standing (resonant) acoustic waves in the tailpipe. The main interest of the paper is in the interaction between these two sound sources. An analytical, approximate solution of the acoustic part of the problem is obtained via the method of matched asymptotic expansions. The sound-generating flow is represented by a discrete vortex method, based on axisymmetric vortex rings. It is demonstrated through numerical examples that inclusion of acoustic feedback from the tailpipe is essential for a good representation of the sound characteristics.

Transition operators in electromagnetic-wave diffraction theory. II - Applications to optics

NASA Technical Reports Server (NTRS)

Hahne, G. E.

1993-01-01

The theory developed by Hahne (1992) for the diffraction of time-harmonic electromagnetic waves from fixed obstacles is briefly summarized and extended. Applications of the theory are considered which comprise, first, a spherical harmonic expansion of the so-called radiation impedance operator in the theory, for a spherical surface, and second, a reconsideration of familiar short-wavelength approximation from the new standpoint, including a derivation of the so-called physical optics method on the basis of quasi-planar approximation to the radiation impedance operator, augmented by the method of stationary phase. The latter includes a rederivation of the geometrical optics approximation for the complete Green's function for the electromagnetic field in the presence of a smooth- and a convex-surfaced perfectly electrically conductive obstacle.

Fully resolved simulations of expansion waves propagating into particle beds

NASA Astrophysics Data System (ADS)

Marjanovic, Goran; Hackl, Jason; Annamalai, Subramanian; Jackson, Thomas; Balachandar, S.

2017-11-01

There is a tremendous amount of research that has been done on compression waves and shock waves moving over particles but very little concerning expansion waves. Using 3-D direct numerical simulations, this study will explore expansion waves propagating into fully resolved particle beds of varying volume fractions and geometric arrangements. The objectives of these simulations are as follows: 1) To fully resolve all (1-way coupled) forces on the particles in a time varying flow and 2) to verify state-of-the-art drag models for such complex flows. We will explore a range of volume fractions, from very low ones that are similar to single particle flows, to higher ones where nozzling effects are observed between neighboring particles. Further, we will explore two geometric arrangements: body centered cubic and face centered cubic. We will quantify the effects that volume fraction and geometric arrangement plays on the drag forces and flow fields experienced by the particles. These results will then be compared to theoretical predictions from a model based on the generalized Faxen's theorem. This work was supported in part by the U.S. Department of Energy under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.

Solving three-body-breakup problems with outgoing-flux asymptotic conditions

NASA Astrophysics Data System (ADS)

Randazzo, J. M.; Buezas, F.; Frapiccini, A. L.; Colavecchia, F. D.; Gasaneo, G.

2011-11-01

An analytically solvable three-body collision system (s wave) model is used to test two different theoretical methods. The first one is a configuration interaction expansion of the scattering wave function using a basis set of Generalized Sturmian Functions (GSF) with purely outgoing flux (CISF), introduced recently in A. L. Frapicinni, J. M. Randazzo, G. Gasaneo, and F. D. Colavecchia [J. Phys. B: At. Mol. Opt. Phys.JPAPEH0953-407510.1088/0953-4075/43/10/101001 43, 101001 (2010)]. The second one is a finite element method (FEM) calculation performed with a commercial code. Both methods are employed to analyze different ways of modeling the asymptotic behavior of the wave function in finite computational domains. The asymptotes can be simulated very accurately by choosing hyperspherical or rectangular contours with the FEM software. In contrast, the CISF method can be defined both in an infinite domain or within a confined region in space. We found that the hyperspherical (rectangular) FEM calculation and the infinite domain (confined) CISF evaluation are equivalent. Finally, we apply these models to the Temkin-Poet approach of hydrogen ionization.

Regularized Chapman-Enskog expansion for scalar conservation laws

NASA Technical Reports Server (NTRS)

Schochet, Steven; Tadmor, Eitan

1990-01-01

Rosenau has recently proposed a regularized version of the Chapman-Enskog expansion of hydrodynamics. This regularized expansion resembles the usual Navier-Stokes viscosity terms at law wave-numbers, but unlike the latter, it has the advantage of being a bounded macroscopic approximation to the linearized collision operator. The behavior of Rosenau regularization of the Chapman-Enskog expansion (RCE) is studied in the context of scalar conservation laws. It is shown that thie RCE model retains the essential properties of the usual viscosity approximation, e.g., existence of traveling waves, monotonicity, upper-Lipschitz continuity..., and at the same time, it sharpens the standard viscous shock layers. It is proved that the regularized RCE approximation converges to the underlying inviscid entropy solution as its mean-free-path epsilon approaches 0, and the convergence rate is estimated.

Long Waves and Journalism Ideology in America, 1835-1985.

ERIC Educational Resources Information Center

Kaul, Arthur J.; McKerns, Joseph P.

Framed by the heuristic device of "long waves" of capitalist development, journalism ideology is historically anchored to competitive media economics. (Long waves are 50-year economic cycles comprised of alternating 25-year periods of economic expansion followed by contraction periods.) With each long wave, a new institutional ecology…

Damping of gravitational waves by matter

NASA Astrophysics Data System (ADS)

Baym, Gordon; Patil, Subodh P.; Pethick, C. J.

2017-10-01

We develop a unified description, via the Boltzmann equation, of damping of gravitational waves by matter, incorporating collisions. We identify two physically distinct damping mechanisms—collisional and Landau damping. We first consider damping in flat spacetime, and then generalize the results to allow for cosmological expansion. In the first regime, maximal collisional damping of a gravitational wave, independent of the details of the collisions in the matter is, as we show, significant only when its wavelength is comparable to the size of the horizon. Thus damping by intergalactic or interstellar matter for all but primordial gravitational radiation can be neglected. Although collisions in matter lead to a shear viscosity, they also act to erase anisotropic stresses, thus suppressing the damping of gravitational waves. Damping of primordial gravitational waves remains possible. We generalize Weinberg's calculation of gravitational wave damping, now including collisions and particles of finite mass, and interpret the collisionless limit in terms of Landau damping. While Landau damping of gravitational waves cannot occur in flat spacetime, the expansion of the universe allows such damping by spreading the frequency of a gravitational wave of given wave vector.

Generalized thermoelastic wave band gaps in phononic crystals without energy dissipation

NASA Astrophysics Data System (ADS)

Wu, Ying; Yu, Kaiping; Li, Xiao; Zhou, Haotian

2016-01-01

We present a theoretical investigation of the thermoelastic wave propagation in the phononic crystals in the context of Green-Nagdhi theory by taking thermoelastic coupling into account. The thermal field is assumed to be steady. Thermoelastic wave band structures of 3D and 2D are derived by using the plane wave expansion method. For the 2D problem, the anti-plane shear mode is not affected by the temperature difference. Thermoelastic wave bands of the in-plane x-y mode are calculated for lead/silicone rubber, aluminium/silicone rubber, and aurum/silicone rubber phononic crystals. The new findings in the numerical results indicate that the thermoelastic wave bands are composed of the pure elastic wave bands and the thermal wave bands, and that the thermal wave bands can serve as the low boundary of the first band gap when the filling ratio is low. In addition, for the lead/silicone rubber phononic crystals the effects of lattice type (square, rectangle, regular triangle, and hexagon) and inclusion shape (circle, oval, and square) on the normalized thermoelastic bandwidth and the upper/lower gap boundaries are analysed and discussed. It is concluded that their effects on the thermoelastic wave band structure are remarkable.

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.

Electron- and positron-molecule scattering: development of the molecular convergent close-coupling method

NASA Astrophysics Data System (ADS)

Zammit, Mark C.; Fursa, Dmitry V.; Savage, Jeremy S.; Bray, Igor

2017-06-01

Starting from first principles, this tutorial describes the development of the adiabatic-nuclei convergent close-coupling (CCC) method and its application to electron and (single-centre) positron scattering from diatomic molecules. We give full details of the single-centre expansion CCC method, namely the formulation of the molecular target structure; solving the momentum-space coupled-channel Lippmann-Schwinger equation; deriving adiabatic-nuclei cross sections and calculating V-matrix elements. Selected results are presented for electron and positron scattering from molecular hydrogen H2 and electron scattering from the vibrationally excited molecular hydrogen ion {{{H}}}2+ and its isotopologues (D2 +, {{{T}}}2+, HD+, HT+ and TD+). Convergence in both the close-coupling (target state) and projectile partial-wave expansions of fixed-nuclei electron- and positron-molecule scattering calculations is demonstrated over a broad energy-range and discussed in detail. In general, the CCC results are in good agreement with experiments.

Tunnel Vision Prismatic Field Expansion: Challenges and Requirements

PubMed Central

Apfelbaum, Henry; Peli, Eli

2015-01-01

Purpose No prismatic solution for peripheral field loss (PFL) has gained widespread acceptance. Field extended by prisms has a corresponding optical scotoma at the prism apices. True expansion can be achieved when each eye is given a different view (through visual confusion). We analyze the effects of apical scotomas and binocular visual confusion in different designs to identify constraints on any solution that is likely to meet acceptance. Methods Calculated perimetry diagrams were compared to perimetry with PFL patients wearing InWave channel prisms and Trifield spectacles. Percept diagrams illustrate the binocular visual confusion. Results Channel prisms provide no benefit at primary gaze. Inconsequential extension was provided by InWave prisms, although accessible with moderate gaze shifts. Higher-power prisms provide greater extension, with greater paracentral scotoma loss, but require uncomfortable gaze shifts. Head turns, not eye scans, are needed to see regions lost to the apical scotomas. Trifield prisms provide field expansion at all gaze positions, but acceptance was limited by disturbing effects of central binocular visual confusion. Conclusions Field expansion when at primary gaze (where most time is spent) is needed while still providing unobstructed central vision. Paracentral multiplexing prisms we are developing that superimpose shifted and see-through views may accomplish that. Translational Relevance Use of the analyses and diagramming techniques presented here will be of value when considering prismatic aids for PFL, and could have prevented many unsuccessful designs and the improbable reports we cited from the literature. New designs must likely address the challenges identified here. PMID:26740910

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)].

Evolving Waves and Turbulence in the Outer Corona and Inner Heliosphere: The Accelerating Expanding Box

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

Tenerani, Anna; Velli, Marco

Alfvénic fluctuations in the solar wind display many properties reflecting an ongoing nonlinear cascade, e.g., a well-defined spectrum in frequency, together with some characteristics more commonly associated with the linear propagation of waves from the Sun, such as the variation of fluctuation amplitude with distance, dominated by solar wind expansion effects. Therefore, both nonlinearities and expansion must be included simultaneously in any successful model of solar wind turbulence evolution. Because of the disparate spatial scales involved, direct numerical simulations of turbulence in the solar wind represent an arduous task, especially if one wants to go beyond the incompressible approximation. Indeed,more » most simulations neglect solar wind expansion effects entirely. Here we develop a numerical model to simulate turbulent fluctuations from the outer corona to 1 au and beyond, including the sub-Alfvénic corona. The accelerating expanding box (AEB) extends the validity of previous expanding box models by taking into account both the acceleration of the solar wind and the inhomogeneity of background density and magnetic field. Our method incorporates a background accelerating wind within a magnetic field that naturally follows the Parker spiral evolution using a two-scale analysis in which the macroscopic spatial effect coupling fluctuations with background gradients becomes a time-dependent coupling term in a homogeneous box. In this paper we describe the AEB model in detail and discuss its main properties, illustrating its validity by studying Alfvén wave propagation across the Alfvén critical point.« less

EUV Waves Driven by the Sudden Expansion of Transequatorial Loops Caused by Coronal Jets

NASA Astrophysics Data System (ADS)

Shen, Yuandeng; Tang, Zehao; Miao, Yuhu; Su, Jiangtao; Liu, Yu

2018-06-01

We present two events to study the driving mechanism of extreme-ultraviolet (EUV) waves that are not associated with coronal mass ejections (CMEs), by using high-resolution observations taken by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. Observational results indicate that the observed EUV waves were accompanied by flares and coronal jets, but not the CMEs that were regarded as drivers of most EUV waves in previous studies. In the first case, it is observed that a coronal jet is ejected along a transequatorial loop system at a plane-of-the-sky (POS) speed of 335 ± 22 km s{}-1; in the meantime, an arc-shaped EUV wave appeared on the eastern side of the loop system. In addition, the EUV wave further interacted with another interconnecting loop system and launched a fast propagating (QFP) magnetosonic wave along the loop system, which had a period of 200 s and a speed of 388 ± 65 km s{}-1, respectively. In the second case, we observed a coronal jet that ejected at a POS speed of 282 ± 44 km s{}-1 along a transequatorial loop system as well as the generation of bright EUV waves on the eastern side of the loop system. Based on the observational results, we propose that the observed EUV waves on the eastern side of the transequatorial loop systems are fast-mode magnetosonic waves and that they are driven by the sudden lateral expansion of the transequatorial loop systems due to the direct impingement of the associated coronal jets, while the QFP wave in the fist case formed due to the dispersive evolution of the disturbance caused by the interaction between the EUV wave and the interconnecting coronal loops. It is noted that EUV waves driven by sudden loop expansions have shorter lifetimes than those driven by CMEs.

Instability of Taylor-Sedov blast waves propagating through a uniform gas

NASA Astrophysics Data System (ADS)

Grun, J.; Stamper, J.; Manka, C.; Resnick, J.; Burris, R.; Crawford, J.; Ripin, B. H.

1991-05-01

An instability in Taylor-Sedov blast waves was measured as the waves propagated through a uniform gas with a low adiabatic index. The first measurements of the instability are given and compared to theoretical predictions. The classical Taylor-Sedov blast waves resulted from the expansion of ablation plasma into an ambient gas from laser-irradiated foils, and photographs were taken using the dark-field imaging method. Visible emission from the blasts were recorded with a four-frame microchannel-plate intensifier camera. Blast waves formed in nitrogen gas are shown to be stable and smooth, whereas the waves propagating through xenon gas are found to be unstable and wrinkled. A power law is fitted to the experimental data, and the adiabatic indices are theorized to cause the different responses in the two gases. The results generally agree with theoretical predictions in spite of some minor discrepancies, and an explanation of the instability mechanism is developed. When the adiabatic index is sufficiently low, the Taylor-Sedov blast waves in a uniform gas will be unstable, and the perturbed amplitudes will grow as a power of time.

Performance of Low Dissipative High Order Shock-Capturing Schemes for Shock-Turbulence Interactions

NASA Technical Reports Server (NTRS)

Sandham, N. D.; Yee, H. C.

1998-01-01

Accurate and efficient direct numerical simulation of turbulence in the presence of shock waves represents a significant challenge for numerical methods. The objective of this paper is to evaluate the performance of high order compact and non-compact central spatial differencing employing total variation diminishing (TVD) shock-capturing dissipations as characteristic based filters for two model problems combining shock wave and shear layer phenomena. A vortex pairing model evaluates the ability of the schemes to cope with shear layer instability and eddy shock waves, while a shock wave impingement on a spatially-evolving mixing layer model studies the accuracy of computation of vortices passing through a sequence of shock and expansion waves. A drastic increase in accuracy is observed if a suitable artificial compression formulation is applied to the TVD dissipations. With this modification to the filter step the fourth-order non-compact scheme shows improved results in comparison to second-order methods, while retaining the good shock resolution of the basic TVD scheme. For this characteristic based filter approach, however, the benefits of compact schemes or schemes with higher than fourth order are not sufficient to justify the higher complexity near the boundary and/or the additional computational cost.

Electrostatics of crossed arrays of strips.

PubMed

Danicki, Eugene

2010-07-01

The BIS-expansion method is widely applied in analysis of SAW devices. Its generalization is presented for two planar periodic systems of perfectly conducting strips arranged perpendicularly on both sides of a dielectric layer. The generalized method can be applied in the evaluation of capacitances of strips on printed circuits boards and certain microwave devices, but primarily it may help in evaluation of 2-D piezoelectric sensors and actuators, with row and column addressing their elements, and also piezoelectric bulk wave resonators.

Effect of Se concentration on photonic bandgap of 1-D As-S-Se/air multilayers

NASA Astrophysics Data System (ADS)

Singh, Rajpal; Suthar, B.; Bhargava, A.

2018-05-01

The photonic band structure of 1-D chalcogenide photonic crystal consisting of As-S-Se/air multilayered structure is studied. The photonic band structure is calculated using plane wave expansion method. The effect of Se constration on the photonic bandgap is studied. It is found that the photonic bandgap increases with Se-concentration and shows the red shift.

Plane wave scattering by bow-tie posts

NASA Astrophysics Data System (ADS)

Lech, Rafal; Mazur, Jerzy

2004-04-01

The theory of scattering in free space by a novel structure of a two-dimensional dielectric-metallic post is developed with the use of a combination of a modified iterative scattering procedure and an orthogonal expansion method. The far scattered field patterns for open structures are derived. The rotation of the post affects its scattered field characteristic, which permits to make adjustments in characteristic of the posts arrays.

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.

Evaluating the role of higher order nonlinearity in water of finite and shallow depth with a direct numerical simulation method of Euler equations

NASA Astrophysics Data System (ADS)

Fernandez, L.; Toffoli, A.; Monbaliu, J.

2012-04-01

In deep water, the dynamics of surface gravity waves is dominated by the instability of wave packets to side band perturbations. This mechanism, which is a nonlinear third order in wave steepness effect, can lead to a particularly strong focusing of wave energy, which in turn results in the formation of waves of very large amplitude also known as freak or rogue waves [1]. In finite water depth, however, the interaction between waves and the ocean floor induces a mean current. This subtracts energy from wave instability and causes it to cease for relative water depth , where k is the wavenumber and h the water depth [2]. Yet, this contradicts field observations of extreme waves such as the infamous 26-m "New Year" wave that have mainly been recorded in regions of relatively shallow water . In this respect, recent studies [3] seem to suggest that higher order nonlinearity in water of finite depth may sustain instability. In order to assess the role of higher order nonlinearity in water of finite and shallow depth, here we use a Higher Order Spectral Method [4] to simulate the evolution of surface gravity waves according to the Euler equations of motion. This method is based on an expansion of the vertical velocity about the surface elevation under the assumption of weak nonlinearity and has a great advantage of allowing the activation or deactivation of different orders of nonlinearity. The model is constructed to deal with an arbitrary order of nonlinearity and water depths so that finite and shallow water regimes can be analyzed. Several wave configurations are considered with oblique and collinear with the primary waves disturbances and different water depths. The analysis confirms that nonlinearity higher than third order play a substantial role in the destabilization of a primary wave train and subsequent growth of side band perturbations.

Oscillations and waves in a spatially distributed system with a 1/f spectrum

NASA Astrophysics Data System (ADS)

Koverda, V. P.; Skokov, V. N.

2018-02-01

A spatially distributed system with a 1/f power spectrum is described by two nonlinear stochastic equations. Conditions for the formation of auto-oscillations have been found using numerical methods. The formation of a 1/f and 1/k spectrum simultaneously with the formation and motion of waves under the action of white noise has been demonstrated. The large extreme fluctuations with 1/f and 1/k spectra correspond to the maximum entropy, which points to the stability of such processes. It is shown that on the background of formation and motion of waves at an external periodic action there appears spatio-temporal stochastic resonance, at which one can observe the expansion of the region of periodic pulsations under the action of white noise.

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.

Under-estimated wave contribution to coastal sea-level rise

NASA Astrophysics Data System (ADS)

Melet, Angélique; Meyssignac, Benoit; Almar, Rafael; Le Cozannet, Gonéri

2018-03-01

Coastal communities are threatened by sea-level changes operating at various spatial scales; global to regional variations are associated with glacier and ice sheet loss and ocean thermal expansion, while smaller coastal-scale variations are also related to atmospheric surges, tides and waves. Here, using 23 years (1993-2015) of global coastal sea-level observations, we examine the contribution of these latter processes to long-term sea-level rise, which, to date, have been relatively less explored. It is found that wave contributions can strongly dampen or enhance the effects of thermal expansion and land ice loss on coastal water-level changes at interannual-to-multidecadal timescales. Along the US West Coast, for example, negative wave-induced trends dominate, leading to negative net water-level trends. Accurate estimates of past, present and future coastal sea-level rise therefore need to consider low-frequency contributions of wave set-up and swash.

Nonlinear wave interactions in shallow water magnetohydrodynamics of astrophysical plasma

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

Klimachkov, D. A., E-mail: klimachkovdmitry@gmail.com; Petrosyan, A. S., E-mail: apetrosy@iki.rssi.ru

2016-05-15

The rotating magnetohydrodynamic flows of a thin layer of astrophysical and space plasmas with a free surface in a vertical external magnetic field are considered in the shallow water approximation. The presence of a vertical external magnetic field changes significantly the dynamics of wave processes in an astrophysical plasma, in contrast to a neutral fluid and a plasma layer in an external toroidal magnetic field. There are three-wave nonlinear interactions in the case under consideration. Using the asymptotic method of multiscale expansions, we have derived nonlinear equations for the interaction of wave packets: three magneto- Poincare waves, three magnetostrophic waves,more » two magneto-Poincare and one magnetostrophic waves, and two magnetostrophic and one magneto-Poincare waves. The existence of decay instabilities and parametric amplification is predicted. We show that a magneto-Poincare wave decays into two magneto-Poincare waves, a magnetostrophic wave decays into two magnetostrophic waves, a magneto-Poincare wave decays into one magneto-Poincare and one magnetostrophic waves, and a magnetostrophic wave decays into one magnetostrophic and one magneto-Poincare waves. There are the following parametric amplification mechanisms: the parametric amplification of magneto-Poincare waves, the parametric amplification of magnetostrophic waves, the amplification of a magneto-Poincare wave in the field of a magnetostrophic wave, and the amplification of a magnetostrophic wave in the field of a magneto-Poincare wave. The instability growth rates and parametric amplification factors have been found for the corresponding processes.« less

General method for eliminating wave reflection in 2D photonic crystal waveguides by introducing extra scatterers based on interference cancellation of waves

NASA Astrophysics Data System (ADS)

Huang, Hao; Ouyang, Zhengbiao

2018-01-01

We propose a general method for eliminating the reflection of waves in 2 dimensional photonic crystal waveguides (2D-PCWs), a kind of 2D material, by introducing extra scatterers inside the 2D-PCWs. The intrinsic reflection in 2D-PCWs is compensated by the backward-scattered waves from these scatterers, so that the overall reflection is greatly reduced and the insertion loss is improved accordingly. We first present the basic theory for the compensation method. Then, as a demonstration, we give four examples of extremely-low-reflection and high-transmission 90°bent 2D-PCWs created according to the method proposed. In the four examples, it is demonstrated by plane-wave expansion method and finite-difference time-domain method that the 90°bent 2D-PCWs can have high transmission ratio greater than 90% in a wide range of operating frequency, and the highest transmission ratio can be greater than 99.95% with a return loss higher than 43 dB, better than that in other typical 90°bent 2D-PCWs. With our method, the bent 2D-PCWs can be optimized to obtain high transmission ratio at different operating wavelengths. As a further application of this method, a waveguide-based optical bridge for light crossing is presented, showing an optimum return loss of 46.85 dB, transmission ratio of 99.95%, and isolation rates greater than 41.77 dB. The method proposed provides also a useful way for improving conventional waveguides made of cables, fibers, or metal walls in the optical, infrared, terahertz, and microwave bands.

Unitarity, analyticity, dispersion relations, and resonances in strongly interacting WLWL, ZLZL, and h h scattering

NASA Astrophysics Data System (ADS)

Delgado, Rafael L.; Dobado, Antonio; Llanes-Estrada, Felipe J.

2015-04-01

If the electroweak symmetry breaking sector turns out to be strongly interacting, the actively investigated effective theory for longitudinal gauge bosons plus Higgs can be efficiently extended to cover the regime of saturation of unitarity (where the perturbative expansion breaks down). This is achieved by dispersion relations, whose subtraction constants and left cut contribution can be approximately obtained in different ways, giving rise to different unitarization procedures. We illustrate the ideas with the inverse amplitude method, one version of the N/D method, and another improved version of the K matrix. In the three cases we get partial waves which are unitary, analytical with the proper left and right cuts, and in some cases poles in the second Riemann sheet that can be understood as dynamically generated resonances. In addition, they reproduce at next to leading order the perturbative expansion for the five partial waves not vanishing (up to J =2 ), and they are renormalization scale (μ ) independent. Also the unitarization formalisms are extended to the coupled channel case. Then we apply the results to the elastic scattering amplitude for the longitudinal components of the gauge bosons V =W ,Z at high energy. We also compute h h →h h and the inelastic process V V →h h which are coupled to the elastic V V channel for custodial isospin I =0 . We numerically compare the three methods for various values of the low-energy couplings and explain the reasons for the differences found in the I =J =1 partial wave. Then we study the resonances appearing in the different elastic and coupled channels in terms of the effective Lagrangian parameters.

New template family for the detection of gravitational waves from comparable-mass black hole binaries

NASA Astrophysics Data System (ADS)

Porter, Edward K.

2007-11-01

In order to improve the phasing of the comparable-mass waveform as we approach the last stable orbit for a system, various resummation methods have been used to improve the standard post-Newtonian waveforms. In this work we present a new family of templates for the detection of gravitational waves from the inspiral of two comparable-mass black hole binaries. These new adiabatic templates are based on reexpressing the derivative of the binding energy and the gravitational wave flux functions in terms of shifted Chebyshev polynomials. The Chebyshev polynomials are a useful tool in numerical methods as they display the fastest convergence of any of the orthogonal polynomials. In this case they are also particularly useful as they eliminate one of the features that plagues the post-Newtonian expansion. The Chebyshev binding energy now has information at all post-Newtonian orders, compared to the post-Newtonian templates which only have information at full integer orders. In this work, we compare both the post-Newtonian and Chebyshev templates against a fiducially exact waveform. This waveform is constructed from a hybrid method of using the test-mass results combined with the mass dependent parts of the post-Newtonian expansions for the binding energy and flux functions. Our results show that the Chebyshev templates achieve extremely high fitting factors at all post-Newtonian orders and provide excellent parameter extraction. We also show that this new template family has a faster Cauchy convergence, gives a better prediction of the position of the last stable orbit and in general recovers higher Signal-to-Noise ratios than the post-Newtonian templates.

The Rate of Beneficial Mutations Surfing on the Wave of a Range Expansion

PubMed Central

Lehe, Rémi; Hallatschek, Oskar; Peliti, Luca

2012-01-01

Many theoretical and experimental studies suggest that range expansions can have severe consequences for the gene pool of the expanding population. Due to strongly enhanced genetic drift at the advancing frontier, neutral and weakly deleterious mutations can reach large frequencies in the newly colonized regions, as if they were surfing the front of the range expansion. These findings raise the question of how frequently beneficial mutations successfully surf at shifting range margins, thereby promoting adaptation towards a range-expansion phenotype. Here, we use individual-based simulations to study the surfing statistics of recurrent beneficial mutations on wave-like range expansions in linear habitats. We show that the rate of surfing depends on two strongly antagonistic factors, the probability of surfing given the spatial location of a novel mutation and the rate of occurrence of mutations at that location. The surfing probability strongly increases towards the tip of the wave. Novel mutations are unlikely to surf unless they enjoy a spatial head start compared to the bulk of the population. The needed head start is shown to be proportional to the inverse fitness of the mutant type, and only weakly dependent on the carrying capacity. The precise location dependence of surfing probabilities is derived from the non-extinction probability of a branching process within a moving field of growth rates. The second factor is the mutation occurrence which strongly decreases towards the tip of the wave. Thus, most successful mutations arise at an intermediate position in the front of the wave. We present an analytic theory for the tradeoff between these factors that allows to predict how frequently substitutions by beneficial mutations occur at invasion fronts. We find that small amounts of genetic drift increase the fixation rate of beneficial mutations at the advancing front, and thus could be important for adaptation during species invasions. PMID:22479175

CCC calculated integrated cross sections of electron-H2 scattering

NASA Astrophysics Data System (ADS)

Zammit, Mark; Fursa, Dmitry; Savage, Jeremy; Bray, Igor

2016-09-01

Recently we applied the molecular convergent close-coupling (CCC) method to electron scattering from molecular hydrogen H2. Convergence of the major integrated cross sections has been explicitly demonstrated in the fixed-nuclei approximation by increasing the number of H2 target states in the close-coupling expansion from 9 to 491. The calculations have been performed using a projectile partial wave expansion with maximum orbital angular momentum Lmax = 8 and total orbital angular momentum projections | M | <= 8 . Coupling to the ionization continuum is modeled via a large pseudo state expansion, which we found is required to obtain reliable elastic and excitation cross sections. Here we present benchmark elastic, single-ionization, electronic excitation and total integrated cross sections over a broad energy range (0.1 to 300 eV) and compare with available experiment and previous calculations. Los Alamos National Laboratory and Curtin University.

Two dimensional J-matrix approach to quantum scattering

NASA Astrophysics Data System (ADS)

Olumegbon, Ismail Adewale

We present an extension of the J-matrix method of scattering to two dimensions in cylindrical coordinates. In the J-matrix approach we select a zeroth order Hamiltonian, H0, which is exactly solvable in the sense that we select a square integrable basis set that enable us to have an infinite tridiagonal representation for H0. Expanding the wavefunction in this basis makes the wave equation equivalent to a three-term recursion relation for the expansion coefficients. Consequently, finding solutions of the recursion relation is equivalent to solving the original H0 problem (i.e., determining the expansion coefficients of the system's wavefunction). The part of the original potential interaction which cannot be brought to an exact tridiagonal form is cut in an NxN basis space and its matrix elements are computed numerically using Gauss quadrature approach. Hence, this approach embodies powerful tools in the analysis of solutions of the wave equation by exploiting the intimate connection and interplay between tridiagonal matrices and the theory of orthogonal polynomials. In such analysis, one is at liberty to employ a wide range of well established methods and numerical techniques associated with these settings such as quadrature approximation and continued fractions. To demonstrate the utility, usefulness, and accuracy of the extended method we use it to obtain the bound states for an illustrative short range potential problem.

Two dimensional J-matrix approach to quantum scattering

NASA Astrophysics Data System (ADS)

Olumegbon, Ismail Adewale

2013-01-01

We present an extension of the J-matrix method of scattering to two dimensions in cylindrical coordinates. In the J-matrix approach we select a zeroth order Hamiltonian, H0, which is exactly solvable in the sense that we select a square integrable basis set that enable us to have an infinite tridiagonal representation for H0. Expanding the wavefunction in this basis makes the wave equation equivalent to a three-term recursion relation for the expansion coefficients. Consequently, finding solutions of the recursion relation is equivalent to solving the original H0 problem (i.e., determining the expansion coefficients of the system's wavefunction). The part of the original potential interaction which cannot be brought to an exact tridiagonal form is cut in an NxN basis space and its matrix elements are computed numerically using Gauss quadrature approach. Hence, this approach embodies powerful tools in the analysis of solutions of the wave equation by exploiting the intimate connection and interplay between tridiagonal matrices and the theory of orthogonal polynomials. In such analysis, one is at liberty to employ a wide range of well established methods and numerical techniques associated with these settings such as quadrature approximation and continued fractions. To demonstrate the utility, usefulness, and accuracy of the extended method we use it to obtain the bound states for an illustrative short range potential problem.

Modulational instability and higher-order rogue waves with parameters modulation in a coupled integrable AB system via the generalized Darboux transformation.

PubMed

Wen, Xiao-Yong; Yan, Zhenya

2015-12-01

We study higher-order rogue wave (RW) solutions of the coupled integrable dispersive AB system (also called Pedlosky system), which describes the evolution of wave-packets in a marginally stable or unstable baroclinic shear flow in geophysical fluids. We propose its continuous-wave (CW) solutions and existent conditions for their modulation instability to form the rogue waves. A new generalized N-fold Darboux transformation (DT) is proposed in terms of the Taylor series expansion for the spectral parameter in the Darboux matrix and its limit procedure and applied to the CW solutions to generate multi-rogue wave solutions of the coupled AB system, which satisfy the general compatibility condition. The dynamical behaviors of these higher-order rogue wave solutions demonstrate both strong and weak interactions by modulating parameters, in which some weak interactions can generate the abundant triangle, pentagon structures, etc. Particularly, the trajectories of motion of peaks and depressions of profiles of the first-order RWs are explicitly analyzed. The generalized DT method used in this paper can be extended to other nonlinear integrable systems. These results may be useful for understanding the corresponding rogue-wave phenomena in fluid mechanics and related fields.

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.).

The behaviour of turbulence anisotropy through shock waves and expansions

NASA Technical Reports Server (NTRS)

Minh, H. H.; Kollmann, W.; Vandromme, D.

1985-01-01

A second order closure has been implemented in an implicit Navier-Stokes solver to study the behavior of the Reynolds stresses under the influence of severe pressure gradients. In the boundary layer zone, the strongly sheared character of the mean flow dominates the turbulence generation mechanisms. However, the pressure gradients play also a very important role for these processes, but at different locations within the boundary layer. This aspect may be emphasized by the analysis of turbulence anisotropy through shock waves and expansions.

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

Sidler, Rolf, E-mail: rsidler@gmail.com; Carcione, José M.; Holliger, Klaus

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in themore » radial direction and a Fourier expansion in the azimuthal direction and a Runge–Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid–solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.« less

Comparison of approximate solutions to the phonon Boltzmann transport equation with the relaxation time approximation: Spherical harmonics expansions and the discrete ordinates method

NASA Astrophysics Data System (ADS)

Christenson, J. G.; Austin, R. A.; Phillips, R. J.

2018-05-01

The phonon Boltzmann transport equation is used to analyze model problems in one and two spatial dimensions, under transient and steady-state conditions. New, explicit solutions are obtained by using the P1 and P3 approximations, based on expansions in spherical harmonics, and are compared with solutions from the discrete ordinates method. For steady-state energy transfer, it is shown that analytic expressions derived using the P1 and P3 approximations agree quantitatively with the discrete ordinates method, in some cases for large Knudsen numbers, and always for Knudsen numbers less than unity. However, for time-dependent energy transfer, the PN solutions differ qualitatively from converged solutions obtained by the discrete ordinates method. Although they correctly capture the wave-like behavior of energy transfer at short times, the P1 and P3 approximations rely on one or two wave velocities, respectively, yielding abrupt, step-changes in temperature profiles that are absent when the angular dependence of the phonon velocities is captured more completely. It is shown that, with the gray approximation, the P1 approximation is formally equivalent to the so-called "hyperbolic heat equation." Overall, these results support the use of the PN approximation to find solutions to the phonon Boltzmann transport equation for steady-state conditions. Such solutions can be useful in the design and analysis of devices that involve heat transfer at nanometer length scales, where continuum-scale approaches become inaccurate.

Scattering Cross Section of Sound Waves by the Modal Element Method

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1994-01-01

#he modal element method has been employed to determine the scattered field from a plane acoustic wave impinging on a two dimensional body. In the modal element method, the scattering body is represented by finite elements, which are coupled to an eigenfunction expansion representing the acoustic pressure in the infinite computational domain surrounding the body. The present paper extends the previous work by developing the algorithm necessary to calculate the acoustics scattering cross section by the modal element method. The scattering cross section is the acoustical equivalent to the Radar Cross Section (RCS) in electromagnetic theory. Since the scattering cross section is evaluated at infinite distance from the body, an asymptotic approximation is used in conjunction with the standard modal element method. For validation, the scattering cross section of the rigid circular cylinder is computed for the frequency range 0.1 is less than or equal to ka is less than or equal to 100. Results show excellent agreement with the analytic solution.

The two-electron atomic systems. S-states

NASA Astrophysics Data System (ADS)

Liverts, Evgeny Z.; Barnea, Nir

2010-01-01

A simple Mathematica program for computing the S-state energies and wave functions of two-electron (helium-like) atoms (ions) is presented. The well-known method of projecting the Schrödinger equation onto the finite subspace of basis functions was applied. The basis functions are composed of the exponentials combined with integer powers of the simplest perimetric coordinates. No special subroutines were used, only built-in objects supported by Mathematica. The accuracy of results and computation time depend on the basis size. The precise energy values of 7-8 significant figures along with the corresponding wave functions can be computed on a single processor within a few minutes. The resultant wave functions have a simple analytical form consisting of elementary functions, that enables one to calculate the expectation values of arbitrary physical operators without any difficulties. Program summaryProgram title: TwoElAtom-S Catalogue identifier: AEFK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 10 185 No. of bytes in distributed program, including test data, etc.: 495 164 Distribution format: tar.gz Programming language: Mathematica 6.0; 7.0 Computer: Any PC Operating system: Any which supports Mathematica; tested under Microsoft Windows XP and Linux SUSE 11.0 RAM:⩾10 bytes Classification: 2.1, 2.2, 2.7, 2.9 Nature of problem: The Schrödinger equation for atoms (ions) with more than one electron has not been solved analytically. Approximate methods must be applied in order to obtain the wave functions or other physical attributes from quantum mechanical calculations. Solution method: The S-wave function is expanded into a triple basis set in three perimetric coordinates. Method of projecting the two-electron Schrödinger equation (for atoms/ions) onto a subspace of the basis functions enables one to obtain the set of homogeneous linear equations F.C=0 for the coefficients C of the above expansion. The roots of equation det(F)=0 yield the bound energies. Restrictions: First, the too large length of expansion (basis size) takes the too large computation time giving no perceptible improvement in accuracy. Second, the order of polynomial Ω (input parameter) in the wave function expansion enables one to calculate the excited nS-states up to n=Ω+1 inclusive. Additional comments: The CPC Program Library includes "A program to calculate the eigenfunctions of the random phase approximation for two electron systems" (AAJD). It should be emphasized that this fortran code realizes a very rough approximation describing only the averaged electron density of the two electron systems. It does not characterize the properties of the individual electrons and has a number of input parameters including the Roothaan orbitals. Running time: ˜10 minutes (depends on basis size and computer speed)

Multimodal method for scattering of sound at a sudden area expansion in a duct with subsonic flow

NASA Astrophysics Data System (ADS)

Kooijman, G.; Testud, P.; Aurégan, Y.; Hirschberg, A.

2008-03-01

The scattering of sound at a sudden area expansion in a duct with subsonic mean flow has been modelled with a multimodal method. Technological applications are for instance internal combustion engine exhaust silencers and silencers in industrial duct systems. Both two-dimensional (2D) rectangular and 2D cylindrical geometry and uniform mean flow as well as non-uniform mean flow profiles are considered. Model results for the scattering of plane waves in case of uniform flow, in which case an infinitely thin shear layer is formed downstream of the area expansion, are compared to results obtained by other models in literature. Generally good agreement is found. Furthermore, model results for the scattering are compared to experimental data found in literature. Also here fairly good correspondence is observed. When employing a turbulent pipe flow profile in the model, instead of a uniform flow profile, the prediction for the downstream transmission- and upstream reflection coefficient is improved. However, worse agreement is observed for the upstream transmission and downstream reflection coefficient. On the contrary, employing a non-uniform jet flow profile, which represents a typical shear layer flow downstream of the expansion, gives worse agreement for the downstream transmission- and the upstream reflection coefficient, whereas prediction for the upstream transmission and downstream reflection coefficient improves.

Wave Propagation in Laterally Varying Media: A Model Expansion Method

DTIC Science & Technology

1991-05-01

91125 .Mr. William 3. Best Prof. F. A. Dahlen 907 Westwood Drive Geological and Geophysical Sciences Vienna, VA 22180 P’inceton University Princeton... William Menke Prof. Charles G. Sammis Lamont-Doherty Geological Observatory Center for Earth Sciences of Columbia University University of Southern...Pineda Court c. 6 William Kikendall Prof. Amos Nur Teledyne Geotech Department of Geophysics 3401 Shiloh Road Stanford University Garland, TX 75041

Annular arc accelerator shock tube

NASA Technical Reports Server (NTRS)

Leibowitz, L. P. (Inventor)

1976-01-01

An annular arc accelerator shock tube employs a cold gas driver to flow a stream of gas from an expansion section through a high voltage electrode section to a test section, thus driving a shock wave in front of it. A glow discharge detects the shock wave and actuates a trigger generator which in turn fires spark-gap switches to discharge a bank of capacitors across a centered cathode and an annular anode in tandem electrode sections. The initial shock wave passes through the anode section from the cathode section thereby depositing energy into the flow gas without the necessity of any diaphragm opening in the gas flow from the expansion section through the electrode sections.

Modified Chapman-Enskog moment approach to diffusive phonon heat transport.

PubMed

Banach, Zbigniew; Larecki, Wieslaw

2008-12-01

A detailed treatment of the Chapman-Enskog method for a phonon gas is given within the framework of an infinite system of moment equations obtained from Callaway's model of the Boltzmann-Peierls equation. Introducing no limitations on the magnitudes of the individual components of the drift velocity or the heat flux, this method is used to derive various systems of hydrodynamic equations for the energy density and the drift velocity. For one-dimensional flow problems, assuming that normal processes dominate over resistive ones, it is found that the first three levels of the expansion (i.e., the zeroth-, first-, and second-order approximations) yield the equations of hydrodynamics which are linearly stable at all wavelengths. This result can be achieved either by examining the dispersion relations for linear plane waves or by constructing the explicit quadratic Lyapunov entropy functionals for the linear perturbation equations. The next order in the Chapman-Enskog expansion leads to equations which are unstable to some perturbations. Precisely speaking, the linearized equations of motion that describe the propagation of small disturbances in the flow have unstable plane-wave solutions in the short-wavelength limit of the dispersion relations. This poses no problem if the equations are used in their proper range of validity.

Propagation of Torsional Alfvén Waves from the Photosphere to the Corona: Reflection, Transmission, and Heating in Expanding Flux Tubes

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

Soler, Roberto; Terradas, Jaume; Oliver, Ramón

It has been proposed that Alfvén waves play an important role in the energy propagation through the solar atmospheric plasma and its heating. Here we theoretically investigate the propagation of torsional Alfvén waves in magnetic flux tubes expanding from the photosphere up to the low corona and explore the reflection, transmission, and dissipation of wave energy. We use a realistic variation of the plasma properties and the magnetic field strength with height. Dissipation by ion–neutral collisions in the chromosphere is included using a multifluid partially ionized plasma model. Considering the stationary state, we assume that the waves are driven belowmore » the photosphere and propagate to the corona, while they are partially reflected and damped in the chromosphere and transition region. The results reveal the existence of three different propagation regimes depending on the wave frequency: low frequencies are reflected back to the photosphere, intermediate frequencies are transmitted to the corona, and high frequencies are completely damped in the chromosphere. The frequency of maximum transmissivity depends on the magnetic field expansion rate and the atmospheric model, but is typically in the range of 0.04–0.3 Hz. Magnetic field expansion favors the transmission of waves to the corona and lowers the reflectivity of the chromosphere and transition region compared to the case with a straight field. As a consequence, the chromospheric heating due to ion–neutral dissipation systematically decreases when the expansion rate of the magnetic flux tube increases.« less

Extrinsic extinction cross-section in the multiple acoustic scattering by fluid particles

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2017-04-01

Cross-sections (and their related energy efficiency factors) are physical parameters used in the quantitative analysis of different phenomena arising from the interaction of waves with a particle (or multiple particles). Earlier works with the acoustic scattering theory considered such quadratic (i.e., nonlinear) quantities for a single scatterer, although a few extended the formalism for a pair of scatterers but were limited to the scattering cross-section only. Therefore, the standard formalism applied to viscous particles is not suitable for the complete description of the cross-sections and energy balance of the multiple-particle system because both absorption and extinction phenomena arise during the multiple scattering process. Based upon the law of the conservation of energy, this work provides a complete comprehensive analysis for the extrinsic scattering, absorption, and extinction cross-sections (i.e., in the far-field) of a pair of viscous scatterers of arbitrary shape, immersed in a nonviscous isotropic fluid. A law of acoustic extinction taking into consideration interparticle effects in wave propagation is established, which constitutes a generalized form of the optical theorem in multiple scattering. Analytical expressions for the scattering, absorption, and extinction cross-sections are derived for plane progressive waves with arbitrary incidence. The mathematical expressions are formulated in partial-wave series expansions in cylindrical coordinates involving the angle of incidence, the addition theorem for the cylindrical wave functions, and the expansion coefficients of the scatterers. The analysis shows that the multiple scattering cross-section depends upon the expansion coefficients of both scatterers in addition to an interference factor that depends on the interparticle distance. However, the extinction cross-section depends on the expansion coefficients of the scatterer located in a particular system of coordinates, in addition to the interference term. Numerical examples illustrate the analysis for two viscous fluid circular cylindrical cross-sections immersed in a non-viscous fluid. Computations for the (non-dimensional) scattering, absorption, and extinction cross-section factors are performed with particular emphasis on varying the angle of incidence, the interparticle distance, and the sizes, and the physical properties of the particles. A symmetric behavior is observed for the dimensionless multiple scattering cross-section, while asymmetries arise for both the dimensionless absorption and extinction cross-sections with respect to the angle of incidence. The present analysis provides a complete analytical and computational method for the prediction of cross-section and energy efficiency factors in multiple acoustic scattering of plane waves of arbitrary incidence by a pair of scatterers. The results can be used as a priori information in the direct or inverse characterization of multiple scattering systems such as acoustically engineered fluid metamaterials with reconfigurable periodicities, cloaking devices, liquid crystals, and other applications.

Scattering of electromagnetic plane wave from a perfect electric conducting strip placed at interface of topological insulator-chiral medium

NASA Astrophysics Data System (ADS)

Shoukat, Sobia; Naqvi, Qaisar A.

2016-12-01

In this manuscript, scattering from a perfect electric conducting strip located at planar interface of topological insulator (TI)-chiral medium is investigated using the Kobayashi Potential method. Longitudinal components of electric and magnetic vector potential in terms of unknown weighting function are considered. Use of related set of boundary conditions yields two algebraic equations and four dual integral equations (DIEs). Integrand of two DIEs are expanded in terms of the characteristic functions with expansion coefficients which must satisfy, simultaneously, the discontinuous property of the Weber-Schafheitlin integrals, required edge and boundary conditions. The resulting expressions are then combined with algebraic equations to express the weighting function in terms of expansion coefficients, these expansion coefficients are then substituted in remaining DIEs. The projection is applied using the Jacobi polynomials. This treatment yields matrix equation for expansion coefficients which is solved numerically. These unknown expansion coefficients are used to find the scattered field. The far zone scattering width is investigated with respect to different parameters of the geometry, i.e, chirality of chiral medium, angle of incidence, size of the strip. Significant effects of different parameters including TI parameter on the scattering width are noted.

Uniform theory of the boundary diffraction wave

NASA Astrophysics Data System (ADS)

Umul, Yusuf Z.

2009-04-01

A uniform version of the potential function of the Maggi-Rubinowicz boundary diffraction wave theory is obtained by using the large argument expansion of the Fresnel integral. The derived function is obtained for the problem of diffraction of plane waves by a circular edge. The results are plotted numerically.

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.

Propagation of Pressure Waves, Caused by a Thermal Shock, in Liquid Metals Containing Gas Bubbles

NASA Astrophysics Data System (ADS)

Okita, Kohei; Takagi, Shu; Matsumoto, Yoichiro

The propagation of pressure waves caused by a thermal shock in liquid mercury containing micro gas bubbles has been simulated numerically. In the present study, we clarify the influences of the introduced bubble size and void fraction on the absorption of thermal expansion of liquid mercury and attenuation of pressure waves. The mass, momentum and energy conservation equations for both bubbly mixture and gas inside each bubble are solved, in which the bubble dynamics is represented by the Keller equation. The results show that when the initial void fraction is larger than the rate of the thermal expansion of liquid mercury, the pressure rise caused by the thermal expansion decreases with decreasing the bubble radius, because of the increase of the natural frequency of bubbly mixture. On the other hand, as the bubble radius increases, the peak of pressure waves which propagate at the sound speed of mixture decreases gradually due to the dispersion effect of mixture. When the natural frequency of the mixture with large bubbles is lower than that of the thremal shock, the peak pressure at the wall increases because the pressure waves propagate through the mixture at the sound speed of liquid mercury. The comparison of the results with and without heat transfer through the gas liquid interface shows that the pressure waves are attenuated greatly by the thermal damping effect with the decrease of the void fraction which enhances the nonlinearity of bubble oscillation.

Analytic Wave Functions for the Half-Filled Lowest Landau Level

NASA Astrophysics Data System (ADS)

Ciftja, Orion

We consider a two-dimensional strongly correlated electronic system in a strong perpendicular magnetic field at half-filling of the lowest Landau level (LLL). We seek to build a wave function that, by construction, lies entirely in the Hilbert space of the LLL. Quite generally, a wave function of this nature can be built as a linear combination of all possible Slater determinants formed by using the complete set of single-electron states that belong to the LLL. However, due to the vast number of Slater determinant states required to form such basis functions, the expansion is impractical for any but the smallest systems. Thus, in practice, the expansion must be truncated to a small number of Slater determinants. Among many possible LLL Slater determinant states, we note a particular special class of such wave functions in which electrons occupy either only even, or only odd angular momentum states. We focus on such a class of wave functions and obtain analytic expressions for various quantities of interest. Results seem to suggest that these special wave functions, while interesting and physically appealing, are unlikely to be a very good approximation for the exact ground state at half-filling factor. The overall quality of the description can be improved by including other additional LLL Slater determinant states. It is during this process that we identify another special family of suitable LLL Slater determinant states to be used in an enlarged expansion.

Strong Langmuir Turbulence and Four-Wave Mixing

NASA Astrophysics Data System (ADS)

Glanz, James

1991-02-01

The staircase expansion is a new mathematical technique for deriving reduced, nonlinear-PDE descriptions from the plasma-moment equations. Such descriptions incorporate only the most significant linear and nonlinear terms of more complex systems. The technique is used to derive a set of Dawson-Zakharov or "master" equations, which unify and generalize previous work and show the limitations of models commonly used to describe nonlinear plasma waves. Fundamentally new wave-evolution equations are derived that admit of exact nonlinear solutions (solitary waves). Analytic calculations illustrate the competition between well-known effects of self-focusing, which require coupling to ion motion, and pure-electron nonlinearities, which are shown to be especially important in curved geometries. Also presented is an N -moment hydrodynamic model derived from the Vlasov equation. In this connection, the staircase expansion is shown to remain useful for all values of N >= 3. The relevance of the present work to nonlocally truncated hierarchies, which more accurately model dissipation, is briefly discussed. Finally, the general formalism is applied to the problem of electromagnetic emission from counterpropagating Langmuir pumps. It is found that previous treatments have neglected order-unity effects that increase the emission significantly. Detailed numerical results are presented to support these conclusions. The staircase expansion--so called because of its appearance when written out--should be effective whenever the largest contribution to the nonlinear wave remains "close" to some given frequency. Thus the technique should have application to studies of wake-field acceleration schemes and anomalous damping of plasma waves.

Sea level variability at the coast: is it dominated by waves even at interdecadal time scales?

NASA Astrophysics Data System (ADS)

Melet, Angelique; Almar, Rafael; Meyssignac, Benoit

2017-04-01

Tide gauge records and satellite altimetry indicate that global mean sea level has risen by 16±3 cm during the 20th century. This rise is essentially due to thermal expansion of the ocean and land ice loss from glaciers and ice sheets in response to anthropogenic emissions of greenhouse gases. It is projected to continue over the 21st century and raise concerns for coastal regions. But coastal sea level variations are influenced by other processes such as tides, atmospheric surges and wave induced run-up and set-up. Here we examine the relative importance of the processes causing sea level variations at the coast over the last 23 years from observational datasets and model reanalyses focusing on coastal sites distributed along the world's coastlines for which tide gauges records are available. We show that the long term wave signal can dampen or enhance the effect of the ocean thermal expansion and land ice loss at the coast, over all time scales from subannnual to multidecadal. We estimate that the effect of waves generally explains 60%±20% of the coastal sea level variations at interannual to multidecadal time scales. In the Eastern Pacific, the wave effect dominates the total budget and counterbalances the thermal expansion of the ocean and land ice loss signals. These results highlight that the wave effect has to be taken into account in sea level predictions and projections.

Amplification of seismic waves beneath active volcanoes

NASA Astrophysics Data System (ADS)

Navon, O.; Lensky, N. G.; Collier, L.; Neuberg, J.; Lyakhovsky, V.

2003-04-01

Long-period (LP) seismic events are typical of many volcanoes and are attributed to energy leaking from waves traveling through the volcanic conduit or along the conduit - country-rock interface. The LP events are triggered locally, at the volcanic edifice, but the source of energy for the formation of tens of events per day is not clear. Energy may be supplied by volatile-release from a supersaturated melt. If bubbles are present in equilibrium with the melt in the conduit, and the melt is suddenly decompressed, transfer of volatiles from the supersaturated melt into the bubbles transforms stored potential energy into expansion work. For example, small dome collapses may decompress the conduit by a few bars and lead to solubility decrease, exsolution of volatiles and, consequently, to work done by the expansion of the bubbles under pressure. This energy is released over a timescale that is similar to that of LP events and may amplify the original weak seismic signals associated with the collapse. Using the formulation of Lensky et al. (2002), following the decompression, when the transfer of volatiles into bubbles is fast enough, expansion accelerates and the bulk viscosity of the bubbly magma is negative. New calculations show that under such conditions a sinusoidal P-wave is amplified. We note that seismic waves created by tectonic earthquakes that are not associated with net decompression, do not lead to net release of volatiles or to net expansion. In this case, the bulk viscosity is positive and waves traveling through the magma should attenuate. The proposed model explains how weak seismic signals may be amplified as they travel through a conduit that contains supersaturated bubbly magma. It provides the general framework for amplifying volcanic seismicity such as the signals associated with long-period events.

Theoretical study on the dispersion curves of Lamb waves in piezoelectric-semiconductor sandwich plates GaAs-FGPM-AlAs: Legendre polynomial series expansion

NASA Astrophysics Data System (ADS)

Othmani, Cherif; Takali, Farid; Njeh, Anouar

2017-06-01

In this paper, the propagation of the Lamb waves in the GaAs-FGPM-AlAs sandwich plate is studied. Based on the orthogonal function, Legendre polynomial series expansion is applied along the thickness direction to obtain the Lamb dispersion curves. The convergence and accuracy of this polynomial method are discussed. In addition, the influences of the volume fraction p and thickness hFGPM of the FGPM middle layer on the Lamb dispersion curves are developed. The numerical results also show differences between the characteristics of Lamb dispersion curves in the sandwich plate for various gradient coefficients of the FGPM middle layer. In fact, if the volume fraction p increases the phase velocity will increases and the number of modes will decreases at a given frequency range. All the developments performed in this paper were implemented in Matlab software. The corresponding results presented in this work may have important applications in several industry areas and developing novel acoustic devices such as sensors, electromechanical transducers, actuators and filters.

Three dimensional cylindrical Kadomtsev-Petviashvili equation in a very dense electron-positron-ion plasma

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

Moslem, W. M.; Sabry, R.; Shukla, P. K.

2010-03-15

By using the hydrodynamic equations of ions, Thomas-Fermi electron/positron density distribution, and Poisson equation, a three-dimensional cylindrical Kadomtsev-Petviashvili (CKP) equation is derived for small but finite amplitude ion-acoustic waves. The generalized expansion method is used to analytically solve the CKP equation. New class of solutions admits a train of well-separated bell-shaped periodic pulses is obtained. At certain condition, the latter degenerates to solitary wave solution. The effects of physical parameters on the solitary pulse structures are examined. Furthermore, the energy integral equation is used to study the existence regions of the localized pulses. The present study might be helpful tomore » understand the excitation of nonlinear ion-acoustic waves in a very dense astrophysical objects such as white dwarfs.« less

CBR anisotropy from primordial gravitational waves in inflationary cosmologies

NASA Astrophysics Data System (ADS)

Allen, Bruce; Koranda, Scott

1994-09-01

We examine stochastic temperature fluctuations of the cosmic background radiation (CBR) arising via the Sachs-Wolfe effect from gravitational wave perturbations produced in the early Universe. These temperature fluctuations are described by an angular correlation function C(γ). A new (more concise and general) derivation of C(γ) is given, and evaluated for inflationary-universe cosmologies. This yields standard results for angles γ greater than a few degrees, but new results for smaller angles, because we do not make standard long-wavelength approximations to the gravitational wave mode functions. The function C(γ) may be expanded in a series of Legendre polynomials; we use numerical methods to compare the coefficients of the resulting expansion in our exact calculation with standard (approximate) results. We also report some progress towards finding a closed form expression for C(γ).

Dynamic of solitary wave solutions in some nonlinear pseudoparabolic models and Dodd-Bullough-Mikhailov equation

NASA Astrophysics Data System (ADS)

Ilhan, O. A.; Bulut, H.; Sulaiman, T. A.; Baskonus, H. M.

2018-02-01

In this study, the modified exp ( - Φ (η )) -expansion function method is used in constructing some solitary wave solutions to the Oskolkov-Benjamin-Bona-Mahony-Burgers, one-dimensional Oskolkov equations and the Dodd-Bullough-Mikhailov equation. We successfully construct some singular solitons and singular periodic waves solutions with the hyperbolic, trigonometric and exponential function structures to these three nonlinear models. Under the choice of some suitable values of the parameters involved, we plot the 2D and 3D graphics to some of the obtained solutions in this study. All the obtained solutions in this study verify their corresponding equation. We perform all the computations in this study with the help of the Wolfram Mathematica software. The obtained solutions in this study may be helpful in explaining some practical physical problems.

Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons

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

Sardar, Sankirtan; Bandyopadhyay, Anup, E-mail: abandyopadhyay1965@gmail.com; Das, K. P.

A three-dimensional KP (Kadomtsev Petviashvili) equation is derived here describing the propagation of weakly nonlinear and weakly dispersive dust ion acoustic wave in a collisionless unmagnetized plasma consisting of warm adiabatic ions, static negatively charged dust grains, nonthermal electrons, and isothermal positrons. When the coefficient of the nonlinear term of the KP-equation vanishes an appropriate modified KP (MKP) equation describing the propagation of dust ion acoustic wave is derived. Again when the coefficient of the nonlinear term of this MKP equation vanishes, a further modified KP equation is derived. Finally, the stability of the solitary wave solutions of the KPmore » and the different modified KP equations are investigated by the small-k perturbation expansion method of Rowlands and Infeld [J. Plasma Phys. 3, 567 (1969); 8, 105 (1972); 10, 293 (1973); 33, 171 (1985); 41, 139 (1989); Sov. Phys. - JETP 38, 494 (1974)] at the lowest order of k, where k is the wave number of a long-wavelength plane-wave perturbation. The solitary wave solutions of the different evolution equations are found to be stable at this order.« less

Spatio-temporal evolutions of non-orthogonal equatorial wave modes derived from observations

NASA Astrophysics Data System (ADS)

Barton, Cory

Equatorial waves have been studied extensively due to their importance to the tropical climate and weather systems. Historically, their activity is diagnosed mainly in the wavenumber-frequency domain. Recently, many studies have projected observational data onto parabolic cylinder functions (PCFs), which represent the meridional structure of individual wave modes, to attain time-dependent spatial wave structures. The non-orthogonality of wave modes has yet posed a problem when attempting to separate data into wave fields where the waves project onto the same structure functions. We propose the development and application of a new methodology for equatorial wave expansion of instantaneous flows using the full equatorial wave spectrum. By creating a mapping from the meridional structure function amplitudes to the equatorial wave class amplitudes, we are able to diagnose instantaneous wave fields and determine their evolution. Because all meridional modes are shared by some subset of the wave classes, we require constraints on the wave class amplitudes to yield a closed system with a unique solution for all waves' spatial structures, including IG waves. A synthetic field is analyzed using this method to determine its accuracy for data of a single vertical mode. The wave class spectra diagnosed using this method successfully match the correct dispersion curves even if the incorrect depth is chosen for the spatial decomposition. In the case of more than one depth scale, waves with varying equivalent depth may be similarly identified using the dispersion curves. The primary vertical mode is the 200 m equivalent depth mode, which is that of the peak projection response. A distinct spectral power peak along the Kelvin wave dispersion curve for this value validates our choice of equivalent depth, although the possibility of depth varying with time and height is explored. The wave class spectra diagnosed assuming this depth scale mostly match their expected dispersion curves, showing that this method successfully partitions the wave spectra by calculating wave amplitudes in physical space. This is particularly striking because the time evolution, and therefore the frequency characteristics, is determined simply by a timeseries of independently-diagnosed instantaneous horizontal fields. We use the wave fields diagnosed by this method to study wave evolution in the context of the stratospheric QBO of zonal wind, confirming the continuous evolution of the selection mechanism for equatorial waves in the middle atmosphere. The amplitude cycle synchronized with the background zonal wind as predicted by QBO theory is present in the wave class fields even though the dynamics are not forced by the method itself. We have additionally identified a time-evolution of the zonal wavenumber spectrum responsible for the amplitude variability in physical space. Similar to the temporal characteristics, the vertical structures are also the result of a simple height cross-section through multiple independently-diagnosed levels.

A direct method to transform between expansions in the configuration state function and Slater determinant bases

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

Olsen, Jeppe, E-mail: jeppe@chem.au.dk

2014-07-21

A novel algorithm is introduced for the transformation of wave functions between the bases of Slater determinants (SD) and configuration state functions (CSF) in the genealogical coupling scheme. By modifying the expansion coefficients as each electron is spin-coupled, rather than performing a single many-electron transformation, the large transformation matrix that plagues previous approaches is avoided and the required number of operations is drastically reduced. As an example of the efficiency of the algorithm, the transformation for a configuration with 30 unpaired electrons and singlet spin is discussed. For this case, the 10 × 10{sup 6} coefficients in the CSF basismore » is obtained from the 150 × 10{sup 6} coefficients in the SD basis in 1 min, which should be compared with the seven years that the previously employed method is estimated to require.« less

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

Zammit, Mark C.; Fursa, Dmitry V.; Savage, Jeremy S.

Starting from first principles, this tutorial describes the development of the adiabatic-nuclei convergent close-coupling (CCC) method and its application to electron and (single-centre) positron scattering from diatomic molecules. In this paper, we give full details of the single-centre expansion CCC method, namely the formulation of the molecular target structure; solving the momentum-space coupled-channel Lippmann-Schwinger equation; deriving adiabatic-nuclei cross sections and calculatingmore » $V$-matrix elements. Selected results are presented for electron and positron scattering from molecular hydrogen H$$_2$$ and electron scattering from the vibrationally excited molecular hydrogen ion H$$_2^+$$ and its isotopologues (D$$_2^+$$, T$$_2^+$$, HD$^+$, HT$^+$ and TD$^+$). Finally, convergence in both the close-coupling (target state) and projectile partial-wave expansions of fixed-nuclei electron- and positron-molecule scattering calculations is demonstrated over a broad energy-range and discussed in detail. In general the CCC results are in good agreement with experiments.« less

An adaptive Bayesian inversion for upper-mantle structure using surface waves and scattered body waves

NASA Astrophysics Data System (ADS)

Eilon, Zachary; Fischer, Karen M.; Dalton, Colleen A.

2018-07-01

We present a methodology for 1-D imaging of upper-mantle structure using a Bayesian approach that incorporates a novel combination of seismic data types and an adaptive parametrization based on piecewise discontinuous splines. Our inversion algorithm lays the groundwork for improved seismic velocity models of the lithosphere and asthenosphere by harnessing the recent expansion of large seismic arrays and computational power alongside sophisticated data analysis. Careful processing of P- and S-wave arrivals isolates converted phases generated at velocity gradients between the mid-crust and 300 km depth. This data is allied with ambient noise and earthquake Rayleigh wave phase velocities to obtain detailed VS and VP velocity models. Synthetic tests demonstrate that converted phases are necessary to accurately constrain velocity gradients, and S-p phases are particularly important for resolving mantle structure, while surface waves are necessary for capturing absolute velocities. We apply the method to several stations in the northwest and north-central United States, finding that the imaged structure improves upon existing models by sharpening the vertical resolution of absolute velocity profiles, offering robust uncertainty estimates, and revealing mid-lithospheric velocity gradients indicative of thermochemical cratonic layering. This flexible method holds promise for increasingly detailed understanding of the upper mantle.

An adaptive Bayesian inversion for upper mantle structure using surface waves and scattered body waves

NASA Astrophysics Data System (ADS)

Eilon, Zachary; Fischer, Karen M.; Dalton, Colleen A.

2018-04-01

We present a methodology for 1-D imaging of upper mantle structure using a Bayesian approach that incorporates a novel combination of seismic data types and an adaptive parameterisation based on piecewise discontinuous splines. Our inversion algorithm lays the groundwork for improved seismic velocity models of the lithosphere and asthenosphere by harnessing the recent expansion of large seismic arrays and computational power alongside sophisticated data analysis. Careful processing of P- and S-wave arrivals isolates converted phases generated at velocity gradients between the mid-crust and 300 km depth. This data is allied with ambient noise and earthquake Rayleigh wave phase velocities to obtain detailed VS and VP velocity models. Synthetic tests demonstrate that converted phases are necessary to accurately constrain velocity gradients, and S-p phases are particularly important for resolving mantle structure, while surface waves are necessary for capturing absolute velocities. We apply the method to several stations in the northwest and north-central United States, finding that the imaged structure improves upon existing models by sharpening the vertical resolution of absolute velocity profiles, offering robust uncertainty estimates, and revealing mid-lithospheric velocity gradients indicative of thermochemical cratonic layering. This flexible method holds promise for increasingly detailed understanding of the upper mantle.

Frequency dependent steering with backward leaky waves via photonic crystal interface layer.

PubMed

Colak, Evrim; Caglayan, Humeyra; Cakmak, Atilla O; Villa, Alessandro D; Capolino, Filippo; Ozbay, Ekmel

2009-06-08

A Photonic Crystal (PC) with a surface defect layer (made of dimers) is studied in the microwave regime. The dispersion diagram is obtained with the Plane Wave Expansion Method. The dispersion diagram reveals that the dimer-layer supports a surface mode with negative slope. Two facts are noted: First, a guided (bounded) wave is present, propagating along the surface of the dimer-layer. Second, above the light line, the fast traveling mode couple to the propagating spectra and as a result a directive (narrow beam) radiation with backward characteristics is observed and measured. In this leaky mode regime, symmetrical radiation patterns with respect to the normal to the PC surface are attained. Beam steering is observed and measured in a 70 degrees angular range when frequency ranges in the 11.88-13.69 GHz interval. Thus, a PC based surface wave structure that acts as a frequency dependent leaky wave antenna is presented. Angular radiation pattern measurements are in agreement with those obtained via numerical simulations that employ the Finite Difference Time Domain Method (FDTD). Finally, the backward radiation characteristics that in turn suggest the existence of a backward leaky mode in the dimer-layer are experimentally verified using a halved dimer-layer structure.

Electron– and positron–molecule scattering: development of the molecular convergent close-coupling method

DOE PAGES

Zammit, Mark C.; Fursa, Dmitry V.; Savage, Jeremy S.; ...

2017-05-22

Starting from first principles, this tutorial describes the development of the adiabatic-nuclei convergent close-coupling (CCC) method and its application to electron and (single-centre) positron scattering from diatomic molecules. In this paper, we give full details of the single-centre expansion CCC method, namely the formulation of the molecular target structure; solving the momentum-space coupled-channel Lippmann-Schwinger equation; deriving adiabatic-nuclei cross sections and calculatingmore » $V$-matrix elements. Selected results are presented for electron and positron scattering from molecular hydrogen H$$_2$$ and electron scattering from the vibrationally excited molecular hydrogen ion H$$_2^+$$ and its isotopologues (D$$_2^+$$, T$$_2^+$$, HD$^+$, HT$^+$ and TD$^+$). Finally, convergence in both the close-coupling (target state) and projectile partial-wave expansions of fixed-nuclei electron- and positron-molecule scattering calculations is demonstrated over a broad energy-range and discussed in detail. In general the CCC results are in good agreement with experiments.« less

Acoustic wave generation by microwaves and applications to nondestructive evaluation.

PubMed

Hosten, Bernard; Bacon, Christophe; Guilliorit, Emmanuel

2002-05-01

Although acoustic wave generation by electromagnetic waves has been widely studied in the case of laser-generated ultrasounds, the literature on acoustic wave generation by thermal effects due to electromagnetic microwaves is very sparse. Several mechanisms have been suggested to explain the phenomenon of microwave generation, i.e. radiation pressure, electrostriction or thermal expansion. Now it is known that the main cause is the thermal expansion due to the microwave absorption. This paper will review the recent advances in the theory and experiments that introduce a new way to generate ultrasonic waves without contact for the purpose of nondestructive evaluation and control. The unidirectional theory based on Maxwell's equations, heat equation and thermoviscoelasticity predicts the generation of acoustic waves at interfaces and inside stratified materials. Acoustic waves are generated by a pulsed electromagnetic wave or a burst at a chosen frequency such that materials can be excited with a broad or narrow frequency range. Experiments show the generation of acoustic waves in water, viscoelastic polymers and composite materials shaped as rod and plates. From the computed and measured accelerations at interfaces, the viscoelastic and electromagnetic properties of materials such as polymers and composites can be evaluated (NDE). Preliminary examples of non-destructive testing applications are presented.

Transmission of a detonation across a density interface

NASA Astrophysics Data System (ADS)

Tang Yuk, K. C.; Mi, X. C.; Lee, J. H. S.; Ng, H. D.

2018-05-01

The present study investigates the transmission of a detonation wave across a density interface. The problem is first studied theoretically considering an incident Chapman-Jouguet (CJ) detonation wave, neglecting its detailed reaction-zone structure. It is found that, if there is a density decrease at the interface, a transmitted strong detonation wave and a reflected expansion wave would be formed; if there is a density increase, one would obtain a transmitted CJ detonation wave followed by an expansion wave and a reflected shock wave. Numerical simulations are then performed considering that the incident detonation has the Zel'dovich-von Neumann-Döring reaction-zone structure. The transient process that occurs subsequently to the detonation-interface interaction has been captured by the simulations. The effects of the magnitude of density change across the interface and different reaction kinetics (i.e., single-step Arrhenius kinetics vs. two-step induction-reaction kinetics) on the dynamics of the transmission process are explored. After the transient relaxation process, the transmitted wave reaches the final state in the new medium. For the cases with two-step induction-reaction kinetics, the transmitted wave fails to evolve to a steady detonation wave if the magnitude of density increase is greater than a critical value. For the cases wherein the transmitted wave can evolve to a steady detonation, the numerical results for both reaction models give final propagation states that agree with the theoretical solutions.

Photoelectron wave function in photoionization: plane wave or Coulomb wave?

PubMed

Gozem, Samer; Gunina, Anastasia O; Ichino, Takatoshi; Osborn, David L; Stanton, John F; Krylov, Anna I

2015-11-19

The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectron wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. The results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion.

Single-drop impingement onto a wavy liquid film and description of the asymmetrical cavity dynamics

NASA Astrophysics Data System (ADS)

van Hinsberg, Nils Paul; Charbonneau-Grandmaison, Marie

2015-07-01

The present paper is devoted to an experimental investigation of the cavity formed upon a single-drop impingement onto a traveling solitary surface wave on a deep pool of the same liquid. The dynamics of the cavity throughout its complete expansion and receding phase are analyzed using high-speed shadowgraphy and compared to the outcomes of drop impingements onto steady liquid surface films having equal thickness. The effects of the surface wave velocity, amplitude and phase, drop impingement velocity, and liquid viscosity on the cavity's diameter and depth evolution are accurately characterized at various time instants. The wave velocity induces a distinct and in time increasing inclination of the cavity in the wave propagation direction. In particular for strong waves an asymmetrical distribution of the radial expansion and retraction velocity along the cavity's circumference is observed. A linear dependency between the absolute Weber number and the typical length and time scales associated with the cavity's maximum depth and maximum diameter is reported.

Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo

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

Filippi, Claudia, E-mail: c.filippi@utwente.nl; Assaraf, Roland, E-mail: assaraf@lct.jussieu.fr; Moroni, Saverio, E-mail: moroni@democritos.it

2016-05-21

We present a simple and general formalism to compute efficiently the derivatives of a multi-determinant Jastrow-Slater wave function, the local energy, the interatomic forces, and similar quantities needed in quantum Monte Carlo. Through a straightforward manipulation of matrices evaluated on the occupied and virtual orbitals, we obtain an efficiency equivalent to algorithmic differentiation in the computation of the interatomic forces and the optimization of the orbital parameters. Furthermore, for a large multi-determinant expansion, the significant computational gain afforded by a recently introduced table method is here extended to the local value of any one-body operator and to its derivatives, inmore » both all-electron and pseudopotential calculations.« less

Apparatus and process for the separation of gases using supersonic expansion and oblique wave compression

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

VanOsdol, John G.

The disclosure provides an apparatus and method for gas separation through the supersonic expansion and subsequent deceleration of a gaseous stream. The gaseous constituent changes phase from the gaseous state by desublimation or condensation during the acceleration producing a collectible constituent, and an oblique shock diffuser decelerates the gaseous stream to a subsonic velocity while maintain the collectible constituent in the non-gaseous state. Following deceleration, the carrier gas and the collectible constituent at the subsonic velocity are separated by a separation means, such as a centrifugal, electrostatic, or impingement separator. In an embodiment, the gaseous stream issues from a combustionmore » process and is comprised of N.sub.2 and CO.sub.2.« less

Reheating signature in the gravitational wave spectrum from self-ordering scalar fields

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

Kuroyanagi, Sachiko; Hiramatsu, Takashi; Yokoyama, Jun'ichi, E-mail: skuro@nagoya-u.jp, E-mail: hiramatz@yukawa.kyoto-u.ac.jp, E-mail: yokoyama@resceu.s.u-tokyo.ac.jp

2016-02-01

We investigate the imprint of reheating on the gravitational wave spectrum produced by self-ordering of multi-component scalar fields after a global phase transition. The equation of state of the Universe during reheating, which usually has different behaviour from that of a radiation-dominated Universe, affects the evolution of gravitational waves through the Hubble expansion term in the equations of motion. This gives rise to a different power-law behavior of frequency in the gravitational wave spectrum. The reheating history is therefore imprinted in the shape of the spectrum. We perform 512{sup 3} lattice simulations to investigate how the ordering scalar field reactsmore » to the change of the Hubble expansion and how the reheating effect arises in the spectrum. We also compare the result with inflation-produced gravitational waves, which has a similar spectral shape, and discuss whether it is possible to distinguish the origin between inflation and global phase transition by detecting the shape with future direct detection gravitational wave experiments such as DECIGO.« less

Linear shoaling of free-surface waves in multi-layer non-hydrostatic models

NASA Astrophysics Data System (ADS)

Bai, Yefei; Cheung, Kwok Fai

2018-01-01

The capability to describe shoaling over sloping bottom is fundamental to modeling of coastal wave transformation. The linear shoaling gradient provides a metric to measure this property in non-hydrostatic models with layer-integrated formulations. The governing equations in Boussinesq form facilitate derivation of the linear shoaling gradient, which is in the form of a [ 2 P + 2 , 2 P ] expansion of the water depth parameter kd with P equal to 1 for a one-layer model and (4 N - 4) for an N-layer model. The expansion reproduces the analytical solution from Airy wave theory at the shallow water limit and maintains a reasonable approximation up to kd = 1.2 and 2 for the one and two-layer models. Additional layers provide rapid and monotonic convergence of the shoaling gradient into deep water. Numerical experiments of wave propagation over a plane slope illustrate manifestation of the shoaling errors through the transformation processes from deep to shallow water. Even though outside the zone of active wave transformation, shoaling errors from deep to intermediate water are cumulative to produce appreciable impact to the wave amplitude in shallow water.

The development of shock wave overpressure driven by channel expansion of high current impulse discharge arc

NASA Astrophysics Data System (ADS)

Xiong, Jia-ming; Li, Lee; Dai, Hong-yu; Wu, Hai-bo; Peng, Ming-yang; Lin, Fu-chang

2018-03-01

During the formation of a high current impulse discharge arc, objects near the discharge arc will be strongly impacted. In this paper, a high power, high current gas switch is used as the site of the impulse discharge arc. The explosion wave theory and the arc channel energy balance equation are introduced to analyze the development of the shock wave overpressure driven by the high current impulse discharge arc, and the demarcation point of the arc channel is given, from which the energy of the arc channel is no longer converted into shock waves. Through the analysis and calculation, it is found that the magnitude of the shock wave overpressure caused by impulse discharge arc expansion is closely related to the arc current rising rate. The arc shock wave overpressure will undergo a slow decay process and then decay rapidly. The study of this paper will perform the function of deepening the understanding of the physical nature of the impulse arc discharge, which can be used to explain the damage effect of the high current impulse discharge arc.

Microwave interferometry technique for obtaining gas interface velocity measurements in an expansion tube facility

NASA Technical Reports Server (NTRS)

Laney, C. C., Jr.

1974-01-01

A microwave interferometer technique to determine the front interface velocity of a high enthalpy gas flow, is described. The system is designed to excite a standing wave in an expansion tube, and to measure the shift in this standing wave as it is moved by the test gas front. Data, in the form of a varying sinusoidal signal, is recorded on a high-speed drum camera-oscilloscope combination. Measurements of average and incremental velocities in excess of 6,000 meters per second were made.

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.

Rarefaction waves, solitons, and holes in a pure electron plasma

NASA Astrophysics Data System (ADS)

Moody, J. D.; Driscoll, C. F.

1995-12-01

The propagation of holes, solitons, and rarefaction waves along the axis of a magnetized pure electron plasma column is described. The time dependence of the radially averaged density perturbation produced by the nonlinear waves is measured at several locations along the plasma column for a wide range of plasma parameters. The rarefaction waves are studied by measuring the free expansion of the plasma into a vacuum. A new hydrodynamic theory is described that quantitatively predicts the free expansion measurements. The rarefaction is initially characterized by a self-similar plasma flow, resulting in a perturbed density and velocity without a characteristic length scale. The electron solitons show a small increase in propagation speed with increasing amplitude and exhibit electron bursts. The holes show a decrease in propagation speed with increasing amplitude. Collisions between holes and solitons show that these objects pass through each other undisturbed, except for a small offset.

TRILEX and G W +EDMFT approach to d -wave superconductivity in the Hubbard model

NASA Astrophysics Data System (ADS)

Vučičević, J.; Ayral, T.; Parcollet, O.

2017-09-01

We generalize the recently introduced TRILEX approach (TRiply irreducible local EXpansion) to superconducting phases. The method treats simultaneously Mott and spin-fluctuation physics using an Eliashberg theory supplemented by local vertex corrections determined by a self-consistent quantum impurity model. We show that, in the two-dimensional Hubbard model, at strong coupling, TRILEX yields a d -wave superconducting dome as a function of doping. Contrary to the standard cluster dynamical mean field theory (DMFT) approaches, TRILEX can capture d -wave pairing using only a single-site effective impurity model. We also systematically explore the dependence of the superconducting temperature on the bare dispersion at weak coupling, which shows a clear link between strong antiferromagnetic (AF) correlations and the onset of superconductivity. We identify a combination of hopping amplitudes particularly favorable to superconductivity at intermediate doping. Finally, we study within G W +EDMFT the low-temperature d -wave superconducting phase at strong coupling in a region of parameter space with reduced AF fluctuations.

Speckle reduction in optical coherence tomography images based on wave atoms

PubMed Central

Du, Yongzhao; Liu, Gangjun; Feng, Guoying; Chen, Zhongping

2014-01-01

Abstract. Optical coherence tomography (OCT) is an emerging noninvasive imaging technique, which is based on low-coherence interferometry. OCT images suffer from speckle noise, which reduces image contrast. A shrinkage filter based on wave atoms transform is proposed for speckle reduction in OCT images. Wave atoms transform is a new multiscale geometric analysis tool that offers sparser expansion and better representation for images containing oscillatory patterns and textures than other traditional transforms, such as wavelet and curvelet transforms. Cycle spinning-based technology is introduced to avoid visual artifacts, such as Gibbs-like phenomenon, and to develop a translation invariant wave atoms denoising scheme. The speckle suppression degree in the denoised images is controlled by an adjustable parameter that determines the threshold in the wave atoms domain. The experimental results show that the proposed method can effectively remove the speckle noise and improve the OCT image quality. The signal-to-noise ratio, contrast-to-noise ratio, average equivalent number of looks, and cross-correlation (XCOR) values are obtained, and the results are also compared with the wavelet and curvelet thresholding techniques. PMID:24825507

Universal relations for spin-orbit-coupled Fermi gas near an s -wave resonance

NASA Astrophysics Data System (ADS)

Zhang, Pengfei; Sun, Ning

2018-04-01

Synthetic spin-orbit-coupled quantum gases have been widely studied both experimentally and theoretically in the past decade. As shown in previous studies, this modification of single-body dispersion will in general couple different partial waves of the two-body scattering and thus distort the wave function of few-body bound states which determines the short-distance behavior of many-body wave function. In this work, we focus on the two-component Fermi gas with one-dimensional or three-dimensional spin-orbit coupling (SOC) near an s -wave resonance. Using the method of effective field theory and the operator product expansion, we derive universal relations for both systems, including the adiabatic theorem, viral theorem, and pressure relation, and obtain the momentum distribution matrix 〈ψa†(q ) ψb(q ) 〉 at large q (a ,b are spin indices). The momentum distribution matrix shows both spin-dependent and spatial anisotropic features. And the large momentum tail is modified at the subleading order thanks to the SOC. We also discuss the experimental implication of these results depending on the realization of the SOC.

Turbulent mixing noise from supersonic jets

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Chen, Ping

1994-01-01

There is now a substantial body of theoretical and experimental evidence that the dominant part of the turbulent noise of supersonic jets is generated directly by the large turbulence structures/instability waves of the jet flow. Earlier, Tam and Burton provided a description of the physical mechanism by which supersonically traveling instability waves can generate sound efficiently. They used the method of matched asymptotic expansions to construct an instability wave solution which is valid in the far field. The present work is an extension of the theory of Tam and Burton. It is argued that the instability wave spectrum of the jet may be regarded as generated by stochastic white noise excitation at the nozzle lip region. The reason why the excitation has white noise characteristics is that near the nozzle lip region the flow in the jet mixing layer has no intrinsic length and time scales. The present stochastic wave model theory of supersonic jet noise contains a single unknown multiplicative constant. Comparisons between the calculated noise directivities at selected Strouhal numbers and experimental measurements of a Mach 2 jet at different jet temperatures have been carried out. Favorable agreements are found.

Photoelectron wave function in photoionization: Plane wave or Coulomb wave? [Does photoionization of neutral targets produce Coulomb or plane waves?

DOE PAGES

Gozem, Samer; Gunina, Anastasia O.; Ichino, Takatoshi; ...

2015-10-28

The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectronmore » wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. Finally, the results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion.« less

Chemical Kinetics in the expansion flow field of a rotating detonation-wave engine

NASA Astrophysics Data System (ADS)

Kailasanath, Kazhikathra; Schwer, Douglas

2014-11-01

Rotating detonation-wave engines (RDE) are a form of continuous detonation-wave engines. They potentially provide further gains in performance than an intermittent or pulsed detonation-wave engine (PDE). The overall flow field in an idealized RDE, primarily consisting of two concentric cylinders, has been discussed in previous meetings. Because of the high pressures involved and the lack of adequate reaction mechanisms for this regime, previous simulations have typically used simplified chemistry models. However, understanding the exhaust species concentrations in propulsion devices is important for both performance considerations as well as estimating pollutant emissions. A key step towards addressing this need will be discussed in this talk. In this approach, an induction parameter model is used for simulating the detonation but a more detailed finite-chemistry model is used in the expansion flow region, where the pressures are lower and the uncertainties in the chemistry model are greatly reduced. Results show that overall radical concentrations in the exhaust flow are substantially lower than from earlier predictions with simplified models. The performance of a baseline hydrogen/air RDE increased from 4940 s to 5000 s with the expansion flow chemistry, due to recombination of radicals and more production of H2O, resulting in additional heat release.

On the convergence of the coupled-wave approach for lamellar diffraction gratings

NASA Technical Reports Server (NTRS)

Li, Lifeng; Haggans, Charles W.

1992-01-01

Among the many existing rigorous methods for analyzing diffraction of electromagnetic waves by diffraction gratings, the coupled-wave approach stands out because of its versatility and simplicity. It can be applied to volume gratings and surface relief gratings, and its numerical implementation is much simpler than others. In addition, its predictions were experimentally validated in several cases. These facts explain the popularity of the coupled-wave approach among many optical engineers in the field of diffractive optics. However, a comprehensive analysis of the convergence of the model predictions has never been presented, although several authors have recently reported convergence difficulties with the model when it is used for metallic gratings in TM polarization. Herein, three points are made: (1) in the TM case, the coupled-wave approach converges much slower than the modal approach of Botten et al; (2) the slow convergence is caused by the use of Fourier expansions for the permittivity and the fields in the grating region; and (3) is manifested by the slow convergence of the eigenvalues and the associated modal fields. The reader is assumed to be familiar with the mathematical formulations of the coupled-wave approach and the modal approach.

Analysis of Oblique Wave Interaction with a Comb-Type Caisson Breakwater

NASA Astrophysics Data System (ADS)

Wang, Xinyu; Liu, Yong; Liang, Bingchen

2018-04-01

This study develops an analytical solution for oblique wave interaction with a comb-type caisson breakwater based on linear potential theory. The fluid domain is divided into inner and outer regions according to the geometrical shape of breakwater. By using periodic boundary condition and separation of variables, series solutions of velocity potentials in inner and outer regions are developed. Unknown expansion coefficients in series solutions are determined by matching velocity and pressure of continuous conditions on the interface between two regions. Then, hydrodynamic quantities involving reflection coefficients and wave forces acting on breakwater are estimated. Analytical solution is validated by a multi-domain boundary element method solution for the present problem. Diffusion reflection due to periodic variations in breakwater shape and corresponding surface elevations around the breakwater are analyzed. Numerical examples are also presented to examine effects of caisson parameters on total wave forces acting on caissons and total wave forces acting on side plates. Compared with a traditional vertical wall breakwater, the wave force acting on a suitably designed comb-type caisson breakwater can be significantly reduced. This study can give a better understanding of the hydrodynamic performance of comb-type caisson breakwaters.

Shear wave speed recovery using moving interference patterns obtained in sonoelastography experiments.

PubMed

McLaughlin, Joyce; Renzi, Daniel; Parker, Kevin; Wu, Zhe

2007-04-01

Two new experiments were created to characterize the elasticity of soft tissue using sonoelastography. In both experiments the spectral variance image displayed on a GE LOGIC 700 ultrasound machine shows a moving interference pattern that travels at a very small fraction of the shear wave speed. The goal of this paper is to devise and test algorithms to calculate the speed of the moving interference pattern using the arrival times of these same patterns. A geometric optics expansion is used to obtain Eikonal equations relating the moving interference pattern arrival times to the moving interference pattern speed and then to the shear wave speed. A cross-correlation procedure is employed to find the arrival times; and an inverse Eikonal solver called the level curve method computes the speed of the interference pattern. The algorithm is tested on data from a phantom experiment performed at the University of Rochester Center for Biomedical Ultrasound.

Modeling a surface-mounted Lamb wave emission-reception system: applications to structural health monitoring.

PubMed

Moulin, Emmanuel; Grondel, Sébastien; Assaad, Jamal; Duquenne, Laurent

2008-12-01

The work described in this paper is intended to present a simple and efficient way of modeling a full Lamb wave emission and reception system. The emitter behavior and the Lamb wave generation are predicted using a two-dimensional (2D) hybrid finite element-normal mode expansion model. Then the receiver electrical response is obtained from a finite element computation with prescribed displacements. A numerical correction is applied to the 2D results in order to account for the in-plane radiation divergence caused by the finite length of the emitter. The advantage of this modular approach is that realistic configurations can be simulated without performing cumbersome modeling and time-consuming computations. It also provides insight into the physical interpretation of the results. A good agreement is obtained between predicted and measured signals. The range of application of the method is discussed.

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.

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

Zeng, Fan W.; Contescu, Cristian I.; Gallego, Nidia C.

Laser ultrasonic line source methods have been used to study elastic anisotropy in nuclear graphites by measuring shear wave birefringence. Depending on the manufacturing processes used during production, nuclear graphites can exhibit various degrees of material anisotropy related to preferred crystallite orientation and to microcracking. In this paper, laser ultrasonic line source measurements of shear wave birefringence on NBG-25 have been performed to assess elastic anisotropy. Laser line sources allow specific polarizations for shear waves to be transmitted – the corresponding wavespeeds can be used to compute bulk, elastic moduli that serve to quantify anisotropy. These modulus values can bemore » interpreted using physical property models based on orientation distribution coefficients and microcrack-modified, single crystal moduli to represent the combined effects of crystallite orientation and microcracking on material anisotropy. Finally, ultrasonic results are compared to and contrasted with measurements of anisotropy based on the coefficient of thermal expansion to show the relationship of results from these techniques.« less

Mode conversion in cold low-density plasma with a sheared magnetic field

DOE PAGES

Dodin, I. Y.; Ruiz, D. E.; Kubo, S.

2017-12-19

Here, a theory is proposed that describes mutual conversion of two electromagnetic modes in cold low-density plasma, specifically, in the high-frequency limit where the ion response is negligible. In contrast to the classic (Landau–Zener-type) theory of mode conversion, the region of resonant coupling in low-density plasma is not necessarily narrow, so the coupling matrix cannot be approximated with its first-order Taylor expansion; also, the initial conditions are set up differently. For the case of strong magnetic shear, a simple method is identified for preparing a two-mode wave such that it transforms into a single-mode wave upon entering high-density plasma. Themore » theory can be used for reduced modeling of wave-power input in fusion plasmas. In particular, applications are envisioned in stellarator research, where the mutual conversion of two electromagnetic modes near the plasma edge is a known issue.« less

Mode conversion in cold low-density plasma with a sheared magnetic field

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

Dodin, I. Y.; Ruiz, D. E.; Kubo, S.

Here, a theory is proposed that describes mutual conversion of two electromagnetic modes in cold low-density plasma, specifically, in the high-frequency limit where the ion response is negligible. In contrast to the classic (Landau–Zener-type) theory of mode conversion, the region of resonant coupling in low-density plasma is not necessarily narrow, so the coupling matrix cannot be approximated with its first-order Taylor expansion; also, the initial conditions are set up differently. For the case of strong magnetic shear, a simple method is identified for preparing a two-mode wave such that it transforms into a single-mode wave upon entering high-density plasma. Themore » theory can be used for reduced modeling of wave-power input in fusion plasmas. In particular, applications are envisioned in stellarator research, where the mutual conversion of two electromagnetic modes near the plasma edge is a known issue.« less

Electronic and magnetic structures of Fe3O4 ferrimagnetic investigated by first principle, mean field and series expansions calculations

NASA Astrophysics Data System (ADS)

Masrour, R.; Hlil, E. K.; Hamedoun, M.; Benyoussef, A.; Mounkachi, O.; El Moussaoui, H.

2015-03-01

Self-consistent ab initio calculations, based on density functional theory (DFT) approach and using a full potential linear augmented plane wave (FLAPW) method, are performed to investigate both electronic and magnetic properties of the Fe3O4. Polarized spin and spin-orbit coupling are included in calculations within the framework of the antiferromagnetic state between two adjacent Fe plans. Magnetic moment considered to lie along (010) axes are computed. Obtained data from ab initio calculations are used as input for the high temperature series expansions (HTSEs) calculations to compute other magnetic parameters. The exchange interactions between the magnetic atoms Fe-Fe in Fe3O4 are given using the mean field theory. The high temperature series expansions (HTSEs) of the magnetic susceptibility of with the magnetic moments, mFe in Fe3O4 is given up to seventh order series in (1/kBT). The Néel temperature TN is obtained by HTSEs of the magnetic susceptibility series combined with the Padé approximant method. The critical exponent γ associated with the magnetic susceptibility is deduced as well.

Evidence of Biot Slow Waves in Electroseismic Measurementss on Laboratory-Scale

NASA Astrophysics Data System (ADS)

Devi, M. S.

2015-12-01

Electroseismic methods which are the opposite of seismo-electric methods have only been little investigated up to now especially in the near surface scale. These methods can generate the solid-fluid relative movement induced by the electric potential in fluid-filled porous media. These methods are the response of electro-osmosis due to the presence of the electrical double layer. Laboratory experiments and numerical simulations of electroseismic studies have been performed. Electroseismic measurements conducted in micro glass beads saturated with demineralized water. Pair of 37 x 37 mm square aluminium grids with 2 mm of aperture and 4 mm of spacing is used as the electric dipole that connected to the electric power source with the voltage output 150 V. A laser doppler vibrometer is the system used to measure velocity of vibrating objects during measurements by placing a line of reflective paper on the surface of media that scattered back a helium-neon laser. The results in homogeneous media shows that the compressional waves induced by an electric signal. We confirm that the results are not the effects of thermal expansion. We also noticed that there are two kinds of the compressional waves are recorded: fast and slow P-waves. The latter, Biot slow waves, indicate the dominant amplitude. Moreover, we found that the transition frequency (ωc) of Biot slow waves depends on mechanical parameters such as porosity and permeability. The ωc is not affected when varying conductivity of the fluid from 25 - 320 μS/cm, although the amplitude slightly changed. For the results in two layer media by placing a sandstone as a top layer shows that a large amount of transmission seismic waves (apparently as Biot slow waves) rather than converted electromagnetic-to-seismic waves. These properties have also been simulated with full waveform numerical simulations relying on Pride's (1994) using our computer code (Garambois & Dietrich, 2002). If it is true that the electric source in the safe voltage range generates seismic waves dominantly, it may be a reason of electro-osmosis dewatering technique to transport liquids. And this source may be used an alternative as a seismic source in geophysical exploration.

Uncertainty analysis for the steady-state flows in a dual throat nozzle

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

Chen, Q.-Y.; Gottlieb, David; Hesthaven, Jan S.

2005-03-20

It is well known that the steady state of an isentropic flow in a dual-throat nozzle with equal throat areas is not unique. In particular there is a possibility that the flow contains a shock wave, whose location is determined solely by the initial condition. In this paper, we consider cases with uncertainty in this initial condition and use generalized polynomial chaos methods to study the steady-state solutions for stochastic initial conditions. Special interest is given to the statistics of the shock location. The polynomial chaos (PC) expansion modes are shown to be smooth functions of the spatial variable x,more » although each solution realization is discontinuous in the spatial variable x. When the variance of the initial condition is small, the probability density function of the shock location is computed with high accuracy. Otherwise, many terms are needed in the PC expansion to produce reasonable results due to the slow convergence of the PC expansion, caused by non-smoothness in random space.« less

Linear-scaling generation of potential energy surfaces using a double incremental expansion

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

König, Carolin, E-mail: carolink@kth.se; Christiansen, Ove, E-mail: ove@chem.au.dk

We present a combination of the incremental expansion of potential energy surfaces (PESs), known as n-mode expansion, with the incremental evaluation of the electronic energy in a many-body approach. The application of semi-local coordinates in this context allows the generation of PESs in a very cost-efficient way. For this, we employ the recently introduced flexible adaptation of local coordinates of nuclei (FALCON) coordinates. By introducing an additional transformation step, concerning only a fraction of the vibrational degrees of freedom, we can achieve linear scaling of the accumulated cost of the single point calculations required in the PES generation. Numerical examplesmore » of these double incremental approaches for oligo-phenyl examples show fast convergence with respect to the maximum number of simultaneously treated fragments and only a modest error introduced by the additional transformation step. The approach, presented here, represents a major step towards the applicability of vibrational wave function methods to sizable, covalently bound systems.« less

Quantitative remote sensing study indicates doubling of coastal erosion rate in past 50 yr along a segment of the Arctic coast of Alaska

USGS Publications Warehouse

Mars, J.C.; Houseknecht, D.W.

2007-01-01

A new quantitative coastal land gained-and-lost method uses image analysis of topographic maps and Landsat thematic mapper short-wave infrared data to document accelerated coastal land loss and thermokarst lake expansion and drainage. The data span 1955-2005 along the Beaufort Sea coast north of Teshekpuk Lake in the National Petroleum Reserve in Alaska. Some areas have undergone as much as 0.9 km of coastal erosion in the past 50 yr. Land loss attributed to coastal erosion more than doubled, from 0.48 km2 yr-1 during 1955-1985 to 1.08 km2 yr-1 during 1985-2005. Coastal erosion has breached thermokarst lakes, causing initial draining of the lakes followed by marine floodng. Although inland thermokarst lakes show some uniform expansion, lakes breached by coastal erosion display lake expansion several orders of magnitude greater than inland lakes. ?? 2007 The Geological Society of America.

Radiation from a D-dimensional collision of shock waves: Two-dimensional reduction and Carter-Penrose diagram

NASA Astrophysics Data System (ADS)

Coelho, Flávio S.; Sampaio, Marco O. P.

2016-05-01

We analyze the causal structure of the two-dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two D-dimensional Aichelburg-Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter-Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green’s functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method.

An outline of cellular automaton universe via cosmological KdV equation

NASA Astrophysics Data System (ADS)

Christianto, V.; Smarandache, F.; Umniyati, Y.

2018-03-01

It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such a sound wave model of cosmology is rarely developed fully into a complete framework. This paper can be considered as our second attempt towards such a complete description of the Universe based on soliton wave solution of cosmological KdV equation. Then we advance further this KdV equation by virtue of Cellular Automaton method to solve the PDEs. We submit wholeheartedly Robert Kuruczs hypothesis that Big Bang should be replaced with a finite cellular automaton universe with no expansion [4][5]. Nonetheless, we are fully aware that our model is far from being complete, but it appears the proposed cellular automaton model of the Universe is very close in spirit to what Konrad Zuse envisaged long time ago. It is our hope that the new proposed method can be verified with observation data. But we admit that our model is still in its infancy, more researches are needed to fill all the missing details.

Waveform inversion for 3-D earth structure using the Direct Solution Method implemented on vector-parallel supercomputer

NASA Astrophysics Data System (ADS)

Hara, Tatsuhiko

2004-08-01

We implement the Direct Solution Method (DSM) on a vector-parallel supercomputer and show that it is possible to significantly improve its computational efficiency through parallel computing. We apply the parallel DSM calculation to waveform inversion of long period (250-500 s) surface wave data for three-dimensional (3-D) S-wave velocity structure in the upper and uppermost lower mantle. We use a spherical harmonic expansion to represent lateral variation with the maximum angular degree 16. We find significant low velocities under south Pacific hot spots in the transition zone. This is consistent with other seismological studies conducted in the Superplume project, which suggests deep roots of these hot spots. We also perform simultaneous waveform inversion for 3-D S-wave velocity and Q structure. Since resolution for Q is not good, we develop a new technique in which power spectra are used as data for inversion. We find good correlation between long wavelength patterns of Vs and Q in the transition zone such as high Vs and high Q under the western Pacific.

Assessing the contributions of surface waves and complex rays to far-field Mie scattering by use of the Debye series

NASA Technical Reports Server (NTRS)

Hovenac, Edward A.; Lock, James A.

1991-01-01

The contributions of complex rays and the secondary radiation shed by surface waves to scattering by a dielectric sphere are calculated in the context of the Debye series expansion of the Mie scattering amplitudes. Also, the contributions of geometrical rays are reviewed and compared with the Debye series. Interference effects between surface waves, complex waves, and geometrical waves are calculated, and the possibility of observing these interference effects is discussed. Experimental data supporting the observation of a surface wave-geometrical pattern is presented.

Nonplanar electrostatic shock waves in dense plasmas

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

Masood, W.; Rizvi, H.

2010-02-15

Two-dimensional quantum ion acoustic shock waves (QIASWs) are studied in an unmagnetized plasma consisting of electrons and ions. In this regard, a nonplanar quantum Kadomtsev-Petviashvili-Burgers (QKPB) equation is derived using the small amplitude perturbation expansion method. Using the tangent hyperbolic method, an analytical solution of the planar QKPB equation is obtained and subsequently used as the initial profile to numerically solve the nonplanar QKPB equation. It is observed that the increasing number density (and correspondingly the quantum Bohm potential) and kinematic viscosity affect the propagation characteristics of the QIASW. The temporal evolution of the nonplanar QIASW is investigated both inmore » Cartesian and polar planes and the results are discussed from the numerical stand point. The results of the present study may be applicable in the study of propagation of small amplitude localized electrostatic shock structures in dense astrophysical environments.« less

The solution of non-linear hyperbolic equation systems by the finite element method

NASA Technical Reports Server (NTRS)

Loehner, R.; Morgan, K.; Zienkiewicz, O. C.

1984-01-01

A finite-element method for the solution of nonlinear hyperbolic systems of equations, such as those encountered in non-self-adjoint problems of transient phenomena in convection-diffusion or in the mixed representation of wave problems, is developed and demonstrated. The problem is rewritten in moving coordinates and reinterpolated to the original mesh by a Taylor expansion prior to a standard Galerkin spatial discretization, and it is shown that this procedure is equivalent to the time-discretization approach of Donea (1984). Numerical results for sample problems are presented graphically, including such shallow-water problems as the breaking of a dam, the shoaling of a wave, and the outflow of a river; compressible flows such as the isothermal flow in a nozzle and the Riemann shock-tube problem; and the two-dimensional scalar-advection, nonlinear-shallow-water, and Euler equations.

Computational investigations of the band structure, and thermodynamic and optical features of thorium-based oxide ThGeO4 using the full-potential linearized augmented plane-wave plus local orbital approach

NASA Astrophysics Data System (ADS)

Chiker, F.; Khachai, H.; Mathieu, C.; Bin-Omran, S.; Kada, Belkacem; Sun, Xiao-Wei; Sandeep; Rai, D. P.; Khenata, R.

2018-05-01

In this study, first-principles investigations were performed using the full-potential linearized augmented plane-wave method of the structural and optoelectronic properties of thorium germinate (ThGeO4), a high-K dielectric material. Under ambient conditions, the structural properties calculated for ThGeO4 in the zircon phase were in excellent agreement with the available experimental data. Furthermore, using the modified Becke -Johnson correction method, the calculated band gaps and optical constants accurately described this compound. Finally, the thermal properties were predicted over a temperature range of 0-700 K and pressures up to 11 GPa using the quasi-harmonic Debye model, where the variations in the heat capacity, primitive cell volume, and thermal expansion coefficients were determined successfully.

Large Alfvén wave power in the plasma sheet boundary layer during the expansion phase of substorms

NASA Astrophysics Data System (ADS)

Keiling, A.; Wygant, J. R.; Cattell, C.; Temerin, M.; Mozer, F. S.; Kletzing, C. A.; Scudder, J.; Russell, C. T.; Lotko, W.; Streltsov, A. V.

2000-10-01

Observations by the Polar satellite of large Poynting flux in the plasma sheet boundary layer at geocentric distances of 4 to 6 RE and between 22 and 3 hrs magnetic local time were correlated with H-bay signatures from ground magnetometer records. We provide evidence that large Poynting fluxes occur during the substorm expansion phase. The Poynting fluxes exceeded 1 ergs/cm²s (125 ergs/cm²s when mapped to 100 km), were dominantly directed toward the ionosphere, and were associated with Alfvén waves. These observations demonstrate the importance of Alfvén wave power as a means of energy transport from the distant magnetotail to the ionosphere during the most dynamic phase of substorms.

Stepwise and Pulse Transient Methods of Thermophysical Parameters Measurement

NASA Astrophysics Data System (ADS)

Malinarič, Svetozár; Dieška, Peter

2016-12-01

Stepwise transient and pulse transient methods are experimental techniques for measuring the thermal diffusivity and conductivity of solid materials. Theoretical models and experimental apparatus are presented, and the influence of the heat source capacity and the heat transfer coefficient is investigated using the experiment simulation. The specimens from low-density polyethylene (LDPE) and polymethylmethacrylate (PMMA) were measured by both methods. Coefficients of variation were better than 0.9 % for LDPE and 2.8 % for PMMA measurements. The time dependence of the temperature response to the input heat flux showed a small drop, which was caused by thermoelastic wave generated by thermal expansions of the heat source.

Efficient Unstructured Grid Adaptation Methods for Sonic Boom Prediction

NASA Technical Reports Server (NTRS)

Campbell, Richard L.; Carter, Melissa B.; Deere, Karen A.; Waithe, Kenrick A.

2008-01-01

This paper examines the use of two grid adaptation methods to improve the accuracy of the near-to-mid field pressure signature prediction of supersonic aircraft computed using the USM3D unstructured grid flow solver. The first method (ADV) is an interactive adaptation process that uses grid movement rather than enrichment to more accurately resolve the expansion and compression waves. The second method (SSGRID) uses an a priori adaptation approach to stretch and shear the original unstructured grid to align the grid with the pressure waves and reduce the cell count required to achieve an accurate signature prediction at a given distance from the vehicle. Both methods initially create negative volume cells that are repaired in a module in the ADV code. While both approaches provide significant improvements in the near field signature (< 3 body lengths) relative to a baseline grid without increasing the number of grid points, only the SSGRID approach allows the details of the signature to be accurately computed at mid-field distances (3-10 body lengths) for direct use with mid-field-to-ground boom propagation codes.

Numerical solutions of ideal quantum gas dynamical flows governed by semiclassical ellipsoidal-statistical distribution.

PubMed

Yang, Jaw-Yen; Yan, Chih-Yuan; Diaz, Manuel; Huang, Juan-Chen; Li, Zhihui; Zhang, Hanxin

2014-01-08

The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wu et al. (Wu et al . 2012 Proc. R. Soc. A 468 , 1799-1823 (doi:10.1098/rspa.2011.0673)) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi-Dirac or Bose-Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas.

Intraluminal bubble dynamics induced by lithotripsy shock wave

NASA Astrophysics Data System (ADS)

Song, Jie; Bai, Jiaming; Zhou, Yufeng

2016-12-01

Extracorporeal shock wave lithotripsy (ESWL) has been the first option in the treatment of calculi in the upper urinary tract since its introduction. ESWL-induced renal injury is also found after treatment and is assumed to associate with intraluminal bubble dynamics. To further understand the interaction of bubble expansion and collapse with the vessel wall, the finite element method (FEM) was used to simulate intraluminal bubble dynamics and calculate the distribution of stress in the vessel wall and surrounding soft tissue during cavitation. The effects of peak pressure, vessel size, and stiffness of soft tissue were investigated. Significant dilation on the vessel wall occurs after contacting with rapid and large bubble expansion, and then vessel deformation propagates in the axial direction. During bubble collapse, large shear stress is found to be applied to the vessel wall at a clinical lithotripter setting (i.e. 40 MPa peak pressure), which may be the mechanism of ESWL-induced vessel rupture. The decrease of vessel size and viscosity of soft tissue would enhance vessel deformation and, consequently, increase the generated shear stress and normal stresses. Meanwhile, a significantly asymmetric bubble boundary is also found due to faster axial bubble expansion and shrinkage than in radial direction, and deformation of the vessel wall may result in the formation of microjets in the axial direction. Therefore, this numerical work would illustrate the mechanism of ESWL-induced tissue injury in order to develop appropriate counteractive strategies for reduced adverse effects.

Two dimensional nonplanar evolution of electrostatic shock waves in pair-ion plasmas

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

Masood, W.; Rizvi, H.

2012-01-15

Electrostatic waves in a two dimensional nonplanar geometry are studied in an unmagnetized, dissipative pair-ion plasma in the presence of weak transverse perturbations. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions in plasmas. The nonplanar Kadomtsev-Petviashvili-Burgers (KPB) as well as the Burgers Kadomtsev-Petviashvili (Burgers KP) equations are derived using the small amplitude expansion method and the range of applicability of both the equations are discussed. The system under consideration is observed to admit compressive rarefactive shocks. The present study may have relevance to understand the formation of twomore » dimensional nonplanar electrostatic shocks in laboratory plasmas.« less

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

Bischoff, A. J., E-mail: alina.bischoff@iom-leipzig.de; Arabi-Hashemi, A.; Ehrhardt, M.

Combining experimental methods and classical molecular dynamics (MD) computer simulations, we explore the martensitic transformation in Fe{sub 70}Pd{sub 30} ferromagnetic shape memory alloy thin films induced by laser shock peening. X-ray diffraction and scanning electron microscope measurements at shock wave pressures of up to 2.5 GPa reveal formation of martensitic variants with preferred orientation of the shorter c-axis of the tetragonal unit cell perpendicular to the surface plane. Moreover, consequential merging of growth islands on the film surface is observed. MD simulations unveil the underlying physics that are characterized by an austenite-martensite transformation with a preferential alignment of the c-axis alongmore » the propagation direction of the shock wave, resulting in flattening and in-plane expansion of surface features.« less

Exploring the distinction between experimental resonant modes and theoretical eigenmodes: from vibrating plates to laser cavities.

PubMed

Tuan, P H; Wen, C P; Yu, Y T; Liang, H C; Huang, K F; Chen, Y F

2014-02-01

Experimentally resonant modes are commonly presumed to correspond to eigenmodes in the same bounded domain. However, the one-to-one correspondence between theoretical eigenmodes and experimental observations is never reached. Theoretically, eigenmodes in numerous classical and quantum systems are the solutions of the homogeneous Helmholtz equation, whereas resonant modes should be solved from the inhomogeneous Helmholtz equation. In the present paper we employ the eigenmode expansion method to derive the wave functions for manifesting the distinction between eigenmodes and resonant modes. The derived wave functions are successfully used to reconstruct a variety of experimental results including Chladni figures generated from the vibrating plate, resonant patterns excited from microwave cavities, and lasing modes emitted from the vertical cavity.

Perturbation method for the second-order nonlinear effect of focused acoustic field around a scatterer in an ideal fluid.

PubMed

Liu, Gang; Jayathilake, Pahala Gedara; Khoo, Boo Cheong

2014-02-01

Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects. Copyright © 2013 Elsevier B.V. All rights reserved.

Convection in deep vertically shaken particle beds. III. Convection mechanisms

NASA Astrophysics Data System (ADS)

Klongboonjit, Sakon; Campbell, Charles S.

2008-10-01

Convection in a deep vertically vibrated two-dimensional cell of granular material occurs in the form of counter-rotating cells that move material from the walls to the center of the channel and back again. At least for deep beds, where for much of the cycle, particles are in long duration contact with their neighbors, convection only appears for a short potion of every third vibrational period. That period is delimited by the interaction of three types of internal waves, a compression wave, and two types of expansion waves. Four mechanisms are identified that drive the four basic motions of convection: (1) particles move upward at the center as the result of compression wave, (2) downward at the wall as a combined effect of frictional holdback by the walls and the downward pull of gravity, (3) from the center to the walls along the free surface due to the heaping of the bed generated by the compression wave, and (4) toward the center in the interior of the box to form the bottom of convection rolls due to the relaxation of compressive stresses caused by an expansion wave. Convection only occurs when the conditions are right for all four mechanisms to be active simultaneously.

Low-Frequency Waves in the Near-Earth Magnetotail before Substorm Expansion Onsets

NASA Astrophysics Data System (ADS)

Miyashita, Y.; Saito, M. H.; Hiraki, Y.; Machida, S.

2013-12-01

Magnetic reconnection and dipolarization, which occur in the near-Earth magnetotail just before substorm expansion onsets, are important processes for the substorm triggering. To understand the triggering of these processes, we have investigated low-frequency waves that were observed in the near-Earth magnetotail before onsets, by performing statistical analysis based on Geotail observations and case studies based on multi-point THEMIS and Geotail observations. Here we focused our examination on ~10 min interval before onsets. We find that small-amplitude Alfven and slow-mode magnetosonic waves with a period of ~1 to 2 min continuously exist for more than 10 min before onsets. Such waves are seen not only in the initial dipolarization region but also midway between the magnetic reconnection and initial dipolarization regions. It seems that the amplitudes of the waves are larger in the off-equator plasma sheet and the plasma sheet boundary layer than at the magnetic equator and in the lobe. After onsets the waves considerably amplify in the plasma sheet. These results may imply that instabilities already begin to grow gradually in a wide region during the substorm growth phase, while their explosive growth begins in localized regions just before onsets.

Gravity–capillary waves in finite depth on flows of constant vorticity

PubMed Central

Hsu, Hung-Chu; Francius, Marc; Kharif, Christian

2016-01-01

This paper considers two-dimensional periodic gravity–capillary waves propagating steadily in finite depth on a linear shear current (constant vorticity). A perturbation series solution for steady periodic waves, accurate up to the third order, is derived using a classical Stokes expansion procedure, which allows us to include surface tension effects in the analysis of wave–current interactions in the presence of constant vorticity. The analytical results are then compared with numerical computations with the full equations. The main results are (i) the phase velocity is strongly dependent on the value of the vorticity; (ii) the singularities (Wilton singularities) in the Stokes expansion in powers of wave amplitude that correspond to a Bond number of 1/2 and 1/3, which are the consequences of the non-uniformity in the ordering of the Fourier coefficients, are found to be influenced by vorticity; (iii) different surface profiles of capillary–gravity waves are computed and the effect of vorticity on those profiles is shown to be important, in particular that the solutions exhibit type-2-like wave features, characterized by a secondary maximum on the surface profile with a trough between the two maxima. PMID:27956873

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

Vincena, Stephen

The aim of the original proposal was a basic plasma study to experimentally investigate the fundamental physics of how dense, fast-flowing, and field-aligned jets of plasma couple energy and momentum to a much larger, ambient, magnetized plasma. Coupling channels that were explored included bulk plasma heating and flow generation; shock wave production; and wave radiation, particularly in the form of shear and compressional Alfvén waves. The wave radiation, particularly to shear Alfvén waves was successfully modeled using the 3D Particle-In-Cell code, OSIRIS. Experimentally, these jets were produced via pulsed Nd:YAG laser ablation of solid carbon (graphite) rods, which were immersedmore » in the main plasma column of the Large Plasma Device (LaPD) at UCLA’s Basic Plasma Science Facility (BaPSF.) The axial expansion of the laser-produced plasma (LPP) was supersonic and with parallel expansion speeds approximately equal to the Alfvén speed. The project was renewed and refocused efforts to then utilize the laser-produced plasmas as a tool for the disruption and reconnection of current sheets in magnetized plasmas« less

An efficient technique for higher order fractional differential equation.

PubMed

Ali, Ayyaz; Iqbal, Muhammad Asad; Ul-Hassan, Qazi Mahmood; Ahmad, Jamshad; Mohyud-Din, Syed Tauseef

2016-01-01

In this study, we establish exact solutions of fractional Kawahara equation by using the idea of [Formula: see text]-expansion method. The results of different studies show that the method is very effective and can be used as an alternative for finding exact solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The solitary wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions. Graphical representations along with the numerical data reinforce the efficacy of the used procedure. The specified idea is very effective, expedient for fractional PDEs, and could be extended to other physical problems.

Asymmetric expansion of the youngest Galactic supernova remnant G1.9+0.3

NASA Astrophysics Data System (ADS)

Reynolds, Stephen P.

2016-06-01

The youngest Galactic supernova remnant (SNR) G1.9+0.3, produced by a (probable) Type Ia SN that exploded around CE 1900, is strongly asymmetric at radio wavelengths, with a single bright maximum in its shell, but exhibits a bilaterally symmetric morphology in X-rays. It has been difficult to understand the origin of these contrasting morphologies. We present the results of expansion measurements of G1.9+0.3 that illuminate the origin of the radio asymmetry. These measurements are based on a comparison of our 2015 400-ks Chandra observation with earlier Chandra observations, including a 1-Ms observation in 2011. The mean expansion rate from 2011 to 2015 is 0.58% per yr, in agreement with previous measurements. We also confirm that the expansion decreases radially away from the remnant's center along the major E-W axis, from 0.77% per yr to 0.53% per yr. Large variations in expansion are also present along the minor N-S axis, but expansion there is strongly asymmetric and varies on small spatial scales. We use the “Demons” method to study the complex motions within G1.9+0.3. This method provides a nonparametric way for measuring these motions globally. We find motions varying by a factor of 5, from 0.09" to 0.44" per year. The slowest shocks are in the north, at the outer boundary of the bright radio emission, with speeds there as low as 3,600 km/s (for an assumed distance of 8.5 kpc), much less than the average shock speed of 12,000 km/s. Such strong deceleration of the northern blast wave most likely arises from the collision of SN ejecta with a much denser than average ambient medium there. The presence of this asymmetric ambient medium naturally explains the radio asymmetry. The SN ejecta have also been strongly decelerated in the N, but they expand faster than the blast wave. In several locations, significant morphological changes and strongly nonradial motions are apparent. The spatially-integrated X-ray flux continues to increase with time. As with Kepler's SN, the most recent historical SN in the Galaxy, the SN ejecta are likely colliding with the asymmetric circumstellar medium (CSM) ejected by the SN progenitor prior to its explosion. G1.9+0.3 fills the gap between distant Type Ia-CSM SNe and older Type Ia-CSM SNRs such as Kepler's SNR, providing us with a unique opportunity to learn about SN Ia progenitors.

Scattering of Airy elastic sheets by a cylindrical cavity in a solid.

PubMed

Mitri, F G

2017-11-01

The prediction of the elastic scattering by voids (and cracks) in materials is an important process in structural health monitoring, phononic crystals, metamaterials and non-destructive evaluation/imaging to name a few examples. Earlier analytical theories and numerical computations considered the elastic scattering by voids in plane waves of infinite extent. However, current research suggesting the use of (limited-diffracting, accelerating and self-healing) Airy acoustical-sheet beams for non-destructive evaluation or imaging applications in elastic solids requires the development of an improved analytical formalism to predict the scattering efficiency used as a priori information in quantitative material characterization. Based on the definition of the time-averaged scattered power flow density, an analytical expression for the scattering efficiency of a cylindrical empty cavity (i.e., void) encased in an elastic medium is derived for compressional and normally-polarized shear-wave Airy beams. The multipole expansion method using cylindrical wave functions is utilized. Numerical computations for the scattering energy efficiency factors for compressional and shear waves illustrate the analysis with particular emphasis on the Airy beam parameters and the non-dimensional frequency, for various elastic materials surrounding the cavity. The ratio of the compressional to the shear wave speed stimulates the generation of elastic resonances, which are manifested as a series of peaks in the scattering efficiency plots. The present analysis provides an improved method for the computations of the scattering energy efficiency factors using compressional and shear-wave Airy beams in elastic materials as opposed to plane waves of infinite extent. Copyright © 2017 Elsevier B.V. All rights reserved.

Engine Cycle Analysis of Air Breathing Microwave Rocket with Reed Valves

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

Fukunari, Masafumi; Komatsu, Reiji; Yamaguchi, Toshikazu

The Microwave Rocket is a candidate for a low cost launcher system. Pulsed plasma generated by a high power millimeter wave beam drives a blast wave, and a vehicle acquires impulsive thrust by exhausting the blast wave. The thrust generation process of the Microwave Rocket is similar to a pulse detonation engine. In order to enhance the performance of its air refreshment, the air-breathing mechanism using reed valves is under development. Ambient air is taken to the thruster through reed valves. Reed valves are closed while the inside pressure is high enough. After the time when the shock wave exhaustsmore » at the open end, an expansion wave is driven and propagates to the thrust-wall. The reed valve is opened by the negative gauge pressure induced by the expansion wave and its reflection wave. In these processes, the pressure oscillation is important parameter. In this paper, the pressure oscillation in the thruster was calculated by CFD combined with the flux through from reed valves, which is estimated analytically. As a result, the air-breathing performance is evaluated using Partial Filling Rate (PFR), the ratio of thruster length to diameter L/D, and ratio of opening area of reed valves to superficial area {alpha}. An engine cycle and predicted thrust was explained.« less

Frequency-dependent Alfvén-wave Propagation in the Solar Wind: Onset and Suppression of Parametric Decay Instability

NASA Astrophysics Data System (ADS)

Shoda, Munehito; Yokoyama, Takaaki; Suzuki, Takeru K.

2018-06-01

Using numerical simulations we investigate the onset and suppression of parametric decay instability (PDI) in the solar wind, focusing on the suppression effect by the wind acceleration and expansion. Wave propagation and dissipation from the coronal base to 1 au is solved numerically in a self-consistent manner; we take into account the feedback of wave energy and pressure in the background. Monochromatic waves with various injection frequencies, f 0, are injected to discuss the suppression of PDI, while broadband waves are applied to compare the numerical results with observation. We find that high-frequency ({f}0≳ {10}-3 {Hz}) Alfvén waves are subject to PDI. Meanwhile, the maximum growth rate of the PDI of low-frequency ({f}0≲ {10}-4 {Hz}) Alfvén waves becomes negative due to acceleration and expansion effects. Medium-frequency ({f}0≈ {10}-3.5 {Hz}) Alfvén waves have a positive growth rate but do not show the signature of PDI up to 1 au because the growth rate is too small. The medium-frequency waves experience neither PDI nor reflection so they propagate through the solar wind most efficiently. The solar wind is shown to possess a frequency-filtering mechanism with respect to Alfvén waves. The simulations with broadband waves indicate that the observed trend of the density fluctuation is well explained by the evolution of PDI while the observed cross-helicity evolution is in agreement with low-frequency wave propagation.

Ground states of larger nuclei

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

Pieper, S.C.; Wiringa, R.B.; Pandharipande, V.R.

1995-08-01

The methods used for the few-body nuclei require operations on the complete spin-isospin vector; the size of this vector makes such methods impractical for nuclei with A > 8. During the last few years we developed cluster expansion methods that do not require operations on the complete vector. We use the same Hamiltonians as for the few-body nuclei and variational wave functions of form similar to the few-body wave functions. The cluster expansions are made for the noncentral parts of the wave functions and for the operators whose expectation values are being evaluated. The central pair correlations in the wavemore » functions are treated exactly and this requires the evaluation of 3A-dimensional integrals which are done with Monte Carlo techniques. Most of our effort was on {sup 16}O, other p-shell nuclei, and {sup 40}Ca. In 1993 the Mathematics and Computer Science Division acquired a 128-processor IBM SP which has a theoretical peak speed of 16 Gigaflops (GFLOPS). We converted our program to run on this machine. Because of the large memory on each node of the SP, it was easy to convert the program to parallel form with very low communication overhead. Considerably more effort was needed to restructure the program from one oriented towards long vectors for the Cray computers at NERSC to one that makes efficient use of the cache of the RS6000 architecture. The SP made possible complete five-body cluster calculations of {sup 16}O for the first time; previously we could only do four-body cluster calculations. These calculations show that the expectation value of the two-body potential is converging less rapidly than we had thought, while that of the three-body potential is more rapidly convergent; the net result is no significant change to our predicted binding energy for {sup 16}O using the new Argonne v{sub 18} potential and the Urbana IX three-nucleon potential. This result is in good agreement with experiment.« less

A coupled-mode model for the hydroelastic analysis of large floating bodies over variable bathymetry regions

NASA Astrophysics Data System (ADS)

Belibassakis, K. A.; Athanassoulis, G. A.

2005-05-01

The consistent coupled-mode theory (Athanassoulis & Belibassakis, J. Fluid Mech. vol. 389, 1999, p. 275) is extended and applied to the hydroelastic analysis of large floating bodies of shallow draught or ice sheets of small and uniform thickness, lying over variable bathymetry regions. A parallel-contour bathymetry is assumed, characterized by a continuous depth function of the form h( {x,y}) {=} h( x ), attaining constant, but possibly different, values in the semi-infinite regions x {<} a and x {>} b. We consider the scattering problem of harmonic, obliquely incident, surface waves, under the combined effects of variable bathymetry and a floating elastic plate, extending from x {=} a to x {=} b and {-} infty {<} y{<}infty . Under the assumption of small-amplitude incident waves and small plate deflections, the hydroelastic problem is formulated within the context of linearized water-wave and thin-elastic-plate theory. The problem is reformulated as a transition problem in a bounded domain, for which an equivalent, Luke-type (unconstrained), variational principle is given. In order to consistently treat the wave field beneath the elastic floating plate, down to the sloping bottom boundary, a complete, local, hydroelastic-mode series expansion of the wave field is used, enhanced by an appropriate sloping-bottom mode. The latter enables the consistent satisfaction of the Neumann bottom-boundary condition on a general topography. By introducing this expansion into the variational principle, an equivalent coupled-mode system of horizontal equations in the plate region (a {≤} x {≤} b) is derived. Boundary conditions are also provided by the variational principle, ensuring the complete matching of the wave field at the vertical interfaces (x{=}a and x{=}b), and the requirements that the edges of the plate are free of moment and shear force. Numerical results concerning floating structures lying over flat, shoaling and corrugated seabeds are presented and compared, and the effects of wave direction, bottom slope and bottom corrugations on the hydroelastic response are presented and discussed. The present method can be easily extended to the fully three-dimensional hydroelastic problem, including bodies or structures characterized by variable thickness (draught), flexural rigidity and mass distributions.

Hyperspherical close-coupling calculations for charge-transfer cross sections in He2++H(1s) collisions at low energies

NASA Astrophysics Data System (ADS)

Liu, Chien-Nan; Le, Anh-Thu; Morishita, Toru; Esry, B. D.; Lin, C. D.

2003-05-01

A theory for ion-atom collisions at low energies based on the hyperspherical close-coupling (HSCC) method is presented. In hyperspherical coordinates the wave function is expanded in analogy to the Born-Oppenheimer approximation where the adiabatic channel functions are calculated with B-spline basis functions while the coupled hyperradial equations are solved by a combination of R-matrix propagation and the slow/smooth variable discretization method. The HSCC method is applied to calculate charge-transfer cross sections for He2++H(1s)→He+(n=2)+H+ reactions at center-of-mass energies from 10 eV to 4 keV. The results are shown to be in general good agreement with calculations based on the molecular orbital (MO) expansion method where electron translation factors (ETF’s) or switching functions have been incorporated in each MO. However, discrepancies were found at very low energies. It is shown that the HSCC method can be used to study low-energy ion-atom collisions without the need to introduce the ad hoc ETF’s, and the results are free from ambiguities associated with the traditional MO expansion approach.

Modeling the Warming Impact of Urban Land Expansion on Hot Weather Using the Weather Research and Forecasting Model: A Case Study of Beijing, China

NASA Astrophysics Data System (ADS)

Liu, Xiaojuan; Tian, Guangjin; Feng, Jinming; Ma, Bingran; Wang, Jun; Kong, Lingqiang

2018-06-01

The impacts of three periods of urban land expansion during 1990-2010 on near-surface air temperature in summer in Beijing were simulated in this study, and then the interrelation between heat waves and urban warming was assessed. We ran the sensitivity tests using the mesoscaleWeather Research and Forecasting model coupled with a single urban canopy model, as well as high-resolution land cover data. The warming area expanded approximately at the same scale as the urban land expansion. The average regional warming induced by urban expansion increased but the warming speed declined slightly during 2000-2010. The smallest warming occurred at noon and then increased gradually in the afternoon before peaking at around 2000 LST—the time of sunset. In the daytime, urban warming was primarily caused by the decrease in latent heat flux at the urban surface. Urbanization led to more ground heat flux during the day and then more release at night, which resulted in nocturnal warming. Urban warming at night was higher than that in the day, although the nighttime increment in sensible heat flux was smaller. This was because the shallower planetary boundary layer at night reduced the release efficiency of near-surface heat. The simulated results also suggested that heat waves or high temperature weather enhanced urban warming intensity at night. Heat waves caused more heat to be stored in the surface during the day, greater heat released at night, and thus higher nighttime warming. Our results demonstrate a positive feedback effect between urban warming and heat waves in urban areas.

Axial and transverse acoustic radiation forces on a fluid sphere placed arbitrarily in Bessel beam standing wave tweezers

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

Mitri, F.G., E-mail: mitri@chevron.com

The axial and transverse radiation forces on a fluid sphere placed arbitrarily in the acoustical field of Bessel beams of standing waves are evaluated. The three-dimensional components of the time-averaged force are expressed in terms of the beam-shape coefficients of the incident field and the scattering coefficients of the fluid sphere using a partial-wave expansion (PWE) method. Examples are chosen for which the standing wave field is composed of either a zero-order (non-vortex) Bessel beam, or a first-order Bessel vortex beam. It is shown here, that both transverse and axial forces can push or pull the fluid sphere to anmore » equilibrium position depending on the chosen size parameter ka (where k is the wave-number and a the sphere’s radius). The corresponding results are of particular importance in biophysical applications for the design of lab-on-chip devices operating with Bessel beams standing wave tweezers. Moreover, potential investigations in acoustic levitation and related applications in particle rotation in a vortex beam may benefit from the results of this study. -- Highlights: •The axial and transverse forces on a fluid sphere in acoustical Bessel beams tweezers are evaluated. •The attraction or repulsion to an equilibrium position in the standing wave field is examined. •Potential applications are in particle manipulation using standing waves.« less

On the pressure field of nonlinear standing water waves

NASA Technical Reports Server (NTRS)

Schwartz, L. W.

1980-01-01

The pressure field produced by two dimensional nonlinear time and space periodic standing waves was calculated as a series expansion in the wave height. The high order series was summed by the use of Pade approximants. Calculations included the pressure variation at great depth, which was considered to be a likely cause of microseismic activity, and the pressure distribution on a vertical barrier or breakwater.

Wave propagation in strongly dispersive superthermal dusty plasma

NASA Astrophysics Data System (ADS)

El-Labany, S. K.; El-Shewy, E. K.; Abd El-Razek, H. N.; El-Rahman, A. A.

2017-04-01

The attributes of acoustic envelope waves in a collisionless dust ion unmagnetized plasmas model composed of cold ions, superthermal electrons and positive-negative dust grains have been studied. Using the derivative expansion technique in a strong dispersive medium, the system model is reduced to a nonlinearly form of Schrodinger equation (NLSE). Rational solution of NLSE in unstable region is responsible for the creation of large shape waves; namely rogue waves. The subjection of instability regions upon electron superthermality (via κ), carrier wave number and dusty grains charge is discussed.

Gravitational waveforms for neutron star binaries from binary black hole simulations

NASA Astrophysics Data System (ADS)

Barkett, Kevin; Scheel, Mark; Haas, Roland; Ott, Christian; Bernuzzi, Sebastiano; Brown, Duncan; Szilagyi, Bela; Kaplan, Jeffrey; Lippuner, Jonas; Muhlberger, Curran; Foucart, Francois; Duez, Matthew

2016-03-01

Gravitational waves from binary neutron star (BNS) and black-hole/neutron star (BHNS) inspirals are primary sources for detection by the Advanced Laser Interferometer Gravitational-Wave Observatory. The tidal forces acting on the neutron stars induce changes in the phase evolution of the gravitational waveform, and these changes can be used to constrain the nuclear equation of state. Current methods of generating BNS and BHNS waveforms rely on either computationally challenging full 3D hydrodynamical simulations or approximate analytic solutions. We introduce a new method for computing inspiral waveforms for BNS/BHNS systems by adding the post-Newtonian (PN) tidal effects to full numerical simulations of binary black holes (BBHs), effectively replacing the non-tidal terms in the PN expansion with BBH results. Comparing a waveform generated with this method against a full hydrodynamical simulation of a BNS inspiral yields a phase difference of < 1 radian over ~ 15 orbits. The numerical phase accuracy required of BNS simulations to measure the accuracy of the method we present here is estimated as a function of the tidal deformability parameter λ.

Gravitational waveforms for neutron star binaries from binary black hole simulations

NASA Astrophysics Data System (ADS)

Barkett, Kevin; Scheel, Mark A.; Haas, Roland; Ott, Christian D.; Bernuzzi, Sebastiano; Brown, Duncan A.; Szilágyi, Béla; Kaplan, Jeffrey D.; Lippuner, Jonas; Muhlberger, Curran D.; Foucart, Francois; Duez, Matthew D.

2016-02-01

Gravitational waves from binary neutron star (BNS) and black hole/neutron star (BHNS) inspirals are primary sources for detection by the Advanced Laser Interferometer Gravitational-Wave Observatory. The tidal forces acting on the neutron stars induce changes in the phase evolution of the gravitational waveform, and these changes can be used to constrain the nuclear equation of state. Current methods of generating BNS and BHNS waveforms rely on either computationally challenging full 3D hydrodynamical simulations or approximate analytic solutions. We introduce a new method for computing inspiral waveforms for BNS/BHNS systems by adding the post-Newtonian (PN) tidal effects to full numerical simulations of binary black holes (BBHs), effectively replacing the nontidal terms in the PN expansion with BBH results. Comparing a waveform generated with this method against a full hydrodynamical simulation of a BNS inspiral yields a phase difference of <1 radian over ˜15 orbits. The numerical phase accuracy required of BNS simulations to measure the accuracy of the method we present here is estimated as a function of the tidal deformability parameter λ .

Optoheterodyne Doppler measurements of the ballistic expansion of the products of the shock wave-induced surface destruction: Experiment and theory

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

Andriyash, A. V.; Astashkin, M. V.; Baranov, V. K.

2016-06-15

The results of optoheterodyne Doppler measurements of the ballistic expansion of the products of surface destruction under shock-wave loading are presented. The possibility of determining the physical characteristics of a rapidly flying dust cloud, including the microparticle velocities, the microparticle sizes, and the areal density of the dust cloud, is shown. A compact stand for performing experiments on shock-wave loading of metallic samples is described. Shock-wave loading is performed by a 100-µm-thick tantalum flyer plate accelerated to a velocity of 2.8 km/s. As the samples, lead plates having various thicknesses and the same surface roughness are used. At a shock-wavemore » pressure of 31.5 GPa, the destruction products are solid microparticles about 50 µm in size. At a pressure of 42 and 88 GPa, a liquid-drop dust cloud with a particle size of 10–15 µm is formed. To interpret the spectral data on the optoheterodyne Doppler measurements of the expansion of the surface destruction products (spalled fragments, dust microparticles), a transport equation for the function of mutual coherence of a multiply scattered field is used. The Doppler spectra of a backscattered signal are calculated with the model developed for the dust cloud that appears when a shock wave reaches the sample surface at the parameters that are typical of an experimental situation. Qualitative changes are found in the spectra, depending on the optical thickness of the dust cloud. The obtained theoretical results are in agreement with the experimental data.« less

Fundamental processes in the expansion, energization, and coupling of single- and multi-Ion plasmas in space: Laboratory simulation experiments

NASA Technical Reports Server (NTRS)

Szuszczewicz, E. P.; Bateman, T. T.

1996-01-01

We have conducted a laboratory investigation into the physics of plasma expansions and their associated energization processes. We studied single- and multi-ion plasma processes in self-expansions, and included light and heavy ions and heavy/light mixtures to encompass the phenomenological regimes of the solar and polar winds and the AMPTE and CRRES chemical release programs. The laboratory experiments provided spatially-distributed time-dependent measurements of total plasma density, temperature, and density fluctuation power spectra with the data confirming the long-theorized electron energization process in an expanding cloud - a result that was impossible to determine in spaceborne experiments (as e.g., in the CRRES program). These results provided the missing link in previous laboratory and spaceborne programs. confirming important elements in our understanding of such solar-terrestrial processes as manifested in expanding plasmas in the solar wind (e.g., CMES) and in ionospheric outflow in plasmaspheric fluctuate refilling after a storm. The energization signatures were seen in an entire series of runs that varied the ion species (Ar', Xe', Kr' and Ne'), and correlative studies included spectral analyses of electrostatic waves collocated with the energized electron distributions. In all cases wave energies were most intense during the times in which the suprathermal populations were present, with wave intensity increasing with the intensity of the suprathermal electron population. This is consistent with theoretical expectations wherein the energization process is directly attributable to wave particle interactions. No resonance conditions were observed, in an overall framework in which the general wave characteristics were broadband with power decreasing with increasing frequency.

Simulations of Magnetohydrodynamic Waves Driven by Photospheric Motions

NASA Astrophysics Data System (ADS)

Mumford, Stuart

2016-04-01

This thesis investigates the properties of various modelled photospheric motions as generation mechanisms for magnetohydrodynamic (MHD) waves in the low solar atmosphere. The solar atmosphere is heated to million-degree temperatures, yet there is no fully understood heating mechanism which can provide the ≈ 300 W/m^2) required to keep the quiet corona at its observed temperatures. MHD waves are one mechanism by which this energy could be provided to the upper solar atmosphere, however, these waves need to be excited. The excitation of these waves, in or below the photosphere is a complex interaction between the plasma and the magnetic field embedded within it. This thesis studies a model of a small-scale magnetic flux tube based upon a magnetic bright point (MBP). These features are very common in the photosphere and have been observed to be affected by the plasma motions. The modelled flux tube has a foot point magnetic field strength of 120 mT and a FWHM of 90 km, and is embedded in a realistic, stratified solar atmosphere based upon the VALIIIc model. To better understand the excitation of MHD waves in this type of magnetic structures, a selection of velocity profiles are implemented to excite waves. Initially a study of five different driving profiles was performed. A uniform torsional driver as well as Archimedean and logarithmic spiral drivers which mimic observed torsional motions in the solar photosphere, along with vertical and horizontal drivers to mimic different motions caused by convection in the photosphere. The results are then analysed using a novel method for extracting the parallel, perpendicular and azimuthal components of the perturbations, which caters to both the linear and non-linear cases. Employing this method yields the identification of the wave modes excited in the numerical simulations and enables a comparison of excited modes via velocity perturbations and wave energy flux. The wave energy flux distribution is calculated, to enable the quantification of the relative strengths of excited modes. The torsional drivers primarily excite Alfvén modes (≈ 60 %) of the total flux) with contributions from the slow mode. The horizontal and vertical drivers primarily excite slow and fast modes respectively, with small variations dependent upon flux surface radius. This analysis is then applied to more in depth studies of the logarithmic spiral driver. Firstly, five different values for the (B_L) spiral expansion factor are chosen which control how rapidly the spiral expands. Larger values of (B_L) make the driving profile more radial. The results of this analysis show that the Alfvén wave is the dominant wave for lower values of the expansion factor, whereas, for the higher values the parallel component is dominant. This transition occurs within the range of the observational constraints, demonstrating that under realistic conditions spiral drivers may not excite most of their wave flux in the Alfvén mode. Finally, the logarithmic spiral is further studied, but with a variety of different periods. Ten periods from 30 to 300 seconds are chosen, and the simulations are again analysed using the flux surface method employed previously. The results of this study are minimal variation in the percentage wave flux in each mode, with no more than 20 % variation in any mode for any flux surface studied. Within this small variation, some non-linear changes in the wave flux were observed, especially around the more important small periods. Due to the short life time of the MBPs it is thought the short period waves would have more effect and therefore this non-linear variation in wave flux could have some impact on the modes present in the solar atmosphere.

Development of the Near-Earth Magnetotail and the Auroral Arc Associated with Substorm Onset: Evidence for a New Model

NASA Astrophysics Data System (ADS)

Miyashita, Y.; Hiraki, Y.; Angelopoulos, V.; Ieda, A.; Machida, S.

2015-12-01

We have studied the time sequence of the development of the near-Earth magnetotail and the auroral arc associated with a substorm onset, using the data from the THEMIS spacecraft and ground-based observatories at high temporal and spatial resolutions. We discuss four steps of the auroral development, linking them to magnetotail changes: the auroral fading, the initial brightening of an auroral onset arc, the enhancement of the wave-like structure, and the poleward expansion. A case study shows that near-Earth magnetic reconnection began at X~-17 RE at least ~3 min before the auroral initial brightening and ~1 min before the auroral fading. Ionospheric large-scale convection also became enhanced just before the auroral fading and before the auroral initial brightening. Then low-frequency waves were amplified in the plasma sheet at X~-10 RE, with the pressure increase due to the arrival of the earthward flow from the near-Earth reconnection site ~20 s before the enhancement of the auroral wave-like structure. Finally, the dipolarization began ~30 s before the auroral poleward expansion. On the basis of the present observations, we suggest that near-Earth magnetic reconnection plays two roles in the substorm triggering. First, it generates a fast earthward flow and Alfvén waves. When the Alfvén waves which propagate much faster than the fast flow reach the ionosphere, large-scale ionospheric convection is enhanced, leading to the auroral initial brightening and subsequent gradual growth of the auroral wave-like structure. Second, when the reconnection-initiated fast flow reaches the near-Earth magnetotail, it promotes rapid growth of an instability, such as the ballooning instability, and the auroral wave-like structure is further enhanced. When the instability grows sufficiently, the dipolarization and the auroral poleward expansion are initiated.

Shock waves generated by sudden expansions of a water jet

NASA Astrophysics Data System (ADS)

Salinas-Vázquez, M.; Echeverría, C.; Porta, D.; Stern, C. E.; Ascanio, G.; Vicente, W.; Aguayo, J. P.

2018-07-01

Direct shadowgraph with parallel light combined with high-speed recording has been used to analyze the water jet of a cutting machine. The use of image processing allowed observing sudden expansions in the jet diameter as well as estimating the jet velocity by means of the Mach angle, obtaining velocities of about 500 m s^{-1}. The technique used here revealed the development of hydrodynamic instabilities in the jet. Additionally, this is the first reporting of the onset of shock waves generated by small fluctuations of a continuous flow of water at high velocity surrounded by air, a result confirmed by a transient computational fluid dynamics simulation.

Particle-in-cell simulation study of a lower-hybrid shock

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

Dieckmann, M. E.; Ynnerman, A.; Sarri, G.

2016-06-15

The expansion of a magnetized high-pressure plasma into a low-pressure ambient medium is examined with particle-in-cell simulations. The magnetic field points perpendicular to the plasma's expansion direction and binary collisions between particles are absent. The expanding plasma steepens into a quasi-electrostatic shock that is sustained by the lower-hybrid (LH) wave. The ambipolar electric field points in the expansion direction and it induces together with the background magnetic field a fast E cross B drift of electrons. The drifting electrons modify the background magnetic field, resulting in its pile-up by the LH shock. The magnetic pressure gradient force accelerates the ambientmore » ions ahead of the LH shock, reducing the relative velocity between the ambient plasma and the LH shock to about the phase speed of the shocked LH wave, transforming the LH shock into a nonlinear LH wave. The oscillations of the electrostatic potential have a larger amplitude and wavelength in the magnetized plasma than in an unmagnetized one with otherwise identical conditions. The energy loss to the drifting electrons leads to a noticeable slowdown of the LH shock compared to that in an unmagnetized plasma.« less

A Sommerfeld toolbox for colored dark sectors

NASA Astrophysics Data System (ADS)

El Hedri, Sonia; Kaminska, Anna; de Vries, Maikel

2017-09-01

We present analytical formulas for the Sommerfeld corrections to the annihilation of massive colored particles into quarks and gluons through the strong interaction. These corrections are essential to accurately compute the dark matter relic density for coannihilation with colored partners. Our formulas allow us to compute the Sommerfeld effect, not only for the lowest term in the angular momentum expansion of the amplitude, but for all orders in the partial wave expansion. In particular, we carefully account for the effects of the spin of the annihilating particle on the symmetry of the two-particle wave function. This work focuses on strongly interacting particles of arbitrary spin in the triplet, sextet and octet color representations. For typical velocities during freeze-out, we find that including Sommerfeld corrections on the next-to-leading order partial wave leads to modifications of up to 10 to 20 percent on the total annihilation cross section. Complementary to QCD, we generalize our results to particles charged under an arbitrary unbroken SU( N) gauge group, as encountered in dark glueball models. In connection with this paper a Mathematica notebook is provided to compute the Sommerfeld corrections for colored particles up to arbitrary order in the angular momentum expansion.

Relative Timing of Substorm-Associated Processes in the Near-Earth Magnetotail and Development of Auroral Onset Arc

NASA Astrophysics Data System (ADS)

Miyashita, Y.; Ieda, A.; Machida, S.; Hiraki, Y.; Angelopoulos, V.; McFadden, J. P.; Auster, H. U.; Mende, S. B.; Donovan, E.; Larson, D. E.

2014-12-01

We have studied the relative timing of the processes in the near-Earth magnetotail and development of auroral onset arc at the beginning of the expansion phase, based on substorm events observed by the THEMIS spacecraft and ground-based all-sky imagers. The THEMIS all-sky imagers can observe auroras over a wide area with temporal and spacial resolutions higher than spacecraft-borne cameras. This enables us to investigate the timing of auroral development in more detail than before. A few min after the appearance and intensification of an auroral onset arc, it begins to form wave-like structure. Then auroral poleward expansion begins another few min later. THEMIS magnetotail observations clearly show that magnetic reconnection is initiated at X~-20 Re at least 1-2 min before the intensification of auroral onset arc. Then low-frequency waves are excited in the plasma sheet at X~-10 Re 2 min before dipolarization, which is simultaneous with the formation of auroral wave-like structure. Dipolarization begins at the same time as the auroral poleward expansion. These results suggest that near-Earth magnetic reconnection plays some role in the development of dipolarization and auroral onset arc.

Nonlocal Symmetry and Interaction Solutions of a Generalized Kadomtsev—Petviashvili Equation

NASA Astrophysics Data System (ADS)

Huang, Li-Li; Chen, Yong; Ma, Zheng-Yi

2016-08-01

A generalized Kadomtsev—Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion (CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomtsev—Petviashvili equation, some Bäcklund transformations (BTs) including auto-BT and non-auto-BT are obtained. The auto-BT leads to a nonlocal symmetry which corresponds to the residual of the truncated Painlevé expansion. Then the nonlocal symmetry is localized to the corresponding nonlocal group by introducing two new variables. Further, by applying the Lie point symmetry method to the prolonged system, a new type of finite symmetry transformation is derived. In addition, the generalized Kadomtsev—Petviashvili equation is proved consistent Riccati expansion (CRE) solvable. As a result, the soliton-cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to be found by other traditional methods. Moreover, figures are given out to show the properties of the explicit analytic interaction solutions. Supported by the Global Change Research Program of China under Grant No. 2015CB953904, National Natural Science Foundation of under Grant Nos. 11275072 and 11435005, Doctoral Program of Higher Education of China under Grant No. 20120076110024, the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No. 61321064, and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No. ZF1213, and Zhejiang Provincial Natural Science Foundation of China under Grant No. LY14A010005

Theory and application of laser ultrasonic shear wave birefringence measurements to the determination of microstructure orientation in transversely isotropic, polycrystalline graphite materials

DOE PAGES

Zeng, Fan W.; Contescu, Cristian I.; Gallego, Nidia C.; ...

2016-12-18

Laser ultrasonic line source methods have been used to study elastic anisotropy in nuclear graphites by measuring shear wave birefringence. Depending on the manufacturing processes used during production, nuclear graphites can exhibit various degrees of material anisotropy related to preferred crystallite orientation and to microcracking. In this paper, laser ultrasonic line source measurements of shear wave birefringence on NBG-25 have been performed to assess elastic anisotropy. Laser line sources allow specific polarizations for shear waves to be transmitted – the corresponding wavespeeds can be used to compute bulk, elastic moduli that serve to quantify anisotropy. These modulus values can bemore » interpreted using physical property models based on orientation distribution coefficients and microcrack-modified, single crystal moduli to represent the combined effects of crystallite orientation and microcracking on material anisotropy. Finally, ultrasonic results are compared to and contrasted with measurements of anisotropy based on the coefficient of thermal expansion to show the relationship of results from these techniques.« less

Construction of CASCI-type wave functions for very large active spaces.

PubMed

Boguslawski, Katharina; Marti, Konrad H; Reiher, Markus

2011-06-14

We present a procedure to construct a configuration-interaction expansion containing arbitrary excitations from an underlying full-configuration-interaction-type wave function defined for a very large active space. Our procedure is based on the density-matrix renormalization group (DMRG) algorithm that provides the necessary information in terms of the eigenstates of the reduced density matrices to calculate the coefficient of any basis state in the many-particle Hilbert space. Since the dimension of the Hilbert space scales binomially with the size of the active space, a sophisticated Monte Carlo sampling routine is employed. This sampling algorithm can also construct such configuration-interaction-type wave functions from any other type of tensor network states. The configuration-interaction information obtained serves several purposes. It yields a qualitatively correct description of the molecule's electronic structure, it allows us to analyze DMRG wave functions converged for the same molecular system but with different parameter sets (e.g., different numbers of active-system (block) states), and it can be considered a balanced reference for the application of a subsequent standard multi-reference configuration-interaction method.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Ultraviolet Laser Lithography of Titania Photonic Crystals for Terahertz-Wave Modulation.

PubMed

Kirihara, Soshu; Nonaka, Koki; Kisanuki, Shoichiro; Nozaki, Hirotoshi; Sakaguchi, Keito

2018-05-18

Three-dimensional (3D) microphotonic crystals with a diamond structure composed of titania microlattices were fabricated using ultraviolet laser lithography, and the bandgap properties in the terahertz (THz) electromagnetic-wave frequency region were investigated. An acrylic resin paste with titania fine particle dispersions was used as the raw material for additive manufacturing. By scanning a spread paste surface with an ultraviolet laser beam, two-dimensional solid patterns were dewaxed and sintered. Subsequently, 3D structures with a relative density of 97% were created via layer lamination and joining. A titania diamond lattice with a lattice constant density of 240 µm was obtained. The properties of the electromagnetic wave were measured using a THz time-domain spectrometer. In the transmission spectra for the Γ-X direction, a forbidden band was observed from 0.26 THz to 0.44 THz. The frequency range of the bandgap agreed well with calculated results obtained using the plane⁻wave expansion method. Additionally, results of a simulation via transmission-line modeling indicated that a localized mode can be obtained by introducing a plane defect between twinned diamond lattice structures.

Simulation of 'pathologic' changes in ICG waveforms resulting from superposition of the 'preejection' and ejection waves induced by left ventricular contraction

NASA Astrophysics Data System (ADS)

Ermishkin, V. V.; Kolesnikov, V. A.; Lukoshkova, E. V.; Sonina, R. S.

2013-04-01

The impedance cardiography (ICG) is widely used for beat-to-beat noninvasive evaluation of the left ventricular stroke volume and contractility. It implies the correct determination of the ejection start and end points and the amplitudes of certain peaks in the differentiated impedance cardiogram. An accurate identification of ejection onset by ICG is often problematic, especially in the cardiologic patients, due to peculiar waveforms. Using a simple theoretical model, we tested the hypothesis that two major processes are responsible for the formation of impedance systolic wave: (1) the changes in the heart geometry and surrounding vessels produced by ventricular contraction, which occur during the isovolumic phase and precede ejection, and (2) expansion of aorta and adjacent arteries during the ejection phase. The former process initiates the preejection wave WpE and the latter triggers the ejection wave WEj. The model predicts a potential mechanism of generating the abnormal shapes of dZ/dt due to the presence of preejection waves and explains the related errors in ICG time and amplitude parameters. An appropriate decomposition method is a promising way to avoid the masking effects of these waves and a further step to correct determination of the onset of ejection and the corresponding peak amplitudes from 'pathologically shaped' ICG signals.

Behavior of piezoelectric wafer active sensor in various media

NASA Astrophysics Data System (ADS)

Kamas, Tuncay

The dissertation addresses structural health monitoring (SHM) techniques using ultrasonic waves generated by piezoelectric wafer active sensors (PWAS) with an emphasis on the development of theoretical models of standing harmonic waves and guided waves. The focal objective of the research is to extend the theoretical study of electro-mechanical coupled PWAS as a resonator/transducer that interacts with standing and traveling waves in various media through electro-mechanical impedance spectroscopy (EMIS) method and guided wave propagation. The analytical models are developed and the coupled field finite element analysis (CF-FEA) models are simulated and verified with experiments. The dissertation is divided into two parts with respect to the developments in EMIS methods and GWP methods. In the first part, analytical and finite element models have been developed for the simulation of PWAS-EMIS in in-plane (longitudinal) and out-of-plane (thickness) mode. Temperature effects on free PWAS-EMIS are also discussed with respect to the in-plane mode. Piezoelectric material degradation on certain electrical and mechanical properties as the temperature increases is simulated by our analytical model for in-plane circular PWAS-EMIS that agrees well with the sets of experiments. Then the thickness mode PWAS-EMIS model was further developed for a PWAS resonator bonded on a plate-like structure. The latter analytical model was to determine the resonance frequencies for the normal mode expansion method through the global matrix method by considering PWAS-substrate and proof mass-PWAS-substrate models. The proof mass concept was adapted to shift the systems resonance frequencies in thickness mode. PWAS in contact with liquid medium on one of its surface has been analytically modeled and simulated the electro-mechanical response of PWAS with various liquids with different material properties such as the density and the viscosity. The second part discusses the guided wave propagation in elastic structures. The feature guided waves in thick structures and in high frequency range are discussed considering weld guided quasi-Rayleigh waves. Furthermore, the weld guided quasi Rayleigh waves and their interaction with damages in thick plates and thick walled pipes are examined by the finite element models and experiments. The dissertation finishes with a summary of contributions followed by conclusions, and suggestions for future work.

The contribution of statistical physics to evolutionary biology.

PubMed

de Vladar, Harold P; Barton, Nicholas H

2011-08-01

Evolutionary biology shares many concepts with statistical physics: both deal with populations, whether of molecules or organisms, and both seek to simplify evolution in very many dimensions. Often, methodologies have undergone parallel and independent development, as with stochastic methods in population genetics. Here, we discuss aspects of population genetics that have embraced methods from physics: non-equilibrium statistical mechanics, travelling waves and Monte-Carlo methods, among others, have been used to study polygenic evolution, rates of adaptation and range expansions. These applications indicate that evolutionary biology can further benefit from interactions with other areas of statistical physics; for example, by following the distribution of paths taken by a population through time. Copyright © 2011 Elsevier Ltd. All rights reserved.

Genetic traces of east-to-west human expansion waves in Eurasia.

PubMed

Chaix, Raphaëlle; Austerlitz, Frédéric; Hegay, Tatyana; Quintana-Murci, Lluís; Heyer, Evelyne

2008-07-01

In this study, we describe the landscape of human demographic expansions in Eurasia using a large continental Y chromosome and mitochondrial DNA dataset. Variation at these two uniparentally-inherited genetic systems retraces expansions that occurred in the past 60 ky, and shows a clear decrease of expansion ages from east to west Eurasia. To investigate the demographic events at the origin of this westward decrease of expansion ages, the estimated divergence ages between Eurasian populations are compared with the estimated expansion ages within each population. Both markers suggest that the demographic expansion diffused from east to west in Eurasia in a demic way, i.e., through migrations of individuals (and not just through diffusion of new technologies), highlighting the prominent role of eastern regions within Eurasia during Palaeolithic times. (c) 2008 Wiley-Liss, Inc.

Ion dynamics of a laser produced aluminium plasma at different ambient pressures

NASA Astrophysics Data System (ADS)

Sankar, Pranitha; Shashikala, H. D.; Philip, Reji

2018-01-01

Plasma is generated by pulsed laser ablation of an Aluminium target using 1064 nm, 7 ns Nd:YAG laser pulses. The spatial and temporal evolution of the whole plasma plume, as well as that of the ionic (Al2+) component present in the plume, are investigated using spectrally resolved time-gated imaging. The influence of ambient gas pressure on the expansion dynamics of Al2+ is studied in particular. In vacuum (10-5 Torr, 10-2 Torr) the whole plume expands adiabatically and diffuses into the ambient. For higher pressures in the range of 1-10 Torr plume expansion is in accordance with the shock wave model, while at 760 Torr the expansion follows the drag model. On the other hand, the expansion dynamics of the Al2+ component, measured by introducing a band pass optical filter in the detection system, fits to the shock wave model for the entire pressure range of 10-2 Torr to 760 Torr. The expansion velocities of the whole plume and the Al2+ component have been measured in vacuum. These dynamics studies are of potential importance for applications such as laser-driven plasma accelerators, ion acceleration, pulsed laser deposition, micromachining, laser-assisted mass spectrometry, ion implantation, and light source generation.

Formation mechanism of guided resonances and bound states in the continuum in photonic crystal slabs

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

Gao, Xingwei; Hsu, Chia Wei; Zhen, Bo

2016-08-25

We develop a formalism, based on the mode expansion method, to describe the guided resonances and bound states in the continuum (BICs) in photonic crystal slabs with one-dimensional periodicity. This approach provides analytic insights to the formation mechanisms of these states: the guided resonances arise from the transverse Fabry–Pérot condition, and the divergence of the resonance lifetimes at the BICs is explained by a destructive interference of radiation from different propagating components inside the slab. As a result, we show BICs at the center and on the edge of the Brillouin zone protected by symmetry, BICs at generic wave vectorsmore » not protected by symmetry, and the annihilation of BICs at low-symmetry wave vectors.« less

Electrostatic shocks and solitons in pair-ion plasmas in a two-dimensional geometry

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

Masood, W.; Mahmood, S.; Imtiaz, N.

2009-12-15

Nonlinear electrostatic waves are studied in unmagnetized, dissipative pair-ion plasmas in the presence of weak transverse perturbations. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions in plasmas. The Kadomtsev-Petviashvili-Burger equation is derived using the small amplitude expansion method. The Kadomtsev-Petviashvili equation for pair-ion plasmas is also presented by ignoring the dissipative effects. Both compressive and rarefactive shocks and solitary waves are found to exist in pair-ion plasmas. The dependence of compression and rarefaction on the temperature ratios between the ion species is numerically shown. The present study maymore » have relevance to the understanding of the formation of electrostatic shocks and solitons in laboratory produced pair-ion plasmas.« less

Analysis of the interaction of a weak normal shock wave with a turbulent boundary layer

NASA Technical Reports Server (NTRS)

Melnik, R. E.; Grossman, B.

1974-01-01

The method of matched asymptotic expansions is used to analyze the interaction of a normal shock wave with an unseparated turbulent boundary layer on a flat surface at transonic speeds. The theory leads to a three-layer description of the interaction in the double limit of Reynolds number approaching infinity and Mach number approaching unity. The interaction involves an outer, inviscid rotational layer, a constant shear-stress wall layer, and a blending region between them. The pressure distribution is obtained from a numerical solution of the outer-layer equations by a mixed-flow relaxation procedure. An analytic solution for the skin friction is determined from the inner-layer equations. The significance of the mathematical model is discussed with reference to existing experimental data.

On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas; Hariharan, S. I.; Maccamy, R. C.

1993-01-01

We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.

Discrete transparent boundary conditions for the mixed KDV-BBM equation

NASA Astrophysics Data System (ADS)

Besse, Christophe; Noble, Pascal; Sanchez, David

2017-09-01

In this paper, we consider artificial boundary conditions for the linearized mixed Korteweg-de Vries (KDV) and Benjamin-Bona-Mahoney (BBM) equation which models water waves in the small amplitude, large wavelength regime. Continuous (respectively discrete) artificial boundary conditions involve non local operators in time which in turn requires to compute time convolutions and invert the Laplace transform of an analytic function (respectively the Z-transform of an holomorphic function). In this paper, we propose a new, stable and fairly general strategy to carry out this crucial step in the design of transparent boundary conditions. For large time simulations, we also introduce a methodology based on the asymptotic expansion of coefficients involved in exact direct transparent boundary conditions. We illustrate the accuracy of our methods for Gaussian and wave packets initial data.

Analysis of Exhaust Plume Effects on Sonic Boom for a 59-Degree Wing Body Model

NASA Technical Reports Server (NTRS)

Castner, Raymond S.

2011-01-01

Reducing or eliminating the operational restrictions of supersonic aircraft over populated areas has led to extensive research at NASA. Restrictions are due to the disturbance of the sonic boom, caused by the coalescence of shock waves formed off the aircraft. Recent work has been performed to reduce the magnitude of the sonic boom N-wave generated by airplane components with focus on shock waves caused by the exhaust nozzle plume. Previous Computational Fluid Dynamics (CFD) analyses showed how the shock wave formed at the nozzle lip interacted with the nozzle boat-tail expansion wave. The nozzle lip shock moved with increasing nozzle pressure ratio (NPR) and reduced the nozzle boat-tail expansion. Lip shock movement caused a favorable change in the observed pressure signature. These results were applied to a simplified supersonic vehicle geometry with no inlets and no tail, in which the goal was to demonstrate how under-expanded nozzle operation reduced the sonic boom signature by twelve percent. A secondary goal was to demonstrate the use of the Cart3D inviscid code for off-body pressure signatures including the nozzle plume effect.

Evaluation method of TiO2-SiO2 ultra-low-expansion glasses with periodic striae using the LFB ultrasonic material characterization system.

PubMed

Kushibiki, Jun-ichi; Arakawa, Mototaka; Ohashi, Yuji; Suzuki, Kouji

2006-09-01

Experimental procedures and standard specimens for characterizing and evaluating TiO2-SiO2 ultra-low expansion glasses with periodic striae using the line-focus-beam (LFB) ultrasonic material characterization system are discussed. Two types of specimens were prepared, with specimen surfaces parallel and perpendicular to the striae plane using two different grades of glass ingots. The inhomogeneities of each of the specimens were evaluated at 225 MHz. It was clarified that parallel specimens are useful for accurately measuring velocity variations of leaky surface acoustic waves (LSAWs) excited on a water-loaded specimen surface associated with the striae. Perpendicular specimens are useful for obtaining periodicities in the striae for LSAW propagation perpendicular to the striae plane on a surface and for precisely measuring averaged velocities for LSAW propagation parallel to the striae plane. The standard velocity of Rayleigh-type LSAWs traveling parallel to the striae plane for the perpendicular specimens was numerically calculated using the measured velocities of longitudinal and shear waves and density. Consequently, a reliable standard specimen with an LSAW velocity of 3308.18 +/- 0.35 m/s at 23 degrees C and its temperature coefficient of 0.39 (m/s)/degrees C was obtained for a TiO2-SiO2 glass with a TiO2 concentration of 7.09 wt%. A basis for the striae analysis using this ultrasonic method was established.

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

Beaucage, Timothy R; Beenfeldt, Eric P; Speakman, Scott A

Among the langasite family of crystals (LGX), the three most popular materials are langasite (LGS, La3Ga5SiO14), langatate (LGT, La3Ga5.5Ta0.5O14) and langanite (LGN, La3Ga5.5Nb0.5O14). The LGX crystals have received significant attention for acoustic wave (AW) device applications due to several properties, which include: (1) piezoelectric constants about two and a half times those of quartz, thus allowing the design of larger bandwidth filters; (2) existence of temperature compensated orientations; (3) high density, with potential for reduced vibration and acceleration sensitivity; and (4) possibility of operation at high temperatures, since the LGX crystals do not present phase changes up to their meltingmore » point above 1400degC. The LGX crystals' capability to operate at elevated temperatures calls for an investigation on the growth quality and the consistency of these materials' properties at high temperature. One of the fundamental crystal properties is the thermal expansion coefficients in the entire temperature range where the material is operational. This work focuses on the measurement of the LGT thermal expansion coefficients from room temperature (25degC) to 1200degC. Two methods of extracting the thermal expansion coefficients have been used and compared: (a) dual push-rod dilatometry, which provides the bulk expansion; and (b) x-ray powder diffraction, which provides the lattice expansion. Both methods were performed over the entire temperature range and considered multiple samples taken from <001> Czochralski grown LGT material. The thermal coefficients of expansion were extracted by approximating each expansion data set to a third order polynomial fit over three temperature ranges reported in this work: 25degC to 400degC, 400degC to 900degC, 900degC to 1200degC. An accuracy of fit better than 35ppm for the bulk expansion and better than 10ppm for the lattice expansion have been obtained with the aforementioned polynomial fitting. The percentage difference between the bulk and the lattice fitted expansion responses over the entire temperature range of 25degC to 1200degC is less than 2% for the three crystalline axes, which indicates the high quality and growth consistency of the LGT crystal measured« less

Dynamics of explosively imploded pressurized tubes

NASA Astrophysics Data System (ADS)

Szirti, Daniel; Loiseau, Jason; Higgins, Andrew; Tanguay, Vincent

2011-04-01

The detonation of an explosive layer surrounding a pressurized thin-walled tube causes the formation of a virtual piston that drives a precursor shock wave ahead of the detonation, generating very high temperatures and pressures in the gas contained within the tube. Such a device can be used as the driver for a high energy density shock tube or hypervelocity gas gun. The dynamics of the precursor shock wave were investigated for different tube sizes and initial fill pressures. Shock velocity and standoff distance were found to decrease with increasing fill pressure, mainly due to radial expansion of the tube. Adding a tamper can reduce this effect, but may increase jetting. A simple analytical model based on acoustic wave interactions was developed to calculate pump tube expansion and the resulting effect on the shock velocity and standoff distance. Results from this model agree quite well with experimental data.

High-resolution submillimeter-wave radiometry of supersonic flow

NASA Technical Reports Server (NTRS)

Dionne, G. F.; Weiss, J. A.; Fitzgerald, J. F.; Fetterman, H. R.; Litvak, M. M.

1983-01-01

The recent development of a high-resolution submillimeter-wave heterodyne radiometer has made possible the first measurements of H2O molecule rotational line excitation temperatures and detailed profiles in supersonic flow. Absorption signals were measured across the flow for the 2/11/ from 2//02/ (752 GHz) para-H2O rotational transition against a hot background. These signals decrease downstream owing to the volume expansion of the gas away from the sonic nozle exit in the high-vacuum chamber. Radiative transfer calculations based on the large-velocity-gradient approximation and multilevel statistical equilibrium agree with these results and with the measured spectral line shapes. The data reveal nearly isentropic gas expansion and cooling. These studies have shown that submillimeter-wave heterodyne radiometry can be useful for remote sensing of supersonic flow with low mass flux, provided the signal transmission is through a dry or thin atmosphere.

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.

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.

Vibration of a single microcapsule with a hard plastic shell in an acoustic standing wave field.

PubMed

Koyama, Daisuke; Kotera, Hironori; Kitazawa, Natsuko; Yoshida, Kenji; Nakamura, Kentaro; Watanabe, Yoshiaki

2011-04-01

Observation techniques for measuring the small vibration of a single microcapsule of tens of nanometers in an acoustic standing wave field are discussed. First, simultaneous optical observation of a microbubble vibration by two methods is investigated, using a high-speed video camera, which permits two-dimensional observation of the bubble vibration, and a laser Doppler vibrometer (LDV), which can observe small bubble vibration amplitudes at high frequency. Bubbles of tens of micrometers size were trapped at the antinode of an acoustic standing wave generated in an observational cell. Bubble vibration at 27 kHz could be observed and the experimental results for the two methods showed good agreement. The radial vibration of microcapsules with a hard plastic shell was observed using the LDV and the measurement of the capsule vibration with radial oscillation amplitude of tens of nanometers was successful. The acoustic radiation force acting on microcapsules in the acoustic standing wave was measured from the trapped position of the standing wave and the radial oscillation amplitude of the capsules was estimated from the theoretical equation of the acoustic radiation force, giving results in good agreement with the LDV measurements. The radial oscillation amplitude of a capsule was found to be proportional to the amplitude of the driving sound pressure. A larger expansion ratio was observed for capsules closer to the resonance condition under the same driving sound pressure and frequency. © 2011 IEEE

The narrow pass band filter of tunable 1D phononic crystals with a dielectric elastomer layer

NASA Astrophysics Data System (ADS)

Wu, Liang-Yu; Wu, Mei-Ling; Chen, Lien-Wen

2009-01-01

In this paper, we study the defect bands of a 1D phononic crystal consisting of aluminum (Al) and polymethyl methacrylate (PMMA) layers with a dielectric elastomer (DE) defect layer. The plane wave expansion (PWE) method and supercell calculation are used to calculate the band structure and the defect bands. The transmission spectra are obtained using the finite element method (FEM). Since the thickness of the dielectric elastomer defect layer is controlled by applying an electric voltage, the frequencies of the defect bands can be tuned. A narrow pass band filter can be developed and designed by using the dielectric elastomer.

Impact of Human Resources on Implementing an Evidence-based HIV Prevention Intervention

PubMed Central

McKay, Virginia R.; Dolcini, M. Margaret; Catania, Joseph A.

2016-01-01

Evidence-based interventions (EBIs) often require competent staff, or human resources (HR), for implementation. The empirical evidence characterizing the influence of HR fluctuations on EBI delivery is limited and conflicting. Using the Interactive Systems Framework, we explored staff fluctuation and the subsequent influence on RESPECT, an HIV prevention EBI. Methods We conducted interviews with staff in two waves (n=53, Wave I; n=37, Wave II) in a national sample of organizations delivering RESPECT (N=29). We analyzed interviews qualitatively to describe changes among RESPECT staff and explore the subsequent influences on RESPECT implementation. Results Organizations reported downsizing, turnover, and expansion of staff positions. Staff changes had multiple influences on RESPECT implementation including clients reached, fidelity to specific RESPECT protocols, and overall sustainability of RESPECT over time. Discussion HR fluctuations are common, and our analyses provide an initial characterization of the relationship between HR fluctuation and EBI implementation. Given the prominent influence of HR on EBI implementation, the Interactive Systems Framework is a useful guiding tool for future examinations. PMID:27150896

Development of a hybrid wave based-transfer matrix model for sound transmission analysis.

PubMed

Dijckmans, A; Vermeir, G

2013-04-01

In this paper, a hybrid wave based-transfer matrix model is presented that allows for the investigation of the sound transmission through finite multilayered structures placed between two reverberant rooms. The multilayered structure may consist of an arbitrary configuration of fluid, elastic, or poro-elastic layers. The field variables (structural displacements and sound pressures) are expanded in terms of structural and acoustic wave functions. The boundary and continuity conditions in the rooms determine the participation factors in the pressure expansions. The displacement of the multilayered structure is determined by the mechanical impedance matrix, which gives a relation between the pressures and transverse displacements at both sides of the structure. The elements of this matrix are calculated with the transfer matrix method. First, the hybrid model is numerically validated. Next a comparison is made with sound transmission loss measurements of a hollow brick wall and a sandwich panel. Finally, numerical simulations show the influence of structural damping, room dimensions and plate dimensions on the sound transmission loss of multilayered structures.

Absorption, scattering, and radiation force efficiencies in the longitudinal wave scattering by a small viscoelastic particle in an isotropic solid.

PubMed

Lopes, J H; Leão-Neto, J P; Silva, G T

2017-11-01

Analytical expressions of the absorption, scattering, and elastic radiation force efficiency factors are derived for the longitudinal plane wave scattering by a small viscoelastic particle in a lossless solid matrix. The particle is assumed to be much smaller than the incident wavelength, i.e., the so-called long-wavelength (Rayleigh) approximation. The efficiencies are dimensionless quantities that represent the absorbed and scattering powers and the elastic radiation force on the particle. In the quadrupole approximation, they are expressed in terms of contrast functions (bulk and shear moduli, and density) between the particle and solid matrix. The results for a high-density polyethylene particle embedded in an aluminum matrix agree with those obtained with the partial wave expansion method. Additionally, the connection between the elastic radiation force and forward scattering function is established through the optical theorem. The present results should be useful for ultrasound characterization of particulate composites, and the development of implanted devices activated by radiation force.

Reduction of shock induced noise in imperfectly expanded supersonic jets using convex optimization

NASA Astrophysics Data System (ADS)

Adhikari, Sam

2007-11-01

Imperfectly expanded jets generate screech noise. The imbalance between the backpressure and the exit pressure of the imperfectly expanded jets produce shock cells and expansion or compression waves from the nozzle. The instability waves and the shock cells interact to generate the screech sound. The mathematical model consists of cylindrical coordinate based full Navier-Stokes equations and large-eddy-simulation turbulence modeling. Analytical and computational analysis of the three-dimensional helical effects provide a model that relates several parameters with shock cell patterns, screech frequency and distribution of shock generation locations. Convex optimization techniques minimize the shock cell patterns and the instability waves. The objective functions are (convex) quadratic and the constraint functions are affine. In the quadratic optimization programs, minimization of the quadratic functions over a set of polyhedrons provides the optimal result. Various industry standard methods like regression analysis, distance between polyhedra, bounding variance, Markowitz optimization, and second order cone programming is used for Quadratic Optimization.

Density of states and dynamical crossover in a dense fluid revealed by exponential mode analysis of the velocity autocorrelation function

NASA Astrophysics Data System (ADS)

Bellissima, S.; Neumann, M.; Guarini, E.; Bafile, U.; Barocchi, F.

2017-01-01

Extending a preceding study of the velocity autocorrelation function (VAF) in a simulated Lennard-Jones fluid [Phys. Rev. E 92, 042166 (2015), 10.1103/PhysRevE.92.042166] to cover higher-density and lower-temperature states, we show that the recently demonstrated multiexponential expansion method allows for a full account and understanding of the basic dynamical processes encompassed by a fundamental quantity as the VAF. In particular, besides obtaining evidence of a persisting long-time tail, we assign specific and unambiguous physical meanings to groups of exponential modes related to the longitudinal and transverse collective dynamics, respectively. We have made this possible by consistently introducing the interpretation of the VAF frequency spectrum as a global density of states in fluids, generalizing a solid-state concept, and by giving to specific spectral components, obtained through the VAF exponential expansion, the corresponding meaning of partial densities of states relative to specific dynamical processes. The clear identification of a high-frequency oscillation of the VAF with the near-top excitation frequency in the dispersion curve of acoustic waves is a neat example of the power of the method. As for the transverse mode contribution, its analysis turns out to be particularly important, because the multiexponential expansion reveals a transition marking the onset of propagating excitations when the density is increased beyond a threshold value. While this finding agrees with the recent literature debating the issue of dynamical crossover boundaries, such as the one identified with the Frenkel line, we can add detailed information on the modes involved in this specific process in the domains of both time and frequency. This will help obtain a still missing full account of transverse dynamics, in both its nonpropagating and propagating aspects which are linked through dynamical transitions depending on both the thermodynamic states and the excitation wave vectors.

Asynchronous arterial systolic expansion as a marker of vascular aging: assessment of the carotid artery with velocity vector imaging.

PubMed

Yang, Woo-In; Shim, Chi Y; Bang, Woo D; Oh, Chang M; Chang, Hyuk J; Chung, Namsik; Ha, Jong-Won

2011-12-01

Arterial elastic properties change with aging. Measurements of pulse wave velocity and augmentation index are useful for the evaluation of arterial stiffness. However, they likely represent only global characteristics of the arterial tree rather than local vascular alterations. The aim of this study was to evaluate whether local vascular properties assessed by velocity vector imaging differed with aging. Vascular properties of carotid arteries with ages were assessed in 100 healthy volunteers (52 men) ranging from 20 to 68 years using velocity vector imaging. The peak circumferential strain and strain rate of the six segments in left common carotid arteries were analyzed and the standard deviation of the time to peak circumferential strain and strain rate of the six segments, representing the synchronicity of the arterial expansion, were calculated. Central blood pressure, augmentation index and pulse wave velocity were assessed by commercially available radial artery tonometry, the SphygmoCor system (AtCor Medical, West Ryde, Australia). A validated generalized transfer function was used to acquire the central aortic pressures and pressure waveforms. Pulse wave velocity, augmentation index and velocity vector imaging parameters showed significant changes with age. However, the age-related changes in pulse wave velocity, augmentation index and velocity vector imaging parameters were different. The increase in pulse wave velocity was more prominent in older individuals, whereas the changes in augmentation index and carotid strain and strain rate were evident earlier, at the age of 30 years. Unlike augmentation index, which showed little change in older individuals, the standard deviation of time to peak strain and strain rate showed a steady increase from younger to older individuals. Asynchronous arterial expansion could be a useful discriminative marker of vascular aging independent of individual's age.

Infrasonic acoustic waves generated by fast air heating in sprite cores

NASA Astrophysics Data System (ADS)

Silva, Caitano L.; Pasko, Victor P.

2014-03-01

Acceleration, expansion, and branching of sprite streamers can lead to concentration of high electrical currents in regions of space, that are observed in the form of bright sprite cores. Driven by this electrical current, a series of chemical processes take place in the sprite plasma. Excitation, followed by quenching of excited electronic states leads to energy transfer from charged to neutral species. The consequence is heating and expansion of air leading to emission of infrasonic acoustic waves. Results indicate that ≳0.01 Pa pressure perturbations on the ground, observed in association with sprites, can only be produced by exceptionally strong currents in sprite cores, exceeding 2 kA.

Present developments in theory of the solar wind

NASA Technical Reports Server (NTRS)

Parker, E. N.

1972-01-01

Current problems and developments in the theory of the large-scale expansion of the solar corona are reviewed. The outstanding question is whether the energy supply to the quiet corona is mainly thermal conduction outward from a region of active heating at its base, or mainly wave propagation outward from the base. It is suggested that the question can be settled only when the properties of the wind can be sampled over a wide range of radial distance from the sun, from far inside the orbit of earth to well beyond. It was suggested that hydromagnetic waves may drive the expansion of the active corona by direct transfer of momentum as well as energy.

Focus expansion and stability of the spread parameter estimate of the power law model for dispersal gradients

USDA-ARS?s Scientific Manuscript database

Empirical and mechanistic modeling indicate that aerially transmitted pathogens follow a power law, resulting in dispersive epidemic waves. The spread parameter (b) of the power law model, which defines the distance travelled by the epidemic wave front, has been found to be approximately 2 for sever...

Plasma waves associated with the first AMPTE magnetotail barium release

NASA Technical Reports Server (NTRS)

Gurnett, D. A.; Anderson, R. R.; Bernhardt, P. A.; Luehr, H.; Haerendel, G.

1986-01-01

Plasma waves observed during the March 21, 1985, AMPTE magnetotail barium release are described. Electron plasma oscillations provided local measurements of the plasma density during both the expansion and decay phases. Immediately after the explosion, the electron density reached a peak of about 400,000/cu cm, and then started decreasing approximately as t to the -2.4 as the cloud expanded. About 6 minutes after the explosion, the electron density suddenly began to increase, reached a secondary peak of about 240/cu cm, and then slowly decayed down to the preevent level over a period of about 15 minutes. The density increase is believed to be caused by the collapse of the ion cloud into the diamagnetic cavity created by the initial expansion. The plasma wave intensities observed during the entire event were quite low. In the diamagnetic cavity, electrostatic emissions were observed near the barium ion plasma frequency, and in another band at lower frequencies. A broadband burst of electrostatic noise was also observed at the boundary of the diamagnetic cavity. Except for electron plasma oscillations, no significant wave activity was observed outside of the diamagnetic cavity.

Wave interactions with multiple semi-immersed Jarlan-type perforated breakwaters

NASA Astrophysics Data System (ADS)

Elbisy, Moussa S.

2017-06-01

This study examines wave interactions with multiple semi-immersed Jarlan-type perforated breakwaters. A numerical model based on linear wave theory and an eigenfunction expansion method has been developed to study the hydrodynamic characteristics of breakwaters. The numerical results show a good agreement with previous analytical results and experimental data for limiting cases of double partially immersed impermeable walls and double and triple Jarlan-type breakwaters. The wave transmission coefficient C T; reflection coefficient C R, and energy dissipation coefficient C E coefficients and the horizontal wave force exerted on the front and rear walls are examined. The results show that C R reaches the maximum value when B/L = 0.46 n while it is smallest when B/L=0.46 n+0.24 ( n=0, 1, 2,...). An economical triple semi-immersed Jarlan-type perforated breakwater can be designed with B/L = 0.25 and C R and C T ranging from 0.25 to 0.32 by choosing a relative draft d/h of 0.35 and a permeability parameter of the perforated front walls being 0.5 for an incident wave number kh nearly equal to 2.0. The triple semi-immersed Jarlan-type perforated breakwaters with significantly reduced C R, will enhance the structure's wave absorption ability, and lead to smaller wave forces compared with the double one. The proposed model may be used to predict the response of a structure in the preliminary design stage for practical engineering.

Quantum Dynamics with Short-Time Trajectories and Minimal Adaptive Basis Sets.

PubMed

Saller, Maximilian A C; Habershon, Scott

2017-07-11

Methods for solving the time-dependent Schrödinger equation via basis set expansion of the wave function can generally be categorized as having either static (time-independent) or dynamic (time-dependent) basis functions. We have recently introduced an alternative simulation approach which represents a middle road between these two extremes, employing dynamic (classical-like) trajectories to create a static basis set of Gaussian wavepackets in regions of phase-space relevant to future propagation of the wave function [J. Chem. Theory Comput., 11, 8 (2015)]. Here, we propose and test a modification of our methodology which aims to reduce the size of basis sets generated in our original scheme. In particular, we employ short-time classical trajectories to continuously generate new basis functions for short-time quantum propagation of the wave function; to avoid the continued growth of the basis set describing the time-dependent wave function, we employ Matching Pursuit to periodically minimize the number of basis functions required to accurately describe the wave function. Overall, this approach generates a basis set which is adapted to evolution of the wave function while also being as small as possible. In applications to challenging benchmark problems, namely a 4-dimensional model of photoexcited pyrazine and three different double-well tunnelling problems, we find that our new scheme enables accurate wave function propagation with basis sets which are around an order-of-magnitude smaller than our original trajectory-guided basis set methodology, highlighting the benefits of adaptive strategies for wave function propagation.

Experimental demonstrations in audible frequency range of band gap tunability and negative refraction in two-dimensional sonic crystal.

PubMed

Pichard, Hélène; Richoux, Olivier; Groby, Jean-Philippe

2012-10-01

The propagation of audible acoustic waves in two-dimensional square lattice tunable sonic crystals (SC) made of square cross-section infinitely rigid rods embedded in air is investigated experimentally. The band structure is calculated with the plane wave expansion (PWE) method and compared with experimental measurements carried out on a finite extend structure of 200 cm width, 70 cm depth and 15 cm height. The structure is made of square inclusions of 5 cm side with a periodicity of L = 7.5 cm placed inbetween two rigid plates. The existence of tunable complete band gaps in the audible frequency range is demonstrated experimentally by rotating the scatterers around their vertical axis. Negative refraction is then analyzed by use of the anisotropy of the equi-frequency surface (EFS) in the first band and of a finite difference time domain (FDTD) method. Experimental results finally show negative refraction in the audible frequency range.

Numerical solutions of ideal quantum gas dynamical flows governed by semiclassical ellipsoidal-statistical distribution

PubMed Central

Yang, Jaw-Yen; Yan, Chih-Yuan; Diaz, Manuel; Huang, Juan-Chen; Li, Zhihui; Zhang, Hanxin

2014-01-01

The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wu et al. (Wu et al. 2012 Proc. R. Soc. A 468, 1799–1823 (doi:10.1098/rspa.2011.0673)) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi–Dirac or Bose–Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas. PMID:24399919

Numerical investigation of internal high-speed viscous flows using a parabolic technique

NASA Technical Reports Server (NTRS)

Anderson, O. L.; Power, G. D.

1985-01-01

A feasibility study has been conducted to assess the applicability of an existing parabolic analysis (ADD-Axisymmetric Diffuser Duct), developed previously for subsonic viscous internal flows, to mixed supersonic/subsonic flows with heat addition simulating a SCRAMJET combustor. A study was conducted with the ADD code modified to include additional convection effects in the normal momentum equation when supersonic expansion and compression waves are present. A set of test problems with weak shock and expansion waves have been analyzed with this modified ADD method and stable and accurate solutions were demonstrated provided the streamwise step size was maintained at levels larger than the boundary layer displacement thickness. Calculations made with further reductions in step size encountered departure solutions consistent with strong interaction theory. Calculations were also performed for a flow field with a flame front in which a specific heat release was imposed to simulate a SCRAMJET combustor. In this case the flame front generated relatively thick shear layers which aggravated the departure solution problem. Qualitatively correct results were obtained for these cases using a marching technique with the convective terms in the normal momentum equation suppressed. It is concluded from the present study that for the class of problems where strong viscous/inviscid interactions are present a global iteration procedure is required.

Huygens-Fresnel picture for electron-molecule elastic scattering★

NASA Astrophysics Data System (ADS)

Baltenkov, Arkadiy S.; Msezane, Alfred Z.

2017-11-01

The elastic scattering cross sections for a slow electron by C2 and H2 molecules have been calculated within the framework of the non-overlapping atomic potential model. For the amplitudes of the multiple electron scattering by a target the wave function of the molecular continuum is represented as a combination of a plane wave and two spherical waves generated by the centers of atomic spheres. This wave function obeys the Huygens-Fresnel principle according to which the electron wave scattering by a system of two centers is accompanied by generation of two spherical waves; their interaction creates a diffraction pattern far from the target. Each of the Huygens waves, in turn, is a superposition of the partial spherical waves with different orbital angular momenta l and their projections m. The amplitudes of these partial waves are defined by the corresponding phases of electron elastic scattering by an isolated atomic potential. In numerical calculations the s- and p-phase shifts are taken into account. So the number of interfering electron waves is equal to eight: two of which are the s-type waves and the remaining six waves are of the p-type with different m values. The calculation of the scattering amplitudes in closed form (rather than in the form of S-matrix expansion) is reduced to solving a system of eight inhomogeneous algebraic equations. The differential and total cross sections of electron scattering by fixed-in-space molecules and randomly oriented ones have been calculated as well. We conclude by discussing the special features of the S-matrix method for the case of arbitrary non-spherical potentials. Contribution to the Topical Issue "Low energy positron and electron interactions", edited by James Sullivan, Ron White, Michael Bromley, Ilya Fabrikant, and David Cassidy.

Propagation characteristics of pulverized coal and gas two-phase flow during an outburst.

PubMed

Zhou, Aitao; Wang, Kai; Fan, Lingpeng; Tao, Bo

2017-01-01

Coal and gas outbursts are dynamic failures that can involve the ejection of thousands tons of pulverized coal, as well as considerable volumes of gas, into a limited working space within a short period. The two-phase flow of gas and pulverized coal that occurs during an outburst can lead to fatalities and destroy underground equipment. This article examines the interaction mechanism between pulverized coal and gas flow. Based on the role of gas expansion energy in the development stage of outbursts, a numerical simulation method is proposed for investigating the propagation characteristics of the two-phase flow. This simulation method was verified by a shock tube experiment involving pulverized coal and gas flow. The experimental and simulated results both demonstrate that the instantaneous ejection of pulverized coal and gas flow can form outburst shock waves. These are attenuated along the propagation direction, and the volume fraction of pulverized coal in the two-phase flow has significant influence on attenuation of the outburst shock wave. As a whole, pulverized coal flow has a negative impact on gas flow, which makes a great loss of large amounts of initial energy, blocking the propagation of gas flow. According to comparison of numerical results for different roadway types, the attenuation effect of T-type roadways is best. In the propagation of shock wave, reflection and diffraction of shock wave interact through the complex roadway types.

Propagation characteristics of pulverized coal and gas two-phase flow during an outburst

PubMed Central

Zhou, Aitao; Wang, Kai; Fan, Lingpeng; Tao, Bo

2017-01-01

Coal and gas outbursts are dynamic failures that can involve the ejection of thousands tons of pulverized coal, as well as considerable volumes of gas, into a limited working space within a short period. The two-phase flow of gas and pulverized coal that occurs during an outburst can lead to fatalities and destroy underground equipment. This article examines the interaction mechanism between pulverized coal and gas flow. Based on the role of gas expansion energy in the development stage of outbursts, a numerical simulation method is proposed for investigating the propagation characteristics of the two-phase flow. This simulation method was verified by a shock tube experiment involving pulverized coal and gas flow. The experimental and simulated results both demonstrate that the instantaneous ejection of pulverized coal and gas flow can form outburst shock waves. These are attenuated along the propagation direction, and the volume fraction of pulverized coal in the two-phase flow has significant influence on attenuation of the outburst shock wave. As a whole, pulverized coal flow has a negative impact on gas flow, which makes a great loss of large amounts of initial energy, blocking the propagation of gas flow. According to comparison of numerical results for different roadway types, the attenuation effect of T-type roadways is best. In the propagation of shock wave, reflection and diffraction of shock wave interact through the complex roadway types. PMID:28727738

Schrödinger propagation of initial discontinuities leads to divergence of moments

NASA Astrophysics Data System (ADS)

Marchewka, A.; Schuss, Z.

2009-09-01

We show that the large phase expansion of the Schrödinger propagation of an initially discontinuous wave function leads to the divergence of average energy, momentum, and displacement, rendering them unphysical states. If initially discontinuous wave functions are considered to be approximations to continuous ones, the determinant of the spreading rate of these averages is the maximal gradient of the initial wave function. Therefore a dilemma arises between the inclusion of discontinuous wave functions in quantum mechanics and the requirement of finite moments.

Stress wave focusing transducers

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

Visuri, S.R., LLNL

Conversion of laser radiation to mechanical energy is the fundamental process behind many medical laser procedures, particularly those involving tissue destruction and removal. Stress waves can be generated with laser radiation in several ways: creation of a plasma and subsequent launch of a shock wave, thermoelastic expansion of the target tissue, vapor bubble collapse, and ablation recoil. Thermoelastic generation of stress waves generally requires short laser pulse durations and high energy density. Thermoelastic stress waves can be formed when the laser pulse duration is shorter than the acoustic transit time of the material: {tau}{sub c} = d/c{sub s} where dmore » = absorption depth or spot diameter, whichever is smaller, and c{sub s} = sound speed in the material. The stress wave due to thermoelastic expansion travels at the sound speed (approximately 1500 m/s in tissue) and leaves the site of irradiation well before subsequent thermal events can be initiated. These stress waves, often evolving into shock waves, can be used to disrupt tissue. Shock waves are used in ophthalmology to perform intraocular microsurgery and photodisruptive procedures as well as in lithotripsy to fragment stones. We have explored a variety of transducers that can efficiently convert optical to mechanical energy. One such class of transducers allows a shock wave to be focused within a material such that the stress magnitude can be greatly increased compared to conventional geometries. Some transducer tips could be made to operate regardless of the absorption properties of the ambient media. The size and nature of the devices enable easy delivery, potentially minimally-invasive procedures, and precise tissue- targeting while limiting thermal loading. The transducer tips may have applications in lithotripsy, ophthalmology, drug delivery, and cardiology.« less

Transcatheter Replacement of Stenotic Aortic Valve Normalizes Cardiac-Coronary Interaction by Restoration of Systolic Coronary Flow Dynamics as Assessed by Wave Intensity Analysis.

PubMed

Rolandi, M Cristina; Wiegerinck, Esther M A; Casadonte, Lorena; Yong, Ze-Yie; Koch, Karel T; Vis, Marije; Piek, Jan J; Baan, Jan; Spaan, Jos A E; Siebes, Maria

2016-04-01

Aortic valve stenosis (AS) can cause angina despite unobstructed coronary arteries, which may be related to increased compression of the intramural microcirculation, especially at the subendocardium. We assessed coronary wave intensity and phasic flow velocity patterns to unravel changes in cardiac-coronary interaction because of transcatheter aortic valve implantation (TAVI). Intracoronary pressure and flow velocity were measured at rest and maximal hyperemia in undiseased vessels in 15 patients with AS before and after TAVI and in 12 control patients. Coronary flow reserve, systolic and diastolic velocity time integrals, and the energies of forward (aorta-originating) and backward (microcirculatory-originating) coronary waves were determined. Coronary flow reserve was 2.8±0.2 (mean±SEM) in control and 1.8±0.1 in AS (P<0.005) and was not restored by TAVI. Compared with control, the resting backward expansion wave was 45% higher in AS. The peak of the systolic forward compression wave was delayed in AS, consistent with a delayed peak aortic pressure, which was partially restored after TAVI. The energy of forward waves doubled after TAVI, whereas the backward expansion wave increased by >30%. The increase in forward compression wave with TAVI was related to an increase in systolic velocity time integral. AS or TAVI did not alter diastolic velocity time integral. Reduced coronary forward wave energy and systolic velocity time integral imply a compromised systolic flow velocity with AS that is restored after TAVI, suggesting an acute relief of excess compression in systole that likely benefits subendocardial perfusion. Vasodilation is observed to be a major determinant of backward waves. © 2016 American Heart Association, Inc.

On the properties of circular beams: normalization, Laguerre-Gauss expansion, and free-space divergence.

PubMed

Vallone, Giuseppe

2015-04-15

Circular beams were introduced as a very general solution to the paraxial wave equation carrying orbital angular momentum. Here, we study their properties by looking at their normalization and their expansion in terms of Laguerre-Gauss modes. We also study their far-field divergence and, for particular cases of the beam parameters, their possible experimental generation.

Effect of thermal expansion on the stability of two-reactant flames

NASA Technical Reports Server (NTRS)

Jackson, T. L.

1986-01-01

The full problem of flame stability for the two-reactant model, which takes into account thermal expansion effects for all disturbance wave lengths, is examined. It is found that the stability problem for the class of two-reactant flames is equivalent to the stability problem for the class of one-reactant flames with an appropriate interpretation of Lewis numbers.

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.

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.

Diamond lattice Heisenberg antiferromagnet

NASA Astrophysics Data System (ADS)

Oitmaa, J.

2018-04-01

We investigate ground-state and high-temperature properties of the nearest-neighbour Heisenberg antiferromagnet on the three-dimensional diamond lattice, using series expansion methods. The ground-state energy and magnetization, as well as the magnon spectrum, are calculated and found to be in good agreement with first-order spin-wave theory, with a quantum renormalization factor of about 1.13. High-temperature series are derived for the free energy, and physical and staggered susceptibilities for spin S  =  1/2, 1 and 3/2, and analysed to obtain the corresponding Curie and Néel temperatures.

Investigation of angular dependence on photonic bandgap for 1-D photonic crystal

NASA Astrophysics Data System (ADS)

Nigam, Anjali; Suthar, B.; Bhargava, A.; Vijay, Y. K.

2018-05-01

In the present communication, we study the one-dimensional photonic crystal structure. The photonic band structure has been obtained using Plane Wave Expansion Method (PWEM). The studied has been extended to investigate the angular dependence on photonic bandgap for 1-D photonic crystal. The photonic bandgap is same both for TE and TM mode for normal incidence, while both mode move separate with an incidence angle. The photonic bandgap is almost unaffected with angle for TE mode while the bandgap decreases with an incidence angle for TM mode.

Investigations of dark, bright, combined dark-bright optical and other soliton solutions in the complex cubic nonlinear Schrödinger equation with δ-potential

NASA Astrophysics Data System (ADS)

Baskonus, Haci Mehmet; Sulaiman, Tukur Abdulkadir; Bulut, Hasan; Aktürk, Tolga

2018-03-01

In this study, using the extended sinh-Gordon equation expansion method, we construct the dark, bright, combined dark-bright optical, singular, combined singular solitons and singular periodic waves solutions to the complex cubic nonlinear Schrödinger equation with δ-potential. The conditions for the existence of the obtained solutions are given. To present the physical feature of the acquired result, the 2D and 3D graphs are plotted under the choice of suitable values of the parameters.

Operator product expansion in Liouville field theory and Seiberg-type transitions in log-correlated random energy models

NASA Astrophysics Data System (ADS)

Cao, Xiangyu; Le Doussal, Pierre; Rosso, Alberto; Santachiara, Raoul

2018-04-01

We study transitions in log-correlated random energy models (logREMs) that are related to the violation of a Seiberg bound in Liouville field theory (LFT): the binding transition and the termination point transition (a.k.a., pre-freezing). By means of LFT-logREM mapping, replica symmetry breaking and traveling-wave equation techniques, we unify both transitions in a two-parameter diagram, which describes the free-energy large deviations of logREMs with a deterministic background log potential, or equivalently, the joint moments of the free energy and Gibbs measure in logREMs without background potential. Under the LFT-logREM mapping, the transitions correspond to the competition of discrete and continuous terms in a four-point correlation function. Our results provide a statistical interpretation of a peculiar nonlocality of the operator product expansion in LFT. The results are rederived by a traveling-wave equation calculation, which shows that the features of LFT responsible for the transitions are reproduced in a simple model of diffusion with absorption. We examine also the problem by a replica symmetry breaking analysis. It complements the previous methods and reveals a rich large deviation structure of the free energy of logREMs with a deterministic background log potential. Many results are verified in the integrable circular logREM, by a replica-Coulomb gas integral approach. The related problem of common length (overlap) distribution is also considered. We provide a traveling-wave equation derivation of the LFT predictions announced in a precedent work.

Correlation of electronic structure and magnetic moment in Ga1-xMnxN : First-principles, mean field and high temperature series expansions calculations

NASA Astrophysics Data System (ADS)

Masrour, R.; Hlil, E. K.

2016-08-01

Self-consistent ab initio calculations based on density-functional theory and using both full potential linearized augmented plane wave and Korring-Kohn-Rostoker-coherent potential approximation methods, are performed to investigate both electronic and magnetic properties of the Ga1-xMnxN system. Magnetic moments considered to lie along (001) axes are computed. Obtained data from ab initio calculations are used as input for the high temperature series expansions (HTSEs) calculations to compute other magnetic parameters such as the magnetic phase diagram and the critical exponent. The increasing of the dilution x in this system has allowed to verify a series of HTSEs predictions on the possibility of ferromagnetism in dilute magnetic insulators and to demonstrate that the interaction changes from antiferromagnetic to ferromagnetic passing through the spins glace phase.

High-latitude filtering in a global grid-point model using model normal modes. [Fourier filters for synoptic weather forecasting

NASA Technical Reports Server (NTRS)

Takacs, L. L.; Kalnay, E.; Navon, I. M.

1985-01-01

A normal modes expansion technique is applied to perform high latitude filtering in the GLAS fourth order global shallow water model with orography. The maximum permissible time step in the solution code is controlled by the frequency of the fastest propagating mode, which can be a gravity wave. Numerical methods are defined for filtering the data to identify the number of gravity modes to be included in the computations in order to obtain the appropriate zonal wavenumbers. The performances of the model with and without the filter, and with a time tendency and a prognostic field filter are tested with simulations of the Northern Hemisphere winter. The normal modes expansion technique is shown to leave the Rossby modes intact and permit 3-5 day predictions, a range not possible with the other high-latitude filters.

On the validity of the use of a localized approximation for helical beams. I. Formal aspects

NASA Astrophysics Data System (ADS)

Gouesbet, Gérard; André Ambrosio, Leonardo

2018-03-01

The description of an electromagnetic beam for use in light scattering theories may be carried out by using an expansion over vector spherical wave functions with expansion coefficients expressed in terms of Beam Shape Coefficients (BSCs). A celebrated method to evaluate these BSCs has been the use of localized approximations (with several existing variants). We recently established that the use of any existing localized approximation is of limited validity in the case of Bessel and Mathieu beams. In the present paper, we address a warning against the use of any existing localized approximation in the case of helical beams. More specifically, we demonstrate that a procedure used to validate any existing localized approximation fails in the case of helical beams. Numerical computations in a companion paper will confirm that existing localized approximations are of limited validity in the case of helical beams.

Bulk Viscosity of Bubbly Magmas and the Amplification of Pressure Waves

NASA Astrophysics Data System (ADS)

Navon, O.; Lensky, N. G.; Neuberg, J. W.; Lyakhovsky, V.

2001-12-01

The bulk viscosity of magma is needed in order to describe the dynamics of a compressible bubbly magma flowing in conduits and to follow the attenuation of pressure waves travelling through a compressible magma. We developed a model for the bulk viscosity of a suspension of gas bubbles in an incompressible Newtonian liquid that exsolves volatiles (e.g. magma). The suspension is modeled as a close pack of spherical cells, consisting of gas bubbles centered in spherical shells of a volatile-bearing liquid. Following a drop in the ambient pressure the resulting dilatational motion and driving pressure are obtained in terms of the two-phase cell parameters, i.e. bubble radius and gas pressure. By definition, the bulk viscosity of a fluid is the relation between changes of the driving pressure with respect to changes in the resulted expansion strain-rate. Thus, we can use the two-phase solution to define the bulk viscosity of a hypothetical cell, composed of a homogeneously compressible, one-phase, continuous fluid. The resulted bulk viscosity is highly non-linear. At the beginning of the expansion process, when gas exsolution is efficient, the expansion rate grows exponentially while the driving pressure decreases slightly. That means that bulk viscosity is formally negative. The negative value reflects the release of the energy stored in the supersaturated liquid (melt) and its conversion to mechanical work during exsolution. Later, when bubbles are large enough and the gas influx decreases significantly, the strain rate decelerates and the bulk viscosity becomes positive as expected in a dissipative system. We demonstrate that amplification of seismic wave travelling through a volcanic conduit filled with a volatile saturated magma may be attributed to the negative bulk viscosity of the compressible magma. Amplification of an expansion wave may, at some level in the conduit, damage the conduit walls and initiate opening of new pathways for magma to erupt.

Influence of the distance between target surface and focal point on the expansion dynamics of a laser-induced silicon plasma with spatial confinement

NASA Astrophysics Data System (ADS)

Zhang, Dan; Chen, Anmin; Wang, Xiaowei; Wang, Ying; Sui, Laizhi; Ke, Da; Li, Suyu; Jiang, Yuanfei; Jin, Mingxing

2018-05-01

Expansion dynamics of a laser-induced plasma plume, with spatial confinement, for various distances between the target surface and focal point were studied by the fast photography technique. A silicon wafer was ablated to induce the plasma with a Nd:YAG laser in an atmospheric environment. The expansion dynamics of the plasma plume depended on the distance between the target surface and focal point. In addition, spatially confined time-resolved images showed the different structures of the plasma plumes at different distances between the target surface and focal point. By analyzing the plume images, the optimal distance for emission enhancement was found to be approximately 6 mm away from the geometrical focus using a 10 cm focal length lens. This optimized distance resulted in the strongest compression ratio of the plasma plume by the reflected shock wave. Furthermore, the duration of the interaction between the reflected shock wave and the plasma plume was also prolonged.

Predicting Molecular Crystal Properties from First Principles: Finite-Temperature Thermochemistry to NMR Crystallography.

PubMed

Beran, Gregory J O; Hartman, Joshua D; Heit, Yonaton N

2016-11-15

Molecular crystals occur widely in pharmaceuticals, foods, explosives, organic semiconductors, and many other applications. Thanks to substantial progress in electronic structure modeling of molecular crystals, attention is now shifting from basic crystal structure prediction and lattice energy modeling toward the accurate prediction of experimentally observable properties at finite temperatures and pressures. This Account discusses how fragment-based electronic structure methods can be used to model a variety of experimentally relevant molecular crystal properties. First, it describes the coupling of fragment electronic structure models with quasi-harmonic techniques for modeling the thermal expansion of molecular crystals, and what effects this expansion has on thermochemical and mechanical properties. Excellent agreement with experiment is demonstrated for the molar volume, sublimation enthalpy, entropy, and free energy, and the bulk modulus of phase I carbon dioxide when large basis second-order Møller-Plesset perturbation theory (MP2) or coupled cluster theories (CCSD(T)) are used. In addition, physical insight is offered into how neglect of thermal expansion affects these properties. Zero-point vibrational motion leads to an appreciable expansion in the molar volume; in carbon dioxide, it accounts for around 30% of the overall volume expansion between the electronic structure energy minimum and the molar volume at the sublimation point. In addition, because thermal expansion typically weakens the intermolecular interactions, neglecting thermal expansion artificially stabilizes the solid and causes the sublimation enthalpy to be too large at higher temperatures. Thermal expansion also frequently weakens the lower-frequency lattice phonon modes; neglecting thermal expansion causes the entropy of sublimation to be overestimated. Interestingly, the sublimation free energy is less significantly affected by neglecting thermal expansion because the systematic errors in the enthalpy and entropy cancel somewhat. Second, because solid state nuclear magnetic resonance (NMR) plays an increasingly important role in molecular crystal studies, this Account discusses how fragment methods can be used to achieve higher-accuracy chemical shifts in molecular crystals. Whereas widely used plane wave density functional theory models are largely restricted to generalized gradient approximation (GGA) functionals like PBE in practice, fragment methods allow the routine use of hybrid density functionals with only modest increases in computational cost. In extensive molecular crystal benchmarks, hybrid functionals like PBE0 predict chemical shifts with 20-30% higher accuracy than GGAs, particularly for 1 H, 13 C, and 15 N nuclei. Due to their higher sensitivity to polarization effects, 17 O chemical shifts prove slightly harder to predict with fragment methods. Nevertheless, the fragment model results are still competitive with those from GIPAW. The improved accuracy achievable with fragment approaches and hybrid density functionals increases discrimination between different potential assignments of individual shifts or crystal structures, which is critical in NMR crystallography applications. This higher accuracy and greater discrimination are highlighted in application to the solid state NMR of different acetaminophen and testosterone crystal forms.

Experimental investigation on aero-optical aberration of shock wave/boundary layer interactions

NASA Astrophysics Data System (ADS)

Ding, Haolin; Yi, Shihe; Fu, Jia; He, Lin

2016-10-01

After streaming through the flow field which including the expansion, shock wave, boundary, etc., the optical wave would be distorted by fluctuations in the density field. Interactions between laminar/turbulent boundary layer and shock wave contain large number complex flow structures, which offer a condition for studying the influences that different flow structures of the complex flow field have on the aero-optical aberrations. Interactions between laminar/turbulent boundary layer and shock wave are investigated in a Mach 3.0 supersonic wind tunnel, based on nanoparticle-tracer planar laser scattering (NPLS) system. Boundary layer separation/attachment, induced suppression waves, induced shock wave, expansion fan and boundary layer are presented by NPLS images. Its spatial resolution is 44.15 μm/pixel. Time resolution is 6ns. Based on the NPLS images, the density fields with high spatial-temporal resolution are obtained by the flow image calibration, and then the optical path difference (OPD) fluctuations of the original 532nm planar wavefront are calculated using Ray-tracing theory. According to the different flow structures in the flow field, four parts are selected, (1) Y=692 600pixel; (2) Y=600 400pixel; (3) Y=400 268pixel; (4) Y=268 0pixel. The aerooptical effects of different flow structures are quantitatively analyzed, the results indicate that: the compressive waves such as incident shock wave, induced shock wave, etc. rise the density, and then uplift the OPD curve, but this kind of shock are fixed in space position and intensity, the aero-optics induced by it can be regarded as constant; The induced shock waves are induced by the coherent structure of large size vortex in the interaction between turbulent boundary layer, its unsteady characteristic decides the induced waves unsteady characteristic; The space position and intensity of the induced shock wave are fixed in the interaction between turbulent boundary layer; The boundary layer aero-optics are induced by the coherent structure of large size vortex, which result in the fluctuation of OPD.

Experiments on the Expansion of a Dense Plasma into a Background Magnetoplasma

NASA Astrophysics Data System (ADS)

Gekelman, Walter; Vanzeeland, Mike; Vincena, Steve; Pribyl, Pat

2003-10-01

There are many situations, which occur in space (coronal mass ejections, or are man-made (upper atmospheric detonations) as well as the initial stages of a supernovae, in which a dense plasma expands into a background magnetized plasma, that can support Alfvèn waves. The upgraded LArge Plasma Device (LAPD) is a machine, at UCLA, in which Alfvèn wave propagation in homogeneous and inhomogeneous plasmas has been studied. We describe a series of experiments,which involve the expansion of a dense (initially, n_laser-plasma/n_0≫1) laser-produced plasma into an ambient highly magnetized background plasma capable of supporting Alfvèn waves will be presented. The 150 MW laser is pulsed at the same 1 Hz repetition rate as the plasma in a highly reproducible experiment. The interaction results in the production of intense shear Alfvèn waves, as well as large density perturbations. The waves propagate away from the target and are observed to become plasma column resonances. In the initial phase the background magnetic field is expelled from a plasma bubble. Currents in the main body of the plasma are generated to neutralize the positively charged bubble. The current system which results, becomes that of a spectrum of shear Alfvèn waves. Spatial patterns of the wave magnetic fields waves are measured at over 10^4 locations. As the dense plasma expands across the magnetic field it seeds the column with shear waves. Most of the Alfvèn wave energy is in shear waves, which become field line resonances after a machine transit time. The interplay between waves, currents, inductive electric fields and space charge is analyzed in great detail. Dramatic movies of the measured wave fields and their associated currents will be presented. Work supported by ONR, and DOE /NSF.

An accurate boundary element method for the exterior elastic scattering problem in two dimensions

NASA Astrophysics Data System (ADS)

Bao, Gang; Xu, Liwei; Yin, Tao

2017-11-01

This paper is concerned with a Galerkin boundary element method solving the two dimensional exterior elastic wave scattering problem. The original problem is first reduced to the so-called Burton-Miller [1] boundary integral formulation, and essential mathematical features of its variational form are discussed. In numerical implementations, a newly-derived and analytically accurate regularization formula [2] is employed for the numerical evaluation of hyper-singular boundary integral operator. A new computational approach is employed based on the series expansions of Hankel functions for the computation of weakly-singular boundary integral operators during the reduction of corresponding Galerkin equations into a discrete linear system. The effectiveness of proposed numerical methods is demonstrated using several numerical examples.

Instability of a Planar Expansion Wave

DTIC Science & Technology

2005-10-11

Israel 3E. T. S. I. Industriales , Universidad de Castilla-La Mancha, 13071 Cuidad Real, Spain Received 18 March 2005; published 11 October 2005 An...modulation amplitude m=dx. As first shown in 3, for ideal gases with moderate values of , like 5 3 or 7 5 , m in a rippled rarefaction wave exhibits...radiating gases . The accuracy of such approximation is beyond the scope of the present paper see 17 and refer- ences therein. A blast wave

Sinc-interpolants in the energy plane for regular solution, Jost function, and its zeros of quantum scattering

NASA Astrophysics Data System (ADS)

Annaby, M. H.; Asharabi, R. M.

2018-01-01

In a remarkable note of Chadan [Il Nuovo Cimento 39, 697-703 (1965)], the author expanded both the regular wave function and the Jost function of the quantum scattering problem using an interpolation theorem of Valiron [Bull. Sci. Math. 49, 181-192 (1925)]. These expansions have a very slow rate of convergence, and applying them to compute the zeros of the Jost function, which lead to the important bound states, gives poor convergence rates. It is our objective in this paper to introduce several efficient interpolation techniques to compute the regular wave solution as well as the Jost function and its zeros approximately. This work continues and improves the results of Chadan and other related studies remarkably. Several worked examples are given with illustrations and comparisons with existing methods.

Communication: Quantum molecular dynamics simulation of liquid para-hydrogen by nuclear and electron wave packet approach.

PubMed

Hyeon-Deuk, Kim; Ando, Koji

2014-05-07

Liquid para-hydrogen (p-H2) is a typical quantum liquid which exhibits strong nuclear quantum effects (NQEs) and thus anomalous static and dynamic properties. We propose a real-time simulation method of wave packet (WP) molecular dynamics (MD) based on non-empirical intra- and inter-molecular interactions of non-spherical hydrogen molecules, and apply it to condensed-phase p-H2. The NQEs, such as WP delocalization and zero-point energy, are taken into account without perturbative expansion of prepared model potential functions but with explicit interactions between nuclear and electron WPs. The developed MD simulation for 100 ps with 1200 hydrogen molecules is realized at feasible computational cost, by which basic experimental properties of p-H2 liquid such as radial distribution functions, self-diffusion coefficients, and shear viscosities are all well reproduced.

Evidence of iridescence in TiO2 nanostructures: An approximation in plane wave expansion method

NASA Astrophysics Data System (ADS)

Quiroz, Heiddy P.; Barrera-Patiño, C. P.; Rey-González, R. R.; Dussan, A.

2016-11-01

Titanium dioxide nanotubes, TiO2 NTs, can be obtained by electrochemical anodization of Titanium sheets. After nanotubes are removed by mechanical stress, residual structures or traces on the surface of titanium sheets can be observed. These traces show iridescent effects. In this paper we carry out both experimental and theoretical study of those interesting and novel optical properties. For the experimental analysis we use angle resolved UV-vis spectroscopy while in the theoretical study is evaluated the photonic spectra using numerical simulations into the frequency-domain and the framework of the wave plane approximation. The iridescent effect is a strong property and independent of the sample. This behavior can be important to design new materials or compounds for several applications such as, cosmetic industry, optoelectronic devices, photocatalysis, sensors, among others.

Monitoring and analysis of thermal deformation waves with a high-speed phase measurement system.

PubMed

Taylor, Lucas; Talghader, Joseph

2015-10-20

Thermal effects in optical substrates are vitally important in determining laser damage resistance in long-pulse and continuous-wave laser systems. Thermal deformation waves in a soda-lime-silica glass substrate have been measured using high-speed interferometry during a series of laser pulses incident on the surface. Two-dimensional images of the thermal waves were captured at a rate of up to six frames per thermal event using a quantitative phase measurement method. The system comprised a Mach-Zehnder interferometer, along with a high-speed camera capable of up to 20,000 frames-per-second. The sample was placed in the interferometer and irradiated with 100 ns, 2 kHz Q-switched pulses from a high-power Nd:YAG laser operating at 1064 nm. Phase measurements were converted to temperature using known values of thermal expansion and temperature-dependent refractive index for glass. The thermal decay at the center of the thermal wave was fit to a function derived from first principles with excellent agreement. Additionally, the spread of the thermal distribution over time was fit to the same function. Both the temporal decay fit and the spatial fit produced a thermal diffusivity of 5×10^-7  m²/s.

Phononic band gap and wave propagation on polyvinylidene fluoride-based acoustic metamaterials

NASA Astrophysics Data System (ADS)

Oltulu, Oral; Simsek, Sevket; Mamedov, Amirullah M.; Ozbay, Ekmel

2016-12-01

In the present work, the acoustic band structure of a two-dimensional phononic crystal (PC) containing an organic ferroelectric (PVDF-polyvinylidene fluoride) and topological insulator (SnTe) was investigated by the plane-wave-expansion (PWE) method. Two-dimensional PC with square lattices composed of SnTe cylindrical rods embedded in the PVDF matrix is studied to find the allowed and stop bands for the waves of certain energy. Phononic band diagram ω = ω(k) for a 2D PC, in which non-dimensional frequencies ωa/2πc (c-velocity of wave) were plotted vs. the wavevector k along the Г-X-M-Г path in the square Brillouin zone shows five stop bands in the frequency range between 10 and 110 kHz. The ferroelectric properties of PVDF and the unusual properties of SnTe as a topological material give us the ability to control the wave propagation through the PC over a wide frequency range of 103-106 Hz. SnTe is a discrete component that allows conducting electricity on its surface but shows insulator properties through its bulk volume. Tin telluride is considered as an acoustic topological insulator as the extension of topological insulators into the field of "topological phononics".

Convergence of the Light-Front Coupled-Cluster Method in Scalar Yukawa Theory

NASA Astrophysics Data System (ADS)

Usselman, Austin

We use Fock-state expansions and the Light-Front Coupled-Cluster (LFCC) method to study mass eigenvalue problems in quantum field theory. Specifically, we study convergence of the method in scalar Yukawa theory. In this theory, a single charged particle is surrounded by a cloud of neutral particles. The charged particle can create or annihilate neutral particles, causing the n-particle state to depend on the n + 1 and n - 1-particle state. Fock state expansion leads to an infinite set of coupled equations where truncation is required. The wave functions for the particle states are expanded in a basis of symmetric polynomials and a generalized eigenvalue problem is solved for the mass eigenvalue. The mass eigenvalue problem is solved for multiple values for the coupling strength while the number of particle states and polynomial basis order are increased. Convergence of the mass eigenvalue solutions is then obtained. Three mass ratios between the charged particle and neutral particles were studied. This includes a massive charged particle, equal masses and massive neutral particles. Relative probability between states can also be explored for more detailed understanding of the process of convergence with respect to the number of Fock sectors. The reliance on higher order particle states depended on how large the mass of the charge particle was. The higher the mass of the charged particle, the more the system depended on higher order particle states. The LFCC method solves this same mass eigenvalue problem using an exponential operator. This exponential operator can then be truncated instead to form a finite system of equations that can be solved using a built in system solver provided in most computational environments, such as MatLab and Mathematica. First approximation in the LFCC method allows for only one particle to be created by the new operator and proved to be not powerful enough to match the Fock state expansion. The second order approximation allowed one and two particles to be created by the new operator and converged to the Fock state expansion results. This showed the LFCC method to be a reliable replacement method for solving quantum field theory problems.

The multifacet graphically contracted function method. I. Formulation and implementation

NASA Astrophysics Data System (ADS)

Shepard, Ron; Gidofalvi, Gergely; Brozell, Scott R.

2014-08-01

The basic formulation for the multifacet generalization of the graphically contracted function (MFGCF) electronic structure method is presented. The analysis includes the discussion of linear dependency and redundancy of the arc factor parameters, the computation of reduced density matrices, Hamiltonian matrix construction, spin-density matrix construction, the computation of optimization gradients for single-state and state-averaged calculations, graphical wave function analysis, and the efficient computation of configuration state function and Slater determinant expansion coefficients. Timings are given for Hamiltonian matrix element and analytic optimization gradient computations for a range of model problems for full-CI Shavitt graphs, and it is observed that both the energy and the gradient computation scale as O(N2n4) for N electrons and n orbitals. The important arithmetic operations are within dense matrix-matrix product computational kernels, resulting in a computationally efficient procedure. An initial implementation of the method is used to present applications to several challenging chemical systems, including N2 dissociation, cubic H8 dissociation, the symmetric dissociation of H2O, and the insertion of Be into H2. The results are compared to the exact full-CI values and also to those of the previous single-facet GCF expansion form.

The multifacet graphically contracted function method. I. Formulation and implementation.

PubMed

Shepard, Ron; Gidofalvi, Gergely; Brozell, Scott R

2014-08-14

The basic formulation for the multifacet generalization of the graphically contracted function (MFGCF) electronic structure method is presented. The analysis includes the discussion of linear dependency and redundancy of the arc factor parameters, the computation of reduced density matrices, Hamiltonian matrix construction, spin-density matrix construction, the computation of optimization gradients for single-state and state-averaged calculations, graphical wave function analysis, and the efficient computation of configuration state function and Slater determinant expansion coefficients. Timings are given for Hamiltonian matrix element and analytic optimization gradient computations for a range of model problems for full-CI Shavitt graphs, and it is observed that both the energy and the gradient computation scale as O(N(2)n(4)) for N electrons and n orbitals. The important arithmetic operations are within dense matrix-matrix product computational kernels, resulting in a computationally efficient procedure. An initial implementation of the method is used to present applications to several challenging chemical systems, including N2 dissociation, cubic H8 dissociation, the symmetric dissociation of H2O, and the insertion of Be into H2. The results are compared to the exact full-CI values and also to those of the previous single-facet GCF expansion form.

Solitons, Lie Group Analysis and Conservation Laws of a (3+1)-Dimensional Modified Zakharov-Kuznetsov Equation in a Multicomponent Magnetised Plasma

NASA Astrophysics Data System (ADS)

Du, Xia-Xia; Tian, Bo; Chai, Jun; Sun, Yan; Yuan, Yu-Qiang

2017-11-01

In this paper, we investigate a (3+1)-dimensional modified Zakharov-Kuznetsov equation, which describes the nonlinear plasma-acoustic waves in a multicomponent magnetised plasma. With the aid of the Hirota method and symbolic computation, bilinear forms and one-, two- and three-soliton solutions are derived. The characteristics and interaction of the solitons are discussed graphically. We present the effects on the soliton's amplitude by the nonlinear coefficients which are related to the ratio of the positive-ion mass to negative-ion mass, number densities, initial densities of the lower- and higher-temperature electrons and ratio of the lower temperature to the higher temperature for electrons, as well as by the dispersion coefficient, which is related to the ratio of the positive-ion mass to the negative-ion mass and number densities. Moreover, using the Lie symmetry group theory, we derive the Lie point symmetry generators and the corresponding symmetry reductions, through which certain analytic solutions are obtained via the power series expansion method and the (G'/G) expansion method. We demonstrate that such an equation is strictly self-adjoint, and the conservation laws associated with the Lie point symmetry generators are derived.

Ecocultural range-expansion scenarios for the replacement or assimilation of Neanderthals by modern humans.

PubMed

Wakano, Joe Yuichiro; Gilpin, William; Kadowaki, Seiji; Feldman, Marcus W; Aoki, Kenichi

2018-02-01

Recent archaeological records no longer support a simple dichotomous characterization of the cultures/behaviors of Neanderthals and modern humans, but indicate much cultural/behavioral variability over time and space. Thus, in modeling the replacement or assimilation of Neanderthals by modern humans, it is of interest to consider cultural dynamics and their relation to demographic change. The ecocultural framework for the competition between hominid species allows their carrying capacities to depend on some measure of the levels of culture they possess. In the present study both population densities and the densities of skilled individuals in Neanderthals and modern humans are spatially distributed and subject to change by spatial diffusion, ecological competition, and cultural transmission within each species. We analyze the resulting range expansions in terms of the demographic, ecological and cultural parameters that determine how the carrying capacities relate to the local densities of skilled individuals in each species. Of special interest is the case of cognitive and intrinsic-demographic equivalence of the two species. The range expansion dynamics may consist of multiple wave fronts of different speeds, each of which originates from a traveling wave solution. Properties of these traveling wave solutions are mathematically derived. Depending on the parameters, these traveling waves can result in replacement of Neanderthals by modern humans, or assimilation of the former by the latter. In both the replacement and assimilation scenarios, the first wave of intrusive modern humans is characterized by a low population density and a low density of skilled individuals, with implications for archaeological visibility. The first invasion is due to weak interspecific competition. A second wave of invasion may be induced by cultural differences between moderns and Neanderthals. Spatially and temporally extended coexistence of the two species, which would have facilitated the transfer of genes from Neanderthal into modern humans and vice versa, is observed in the traveling waves, except when niche overlap between the two species is extremely high. Archaeological findings on the spatial and temporal distributions of the Initial Upper Palaeolithic and the Early Upper Palaeolithic and of the coexistence of Neanderthals and modern humans are discussed. Copyright © 2017 Elsevier Inc. All rights reserved.

Exhaust Nozzle Plume Effects on Sonic Boom Test Results for Vectored Nozzles

NASA Technical Reports Server (NTRS)

Castner, Raymond

2012-01-01

Reducing or eliminating the operational restrictions of supersonic aircraft over populated areas has led to extensive research at NASA. Restrictions were due to the disturbance of the sonic boom, caused by the coalescence of shock waves formed off the aircraft. Recent work has been performed to reduce the magnitude of the sonic boom N-wave generated by airplane components with a focus on shock waves caused by the exhaust nozzle plume. Previous Computational Fluid Dynamics (CFD) analysis showed how the shock wave formed at the nozzle lip interacts with the nozzle boat-tail expansion wave. An experiment was conducted in the 1- by 1-foot Supersonic Wind Tunnel (SWT) at the NASA Glenn Research Center. Results show how the shock generated at the nozzle lip affects the near field pressure signature, and thereby the potential sonic boom contribution for a nozzle at vector angles from 3 to 8 . The experiment was based on the NASA F-15 nozzle used in the Lift and Nozzle Change Effects on Tail Shock experiment, which possessed a large external boat-tail angle. In this case, the large boat-tail angle caused a dramatic expansion, which dominated the near field pressure signature. The impact of nozzle vector angle and nozzle pressure ratio are summarized.

Acoustic scattering of a Bessel vortex beam by a rigid fixed spheroid

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2015-12-01

Partial-wave series representation of the acoustic scattering field of high-order Bessel vortex beams by rigid oblate and prolate spheroids using the modal matching method is developed. The method, which is applicable to slightly elongated objects at low-to-moderate frequencies, requires solving a system of linear equations which depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated partial-wave series expansions (PWSEs), and satisfying the Neumann boundary condition for a rigid immovable surface in the least-squares sense. This original semi-analytical approach developed for Bessel vortex beams is demonstrated for finite oblate and prolate spheroids, where the mathematical functions describing the spheroidal geometry are written in a form involving single angular (polar) integrals that are numerically computed. The transverse (θ = π / 2) and 3D scattering directivity patterns are evaluated in the far-field for both prolate and oblate spheroids, with particular emphasis on the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid) not exceeding 3:1, the half-cone angle β and order m of the Bessel vortex beam, as well as the dimensionless size parameter kr0. Periodic oscillations in the magnitude plots of the far-field scattering form function are observed, which result from the interference of the reflected waves with the circumferential (Franz') waves circumnavigating the surface of the spheroid in the surrounding fluid. Moreover, the 3D directivity patterns illustrate the far-field scattering from the spheroid, that vanishes in the forward (θ = 0) and backward (θ = π) directions. Particular applications in underwater acoustics and scattering, acoustic levitation and the detection of submerged elongated objects using Bessel vortex waves to name a few, would benefit from the results of the present investigation.

Rapid Non-Gaussian Uncertainty Quantification of Seismic Velocity Models and Images

NASA Astrophysics Data System (ADS)

Ely, G.; Malcolm, A. E.; Poliannikov, O. V.

2017-12-01

Conventional seismic imaging typically provides a single estimate of the subsurface without any error bounds. Noise in the observed raw traces as well as the uncertainty of the velocity model directly impact the uncertainty of the final seismic image and its resulting interpretation. We present a Bayesian inference framework to quantify uncertainty in both the velocity model and seismic images, given noise statistics of the observed data.To estimate velocity model uncertainty, we combine the field expansion method, a fast frequency domain wave equation solver, with the adaptive Metropolis-Hastings algorithm. The speed of the field expansion method and its reduced parameterization allows us to perform the tens or hundreds of thousands of forward solves needed for non-parametric posterior estimations. We then migrate the observed data with the distribution of velocity models to generate uncertainty estimates of the resulting subsurface image. This procedure allows us to create both qualitative descriptions of seismic image uncertainty and put error bounds on quantities of interest such as the dip angle of a subduction slab or thickness of a stratigraphic layer.

40 CFR 230.41 - Wetlands.

Code of Federal Regulations, 2010 CFR

2010-07-01

... circulation patterns that flush large expanses of wetland systems, by interfering with the filtration function... buffer zone shielding upland areas from wave actions, storm damage and erosion. ...

Experimental studies of hypersonic shock-wave boundary-layer interactions

NASA Technical Reports Server (NTRS)

Lu, Frank K.

1992-01-01

Two classes of shock-wave boundary-layer interactions were studied experimentally in a shock tunnel in which a low Reynolds number, turbulent flow at Mach 8 was developed on a cold, flat test surface. The two classes of interactions were: (1) a swept interaction generated by a wedge ('fin') mounted perpendicularly on the flat plate; and (2) a two-dimensional, unseparated interaction induced by a shock impinging near an expansion corner. The swept interaction, with wedge angles of 5-20 degrees, was separated and there was also indication that the strongest interactions prossessed secondary separation zones. The interaction spread out extensively from the inviscid shock location although no indication of quasi-conical symmetry was evident. The surface pressure from the upstream influence to the inviscid shock was relatively low compared to the inviscid downstream value but it rose rapidly past the inviscid shock location. However, the surface pressure did not reach the downstream inviscid value and reasons were proposed for this anomalous behavior compared to strongly separated, supersonic interactions. The second class of interactions involved weak shocks impinging near small expansion corners. As a prelude to studying this interaction, a hypersonic similarity parameter was identified for the pure, expansion corner flow. The expansion corner severely damped out surface pressure fluctuations. When a shock impinged upstream of the corner, no significant changes to the surface pressure were found as compared to the case when the shock impinged on a flat plate. But, when the shock impinged downstream of the corner, a close coupling existed between the two wave systems, unlike the supersonic case. This close coupling modified the upstream influence. Regardless of whether the shock impinged ahead or behind the corner, the downstream region was affected by the close coupling between the shock and the expansion. Not only was the mean pressure distribution modified but the unsteadiness in the surface pressure was reduced compared to the flat-plate case.

Modeled and Measured Partially Coherent Illumination Speckle Effects from Sloped Surfaces for Tactical Tracking

DTIC Science & Technology

2015-03-26

long-wave infrared ( LWIR ) passive imaging, or eliminating dependence upon target emission and solar reflection. Figure 1.1 shows one example of a...levels of illumination nonuniformity were still present in each IFOV. Thus, further expansion of the beam such that the minimum diffraction- limited... LWIR – long-wave infrared, sometimes defined as the 8 to 12 µm spectral window MWIR – mid-wave infrared, sometimes defined as the 3 to 5 µm spectral

A highly optimized code for calculating atomic data at neutron star magnetic field strengths using a doubly self-consistent Hartree-Fock-Roothaan method

NASA Astrophysics Data System (ADS)

Schimeczek, C.; Engel, D.; Wunner, G.

2012-07-01

Our previously published code for calculating energies and bound-bound transitions of medium-Z elements at neutron star magnetic field strengths [D. Engel, M. Klews, G. Wunner, Comput. Phys. Comm. 180 (2009) 302-311] was based on the adiabatic approximation. It assumes a complete decoupling of the (fast) gyration of the electrons under the action of the magnetic field and the (slow) bound motion along the field under the action of the Coulomb forces. For the single-particle orbitals this implied that each is a product of a Landau state and an (unknown) longitudinal wave function whose B-spline coefficients were determined self-consistently by solving the Hartree-Fock equations for the many-electron problem on a finite-element grid. In the present code we go beyond the adiabatic approximation, by allowing the transverse part of each orbital to be a superposition of Landau states, while assuming that the longitudinal part can be approximated by the same wave function in each Landau level. Inserting this ansatz into the energy variational principle leads to a system of coupled equations in which the B-spline coefficients depend on the weights of the individual Landau states, and vice versa, and which therefore has to be solved in a doubly self-consistent manner. The extended ansatz takes into account the back-reaction of the Coulomb motion of the electrons along the field direction on their motion in the plane perpendicular to the field, an effect which cannot be captured by the adiabatic approximation. The new code allows for the inclusion of up to 8 Landau levels. This reduces the relative error of energy values as compared to the adiabatic approximation results by typically a factor of three (1/3 of the original error), and yields accurate results also in regions of lower neutron star magnetic field strengths where the adiabatic approximation fails. Further improvements in the code are a more sophisticated choice of the initial wave functions, which takes into account the shielding of the core potential for outer electrons by inner electrons, and an optimal finite-element decomposition of each individual longitudinal wave function. These measures largely enhance the convergence properties compared to the previous code, and lead to speed-ups by factors up to two orders of magnitude compared with the implementation of the Hartree-Fock-Roothaan method used by Engel and Wunner in [D. Engel, G. Wunner, Phys. Rev. A 78 (2008) 032515]. New version program summaryProgram title: HFFER II Catalogue identifier: AECC_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECC_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: v 55 130 No. of bytes in distributed program, including test data, etc.: 293 700 Distribution format: tar.gz Programming language: Fortran 95 Computer: Cluster of 1-13 HP Compaq dc5750 Operating system: Linux Has the code been vectorized or parallelized?: Yes, parallelized using MPI directives. RAM: 1 GByte per node Classification: 2.1 External routines: MPI/GFortran, LAPACK, BLAS, FMlib (included in the package) Catalogue identifier of previous version: AECC_v1_0 Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 302 Does the new version supersede the previous version?: Yes Nature of problem: Quantitative modellings of features observed in the X-ray spectra of isolated magnetic neutron stars are hampered by the lack of sufficiently large and accurate databases for atoms and ions up to the last fusion product, iron, at strong magnetic field strengths. Our code is intended to provide a powerful tool for calculating energies and oscillator strengths of medium-Z atoms and ions at neutron star magnetic field strengths with sufficient accuracy in a routine way to create such databases. Solution method: The Slater determinants of the atomic wave functions are constructed from single-particle orbitals ψi which are products of a wave function in the z direction (the direction of the magnetic field) and an expansion of the wave function perpendicular to the direction of the magnetic field in terms of Landau states, ψi(ρ,φ,z)=Pi(z)∑n=0NLtinϕni(ρ,φ). The tin are expansion coefficients, and the expansion is cut off at some maximum Landau level quantum number n=NL. In the previous version of the code only the lowest Landau level was included (NL=0), in the new version NL can take values of up to 7. As in the previous version of the code, the longitudinal wave functions are expanded in terms of sixth-order B-splines on finite elements on the z axis, with a combination of equidistant and quadratically widening element borders. Both the B-spline expansion coefficients and the Landau weights tin of all orbitals have to be determined in a doubly self-consistent way: For a given set of Landau weights tin, the system of linear equations for the B-spline expansion coefficients, which is equivalent to the Hartree-Fock equations for the longitudinal wave functions, is solved numerically. In the second step, for frozen B-spline coefficients new Landau weights are determined by minimizing the total energy with respect to the Landau expansion coefficients. Both steps require solving non-linear eigenvalue problems of Roothaan type. The procedure is repeated until convergence of both the B-spline coefficients and the Landau weights is achieved. Reasons for new version: The former version of the code was restricted to the adiabatic approximation, which assumes the quantum dynamics of the electrons in the plane perpendicular to the magnetic field to be fixed in the lowest Landau level, n=0. This approximation is valid only if the magnetic field strengths are large compared to the reference magnetic field BZ, for a nuclear charge Z,BZ=Z24.70108×105 T. Summary of revisions: In the new version, the transverse parts of the orbitals are expanded in terms of Landau states up to n=7, and the expansion coefficients are determined, together with the longitudinal wave functions, in a doubly self-consistent way. Thus the back-reaction of the quantum dynamics along the magnetic field direction on the quantum dynamics in the plane perpendicular to it is taken into account. The new ansatz not only increases the accuracy of the results for energy values and transition strengths obtained so far, but also allows their calculation for magnetic field strengths down to B≳BZ, where the adiabatic approximation fails. Restrictions: Intense magnetic field strengths are required, since the expansion of the transverse single-particle wave functions using 8 Landau levels will no longer produce accurate results if the scaled magnetic field strength parameter βZ=B/BZ becomes much smaller than unity. Unusual features: A huge program speed-up is achieved by making use of pre-calculated binary files. These can be calculated with additional programs provided with this package. Running time: 1-30 min.

A shock wave capability for the improved Two-Dimensional Kinetics (TDK) computer program

NASA Technical Reports Server (NTRS)

Nickerson, G. R.; Dang, L. D.

1984-01-01

The Two Dimensional Kinetics (TDK) computer program is a primary tool in applying the JANNAF liquid rocket engine performance prediction procedures. The purpose of this contract has been to improve the TDK computer program so that it can be applied to rocket engine designs of advanced type. In particular, future orbit transfer vehicles (OTV) will require rocket engines that operate at high expansion ratio, i.e., in excess of 200:1. Because only a limited length is available in the space shuttle bay, it is possible that OTV nozzles will be designed with both relatively short length and high expansion ratio. In this case, a shock wave may be present in the flow. The TDK computer program was modified to include the simulation of shock waves in the supersonic nozzle flow field. The shocks induced by the wall contour can produce strong perturbations of the flow, affecting downstream conditions which need to be considered for thrust chamber performance calculations.

Theoretical analysis of rotating two phase detonation in a rocket motor

NASA Technical Reports Server (NTRS)

Shen, I.; Adamson, T. C., Jr.

1973-01-01

Tangential mode, non-linear wave motion in a liquid propellant rocket engine is studied, using a two phase detonation wave as the reaction model. Because the detonation wave is followed immediately by expansion waves, due to the side relief in the axial direction, it is a Chapman-Jouguet wave. The strength of this wave, which may be characterized by the pressure ratio across the wave, as well as the wave speed and the local wave Mach number, are related to design parameters such as the contraction ratio, chamber speed of sound, chamber diameter, propellant injection density and velocity, and the specific heat ratio of the burned gases. In addition, the distribution of flow properties along the injector face can be computed. Numerical calculations show favorable comparison with experimental findings. Finally, the effects of drop size are discussed and a simple criterion is found to set the lower limit of validity of this strong wave analysis.

Protostellar Collapse with a Shock

NASA Technical Reports Server (NTRS)

Tsai, John C.; Hsu, Juliana J.

1995-01-01

We reexamine both numerically and analytically the collapse of the singular isothermal sphere in the context of low-mass star formation. We consider the case where the onset of collapse is initiated by some arbitrary process which is accompanied by a central output of either heat or kinetic energy. We find two classes of numerical solutions describing this manner of collapse. The first approaches in time the expansion wave solution of Shu, while the second class is characterized by an ever-decreasing central accretion rate and the presence of an outwardly propagating weak shock. The collapse solution which represents the dividing case between these two classes is determined analytically by a similarity analysis. This solution shares with the expansion wave solution the properties that the gas remains stationary with an r(exp -2) density profile at large radius and that, at small radius, the gas free-falls onto a nascent core at a constant rate which depends only on the isothermal sound speed. This accretion rate is a factor of approx. 0.1 that predicted by the expansion wave solution. This reduction is due in part to the presence of a weak shock which propagates outward at 1.26 times the sound speed. Gas in the postshock region first moves out subsonically but is then decelerated and begins to collapse. The existence of two classes of numerical collapse solutions is explained in terms of the instability to radial perturbations of the analytic solution. Collapse occurring in the manner described by some of our solutions would eventually unbind a finite-sized core. However, this does not constitute a violation of the instability properties of the singular isothermal sphere which is unstable both to collapse and to expansion. To emphasize this, we consider a purely expanding solution for isothermal spheres. This solution is found to be self-similar and results in a uniform density core in the central regions of the gas. Our solutions may be relevant to the 'luminosity' problem of protostellar cores since the predicted central accretion rates are significantly reduced relative to that of the expansion wave solution. Furthermore, our calculations indicate that star-forming cloud cores are not very tightly bound and that modest disturbances can easily result in both termination of infall and dispersal of unaccreted material.

Protostellar Collapse with a Shock

NASA Technical Reports Server (NTRS)

Tsai, John C.; Hsu, Juliana J. L.

1995-01-01

We reexamine both numerically and analytically the collapse of the singular isothermal sphere in the context of low-mass star formation. We consider the case where the onset of collapse is initiated by some arbitrary process which is accompanied by a central output of either heat or kinetic energy. We find two classes of numerical solutions describing this manner of collapse. The first approaches in time the expansion wave solution of Shu, while the second class is characterized by an ever-decreasing central accretion rate and the presence of an outwardly propagating weak shock. The collapse solution which represents the dividing case between these two classes is determined analytically by a similarity analysis. This solution shares with the expansion wave solution the properties that the gas remains stationary with an r(sup -2) density profile at large radius and that, at small radius, the gas free-falls onto a nascent core at a constant rate which depends only on the isothermal sound speed. This accretion rate is a factor of approx. 0.1 that predicted by the expansion wave solution. This reduction is due in part to the presence of a weak shock which propagates outward at 1.26 times the sound speed. Gas in the postshock region first moves out subsonically but is then decelerated and begins to collapse. The existence of two classes of numerical collapse solutions is explained in terms of the instability to radial perturbations of the analytic solution. Collapse occurring in the manner described by some of our solutions would eventually unbind a finite-sized core. However, this does not constitute a violation of the instability properties of the singular isothermal sphere which is unstable both to collapse and to expansion. To emphasize this, we consider a purely expanding solution for isothermal spheres. This solution is found to be self-similar and results in a uniform density core in the central regions of the gas. Our solutions may be relevant to the 'luminosity' problem of protostellar cores since the predicted central accretion rates are significantly reduced relative to that of the expansion wave solution. Furthermore, our calculations indicate that star-forming cloud cores are not very tightly bound and that modest disturbances can easily result in both termination of infall and dispersal of unaccreted material.

Compressible Boundary Layer Investigation for Ramjet/scramjet Inlets and Nozzles

NASA Astrophysics Data System (ADS)

Goldfeld, M. A.; Starov, A. V.; Semenova, Yu. V.

2005-02-01

The results of experimental investigation of a turbulent boundary layer on compression and expansion surfaces are presented. They include the study of the shock wave and/or expansion fan action upon the boundary layer, boundary layer separation and its relaxation. Complex events of paired interactions and the flow on compression convex-concave surfaces were studied [M. Goldfeld, 1993]. The possibility and conditions of the boundary layer relaminarization behind the expansion fan and its effect on the relaxation length are presented. Different model configurations for wide range conditions were investigated. Comparison of results for different interactions was carried out.

Ultra high resolution molecular beam cars spectroscopy with application to planetary atmospheric molecules

NASA Technical Reports Server (NTRS)

Byer, R. L.

1982-01-01

The measurement of high resolution pulsed and continuous wave (CW) coherent anti-Stokes Raman spectroscopy (CARS) measurements in pulsed and steady state supersonic expansions were demonstrated. Pulsed molecular beam sources were characterized, and saturation of a Raman transition and, for the first time, the Raman spectrum of a complex molecular cluster were observed. The observation of CW CARS spectra in a molecular expansion and the effects of transit time broadening is described. Supersonic expansion is established as a viable technique for high resolution Raman spectroscopy of cold molecules with resolutions of 100 MH2.

Acoustic and elastic multiple scattering and radiation from cylindrical structures

NASA Astrophysics Data System (ADS)

Amirkulova, Feruza Abdukadirovna

Multiple scattering (MS) and radiation of waves by a system of scatterers is of great theoretical and practical importance and is required in a wide variety of physical contexts such as the implementation of "invisibility" cloaks, the effective parameter characterization, and the fabrication of dynamically tunable structures, etc. The dissertation develops fast, rapidly convergent iterative techniques to expedite the solution of MS problems. The formulation of MS problems reduces to a system of linear algebraic equations using Graf's theorem and separation of variables. The iterative techniques are developed using Neumann expansion and Block Toeplitz structure of the linear system; they are very general, and suitable for parallel computations and a large number of MS problems, i.e. acoustic, elastic, electromagnetic, etc., and used for the first time to solve MS problems. The theory is implemented in Matlab and FORTRAN, and the theoretical predictions are compared to computations obtained by COMSOL. To formulate the MS problem, the transition matrix is obtained by analyzing an acoustic and an elastic single scattering of incident waves by elastic isotropic and anisotropic solids. The mathematical model of wave scattering from multilayered cylindrical and spherical structures is developed by means of an exact solution of dynamic 3D elasticity theory. The recursive impedance matrix algorithm is derived for radially heterogeneous anisotropic solids. An explicit method for finding the impedance in piecewise uniform, transverse-isotropic material is proposed; the solution is compared to elasticity theory solutions involving Buchwald potentials. Furthermore, active exterior cloaking devices are modeled for acoustic and elastic media using multipole sources. A cloaking device can render an object invisible to some incident waves as seen by some external observer. The active cloak is generated by a discrete set of multipole sources that destructively interfere with an incident wave to produce zero total field over a finite spatial region. The approach precisely determines the necessary source amplitudes and enables a cloaked region to be determined using Graf's theorem. To apply the approach, the infinite series of multipole expansions are truncated, and the accuracy of cloaking is studied by modifying the truncation parameter.

The antagonistic modulation of Arp2/3 activity by N-WASP, WAVE2 and PICK1 defines dynamic changes in astrocyte morphology.

PubMed

Murk, Kai; Blanco Suarez, Elena M; Cockbill, Louisa M R; Banks, Paul; Hanley, Jonathan G

2013-09-01

Astrocytes exhibit a complex, branched morphology, allowing them to functionally interact with numerous blood vessels, neighboring glial processes and neuronal elements, including synapses. They also respond to central nervous system (CNS) injury by a process known as astrogliosis, which involves morphological changes, including cell body hypertrophy and thickening of major processes. Following severe injury, astrocytes exhibit drastically reduced morphological complexity and collectively form a glial scar. The mechanistic details behind these morphological changes are unknown. Here, we investigate the regulation of the actin-nucleating Arp2/3 complex in controlling dynamic changes in astrocyte morphology. In contrast to other cell types, Arp2/3 inhibition drives the rapid expansion of astrocyte cell bodies and major processes. This intervention results in a reduced morphological complexity of astrocytes in both dissociated culture and in brain slices. We show that this expansion requires functional myosin II downstream of ROCK and RhoA. Knockdown of the Arp2/3 subunit Arp3 or the Arp2/3 activator N-WASP by siRNA also results in cell body expansion and reduced morphological complexity, whereas depleting WAVE2 specifically reduces the branching complexity of astrocyte processes. By contrast, knockdown of the Arp2/3 inhibitor PICK1 increases astrocyte branching complexity. Furthermore, astrocyte expansion induced by ischemic conditions is delayed by PICK1 knockdown or N-WASP overexpression. Our findings identify a new morphological outcome for Arp2/3 activation in restricting rather than promoting outwards movement of the plasma membrane in astrocytes. The Arp2/3 regulators PICK1, and N-WASP and WAVE2 function antagonistically to control the complexity of astrocyte branched morphology, and this mechanism underlies the morphological changes seen in astrocytes during their response to pathological insult.

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

Vogel, A.; Scammon, R.J.; Godwin, R.P.

Biological tissue is more susceptible to damage from tensile stress than to compressive stress. Tensile stress may arise through the thermoelastic response of laser-irradiated media. Optical breakdown, however, has to date been exclusively associated with compressive stress. The authors show that this is appropriate for water, but not for tissues for which the elastic-plastic material response needs to be considered. The acoustic transients following optical breakdown in water and cornea were measured with a fast hydrophone and the cavitation bubble dynamics, which is closely linked to the stress wave generation, was documented by flash photography. Breakdown in water produced amore » monopolar acoustic signal and a bubble oscillation in which the expansion and collapse phases were symmetric. Breakdown in cornea produced a bipolar acoustic signal coupled with a pronounced shortening of the bubble expansion phase and a considerable prolongation of its collapse phase. The tensile stress wave is related to the abrupt end of the bubble expansion. Numerical simulations using the MESA-2D code were performed assuming elastic-plastic material behavior in a wide range of values for the shear modulus and yield strength. The calculations revealed that consideration of the elastic-plastic material response is essential to reproduce the experimentally observed bipolar stress waves. The tensile stress evolves during the outward propagation of the acoustic transient and reaches an amplitude of 30--40% of the compressive pulse.« less

On hydromagnetic oscillations in a rotating cavity.

NASA Technical Reports Server (NTRS)

Gans, R. F.

1971-01-01

Time-dependent hydromagnetic phenomena in a rotating spherical cavity are investigated in the framework of an interior boundary-layer expansion. The first type of wave is a modification of the hydrodynamic inertial wave, the second is a pseudo-geostrophic wave and is involved in spinup, and the third is related to the MAC waves of Braginskii (1967). It is shown that the MAC waves must satisfy more than the usual normal boundary conditions, and that reference must be made to the boundary-layer solution to resolve the ambiguity regarding which conditions are to be taken. The boundary-layer structure is investigated in detail to display the interactions between applied field, viscosity, electrical conductivity, frequency and latitu de.

Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

NASA Astrophysics Data System (ADS)

Chakrabarti, Aloknath; Mohapatra, Smrutiranjan

2013-09-01

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates, separated by a gap of finite width, floating horizontally on water of finite depth, are investigated in the present work for a two-dimensional time-harmonic case. Within the frame of linear water wave theory, the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions. Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem. In both the problems, the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates. Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations. The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration. The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

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

Basis convergence of range-separated density-functional theory.

PubMed

Franck, Odile; Mussard, Bastien; Luppi, Eleonora; Toulouse, Julien

2015-02-21

Range-separated density-functional theory (DFT) is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with cardinal number X of the Dunning basis sets cc - p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.

Long-distance dispersal suppresses introgression of local alleles during range expansions

PubMed Central

Amorim, C E G; Hofer, T; Ray, N; Foll, M; Ruiz-Linares, A; Excoffier, L

2017-01-01

During range expansions, even low levels of interbreeding can lead to massive introgression of local alleles into an invader's genome. Nonetheless, this pattern is not always observed in human populations. For instance, European Americans in North America are barely introgressed by Amerindian genes in spite of known contact and admixture. With coalescent spatially explicit simulations, we examined the impact of long-distance dispersal (LDD) events on introgression of local alleles into the invading population using a set of different demographic scenarios applicable to a diverse range of natural populations and species. More specifically, we consider two distinct LDD models: one where LDD events originate in the range core and targets only the expansion front and a second one where LDD events can occur from any area to any other. We find that LDD generally prevents introgression, but that LDD events specifically targeting the expansion front are most efficient in suppressing introgression. This is likely due to the fact that LDD allows for the presence of a larger number of invader alleles at the wave front, where effective population size is thus increased and local introgressed alleles are rapidly outnumbered. We postulate that the documented settlement of pioneers directly on the wave front in North America has contributed to low levels of Amerindian admixture observed in European Americans and that this phenomenon may well explain the lack of introgression after a range expansion in natural populations without the need to evoke other mechanisms such as natural selection. PMID:27577693

Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional

NASA Astrophysics Data System (ADS)

Chacón, Enrique; Tarazona, Pedro

2016-06-01

We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau-Ginzburg-Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.

Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional.

PubMed

Chacón, Enrique; Tarazona, Pedro

2016-06-22

We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau-Ginzburg-Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.

Different approach to the modeling of nonfree particle diffusion

NASA Astrophysics Data System (ADS)

Buhl, Niels

2018-03-01

A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore networks to general geometric domains can be considered and that the (free random walk) central limit theorem can be generalized to cover also the nonfree case. The latter gives rise to a continuum-limit description of the diffusive motion where the effect of partially absorbing barriers is accounted for in a natural and non-Markovian way that, in contrast to the traditional approach, quantifies the absorptivity of a barrier in terms of a dimensionless parameter in the range 0 to 1. The generalized theorem gives two general analytic expressions for the continuum-limit propagator: an infinite sum of Gaussians and an infinite sum of plane waves. These expressions entail the known method-of-images and Laplace eigenfunction expansions as special cases and show how the presence of partially absorbing barriers can lead to phenomena such as line splitting and band gap formation in the plane wave wave-number spectrum.

Expansion of a quantum wave packet in a one-dimensional disordered potential in the presence of a uniform bias force

NASA Astrophysics Data System (ADS)

Crosnier de Bellaistre, C.; Trefzger, C.; Aspect, A.; Georges, A.; Sanchez-Palencia, L.

2018-01-01

We study numerically the expansion dynamics of an initially confined quantum wave packet in the presence of a disordered potential and a uniform bias force. For white-noise disorder, we find that the wave packet develops asymmetric algebraic tails for any ratio of the force to the disorder strength. The exponent of the algebraic tails decays smoothly with that ratio and no evidence of a critical behavior on the wave density profile is found. Algebraic localization features a series of critical values of the force-to-disorder strength where the m th position moment of the wave packet diverges. Below the critical value for the m th moment, we find fair agreement between the asymptotic long-time value of the m th moment and the predictions of diagrammatic calculations. Above it, we find that the m th moment grows algebraically in time. For correlated disorder, we find evidence of systematic delocalization, irrespective to the model of disorder. More precisely, we find a two-step dynamics, where both the center-of-mass position and the width of the wave packet show transient localization, similar to the white-noise case, at short time and delocalization at sufficiently long time. This correlation-induced delocalization is interpreted as due to the decrease of the effective de Broglie wavelength, which lowers the effective strength of the disorder in the presence of finite-range correlations.

A new multi-domain method based on an analytical control surface for linear and second-order mean drift wave loads on floating bodies

NASA Astrophysics Data System (ADS)

Liang, Hui; Chen, Xiaobo

2017-10-01

A novel multi-domain method based on an analytical control surface is proposed by combining the use of free-surface Green function and Rankine source function. A cylindrical control surface is introduced to subdivide the fluid domain into external and internal domains. Unlike the traditional domain decomposition strategy or multi-block method, the control surface here is not panelized, on which the velocity potential and normal velocity components are analytically expressed as a series of base functions composed of Laguerre function in vertical coordinate and Fourier series in the circumference. Free-surface Green function is applied in the external domain, and the boundary integral equation is constructed on the control surface in the sense of Galerkin collocation via integrating test functions orthogonal to base functions over the control surface. The external solution gives rise to the so-called Dirichlet-to-Neumann [DN2] and Neumann-to-Dirichlet [ND2] relations on the control surface. Irregular frequencies, which are only dependent on the radius of the control surface, are present in the external solution, and they are removed by extending the boundary integral equation to the interior free surface (circular disc) on which the null normal derivative of potential is imposed, and the dipole distribution is expressed as Fourier-Bessel expansion on the disc. In the internal domain, where the Rankine source function is adopted, new boundary integral equations are formulated. The point collocation is imposed over the body surface and free surface, while the collocation of the Galerkin type is applied on the control surface. The present method is valid in the computation of both linear and second-order mean drift wave loads. Furthermore, the second-order mean drift force based on the middle-field formulation can be calculated analytically by using the coefficients of the Fourier-Laguerre expansion.

Three-Component Soliton States in Spinor F =1 Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Bersano, T. M.; Gokhroo, V.; Khamehchi, M. A.; D'Ambroise, J.; Frantzeskakis, D. J.; Engels, P.; Kevrekidis, P. G.

2018-02-01

Dilute-gas Bose-Einstein condensates are an exceptionally versatile test bed for the investigation of novel solitonic structures. While matter-wave solitons in one- and two-component systems have been the focus of intense research efforts, an extension to three components has never been attempted in experiments. Here, we experimentally demonstrate the existence of robust dark-bright-bright (DBB) and dark-dark-bright solitons in a multicomponent F =1 condensate. We observe lifetimes on the order of hundreds of milliseconds for these structures. Our theoretical analysis, based on a multiscale expansion method, shows that small-amplitude solitons of these types obey universal long-short wave resonant interaction models, namely, Yajima-Oikawa systems. Our experimental and analytical findings are corroborated by direct numerical simulations highlighting the persistence of, e.g., the DBB soliton states, as well as their robust oscillations in the trap.

Three-Component Soliton States in Spinor F=1 Bose-Einstein Condensates.

PubMed

Bersano, T M; Gokhroo, V; Khamehchi, M A; D'Ambroise, J; Frantzeskakis, D J; Engels, P; Kevrekidis, P G

2018-02-09

Dilute-gas Bose-Einstein condensates are an exceptionally versatile test bed for the investigation of novel solitonic structures. While matter-wave solitons in one- and two-component systems have been the focus of intense research efforts, an extension to three components has never been attempted in experiments. Here, we experimentally demonstrate the existence of robust dark-bright-bright (DBB) and dark-dark-bright solitons in a multicomponent F=1 condensate. We observe lifetimes on the order of hundreds of milliseconds for these structures. Our theoretical analysis, based on a multiscale expansion method, shows that small-amplitude solitons of these types obey universal long-short wave resonant interaction models, namely, Yajima-Oikawa systems. Our experimental and analytical findings are corroborated by direct numerical simulations highlighting the persistence of, e.g., the DBB soliton states, as well as their robust oscillations in the trap.

Narrow sidebranch arrays for low frequency duct noise control.

PubMed

Tang, S K

2012-11-01

The present study investigates the sound transmission loss across a section of an infinitely long duct where one or more narrow sidebranch tubes are installed flushed with the duct wall. The finite-element method is used to compute the wave propagation characteristics, and a simplified theoretical analysis is carried out at the same time to explain the wave mechanism at frequencies of high sound reduction. Results show that the high sound transmission loss at a particular frequency is due to the concerted actions of three consecutive sidebranch tubes with the most upstream one in the resonant state. The expansion chamber effect of the setup also plays a role in enhancing sound attenuation at non-resonance frequencies. Broadband performance of the device can be greatly enhanced by appropriate arrangements of tube lengths and/or by coupling arrays on the two sides of the duct.

Communication: Quantum molecular dynamics simulation of liquid para-hydrogen by nuclear and electron wave packet approach

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

Hyeon-Deuk, Kim, E-mail: kim@kuchem.kyoto-u.ac.jp; Japan Science and Technology Agency, PRESTO, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012; Ando, Koji

2014-05-07

Liquid para-hydrogen (p-H{sub 2}) is a typical quantum liquid which exhibits strong nuclear quantum effects (NQEs) and thus anomalous static and dynamic properties. We propose a real-time simulation method of wave packet (WP) molecular dynamics (MD) based on non-empirical intra- and inter-molecular interactions of non-spherical hydrogen molecules, and apply it to condensed-phase p-H{sub 2}. The NQEs, such as WP delocalization and zero-point energy, are taken into account without perturbative expansion of prepared model potential functions but with explicit interactions between nuclear and electron WPs. The developed MD simulation for 100 ps with 1200 hydrogen molecules is realized at feasible computationalmore » cost, by which basic experimental properties of p-H{sub 2} liquid such as radial distribution functions, self-diffusion coefficients, and shear viscosities are all well reproduced.« less

Three-Dimensional Electromagnetic Scattering from Layered Media with Rough Interfaces for Subsurface Radar Remote Sensing

NASA Astrophysics Data System (ADS)

Duan, Xueyang

The objective of this dissertation is to develop forward scattering models for active microwave remote sensing of natural features represented by layered media with rough interfaces. In particular, soil profiles are considered, for which a model of electromagnetic scattering from multilayer rough surfaces with or without buried random media is constructed. Starting from a single rough surface, radar scattering is modeled using the stabilized extended boundary condition method (SEBCM). This method solves the long-standing instability issue of the classical EBCM, and gives three-dimensional full wave solutions over large ranges of surface roughnesses with higher computational efficiency than pure numerical solutions, e.g., method of moments (MoM). Based on this single surface solution, multilayer rough surface scattering is modeled using the scattering matrix approach and the model is used for a comprehensive sensitivity analysis of the total ground scattering as a function of layer separation, subsurface statistics, and sublayer dielectric properties. The buried inhomogeneities such as rocks and vegetation roots are considered for the first time in the forward scattering model. Radar scattering from buried random media is modeled by the aggregate transition matrix using either the recursive transition matrix approach for spherical or short-length cylindrical scatterers, or the generalized iterative extended boundary condition method we developed for long cylinders or root-like cylindrical clusters. These approaches take the field interactions among scatterers into account with high computational efficiency. The aggregate transition matrix is transformed to a scattering matrix for the full solution to the layered-medium problem. This step is based on the near-to-far field transformation of the numerical plane wave expansion of the spherical harmonics and the multipole expansion of plane waves. This transformation consolidates volume scattering from the buried random medium with the scattering from layered structure in general. Combined with scattering from multilayer rough surfaces, scattering contributions from subsurfaces and vegetation roots can be then simulated. Solutions of both the rough surface scattering and random media scattering are validated numerically, experimentally, or both. The experimental validations have been carried out using a laboratory-based transmit-receive system for scattering from random media and a new bistatic tower-mounted radar system for field-based surface scattering measurements.

Intensity dependence of non-linear kinetic behaviour of stimulated Raman scattering in fusion relevant plasmas

NASA Astrophysics Data System (ADS)

Mašek, Martin; Rohlena, Karel

2015-05-01

Influence of kinetic effects on 3-wave interaction was examined within the frame of stimulated Raman backward scattering (SRBS) in a rarefied laser corona. The plasma is supposed to be weakly collisional with a negligible density gradient. The model is centred on the physical situation of shock ignition at a large scale direct drive compression experiments. The modelling uses a 1D geometry in a Maxwell-Vlasov model. The method used is a truncated Fourier-Hermite expansion numerically stabilized by a model collisional term with a realistic value of the collision frequency. In parallel, besides the linear theory of SRBS, a coupled mode 3-wave equation system (laser driving wave, Raman back-scattered wave and the daughter forward scattered plasma wave) is solved to demonstrate the correspondence between the full kinetic model and 3-wave interaction with no electron kinetics involved to identify the differences between both the solutions arising due to the electron kinetic effects. We concentrated mainly on the Raman reflectivity, which is one of the important parameters controlling the efficiency of the shock ignition scheme. It was found that the onset of the kinetic effects has a distinct intensity threshold, above which the Raman reflectivity may go down due to the electron kinetics. In addition, we were trying to identify the most important features of the electron phase space behaviour, such as particle trapping in potential minima of the generated plasma wave and its consequences for the 3-wave interaction. The role of the trapped electrons seems to be crucial for a deformation of the plasma wave dispersion curve, as indicated in some earlier work.

Shock Tunnel Studies of Scramjet Phenomena

NASA Technical Reports Server (NTRS)

Stalker, R. J.

1996-01-01

Work focussed on a large number of preliminary studies of supersonic combustion in a simple combustion duct - thrust nozzle combination, investigating effects of Mach number, equivalence ratio, combustor divergence, fuel injecting angle and other parameters with an influence on the combustion process. This phase lasted for some three or four years, during which strongest emphasis was placed on responding to the request for preliminary experimental information on high enthalpy effects, to support the technology maturation activities of the NASP program. As the need for preliminary data became less urgent, it was possible to conduct more systematic studies of high enthalpy combustion phenomena, and to initiate other projects aimed at improving the facilities and instrumentation used for studying scramjet phenomena at high enthalpies. The combustion studies were particularly directed towards hypersonic combustion, and to the effects of injecting fuel along the combustion chamber wall. A substantial effort was directed towards a study of the effect of scale on the supersonic combustion process. The influence of wave phenomena (both compression waves and expansion waves) on the realization of thrust from a supersonic combustion process was also investigated. The effect of chemical kinetics was looked into, particularly as it affected the composition of the test flow provided by a ground facility. The effect of injection of the fuel through wall orifices was compared with injection from a strut spanning the stream, and the effect of heating the fuel prior to injection was investigated. Studies of fuel-air mixing by shock impingement were also done, as well as mass spectrometer surveys of a combustion wake. The use of hypersonic nozzles with an expansion tube was investigated. A new method was developed for measuring the forces acting of a model in less than one millisecond. Also included in this report are listings of published journal papers and conference presentations.

A novel slithering locomotion mechanism for a snake-like soft robot

NASA Astrophysics Data System (ADS)

Cao, Yunteng; Liu, Yilun; Chen, Youlong; Zhu, Liangliang; Yan, Yuan; Chen, Xi

2017-02-01

A novel mechanism for slithering locomotion of a snake-like soft robot is presented. A rectangular beam with an isotropic coefficient of friction of its contact surface with the flat ground can move forward or backward when actuated by a periodic traveling sinusoidal wave. The Poisson's ratio of the beam plays an important role in the slithering locomotion speed and direction, particularly when it is negative. A theoretical model is proposed to elucidate the slithering locomotion mechanism, which is analogous to the rolling of a wheel on ground. There are two key factors of slithering locomotion: a rotational velocity field and a corresponding local contact region between the beam and ground. During wriggling motion of the rectangular beam, a rotational velocity field is observed near the maximum curvature point of the beam. If the beam has a negative Poisson's ratio, the axial tension will cause a lateral expansion so that the contact region between the beam and ground is located at the outer edge of the maximum curvature (the largest lateral expansion point). The direction of the beam's velocity at this outer edge is usually opposite to the traveling wave direction, so the friction force propels the beam in the direction of the traveling wave. A similar scenario is found for the relatively large amplitude of wriggling motion when the beam's Poisson's ratio is positive. Finite element method (FEM) simulation was conducted to verify the slithering locomotion mechanism, and good agreement was found between the FEM simulation results and theoretical predictions. The insights obtained here present a simple, novel and straightforward mechanism for slithering locomotion and are helpful for future designs of snake-like soft robots.

Modeling boundary measurements of scattered light using the corrected diffusion approximation

PubMed Central

Lehtikangas, Ossi; Tarvainen, Tanja; Kim, Arnold D.

2012-01-01

We study the modeling and simulation of steady-state measurements of light scattered by a turbid medium taken at the boundary. In particular, we implement the recently introduced corrected diffusion approximation in two spatial dimensions to model these boundary measurements. This implementation uses expansions in plane wave solutions to compute boundary conditions and the additive boundary layer correction, and a finite element method to solve the diffusion equation. We show that this corrected diffusion approximation models boundary measurements substantially better than the standard diffusion approximation in comparison to numerical solutions of the radiative transport equation. PMID:22435102

Free-stream disturbance, continuous Eigenfunctions, boundary-layer instability and transition

NASA Technical Reports Server (NTRS)

Grosch, C. E.

1980-01-01

A rational foundation is presented for the application of the linear shear flows to transition prediction, and an explicit method is given for carrying out the necessary calculations. The expansions used are shown to be complete. Sample calculations show that a typical boundary layer is very sensitive to vorticity disturbances in the inner boundary layer, near the critical layer. Vorticity disturbances three or four boundary layer thicknesses above the boundary are nearly uncoupled from the boundary layer in that the amplitudes of the discrete Tollmien-Schlicting waves are an extremely small fraction of the amplitude of the disturbance.

Circularly polarized guided modes in dielectrically chiral photonic crystal fiber.

PubMed

Li, Junqing; Su, Qiyao; Cao, Yusheng

2010-08-15

The effect of dielectric chirality on the polarization states and mode indices of guided modes in photonic crystal fiber (PCF) is investigated by a modified plane-wave expansion (PWE) method. Using a solid-core chiral PCF as a numerical example, we show that circular polarization is the eigenstate of the fundamental mode. Mode index divergence between right-handed circularly polarized (RCP) and left-handed circularly polarized (LCP) states is demonstrated. Chirality's effect on mode index and circular birefringence (CB) in such a PCF is found to be similar to that in bulk chiral media.

Rarefaction waves in van der Waals fluids with an arbitrary number of degrees of freedom

DOE PAGES

Yuen, Albert; Barnard, John J.

2015-09-30

The isentropic expansion of an instantaneously and homogeneously heated foil is calculated using a 1D fluid model. The initial temperature and density are assumed to be in the vicinity of the critical temperature and solid density, respectively. The fluid is assumed to satisfy the van der Waals equation of state with an arbitrary number of degrees of freedom. Self-similar Riemann solutions are found. With a larger number of degrees of freedom f, depending on the initial dimensionless entropymore » $$˜\\atop{s_0}$$, a richer family of foil expansion behaviors have been found. We calculate the domain in parameter space where these behaviors occur. In total, eight types of rarefaction waves are found and described.« less

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.

Applicability of modified effective-range theory to positron-atom and positron-molecule scattering

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

Idziaszek, Zbigniew; Karwasz, Grzegorz; Instytut Fizyki, Uniwersytet Mikolaja Kopernika, 87-100 Torun

2006-06-15

We analyze low-energy scattering of positrons on Ar atoms and N{sub 2} molecules using the modified effective-range theory (MERT) developed by O'Malley, et al. [J. Math. Phys. 2, 491 (1961)]. We use the formulation of MERT based on exact solutions of the Schroedinger equation with polarization potential rather than low-energy expansions of phase shifts into momentum series. We show that MERT describes the experimental data well, provided that effective-range expansion is performed both for s- and p-wave scattering, which dominate in the considered regime of positron energies (0.4-2 eV). We estimate the values of the s-wave scattering length and themore » effective range for e{sup +}-Ar and e{sup +}-N{sub 2} collisions.« less

Liquid phase evaporation on the normal shock wave in moist air transonic flows in nozzles

NASA Astrophysics Data System (ADS)

Dykas, Sławomir; Szymański, Artur; Majkut, Mirosław

2017-06-01

This paper presents a numerical analysis of the atmospheric air transonic flow through de Laval nozzles. By nature, atmospheric air always contains a certain amount of water vapor. The calculations were made using a Laval nozzle with a high expansion rate and a convergent-divergent (CD) "half-nozzle", referred to as a transonic diffuser, with a much slower expansion rate. The calculations were performed using an in-house CFD code. The computational model made it possible to simulate the formation of the liquid phase due to spontaneous condensation of water vapor contained in moist air. The transonic flow calculations also take account of the presence of a normal shock wave in the nozzle supersonic part to analyze the effect of the liquid phase evaporation.

Shock tunnel studies of scramjet phenomena, supplement 5

NASA Technical Reports Server (NTRS)

Casey, R.; Stalker, R. J.; Brescianini, C. P.; Morgan, R. G.; Jacobs, P. A.; Wendt, M.; Ward, N. R.; Akman, N.; Allen, G. A.; Skinner, K.

1990-01-01

A series of reports are presented on SCRAMjet studies, shock tunnel studies, and expansion tube studies. The SCRAMjet studies include: (1) Investigation of a Supersonic Combustion Layer; (2) Wall Injected SCRAMjet Experiments; (3) Supersonic Combustion with Transvers, Circular, Wall Jets; (4) Dissociated Test Gas Effects on SCRAMjet Combustors; (5) Use of Silane as a Fuel Additive for Hypersonic Thrust Production, (6) Pressure-length Correlations in Supersonic Combustion; (7) Hot Hydrogen Injection Technique for Shock Tunnels; (8) Heat Release - Wave Interaction Phenomena in Hypersonic Flows; (9) A Study of the Wave Drag in Hypersonic SCRAMjets; (10) Parametric Study of Thrust Production in the Two Dimensional SCRAMjet; (11) The Design of a Mass Spectrometer for use in Hypersonic Impulse Facilities; and (12) Development of a Skin Friction Gauge for use in an Impulse Facility. The shock tunnel studies include: (1) Hypervelocity flow in Axisymmetric Nozzles; (2) Shock Tunnel Development; and (3) Real Gas Efects in Hypervelocity Flows over an Inclined Cone. The expansion tube studies include: (1) Investigation of Flow Characteristics in TQ Expansion Tube; and (2) Disturbances in the Driver Gas of a Shock Tube.

High Density Waves of the Bacterium Pseudomonas aeruginosa in Propagating Swarms Result in Efficient Colonization of Surfaces

PubMed Central

Du, Huijing; Xu, Zhiliang; Anyan, Morgen; Kim, Oleg; Leevy, W. Matthew; Shrout, Joshua D.; Alber, Mark

2012-01-01

This work describes a new, to our knowledge, strategy of efficient colonization and community development where bacteria substantially alter their physical environment. Many bacteria move in groups, in a mode described as swarming, to colonize surfaces and form biofilms to survive external stresses, including exposure to antibiotics. One such bacterium is Pseudomonas aeruginosa, which is an opportunistic pathogen responsible for both acute and persistent infections in susceptible individuals, as exampled by those for burn victims and people with cystic fibrosis. Pseudomonas aeruginosa often, but not always, forms branched tendril patterns during swarming; this phenomena occurs only when bacteria produce rhamnolipid, which is regulated by population-dependent signaling called quorum sensing. The experimental results of this work show that P. aeruginosa cells propagate as high density waves that move symmetrically as rings within swarms toward the extending tendrils. Biologically justified cell-based multiscale model simulations suggest a mechanism of wave propagation as well as a branched tendril formation at the edge of the population that depends upon competition between the changing viscosity of the bacterial liquid suspension and the liquid film boundary expansion caused by Marangoni forces. Therefore, P. aeruginosa efficiently colonizes surfaces by controlling the physical forces responsible for expansion of thin liquid film and by propagating toward the tendril tips. The model predictions of wave speed and swarm expansion rate as well as cell alignment in tendrils were confirmed experimentally. The study results suggest that P. aeruginosa responds to environmental cues on a very short timescale by actively exploiting local physical phenomena to develop communities and efficiently colonize new surfaces. PMID:22947877