Derivation of equations for scalar and fermion fields using properties of dispersion-codispersion operators

International Nuclear Information System (INIS)

Raoelina Andriambololona; Ranaivoson, R.T.R; Hanitriarivo, R.; Harison, V.

2014-01-01

We establish equations for scalar and fermion fields using results obtained from a study on a phase space representation of quantum theory that we have performed in a previous work. Our approaches are similar to the historical ones to obtain Klein-Gordon and Dirac equations but the main difference is that ours are based on the use of properties of operators called dispersion-codispersion operators. We begin with a brief recall about the dispersion-codispersion operators. Then, introducing a mass operator with its canonical conjugate coordinate and applying rules of quantization, based on the use of dispersion - codispersion operators , we deduce a second order differential operator relation from the relativistic expression relying energy, momentum and mass. Using Dirac matrices, we derive from this second order differential operator relation a first order one. The application of the second order differential operator relation on a scalar function gives the equation for the scalar field and the use of the first order differential operator relation leads to the equation for fermion field.

Pierce-type dispersion relation for an intense relativistic electron beam interacting with a slow-wave structure

International Nuclear Information System (INIS)

Chen, C.

1994-01-01

A Pierce-type dispersion relation is derived for the interaction of an intense relativistic electron beam with a cylindrical slow-wave structure of arbitrary corrugation depth. It is shown that near a resonance, the Pierce parameter can be expressed in terms of the vacuum dispersion function and the beam current. The dispersion relation is valid in both the low-current (Compton) regime and the high-current (Raman) regime. The dispersion characteristics of the interaction, such as the linear instability growth rate and bandwidth, are analyzed for both regimes

Scaling relations for soliton compression and dispersive-wave generation in tapered optical fibers

DEFF Research Database (Denmark)

Lægsgaard, Jesper

2018-01-01

In this paper, scaling relations for soliton compression in tapered optical fibers are derived and discussed. The relations allow simple and semi-accurate estimates of the compression point and output noise level, which is useful, for example, for tunable dispersive-wave generation with an agile ...

Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with initial stresses.

Science.gov (United States)

Guo, Xiao; Wei, Peijun

2016-03-01

The dispersion relations of elastic waves in a one-dimensional phononic crystal formed by periodically repeating of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are studied in this paper. The influences of initial stress on the dispersive relation are considered based on the incremental stress theory. First, the incremental stress theory of elastic solid is extended to the magneto-electro-elasto solid. The governing equations, constitutive equations, and boundary conditions of the incremental stresses in a magneto-electro-elasto solid are derived with consideration of the existence of initial stresses. Then, the transfer matrices of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are formulated, respectively. The total transfer matrix of a single cell in the phononic crystal is obtained by the multiplication of two transfer matrixes related with two adjacent slabs. Furthermore, the Bloch theorem is used to obtain the dispersive equations of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. The oblique propagation and the normal propagation situations are both considered. In the case of normal propagation of elastic waves, the analytical expressions of the dispersion equation are derived and compared with other literatures. The influences of initial stresses, including the normal initial stresses and shear initial stresses, on the dispersive relations are both discussed based on the numerical results. Copyright © 2015 Elsevier B.V. All rights reserved.

Neutron optical potential of 28Si derived from the dispersion relation

International Nuclear Information System (INIS)

Kitazawa, H.; Igarasi, S.; Katsuragi, D.; Harima, Y.

1992-01-01

Based upon the dispersion theory, an optical potential of 28 Si was determined at the neutron energies from the Fermi energy to 20 MeV. In particular, discussion was given on a characteristic behavior of the optical potential for low-energy neutrons. Moreover, the validity of the dispersion theory was investigated for neutron single-particle bound states in 29 Si. (orig.)

Multipole expansion of the retarded interatomic dispersion energy: derivation from quantum electrodynamics

NARCIS (Netherlands)

Michels, M.A.J.; Suttorp, L.G.

1972-01-01

The multipole expansion of the retarded dispersion energy of two atoms in nondegenerate ground states is derived. The result shows that multipoles of different order may give rise to dispersion energies varying in the same way for large interatomic separations.

Dispersion correction derived from first principles for density functional theory and Hartree-Fock theory.

Science.gov (United States)

Guidez, Emilie B; Gordon, Mark S

2015-03-12

The modeling of dispersion interactions in density functional theory (DFT) is commonly performed using an energy correction that involves empirically fitted parameters for all atom pairs of the system investigated. In this study, the first-principles-derived dispersion energy from the effective fragment potential (EFP) method is implemented for the density functional theory (DFT-D(EFP)) and Hartree-Fock (HF-D(EFP)) energies. Overall, DFT-D(EFP) performs similarly to the semiempirical DFT-D corrections for the test cases investigated in this work. HF-D(EFP) tends to underestimate binding energies and overestimate intermolecular equilibrium distances, relative to coupled cluster theory, most likely due to incomplete accounting for electron correlation. Overall, this first-principles dispersion correction yields results that are in good agreement with coupled-cluster calculations at a low computational cost.

Dispersion relation and Landau damping of waves in high-energy density plasmas

International Nuclear Information System (INIS)

Zhu Jun; Ji Peiyong

2012-01-01

We present a theoretical investigation on the propagation of electromagnetic waves and electron plasma waves in high energy density plasmas using the covariant Wigner function approach. Based on the covariant Wigner function and Dirac equation, a relativistic quantum kinetic model is established to describe the physical processes in high-energy density plasmas. With the zero-temperature Fermi–Dirac distribution, the dispersion relation and Landau damping of waves containing the relativistic quantum corrected terms are derived. The relativistic quantum corrections to the dispersion relation and Landau damping are analyzed by comparing our results with those obtained in classical and non-relativistic quantum plasmas. We provide a detailed discussion on the Landau damping obtained in classical plasmas, non-relativistic Fermi plasmas and relativistic Fermi plasmas. The contributions of the Bohm potential, the Fermi statistics pressure and relativistic effects to the dispersion relation and Landau damping of waves are quantitatively calculated with real plasma parameters. (paper)

Dispersion relation and self-collimation frequency of spoof surface plasmon using tight binding model

International Nuclear Information System (INIS)

Bhattacharya, Sayak; Shah, Kushal

2015-01-01

The analytical dispersion relation of spoof surface plasmon (SSP) is known only in the low-frequency limit and thus cannot be used to describe various practically important characteristics of SSP in the high-frequency limit (such as multimodal nature, anisotropic propagation, self-collimation). In this article, we consider a square lattice of holes made on a perfect electric conductor and derive a closed form expression of the SSP dispersion relation in the high-frequency limit using a tight binding model. Instead of using prior knowledge of the band diagram along the entire first Brillouin zone (BZ) edge, we analytically determine the hopping parameters by using the eigenfrequencies only at the three high-symmetry points of the square lattice. Using this dispersion relation, we derive an expression for the self-collimation frequency of SSP. We show that this analytical formulation is also applicable to dielectric photonic crystals and can be used to predict the frequencies corresponding to centimetre-scale supercollimation and second band self-collimation in these structures. Finally, we show that our analytical results are in agreement with the simulation results for both SSP and photonic crystals. (paper)

Analytical solution of dispersion relations for the nuclear optical model

Energy Technology Data Exchange (ETDEWEB)

VanderKam, J.M. [Center for Communications Research, Thanet Road, Princeton, NJ 08540 (United States); Weisel, G.J. [Triangle Universities Nuclear Laboratory, and Duke University, Box 90308, Durham, NC 27708-0308 (United States); Penn State Altoona, 3000 Ivyside Park, Altoona, PA 16601-3760 (United States); Tornow, W. [Triangle Universities Nuclear Laboratory, and Duke University, Box 90308, Durham, NC 27708-0308 (United States)

2000-12-01

Analytical solutions of dispersion integral relations, linking the real and imaginary parts of the nuclear optical model, have been derived. These are displayed for some widely used forms of the volume- and surface-absorptive nuclear potentials. When the analytical solutions are incorporated into the optical-model search code GENOA, replacing a numerical integration, the code runs three and a half to seven times faster, greatly aiding the analysis of direct-reaction, elastic scattering data. (author)

Observables and dispersion relations in κ-Minkowski spacetime

Science.gov (United States)

Aschieri, Paolo; Borowiec, Andrzej; Pachoł, Anna

2017-10-01

We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator. This general noncommutative geometry construction is then exemplified in the case of κ-Minkowski spacetime. The corresponding quantum Poincaré-Weyl Lie algebra of in-finitesimal translations, rotations and dilatations is obtained. The d'Alembert wave operator coincides with the quadratic Casimir of quantum translations and it is deformed as in Deformed Special Relativity theories. Also momenta (infinitesimal quantum translations) are deformed, and correspondingly the Einstein-Planck relation and the de Broglie one. The energy-momentum relations (dispersion relations) are consequently deduced. These results complement those of the phenomenological literature on the subject.

Dispersion relation of Raman FEL with helical Wiggler and ion channel

International Nuclear Information System (INIS)

Hosseinalinezhad, M.; Bahmani, M.; Hasanbeigi, A.; Salehkoutahi, M.

2012-01-01

In this paper the theory of free electron laser with helical wiggler and ion channel guiding has been presented. The equations of motion for an electron have been analyzed. A formula for the dispersion relation is then derived in the low-gain-per-pass limit. The results of a numerical study of the growth rate enhancement due to the ion channel are presented and discussed.

Getting super-excited with modified dispersion relations

Energy Technology Data Exchange (ETDEWEB)

Ashoorioon, Amjad; Casadio, Roberto [INFN—Sezione di Bologna, viale B. Pichat 6/2, I-40127 Bologna (Italy); Geshnizjani, Ghazal; Kim, Hyung J., E-mail: amjad.ashoorioon@bo.infn.it, E-mail: roberto.casadio@bo.infn.it, E-mail: ggeshniz@uwaterloo.ca, E-mail: h268kim@uwaterloo.ca [Department of Applied Mathematics, University of Waterloo Waterloo, Ontario, N2L 3G1 (Canada)

2017-09-01

We demonstrate that in some regions of parameter space, modified dispersion relations can lead to highly populated excited states, which we dub as 'super-excited' states. In order to prepare such super-excited states, we invoke dispersion relations that have negative slope in an interim sub-horizon phase at high momenta. This behaviour of quantum fluctuations can lead to large corrections relative to the Bunch-Davies power spectrum, which mimics highly excited initial conditions. We identify the Bogolyubov coefficients that can yield these power spectra. In the course of this computation, we also point out the shortcomings of the gluing method for evaluating the power spectrum and the Bogolyubov coefficients. As we discuss, there are other regions of parameter space, where the power spectrum does not get modified. Therefore, modified dispersion relations can also lead to so-called 'calm excited states'. We conclude by commenting on the possibility of obtaining these modified dispersion relations within the Effective Field Theory of Inflation.

Acoustic modes of the phonon dispersion relation of NbD/sub x/ alloys

International Nuclear Information System (INIS)

Rowe, J.M.; Vagelatos, N.; Rush, J.J.; Flotow, H.E.

1975-01-01

The acoustic modes of the phonon dispersion relation in Nb, NbD 0 . 15 , and NbD 0 . 45 were measured at 473 0 K for phonons with wave vectors along the [100], [110], and [111] axes by coherent neutron scattering. The observed neutron groups for both alloys were well defined, with little or no apparent broadening. Results are compared to similar data for Nb--Mo alloys and with previous lattice-dynamics results for PdD 0 . 63 . This comparison shows that despite differences in detail, the general features of the dispersion relations of NbD/sub x/ and Nb--Mo are similar after allowing for the differences in lattice parameters for the two alloys. The measured dispersion curves and derived phonon frequency distributions for the Nb--D alloys are quite different from the analogous results for PdD 0 . 63 in that the average acoustic phonon frequencies increase with increasing deuterium concentration and lattice parameter

Approximate Dispersion Relations for Waves on Arbitrary Shear Flows

Science.gov (United States)

Ellingsen, S. À.; Li, Y.

2017-12-01

An approximate dispersion relation is derived and presented for linear surface waves atop a shear current whose magnitude and direction can vary arbitrarily with depth. The approximation, derived to first order of deviation from potential flow, is shown to produce good approximations at all wavelengths for a wide range of naturally occuring shear flows as well as widely used model flows. The relation reduces in many cases to a 3-D generalization of the much used approximation by Skop (1987), developed further by Kirby and Chen (1989), but is shown to be more robust, succeeding in situations where the Kirby and Chen model fails. The two approximations incur the same numerical cost and difficulty. While the Kirby and Chen approximation is excellent for a wide range of currents, the exact criteria for its applicability have not been known. We explain the apparently serendipitous success of the latter and derive proper conditions of applicability for both approximate dispersion relations. Our new model has a greater range of applicability. A second order approximation is also derived. It greatly improves accuracy, which is shown to be important in difficult cases. It has an advantage over the corresponding second-order expression proposed by Kirby and Chen that its criterion of accuracy is explicitly known, which is not currently the case for the latter to our knowledge. Our second-order term is also arguably significantly simpler to implement, and more physically transparent, than its sibling due to Kirby and Chen.Plain Language SummaryIn order to answer key questions such as how the ocean surface affects the climate, erodes the coastline and transports nutrients, we must understand how waves move. This is not so easy when depth varying currents are present, as they often are in coastal waters. We have developed a modeling tool for accurately predicting wave properties in such situations, ready for use, for example, in the complex oceanographic computer models. Our

Dispersion bias, dispersion effect, and the aerosol-cloud conundrum

International Nuclear Information System (INIS)

Liu Yangang; Daum, Peter H; Guo Huan; Peng Yiran

2008-01-01

This work examines the influences of relative dispersion (the ratio of the standard deviation to the mean radius of the cloud droplet size distribution) on cloud albedo and cloud radiative forcing, derives an analytical formulation that accounts explicitly for the contribution from droplet concentration and relative dispersion, and presents a new approach to parameterize relative dispersion in climate models. It is shown that inadequate representation of relative dispersion in climate models leads to an overestimation of cloud albedo, resulting in a negative bias of global mean shortwave cloud radiative forcing that can be comparable to the warming caused by doubling CO 2 in magnitude, and that this dispersion bias is likely near its maximum for ambient clouds. Relative dispersion is empirically expressed as a function of the quotient between cloud liquid water content and droplet concentration (i.e., water per droplet), yielding an analytical formulation for the first aerosol indirect effect. Further analysis of the new expression reveals that the dispersion effect not only offsets the cooling from the Twomey effect, but is also proportional to the Twomey effect in magnitude. These results suggest that unrealistic representation of relative dispersion in cloud parameterization in general, and evaluation of aerosol indirect effects in particular, is at least in part responsible for several outstanding puzzles of the aerosol-cloud conundrum: for example, overestimation of cloud radiative cooling by climate models compared to satellite observations; large uncertainty and discrepancy in estimates of the aerosol indirect effect; and the lack of interhemispheric difference in cloud albedo.

Dispersion relations for 1D high-gain FELs

International Nuclear Information System (INIS)

Webb, S.D.; Litvinenko, V.N.

2010-01-01

We present analytical results for the one-dimensional dispersion relation for high-gain FELs. Using kappa-n distributions, we obtain analytical relations between the dispersion relations for various order kappa distributions. Since an exact solution exists for the kappa-1 (Lorentzian) distribution, this provides some insight into the number of modes on the way to the Gaussian distribution.

Phonon dispersion relations for caesium thiocyanate

International Nuclear Information System (INIS)

Irving, M.A.; Smith, T.F.; Elcombe, M.M.

1984-01-01

Room temperature phonon dispersion relations for frequencies below 2 THz have been measured, along the three orthorhombic axes and selected diagonal directions by neutron inelastic scattering, for caesium thiocyanate. These curves, which represent 13 acoustic modes and 11 optic modes of vibration, do not agree with the dispersion behaviour calculated from the rigid-ion model developed by Ti and Ra to describe their Raman scattering observations

The nonlinear effects on the characteristics of gravity wave packets: dispersion and polarization relations

Directory of Open Access Journals (Sweden)

S.-D. Zhang

2000-10-01

Full Text Available By analyzing the results of the numerical simulations of nonlinear propagation of three Gaussian gravity-wave packets in isothermal atmosphere individually, the nonlinear effects on the characteristics of gravity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean flows are accelerated and the vertical wavelengths show clear reduction due to nonlinearity. On the other hand, though nonlinear effects exist, the time variations of the frequencies of gravity wave packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the predictions of the polarization relation of gravity waves. This indicates that the dispersion and polarization relations based on the linear gravity wave theory can be applied extensively in the nonlinear region.Key words: Meteorology and atmospheric dynamics (middle atmosphere dynamics; waves and tides

Properties of aqueous dispersion of chitosan and chondroitin sulfate complex derived from aquatic organisms

Directory of Open Access Journals (Sweden)

Novikov V. Yu.

2016-09-01

Full Text Available Investigation of production of chondroitin sulfate, chitosan and polyelectrolyte complexes based on them received from the local marine raw materials is relevant from the point of view of developing a comprehensive waste-free technology for natural raw materials processing. The objects of study are chitosan derived from the shell of the Kamchatka crab Paralithodes camtschaticus and chondroitin sulfate derived from cartilage of salmon Salmon salar. To determine the surface tension of polyelectrolyte complex solutions and dispersions the Wilhelmy method has been used, the effective radius of particle dispersion has been calculated by light scattering, measurements of effective viscosity have been carried out under shear deformation. The conditions of formation, surface and rheological properties of the chitosan and chondroitin sulfate complex extracted from aquatic organisms in the Barents Sea have been studied. Obtaining conditions and molar ratios of these polyelectrolytes in which the aqueous dispersion of the complex remains stable for a long time have been established. It has been found that by addition of chondroitin sulfate solution to chitosan solution in molar ratios of 1 : 3; 1 : 6 the dispersion of the polyelectrolyte complex stable for 2 to 3 days has been formed. The polyelectrolyte complex dispersions behave as non-Newtonian pseudoplastic liquid. When the molar ratio of the mixed solution is 1 : 1 (regardless of the sequence of mixing suspension of the polyelectrolyte complex has been formed, then there is precipitation. Equilibrium surface tension of the aqueous dispersion of the polyelectrolyte complex is higher than that of solutions of chondroitin sulfate and chitosan. The effective radius of particles in the complex dispersion has been determined. The effective radius of the particles in the complex dispersion depends on the molar ratio of chondroitin sulfate : chitosan. A qualitative scheme of formation of polyelectrolyte

Planck-scale-modified dispersion relations in FRW spacetime

Science.gov (United States)

Rosati, Giacomo; Amelino-Camelia, Giovanni; Marcianò, Antonino; Matassa, Marco

2015-12-01

In recent years, Planck-scale modifications of the dispersion relation have been attracting increasing interest also from the viewpoint of possible applications in astrophysics and cosmology, where spacetime curvature cannot be neglected. Nonetheless, the interplay between Planck-scale effects and spacetime curvature is still poorly understood, particularly in cases where curvature is not constant. These challenges have been so far postponed by relying on an ansatz, first introduced by Jacob and Piran. We propose here a general strategy of analysis of the effects of modifications of the dispersion relation in Friedmann-Robertson-Walker spacetimes, applicable both to cases where the relativistic equivalence of frames is spoiled ("preferred-frame scenarios") and to the alternative possibility of "DSR-relativistic theories," theories that are fully relativistic but with relativistic laws deformed so that the modified dispersion relation is observer independent. We show that the Jacob-Piran ansatz implicitly assumes that spacetime translations are not affected by the Planck scale, while under rather general conditions, the same Planck-scale quantum-spacetime structures producing modifications of the dispersion relation also affect translations. Through the explicit analysis of one of the effects produced by modifications of the dispersion relation, an effect amounting to Planck-scale corrections to travel times, we show that our concerns are not merely conceptual but rather can have significant quantitative implications.

Dispersal patterns of red foxes relative to population density

Science.gov (United States)

Allen, Stephen H.; Sargeant, Alan B.

1993-01-01

Factors affecting red fox (Vulpes vulpes) dispersal patterns are poorly understood but warranted investigation because of the role of dispersal in rebuilding depleted populations and transmission of diseases. We examined dispersal patterns of red foxes in North Dakota based on recoveries of 363 of 854 foxes tagged as pups and relative to fox density. Foxes were recovered up to 8.6 years after tagging; 79% were trapped or shot. Straight-line distances between tagging and recovery locations ranged from 0 to 302 km. Mean recovery distances increased with age and were greater for males than females, but longest individual recovery distances were by females. Dispersal distances were not related to population density for males (P = 0.36) or females (P = 0.96). The proportion of males recovered that dispersed was inversely related to population density (r = -0.94; n = 5; P = 0.02), but not the proportion of females (r = -0.49; n = 5; P = 0.40). Dispersal directions were not uniform for either males (P = 0.003) or females (P = 0.006); littermates tended to disperse in similar directions (P = 0.09). A 4-lane interstate highway altered dispersal directions (P = 0.001). Dispersal is a strong innate behavior of red foxes (especially males) that results in many individuals of both sexes traveling far from natal areas. Because dispersal distance was unaffected by fox density, populations can be rebuilt and diseases transmitted long distances regardless of fox abundance.

Dispersion relation for pure dust Bernstein waves in a non-Maxwellian magnetized dusty plasma

International Nuclear Information System (INIS)

Deeba, F.; Ahmad, Zahoor; Murtaza, G.

2011-01-01

Pure dust Bernstein waves are investigated using non-Maxwellian kappa and (r,q) distribution functions in a collisionless, uniform magnetized dusty plasma. Dispersion relations for both the distributions are derived by considering waves whose frequency is of the order of dust cyclotron frequency, and dispersion curves are plotted. It is observed that the propagation band for dust Bernstein waves is rather narrow as compared with that of the electron Bernstein waves. However, the band width increases for higher harmonics, for both kappa and (r,q) distributions. Effect of dust charge on dispersion curves is also studied, and one observes that with increasing dust charge, the dispersion curves shift toward the lower frequencies. Increasing the dust to ion density ratio ((n d0 /n i0 )) causes the dispersion curve to shift toward the higher frequencies. It is also found that for large values of spectral index kappa (κ), the dispersion curves approach to the Maxwellian curves. The (r,q) distribution approaches the kappa distribution for r = 0, whereas for r > 0, the dispersion curves show deviation from the Maxwellian curves as expected. Relevance of this work can be found in astrophysical plasmas, where non-Maxwellian velocity distributions as well as dust particles are commonly observed.

Dispersion relation for pure dust Bernstein waves in a non-Maxwellian magnetized dusty plasma

Energy Technology Data Exchange (ETDEWEB)

Deeba, F. [National Tokamak Fusion Program, PAEC, P.O. Box 3329, Islamabad 44000 (Pakistan); Department of Physics, G.C. University, Lahore 54000 (Pakistan); Ahmad, Zahoor [National Tokamak Fusion Program, PAEC, P.O. Box 3329, Islamabad 44000 (Pakistan); Murtaza, G. [Salam Chair in Physics, G.C. University, Lahore 54000 (Pakistan)

2011-07-15

Pure dust Bernstein waves are investigated using non-Maxwellian kappa and (r,q) distribution functions in a collisionless, uniform magnetized dusty plasma. Dispersion relations for both the distributions are derived by considering waves whose frequency is of the order of dust cyclotron frequency, and dispersion curves are plotted. It is observed that the propagation band for dust Bernstein waves is rather narrow as compared with that of the electron Bernstein waves. However, the band width increases for higher harmonics, for both kappa and (r,q) distributions. Effect of dust charge on dispersion curves is also studied, and one observes that with increasing dust charge, the dispersion curves shift toward the lower frequencies. Increasing the dust to ion density ratio ((n{sub d0}/n{sub i0})) causes the dispersion curve to shift toward the higher frequencies. It is also found that for large values of spectral index kappa ({kappa}), the dispersion curves approach to the Maxwellian curves. The (r,q) distribution approaches the kappa distribution for r = 0, whereas for r > 0, the dispersion curves show deviation from the Maxwellian curves as expected. Relevance of this work can be found in astrophysical plasmas, where non-Maxwellian velocity distributions as well as dust particles are commonly observed.

Dispersion relation of linearly polarized strong electromagnetic waves

Energy Technology Data Exchange (ETDEWEB)

Ferrari, A; Massaglia, S [Consiglio Nazionale delle Ricerche, Turin (Italy). Lab. di Cosmo-Geofisica; Dobrowolny, M [Comitato Nazionale per l' Energia Nucleaire, Frascati (Italy). Lab. Plasma Spazio

1975-12-15

A numerical study is presented of the dispersion relation of linearly polarized strong electromagnetic waves in a cold electron plasma. The nonlinear effects introduced by the relativistic motion of electrons are: (1) the dispersion relation depends explicitly on the field strength ..cap alpha..=eE/sub 0//mc..omega../sub 0/, and (2) the propagation of modes with frequencies below the formal electron plasma frequency is allowed.

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

Energy Technology Data Exchange (ETDEWEB)

Colangelo, Gilberto [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern (Switzerland); Hoferichter, Martin [Institute for Nuclear Theory, University of Washington, Seattle, WA 98195-1550 (United States); Kavli Institute for Theoretical Physics, University of California,Santa Barbara, CA 93106 (United States); Procura, Massimiliano [Theoretical Physics Department, CERN, Geneva (Switzerland); Stoffer, Peter [Helmholtz-Institut für Strahlen- und Kernphysik (Theory)and Bethe Center for Theoretical Physics, University of Bonn, 53115 Bonn (Germany); Department of Physics, University of California at San Diego, La Jolla, CA 92093 (United States)

2017-04-27

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

Dispersion relations in real and virtual Compton scattering

International Nuclear Information System (INIS)

Drechsel, D.; Pasquini, B.; Vanderhaeghen, M.

2003-01-01

A unified presentation is given on the use of dispersion relations in the real and virtual Compton scattering processes off the nucleon. The way in which dispersion relations for Compton scattering amplitudes establish connections between low energy nucleon structure quantities, such as polarizabilities or anomalous magnetic moments, and the nucleon excitation spectrum is reviewed. We discuss various sum rules for forward real and virtual Compton scattering, such as the Gerasimov-Drell-Hearn sum rule and its generalizations, the Burkhardt-Cottingham sum rule, as well as sum rules for forward nucleon polarizabilities, and review their experimental status. Subsequently, we address the general case of real Compton scattering (RCS). Various types of dispersion relations for RCS are presented as tools for extracting nucleon polarizabilities from the RCS data. The information on nucleon polarizabilities gained in this way is reviewed and the nucleon structure information encoded in these quantities is discussed. The dispersion relation formalism is then extended to virtual Compton scattering (VCS). The information on generalized nucleon polarizabilities extracted from recent VCS experiments is described, along with its interpretation in nucleon structure models. As a summary, the physics content of the existing data is discussed and some perspectives for future theoretical and experimental activities in this field are presented

Low-energy theorems for Compton scattering up to order e/sup 4/. [Scattering amplitudes dispersion relations

Energy Technology Data Exchange (ETDEWEB)

Pippig, G

1975-01-01

Taking the Compton scattering of pions and deuterons as an example it is shown that low-energy theorems which are valid for the order e/sup 2/ are also valid for the next higher order of electromagnetic interactions. The imaginary component of the scattering amplitude was exactly calculated for the energy of incident photons in the order e/sup 4/ up to the desired one, whereas the real component was obtained from dispersion relations. It is proved that the results derived from the dispersion theory of strong interactions are equivalent to those obtained from quantum electrodynamics for spin 0 and spin 1, respectively.

Dispersion-induced nonlinearities in semiconductors

DEFF Research Database (Denmark)

Mørk, Jesper; Mecozzi, A.

2002-01-01

A dispersive and saturable medium is shown, under very general conditions, to possess ultrafast dynamic behaviour due to non-adiabatic polarisation dynamics. Simple analytical expressions relating the effect to the refractive index dispersion of a semiconductor ire derived and the magnitude...... of the equivalent Kerr coefficient is shown to be in qualitative agreement with measurements on active semiconductor waveguides....

Trajectory and Relative Dispersion Case Studies and Statistics from the Green River Mesoscale Deformation, Dispersion, and Dissipation Program

Science.gov (United States)

Niemann, Brand Lee

A major field program to study beta-mesoscale transport and dispersion over complex mountainous terrain was conducted during 1969 with the cooperation of three government agencies at the White Sands Missile Range in central Utah. The purpose of the program was to measure simultaneously on a large number of days the synoptic and mesoscale wind fields, the relative dispersion between pairs of particle trajectories and the rate of small scale turbulence dissipation. The field program included measurements during more than 60 days in the months of March, June, and November. The large quantity of data generated from this program has been processed and analyzed to provide case studies and statistics to evaluate and refine Lagrangian variable trajectory models. The case studies selected to illustrate the complexities of mesoscale transport and dispersion over complex terrain include those with terrain blocking, lee waves, and stagnation, as well as those with large vertical wind shears and horizontal wind field deformation. The statistics of relative particle dispersion were computed and compared to the classical theories of Richardson and Batchelor and the more recent theories of Lin and Kao among others. The relative particle dispersion was generally found to increase with travel time in the alongwind and crosswind directions, but in a more oscillatory than sustained or even accelerated manner as predicted by most theories, unless substantial wind shears or finite vertical separations between particles were present. The relative particle dispersion in the vertical was generally found to be small and bounded even when substantial vertical motions due to lee waves were present because of the limiting effect of stable temperature stratification. The data show that velocity shears have a more significant effect than turbulence on relative particle dispersion and that sufficient turbulence may not always be present above the planetary boundary layer for "wind direction shear

Stabilization of silica nanoparticles dispersions by surface modification with silicon derivative of thiacalix[4]arene

Energy Technology Data Exchange (ETDEWEB)

Gorbachuk, Vladimir V.; Ziatdinova, Ramilia V. [Kazan Federal University, A.M. Butlerov’ Chemical Institute (Russian Federation); Evtugyn, Vladimir G. [Kazan Federal University, Interdisciplinary Centre for Analytical Microscopy (Russian Federation); Stoikov, Ivan I., E-mail: ivan.stoikov@mail.ru [Kazan Federal University, A.M. Butlerov’ Chemical Institute (Russian Federation)

2015-03-15

For the first time, silica nanopowder functionalized with thiacalixarene derivatives was synthesized by ultrasonication of nanoparticles (diameter 23.7 ± 2.4 nm) with organosilicon derivative of thiacalixarene in glacial acetic acid. The protocol resulted in the formation of colloidal solution of low-disperse (polydispersity index of 0.11) submicron-sized (diameter 192.5 nm) clusters of nanoparticles according to the dynamic light scattering data. As defined by scanning electron microscopy (SEM), mean diameter of thiacalixarene-functionalized nanoparticles is equal to 25.5 ± 2.5 nm and the shape is close to spherical. SEM images confirm low aggregation of thiacalixarene-modified nanoparticle compared to initial silica nanopowder (mean diameter of aggregates 330 and 429 nm, correspondingly). According to the thermogravimetry/differential scanning calorimetry and elemental analysis of the nanoparticles obtained, 5 % of the powder mass was related to thiacalixarene units. The effect of thiacalixarene functionalization of silica nanoparticles on linear polydimethylsiloxane (PDMS)—silica dispersions was modeled to achieve high resistance toward liquid media required for similar sol–gel prepared PDMS-based materials applied for solid-phase microextraction. In such a manner, the influence of thiacalixarene-modified nanofiller on thermal stability and resistance against polar organic solvents was estimated. Similarity of decomposition temperature of both thiacalixarene-functionalized nanoparticles and non-functionalized silica nanoparticles was found. Swelling/solubility behavior observed was related to partial dissolution of PDMS/silica (10 % mixture) in alcohols. Thiacalixarene-functionalized silica particles exerted significantly higher resistance of PDMS/silica composites toward alcohol solvents.

Stabilization of silica nanoparticles dispersions by surface modification with silicon derivative of thiacalix[4]arene

International Nuclear Information System (INIS)

Gorbachuk, Vladimir V.; Ziatdinova, Ramilia V.; Evtugyn, Vladimir G.; Stoikov, Ivan I.

2015-01-01

For the first time, silica nanopowder functionalized with thiacalixarene derivatives was synthesized by ultrasonication of nanoparticles (diameter 23.7 ± 2.4 nm) with organosilicon derivative of thiacalixarene in glacial acetic acid. The protocol resulted in the formation of colloidal solution of low-disperse (polydispersity index of 0.11) submicron-sized (diameter 192.5 nm) clusters of nanoparticles according to the dynamic light scattering data. As defined by scanning electron microscopy (SEM), mean diameter of thiacalixarene-functionalized nanoparticles is equal to 25.5 ± 2.5 nm and the shape is close to spherical. SEM images confirm low aggregation of thiacalixarene-modified nanoparticle compared to initial silica nanopowder (mean diameter of aggregates 330 and 429 nm, correspondingly). According to the thermogravimetry/differential scanning calorimetry and elemental analysis of the nanoparticles obtained, 5 % of the powder mass was related to thiacalixarene units. The effect of thiacalixarene functionalization of silica nanoparticles on linear polydimethylsiloxane (PDMS)—silica dispersions was modeled to achieve high resistance toward liquid media required for similar sol–gel prepared PDMS-based materials applied for solid-phase microextraction. In such a manner, the influence of thiacalixarene-modified nanofiller on thermal stability and resistance against polar organic solvents was estimated. Similarity of decomposition temperature of both thiacalixarene-functionalized nanoparticles and non-functionalized silica nanoparticles was found. Swelling/solubility behavior observed was related to partial dissolution of PDMS/silica (10 % mixture) in alcohols. Thiacalixarene-functionalized silica particles exerted significantly higher resistance of PDMS/silica composites toward alcohol solvents

Chiral symmetry and dispersion relations: from $\\pi \\pi$ scattering to hadronic light-by-light.

CERN Multimedia

CERN. Geneva

2018-01-01

Chiral symmetry provides strong constraints on hadronic matrix elements at low energy, which are most efficiently derived with chiral perturbation theory. As an effective quantum field theory the latter also accounts for rescattering or unitarity effects, albeit only perturbatively, via the loop expansion. In cases where rescattering effects are important it becomes necessary to go beyond the perturbative expansion, e.g. by using dispersion relations. A matching between the chiral and the dispersive representation provides in several cases results of high precision. I will discuss this approach with the help of a few examples, like $\\pi \\pi$ scattering (which has been tested successfully by CERN experiments like NA48/2 and DIRAC), $\\eta \\to 3 \\pi$ and the hadronic light-by-light contribution to $(g-2)_\\mu$. For the latter quantity the implementation of the dispersive approach has opened up the way to a model-independent calculation and the concrete possibility to significantly reduce the theoretical uncertain...

Relativistic energy-dispersion relations of 2D rectangular lattices

Science.gov (United States)

Ata, Engin; Demirhan, Doğan; Büyükkılıç, Fevzi

2017-04-01

An exactly solvable relativistic approach based on inseparable periodic well potentials is developed to obtain energy-dispersion relations of spin states of a single-electron in two-dimensional (2D) rectangular lattices. Commutation of axes transfer matrices is exploited to find energy dependencies of the wave vector components. From the trace of the lattice transfer matrix, energy-dispersion relations of conductance and valence states are obtained in transcendental form. Graphical solutions of relativistic and nonrelativistic transcendental energy-dispersion relations are plotted to compare how lattice parameters V0, core and interstitial size of the rectangular lattice affects to the energy-band structures in a situation core and interstitial diagonals are of equal slope.

Factoring the dispersion relation in the presence of Lorentz violation

International Nuclear Information System (INIS)

Colladay, Don; McDonald, Patrick; Mullins, David

2010-01-01

We produce an explicit formula for the dispersion relation for the Dirac equation in the standard model extension in the presence of Lorentz violation. Our expression is obtained using novel techniques which exploit the algebra of quaternions. The dispersion relation is found to conveniently factor in two special cases that each involve a mutually exclusive set of nonvanishing Lorentz-violating parameters. This suggests that a useful approach to studies of Lorentz-violating models is to split the parameter space into two separate pieces, each of which yields a simple, tractable dispersion relation that can be used for analysis.

Chaotic Lagrangian models for turbulent relative dispersion.

Science.gov (United States)

Lacorata, Guglielmo; Vulpiani, Angelo

2017-04-01

A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model are accurately analyzed by computing the finite-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as Lagrangian predictability studies.

Dispersion relations for η '→ η π π

Science.gov (United States)

Isken, Tobias; Kubis, Bastian; Schneider, Sebastian P.; Stoffer, Peter

2017-07-01

We present a dispersive analysis of the decay amplitude for η '→ η π π that is based on the fundamental principles of analyticity and unitarity. In this framework, final-state interactions are fully taken into account. Our dispersive representation relies only on input for the {π π } and {π }η scattering phase shifts. Isospin symmetry allows us to describe both the charged and neutral decay channel in terms of the same function. The dispersion relation contains subtraction constants that cannot be fixed by unitarity. We determine these parameters by a fit to Dalitz-plot data from the VES and BES-III experiments. We study the prediction of a low-energy theorem and compare the dispersive fit to variants of chiral perturbation theory.

Dispersal from deep ocean sources: physical and related scientific processes

International Nuclear Information System (INIS)

Robinson, A.R.; Kupferman, S.L.

1985-02-01

This report presents the results of the workshop ''Dispersal from Deep Ocean Sources: Physical and Related Scientific Processes,'' together with subsequent developments and syntheses of the material discussed there. The project was undertaken to develop usable predictive descriptions of dispersal from deep oceanic sources. Relatively simple theoretical models embodying modern ocean physics were applied, and observational and experimental data bases were exploited. All known physical processes relevant to the dispersal of passive, conservative tracers were discussed, and contact points for inclusion of nonconservative processes (biological and chemical) were identified. Numerical estimates of the amplitude, space, and time scales of dispersion were made for various mechanisms that control the evolution of the dispersal as the material spreads from a bottom point source to small-, meso-, and world-ocean scales. Recommendations for additional work are given. The volume is presented as a handbook of dispersion processes. It is intended to be updated as new results become available

A linearized dispersion relation for orthorhombic pseudo-acoustic modeling

KAUST Repository

Song, Xiaolei; Alkhalifah, Tariq Ali

2012-01-01

Wavefield extrapolation in acoustic orthorhombic anisotropic media suffers from wave-mode coupling and stability limitations in the parameter range. We introduce a linearized form of the dispersion relation for acoustic orthorhombic media to model acoustic wavefields. We apply the lowrank approximation approach to handle the corresponding space-wavenumber mixed-domain operator. Numerical experiments show that the proposed wavefield extrapolator is accurate and practically free of dispersions. Further, there is no coupling of qSv and qP waves, because we use the analytical dispersion relation. No constraints on Thomsen's parameters are required for stability. The linearized expression may provide useful application for parameter estimation in orthorhombic media.

A linearized dispersion relation for orthorhombic pseudo-acoustic modeling

KAUST Repository

Song, Xiaolei

2012-11-04

Wavefield extrapolation in acoustic orthorhombic anisotropic media suffers from wave-mode coupling and stability limitations in the parameter range. We introduce a linearized form of the dispersion relation for acoustic orthorhombic media to model acoustic wavefields. We apply the lowrank approximation approach to handle the corresponding space-wavenumber mixed-domain operator. Numerical experiments show that the proposed wavefield extrapolator is accurate and practically free of dispersions. Further, there is no coupling of qSv and qP waves, because we use the analytical dispersion relation. No constraints on Thomsen\\'s parameters are required for stability. The linearized expression may provide useful application for parameter estimation in orthorhombic media.

On dispersive derivation of triangle anomaly

International Nuclear Information System (INIS)

Horejsi, J.

1985-01-01

A straightforward generalization of the results of some previous treatments, in which the Adler-Bell-Jachiw triangle anomaly has been recovered with the help of dispersion relation is presented. The absorptive part of the VVA triangle diagram with the external momenta k, p at vector vertices such as K 2 =p 2 =0 is considered. An integral of the imaginary part of the relevant invariant amplitude is calculated explicitly. It is shown that the anomalous contribution to the axial Ward identity is reproduced. This also enables one to demonstrate the delta-like behaviour of sich an imaginary part in k 2 → 0, m → 0 limit

Laplace-Fourier-domain dispersion analysis of an average derivative optimal scheme for scalar-wave equation

Science.gov (United States)

Chen, Jing-Bo

2014-06-01

By using low-frequency components of the damped wavefield, Laplace-Fourier-domain full waveform inversion (FWI) can recover a long-wavelength velocity model from the original undamped seismic data lacking low-frequency information. Laplace-Fourier-domain modelling is an important foundation of Laplace-Fourier-domain FWI. Based on the numerical phase velocity and the numerical attenuation propagation velocity, a method for performing Laplace-Fourier-domain numerical dispersion analysis is developed in this paper. This method is applied to an average-derivative optimal scheme. The results show that within the relative error of 1 per cent, the Laplace-Fourier-domain average-derivative optimal scheme requires seven gridpoints per smallest wavelength and smallest pseudo-wavelength for both equal and unequal directional sampling intervals. In contrast, the classical five-point scheme requires 23 gridpoints per smallest wavelength and smallest pseudo-wavelength to achieve the same accuracy. Numerical experiments demonstrate the theoretical analysis.

Compact dispersion relations for parametric instabilities of electromagnetic waves in magnetized plasmas

International Nuclear Information System (INIS)

Cohen, B.I.

1987-01-01

The existence of compact dispersion relations for parametric instabilities of coherent electromagnetic waves in magnetized plasmas is addressed here. In general, comprehensive dispersion relations for parametric instabilities in unmagnetized plasmas become more complicated in the presence of an applied time-independent magnetic field. This is demonstrated with a fluid perturbation theory. A compact dispersion relation for parametric instabilities in unmagnetized plasma is heuristically extended here to the case of a magnetized plasma. This dispersion relation gives the correct results in a variety of circumstances of interest in considering electron cyclotron heating applications

THE STELLAR VELOCITY DISPERSION OF A COMPACT MASSIVE GALAXY AT z = 1.80 USING X-SHOOTER: CONFIRMATION OF THE EVOLUTION IN THE MASS-SIZE AND MASS-DISPERSION RELATIONS ,

International Nuclear Information System (INIS)

Van de Sande, Jesse; Franx, Marijn; Labbe, Ivo; Kriek, Mariska; Van Dokkum, Pieter G.; Bezanson, Rachel; Whitaker, Katherine E.; Brammer, Gabriel; Groot, Paul J.; Kaper, Lex

2011-01-01

Recent photometric studies have shown that early-type galaxies at fixed stellar mass were smaller and denser at earlier times. In this Letter, we assess that finding by deriving the dynamical mass of such a compact quiescent galaxy at z = 1.8. We have obtained a high-quality spectrum with full UV-NIR wavelength coverage of galaxy NMBS-C7447 using X-Shooter on the Very Large Telescope. We determined a velocity dispersion of 294 ± 51 km s -1 . Given this velocity dispersion and the effective radius of 1.64 ± 0.15 kpc (as determined from Hubble Space Telescope Wide Field Camera 3 F160W observations) we derive a dynamical mass of (1.7 ± 0.5) x 10 11 M sun . Comparison of the full spectrum with stellar population synthesis models indicates that NMBS-C774 has a relatively young stellar population (0.40 Gyr) with little or no star formation and a stellar mass of M * ∼ 1.5 x 10 11 M sun . The dynamical and photometric stellar masses are in good agreement. Thus, our study supports the conclusion that the mass densities of quiescent galaxies were indeed higher at earlier times, and this earlier result is not caused by systematic measurement errors. By combining available spectroscopic measurements at different redshifts, we find that the velocity dispersion at fixed dynamical mass was a factor of ∼1.8 higher at z = 1.8 compared with z = 0. Finally, we show that the apparent discrepancies between the few available velocity dispersion measurements at z > 1.5 are consistent with the intrinsic scatter of the mass-size relation.

Wave dispersion relations in two-dimensional Yukawa systems

International Nuclear Information System (INIS)

Liu Yanhong; Liu Bin; Chen Yanping; Yang Size; Wang Long; Wang Xiaogang

2003-01-01

Collective modes in a two-dimensional Yukawa system are investigated by molecular dynamics simulation in a wide range of coupling parameter Γ and screening strength κ. The dispersion relations and sound speeds of the transverse and longitudinal waves obtained for hexagonal lattice are in agreement with the theoretical results. The negative dispersion of the longitudinal wave is demonstrated. Frequency gaps are found on the dispersion curves of the transverse wave due to scattering of the waves on lattice defects for proper values of Γ. The common frequency of transverse and longitudinal waves drops dramatically with the increasing screening strength κ

Quantum-optical input-output relations for dispersive and lossy multilayer dielectric plates

International Nuclear Information System (INIS)

Gruner, T.; Welsch, D.

1996-01-01

Using the Green-function approach to the problem of quantization of the phenomenological Maxwell theory, the propagation of quantized radiation through dispersive and absorptive multilayer dielectric plates is studied. Input-output relations are derived, with special emphasis on the determination of the quantum noise generators associated with the absorption of radiation inside the dielectric matter. The input-output relations are used to express arbitrary correlation functions of the outgoing field in terms of correlation functions of the incoming field and those of the noise generators. To illustrate the theory, photons at dielectric tunneling barriers are considered. It is shown that inclusion in the calculations of losses in the photonic band gaps may substantially change the barrier traversal times. copyright 1996 The American Physical Society

Dispersion relations in three-particle systems

International Nuclear Information System (INIS)

Grach, I.L.; Harodetskij, I.M.; Shmatikov, M.Zh.

1979-01-01

Positions of all dynamical singularities of the triangular nonrelativistic diagram are calculated including the form factors. The jumps of the amplitude are written in an analitical form. The dispersion method predictions for bound states in the three-particle system are compared with the results of the Amado exactly solvable model. It is shown that the one-channel N/D method is equivalent to the pole approximation in the Amado model, and that the three-particle s channel unitarity should be taken into account calculating (in the dispersion method) the ground and excited states of the three-particle system. The relation of the three-particle unitary contribution to the Thomas theorem and Efimov effect is briefly discussed

Derivation of simplified basic equations of gas-liquid two-phase dispersed flow based on two-fluid model

International Nuclear Information System (INIS)

Kataoka, Isao; Tomiyama, Akio

2004-01-01

The simplified and physically reasonable basic equations for the gas-liquid dispersed flow were developed based on some appropriate assumptions and the treatment of dispersed phase as isothermal rigid particles. Based on the local instant formulation of mass, momentum and energy conservation of the dispersed flow, time-averaged equations were obtained assuming that physical quantities in the dispersed phase are uniform. These assumptions are approximately valid when phase change rate and/or chemical reaction rate are not so large at gas-liquid interface and there is no heat generation in within the dispersed phase. Detailed discussions were made on the characteristics of obtained basic equations and physical meanings of terms consisting the basic equations. It is shown that, in the derived averaged momentum equation, the terms of pressure gradient and viscous momentum diffusion do not appear and, in the energy equation, the term of molecular thermal diffusion heat flux does not appear. These characteristics of the derived equations were shown to be very consistent concerning the physical interpretation of the gas-liquid dispersed flow. Furthermore, the obtained basic equations are consistent with experiments for the dispersed flow where most of averaged physical quantities are obtained assuming that the distributions of those are uniform within the dispersed phase. Investigation was made on the problem whether the obtained basic equations are well-posed or ill-posed for the initial value problem. The eigenvalues of the simplified mass and momentum equations are calculated for basic equations obtained here and previous two-fluid basic equations with one pressure model. Well-posedness and ill-posedness are judged whether the eigenvalues are real or imaginary. The result indicated the newly developed basic equations always constitute the well-posed initial value problem while the previous two-fluid basic equations based on one pressure model constitutes ill

Dispersion relation of electromagnetic waves in one-dimensional plasma photonic crystals

International Nuclear Information System (INIS)

Hojo, Hitoshi; Mase, Atsushi

2004-01-01

The dispersion relation of electromagnetic waves in one-dimensional plasma photonic crystals is studied. The plasma photonic crystal is a periodic array composed of alternating thin plasma and dielectric material. The dispersion relation is obtained by solving a Maxwell wave equation using a method analogous to Kronig-Penny's problem in quantum mechanics, and it is found that the frequency gap and cut-off appear in the dispersion relation. The frequency gap is shown to become larger with the increase of the plasma density as well as plasma width. (author)

General characteristics of relative dispersion in the ocean

Science.gov (United States)

Corrado, Raffaele; Lacorata, Guglielmo; Palatella, Luigi; Santoleri, Rosalia; Zambianchi, Enrico

2017-04-01

The multi-scale and nonlinear nature of the ocean dynamics dramatically affects the spreading of matter, like pollutants, marine litter, etc., of physical and chemical seawater properties, and the biological connectivity inside and among different basins. Based on the Finite-Scale Lyapunov Exponent analysis of the largest available near-surface Lagrangian data set from the Global Drifter Program, our results show that, despite the large variety of flow features, relative dispersion can ultimately be described by a few parameters common to all ocean sub-basins, at least in terms of order of magnitude. This provides valuable information to undertake Lagrangian dispersion studies by means of models and/or of observational data. Moreover, our results show that the relative dispersion rates measured at submesoscale are significantly higher than for large-scale dynamics. Auxiliary analysis of high resolution GPS-tracked drifter hourly data as well as of the drogued/undrogued status of the buoys is provided in support of our conclusions. A possible application of our study, concerning reverse drifter motion and error growth analysis, is proposed relatively to the case of the missing Malaysia Airlines MH370 aircraft.

Long wave dispersion relations for surface waves in a magnetically structured atmosphere

International Nuclear Information System (INIS)

Rae, I.C.; Roberts, B.

1983-01-01

A means of obtaining approximate dispersion relations for long wavelength magnetoacoustic surface waves propagating in a magnetically structured atmosphere is presented. A general dispersion relation applying to a wide range of magnetic profiles is obtained, and illustrated for the special cases of a single interface and a magnetic slab. In the slab geometry, for example, the dispersion relation contains both the even (sausage) and odd (kink) modes in one formalism

The use of dispersion relations to construct unified nucleon optical potentials

International Nuclear Information System (INIS)

Hodgson, P.E.

1991-01-01

The dispersion relations provide a simple and accurate way of parametrizing the optical potential for a particular nucleus over a range of energies. A method is proposed for obtaining a global nucleon optical potential incorporating the dispersion relations. (author). 9 refs, 3 figs

Covariant kinetic dispersion theory of linear transverse waves parallel propagating in magnetized plasmas with thermal anisotropy

International Nuclear Information System (INIS)

Lazar, M.; Schlickeiser, R.

2006-01-01

The properties of transverse waves parallel propagating in magnetized plasmas with arbitrary composition and thermally anisotropic, are investigated on the basis of relativistic Vlasov-Maxwell equations. The transverse dispersion relations for plasmas with arbitrary distribution functions are derived. These dispersion relations describe the linear response of the system to the initial perturbations and thus define all existing linear (transverse) plasma modes in the system. By analytic continuation the dispersion relations in the whole complex frequency plane are constructed. Further analysis is restricted to the important case of anisotropic bi-Maxwellian equilibrium plasma distribution functions. Explicit forms of the relativistically correct transverse dispersion relations are derived that hold for any values of the plasma temperatures and the temperature anisotropy. In the limit of nonrelativistic plasma temperatures the dispersion relations are expressed in terms of plasma dispersion function, however, the dependence on frequency and wave numbers is markedly different from the standard noncovariant nonrelativistic analysis. Only in the strictly unphysical formal limit of an infinitely large speed of light, c→∞, does the nonrelativistic dispersion relations reduce to the standard noncovariant dispersion relations

Influence of Complete Coriolis Force on the Dispersion Relation of Ocean Internal-wave in a Background Currents Field

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Liu Yongjun

2015-01-01

Full Text Available In this thesis, the influence of complete Coriolis force (the model includes both the vertical and horizontal components of Coriolis force on the dispersion relation of ocean internal-wave under background currents field are studied, it is important to the study of ocean internal waves in density-stratified ocean. We start from the control equation of sea water movement in the background of the non-traditional approximation, and the vertical velocity solution is derived where buoyancy frequency N(z gradually varies with the ocean depth z. The results show that the influence of complete Coriolis force on the dispersion relation of ocean internal-wave under background currents field is obvious, and these results provide strong evidence for the understanding of dynamic process of density stratified ocean internal waves.

Quasi-pions with temperature dependent dispersion relation

International Nuclear Information System (INIS)

Gorenstein, M.I.

1995-01-01

We construct the procedure to calculate thermodynamical functions for a system of quasi-particles with temperature dependent dispersion relation. Two models for the hot quasi-pion system are considered to illustrate the importance of thermodynamical self consistency requirements. 8 refs., 9 figs

A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions

Directory of Open Access Journals (Sweden)

Taohua Liu

2017-01-01

Full Text Available Fractional advection-dispersion equations, as generalizations of classical integer-order advection-dispersion equations, are used to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, we develop an implicit finite difference method for fractional advection-dispersion equations with fractional derivative boundary conditions. First-order consistency, solvability, unconditional stability, and first-order convergence of the method are proven. Then, we present a fast iterative method for the implicit finite difference scheme, which only requires storage of O(K and computational cost of O(Klog⁡K. Traditionally, the Gaussian elimination method requires storage of O(K2 and computational cost of O(K3. Finally, the accuracy and efficiency of the method are checked with a numerical example.

Modified dispersion relations, inflation, and scale invariance

Science.gov (United States)

Bianco, Stefano; Friedhoff, Victor Nicolai; Wilson-Ewing, Edward

2018-02-01

For a certain type of modified dispersion relations, the vacuum quantum state for very short wavelength cosmological perturbations is scale-invariant and it has been suggested that this may be the source of the scale-invariance observed in the temperature anisotropies in the cosmic microwave background. We point out that for this scenario to be possible, it is necessary to redshift these short wavelength modes to cosmological scales in such a way that the scale-invariance is not lost. This requires nontrivial background dynamics before the onset of standard radiation-dominated cosmology; we demonstrate that one possible solution is inflation with a sufficiently large Hubble rate, for this slow roll is not necessary. In addition, we also show that if the slow-roll condition is added to inflation with a large Hubble rate, then for any power law modified dispersion relation quantum vacuum fluctuations become nearly scale-invariant when they exit the Hubble radius.

The Theory of Thermodynamics for Chemical Reactions in Dispersed Heterogeneous Systems

Science.gov (United States)

Yongqiang; Baojiao; Jianfeng

1997-07-01

In this paper, the expressions of Gibbs energy change, enthalpy change, entropy change, and equilibrium constant for chemical reactions in dispersed heterogeneous systems are derived using classical thermodynamics theory. The thermodynamical relations for the same reaction system between the dispersed and the block state are also derived. The effects of degree of dispersion on thermodynamical properties, reaction directions, and chemical equilibria are discussed. The results show that the present equation of thermodynamics for chemical reactions is only a special case of the above-mentioned formulas and that the effect of the dispersity of a heterogeneous system on the chemical reaction obeys the Le Chatelier principle of movement of equilibria.

From field theory to phenomenology: the history of dispersion relations

International Nuclear Information System (INIS)

Pickering, A.

1989-01-01

The authors chart the history of quantum field theory (QFT) in the 1950s with reference to the ideas of dispersion relations. QFT failed to explain strong interaction physics and so was discarded. Connections are drawn between a central group of particle theorists working on applying Kramers-Kronig light scattering relations to high energy particle scattering and the way physics developed. The concepts of single and double dispersion relations and Regge poles, when connected with the large quantity of empirical data from the large particle accelerators of the 1950s, could not be embodied within QFT, which then fell into decline. (UK)

Interatomic methods for the dispersion energy derived from the adiabatic connection fluctuation-dissipation theorem

Science.gov (United States)

Tkatchenko, Alexandre; Ambrosetti, Alberto; DiStasio, Robert A.

2013-02-01

Interatomic pairwise methods are currently among the most popular and accurate ways to include dispersion energy in density functional theory calculations. However, when applied to more than two atoms, these methods are still frequently perceived to be based on ad hoc assumptions, rather than a rigorous derivation from quantum mechanics. Starting from the adiabatic connection fluctuation-dissipation (ACFD) theorem, an exact expression for the electronic exchange-correlation energy, we demonstrate that the pairwise interatomic dispersion energy for an arbitrary collection of isotropic polarizable dipoles emerges from the second-order expansion of the ACFD formula upon invoking the random-phase approximation (RPA) or the full-potential approximation. Moreover, for a system of quantum harmonic oscillators coupled through a dipole-dipole potential, we prove the equivalence between the full interaction energy obtained from the Hamiltonian diagonalization and the ACFD-RPA correlation energy. This property makes the Hamiltonian diagonalization an efficient method for the calculation of the many-body dispersion energy. In addition, we show that the switching function used to damp the dispersion interaction at short distances arises from a short-range screened Coulomb potential, whose role is to account for the spatial spread of the individual atomic dipole moments. By using the ACFD formula, we gain a deeper understanding of the approximations made in the interatomic pairwise approaches, providing a powerful formalism for further development of accurate and efficient methods for the calculation of the dispersion energy.

Investigation of dispersion-relation-preserving scheme and spectral analysis methods for acoustic waves

Science.gov (United States)

Vanel, Florence O.; Baysal, Oktay

1995-01-01

Important characteristics of the aeroacoustic wave propagation are mostly encoded in their dispersion relations. Hence, a computational aeroacoustic (CAA) algorithm, which reasonably preserves these relations, was investigated. It was derived using an optimization procedure to ensure, that the numerical derivatives preserved the wave number and angular frequency of the differential terms in the linearized, 2-D Euler equations. Then, simulations were performed to validate the scheme and a compatible set of discretized boundary conditions. The computational results were found to agree favorably with the exact solutions. The boundary conditions were transparent to the outgoing waves, except when the disturbance source was close to a boundary. The time-domain data generated by such CAA solutions were often intractable until their spectra was analyzed. Therefore, the relative merits of three different methods were included in the study. For simple, periodic waves, the periodogram method produced better estimates of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window was more effective when used with the weighted-overlapped-segment-averaging and Blackman-Tukey methods gave better results than the periodogram method. Finally, it was demonstrated that the representation of time domain-data was significantly dependent on the particular spectral analysis method employed.

Age--velocity-dispersion relation in the solar neighborhood

International Nuclear Information System (INIS)

Carlberg, R.G.; Dawson, P.C.; Hsu, T.; VandenBerg, D.A.

1985-01-01

The age--velocity-dispersion relation for stars in the solar neighborhood is examined as an indicator of the dominant acceleration mechanism of the stars and the formation history of the local disk. Twarog's sample of F stars, for which ages and photometric distances can be determined, is combined with astrometric data to obtain tangential velocities of a set of stars with a large age range. The resulting age--velocity-dispersion relation rises fairly steeply for stars less than 6 Gyr old, thereafter becoming nearly constant with age. These data are consistent with a simple model in which no local disk is initially present, following which stars are born at a constant rate in time and heated by transient spiral waves. The corresponding age-metallicity relation complements this dynamical measure of the formation history of the disk. The use of new stellar models and a revised metallicity calibration leads to quantitative differences from previous work

Comparison of some dispersion-corrected and traditional functionals as applied to peptides and conformations of cyclohexane derivatives

OpenAIRE

Marianski, Mateusz; Asensio, Amparo; Dannenberg, J. J.

2012-01-01

We compare the energetic and structural properties of fully optimized α-helical and antiparallel β-sheet polyalanines and the energetic differences between axial and equatorial conformations of three cyclohexane derivatives (methyl, fluoro, and chloro) as calculated using several functionals designed to treat dispersion (B97-D, ωB97x-D, M06, M06L, and M06-2X) with other traditional functionals not specifically parametrized to treat dispersion (B3LYP, X3LYP, and PBE1PBE) and with experimental ...

Dispersion relations for η{sup '} → ηππ

Energy Technology Data Exchange (ETDEWEB)

Isken, Tobias; Kubis, Bastian; Schneider, Sebastian P. [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); Stoffer, Peter [Universitaet Bonn, Helmholtz-Institut fuer Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Bonn (Germany); University of California at San Diego, Department of Physics, La Jolla, CA (United States)

2017-07-15

We present a dispersive analysis of the decay amplitude for η{sup '} → ηππ that is based on the fundamental principles of analyticity and unitarity. In this framework, final-state interactions are fully taken into account. Our dispersive representation relies only on input for the ππ and πη scattering phase shifts. Isospin symmetry allows us to describe both the charged and neutral decay channel in terms of the same function. The dispersion relation contains subtraction constants that cannot be fixed by unitarity. We determine these parameters by a fit to Dalitz-plot data from the VES and BES-III experiments. We study the prediction of a low-energy theorem and compare the dispersive fit to variants of chiral perturbation theory. (orig.)

Modified dispersion relations and black hole physics

International Nuclear Information System (INIS)

Ling Yi; Li Xiang; Hu Bo

2006-01-01

A modified formulation of the energy-momentum relation is proposed in the context of doubly special relativity. We investigate its impact on black hole physics. It turns out that such a modification will give corrections to both the temperature and the entropy of black holes. In particular, this modified dispersion relation also changes the picture of Hawking radiation greatly when the size of black holes approaches the Planck scale. It can prevent black holes from total evaporation, as a result providing a plausible mechanism to treat the remnant of black holes as a candidate for dark matter

STATISTICALLY DETERMINED DISPERSION RELATIONS OF MAGNETIC FIELD FLUCTUATIONS IN THE TERRESTRIAL FORESHOCK

International Nuclear Information System (INIS)

Hnat, B.; O’Connell, D.; Nakariakov, V. M.; Sundberg, T.

2016-01-01

We obtain dispersion relations of magnetic field fluctuations for two crossings of the terrestrial foreshock by Cluster spacecraft. These crossings cover plasma conditions that differ significantly in their plasma β and in the density of the reflected ion beam, but not in the properties of the encountered ion population, both showing shell-like distribution function. Dispersion relations are reconstructed using two-point instantaneous wave number estimations from pairs of Cluster spacecraft. The accessible range of wave vectors, limited by the available spacecraft separations, extends to ≈2 × 10 4 km. Results show multiple branches of dispersion relations, associated with different powers of magnetic field fluctuations. We find that sunward propagating fast magnetosonic waves and beam resonant modes are dominant for the high plasma β interval with a dense beam, while the dispersions of the interval with low beam density include Alfvén and fast magnetosonic modes propagating sunward and anti-sunward.

STATISTICALLY DETERMINED DISPERSION RELATIONS OF MAGNETIC FIELD FLUCTUATIONS IN THE TERRESTRIAL FORESHOCK

Energy Technology Data Exchange (ETDEWEB)

Hnat, B.; O’Connell, D.; Nakariakov, V. M. [Centre for Fusion, Space and Astrophysics, University of Warwick (United Kingdom); Sundberg, T., E-mail: B.Hnat@warwick.ac.uk [School of Physics and Astronomy, Queen Mary University of London (United Kingdom)

2016-08-20

We obtain dispersion relations of magnetic field fluctuations for two crossings of the terrestrial foreshock by Cluster spacecraft. These crossings cover plasma conditions that differ significantly in their plasma β and in the density of the reflected ion beam, but not in the properties of the encountered ion population, both showing shell-like distribution function. Dispersion relations are reconstructed using two-point instantaneous wave number estimations from pairs of Cluster spacecraft. The accessible range of wave vectors, limited by the available spacecraft separations, extends to ≈2 × 10{sup 4} km. Results show multiple branches of dispersion relations, associated with different powers of magnetic field fluctuations. We find that sunward propagating fast magnetosonic waves and beam resonant modes are dominant for the high plasma β interval with a dense beam, while the dispersions of the interval with low beam density include Alfvén and fast magnetosonic modes propagating sunward and anti-sunward.

Both solubility and chemical stability of curcumin are enhanced by solid dispersion in cellulose derivative matrices.

Science.gov (United States)

Li, Bin; Konecke, Stephanie; Wegiel, Lindsay A; Taylor, Lynne S; Edgar, Kevin J

2013-10-15

Amorphous solid dispersions (ASD) of curcumin (Cur) in cellulose derivative matrices, hydroxypropylmethylcellulose acetate succinate (HPMCAS), carboxymethylcellulose acetate butyrate (CMCAB), and cellulose acetate adipate propionate (CAAdP) were prepared in order to investigate the structure-property relationship and identify polymer properties necessary to effectively increase Cur aqueous solution concentration. XRD results indicated that all investigated solid dispersions were amorphous, even at a 9:1 Cur:polymer ratio. Both stability against crystallization and Cur solution concentration from these ASDs were significantly higher than those from physical mixtures and crystalline Cur. Remarkably, curcumin was also stabilized against chemical degradation in solution. Chemical stabilization was polymer-dependent, with stabilization in CAAdP>CMCAB>HPMCAS>PVP, while matrices enhanced solution concentration as PVP>HPMCAS>CMCAB≈CAAdP. HPMCAS/Cur dispersions have useful combinations of pH-triggered release profile, chemical stabilization, and strong enhancement of Cur solution concentration. Copyright © 2013 Elsevier Ltd. All rights reserved.

Spin-wave dispersion relations in disordered Fe-V alloys

International Nuclear Information System (INIS)

Nakai, Y.; Schibuya, N.; Kunitomi, N.; Wakabayashi, N.; Cooke, J.F.

1982-01-01

The spin-wave dispersion relations of the ferromagnetic disordered alloys Fe/sub 1-x/V/sub x/(x = 0.076, 0.135, 0.160, and 0.187) were studied by means of the inelastic scattering of neutrons. The observed dispersion relations are adequately represented by the power law, E = Dq 2 (1-βq 2 ), in a wide energy range up to 80 meV. The concentration dependence of the exchange stiffness constant D shows good agreement with previous results obtained by means of the small-angle scattering of neutrons and by the analysis of the temperature dependence of the bulk magnetization. The observed results can be explained by the Heisenberg model and, to some extent, by the itinerant-electron model

The effect of broadened linewidth induced by dispersion on the performance of resonant optical gyroscope

Science.gov (United States)

Zhang, Hao; Li, Wenxiu; Han, Peng; Chang, Xiaoyang; Liu, Jiaming; Lin, Jian; Xue, Xia; Zhu, Fang; Yang, Yang; Liu, Xiaojing; Zhang, Xiaofu; Huang, Anping; Xiao, Zhisong; Fang, Jiancheng

2018-01-01

Anomalous dispersion enhancement physical mechanism for Sagnac effect is described by special relativity derivation, and three kinds of definitions of minimum detectable angular rate of resonance optical gyroscope (ROG) are compared and the relations among them are investigated. The effect of linewidth broadening induced by anomalous dispersion on the sensitivity of ROG is discussed in this paper. Material dispersion-broadened resonance linewidth deteriorates the performance of a passive ROG and dispersion enhancement effect, while the sensitivity of a structural dispersion ROG is enhanced by two orders of magnitude even considering the dispersion-broadened resonance linewidth.

Comparison of Forward Dispersion Relations with Experiments around 10 GeV

DEFF Research Database (Denmark)

Lautrup, B.; Møller-Nielsen, Peter; Olesen, P.

1965-01-01

no assumptions whatsoever about the unknown cross sections above 20 GeV. On account of the large systematic errors in the measured real parts, no definite conclusion can be drawn as to the validity of forward dispersion relations. In estimating the standard deviations in the dispersion integrals, a Monte Carlo...

Lateral dispersion coefficients as functions of averaging time

International Nuclear Information System (INIS)

Sheih, C.M.

1980-01-01

Plume dispersion coefficients are discussed in terms of single-particle and relative diffusion, and are investigated as functions of averaging time. To demonstrate the effects of averaging time on the relative importance of various dispersion processes, and observed lateral wind velocity spectrum is used to compute the lateral dispersion coefficients of total, single-particle and relative diffusion for various averaging times and plume travel times. The results indicate that for a 1 h averaging time the dispersion coefficient of a plume can be approximated by single-particle diffusion alone for travel times <250 s and by relative diffusion for longer travel times. Furthermore, it is shown that the power-law formula suggested by Turner for relating pollutant concentrations for other averaging times to the corresponding 15 min average is applicable to the present example only when the averaging time is less than 200 s and the tral time smaller than about 300 s. Since the turbulence spectrum used in the analysis is an observed one, it is hoped that the results could represent many conditions encountered in the atmosphere. However, as the results depend on the form of turbulence spectrum, the calculations are not for deriving a set of specific criteria but for demonstrating the need in discriminating various processes in studies of plume dispersion

Dispersion relations for the self-energy in noncommutative field theories

International Nuclear Information System (INIS)

Brandt, F.T.; Das, Ashok; Frenkel, J.

2002-01-01

We study the IR-UV connection in noncommutative φ 3 theory as well as in noncommutative QED from the point of view of the dispersion relation for self-energy. We show that, although the imaginary part of the self-energy is well behaved as the parameter of noncommutativity vanishes, the real part becomes divergent as a consequence of the high energy behavior of the dispersion integral. Some other interesting features that arise from this analysis are also briefly discussed

The dispersion relation of a gravitating spiral system

International Nuclear Information System (INIS)

Evangelidis, E.

1977-01-01

The dispersion relation has been found for a galaxy, without the assumption that the centrifugal force is balanced by the gravitational force. It has been shown that such a system (1) can be gravitationally unstable under appropriate conditions, and (2) that there is no resonance at ω=2Ω (Ω=angular velocity of the Galaxy). (Auth.)

Pulse Propagation in Presence of Polarization Mode Dispersion and Chromatic Dispersion in Single Mode Fibers

Directory of Open Access Journals (Sweden)

Hassan Abid Yasser

2013-01-01

Full Text Available The presence of (first and second orders polarization mode dispersion (PMD, chromatic dispersion, and initial chirp makes effects on the propagated pulses in single mode fiber. Nowadays, there is not an accurate mathematical formula that describes the pulse shape in the presence of these effects. In this work, a theoretical study is introduced to derive a generalized formula. This formula is exactly approached to mathematical relations used in their special cases. The presence of second-order PMD (SOPMD will not affect the orthogonality property between the principal states of polarization. The simulation results explain that the interaction of the SOPMD components with the conventional effects (chromatic dispersion and chirp will cause a broadening/narrowing and shape distortion. This changes depend on the specified values of SOPMD components as well as the present conventional parameters.

Dispersion Differences and Consistency of Artificial Periodic Structures.

Science.gov (United States)

Cheng, Zhi-Bao; Lin, Wen-Kai; Shi, Zhi-Fei

2017-10-01

Dispersion differences and consistency of artificial periodic structures, including phononic crystals, elastic metamaterials, as well as periodic structures composited of phononic crystals and elastic metamaterials, are investigated in this paper. By developing a K(ω) method, complex dispersion relations and group/phase velocity curves of both the single-mechanism periodic structures and the mixing-mechanism periodic structures are calculated at first, from which dispersion differences of artificial periodic structures are discussed. Then, based on a unified formulation, dispersion consistency of artificial periodic structures is investigated. Through a comprehensive comparison study, the correctness for the unified formulation is verified. Mathematical derivations of the unified formulation for different artificial periodic structures are presented. Furthermore, physical meanings of the unified formulation are discussed in the energy-state space.

A Neutron Study for Phonon Dispersion Relations in HgTe

DEFF Research Database (Denmark)

Kepa, H.; Gebicki, W.; Giebultowicz, T.

1980-01-01

Dispersion relations for acoustic phonons in mercury telluride in three high symmetry directions [111], [110] and [001] are presented. The eleven-parameter rigid-ion model is fitted to the experimental data....

Comment on “Frequency-dependent dispersion in porous media”

KAUST Repository

Davit, Yohan

2012-07-10

In a recent paper, Valdès-Parada and Alvarez-Ramirez used the technique of volume averaging to derive a "frequency-dependent" dispersion tensor, Dγ*, the goal of which is to describe solute transport in porous media undergoing periodic processes. We describe two issues related to this dispersion tensor. First, we demonstrate that the definition of Dγ* is erroneous and derive a corrected version, Dγ*c. With this modification, the approach of Valdès-Parada and Alvarez-Ramirez becomes strictly equivalent to the one devised by Moyne. Second, we show that the term "frequency-dependent dispersion" is misleading because Dγ* and Dγ*c do not depend on the process operating frequency, χ. The study carried out by Valdès-Parada and Alvarez-Ramirez represents a spectral analysis of the relaxation of Dγ* towards its steady-state, independent of any periodic operation or excitation. © 2012 American Physical Society.

The complex dispersion relation of surface plasmon polaritons at gold/para-hexaphenylene interfaces

DEFF Research Database (Denmark)

Lemke, Christoph; Leißner, Till; Klick, Alwin

2014-01-01

Two-photon photoemission electron microscopy (2P-PEEM) is used to measure the real and imaginary part of the dispersion relation of surface plasmon polaritons at different interface systems. A comparison of calculated and measured dispersion data for a gold/vacuum interface demonstrates...

Comment on “Frequency-dependent dispersion in porous media”

KAUST Repository

Davit, Yohan; Quintard, Michel

2012-01-01

describe two issues related to this dispersion tensor. First, we demonstrate that the definition of Dγ* is erroneous and derive a corrected version, Dγ*c. With this modification, the approach of Valdès-Parada and Alvarez-Ramirez becomes strictly equivalent

Wave dispersion relation of two-dimensional plasma crystals in a magnetic field

International Nuclear Information System (INIS)

Uchida, G.; Konopka, U.; Morfill, G.

2004-01-01

The wave dispersion relation in a two-dimensional strongly coupled plasma crystal is studied by theoretical analysis and molecular dynamics simulation taking into account a constant magnetic field parallel to the crystal normal. The expression for the wave dispersion relation clearly shows that high-frequency and low-frequency branches exist as a result of the coupling of longitudinal and transverse modes due to the Lorenz force acting on the dust particles. The high-frequency and the low-frequency branches are found to belong to right-hand and left-hand polarized waves, respectively

Dispersion Models to Forecast Traffic-related Emissions in Urban Areas

Directory of Open Access Journals (Sweden)

Davide Scannapieco

2011-11-01

Full Text Available Down the centuries, a direct link had been developed between increase in mobility and increase in wealth. On the other hand, air emission of greenhouse gases (GHG due to vehicles equipped with internal combustion engines can be regarded as a negative pressure over the environment. In the coming decades, road transport is likely to remain a significant contributor to air pollution in cities. Many urban trips cover distances of less than 6 km. Since the effectiveness of catalytic converters in the initial minutes of engine operation is small, the average emission per distance driven is very high in urban areas. Also, poorly maintained vehicles that lack exhaust aftertreatment systems are responsible for a major part of pollutant emissions. Therefore in urban areas, where higher concentrations of vehicles can be easily found, air pollution represents a critical issue, being it related with both environment and human health protection: in truth, research in recent decades consistently indicates the adverse effects of outdoor air pollution on human health, and the evidence points to air pollution stemming from transport as an important contributor to these effects. Several institutions (EEA, USEPA, etc. focused their interest in dispersion models because of their potential effectiveness to forecast atmospheric pollution. Furthermore, air micropollutants such as Polycyclic Aromatic Compounds (PAH and Metallic Trace Elements (MTE are traffic-related and although very low concentrations their dispersion is a serious issue. However, dispersion models are usefully implemented to better manage this estimation problem. Nonetheless, policy makers and land managers have to deal with model selection, taking into account that several dispersion models are available, each one of them focused on specific goals (e.g., wind transport of pollutants, land morphology implementation, evaluation of micropollutants transport, etc.; a further aspect to be considered is

Evaluation of regional and local atmospheric dispersion models for the analysis of traffic-related air pollution in urban areas

Science.gov (United States)

Fallah-Shorshani, Masoud; Shekarrizfard, Maryam; Hatzopoulou, Marianne

2017-10-01

Dispersion of road transport emissions in urban metropolitan areas is typically simulated using Gaussian models that ignore the turbulence and drag induced by buildings, which are especially relevant for areas with dense downtown cores. To consider the effect of buildings, street canyon models are used but often at the level of single urban corridors and small road networks. In this paper, we compare and validate two dispersion models with widely varying algorithms, across a modelling domain consisting of the City of Montreal, Canada accounting for emissions of more 40,000 roads. The first dispersion model is based on flow decomposition into the urban canopy sub-flow as well as overlying airflow. It takes into account the specific height and geometry of buildings along each road. The second model is a Gaussian puff dispersion model, which handles complex terrain and incorporates three-dimensional meteorology, but accounts for buildings only through variations in the initial vertical mixing coefficient. Validation against surface observations indicated that both models under-predicted measured concentrations. Average weekly exposure surfaces derived from both models were found to be reasonably correlated (r = 0.8) although the Gaussian dispersion model tended to underestimate concentrations around the roadways compared to the street canyon model. In addition, both models were used to estimate exposures of a representative sample of the Montreal population composed of 1319 individuals. Large differences were noted whereby exposures derived from the Gaussian puff model were significantly lower than exposures derived from the street canyon model, an expected result considering the concentration of population around roadways. These differences have large implications for the analyses of health effects associated with NO2 exposure.

Dispersion Relation for Skeletal Vibrations in Deuterated Polyethylene

Energy Technology Data Exchange (ETDEWEB)

Feldkamp, L. A.; Venkataraman, G.; King, J. S. [Department of Nuclear Engineering, University of Michigan, Ann Arbor, MI (United States)

1968-09-15

The low frequency vibrations in polyethylene have been studied previously, utilizing the incoherent scattering technique which yields an amplitude-weighted density of states. In the present work the dispersion relations have been obtained directly by observing the coherent scattering from a deuterated sample. This represents the first such measurement on a crystalline polymer. A target in which the molecular chain axes were approximately parallel was prepared by stretching polycrystalline material. The FWHM of the rocking curve for the (002) reflection was measured to be 9 Degree-Sign . Constant-Q and constant-E scans were made on the University of Michigan triple-axis spectrometer at room temperature to observe phonons propagating along the chain direction. The resulting dispersion curve for the v{sub 5} mode follows generally the calculated curve of Tasumi and Krimm with systematically lower frequencies. The maximum frequency of 1.36 x 10{sup 13} Hz agrees with the cut-off frequency determined previously from the incoherent scattering spectrum. (author)

Dispersion characteristics of planar grating with arbitrary grooves for terahertz Smith-Purcell radiation

International Nuclear Information System (INIS)

Cao, Miaomiao; Li, Ke; Liu, Wenxin; Wang, Yong

2015-01-01

In this paper, a novel method of getting the dispersion relations in planar grating with arbitrary grooves for terahertz Smith-Purcell radiation is investigated analytically. The continuous profile of the groove is approximately replaced by a series of rectangular steps. By making use of field matches method and the continuity of transverse admittance, the universal dispersion equation for grating with arbitrarily shaped grooves is derived. By solving the dispersion equation in presence of electron beam, the growth rate is obtained directly and the dependence on beam parameters is analyzed. Comparisons of the dispersion characteristics among some special groove shapes have been made by numerical calculation. The results show that the rectangular-step approximation method provides a novel approach to obtain the universal dispersion relation for grating with arbitrary grooves for Smith-Purcell radiation

Numerical study on general dispersion relation of anisotropic and weakly relativistic plasma

International Nuclear Information System (INIS)

Ke Fujiu; Chen Yanping

1987-01-01

The key problem in heating and instability studies in plasma physics is to obtain dispersive equation and its solution. This paper presents the general dispersive equation and corresponding procedure for electromagnetic wave which nearly poloidally impinges on anisotropic, weakly relativistic Maxwellian plasma with inhomogeneous density in nonuniform magnetic field (such as plasma in TOKAMAK). The double index function F ij , significant in plasma physics, was expanded as single index function F 1 , and then the values were calculated by means of dispersive function. It was also pointed out that the severe error would be involved in the calculation of F ij from recurrence relation of F 11

Amphetamine derivative related deaths.

Science.gov (United States)

Lora-Tamayo, C; Tena, T; Rodríguez, A

1997-02-28

Amphetamine its methylendioxy (methylendioxyamphetamine methylenedioxymethylamphetamine, methylenedioxyethylamphetamine) and methoxy derivatives (p-methoxyamphetamine and p-methoxymethylamphetamine) are widely abused in Spanish society. We present here the results of a systematic study of all cases of deaths brought to the attention of the Madrid department of the Instituto Nacional de Toxicologia from 1993 to 1995 in which some of these drugs have been found in the cadaveric blood. The cases were divided into three categories: amphetamine and derivatives, amphetamines and alcohol, amphetamines and other drugs. Data on age, sex, clinical symptoms, morphological findings, circumstances of death, when known, and concentration of amphetamine derivatives, alcohol and other drugs in blood are given for each group. The information provided here may prove to be useful for the forensic interpretation of deaths which are directly or indirectly related to abuse of amphetamine derivatives.

Prediction of HIFU Propagation in a Dispersive Medium via Khokhlov–Zabolotskaya–Kuznetsov Model Combined with a Fractional Order Derivative

Directory of Open Access Journals (Sweden)

Shilei Liu

2018-04-01

Full Text Available High intensity focused ultrasound (HIFU has been proven to be promising in non-invasive therapies, in which precise prediction of the focused ultrasound field is crucial for its accurate and safe application. Although the Khokhlov–Zabolotskaya–Kuznetsov (KZK equation has been widely used in the calculation of the nonlinear acoustic field of HIFU, some deviations still exist when it comes to dispersive medium. This problem also exists as an obstacle to the Westervelt model and the Spherical Beam Equation. Considering that the KZK equation is the most prevalent model in HIFU applications due to its accurate and simple simulation algorithms, there is an urgent need to improve its performance in dispersive medium. In this work, a modified KZK (mKZK equation derived from a fractional order derivative is proposed to calculate the nonlinear acoustic field in a dispersive medium. By correcting the power index in the attenuation term, this model is capable of providing improved prediction accuracy, especially in the axial position of the focal area. Simulation results using the obtained model were further compared with the experimental results from a gel phantom. Good agreements were found, indicating the applicability of the proposed model. The findings of this work will be helpful in making more accurate treatment plans for HIFU therapies, as well as facilitating the application of ultrasound in acoustic hyperthermia therapy.

A new approximation of the dispersion relations occurring in the sound-attenuation problem of turbofan aircraft engines

Directory of Open Access Journals (Sweden)

Robert SZABO

2011-12-01

Full Text Available The dispersion relations, appearing in the analysis of the stability of a gas flow in a straight acoustically-lined duct with respect to perturbations produced by a time harmonic source, beside the wave number and complex frequency contain the solution of a boundary value problem of the Pridmore-Brown equation depending on the wave number and frequency. For this reason, in practice the dispersion relations are rarely simple enough for carried out the zeros. The determination of zeros of these dispersion relations is crucial for the prediction of the perturbation attenuation or amplification. In this paper an approximation of the dispersion relations is given. Our approach preserves the general character of the mean flow, the general Pridmore-Brown equation and it’s only in the shear flow that we replace the exact solution of the boundary value problem with its Taylor polynomial approximate. In this way new approximate dispersion relations are obtained which zero’s can be found by computer.

Mord studies in IR region by new dispersion relation

International Nuclear Information System (INIS)

Murthy, V.R.; Kumar, R. Jeevan

1994-01-01

This is the continuation of the series reporting MORD studies to typical problem in Chemistry and Polymer Science. In our earlier papers the MORDsup1.2 studied only in visible region. In this present investigation we extended the application of the New Dispersion Relation in IR region to determine the MORD and tested to some simple systems

Rainbows without unicorns: metric structures in theories with modified dispersion relations

International Nuclear Information System (INIS)

Lobo, Iarley P.; Loret, Niccolo; Nettel, Francisco

2017-01-01

Rainbow metrics are a widely used approach to the metric formalism for theories with modified dispersion relations. They have had a huge success in the quantum gravity phenomenology literature, since they allow one to introduce momentum-dependent space-time metrics into the description of systems with a modified dispersion relation. In this paper, we introduce the reader to some realizations of this general idea: the original rainbow metrics proposal, the momentum-space-inspired metric and a Finsler geometry approach. As the main result of this work we also present an alternative definition of a four-velocity dependent metric which allows one to handle the massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations. (orig.)

Rainbows without unicorns: metric structures in theories with modified dispersion relations

Science.gov (United States)

Lobo, Iarley P.; Loret, Niccoló; Nettel, Francisco

2017-07-01

Rainbow metrics are a widely used approach to the metric formalism for theories with modified dispersion relations. They have had a huge success in the quantum gravity phenomenology literature, since they allow one to introduce momentum-dependent space-time metrics into the description of systems with a modified dispersion relation. In this paper, we introduce the reader to some realizations of this general idea: the original rainbow metrics proposal, the momentum-space-inspired metric and a Finsler geometry approach. As the main result of this work we also present an alternative definition of a four-velocity dependent metric which allows one to handle the massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations.

Rainbows without unicorns: metric structures in theories with modified dispersion relations

Energy Technology Data Exchange (ETDEWEB)

Lobo, Iarley P. [Universita ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); ICRANet, Pescara (Italy); CAPES Foundation, Ministry of Education of Brazil, Brasilia (Brazil); Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); INFN Sezione Roma 1 (Italy); Loret, Niccolo [Ruder Boskovic Institute, Division of Theoretical Physics, Zagreb (Croatia); Nettel, Francisco [Universita ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); Universidad Nacional Autonoma de Mexico, Instituto de Ciencias Nucleares, Mexico (Mexico); INFN Sezione Roma 1 (Italy)

2017-07-15

Rainbow metrics are a widely used approach to the metric formalism for theories with modified dispersion relations. They have had a huge success in the quantum gravity phenomenology literature, since they allow one to introduce momentum-dependent space-time metrics into the description of systems with a modified dispersion relation. In this paper, we introduce the reader to some realizations of this general idea: the original rainbow metrics proposal, the momentum-space-inspired metric and a Finsler geometry approach. As the main result of this work we also present an alternative definition of a four-velocity dependent metric which allows one to handle the massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations. (orig.)

Relativistic plasma dispersion functions

International Nuclear Information System (INIS)

Robinson, P.A.

1986-01-01

The known properties of plasma dispersion functions (PDF's) for waves in weakly relativistic, magnetized, thermal plasmas are reviewed and a large number of new results are presented. The PDF's required for the description of waves with small wave number perpendicular to the magnetic field (Dnestrovskii and Shkarofsky functions) are considered in detail; these functions also arise in certain quantum electrodynamical calculations involving strongly magnetized plasmas. Series, asymptotic series, recursion relations, integral forms, derivatives, differential equations, and approximations for these functions are discussed as are their analytic properties and connections with standard transcendental functions. In addition a more general class of PDF's relevant to waves of arbitrary perpendicular wave number is introduced and a range of properties of these functions are derived

Wandering stars: age-related habitat use and dispersal of Javan Hawk-eagles (Spizaetus bartelsi)

NARCIS (Netherlands)

Nijman, V.; Balen, van S.

2003-01-01

Natal dispersal and philopatry have rarely been studied in tropical forest raptors. Especially with respect to endangered species with fragmented distributions more knowledge of dispersal and age-related habitat preferences is needed for proper management. We conducted an island-wide study on

Black hole radiation with modified dispersion relation in tunneling paradigm: Static frame

Directory of Open Access Journals (Sweden)

Jun Tao

2017-09-01

Full Text Available To study possible deviations from the Hawking's prediction, we assume that the dispersion relations of matter fields are modified at high energies and use the Hamilton–Jacobi method to investigate the corresponding effects on the Hawking radiation in this paper. The preferred frame is the static frame of the black hole. The dispersion relation adopted agrees with the relativistic one at low energies but is modified near the Planck mass mp. We calculate the corrections to the Hawking temperature for massive and charged particles to O(mp−2 and massless and neutral particles to all orders. Our results suggest that the thermal spectrum of radiations near horizon is robust, e.g. corrections to the Hawking temperature are suppressed by mp. After the spectrum of radiations near the horizon is obtained, we use the brick wall model to compute the thermal entropy of a massless scalar field near the horizon of a 4D spherically symmetric black hole. We find that the subleading logarithmic term of the entropy does not depend on how the dispersion relations of matter fields are modified. Finally, the luminosities of black holes are computed by using the geometric optics approximation.

Dispersion and energy conservation relations of surface waves in semi-infinite plasma

International Nuclear Information System (INIS)

Atanassov, V.

1981-01-01

The hydrodynamic theory of surface wave propagation in semi-infinite homogeneous isotropic plasma is considered. Explicit linear surface wave solutions are given for the electric and magnetic fields, charge and current densities. These solutions are used to obtain the well-known dispersion relations and, together with the general energy conservation equation, to find appropriate definitions for the energy and the energy flow densities of surface waves. These densities are associated with the dispersion relation and the group velocity by formulae similar to those for bulk waves in infinite plasmas. Both cases of high-frequency (HF) and low-frequency (LF) surface waves are considered. (author)

Improved pion pion scattering amplitude from dispersion relation formalism

International Nuclear Information System (INIS)

Cavalcante, I.P.; Coutinho, Y.A.; Borges, J. Sa

2005-01-01

Pion-pion scattering amplitude is obtained from Chiral Perturbation Theory at one- and two-loop approximations. Dispersion relation formalism provides a more economic method, which was proved to reproduce the analytical structure of that amplitude at both approximation levels. This work extends the use of the formalism in order to compute further unitarity corrections to partial waves, including the D-wave amplitude. (author)

Reactimeter dispersion equation

OpenAIRE

A.G. Yuferov

2016-01-01

The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...

Theoretical model based on the memory effect for the strange photoisomerization kinetics of diarylethene derivatives dispersed on polymer films

International Nuclear Information System (INIS)

Seki, Kazuhiko; Tachiya, M.

2007-01-01

In the present paper the authors present a theoretical model to explain the kinetics involving the induction period observed by Irie et al. [Nature (London) 420, 759 (2002)] for photoisomerization of diarylethene derivatives dispersed on polymer films at a single molecular level. In the model we assume that both ground state and excited state free energy landscapes which result from the interaction between the photochromic molecule and the surrounding polymer are rugged and have several local minima along the pathway to the critical point at which isomerization actually occurs. We assume that after one photoexcitation a fraction of the photochromic molecule moves to a new local minimum and stays there, although the other fraction returns to the original local minimum. The former effect is referred to as the memory effect. After repeated photoexcitations the photochromic molecule moves gradually from one local minimum to another in the pathway to the isomerization point. It finally reaches the isomerization point, where isomerization occurs. Their model successfully reproduces the kinetics of photoisomerization of diarylethene derivatives dispersed on polymer films observed experimentally

Pion-pair formation and the pion dispersion relation in a hot pion gas

Energy Technology Data Exchange (ETDEWEB)

Chanfay, G. [Lyon-1 Univ., 69 - Villeurbanne (France). Inst. de Physique Nucleaire; Alm, T. [Rostock Univ. (Germany); Schuck, P. [Grenoble-1 Univ., 38 (France). Inst. des Sciences Nucleaires; Welke, G. [Wayne State Univ., Detroit, MI (United States). Dept. of Physics and Astronomy

1996-09-01

The possibility of pion-pair formation in a hot pion gas, based on the bosonic gap equation, is pointed out and discussed in detail. The critical temperature for condensation of pion pairs (Evans-Rashind transition) is determined as a function of the pion density. As for fermions, this phase transition is signaled by the appearance of a pole in the two-particle propagator. In Bose systems there exists a second, lower critical temperature, associated with the appearance of the single-particle condensate. Between the two critical temperatures the pion dispersion relation changes from the usual quasiparticle dispersion to a Bogoliubov-like dispersion relation at low momenta. This generalizes the non-relativistic results for an attractive Bose gas by Evans et al. Possible consequences for the inclusive pion spectra measured in heavy-ion collisions at ultra-relativistic energies are discussed. 21 refs.

Comparison of some dispersion-corrected and traditional functionals as applied to peptides and conformations of cyclohexane derivatives

Science.gov (United States)

Marianski, Mateusz; Asensio, Amparo; Dannenberg, J. J.

2012-07-01

We compare the energetic and structural properties of fully optimized α-helical and antiparallel β-sheet polyalanines and the energetic differences between axial and equatorial conformations of three cyclohexane derivatives (methyl, fluoro, and chloro) as calculated using several functionals designed to treat dispersion (B97-D, ωB97x-D, M06, M06L, and M06-2X) with other traditional functionals not specifically parametrized to treat dispersion (B3LYP, X3LYP, and PBE1PBE) and with experimental results. Those functionals developed to treat dispersion significantly overestimate interaction enthalpies of folding for the α-helix and predict unreasonable structures that contain Ramachandran ϕ and ψ and C = O…N H-bonding angles that are out of the bounds of databases compiled the β-sheets. These structures are consistent with overestimation of the interaction energies. For the cyclohexanes, these functionals overestimate the stabilities of the axial conformation, especially when used with smaller basis sets. Their performance improves when the basis set is improved from D95** to aug-cc-pVTZ (which would not be possible with systems as large as the peptides).

On the Sensitivity of Neutrino Telescopes to a Modified Dispersion Relation

International Nuclear Information System (INIS)

Bustamante, M.; Gago, A. M.; Bazo, J. L.; Miranda, O. G.

2008-01-01

We consider a modified dispersion relation and its effect on the flavour ratios of high-energy neutrinos originated at distant astrophysical sources such as active galactic nuclei. This dispersion relation arise naturally in different new physics (NP) effects such as violation of CPT invariance, of the equivalence principle and of Lorentz invariance. It is a common notion in the literature that by using the flux of high-energy neutrinos expected from distant astrophysical sources, the sensitivity to possible NP effects may be improved beyond the current bounds. However, performing a realistic analysis that takes into account the expected number of events in future neutrino telescopes, we find that the average detected flavour ratios with and without the inclusion of new physics have essentially the same value, making difficult to obtain an improved bound for this type of new physics

Improvements in or relating to dispersions

International Nuclear Information System (INIS)

Woodhead, J.L.

1981-01-01

A process is described for the preparation of an aqueous dispersion of ceria which comprises forming a slurry of cerium IV hydroxide with water and an acid, the acid being capable of causing deaggregation of aggregated crystallites in the cerium IV hydroxide, heating the slurry for such a time and at such a temperature that the pH reaches a steady value, the quantity of acid in the slurry being such that the steady value of pH is below 5.4, thereby to produce a conditioned slurry, and admixing water with the conditioned slurry to produce an aqueous dispersion of ceria. (author)

Dispersion relation for elastic electron-hydrogen atom forward scattering amplitude

International Nuclear Information System (INIS)

Kuchiev, M.Yu.; Amusia, M.Ya.

1978-01-01

The elastic e+H forward scattering amplitude is an analytical function in the complex energy E plane and has two cuts on the real axis: 0 < E < infinity and -infinity < E < -B, B being the hydrogen ionization potential. The e+H dispersion relation contains two integrals over the right and left cuts. (Auth.)

Dispersion relation for long-wave neutrons and the possibility of its precise experimental verification

International Nuclear Information System (INIS)

Frank, A.I.; Nosov, V.G.

1995-01-01

Modern theoretical concepts concerning the dispersion relation for slow neutrons in matter are considered. The generally accepted optical-potential model is apparently not quite accurate and should be supplemented with some small corrections in the energy range attainable in experiments. For ultracold neutrons, these corrections are related to the proximity of the applicability boundary of the theory; for cold neutrons, these corrections are due to correlations in the positions of scatters. The accuracy of existing experiments is insufficient for confirmation or refutation these conclusions. A precision experiment is proposed to verify the dispersion relation for long-wave neutrons. 30 refs., 3 figs

Mathematical modeling of disperse two-phase flows

CERN Document Server

Morel, Christophe

2015-01-01

This book develops the theoretical foundations of disperse two-phase flows, which are characterized by the existence of bubbles, droplets or solid particles finely dispersed in a carrier fluid, which can be a liquid or a gas. Chapters clarify many difficult subjects, including modeling of the interfacial area concentration. Basic knowledge of the subjects treated in this book is essential to practitioners of Computational Fluid Dynamics for two-phase flows in a variety of industrial and environmental settings. The author provides a complete derivation of the basic equations, followed by more advanced subjects like turbulence equations for the two phases (continuous and disperse) and multi-size particulate flow modeling. As well as theoretical material, readers will discover chapters concerned with closure relations and numerical issues. Many physical models are presented, covering key subjects including heat and mass transfers between phases, interfacial forces and fluid particles coalescence and breakup, a...

Study of Phonon Dispersion Relations in Cuprous Oxide by Inelastic Neutron Scattering

DEFF Research Database (Denmark)

Beg, M. M.; Shapiro, S. M.

1976-01-01

Phonon dispersion relations in Cu2O have been studied at 20°C using inelastic neutron scattering. Seven acoustic branches and twelve optical branches have been studied in detail in the three symmetry directions [00ζ], [ζζ0], and [ζζζ] of the cubic lattice. Four of the six zone-center phonons have...... been observed and the assignments and energies are confirmed as Γ25=87±2 cm-1, Γ12′=105±3 cm-1, Γ15=146±1 cm-1, and Γ2′≈347 cm-1. The dispersion relations agree only qualitatively with the rigid-ion-model calculations. It is suggested that more detailed calculations may be performed in the light...

Derivative analyticity relations and asymptotic energies

International Nuclear Information System (INIS)

Fischer, J.

1976-01-01

On the basis of general principles of the S-matrix theory theorems are derived showing that derivative analyticity relations analogous to those of Bronzen, Kane and Sukhatme hold at asymptotic energies if the high-energy limits of certain physical quantities exist

Phonon dispersion relation in zircon, ZrSiO4 using inelastic neutron scattering at a pulsed neutron source

International Nuclear Information System (INIS)

Mittal, R.; Chaplot, S.L.; Parthasarathy, R.; Bull, M.J.; Harris, M.J.

2000-01-01

The coherent inelastic neutron scattering technique is used for the measurements of phonon dispersion relation in a geophysically important mineral zircon using PRISMA spectrometer as ISIS, UK. Lattice dynamical calculations of the phonon dispersion relation are carried out using a shell model. The one-phonon structure factors are calculated for selecting the Bragg points for the measurements and assignment of phonons to different branches. The calculations are in good agreement with the measured phonon dispersion relation. (author)

Theoretical Re-evaluations of Scaling Relations between SMBHs and Their Host Galaxies–2. Importance of AGN Feedback Suggested by Stellar Age–Velocity Dispersion Relation

Directory of Open Access Journals (Sweden)

Hikari Shirakata

2017-09-01

Full Text Available We present the galactic stellar age—velocity dispersion relation obtained from a semi-analytic model of galaxy formation. We divide galaxies into two populations: galaxies which have over-massive/under-massive black holes (BHs against the best-fitting BH mass—velocity dispersion relation. We find that galaxies with larger velocity dispersion have older stellar ages. We also find that galaxies with over-massive BHs have older stellar ages. These results are consistent with observational results obtained from Martín-Navarro et al. (2016. We tested the model with weak AGN feedback and find that galaxies with larger velocity dispersion have a younger stellar age.

Theoretical Re-evaluations of Scaling Relations between SMBHs and Their Host Galaxies–2. Importance of AGN Feedback Suggested by Stellar Age–Velocity Dispersion Relation

International Nuclear Information System (INIS)

Shirakata, Hikari; Kawaguchi, Toshihiro; Okamoto, Takashi; Ishiyama, Tomoaki

2017-01-01

We present the galactic stellar age—velocity dispersion relation obtained from a semi-analytic model of galaxy formation. We divide galaxies into two populations: galaxies which have over-massive/under-massive black holes (BHs) against the best-fitting BH mass—velocity dispersion relation. We find that galaxies with larger velocity dispersion have older stellar ages. We also find that galaxies with over-massive BHs have older stellar ages. These results are consistent with observational results obtained from Martín-Navarro et al. (2016). We tested the model with weak AGN feedback and find that galaxies with larger velocity dispersion have a younger stellar age.

Theoretical Re-evaluations of Scaling Relations between SMBHs and Their Host Galaxies–2. Importance of AGN Feedback Suggested by Stellar Age–Velocity Dispersion Relation

Energy Technology Data Exchange (ETDEWEB)

Shirakata, Hikari [Department of Cosmosciences, Graduate School of Science, Hokkaido University, Sapporo (Japan); Kawaguchi, Toshihiro [Department of Economics, Management and Information Science, Onomichi City University, Onomichi, Hiroshima (Japan); Okamoto, Takashi [Department of Cosmosciences, Graduate School of Science, Hokkaido University, Sapporo (Japan); Ishiyama, Tomoaki, E-mail: shirakata@astro1.sci.hokudai.ac.jp [Institute of Management and Information Technologies, Chiba University, Chiba (Japan)

2017-09-12

We present the galactic stellar age—velocity dispersion relation obtained from a semi-analytic model of galaxy formation. We divide galaxies into two populations: galaxies which have over-massive/under-massive black holes (BHs) against the best-fitting BH mass—velocity dispersion relation. We find that galaxies with larger velocity dispersion have older stellar ages. We also find that galaxies with over-massive BHs have older stellar ages. These results are consistent with observational results obtained from Martín-Navarro et al. (2016). We tested the model with weak AGN feedback and find that galaxies with larger velocity dispersion have a younger stellar age.

ICRH programmes for antennas and for plasma dispersion relation

International Nuclear Information System (INIS)

Soell, M.; Springmann, E.

1984-02-01

This report describes the computer programmes used for designing the ICRH antennas at IPP. In the first part of the report the underlying physical principles are discussed on which the programmes are based. 2-D (two-dimensional) and 3-D (three-dimensional) models are used. In the second part the input and output of the programmes is described, and in the third part some results on ICRH antennas built for existing machines at IPP and antennas for machines which are in the design and construction phase are presented. In Appendix I the formulae for the 2-D model including plasma density profiles are described and an investigation of this 2-D model on folded dipol antennae is given. In Appendix II the main formulae for a computer program for the complete hot dispersion relation is given; the application of the program for an ASDEX plasma (dispersion for the fast wave and Bernstein wave) is shown. (orig.)

Dispersion relation and growth rate of a relativistic electron beam propagating through a Langmuir wave wiggler

Science.gov (United States)

Zirak, H.; Jafari, S.

2015-06-01

In this study, a theory of free-electron laser (FEL) with a Langmuir wave wiggler in the presence of an axial magnetic field has been presented. The small wavelength of the plasma wave (in the sub-mm range) allows obtaining higher frequency than conventional wiggler FELs. Electron trajectories have been obtained by solving the equations of motion for a single electron. In addition, a fourth-order Runge-Kutta method has been used to simulate the electron trajectories. Employing a perturbation analysis, the dispersion relation for an electromagnetic and space-charge waves has been derived by solving the momentum transfer, continuity, and wave equations. Numerical calculations show that the growth rate increases with increasing the e-beam energy and e-beam density, while it decreases with increasing the strength of the axial guide magnetic field.

Traits related to species persistence and dispersal explain changes in plant communities subjected to habitat loss

DEFF Research Database (Denmark)

Marini, Lorenzo; Bruun, Hans Henrik; Heikkinen, Risto

2012-01-01

Aim Habitat fragmentation is a major driver of biodiversity loss but it is insufficiently known how much its effects vary among species with different life-history traits; especially in plant communities, the understanding of the role of traits related to species persistence and dispersal in dete...... rural landscapes in NW Europe, mitigating the spatial isolation of remaining grasslands should be accompanied by restoration measures aimed at improving habitat quality for low competitors, abiotically dispersed and perennial, clonal species.......Aim Habitat fragmentation is a major driver of biodiversity loss but it is insufficiently known how much its effects vary among species with different life-history traits; especially in plant communities, the understanding of the role of traits related to species persistence and dispersal...... in determining dynamics of species communities in fragmented landscapes is still limited. The primary aim of this study was to test how plant traits related to persistence and dispersal and their interactions modify plant species vulnerability to decreasing habitat area and increasing isolation. Location Five...

The Green's function approach to the neutron-inelastic-scattering determination of magnon dispersion relations for isotropic disordered magnets

International Nuclear Information System (INIS)

Czachor, A.; Al-Wahsh, H.

1999-01-01

Complete text of publication follows. To determine the neutron inelastic coherent scattering (MS) cross section for disordered magnets a system of equations of motion for the Green functions (GF) related to the localized-spin correlation-functions, has been exploited. The higher-order Green functions are decoupled using a symmetric 'equal access' (EA) form of the RPA decoupling scheme. The quasi-crystal approximation (QCA) was applied to construct the space-time Fourier transformed GF Q (ω)> related to neutron scattering. On assuming isotropy of the magnetic structure and a short range coupling between the spins (on the sphere approximation, OSA) we have found an explicit analytic form of this function. Poles of the Q (ω)> determine the dispersion relation ω = ω Q for elementary excitations, such as they are seen in the MS experiment - the positions of the MS profile maxima in the ω-Q space. Single formula for the dispersion relations derived here covers a variety of isotropic spin structures: in particular disordered 'longitudinal' ferrornagnets (ω ∼Q z , Q→ 0), disordered 'transverse' spin structures (ω ∼Q, Q→0), and some intermediate cases. For the system of spins coupled identically - the magnetization and the magnetic susceptibility calculated within the present EA-RPA approach do agree with the results of exact calculations. It provides an interesting insight into the nature of the RPA approach do agree with the results of exact calculations. It provides an interesting insight into the nature of the RPA - treatment of the localized spin dynamics. (author)

Dispersion relations in the noncommutative φ3 and Wess-Zumino model in the Yang-Feldman formalism

International Nuclear Information System (INIS)

Doescher, C.; Zahn, J.

2006-05-01

We study dispersion relations in the noncommutative φ 3 and Wess-Zumino model in the Yang-Feldman formalism at one-loop order. Non-planar graphs lead to a distortion of the dispersion relation. We find that this effect is small if the scale of noncommutativity is identified with the Planck scale and parameters typical for a Higgs field are employed. (Orig.)

Relation of wave energy and momentum with the plasma dispersion relation in an inhomogeneous plasma

International Nuclear Information System (INIS)

Berk, H.L.; Pfirsch, D.

1988-01-01

The expressions for wave energy and angular momentum commonly used in homogeneous and near-homogeneous media is generalized to inhomogeneous media governed by a nonlocal conductivity tensor. The expression for wave energy applies to linear excitations in an arbitrary three-dimensional equilibrium, while the expression for angular momentum applies to linear excitations of azimuthally symmetric equilibria. The wave energy E-script/sub wave/ is interpreted as the energy transferred from linear external sources to the plasma if there is no dissipation. With dissipation, such a simple interpretation is lacking as energy is also thermally absorbed. However, for azimuthally symmetric equilibria, the expression for the wave energy in a frame rotating with a frequency ω can be unambiguously separated from thermal energy. This expression is given by E-script/sub wave/ -ωL/sub wave/ l, where L/sub wave/ is the wave angular momentum defined in the text and l the azimuthal wavenumber and it is closely related to the real part of a dispersion relation for marginal stability. The imaginary part of the dispersion is closely related to the energy input into a system. Another useful quantity discussed is the impedance form, which can be used for three-dimensional equilibrium without an ignorable coordinate and the expression is closely related to the wave impedance used in antenna theory. Applications to stability theory are also discussed

Selfing ability and dispersal are positively related, but not affected by range position: a multispecies study on southern African Asteraceae.

Science.gov (United States)

de Waal, C; Rodger, J G; Anderson, B; Ellis, A G

2014-05-01

Dispersal and breeding system traits are thought to affect colonization success. As species have attained their present distribution ranges through colonization, these traits may vary geographically. Although several theories predict associations between dispersal ability, selfing ability and the relative position of a population within its geographic range, there is little theoretical or empirical consensus on exactly how these three variables are related. We investigated relationships between dispersal ability, selfing ability and range position across 28 populations of 13 annual, wind-dispersed Asteraceae species from the Namaqualand region of South Africa. Controlling for phylogeny, relative dispersal ability--assessed from vertical fall time of fruits--was positively related to an index of autofertility--determined from hand-pollination experiments. These findings support the existence of two discrete syndromes: high selfing ability associated with good dispersal and obligate outcrossing associated with lower dispersal ability. This is consistent with the hypothesis that selection for colonization success drives the evolution of an association between these traits. However, no general effect of range position on dispersal or breeding system traits was evident. This suggests selection on both breeding system and dispersal traits acts consistently across distribution ranges. © 2014 The Authors. Journal of Evolutionary Biology © 2014 European Society For Evolutionary Biology.

Stellar Velocity Dispersion: Linking Quiescent Galaxies to Their Dark Matter Halos

Science.gov (United States)

Zahid, H. Jabran; Sohn, Jubee; Geller, Margaret J.

2018-06-01

We analyze the Illustris-1 hydrodynamical cosmological simulation to explore the stellar velocity dispersion of quiescent galaxies as an observational probe of dark matter halo velocity dispersion and mass. Stellar velocity dispersion is proportional to dark matter halo velocity dispersion for both central and satellite galaxies. The dark matter halos of central galaxies are in virial equilibrium and thus the stellar velocity dispersion is also proportional to dark matter halo mass. This proportionality holds even when a line-of-sight aperture dispersion is calculated in analogy to observations. In contrast, at a given stellar velocity dispersion, the dark matter halo mass of satellite galaxies is smaller than virial equilibrium expectations. This deviation from virial equilibrium probably results from tidal stripping of the outer dark matter halo. Stellar velocity dispersion appears insensitive to tidal effects and thus reflects the correlation between stellar velocity dispersion and dark matter halo mass prior to infall. There is a tight relation (≲0.2 dex scatter) between line-of-sight aperture stellar velocity dispersion and dark matter halo mass suggesting that the dark matter halo mass may be estimated from the measured stellar velocity dispersion for both central and satellite galaxies. We evaluate the impact of treating all objects as central galaxies if the relation we derive is applied to a statistical ensemble. A large fraction (≳2/3) of massive quiescent galaxies are central galaxies and systematic uncertainty in the inferred dark matter halo mass is ≲0.1 dex thus simplifying application of the simulation results to currently available observations.

Tracer dispersion in two-dimensional rough fractures.

Science.gov (United States)

Drazer, G; Koplik, J

2001-05-01

Tracer diffusion and hydrodynamic dispersion in two-dimensional fractures with self-affine roughness are studied by analytic and numerical methods. Numerical simulations were performed via the lattice-Boltzmann approach, using a boundary condition for tracer particles that improves the accuracy of the method. The reduction in the diffusive transport, due to the fractal geometry of the fracture surfaces, is analyzed for different fracture apertures. In the limit of small aperture fluctuations we derive the correction to the diffusive coefficient in terms of the tortuosity, which accounts for the irregular geometry of the fractures. Dispersion is studied when the two fracture surfaces are simply displaced normally to the mean fracture plane and when there is a lateral shift as well. Numerical results are analyzed using the Lambda parameter, related to convective transport within the fracture, and simple arguments based on lubrication approximation. At very low Péclet number, in the case where fracture surfaces are laterally shifted, we show using several different methods that convective transport reduces dispersion.

Numerical method for the dispersion relation of a hot and inhomogeneous plasma with an electron beam

International Nuclear Information System (INIS)

Devia, A.; Orrego, C.E.; Buitrago, G.

1990-01-01

A numerical method that is based in kinetic theory (Vlasov-Poison equations) was developed in order to calculate the dispersion relation for the interaction between a hot cylindrical and electron beam in any temperature and density. The plasma-beam system is located in a strong magnetic field. Many examples showing the effect of the temperatures and densities on the dispersion relation are given. (Author)

Relation between the behaviors of P-wave and QT dispersions in elderly patients with heart failure

Directory of Open Access Journals (Sweden)

Szlejf Cláudia

2002-01-01

Full Text Available OBJECTIVE: To assess the relation between P-wave and QT dispersions in elderly patients with heart failure. METHODS: Forty-seven elderly patients (75.6±6 years with stable heart failure in NYHA functional classes II or III and with ejection fractions of 37±6% underwent body surface mapping to analyze P-wave and QT dispersions. The degree of correlation between P-wave and QT dispersions was assessed, and P-wave dispersion values in patients with QT dispersion greater than and smaller than 100 ms were compared. RESULTS: The mean values of P-wave and QT dispersions were 54±14 ms and 68±27 ms, respectively. The correlation between the 2 variables was R=0.41 (p=0.04. In patients with QT dispersion values > 100 ms, P-wave dispersion was significantly greater than in those with QT dispersion values < 100 ms (58±16 vs 53±12 ms, p=0.04 . CONCLUSION: Our results suggest that, in elderly patients with heart failure, a correlation between the values of P-wave and QT dispersions exists. These findings may have etiopathogenic, pathophysiologic, prognostic, and therapeutic implications, which should be investigated in other studies.

Analytical study of dispersion relations for shear horizontal wave propagation in plates with periodic stubs

KAUST Repository

Xu, Yanlong

2015-08-01

The coupled mode theory with coupling of diffraction modes and waveguide modes is usually used on the calculations of transmission and reflection coefficients for electromagnetic waves traveling through periodic sub-wavelength structures. In this paper, I extend this method to derive analytical solutions of high-order dispersion relations for shear horizontal (SH) wave propagation in elastic plates with periodic stubs. In the long wavelength regime, the explicit expression is obtained by this theory and derived specially by employing an effective medium. This indicates that the periodical stubs are equivalent to an effective homogenous layer in the long wavelength. Notably, in the short wavelength regime, high-order diffraction modes in the plate and high-order waveguide modes in the stubs are considered with modes coupling to compute the band structures. Numerical results of the coupled mode theory fit pretty well with the results of the finite element method (FEM). In addition, the band structures\\' evolution with the height of the stubs and the thickness of the plate shows clearly that the method can predict well the Bragg band gaps, locally resonant band gaps and high-order symmetric and anti-symmetric thickness-twist modes for the periodically structured plates. © 2015 Elsevier B.V.

New photon-nucleon dispersion relation for evaluating the Thomson limit using rising total cross sections

International Nuclear Information System (INIS)

Dean, N.W.

1978-01-01

New data showing that the photon-nucleon total cross section increases with energy for ν > or = 50 GeV invalidate earlier comparisons with dispersion relations. Parametrization of the data are presented and used in a new formulation of the dispersion relations, in which an assumed asymptotic behavior avoids the need for subtraction. With this form the fitted amplitude can be compared directly with the Thomson limit. The experimental uncertainties are shown to have a significant effect upon such a comparison

Diffusion related isotopic fractionation effects with one-dimensional advective–dispersive transport

Energy Technology Data Exchange (ETDEWEB)

Xu, Bruce S. [Civil Engineering Department, University of Toronto, 35 St George Street, Toronto, ON M5S 1A4 (Canada); Lollar, Barbara Sherwood [Earth Sciences Department, University of Toronto, 22 Russell Street, Toronto, ON M5S 3B1 (Canada); Passeport, Elodie [Civil Engineering Department, University of Toronto, 35 St George Street, Toronto, ON M5S 1A4 (Canada); Chemical Engineering and Applied Chemistry Department, University of Toronto, 200 College Street, Toronto, ON M5S 3E5 (Canada); Sleep, Brent E., E-mail: sleep@ecf.utoronto.ca [Civil Engineering Department, University of Toronto, 35 St George Street, Toronto, ON M5S 1A4 (Canada)

2016-04-15

Aqueous phase diffusion-related isotope fractionation (DRIF) for carbon isotopes was investigated for common groundwater contaminants in systems in which transport could be considered to be one-dimensional. This paper focuses not only on theoretically observable DRIF effects in these systems but introduces the important concept of constraining “observable” DRIF based on constraints imposed by the scale of measurements in the field, and on standard limits of detection and analytical uncertainty. Specifically, constraints for the detection of DRIF were determined in terms of the diffusive fractionation factor, the initial concentration of contaminants (C{sub 0}), the method detection limit (MDL) for isotopic analysis, the transport time, and the ratio of the longitudinal mechanical dispersion coefficient to effective molecular diffusion coefficient (D{sub mech}/D{sub eff}). The results allow a determination of field conditions under which DRIF may be an important factor in the use of stable carbon isotope measurements for evaluation of contaminant transport and transformation for one-dimensional advective–dispersive transport. This study demonstrates that for diffusion-dominated transport of BTEX, MTBE, and chlorinated ethenes, DRIF effects are only detectable for the smaller molar mass compounds such as vinyl chloride for C{sub 0}/MDL ratios of 50 or higher. Much larger C{sub 0}/MDL ratios, corresponding to higher source concentrations or lower detection limits, are necessary for DRIF to be detectable for the higher molar mass compounds. The distance over which DRIF is observable for VC is small (less than 1 m) for a relatively young diffusive plume (< 100 years), and DRIF will not easily be detected by using the conventional sampling approach with “typical” well spacing (at least several meters). With contaminant transport by advection, mechanical dispersion, and molecular diffusion this study suggests that in field sites where D{sub mech}/D{sub eff} is

Diffusion related isotopic fractionation effects with one-dimensional advective–dispersive transport

International Nuclear Information System (INIS)

Xu, Bruce S.; Lollar, Barbara Sherwood; Passeport, Elodie; Sleep, Brent E.

2016-01-01

Aqueous phase diffusion-related isotope fractionation (DRIF) for carbon isotopes was investigated for common groundwater contaminants in systems in which transport could be considered to be one-dimensional. This paper focuses not only on theoretically observable DRIF effects in these systems but introduces the important concept of constraining “observable” DRIF based on constraints imposed by the scale of measurements in the field, and on standard limits of detection and analytical uncertainty. Specifically, constraints for the detection of DRIF were determined in terms of the diffusive fractionation factor, the initial concentration of contaminants (C_0), the method detection limit (MDL) for isotopic analysis, the transport time, and the ratio of the longitudinal mechanical dispersion coefficient to effective molecular diffusion coefficient (D_m_e_c_h/D_e_f_f). The results allow a determination of field conditions under which DRIF may be an important factor in the use of stable carbon isotope measurements for evaluation of contaminant transport and transformation for one-dimensional advective–dispersive transport. This study demonstrates that for diffusion-dominated transport of BTEX, MTBE, and chlorinated ethenes, DRIF effects are only detectable for the smaller molar mass compounds such as vinyl chloride for C_0/MDL ratios of 50 or higher. Much larger C_0/MDL ratios, corresponding to higher source concentrations or lower detection limits, are necessary for DRIF to be detectable for the higher molar mass compounds. The distance over which DRIF is observable for VC is small (less than 1 m) for a relatively young diffusive plume (< 100 years), and DRIF will not easily be detected by using the conventional sampling approach with “typical” well spacing (at least several meters). With contaminant transport by advection, mechanical dispersion, and molecular diffusion this study suggests that in field sites where D_m_e_c_h/D_e_f_f is larger than 10, DRIF

Relating Derived Relations as a Model of Analogical Reasoning: Reaction Times and Event-Related Potentials

Science.gov (United States)

Barnes-Holmes, Dermot; Regan, Donal; Barnes-Holmes, Yvonne; Commins, Sean; Walsh, Derek; Stewart, Ian; Smeets, Paul M.; Whelan, Robert; Dymond, Simon

2005-01-01

The current study aimed to test a Relational Frame Theory (RFT) model of analogical reasoning based on the relating of derived same and derived difference relations. Experiment 1 recorded reaction time measures of similar-similar (e.g., "apple is to orange as dog is to cat") versus different-different (e.g., "he is to his brother as…

A new numerical method to solve the dispersion relation in multispecies plasma

International Nuclear Information System (INIS)

Cereceda, C.; Puerta, J.

2000-01-01

In this paper a new accurate and fast method for solving the linear dispersion relation for multispecies plasma is introduced. The method uses a four poles fractional approximation for the Z dispersion function, transforming the dispersion relation into a polynomial form. Time and space growth rates are then calculated. Calculations for a single beam - plasma are carried out being in good agreement with several authors. This method is very effective to simplify the calculation of growth rates in multi-ion plasmas. For multispecies plasmas several new modes of propagation arise. For two ion beam - plasma system, two slow modes can propagate, both which are unstable. Two maxima in the growth rates corresponding to each of these modes can be excited. The instability of one of the slow modes is fed by the energy of the light ion beam and the other one is fed by heavy beam ions. Each one of these two maxima is increased when the concentration of the corresponding species increases. But even for a small concentration of the light beam, the growth rate of the mode fed by it is the largest one, because in the single ion beam-plasma system the lighter ion yields the largest growth rate. (orig.)

EXPERIMENTAL DETERMINATION OF WHISTLER WAVE DISPERSION RELATION IN THE SOLAR WIND

Energy Technology Data Exchange (ETDEWEB)

Stansby, D.; Horbury, T. S.; Chen, C. H. K.; Matteini, L., E-mail: david.stansby14@imperial.ac.uk [Department of Physics, Imperial College London, London SW7 2AZ (United Kingdom)

2016-09-20

The origins and properties of large-amplitude whistler wavepackets in the solar wind are still unclear. In this Letter, we utilize single spacecraft electric and magnetic field waveform measurements from the ARTEMIS mission to calculate the plasma frame frequency and wavevector of individual wavepackets over multiple intervals. This allows direct comparison of experimental measurements with theoretical dispersion relations to identify the observed waves as whistler waves. The whistlers are right-hand circularly polarized, travel anti-sunward, and are aligned with the background magnetic field. Their dispersion is strongly affected by the local electron parallel beta in agreement with linear theory. The properties measured are consistent with the electron heat flux instability acting in the solar wind to generate these waves.

Solubility enhancement of benfotiamine, a lipid derivative of thiamine by solid dispersion technique.

Science.gov (United States)

Patel, S M; Patel, R P; Prajapati, B G

2012-03-01

The present study was aimed to increase the solubility of the poorly water soluble drug benfotiamine using hydrophilic polymers (PVP K-30 and HPMC E4). Solid dispersions were prepared by kneading method. Phase solubility study, in-vitro dissolution of pure drug, physical mixtures and solid dispersions were carried out. PVP and HPMC were found to be effective in increasing the dissolution of Benfotiamine in solid dispersions when compared to pure drug. FT-IR, differential scanning calorimetry and X-ray diffractometry studies were carried out in order to characterize the drug and solid dispersion. To conclude that, the prepared solid dispersion of PVP-30 may to effectively used for the enhancement of solubility of poorly water soluble drugs such as benfotiamine.

Solubility enhancement of benfotiamine, a lipid derivative of thiamine by solid dispersion technique

Directory of Open Access Journals (Sweden)

S M Patel

2012-01-01

Full Text Available The present study was aimed to increase the solubility of the poorly water soluble drug benfotiamine using hydrophilic polymers (PVP K-30 and HPMC E4. Solid dispersions were prepared by kneading method. Phase solubility study, in-vitro dissolution of pure drug, physical mixtures and solid dispersions were carried out. PVP and HPMC were found to be effective in increasing the dissolution of Benfotiamine in solid dispersions when compared to pure drug. FT-IR, differential scanning calorimetry and X-ray diffractometry studies were carried out in order to characterize the drug and solid dispersion. To conclude that, the prepared solid dispersion of PVP-30 may to effectively used for the enhancement of solubility of poorly water soluble drugs such as benfotiamine.

Relating derived relations as a model of analogical reasoning: reaction times and event-related potentials.

Science.gov (United States)

Barnes-Holmes, Dermot; Regan, Donal; Barnes-Holmes, Yvonne; Commins, Sean; Walsh, Derek; Stewart, Ian; Smeets, Paul M; Whelan, Robert; Dymond, Simon

2005-11-01

The current study aimed to test a Relational Frame Theory (RFT) model of analogical reasoning based on the relating of derived same and derived difference relations. Experiment 1 recorded reaction time measures of similar-similar (e.g., "apple is to orange as dog is to cat") versus different-different (e.g., "he is to his brother as chalk is to cheese") derived relational responding, in both speed-contingent and speed-noncontingent conditions. Experiment 2 examined the event-related potentials (ERPs) associated with these two response patterns. Both experiments showed similar-similar responding to be significantly faster than different-different responding. Experiment 2 revealed significant differences between the waveforms of the two response patterns in the left-hemispheric prefrontal regions; different-different waveforms were significantly more negative than similar-similar waveforms. The behavioral and neurophysiological data support the RFT prediction that, all things being equal, similar-similar responding is relationally "simpler" than, and functionally distinct from, different-different analogical responding. The ERP data were fully consistent with findings in the neurocognitive literature on analogy. These findings strengthen the validity of the RFT model of analogical reasoning and supplement the behavior-analytic approach to analogy based on the relating of derived relations.

The effect of inertially viscous interphase interaction on the acoustic characteristics of disperse media

International Nuclear Information System (INIS)

Vladimir S Fedotovsky; Tatiana N Vereshchagina; Alexey V Derbenev

2005-01-01

Full text of publication follows: The vibratory-wave dynamics of disperse media with uniformly distributed spherical and ellipsoidal inclusions is considered on the basis of the concept of effective dynamic properties. The notions of effective dynamic density and translation viscosity taking account of the effects of the inertial and viscous interaction of liquid and disperse inclusions are introduced. The effective dynamic properties governing the process of wave propagation in disperse media depend both on the density, viscosity and concentration of components and on the form and orientation of inclusions. It is shown that for disperse media with inclusions as oblate ellipsoids of rotation the effective dynamic density takes the maximum value, whereas for the medium with inclusions as extended ellipsoids - the minimum one. The dynamic density of the medium with spherical inclusions takes the intermediate value. Based on the offered concept, the relations for sound velocity and attenuation in disperse media are derived. It is shown that the acoustic characteristics of disperse media essentially depend on the form of the ellipsoidal inclusions and their orientation relative to the direction of wave propagation. (authors)

Correction of Cardy–Verlinde formula for Fermions and Bosons with modified dispersion relation

Energy Technology Data Exchange (ETDEWEB)

Sadatian, S. Davood, E-mail: sd-sadatian@um.ac.ir; Dareyni, H.

2017-05-15

Cardy–Verlinde formula links the entropy of conformal symmetry field to the total energy and its Casimir energy in a D-dimensional space. To correct black hole thermodynamics, modified dispersion relation can be used which is proposed as a general feature of quantum gravity approaches. In this paper, the thermodynamics of Schwarzschild four-dimensional black hole is corrected using the modified dispersion relation for Fermions and Bosons. Finally, using modified thermodynamics of Schwarzschild four-dimensional black hole, generalization for Cardy–Verlinde formula is obtained. - Highlights: • The modified Cardy–Verlinde formula obtained using MDR for Fermions and Bosons. • The modified entropy of the black hole used to correct the Cardy–Verlinde formula. • The modified entropy of the CFT has been obtained.

Dispersion relation approach to sub-barrier heavy ion fusion reactions

International Nuclear Information System (INIS)

Franzin, V.L.M.; Hussein, M.S.

1986-07-01

With the aid of an inverse dispersion relation, which gives the imaginary part of the fusion inclusive polarization potential (IPP) in terms of the principal part integral involving the real part of the IPP, the sub-barrier fusion of heavy ions is discussed. The system 16 O+ A Sm is taken as an example. The reactive content of the extracted IPP is analysed within the coupled channels theory. (Author) [pt

A new derivation of Luescher F-term and fluctuations around the giant magnon

International Nuclear Information System (INIS)

Heller, Michal P.; Janik, Romuald A.; Lukowski, Tomasz

2008-01-01

In this paper we give a new derivation of the generalized Luescher F-term formula from a summation over quadratic fluctuations around a given soliton. The result is very general providing that S-matrix is diagonal and is valid for arbitrary dispersion relation. We then apply this formalism to compute the leading finite size corrections to the giant magnon dispersion relation coming from quantum fluctuations.

Dispersion relation analysis of the neutral kaon regeneration amplitude in carbon

CERN Document Server

Angelopoulos, Angelos; Locher, M P; Markushin, V E; Aslanides, Elie; Backenstoss, Gerhard; Bargassa, P; Behnke, O; Benelli, A; Bertin, V; Blanc, F; Bloch, P; Carlson, P J; Carroll, M; Cawley, E; Chertok, M B; Danielsson, M; Dejardin, M; Derré, J; Ealet, A; Eleftheriadis, C; Faravel, L; Festcher, W; Fidecaro, Maria; Filipcic, A; Francis, D; Fry, J; Gabathuler, Erwin; Gamet, R; Gerber, H J; Go, A; Haselden, A; Hayman, P J; Henry-Coüannier, F; Hollander, R W; Jon-And, K; Kettle, P R; Kokkas, P; Kreuger, R; Le Gac, R; Leimgruber, F; Mandic, I; Manthos, N; Marel, Gérard; Mikuz, M; Miller, J; Montanet, François; Müller, A; Nakada, Tatsuya; Pagels, B; Papadopoulos, I M; Pavlopoulos, P; Polivka, G; Rickenbach, R; Roberts, B L; Ruf, T; Schäfer, M; Schaller, L A; Schietinger, T; Schopper, A; Tauscher, Ludwig; Thibault, C; Touchard, F; Touramanis, C; van Eijk, C W E; Vlachos, S; Weber, P; Wigger, O; Wolter, M; Zavrtanik, D; Zimmerman, D

1999-01-01

We apply a forward dispersion relation to the regeneration amplitude for kaon scattering on /sup 12/C using all available data. The CPLEAR data at low energies allow the determination of the net contribution from the subthreshold $9 region which turns out to be much smaller than earlier evaluations, solving a long standing puzzle. (29 refs).

Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space

Energy Technology Data Exchange (ETDEWEB)

Zahn, J.W.

2006-12-15

We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation function of the field strength in noncommutative quantum electrodynamics to second order. At this, we take into account the covariant coordinates that allow the construction of local gauge invariant quantities (observables). It turns out that this does not remove the well-known severe infrared problem, as one might have hoped. Instead, things become worse, since nonlocal divergences appear. We also show that these cancel in a supersymmetric version of the theory if the covariant coordinates are adjusted accordingly. Furthermore, we study the {phi}{sup 3} and the Wess-Zumino model and show that the distortion of the dispersion relations is moderate for parameters typical for the Higgs field. We also discuss the formulation of gauge theories on noncommutative spaces and study classical electrodynamics on the noncommutative Minkowski space using covariant coordinates. In particular, we compute the change of the speed of light due to nonlinear effects in the presence of a background field. Finally, we examine the so-called twist approach to quantum field theory on the noncommutative Minkowski space and point out some conceptual problems of this approach. (orig.)

Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space

International Nuclear Information System (INIS)

Zahn, J.W.

2006-12-01

We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation function of the field strength in noncommutative quantum electrodynamics to second order. At this, we take into account the covariant coordinates that allow the construction of local gauge invariant quantities (observables). It turns out that this does not remove the well-known severe infrared problem, as one might have hoped. Instead, things become worse, since nonlocal divergences appear. We also show that these cancel in a supersymmetric version of the theory if the covariant coordinates are adjusted accordingly. Furthermore, we study the Φ 3 and the Wess-Zumino model and show that the distortion of the dispersion relations is moderate for parameters typical for the Higgs field. We also discuss the formulation of gauge theories on noncommutative spaces and study classical electrodynamics on the noncommutative Minkowski space using covariant coordinates. In particular, we compute the change of the speed of light due to nonlinear effects in the presence of a background field. Finally, we examine the so-called twist approach to quantum field theory on the noncommutative Minkowski space and point out some conceptual problems of this approach. (orig.)

Magnon dispersion relation and exchange interactions in MnF2

DEFF Research Database (Denmark)

Nikotin, O.; Lindgård, Per-Anker; Dietrich, O. W.

1969-01-01

The magnon dispersion relation for MnF2 at 4·2 °K has been measured by means of the triple-axis neutron scattering technique along the symmetry lines in the (010) plane of the Brillouin zone. Using an exact dipole model, the three nearest-neighbour exchange constants were found to be J1 = 0·028 ± 0......·001 mev, J2 = -0·152 ± 0·001 mev and J3 = -0·004 ± 0·001 mev. The second moment was also calculated with this model. The density of magnon states was evaluated by applying a six-parameter simulation of the dispersion surface. The critical points in the density of states agree well with those obtained...... by optical double-magnon experiments, whereas the detailed shape of the density of states differs significantly, indicating that the effect of magnon-magnon interactions rather than that of distant-neighbour exchange is of primary importance in the optical measurements....

Theoretical Analysis of the Relative Significance of Thermodynamic and Kinetic Dispersion in the dc and ac Voltammetry of Surface-Confined Molecules

KAUST Repository

Morris, Graham P.; Baker, Ruth E.; Gillow, Kathryn; Davis, Jason J.; Gavaghan, David J.; Bond, Alan M.

2015-01-01

© 2015 American Chemical Society. Commonly, significant discrepancies are reported in theoretical and experimental comparisons of dc voltammograms derived from a monolayer or close to monolayer coverage of redox-active surface-confined molecules. For example, broader-than-predicted voltammetric wave shapes are attributed to the thermodynamic or kinetic dispersion derived from distributions in reversible potentials (E⁰) and electrode kinetics (k⁰), respectively. The recent availability of experimentally estimated distributions of E⁰ and k⁰ values derived from the analysis of data for small numbers of surface-confined modified azurin metalloprotein molecules now allows more realistic modeling to be undertaken, assuming the same distributions apply under conditions of high surface coverage relevant to voltammetric experiments. In this work, modeling based on conventional and stochastic kinetic theory is considered, and the computationally far more efficient conventional model is shown to be equivalent to the stochastic one when large numbers of molecules are present. Perhaps unexpectedly, when experimentally determined distributions of E⁰ and k⁰ are input into the model, thermodynamic dispersion is found to be unimportant and only kinetic dispersion contributes significantly to the broadening of dc voltammograms. Simulations of ac voltammetric experiments lead to the conclusion that the ac method, particularly when the analysis of kinetically very sensitive higher-order harmonics is undertaken, are far more sensitive to kinetic dispersion than the dc method. ac methods are therefore concluded to provide a potentially superior strategy for addressing the inverse problem of determining the k⁰ distribution that could give rise to the apparent anomalies in surface-confined voltammetry.

Theoretical Analysis of the Relative Significance of Thermodynamic and Kinetic Dispersion in the dc and ac Voltammetry of Surface-Confined Molecules

KAUST Repository

Morris, Graham P.

2015-05-05

© 2015 American Chemical Society. Commonly, significant discrepancies are reported in theoretical and experimental comparisons of dc voltammograms derived from a monolayer or close to monolayer coverage of redox-active surface-confined molecules. For example, broader-than-predicted voltammetric wave shapes are attributed to the thermodynamic or kinetic dispersion derived from distributions in reversible potentials (E⁰) and electrode kinetics (k⁰), respectively. The recent availability of experimentally estimated distributions of E⁰ and k⁰ values derived from the analysis of data for small numbers of surface-confined modified azurin metalloprotein molecules now allows more realistic modeling to be undertaken, assuming the same distributions apply under conditions of high surface coverage relevant to voltammetric experiments. In this work, modeling based on conventional and stochastic kinetic theory is considered, and the computationally far more efficient conventional model is shown to be equivalent to the stochastic one when large numbers of molecules are present. Perhaps unexpectedly, when experimentally determined distributions of E⁰ and k⁰ are input into the model, thermodynamic dispersion is found to be unimportant and only kinetic dispersion contributes significantly to the broadening of dc voltammograms. Simulations of ac voltammetric experiments lead to the conclusion that the ac method, particularly when the analysis of kinetically very sensitive higher-order harmonics is undertaken, are far more sensitive to kinetic dispersion than the dc method. ac methods are therefore concluded to provide a potentially superior strategy for addressing the inverse problem of determining the k⁰ distribution that could give rise to the apparent anomalies in surface-confined voltammetry.

A robust approach for analysing dispersion of elastic waves in an orthotropic cylindrical shell

Science.gov (United States)

Kaplunov, J.; Nobili, A.

2017-08-01

Dispersion of elastic waves in a thin orthotropic cylindrical shell is considered, within the framework of classical 2D Kirchhoff-Love theory. In contrast to direct multi-parametric analysis of the lowest propagating modes, an alternative robust approach is proposed that simply requires evaluation of the evanescent modes (quasi-static edge effect), which, at leading order, do not depend on vibration frequency. A shortened dispersion relation for the propagating modes is then derived by polynomial division and its accuracy is numerically tested against the full Kirchhoff-Love dispersion relation. It is shown that the same shortened relation may be also obtained from a refined dynamic version of the semi-membrane theory for cylindrical shells. The presented results may be relevant for modelling various types of nanotubes which, according to the latest experimental findings, possess strong material anisotropy.

Efficient approximations of dispersion relations in optical waveguides with varying refractive-index profiles.

Science.gov (United States)

Li, Yutian; Zhu, Jianxin

2015-05-04

In this paper we consider the problem of computing the eigen-modes for the varying refractive-index profile in an open waveguide. We first approximate the refractive-index by a piecewise polynomial of degree two, and the corresponding Sturm-Liouville problem (eigenvalue problem) of the Helmholtz operator in each layer can be solved analytically by the Kummer functions. Then, analytical approximate dispersion equations are established for both TE and TM cases. Furthermore, the approximate dispersion equations converge fast to the exact ones for the continuous refractive-index function as the maximum value of the subinterval sizes tends to zero. Suitable numerical methods, such as Müller's method or the chord secant method, may be applied to the dispersion relations to compute the eigenmodes. Numerical simulations show that our method is very practical and efficient for computing eigenmodes.

Scaling of Natal Dispersal Distances in Terrestrial Birds and Mammals

Directory of Open Access Journals (Sweden)

Glenn D. Sutherland

2000-07-01

Full Text Available Natal dispersal is a process that is critical in the spatial dynamics of populations, including population spread, recolonization, and gene flow. It is a central focus of conservation issues for many vertebrate species. Using data for 77 bird and 68 mammal species, we tested whether median and maximum natal dispersal distances were correlated with body mass, diet type, social system, taxonomic family, and migratory status. Body mass and diet type were found to predict both median and maximum natal dispersal distances in mammals: large species dispersed farther than small ones, and carnivorous species dispersed farther than herbivores and omnivores. Similar relationships occurred for carnivorous bird species, but not for herbivorous or omnivorous ones. Natal dispersal distances in birds or mammals were not significantly related to broad categories of social systems. Only in birds were factors such as taxonomic relatedness and migratory status correlated with natal dispersal, and then only for maximum distances. Summary properties of dispersal processes appeared to be derived from interactions among behavioral and morphological characteristics of species and from their linkages to the dynamics of resource availability in landscapes. In all the species we examined, most dispersers moved relatively short distances, and long-distance dispersal was uncommon. On the basis of these findings, we fit an empirical model based on the negative exponential distribution for calculating minimum probabilities that animals disperse particular distances from their natal areas. This model, coupled with knowledge of a species' body mass and diet type, can be used to conservatively predict dispersal distances for different species and examine possible consequences of large-scale habitat alterations on connectedness between populations. Taken together, our results can provide managers with the means to identify species vulnerable to landscape-level habitat changes

Selective dispersive liquid–liquid microextraction and preconcentration of Ni(II) into a micro droplet followed by ETAAS determination using a yellow Schiff's base bisazanyl derivative

International Nuclear Information System (INIS)

Alizadeh, Kamal; Nemati, Hadi; Zohrevand, Somaieh; Hashemi, Payman; Kakanejadifard, Ali; Shamsipur, Mojtaba; Ganjali, Mohammad Reza; Faridbod, Farnoush

2013-01-01

A simple, rapid and sensitive method was developed for the selective separation and preconcentration of Ni(II) using dispersive liquid–liquid microextraction, by a yellow Schiff's base bisazanyl derivative, as a selective complexing agent. In this method, a mixture of 45 μL chloroform (extraction solvent) and 450 μL tetrahydrofuran (dispersive solvent) is rapidly injected by syringe into a 5 mL aqueous sample containing 3% (w/v) sodium chloride and an appropriate amount of the Schiff's base. As a result, a cloudy solution is formed by entire dispersion of the extraction solvent into the aqueous phase. After centrifuging for 5 min at 5000 rpm, the sedimented phase is directly injected into the electrothermal atomic absorption spectrometry for Ni(II) determination. Some important parameters, such as kind and volume of extraction and dispersive solvents, extraction time, salt effect, pH and concentration of the chelating agent have been optimized. Under the optimum conditions, the enrichment factor for the presented method is 138. The calibration curve was linear over a nickel concentration range of 10–50 ng mL −1 . The detection limit and relative standard deviation were 0.04 ng mL −1 and 2.1%, respectively. The method was successfully applied to the extraction and determination of Ni(II) in different water samples. - Highlights: ► A new synthesized schiff's base was used for selective separation of Ni(II) ions. ► The method based on DLLME was successfully applied to the determination of Ni(II). ► A cloudy solution is formed by entire dispersion of the extraction solvent into the aqueous phase. ► In this work, the response surface analysis was used for the optimization purpose. ► The curvature of response surface reflects the interactive effect of the variables.

Subtracted Dispersion Relations for In-medium Meson Correlators in QCD Sum Rules

Energy Technology Data Exchange (ETDEWEB)

Florkowski, W; Broniowski, W [The H. Niewodniczanski Institute of Nuclear Physics, Cracow (Poland)

1999-01-01

We analyze subtracted dispersion relations for meson correlators at finite baryon density and temperature. Such relations are needed for QCD sum rules. We point out that importance of scattering terms, as well as finite, well-defined subtraction constants. Both are necessary for consistency, in particular for the equality of the longitudinal and transverse correlators in the limit of the vanishing three-momentum of mesons relative to the medium. We present detailed calculations in various mesonic channels of the Fermi gas of nucleons. (author)

Three-particle physics and dispersion relation theory

CERN Document Server

Anisovich, A V; Matveev, M A; Nikonov, V A; Nyiri, J; Sarantsev, A V

2013-01-01

The necessity of describing three-nucleon and three-quark systems have led to a constant interest in the problem of three particles. The question of including relativistic effects appeared together with the consideration of the decay amplitude in the framework of the dispersion technique. The relativistic dispersion description of amplitudes always takes into account processes connected with the investigated reaction by the unitarity condition or by virtual transitions; in the case of three-particle processes they are, as a rule, those where other many-particle states and resonances are produced. The description of these interconnected reactions and ways of handling them is the main subject of the book.

Spatial dispersion effects in spectral line broadening by pressure. I. The Bouguer Law and absorption coefficient

International Nuclear Information System (INIS)

Cherkasov, M.R.

1995-01-01

Based on the general principles of semiclassical electrodynamics, the Bouguer law is derived, and the expression for the absorption coefficient is obtained, formally including all effects related to the phenomenon of spatial dispersion

Relative dispersion of clustered drifters in a small micro-tidal estuary

Science.gov (United States)

Suara, Kabir; Chanson, Hubert; Borgas, Michael; Brown, Richard J.

2017-07-01

Small tide-dominated estuaries are affected by large scale flow structures which combine with the underlying bed generated smaller scale turbulence to significantly increase the magnitude of horizontal diffusivity. Field estimates of horizontal diffusivity and its associated scales are however rare due to limitations in instrumentation. Data from multiple deployments of low and high resolution clusters of GPS-drifters are used to examine the dynamics of a surface flow in a small micro-tidal estuary through relative dispersion analyses. During the field study, cluster diffusivity, which combines both large- and small-scale processes ranged between, 0.01 and 3.01 m2/s for spreading clusters and, -0.06 and -4.2 m2/s for contracting clusters. Pair-particle dispersion, Dp2, was scale dependent and grew as Dp2 ∼ t1.83 in streamwise and Dp2 ∼ t0.8 in cross-stream directions. At small separation scale, pair-particle (d law and became weaker as separation scale increases. Pair-particle diffusivity was described as Kp ∼ d1.01 and Kp ∼ d0.85 in the streamwise and cross-stream directions, respectively for separation scales ranging from 0.1 to 10 m. Two methods were used to identify the mechanism responsible for dispersion within the channel. The results clearly revealed the importance of strain fields (stretching and shearing) in the spreading of particles within a small micro-tidal channel. The work provided input for modelling dispersion of passive particle in shallow micro-tidal estuaries where these were not previously experimentally studied.

An efficient method of reducing glass dispersion tolerance sensitivity

Science.gov (United States)

Sparrold, Scott W.; Shepard, R. Hamilton

2014-12-01

Constraining the Seidel aberrations of optical surfaces is a common technique for relaxing tolerance sensitivities in the optimization process. We offer an observation that a lens's Abbe number tolerance is directly related to the magnitude by which its longitudinal and transverse color are permitted to vary in production. Based on this observation, we propose a computationally efficient and easy-to-use merit function constraint for relaxing dispersion tolerance sensitivity. Using the relationship between an element's chromatic aberration and dispersion sensitivity, we derive a fundamental limit for lens scale and power that is capable of achieving high production yield for a given performance specification, which provides insight on the point at which lens splitting or melt fitting becomes necessary. The theory is validated by comparing its predictions to a formal tolerance analysis of a Cooke Triplet, and then applied to the design of a 1.5x visible linescan lens to illustrate optimization for reduced dispersion sensitivity. A selection of lenses in high volume production is then used to corroborate the proposed method of dispersion tolerance allocation.

Phonons and their dispersion in model ferroelastics Hg2Hal2

Science.gov (United States)

Roginskii, E. M.; Kvasov, A. A.; Markov, Yu. F.; Smirnov, M. B.

2012-05-01

Dispersion relations of the acoustic and optical phonon frequencies have been calculated and plotted, and the density of states of the phonon spectrum of Hg2Cl2 and Hg2Br2 crystals has been derived. The effect of hydrostatic pressure on the frequencies of acoustic and optical phonons and their dispersion has been theoretically analyzed. It has been found that an increase in the pressure leads to a strong softening of the slowest acoustic TA branch (the soft mode) at the X point of the Brillouin zone boundary, which is consistent with the phenomenological Landau theory and correlates with experiment.

Dispersion and absorption of longitudinal electro-kinetic wave in ion-implanted GaN semiconductor plasmas

Energy Technology Data Exchange (ETDEWEB)

Soni, Dilip [Government P G Madhav Science College, Ujjain (M P) (India); Sharma, Giriraj, E-mail: grsharma@gmail.com [SRJ Government Girls’ College, Neemuch (M P) (India); Saxena, Ajay [Government College, Garoth, Dist. Mandsaur (M P) (India); Jadhav, Akhilesh [Government J Yoganandam Chhattisgarh College, Raipur (C G) (India)

2015-07-31

An analytical study on propagation characteristics of longitudinal electro-kinetic (LEK) waves is presented. Based on multi-fluid model of plasma, we have derived a dispersion relation for LEK waves in colloid laden GaN semiconductor plasmas. It is assumed that ions are implanted to form colloids in the GaN sample. The colloids are continuously bombarded by the plasma particles and stick on them, but they acquire a net negative charge due to relatively higher mobility of electrons. It is found from the dispersion relation that the presence of charged colloids not only modifies the existing modes but also supports new novel modes of LEKWs. It is hoped that the study would enhance understanding on dispersion and absorption of LEKWs and help in singling out the appropriate configurations in which GaN crystal would be better suited for fabrication of microwave devices.

Kinetic transverse dispersion relation for relativistic magnetized electron-positron plasmas with Maxwell-Jüttner velocity distribution functions

Energy Technology Data Exchange (ETDEWEB)

López, Rodrigo A. [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción (Chile); Moya, Pablo S. [NASA Goddard Space Flight Center, Heliophysics Science Division, Geospace Physics Laboratory, Mail Code 673, Greenbelt, Maryland 20771 (United States); Department of Physics, Catholic University of America, Washington DC, DC 20064 (United States); Muñoz, Víctor [Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago (Chile); Viñas, Adolfo F. [NASA Goddard Space Flight Center, Heliophysics Science Division, Geospace Physics Laboratory, Mail Code 673, Greenbelt, Maryland 20771 (United States); Valdivia, J. Alejandro [Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago (Chile); Centro para el Desarrollo de la Nanociencia y la Nanotecnología, CEDENNA, Santiago (Chile)

2014-09-15

We use a kinetic treatment to study the linear transverse dispersion relation for a magnetized isotropic relativistic electron-positron plasma with finite relativistic temperature. The explicit linear dispersion relation for electromagnetic waves propagating along a constant background magnetic field is presented, including an analytical continuation to the whole complex frequency plane for the case of Maxwell-Jüttner velocity distribution functions. This dispersion relation is studied numerically for various temperatures. For left-handed solutions, the system presents two branches, the electromagnetic ordinary mode and the Alfvén mode. In the low frequency regime, the Alfvén branch has two dispersive zones, the normal zone (where ∂ω/∂k > 0) and an anomalous zone (where ∂ω/∂k < 0). We find that in the anomalous zone of the Alfvén branch, the electromagnetic waves are damped, and there is a maximum wave number for which the Alfvén branch is suppressed. We also study the dependence of the Alfvén velocity and effective plasma frequency with the temperature. We complemented the analytical and numerical approaches with relativistic full particle simulations, which consistently agree with the analytical results.

On the relative contributions of wind vs. animals to seed dispersal of four Sierra Nevada pines.

Science.gov (United States)

Vander Wall, Stephen B

2008-07-01

Selective pressures that influence the form of seed dispersal syndromes are poorly understood. Morphology of plant propagules is often used to infer the means of dispersal, but morphology can be misleading. Several species of pines, for example, have winged seeds adapted for wind dispersal but owe much of their establishment to scatter-hoarding animals. Here the relative importance of wind vs. animal dispersal is assessed for four species of pines of the eastern Sierra Nevada that have winged seeds but differed in seed size: lodgepole pine (Pinus contorta murrayana, 8 mg); ponderosa pine (Pinus ponderosa ponderosa, 56 mg); Jeffrey pine (Pinus jeffreyi, 160 mg); and sugar pine (Pinus lambertiana, 231 mg). Pre-dispersal seed mortality eliminated much of the ponderosa pine seed crop (66%), but had much less effect on Jeffrey pine (32% of seeds destroyed), lodgepole pine (29%), and sugar pine (7%). When cones opened most filled seeds were dispersed by wind. Animals removed > 99% of wind-dispersed Jeffrey and sugar pine seeds from the ground within 60 days, but animals gathered only 93% of lodgepole pine seeds and 38% of ponderosa pine seeds during the same period. Animals gathered and scatter hoarded radioactively labeled ponderosa, Jeffrey, and sugar pine seeds, making a total of 2103 caches over three years of study. Only three lodgepole pine caches were found. Caches typically contained 1-4 seeds buried 5-20 mm deep, depths suitable for seedling emergence. Although Jeffrey and sugar pine seeds are initially wind dispersed, nearly all seedlings arise from animal caches. Lodgepole pine is almost exclusively wind dispersed, with animals acting as seed predators. Animals treated ponderosa pine in an intermediate fashion. Two-phased dispersal of large, winged pine seeds appears adaptive; initial wind dispersal helps to minimize pre-dispersal seed mortality whereas scatter hoarding by animals places seeds in sites with a higher probability of seedling establishment.

Using Photosensitive Dye To Improve Multi Walled Carbon Nanotubes Dispersion

Energy Technology Data Exchange (ETDEWEB)

Diaz Costanzo, Guadalupe; Goyanes, Silvia [Laboratorio de PolImeros y Materiales Compuestos, Dpto. de Fisica, FCEyN, Universidad de Buenos Aires (Argentina) (Argentina); Ledesma, Silvia, E-mail: ledesma@df.uba.ar [Laboratorio de Procesado de Imagenes, Dpto. de Fisica, FCEyN, Universidad de Buenos Aires (Argentina) (Argentina)

2011-01-01

As already well-known, the outstanding mechanical and electrical properties of carbon nanotubes (CNT) are partially lost when CNT aggregate. The fact that CNT tend to aggregate makes difficult to put them into a host matrix, for example. Until now, achieving stable dispersions of CNT is still a challenge. In the present work, we show that the addition of an azobenzene derivative, Disperse Orange 3 (DO3) to dispersions of multi walled carbon nanotubes (MWCNT) in the organic solvent tetrahydrofuran (THF) efficiently helps debundling MWCNT and makes dispersions stable for days. We report UV-Vis optical absorption experiments that suggest an interaction between MWCNT and DO3 molecules following the behavior qualitatively observed. Dispersions with MWCNT and DO3 in THF were observed qualitatively over time. Successful suspensions (for the higher DO3 concentrations studied) were stable for several days. Also, we prepared polymeric films doped with MWCNT non-covalent functionalized with DO3 in one of the proper DO3/MWCNT weight relation where stable supensions were obtained. In this study we show preliminary results where the optical response of these samples was also measured.

Dispersion relation for localized magnetic polaritons propagating at ...

Indian Academy of Sciences (India)

Abstract. Localized magnetic polaritons are investigated in the systems consisting of two magnetic superlattices, coupled by a ferromagnetic contact layer. The general dis- persion relation for localized magnetic polaritons are derived in the framework of the electromagnetic wave theory in the Voigt geometry by the 'transfer' ...

Inelastic Neutron Scattering Measurements of Phonon Dispersion Relations in Andalusite and Sillimanite, Al2SiO5

International Nuclear Information System (INIS)

Goel, P.

2001-01-01

This paper reports inelastic neutron scattering (INS) measurements of the phonon dispersion relations of the aluminum silicate minerals andalusite and sillimanite, Al 2 SiO 5 . The single crystal INS measurements were undertaken using the Triple-axis-spectrometer at the Dhruva reactor, Trombay for andalusite and at the Oak Ridge National Laboratory, USA for sillimanite. The phonon dispersion relations (upto 50 mev) along various high symmetry directions have been measured and have been analyzed on the basis of lattice dynamics shell model calculations. The calculated structure factors based on the model calculations were used as guides for planning these single crystal measurements and were used to identify regions in reciprocal space with large cross-sections. The calculated structure factors have been very useful in the planning, execution and analysis of the experimental data. The calculated phonon dispersion relations are found to be in good agreement with the measured data

Derivation of Einstein-Cartan theory from general relativity

Science.gov (United States)

Petti, Richard

2015-04-01

General relativity cannot describe exchange of classical intrinsic angular momentum and orbital angular momentum. Einstein-Cartan theory fixes this problem in the least invasive way. In the late 20th century, the consensus view was that Einstein-Cartan theory requires inclusion of torsion without adequate justification, it has no empirical support (though it doesn't conflict with any known evidence), it solves no important problem, and it complicates gravitational theory with no compensating benefit. In 1986 the author published a derivation of Einstein-Cartan theory from general relativity, with no additional assumptions or parameters. Starting without torsion, Poincaré symmetry, classical or quantum spin, or spinors, it derives torsion and its relation to spin from a continuum limit of general relativistic solutions. The present work makes the case that this computation, combined with supporting arguments, constitutes a derivation of Einstein-Cartan theory from general relativity, not just a plausibility argument. This paper adds more and simpler explanations, more computational details, correction of a factor of 2, discussion of limitations of the derivation, and discussion of some areas of gravitational research where Einstein-Cartan theory is relevant.

Calculation of the Green functions by the coupling constant dispersion relations

International Nuclear Information System (INIS)

Bogomalny, E.B.

1977-01-01

The discontinuities of the Green functions on the cut in the complex plane of the coupling constant are calculated by the steepest descent method. The saddle points are given by the solutions of the classical field equations at those values of the coupling constant for which the classical theory has no ground state. The Green functions at the physical values of the coupling constant are determined by dispersion relations. (Auth.)

Diffusion and sorption in particles and two-dimensional dispersion in a porous media

International Nuclear Information System (INIS)

Rasmuson, A.

1980-01-01

A solution of the two-dimensional differential equation of dispersion from a disk source, coupled with a differential equation of diffusion and sorption in particles, is developed. The solution is obtained by the successive use of the Laplace and the Hankel transforms and is given in the form of an infinite double-integral. If the lateral dispersion is negligible, the solution is shown to simplify to a solution presented earlier. Dimensionless quantities are introduced. A steady-state condition is obtained after long time. This is investigated in some detail. An expression is derived for the highest concentration which may be expected at a point in space. An important relation is obtained when longitudinal dispersion is neglected. The solution for any value of the lateral dispersion coefficient and radial distance from the source is then obtained by simple multiplication of a solution for no lateral dispersion with the steady-state value. A method for integrating the infinite double integral is given. Some typical examples are shown. (Auth.)

Derivation of Hamaker Dispersion Energy of Amorphous Carbon Surfaces in Contact with Liquids Using Photoelectron Energy-Loss Spectra

Science.gov (United States)

Godet, Christian; David, Denis

2017-12-01

Hamaker interaction energies and cutoff distances have been calculated for disordered carbon films, in contact with purely dispersive (diiodomethane) or polar (water) liquids, using their experimental dielectric functions ɛ ( q, ω) obtained over a broad energy range. In contrast with previous works, a q-averaged q is derived from photoelectron energy-loss spectroscopy (XPS-PEELS) where the energy loss function (ELF) q is a weighted average over allowed transferred wave vector values, q, given by the physics of bulk plasmon excitation. For microcrystalline diamond and amorphous carbon films with a wide range of (sp3/sp2 + sp3) hybridization, non-retarded Hamaker energies, A 132 ( L < 1 nm), were calculated in several configurations, and distance and wavenumber cutoff values were then calculated based on A 132 and the dispersive work of adhesion obtained from contact angles. A geometric average approximation, H 0 CVL = ( H 0 CVC H 0 LVL )1/2, holds for the cutoff separation distances obtained for carbon-vacuum-liquid (CVL), carbon-vacuum-carbon (CVC) and liquid-vacuum-liquid (LVL) equilibrium configurations. The linear dependence found for A CVL, A CLC and A CLV values as a function of A CVC, for each liquid, allows predictive relationships for Hamaker energies (in any configuration) using experimental determination of the dispersive component of the surface tension, {γ}_{CV}^d , and a guess value of the cutoff distance H 0 CVC of the solid. [Figure not available: see fulltext.

Dispersion strengthening of aluminium-aluminium-oxide products

DEFF Research Database (Denmark)

Hansen, Niels

1970-01-01

The true stress-true strain curves at room temperature and at 400°C were determined for various types of aluminium-aluminium-oxide products containing from 0.2 to 4.7 weight per cent of aluminium oxide. The effect of particles on the initial flow stress and the flow stress for 0.2% offset at room...... temperature and at 400°C is in agreement with Orowan's theory. The increase in flow stress at room temperature for strain values below 3 per cent was related to the plastic strain by the equation σ-σoy=k1ε 1/2, where σoy is the initial flow stress and where k1 increases for increasing volume fraction...... and decreasing particle size of the dispersed particles. A general expression for k1 was derived for the relationship between the dislocation density and the strain in dispersion-strengthened products...

Dispersion corrections to the forward Rayleigh scattering amplitudes of tantalum, mercury and lead derived using photon interaction cross sections

Energy Technology Data Exchange (ETDEWEB)

Appaji Gowda, S.B. [Department of Studies in Physics, Manasagangothri, University of Mysore, Mysore 570006 (India); Umesh, T.K. [Department of Studies in Physics, Manasagangothri, University of Mysore, Mysore 570006 (India)]. E-mail: tku@physics.uni-mysore.ac.in

2006-01-15

Dispersion corrections to the forward Rayleigh scattering amplitudes of tantalum, mercury and lead in the photon energy range 24-136 keV have been determined by a numerical evaluation of the dispersion integral that relates them through optical theorem to the photo effect cross sections. The photo effect cross sections have been extracted by subtracting the coherent and incoherent scattering contribution from the measured total attenuation cross section, using high-resolution high-purity germanium detector in a narrow beam good geometry set up. The real part of the dispersion correction to which the relativistic corrections calculated by Kissel and Pratt (S-matrix approach) or Creagh and McAuley (multipole corrections) have been included are in better agreement with the available theoretical values.

An expert system for dispersion model interpretation

International Nuclear Information System (INIS)

Skyllingstad, E.D.; Ramsdell, J.V.

1988-10-01

A prototype expert system designed to diagnose dispersion model uncertainty is described in this paper with application to a puff transport model. The system obtains qualitative information from the model user and through an expert-derived knowledge base, performs a rating of the current simulation. These results can then be used in combination with dispersion model output for deciding appropriate evacuation measures. Ultimately, the goal of this work is to develop an expert system that may be operated accurately by an individual uneducated in meteorology or dispersion modeling. 5 refs., 3 figs

Measurement of average density and relative volumes in a dispersed two-phase fluid

Science.gov (United States)

Sreepada, Sastry R.; Rippel, Robert R.

1992-01-01

An apparatus and a method are disclosed for measuring the average density and relative volumes in an essentially transparent, dispersed two-phase fluid. A laser beam with a diameter no greater than 1% of the diameter of the bubbles, droplets, or particles of the dispersed phase is directed onto a diffraction grating. A single-order component of the diffracted beam is directed through the two-phase fluid and its refraction is measured. Preferably, the refracted beam exiting the fluid is incident upon a optical filter with linearly varing optical density and the intensity of the filtered beam is measured. The invention can be combined with other laser-based measurement systems, e.g., laser doppler anemometry.

Quasiparticles of widely tuneable inertial mass: The dispersion relation of atomic Josephson vortices and related solitary waves

Directory of Open Access Journals (Sweden)

Sophie S. Shamailov, Joachim Brand

2018-03-01

Full Text Available Superconducting Josephson vortices have direct analogues in ultracold-atom physics as solitary-wave excitations of two-component superfluid Bose gases with linear coupling. Here we numerically extend the zero-velocity Josephson vortex solutions of the coupled Gross-Pitaevskii equations to non-zero velocities, thus obtaining the full dispersion relation. The inertial mass of the Josephson vortex obtained from the dispersion relation depends on the strength of linear coupling and has a simple pole divergence at a critical value where it changes sign while assuming large absolute values. Additional low-velocity quasiparticles with negative inertial mass emerge at finite momentum that are reminiscent of a dark soliton in one component with counter-flow in the other. In the limit of small linear coupling we compare the Josephson vortex solutions to sine-Gordon solitons and show that the correspondence between them is asymptotic, but significant differences appear at finite values of the coupling constant. Finally, for unequal and non-zero self- and cross-component nonlinearities, we find a new solitary-wave excitation branch. In its presence, both dark solitons and Josephson vortices are dynamically stable while the new excitations are unstable.

$K^{\\pm}n$ forward dispersion relations and the KN$\\Sigma$ coupling constant

CERN Document Server

Baillon, Paul; Ferro-Luzzi, M; Jenni, Peter; Perreau, J M; Tripp, R D; Ypsilantis, Thomas; Déclais, Y; Séguinot, Jacques

1976-01-01

Recent measurements of the K/sup -/n forward scattering amplitude at 1.2, 1.4, 2.6 GeV/c are used in a once-subtracted dispersion relation to determine the value of the KN Sigma coupling constant. The result is g/sub Sigma //sup 2/=1.9+or-3.2, in agreement with the prediction of the SU(3) theory.

Microtubule-Associated Proteins in Mesial Temporal Lobe Epilepsy with and without Psychiatric Comorbidities and Their Relation with Granular Cell Layer Dispersion

Directory of Open Access Journals (Sweden)

Ludmyla Kandratavicius

2013-01-01

Full Text Available Background. Despite strong association between epilepsy and psychiatric comorbidities, biological substrates are unknown. We have previously reported decreased mossy fiber sprouting in mesial temporal lobe epilepsy (MTLE patients with psychosis and increased in those with major depression. Microtubule associated proteins (MAPs are essentially involved in dendritic and synaptic sprouting. Methods. MTLE hippocampi of subjects without psychiatric history, MTLE + major depression, and MTLE + interictal psychosis derived from epilepsy surgery and control necropsies were investigated for neuronal density, granular layer dispersion, and MAP2 and tau immunohistochemistry. Results. Altered MAP2 and tau expression in MTLE and decreased tau expression in MTLE with psychosis were found. Granular layer dispersion correlated inversely with verbal memory scores, and with MAP2 and tau expression in the entorhinal cortex. Patients taking fluoxetine showed increased neuronal density in the granular layer and those taking haloperidol decreased neuronal density in CA3 and subiculum. Conclusions. Our results indicate relations between MAPs, granular layer dispersion, and memory that have not been previously investigated. Differential MAPs expression in human MTLE hippocampi with and without psychiatric comorbidities suggests that psychopathological states in MTLE rely on differential morphological and possibly neurochemical backgrounds. This clinical study was approved by our institution’s Research Ethics Board (HC-FMRP no. 1270/2008 and is registered under the Brazilian National System of Information on Ethics in Human Research (SISNEP no. 0423.0.004.000-07.

A Riemann problem with small viscosity and dispersion

Directory of Open Access Journals (Sweden)

Kayyunnapara Thomas Joseph

2006-09-01

Full Text Available In this paper we prove existence of global solutions to a hyperbolic system in elastodynamics, with small viscosity and dispersion terms and derive estimates uniform in the viscosity-dispersion parameters. By passing to the limit, we prove the existence of solution the Riemann problem for the hyperbolic system with arbitrary Riemann data.

Better resolved low frequency dispersions by the apt use of Kramers-Kronig relations, differential operators and all-in-1 modelling

Directory of Open Access Journals (Sweden)

Jan van Turnhout

2016-05-01

Full Text Available The dielectric spectra of colloidal systems often contain a typical low frequency dispersion, which usually remains unnoticed, because of the presence of strong conduction losses. The KK relations offer a means for converting  into  data. This allows us to calculate conduction free  spectra in which the l.f. dispersion will show up undisturbed. This interconversion can be done on line with a moving frame of logarithmically spaced  data. The coefficients of the conversion frames were obtained by kernel matching and by using symbolic differential operators. Logarithmic derivatives and differences of  and  provide another option for conduction free data analysis. These difference-based functions actually derived from approximations to the distribution function, have the additional advantage of improving the resolution power of dielectric studies. A high resolution is important because of the rich relaxation structure of colloidal suspensions. The development of all-in-1 modelling facilitates the conduction free and high resolution data analysis. This mathematical tool allows the apart-together fitting of multiple data and multiple model functions. It proved also useful to go around the KK conversion altogether. This was achieved by the combined approximating  and  data with a complex rational fractional power function. The all-in-1 minimization turned out to be also highly useful for the dielectric modelling of a suspension with the complex dipolar coefficient. It guarantees a secure correction for the electrode polarization, so that the modelling with the help of the differences  and  can zoom in on the genuine colloidal relaxations.

Sound dispersion in a spin-1 Ising system near the second-order phase transition point

International Nuclear Information System (INIS)

Erdem, Ryza; Keskin, Mustafa

2003-01-01

Sound dispersion relation is derived for a spin-1 Ising system and its behaviour near the second-order phase transition point or the critical point is analyzed. The method used is a combination of molecular field approximation and Onsager theory of irreversible thermodynamics. If we assume a linear coupling of sound wave with the order parameter fluctuations in the system, we find that the dispersion which is the relative sound velocity change with frequency behaves as ω 0 ε 0 , where ω is the sound frequency and ε the temperature distance from the critical point. In the ordered region, one also observes a frequency-dependent velocity or dispersion minimum which is shifted from the corresponding attenuation maxima. These phenomena are in good agreement with the calculations of sound velocity in other magnetic systems such as magnetic metals, magnetic insulators, and magnetic semiconductors

Advances and Problems in Mathematical Modelling of Dispersion of ...

African Journals Online (AJOL)

Most expressions for dispersion of pollutants have failed to give accurate predictions in both channel and natural stream flows. This paper outlines the basic concepts on which the fundamental dispersion equations have been derived. Some of the advances on these equations are examined and their deficiencies pointed ...

Interpretation of uncertainty relations for three or more observables

International Nuclear Information System (INIS)

Shirokov, M.I.

2003-01-01

Conventional quantum uncertainty relations (URs) contain dispersions of two observables. Generalized URs are known which contain three or more dispersions. They are derived here starting with suitable generalized Cauchy inequalities. It is shown what new information the generalized URs provide. Similar interpretation is given to generalized Cauchy inequalities

Integrating individual movement behaviour into dispersal functions.

Science.gov (United States)

Heinz, Simone K; Wissel, Christian; Conradt, Larissa; Frank, Karin

2007-04-21

Dispersal functions are an important tool for integrating dispersal into complex models of population and metapopulation dynamics. Most approaches in the literature are very simple, with the dispersal functions containing only one or two parameters which summarise all the effects of movement behaviour as for example different movement patterns or different perceptual abilities. The summarising nature of these parameters makes assessing the effect of one particular behavioural aspect difficult. We present a way of integrating movement behavioural parameters into a particular dispersal function in a simple way. Using a spatial individual-based simulation model for simulating different movement behaviours, we derive fitting functions for the functional relationship between the parameters of the dispersal function and several details of movement behaviour. This is done for three different movement patterns (loops, Archimedean spirals, random walk). Additionally, we provide measures which characterise the shape of the dispersal function and are interpretable in terms of landscape connectivity. This allows an ecological interpretation of the relationships found.

Seed dispersal in fens

Science.gov (United States)

Middleton, B.; Van Diggelen, R.; Jensen, K.

2006-01-01

Question: How does seed dispersal reduce fen isolation and contribute to biodiversity? Location: European and North American fens. Methods: This paper reviews the literature on seed dispersal to fens. Results: Landscape fragmentation may reduce dispersal opportunities thereby isolating fens and reducing genetic exchange. Species in fragmented wetlands may have lower reproductive success, which can lead to biodiversity loss. While fens may have always been relatively isolated from each other, they have become increasingly fragmented in modern times within agricultural and urban landscapes in both Europe and North America. Dispersal by water, animals and wind has been hampered by changes related to development in landscapes surrounding fens. Because the seeds of certain species are long-lived in the seed bank, frequent episodes of dispersal are not always necessary to maintain the biodiversity of fens. However, of particular concern to restoration is that some dominant species, such as the tussock sedge Carex stricta, may not disperse readily between fens. Conclusions: Knowledge of seed dispersal can be used to maintain and restore the biodiversity of fens in fragmented landscapes. Given that development has fragmented landscapes and that this situation is not likely to change, the dispersal of seeds might be enhanced by moving hay or cattle from fens to damaged sites, or by reestablishing lost hydrological connections. ?? IAVS; Opulus Press.

[Pharmacokinetics and relative bioavailability of THC and THC-solid dispersion orally to mice at single dose].

Science.gov (United States)

Liao, Li; Hua, Hua; Zhao, Jun-Ning; Luo, Heng; Yang, An-Dong

2014-03-01

To establish a fast sensitive, reproducible LC-MS/MS method to study pharmacokinetic properties of THC, and compare relative bioavailability of THC and its solid dispersion in mice. 200 mice were divided randomly into two groups, and administered orally with THC and THC-solid dispersion after fasting (calculate on THC:400 mg x kg(-1)), used HPLC-MS/MS method to determine the THC concentration of each period at the following times: baseline ( predose ), 15, 30, 45 min, 1, 1.5, 2, 3, 4, 6, 24 h after dosing. Calculating the pharmacokinetic parameters according to the C-t curv, and then use the Phoenix WinNonlin software for data analysis. The calibration curves were linear over the range 9.06-972 microg x L(-1) for THC (R2 = 0.999). The limit of detection (LOD) was 0.7 microg x L(-1), respectively. The average extraction recoveries for THC was above 75%, The methodology recoveries were between 79% and 108%. The intra-day and inter-day RSD were less than 13%, the stability test showed that the plasma samples was stable under different conditions (RSD THC and THC-solid dispersion orally to mice shows as fllows: T(max), were 60 and 15 min, AUC(0-t) were 44 500.43 and 57 497.81 mg x L(-1) x min, AUC(0-infinity) were 51 226.00 and 68 031.48 mg x L(-1) x min, MRT(0-infinity) were 596.915 6, 661.747 7 min, CL(z)/F were 0.007 809 and 0.005 88 L x min(-1) x kg(-1). Compared with THC, the MRT and t1/2 of the THC-solid dispersion were all slightly extended, the t(max) was significantly reduced, AUC(0-24 h), AUC(0-infinity) and C(max) were all significantly higher, the relative bioavailability of THC-solid dispersion is 1.34 times of THC. The results of the experiment shows that the precision, accuracy, recovery and applicability were found to be adequate for the pharmacokinetic studies. After oral administration to mice, the relative bioavailability of THC-solid dispersion show significant improvement compared to THC.

A generalized advection dispersion equation

Indian Academy of Sciences (India)

This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of.

Bounds on Cubic Lorentz-Violating Terms in the Fermionic Dispersion Relation

OpenAIRE

Bertolami, O.; Rosa, J. G.

2004-01-01

We study the recently proposed Lorentz-violating dispersion relation for fermions and show that it leads to two distinct cubic operators in the momentum. We compute the leading order terms that modify the non-relativistic equations of motion and use experimental results for the hyperfine transition in the ground state of the ${}^9\\textrm Be^+$ ion to bound the values of the Lorentz-violating parameters $\\eta_1$ and $\\eta_2$ for neutrons. The resulting bounds depend on the value of the Lorenz-...

Dispersion relation of test waves in an electron beam plasma system

International Nuclear Information System (INIS)

Hayashi, N.; Tanaka, M.; Shinohara, S.; Kawai, Y.

1994-01-01

Test waves are propagated in an electron beam plasma system and the dispersion relation is measured. At the center of the experimental region a beam mode is excited. Near the chamber wall an electron plasma wave is excited and propagates from the chamber wall to the center of the experimental region. It is also found that observed unstable waves are standing wave which is formed by superposing the beam modes propagating in the opposite directions each other. (author). 6 refs, 6 figs

The dispersion relation for the forward elastic electron-atom scattering amplitude

International Nuclear Information System (INIS)

Amusia, M.Y.

1978-01-01

The analytical properties of forward elastic electron-atom scattering amplitude are discussed. It is noted that the occurrence of exchange between the incoming and atomic electrons leads to the appearance of a number of singularities on the negative real axis in the complex energy plane. The conclusion is drawn that the dispersion relation for the forward electron-atom scattering amplitude should also include an integration over the negative energy from - I to - infinity, where I is the ionization potential. (author)

The influence of the directional energy distribution on the nonlinear dispersion relation in a random gravity wave field

Science.gov (United States)

Huang, N. E.; Tung, C.-C.

1977-01-01

The influence of the directional distribution of wave energy on the dispersion relation is calculated numerically using various directional wave spectrum models. The results indicate that the dispersion relation varies both as a function of the directional energy distribution and the direction of propagation of the wave component under consideration. Furthermore, both the mean deviation and the random scatter from the linear approximation increase as the energy spreading decreases. Limited observational data are compared with the theoretical results. The agreement is favorable.

17 CFR 39.5 - Information relating to derivatives clearing organization operations.

Science.gov (United States)

2010-04-01

... 17 Commodity and Securities Exchanges 1 2010-04-01 2010-04-01 false Information relating to derivatives clearing organization operations. 39.5 Section 39.5 Commodity and Securities Exchanges COMMODITY FUTURES TRADING COMMISSION DERIVATIVES CLEARING ORGANIZATIONS § 39.5 Information relating to derivatives...

Dispersion relation for Bernstein waves using a new transformation for the modified Bessel function

International Nuclear Information System (INIS)

Sato, Masumi

1985-01-01

Aitken's or Shanks' transformation of the exponent-modified Bessel function produces better approximations. Dispersion relations for the hybrid and Bernstein waves using these provide better thermal and parallel wavenumber corrections. They also predict more closely the evolution and mode-conversion of these waves. (author)

Statistical description of turbulent dispersion

NARCIS (Netherlands)

Brouwers, J.J.H.

2012-01-01

We derive a comprehensive statistical model for dispersion of passive or almost passive admixture particles such as fine particulate matter, aerosols, smoke and fumes, in turbulent flow. The model rests on the Markov limit for particle velocity. It is in accordance with the asymptotic structure of

Dispersion approach to anomalies in the axial-vector Ward-Takahashi identities

Energy Technology Data Exchange (ETDEWEB)

Nishijima, K. Sasaki, R. (Tokyo Univ. (Japan). Dept. of Physic)

1975-01-01

On the basis of dispersion relations and unitarity anomalous Ward-Takahashi identities for the axial-vector current are derived in quantum electrodynamics. In this derivation use of divergent unrenormalized expressions is intentionally avoided, and only finite renormalized expressions are employed from the start. The origin of the anormalies is attributed to a mismatch of the subtraction conditions present in the naive Ward-Takahashi identities. The resulting anomalous Ward-Takahashi identities are valid in every order of the perturbation expansion and can be cast in the form of an operator equation. In the course of this derivation we encounter the problem of how to regularize operator products and a possible solution of this problem is provided in terms of subtraction conditions.

Dispersion approach to anomalies in the axial-vector Ward-Takahashi identities

International Nuclear Information System (INIS)

Nishijima, Kazuhiko; Sasaki, Ryu

1975-01-01

On the basis of dispersion relations and unitarity anomalous Ward-Takahashi identities for the axial-vector current are derived in quantum electrodynamics. In this derivation use of divergent unrenormalized expressions is intentionally avoided, and only finite renormalized expressions are employed from the start. The origin of the anormalies is attributed to a mismatch of the subtraction conditions present in the naive Ward-Takahashi identities. The resulting anomalous Ward-Takahashi identities are valid in every order of the perturbation expansion and can be cast in the form of an operator equation. In the course of this derivation we encounter the problem of how to regularize operator products and a possible solution of this problem is provided in terms of subtraction conditions. (auth.)

Application of derivative and derivative ratio spectrophotometry to simultaneous trace determination of rhodamine B and rhodamine 6G after dispersive liquid-liquid microextraction.

Science.gov (United States)

Xiao, Ni; Deng, Jian; Huang, Kaihui; Ju, Saiqin; Hu, Canhui; Liang, Jun

2014-07-15

Two novel methods, first derivative spectrophotometric method ((1)D) and first derivative ratio spectrophotometric method ((1)DR), have been developed for the simultaneous trace determination of rhodamine B (RhB) and rhodamine 6G (Rh6G) in food samples after dispersive liquid-liquid microextraction (DLLME). The combination of derivative spectrophotometric techniques and DLLME procedure endows the presented methods with enhanced sensitivity and selectivity. Under optimum conditions, the linear calibration curves ranged from 5 to 450 ng mL(-1), with the correlation coefficients (r) of 0.9997 for RhB and 0.9977 for Rh6G by (1)D method, and 0.9987 for RhB and 0.9958 for Rh6G by (1)DR method, respectively. The calculated limits of detection (LODs) based on the variability of the blank solutions (S/N = 3 criterion) for 11 measurements were in the range of 0.48-1.93 ng mL(-1). The recoveries ranged from 88.1% to 111.6% (with RSD less than 4.4%) and 91.5-110.5% (with RSD less than 4.7%) for (1)D and (1)DR method, respectively. The influence of interfering substances such as foreign ions and food colorants which might be present in the food samples on the signals of RhB and Rh6G was examined. The developed methods have been successfully applied to the determination of RhB and Rh6G in black tea, red wine and chilli powder samples with the characteristics of simplicity, cost-effectiveness, environmental friendliness, and could be valuable for routine analysis. Copyright © 2014 Elsevier B.V. All rights reserved.

Evolution of velocity dispersion along cold collisionless flows

International Nuclear Information System (INIS)

Banik, Nilanjan; Sikivie, Pierre

2016-01-01

We found that the infall of cold dark matter onto a galaxy produces cold collisionless flows and caustics in its halo. If a signal is found in the cavity detector of dark matter axions, the flows will be readily apparent as peaks in the energy spectrum of photons from axion conversion, allowing the densities, velocity vectors and velocity dispersions of the flows to be determined. We also discuss the evolution of velocity dispersion along cold collisionless flows in one and two dimensions. A technique is presented for obtaining the leading behaviour of the velocity dispersion near caustics. The results are used to derive an upper limit on the energy dispersion of the Big Flow from the sharpness of its nearby caustic, and a prediction for the dispersions in its velocity components

Giant magnon solution and dispersion relation in string theory in AdS3×S3×T4 with mixed flux

International Nuclear Information System (INIS)

Hoare, B.; Stepanchuk, A.; Tseytlin, A.A.

2014-01-01

We address the question of the exact form of the dispersion relation for light-cone string excitations in string theory in AdS 3 ×S 3 ×T 4 with mixed R–R and NS–NS 3-form fluxes. The analogy with string theory in AdS 5 ×S 5 suggests that in addition to the data provided by the perturbative near-BMN expansion and symmetry algebra considerations there is another source of information for the dispersion relation – the semiclassical giant magnon solution. In earlier work in (arXiv:1303.1037) and (arXiv:1304.4099) we found that the symmetry algebra constraints, which are consistent with a perturbative expansion, do not completely determine the form of the dispersion relation. The aim of the present paper is to fix the dispersion relation by constructing a generalisation of the known dyonic giant magnon soliton on S 3 to the presence of a non-zero NS–NS flux described by a WZ term in the string action (with coefficient q). We find that the angular momentum of this soliton gets shifted by a term linear in world-sheet momentum p. We also discuss the symmetry algebra of the string light-cone S-matrix and show that the exact dispersion relation, which should have the correct perturbative BMN and semiclassical giant magnon limits, should also contain such a linear momentum term. The simplicity of the resulting bound-state picture provides a strong argument in favour of this dispersion relation

Noise figure of amplified dispersive Fourier transformation

International Nuclear Information System (INIS)

Goda, Keisuke; Jalali, Bahram

2010-01-01

Amplified dispersive Fourier transformation (ADFT) is a powerful tool for fast real-time spectroscopy as it overcomes the limitations of traditional optical spectrometers. ADFT maps the spectrum of an optical pulse into a temporal waveform using group-velocity dispersion and simultaneously amplifies it in the optical domain. It greatly simplifies spectroscopy by replacing the diffraction grating and detector array in the conventional spectrometer with a dispersive fiber and single-pixel photodetector, enabling ultrafast real-time spectroscopic measurements. Following our earlier work on the theory of ADFT, here we study the effect of noise on ADFT. We derive the noise figure of ADFT and discuss its dependence on various parameters.

Optimizing optical pre-dispersion using transmit DSP for mitigation of Kerr nonlinearities in dispersion managed cables

Science.gov (United States)

Hopkins, James; Gaudette, Jamie; Mehta, Priyanth

2013-10-01

With the advent of digital signal processing (DSP) in optical transmitters and receivers, the ability to finely tune the ratio of pre and post dispersion compensation can be exploited to best mitigate the nonlinear penalties caused by the Kerr effect. A portion of the nonlinear penalty in optical communication channels has been explained by an increase in peak to average power ratio (PAPR) inherent in highly dispersed signals. The standard approach for minimizing these impairments applies 50% pre dispersion compensation and 50% post dispersion compensation, thereby decreasing average PAPR along the length of the cable, as compared with either 100% pre or post dispersion compensation. In this paper we demonstrate that simply considering the net accumulated dispersion, and applying 50/50 pre/post dispersion is not necessarily the best way to minimize PAPR and subsequent Kerr nonlinearities. Instead, we consider the cumulative dispersion along the entire length of the cable, and, taking into account this additional information, derive an analytic formula for the minimization of PAPR. Alignment with simulation and experimental measurements is presented using a commercially available 100Gb/s dual-polarization binary phase-shift-keying (DP-BPSK) coherent modem, with transmitter and receiver DSP. Measurements are provided from two different 5000km dispersion managed Submarine test-beds, as well as a 3800km terrestrial test-bed with a mixture of SMF-28 and TWRS optical fiber. This method is shown to deviate significantly from the conventional 50/50 method described above, in dispersion managed communications systems, and more closely aligns with results obtained from simulation and data collected from laboratory test-beds.

The dispersion relation of charge and current compensated relativistic electron beam-plasma system

International Nuclear Information System (INIS)

Vrba, P.; Schroetter, J.; Jarosova, P.; Koerbel, S.

1978-01-01

The unstable regions of relativistic electron beam-plasma system were determined by analysing the general dispersion relation numerically. The external parameters were varied to ensure more effective instability excitations. The full charge- and current compensation presumptions lead to the new synchronism predictions. The slow space charge wave and slow cyclotron wave of the return current are synchronous with the plasma ion wave. (author)

Performance Analysis of Ad Hoc Dispersed Spectrum Cognitive Radio Networks over Fading Channels

Directory of Open Access Journals (Sweden)

Mohammad Muneer

2011-01-01

Full Text Available Cognitive radio systems can utilize dispersed spectrum, and thus such approach is known as dispersed spectrum cognitive radio systems. In this paper, we first provide the performance analysis of such systems over fading channels. We derive the average symbol error probability of dispersed spectrum cognitive radio systems for two cases, where the channel for each frequency diversity band experiences independent and dependent Nakagami- fading. In addition, the derivation is extended to include the effects of modulation type and order by considering M-ary phase-shift keying ( -PSK and M-ary quadrature amplitude modulation -QAM schemes. We then consider the deployment of such cognitive radio systems in an ad hoc fashion. We consider an ad hoc dispersed spectrum cognitive radio network, where the nodes are assumed to be distributed in three dimension (3D. We derive the effective transport capacity considering a cubic grid distribution. Numerical results are presented to verify the theoretical analysis and show the performance of such networks.

Unified description of the neutron-/sup 208/Pb mean field between -20 and +165 MeV from the dispersion relation constraint

International Nuclear Information System (INIS)

Johnson, C.H.; Horen, D.J.; Mahaux, C.

1987-01-01

The real part of the central neutron-/sup 208/Pb mean field is the sum of a Hartree-Fock component plus a dispersive component. In keeping with theoretical expectations, the Hartree-Fock field is assumed to have a Woods-Saxon shape whose depth decreases exponentially with increasing energy and whose radius and diffuseness are independent of energy. The dispersive component is determined from the imaginary part of the optical-model potential by making use of the dispersion relation which connects these two quantities. The imaginary part is written as the sum of a volume and a surface-peaked contribution. The dispersion relation then implies that the real dispersive contribution is also the sum of volume and surface-peaked components. The parameters of the complex mean field are determined by fitting the available differential and polarization cross sections in the energy domain [4, 40 MeV] and the total cross sections in the domain [1,120 MeV]; these data are contained in previous published or unpublished reports, but new measurements of the total cross sections are presented from 1 to 25 MeV. Good fits to these cross sections, and also to unpublished total cross sections for energies up to 165 MeV, are obtained despite the fact that the number of adjusted parameters is quite small because of our use of the constraint implied by the dispersion relation

Structure factors and phonon dispersion in liquid Li0.61Na0.39 alloy

International Nuclear Information System (INIS)

Pratap, Arun; Lad, Kirit N.; Raval, K.G.

2004-01-01

The phonon spectra for liquid Li and Na have been computed through the phenomenological model of Bhatia and Singh for disordered systems like liquids and glasses and the obtained results have been compared with the available data obtained by inelastic neutron scattering (INS) and inelastic X-ray scattering (IXS) experiments. The effective pair potentials and their space derivatives are important ingredients in the computation of the dispersion curves. The pair potentials are obtained using the pseudo-potential theory. The empty core model proposed by Ashcroft is widely used for pseudo-potential calculations for alkali metals. But, it is thought to be unsuitable for Li because of its simple 1s electronic structure. However, it can be used with an additional term known as Born-Mayer (BM) core term. The influence of the BM core term on the phonon dispersion is discussed. The same pseudo-potential formalism has been employed to obtain the dispersion relation in liquid Li 0.61 Na 0.39 alloy. Apart from the phonon spectra, the Ashcroft-Langreth structure factors in the alloy are derived in the Percus-Yevick approximation. (author)

Dispersion Forces

CERN Document Server

Buhmann, Stefan Yoshi

2012-01-01

In this book, a modern unified theory of dispersion forces on atoms and bodies is presented which covers a broad range of advanced aspects and scenarios. Macroscopic quantum electrodynamics is shown to provide a powerful framework for dispersion forces which allows for discussing general properties like their non-additivity and the relation between microscopic and macroscopic interactions. It is demonstrated how the general results can be used to obtain dispersion forces on atoms in the presence of bodies of various shapes and materials. Starting with a brief recapitulation of volume I, this volume II deals especially with bodies of irregular shapes, universal scaling laws, dynamical forces on excited atoms, enhanced forces in cavity quantum electrodynamics, non-equilibrium forces in thermal environments and quantum friction. The book gives both the specialist and those new to the field a thorough overview over recent results in the field. It provides a toolbox for studying dispersion forces in various contex...

Comparison of turbulent particle dispersion models in turbulent shear flows

Directory of Open Access Journals (Sweden)

S. Laín

2007-09-01

Full Text Available This work compares the performance of two Lagrangian turbulent particle dispersion models: the standard model (e.g., that presented in Sommerfeld et al. (1993, in which the fluctuating fluid velocity experienced by the particle is composed of two components, one correlated with the previous time step and a second one randomly sampled from a Wiener process, and the model proposed by Minier and Peirano (2001, which is based on the PDF approach and performs closure at the level of acceleration of the fluid experienced by the particle. Formulation of a Langevin equation model for the increments of fluid velocity seen by the particle allows capturing some underlying physics of particle dispersion in general turbulent flows while keeping the mathematical manipulation of the stochastic model simple, thereby avoiding some pitfalls and simplifying the derivation of macroscopic relations. The performance of both dispersion models is tested in the configurations of grid-generated turbulence (Wells and Stock (1983 experiments, simple shear flow (Hyland et al., 1999 and confined axisymmetric jet flow laden with solids (Hishida and Maeda (1987 experiments.

Relative toxicity of oil dispersants to Mytilus viridis and Macrobrachium idella

Digital Repository Service at National Institute of Oceanography (India)

DeSilva, C.; Row, A.

) was almost identical for both the species tested, although there was a significant shift in the range of LC sub(50) values, indicating that one species is less sensitive than the other. Oil dispersant mixtures were less toxic than the dispersants alone...

Nuclear risk from atmospheric dispersion in Northern Europe

International Nuclear Information System (INIS)

Lauritzen, B.

2007-04-01

The aim of the 2005-06 NKS-B NordRisk project has been to present practical methods for probabilistic risk assessment from long-range atmospheric transport and deposition of radioactive material. In this project an atlas of long-range atmospheric dispersion and deposition patterns derived from archived numerical weather prediction (NWP) model data coupled to an atmospheric dispersion model has been produced, and a PC-based software tool has been developed, based on a simplified description of the long-term, long-range atmospheric dispersion and deposition. The atlas and the software tool may allow for a rapid, first assessment of the risks following a nuclear emergency, when detailed information on the long-range atmospheric dispersion and deposition is not available. (au)

Dispersion-induced non-linearities in semiconductors

DEFF Research Database (Denmark)

Mørk, Jesper; Mecozzi, A.

1999-01-01

We show that index dispersion in connection with the standard (slow) saturation of the medium due to carrier density changes, lead to ultrafast gain and index dynamics. Analytical formulas are derived, and it is shown that these new contributions may dominate experimentally observed results....

The Mean and Scatter of the Velocity Dispersion-Optical Richness Relation for MaxBCG Galaxy Clusters

Energy Technology Data Exchange (ETDEWEB)

Becker, M.R.; McKay, T.A.; /Michigan U.; Koester, B.; /Chicago U., Astron. Astrophys. Ctr.; Wechsler, R.H.; /KIPAC, Menlo Park /SLAC /Stanford U., Phys. Dept.; Rozo, E.; /Ohio State U.; Evrard, A.; /Michigan U. /Michigan U., MCTP; Johnston, D.; /Caltech, JPL; Sheldon, E.; /New York U.; Annis, J.; /Fermilab; Lau, E.; /Chicago U., Astron. Astrophys. Ctr.; Nichol, R.; /Portsmouth U., ICG; Miller, C.; /Michigan U.

2007-06-05

The distribution of galaxies in position and velocity around the centers of galaxy clusters encodes important information about cluster mass and structure. Using the maxBCG galaxy cluster catalog identified from imaging data obtained in the Sloan Digital Sky Survey, we study the BCG--galaxy velocity correlation function. By modeling its non-Gaussianity, we measure the mean and scatter in velocity dispersion at fixed richness. The mean velocity dispersion increases from 202 {+-} 10 km s{sup -1} for small groups to more than 854 {+-} 102 km s{sup -1} for large clusters. We show the scatter to be at most 40.5{+-}3.5%, declining to 14.9{+-}9.4% in the richest bins. We test our methods in the C4 cluster catalog, a spectroscopic cluster catalog produced from the Sloan Digital Sky Survey DR2 spectroscopic sample, and in mock galaxy catalogs constructed from N-body simulations. Our methods are robust, measuring the scatter to well within one-sigma of the true value, and the mean to within 10%, in the mock catalogs. By convolving the scatter in velocity dispersion at fixed richness with the observed richness space density function, we measure the velocity dispersion function of the maxBCG galaxy clusters. Although velocity dispersion and richness do not form a true mass--observable relation, the relationship between velocity dispersion and mass is theoretically well characterized and has low scatter. Thus our results provide a key link between theory and observations up to the velocity bias between dark matter and galaxies.

Preserving the Helmholtz dispersion relation: One-way acoustic wave propagation using matrix square roots

Science.gov (United States)

Keefe, Laurence

2016-11-01

Parabolized acoustic propagation in transversely inhomogeneous media is described by the operator update equation U (x , y , z + Δz) =eik0 (- 1 +√{ 1 + Z }) U (x , y , z) for evolution of the envelope of a wavetrain solution to the original Helmholtz equation. Here the operator, Z =∇T2 + (n2 - 1) , involves the transverse Laplacian and the refractive index distribution. Standard expansion techniques (on the assumption Z << 1)) produce pdes that approximate, to greater or lesser extent, the full dispersion relation of the original Helmholtz equation, except that none of them describe evanescent/damped waves without special modifications to the expansion coefficients. Alternatively, a discretization of both the envelope and the operator converts the operator update equation into a matrix multiply, and existing theorems on matrix functions demonstrate that the complete (discrete) Helmholtz dispersion relation, including evanescent/damped waves, is preserved by this discretization. Propagation-constant/damping-rates contour comparisons for the operator equation and various approximations demonstrate this point, and how poorly the lowest-order, textbook, parabolized equation describes propagation in lined ducts.

One-dimensional deterministic transport in neurons measured by dispersion-relation phase spectroscopy

Energy Technology Data Exchange (ETDEWEB)

Wang Ru [Quantitative Light Imaging Laboratory, Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801 (United States); Wang Zhuo; Leigh, Joe; Popescu, Gabriel [Quantitative Light Imaging Laboratory, Department of Electrical and Computer Engineering, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801 (United States); Sobh, Nahil [Beckman Institute for Advanced Science and Technology, Department of Civil and Environmental Engineering, and Department of Mechanical Engineering and Sciences, University of Illinois at Urbana-Champaign, Urbana, IL 61801 (United States); Millet, Larry; Gillette, Martha U [Department of Cell and Developmental Biology, University of Illinois at Urbana-Champaign, Urbana, IL 61801 (United States); Levine, Alex J, E-mail: alevine@chem.ucla.edu, E-mail: gpopescu@illinois.edu [Department of Chemistry and Biochemistry and Department of Physics and Astronomy, University of California at Los Angeles, Los Angeles, CA 90095 (United States)

2011-09-21

We studied the active transport of intracellular components along neuron processes using a new method developed in our laboratory: dispersion-relation phase spectroscopy. This method is able to quantitatively map spatially the heterogeneous dynamics of the concentration field of the cargos at submicron resolution without the need for tracking individual components. The results in terms of density correlation function reveal that the decay rate is linear in wavenumber, which is consistent with a narrow Lorentzian distribution of cargo velocity. (paper)

Cross-Domain Analogies as Relating Derived Relations among Two Separate Relational Networks

Science.gov (United States)

Ruiz, Francisco J; Luciano, Carmen

2011-01-01

Contemporary behavior analytic research is making headway in analyzing analogy as the establishment of a relation of coordination among common types of trained or derived relations. Previous studies have been focused on within-domain analogy. The current study expands previous research by analyzing cross-domain analogy as relating relations among separate relational networks and by correlating participants' performance with a standard measure of analogical reasoning. In two experiments, adult participants first completed general intelligence and analogical reasoning tests. Subsequently, they were exposed to a computerized conditional discrimination training procedure designed to create two relational networks, each consisting of two 3-member equivalence classes. The critical test was a two-part analogical test in which participants had to relate combinatorial relations of coordination and distinction between the two relational networks. In Experiment 1, combinatorial relations for each network were individually tested prior to analogical testing, but in Experiment 2 they were not. Across both experiments, 65% of participants passed the analogical test on the first attempt. Moreover, results from the training procedure were strongly correlated with the standard measure of analogical reasoning. PMID:21547072

Design and development of a dust dispersion chamber to quantify the dispersibility of rock dust.

Science.gov (United States)

Perera, Inoka E; Sapko, Michael J; Harris, Marcia L; Zlochower, Isaac A; Weiss, Eric S

2016-01-01

Dispersible rock dust must be applied to the surfaces of entries in underground coal mines in order to inert the coal dust entrained or made airborne during an explosion and prevent propagating explosions. 30 CFR. 75.2 states that "… [rock dust particles] when wetted and dried will not cohere to form a cake which will not be dispersed into separate particles by a light blast of air …" However, a proper definition or quantification of "light blast of air" is not provided. The National Institute for Occupational Safety and Health (NIOSH) has, consequently, designed a dust dispersion chamber to conduct quantitative laboratory-scale dispersibility experiments as a screening tool for candidate rock dusts. A reproducible pulse of air is injected into the chamber and across a shallow tray of rock dust. The dust dispersed and carried downwind is monitored. The mass loss of the dust tray and the airborne dust measurements determine the relative dispersibility of the dust with respect to a Reference rock dust. This report describes the design and the methodology to evaluate the relative dispersibility of rock dusts with and without anti-caking agents. Further, the results of this study indicate that the dispersibility of rock dusts varies with particle size, type of anti-caking agent used, and with the untapped bulk density. Untreated rock dusts, when wetted and dried forming a cake that was much less dispersible than the reference rock dust used in supporting the 80% total incombustible content rule.

Relations between elliptic multiple zeta values and a special derivation algebra

International Nuclear Information System (INIS)

Broedel, Johannes; Matthes, Nils; Schlotterer, Oliver

2016-01-01

We investigate relations between elliptic multiple zeta values (eMZVs) and describe a method to derive the number of indecomposable elements of given weight and length. Our method is based on representing eMZVs as iterated integrals over Eisenstein series and exploiting the connection with a special derivation algebra. Its commutator relations give rise to constraints on the iterated integrals over Eisenstein series relevant for eMZVs and thereby allow to count the indecomposable representatives. Conversely, the above connection suggests apparently new relations in the derivation algebra. Under https://tools.aei.mpg.de/emzv we provide relations for eMZVs over a wide range of weights and lengths. (paper)

Black hole radiation with modified dispersion relation in tunneling paradigm: free-fall frame

Energy Technology Data Exchange (ETDEWEB)

Wang, Peng; Yang, Haitang; Ying, Shuxuan [Sichuan University, Center for Theoretical Physics, College of Physical Science and Technology, Chengdu (China)

2016-01-15

Due to the exponential high gravitational red shift near the event horizon of a black hole, it might appear that the Hawking radiation would be highly sensitive to some unknown high energy physics. To study the effects of any unknown physics at the Planck scale on the Hawking radiation, the dispersive field theory models have been proposed, which are variations of Unruh's sonic black hole analogy. In this paper, we use the Hamilton-Jacobi method to investigate the dispersive field theory models. The preferred frame is the free-fall frame of the black hole. The dispersion relation adopted agrees with the relativistic one at low energy but is modified near the Planck mass m{sub p}. The corrections to the Hawking temperature are calculated for massive and charged particles to O(m{sub p}{sup -2}) and neutral and massless particles with λ = 0 to all orders. The Hawking temperature of radiation agrees with the standard one at the leading order. After the spectrum of radiation near the horizon is obtained, we use the brick wall model to compute the thermal entropy of a massless scalar field near the horizon of a 4D spherically symmetric black hole and a 2D one. Finally, the luminosity of a Schwarzschild black hole is calculated by using the geometric optics approximation. (orig.)

Modal expansions in periodic photonic systems with material loss and dispersion

DEFF Research Database (Denmark)

Wolff, Christian; Busch, Kurt; Mortensen, N. Asger

2018-01-01

in the presence of material dispersion can be overcome. We then formulate expressions for the band-structure derivative (∂ω)/(∂k) (complex group velocity) and the local and total density of transverse optical states. Our exact expressions hold for 3D periodic arrays of materials with arbitrary dispersion...

Effect of initial stresses on dispersion relation of transverse waves in a piezoelectric layered cylinder

International Nuclear Information System (INIS)

Abd-alla, Abo-el-nour N.; Al-sheikh, Fatimah; Al-Hossain, Abdullah Y.

2009-01-01

Effect of initial stresses on dispersion relation for transverse surface waves circulating around a piezoelectric cylinder covered with perfectly conducting layers is investigated. Two overlay materials are considered: Gold and Aluminum. The piezoelectric substrate is considered to have the symmetry of a hexagonal crystal, and the layer is perfectly conducting. The dispersion equation has been given in the form of determinant involving Bessel functions. The roots of the dispersion equation give the values of the characteristic circular frequency parameters of the first three modes for various geometries. These roots are numerically calculated by 'Bisection method iterations technique' and presented graphically for various thickness of the overlayer and for different values of the initial stress. The effects of the initial stress on the natural frequencies are illustrated on the figures. It is found that both the thickness of the overlayer and the initial stress have a substantial effect on the dispersion behavior. The results obtained in this paper may not only help us get insight into the electro-mechanical coupling behavior of the piezoelectric composites cylinders, but can also offer theoretical basis and meaningful suggestions for the design of piezoelectric probes and electro-acoustic devices in the nondestructive evaluation technology. Finally, the results are compared graphically when the overlay is Gold or Aluminum with some special cases which do not have initial stresses and electric field.

Chromatic dispersion of liquid crystal infiltrated capillary tubes and photonic crystal fibers

DEFF Research Database (Denmark)

Rasmussen, Per Dalgaard; Lægsgaard, Jesper; Bang, Ole

2006-01-01

We consider chromatic dispersion of capillary tubes and photonic crystal fibers infiltrated with liquid crystals. A perturbative scheme for inclusion of material dispersion of both liquid crystal and the surrounding waveguide material is derived. The method is used to calculate the chromatic...

From dispersion relations to spectral dimension - and back again

International Nuclear Information System (INIS)

Sotiriou, Thomas P.; Visser, Matt; Weinfurtner, Silke

2011-01-01

The so-called spectral dimension is a scale-dependent number associated with both geometries and field theories that has recently attracted much attention, driven largely, though not exclusively, by investigations of causal dynamical triangulations and Horava gravity as possible candidates for quantum gravity. We advocate the use of the spectral dimension as a probe for the kinematics of these (and other) systems in the region where spacetime curvature is small, and the manifold is flat to a good approximation. In particular, we show how to assign a spectral dimension (as a function of so-called diffusion time) to any arbitrarily specified dispersion relation. We also analyze the fundamental properties of spectral dimension using extensions of the usual Seeley-DeWitt and Feynman expansions and by using saddle point techniques. The spectral dimension turns out to be a useful, robust, and powerful probe, not only of geometry, but also of kinematics.

An Extended Newmark-FDTD Method for Complex Dispersive Media

Directory of Open Access Journals (Sweden)

Yu-Qiang Zhang

2018-01-01

Full Text Available Based on polarizability in the form of a complex quadratic rational function, a novel finite-difference time-domain (FDTD approach combined with the Newmark algorithm is presented for dealing with a complex dispersive medium. In this paper, the time-stepping equation of the polarization vector is derived by applying simultaneously the Newmark algorithm to the two sides of a second-order time-domain differential equation obtained from the relation between the polarization vector and electric field intensity in the frequency domain by the inverse Fourier transform. Then, its accuracy and stability are discussed from the two aspects of theoretical analysis and numerical computation. It is observed that this method possesses the advantages of high accuracy, high stability, and a wide application scope and can thus be applied to the treatment of many complex dispersion models, including the complex conjugate pole residue model, critical point model, modified Lorentz model, and complex quadratic rational function.

Left-cut contribution to the dispersion relation for the elastic electron - atomic-hydrogen scattering amplitude

International Nuclear Information System (INIS)

Amusia, M.Ya.; Kuchiev, M.Yu.

1979-01-01

The jump in the electron - atomic-hydrogen forward scattering amplitude at the cut extending to the left from E = -0.5 au is calculated as a function of the incident electron energy, E, by using the second Born approximation. The contribution from this singularity to the dispersion relation is determined. (Auth.)

Analytic properties of the whistler dispersion function

International Nuclear Information System (INIS)

Daniell, G.J.

1986-01-01

The analytic properties of the dispersion function of a whistler are investigated in the complex frequency plane. It possesses a pole and a branch point at a frequency equal to the minimum value of the electron gyrofrequency along the path of propagation. An integral equation relates the dispersion function to the distribution of magnetospheric electrons along the path and the solution of this equation is obtained. It is found that the electron density in the equatorial plane is very simply related to the dispersion function. A discussion of approximate formulae to represent the dispersion shows how particular terms can be related to attributes of the electron density distribution, and a new approximate formula is proposed. (author)

Dispersal kernel estimation: A comparison of empirical and modelled particle dispersion in a coastal marine system

Science.gov (United States)

Hrycik, Janelle M.; Chassé, Joël; Ruddick, Barry R.; Taggart, Christopher T.

2013-11-01

Early life-stage dispersal influences recruitment and is of significance in explaining the distribution and connectivity of marine species. Motivations for quantifying dispersal range from biodiversity conservation to the design of marine reserves and the mitigation of species invasions. Here we compare estimates of real particle dispersion in a coastal marine environment with similar estimates provided by hydrodynamic modelling. We do so by using a system of magnetically attractive particles (MAPs) and a magnetic-collector array that provides measures of Lagrangian dispersion based on the time-integration of MAPs dispersing through the array. MAPs released as a point source in a coastal marine location dispersed through the collector array over a 5-7 d period. A virtual release and observed (real-time) environmental conditions were used in a high-resolution three-dimensional hydrodynamic model to estimate the dispersal of virtual particles (VPs). The number of MAPs captured throughout the collector array and the number of VPs that passed through each corresponding model location were enumerated and compared. Although VP dispersal reflected several aspects of the observed MAP dispersal, the comparisons demonstrated model sensitivity to the small-scale (random-walk) particle diffusivity parameter (Kp). The one-dimensional dispersal kernel for the MAPs had an e-folding scale estimate in the range of 5.19-11.44 km, while those from the model simulations were comparable at 1.89-6.52 km, and also demonstrated sensitivity to Kp. Variations among comparisons are related to the value of Kp used in modelling and are postulated to be related to MAP losses from the water column and (or) shear dispersion acting on the MAPs; a process that is constrained in the model. Our demonstration indicates a promising new way of 1) quantitatively and empirically estimating the dispersal kernel in aquatic systems, and 2) quantitatively assessing and (or) improving regional hydrodynamic

Further study of a new dispersion relation for electron-atom scattering

International Nuclear Information System (INIS)

Bhatia, A.K.; Temkin, A.

1988-01-01

A new recently proposed dispersion relation (DR) [Temkin, Bhatia, and Kim, J. Phys. B 19, L707 (1986)] is tested for e-He scattering; the results show that the new DR is not satisfied. Therefore we start to investigate the analytic structure of the difference amplitude, previously assumed to be nonsingular, on the negative scattering energy axis. Even under severe approximations we find that the difference amplitude contains both poles and branch points. This suggests, however, a useful approximation of these contributions to the DR which gives very satisfactory agreement in both e-H and e-He scattering. We conclude with some brief general remarks on this problem

Schottky diode model for non-parabolic dispersion in narrow-gap semiconductor and few-layer graphene

Science.gov (United States)

Ang, Yee Sin; Ang, L. K.; Zubair, M.

Despite the fact that the energy dispersions are highly non-parabolic in many Schottky interfaces made up of 2D material, experimental results are often interpreted using the conventional Schottky diode equation which, contradictorily, assumes a parabolic energy dispersion. In this work, the Schottky diode equation is derived for narrow-gap semiconductor and few-layer graphene where the energy dispersions are highly non-parabolic. Based on Kane's non-parabolic band model, we obtained a more general Kane-Schottky scaling relation of J (T2 + γkBT3) which connects the contrasting J T2 in the conventional Schottky interface and the J T3 scaling in graphene-based Schottky interface via a non-parabolicity parameter, γ. For N-layer graphene of ABC -stacking and of ABA -stacking, the scaling relation follows J T 2 / N + 1 and J T3 respectively. Intriguingly, the Richardson constant extracted from the experimental data using an incorrect scaling can differ with the actual value by more than two orders of magnitude. Our results highlights the importance of using the correct scaling relation in order to accurately extract important physical properties, such as the Richardson constant and the Schottky barrier's height.

Nonlinear Dispersive Elastic Waves in Solids: Exact, Approximate, and Numerical Solutions

Science.gov (United States)

Khajehtourian, Romik

Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or fluid flow are all likely to involve wave dynamics at some level. A particular class of problems is concerned with the propagation of elastic waves in a solid medium, such as a fiber-reinforced composite material responding to vibratory excitations, or soil and rock admitting seismic waves moments after the onset of an earthquake, or phonon transport in a semiconducting crystal like silicon. Regardless of the type of wave, the dispersion relation provides a fundamental characterization of the elastodynamic properties of the medium. The first part of the dissertation examines the propagation of a large-amplitude elastic wave in a one-dimensional homogeneous medium with a focus on the effects of inherent nonlinearities on the dispersion relation. Considering a thin rod, where the thickness is small compared to the wavelength, an exact, closed-form formulation is presented for the treatment of two types of nonlinearity in the strain-displacement gradient relation: Green-Lagrange and Hencky. The derived relation is then verified by direct time-domain simulations, examining both instantaneous dispersion (by direct observation) and short-term, pre-breaking dispersion (by Fourier transformation). A high-order perturbation analysis is also conducted yielding an explicit analytical space-time solution, which is shown to be spectrally accurate. The results establish a perfect match between theory and simulation and reveal that regardless of the strength of the nonlinearity, the dispersion relation fully embodies all information pertaining to the nonlinear harmonic generation mechanism that unfolds as an arbitrary-profiled wave evolves in the medium. In the second part of the dissertation, the analysis is extended to a continuous periodic thin rod exhibiting multiple phases or embedded local resonators. The

Canine goniodysgenesis-related glaucoma: a morphologic review of 100 cases looking at inflammation and pigment dispersion.

Science.gov (United States)

Reilly, Christopher M; Morris, Rebecca; Dubielzig, Richard R

2005-01-01

To investigate the role of pigment dispersion and inflammation in the pathogenesis of goniodysgenesis-related glaucoma (GDRG). Cases of GDRG were selected when the duration of the disease was specified and there was not any confounding pathology. Cases were grouped into 7-day (chronic) durations, based on the time required to effect end-stage retinal damage. Acute cases were further divided into pigment dispersion: segmental loss of posterior iris pigment epithelium, clumping of posterior iris pigment epithelium, pigmented cells in the trabecular meshwork or anterior chamber and preferential settling of pigmented cells in the ventral aspect of the iridocorneal angle. Slides were also evaluated for the presence of neutrophils and/or lymphoplasmacytic cells in the trabecular meshwork (TM). Differences between groups were analyzed statistically. Of 100 cases evaluated, 34 were 7-days (chronic) in duration. Of all globes examined, 96% had at least one sign of pigment dispersion, with no significant difference between groups. Two or more signs of pigment dispersion were present in 76% of all globes. The 4-7-day group was significantly more likely than the 7-day groups. Neutrophils were present in the TM of 86% of 7-day cases to have neutrophils in the TM, with 65% and 17% [corrected] positive cases, respectively. Lymphoplasmacytic inflammation was present in 53% of all cases, with no significant difference between groups. Cases in the 7-day cases to have both types of inflammation. Our results indicate that both acute inflammation and pigment dispersion may be key factors in the pathogenesis of GDRG. Pigment dispersion is prevalent at all time points and increases during the first 7 days. The finding of iris pigment epithelial loss supports the theory that pupillary block associated with iris-lens touching may be important in the pathogenesis of GDRG.

Taylor dispersion in wind-driven current

Science.gov (United States)

Li, Gang; Wang, Ping; Jiang, Wei-Quan; Zeng, Li; Li, Zhi; Chen, G. Q.

2017-12-01

Taylor dispersion associated with wind-driven currents in channels, shallow lakes and estuaries is essential to hydrological environmental management. For solute dispersion in a wind-driven current, presented in this paper is an analytical study of the evolution of concentration distribution. The concentration moments are intensively derived for an accurate presentation of the mean concentration distribution, up to the effect of kurtosis. The vertical divergence of concentration is then deduced by Gill's method of series expansion up to the fourth order. Based on the temporal evolution of the vertical concentration distribution, the dispersion process in the wind-driven current is concretely characterized. The uniform shear leads to a special symmetrical distribution of mean concentration free of skewness. The non-uniformity of vertical concentration is caused by convection and smeared out gradually by the effect of diffusion, but fails to disappear even at large times.

Transfer function of radio over fiber multimode fiber optic links considering third-order dispersion.

Science.gov (United States)

Capmany, J; Gasulla, Ivana

2007-08-20

Although a considerable number of multimode fiber (MMF) links operate in a wavelength region around 850 nm where chromatic dispersion of a given modal group mu is described adequately by the second derivative beta(mu) (2) of the propagation constant beta(mu)(omega), there is also an increasing interest in MMF links transmitting in the second spectral window (@1300nm) where this second derivative vanishes being thus necessary to consider the third derivative beta(mu) (3) in the evaluation of the transfer function of the multimode fiber link. We present in this paper, for the first time to our knowledge, an analytical model for the transfer function of a multimode fiber (MMF) optic link taken into account the impact of third-order dispersion. The model extends the operation of a previously reported one for second-order dispersion. Our results show that the performance of broadband radio over fiber transmission through middle-reach distances can be improved by working at the minimum-dispersion wavelength as long as low-linewidth lasers are employed.

Advection models of longitudinal dispersion in rivers

NARCIS (Netherlands)

Kranenburg, C.

1996-01-01

A derivation is presented of a general cross-section averaged model of longitudinal dispersion, which is based on the notion of the advection of tracer particles. Particle displacement length and particle travel time are conceived as stochastic variables, and a joint probability density function is

The non-pair forces and phonon dispersion in heavy alkali metals

International Nuclear Information System (INIS)

Aradhana, Km.; Rathore, R.P.S.

1990-01-01

Two types of non-pair forces, one from the Born-Mayer and the other from the Morse potential, are derived to discuss the response of electrons in heavy alkali metals, i.e., rubidium and cesium. The potentials are added to the two-body potential of Morse to account also for the ion-ion interactions. The potentials so obtained are employed to predict the phonon dispersion relations in bcc metals, which are also compared with recent precise neutron scattering data. (author). 1 fig, 3 tabs., 24 refs

Vertical dispersion produced by random closed orbit distortions and sextupoles

International Nuclear Information System (INIS)

Suzuki, Toshio.

1977-01-01

Vertical dispersion appears even in a machine designed with plane symmetry because of vertical closed orbit distortions, linear coupling and coupling due to sextupoles. This gives rise to several undesirable effects in an electron-positron storage ring such as PEP. Vertical dispersion at the interaction point will increase beam height and reduce luminosity. Vertical dispersion around the ring will modify vertical emittance and partition numbers for synchrotron radiation damping. It will also induce betatron-synchrotron resonance and affect chromaticity correction. Vertical dispersion due to random closed orbit distortions and sextupoles has been studied by Piwinski, and he has indicated that correction of chromaticity and chromatic change of β-function is important. However, he has assumed one error element and evaluated the dispersion at the position of the element. We generalize his argument to a more realistic case and derive more precise criteria for the correction of vertical dispersion. Horizontal dispersion due to perturbations is also studied. Vertical dispersion due to linear coupling is neglected in this note, since it has been studied by other authors. 7 refs

Derived more-less relational mands in children diagnosed with autism.

LENUS (Irish Health Repository)

Murphy, Carol

2009-01-01

In Experiment 1, more and less relations were trained for arbitrary Stimuli A1 and A2 with 3 children with autism. The following conditional discriminations were then trained: A1-B1, A2-B2, B1-C1, B2-C2. In subsequent tests, participants showed derived more-less mands (mand with C1 for more and mand with C2 for less). A training procedure reversed the B-C conditional discriminations, and participants then showed derived reversed more-less mands (mand with C1 for less, C2 for more). Baseline B-C relations were retrained, and participants subsequently demonstrated a return to the original derived manding. A second experiment with 1 prior participant and 1 naive participant removed a possible confounding effect. Establishing derived manding may be an advantageous component when teaching a mand repertoire in applied settings.

Analytical Characterization of SPM Impact on XPM-Induced Degradation in Dispersion-Compensated WDM Systems

Science.gov (United States)

Luís, Ruben S.; Cartaxo, Adolfo V. T.

2005-03-01

This paper proposes the definition of a cross-phase modulation (XPM)-induced power penalty for intensity modulation/direct detection (IM-DD) systems as a function of the normalized variance of the XPM-induced IM. This allows the definition of 1-dB power penalty reference values. New expressions of the equivalent linear model transfer functions for the XPM-induced IM and phase modulation (PM) that include the influence of self-phase modulation (SPM) as well as group-velocity dispersion are derived. The new expressions allow a significant extension for higher powers and dispersion parameters of expressions derived in previous papers for single-segment and multisegment fiber systems with dispersion compensation. Good agreement between analytical results and numerical simulations is obtained. Consistency with work performed numerically and experimentally by other authors is shown, validating the proposed model. Using the proposed model, the influence of residual dispersion and SPM on the limitations imposed by XPM on the performance of dispersion-compensated systems is assessed. It is shown that inline residual dispersion may lead to performance improvement for a properly tuned total residual dispersion. The influence of SPM is shown to degrade the system performance when nonzero-dispersion-shifted fiber is used. However, systems using standard single-mode fiber may benefit from the presence of SPM.

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

International Nuclear Information System (INIS)

Meyers, M.D.; Huang, C.-K.; Zeng, Y.; Yi, S.A.; Albright, B.J.

2015-01-01

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTD scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models

On the numerical dispersion of electromagnetic particle-in-cell code: Finite grid instability

Science.gov (United States)

Meyers, M. D.; Huang, C.-K.; Zeng, Y.; Yi, S. A.; Albright, B. J.

2015-09-01

The Particle-In-Cell (PIC) method is widely used in relativistic particle beam and laser plasma modeling. However, the PIC method exhibits numerical instabilities that can render unphysical simulation results or even destroy the simulation. For electromagnetic relativistic beam and plasma modeling, the most relevant numerical instabilities are the finite grid instability and the numerical Cherenkov instability. We review the numerical dispersion relation of the Electromagnetic PIC model. We rigorously derive the faithful 3-D numerical dispersion relation of the PIC model, for a simple, direct current deposition scheme, which does not conserve electric charge exactly. We then specialize to the Yee FDTD scheme. In particular, we clarify the presence of alias modes in an eigenmode analysis of the PIC model, which combines both discrete and continuous variables. The manner in which the PIC model updates and samples the fields and distribution function, together with the temporal and spatial phase factors from solving Maxwell's equations on the Yee grid with the leapfrog scheme, is explicitly accounted for. Numerical solutions to the electrostatic-like modes in the 1-D dispersion relation for a cold drifting plasma are obtained for parameters of interest. In the succeeding analysis, we investigate how the finite grid instability arises from the interaction of the numerical modes admitted in the system and their aliases. The most significant interaction is due critically to the correct representation of the operators in the dispersion relation. We obtain a simple analytic expression for the peak growth rate due to this interaction, which is then verified by simulation. We demonstrate that our analysis is readily extendable to charge conserving models.

mathematical modelling of atmospheric dispersion of pollutants

International Nuclear Information System (INIS)

Mohamed, M.E.

2002-01-01

the main objectives of this thesis are dealing with environmental problems adopting mathematical techniques. in this respect, atmospheric dispersion processes have been investigated by improving the analytical models to realize the realistic physical phenomena. to achieve these aims, the skeleton of this work contained both mathematical and environmental topics,performed in six chapters. in chapter one we presented a comprehensive review study of most important informations related to our work such as thermal stability , plume rise, inversion, advection , dispersion of pollutants, gaussian plume models dealing with both radioactive and industrial contaminants. chapter two deals with estimating the decay distance as well as the decay time of either industrial or radioactive airborne pollutant. further, highly turbulent atmosphere has been investigated as a special case in the three main thermal stability classes namely, neutral, stable, and unstable atmosphere. chapter three is concerned with obtaining maximum ground level concentration of air pollutant. the variable effective height of pollutants has been considered throughout the mathematical treatment. as a special case the constancy of effective height has been derived mathematically and the maximum ground level concentration as well as its location have been established

Intraindividual Variability across Neuropsychological Tests: Dispersion and Disengaged Lifestyle Increase Risk for Alzheimer’s Disease

Directory of Open Access Journals (Sweden)

Drew W. R. Halliday

2018-03-01

Full Text Available Objective: Increased intraindividual variability (IIV in function has been linked to various age-related outcomes including cognitive decline and dementia. Most studies have operationalized IIV as fluctuations across trials (e.g., response latencies for a single task, with comparatively few studies examining variability across multiple tasks for a given individual. In the present study, we derive a multivariable operationalization of dispersion across a broad profile of neuropsychological measures and use this index along with degree of engaged lifestyle to predict risk of cognitive impairment. Participants and Methods: Participants (n = 60 were community-dwelling older adults aged 65+ years (M = 74.1, SD = 6.5 participating in a cross-sectional investigation of risk factors for amnestic mild cognitive impairment (a-MCI and probable Alzheimer’s Disease (AD. Participants were classified into three subgroups based on test performance and clinical judgement. Healthy controls (n = 30 scored better than −1 SD relative to existing norms on all classification measures, in the absence of memory complaints or functional impairments. The a-MCI group (n = 23 had self- or informant-reported memory complaints and scored 1 SD or more below the mean for at least one memory task while scoring better than 1 SD below the mean for all other cognitive domains, in the absence of functional impairments. The AD group (n = 7 scored at least 2 SD below the mean for two cognitive domains (including memory with impairments in functioning. Measures spanned a range of cognitive domains (episodic memory, executive function, language, with the derived dispersion estimates reflecting variability across an individual’s neuropsychological profile relative to the group average. Further, an Activities Lifestyle Questionnaire, indexing social, cognitive, and physical behaviors, was administered to assess the protective benefits of engaged lifestyle. Results: Multinomial

An Analysis of the New LHC Data through the Dispersion Relations

CERN Document Server

Selyugin, O.V.

2017-01-01

We analyse the tension between the (indirect) measurements of the total cross section, and show the impact of various assumptions on the extraction of the parameters from the elastic scattering amplitude, with a special attention to the total cross section. In particular, the determination of the phase of the elastic scattering amplitude will play an important role, and we shall study it via dispersion relations. We shall also examine the origin of the dependence on momentum transfer of the slopes of the different parts of the scattering amplitude in different models. We shall also give the results of another similar analysis based on a Regge-trajectory approach for the hadron scattering amplitude.

Modified Dispersion Relations: from Black-Hole Entropy to the Cosmological Constant

Science.gov (United States)

Garattini, Remo

2012-07-01

Quantum Field Theory is plagued by divergences in the attempt to calculate physical quantities. Standard techniques of regularization and renormalization are used to keep under control such a problem. In this paper we would like to use a different scheme based on Modified Dispersion Relations (MDR) to remove infinities appearing in one loop approximation in contrast to what happens in conventional approaches. In particular, we apply the MDR regularization to the computation of the entropy of a Schwarzschild black hole from one side and the Zero Point Energy (ZPE) of the graviton from the other side. The graviton ZPE is connected to the cosmological constant by means of of the Wheeler-DeWitt equation.

Evaluation of the real parts of fermion and boson propagators using dispersion relations

International Nuclear Information System (INIS)

Davies, K.T.R.; Davies, R.W.

1991-01-01

General methods are developed for efficiently evaluating principal-value integrals containing fermion and boson causal propagators. These methods are particularly applicable to integrals containing step functions which appear in the zero temperature limit of infinite nuclear matter. Examples are given for the Green functions that occur in the solution of Dyson's equations, with the inclusion of nucleon-delta-mesonic interactions. It is shown how to discretize in order to evaluate numerically the real parts of the propagators. If the real and purely imaginary self-energies of a propagator obey a dispersion relation, then the propagator itself satisfies such a relation. Finally, we discuss the two types of resonances occurring in the pion Green function. (orig.)

Nuclear risk from atmospheric dispersion in Northern Europe - Summary Report

DEFF Research Database (Denmark)

Lauritzen, Bent

The objective of the NordRisk II project has been to derive practical means for assessing the risks from long-range atmospheric dispersion of radioac-tive materials. An atlas over different atmospheric dispersion and deposi-tion scenarios has been developed using historical numerical weather pre......-diction (NWP) model data. The NWP model data covers three years span-ning the climate variability associated with the North Atlantic Oscillation, and the atlas considers radioactive releases from 16 release sites in and near the Nordic countries. A statistical analysis of the long-range disper......-sion and deposition patterns is undertaken to quantify the mean dispersion and deposition as well as the variability. Preliminary analyses show that the large-scale atmospheric dispersion and deposition is near-isotropic, irrespective of the release site and detailed climatology, and allows for a simple...

Derivation of special relativity from Maxwell and Newton.

Science.gov (United States)

Dunstan, D J

2008-05-28

Special relativity derives directly from the principle of relativity and from Newton's laws of motion with a single undetermined parameter, which is found from Faraday's and Ampère's experimental work and from Maxwell's own introduction of the displacement current to be the -c(-2) term in the Lorentz transformations. The axiom of the constancy of the speed of light is quite unnecessary. The behaviour and the mechanism of the propagation of light are not at the foundations of special relativity.

Dispersion analysis and measurement of circular cylindrical wedge-like acoustic waveguides.

Science.gov (United States)

Yu, Tai-Ho

2015-09-01

This study investigated the propagation of flexural waves along the outer edge of a circular cylindrical wedge, the phase velocities, and the corresponding mode displacements. Thus far, only approximate solutions have been derived because the corresponding boundary-value problems are complex. In this study, dispersion curves were determined using the bi-dimensional finite element method and derived through the separation of variables and the Hamilton principle. Modal displacement calculations clarified that the maximal deformations appeared at the outer edge of the wedge tip. Numerical examples indicated how distinct thin-film materials deposited on the outer surface of the circular cylindrical wedge influenced the dispersion curves. Additionally, dispersion curves were measured using a laser-induced guided wave, a knife-edge measurement scheme, and a two-dimensional fast Fourier transform method. Both the numerical and experimental results correlated closely, thus validating the numerical solution. Copyright © 2015 Elsevier B.V. All rights reserved.

The competing effects of microbially derived polymeric and low molecular-weight substances on the dispersibility of CeO2 nanoparticles

Energy Technology Data Exchange (ETDEWEB)

Nakano, Yuriko; Ochiai, Asumi; Kawamoto, Keisuke; Takeda, Ayaka; Ichiyoshi, Kenta; Ohnuki, Toshihiko; Hochella, Michael F.; Utsunomiya, Satoshi

2018-02-26

To understand the competing effects of the components in extracellular substances (ES), polymeric substances (PS) and low-molecular-weight small substances (SS) <1 kDa derived from microorganisms, on the colloidal stability of cerium dioxide nanoparticles (CeNPs), we investigated their adsorption to sparingly soluble CeNPs at room temperature at pH 6.0. The ES was extracted from the fungus S. cerevisiae. The polypeptides and phosphates in all components preferentially adsorbed onto the CeNPs. The zeta potentials of ES + CeNPs, PS + CeNPs, and SS + CeNPs overlapped on the plot of PS itself, indicating the surface charge of the polymeric substances controls the zeta potentials. The sizes of the CeNP aggregates, 100–1300 nm, were constrained by the zeta potentials. The steric barrier derived from the polymers, even in SS, enhanced the CeNP dispersibility at pH 1.5–10. Consequently, the PS and SS had similar effects on modifying the CeNP surfaces. The adsorption of ES, which contains PS + SS, can suppress the aggregation of CeNPs over a wider pH range than that for PS only. The present study addresses the non-negligible effects of small-sized molecules derived from microbial activity on the migration of CeNP in aquatic environments, especially where bacterial consortia prevail.

High-order FDTD methods for transverse electromagnetic systems in dispersive inhomogeneous media.

Science.gov (United States)

Zhao, Shan

2011-08-15

This Letter introduces a novel finite-difference time-domain (FDTD) formulation for solving transverse electromagnetic systems in dispersive media. Based on the auxiliary differential equation approach, the Debye dispersion model is coupled with Maxwell's equations to derive a supplementary ordinary differential equation for describing the regularity changes in electromagnetic fields at the dispersive interface. The resulting time-dependent jump conditions are rigorously enforced in the FDTD discretization by means of the matched interface and boundary scheme. High-order convergences are numerically achieved for the first time in the literature in the FDTD simulations of dispersive inhomogeneous media. © 2011 Optical Society of America

Long-distance Dispersal Patterns of Male Cerulean Warblers (Dendroica cerulea Measured by Stable-hydrogen Isotopes

Directory of Open Access Journals (Sweden)

M. Katherine. Girvan

2007-12-01

Full Text Available Despite the fundamental role played by long-distance dispersal in population dynamics, the mechanisms promoting or inhibiting dispersal by migratory songbirds are poorly understood. We used stable-hydrogen isotopes (δD to evaluate several hypotheses related to long-distance dispersal in the Cerulean Warbler (Dendroica cerulea, a migratory songbird at the center of considerable conservation attention. Feather samples were collected from 103 males throughout the breeding range. We assumed feathers were molted in late summer on the breeding grounds and thus δD values provided an estimate of breeding or hatching location for the previous year. We used a likelihood-based assignment test to estimate the origin of birds the previous year and derived expected δD values for the entire Cerulean Warbler breeding range from precipitation-based maps. Using Bayes' Rule, we also incorporated a prior probability of breeding origin based on estimated rates of site fidelity and survival between breeding seasons. We found that long-distance breeding dispersal by adult male Cerulean Warblers was a fairly common occurrence with 20 of 71 (28.2% individuals originating from a region other than the one they were sampled in. Surprisingly, long-distance natal dispersal was uncommon; only three of 32 (9.4% second-year birds were estimated to have hatched in a region outside their capture region. Young males may be using a form of post-fledging prospecting or conspecific attraction when selecting their first breeding habitats. Populations on the breeding range periphery, such as Ontario and Tennessee, tended to receive fewer long-distance dispersers than did other regions but produced more dispersing individuals than did core regions, suggesting that these areas could act as important sources for other regions. The tendency of a region to produce dispersing individuals was not significantly related to its relative abundance, implying that population abundance is not a

Meteorological uncertainty of atmospheric dispersion model results (MUD)

International Nuclear Information System (INIS)

Havskov Soerensen, J.; Amstrup, B.; Feddersen, H.

2013-08-01

The MUD project addresses assessment of uncertainties of atmospheric dispersion model predictions, as well as possibilities for optimum presentation to decision makers. Previously, it has not been possible to estimate such uncertainties quantitatively, but merely to calculate the 'most likely' dispersion scenario. However, recent developments in numerical weather prediction (NWP) include probabilistic forecasting techniques, which can be utilised also for long-range atmospheric dispersion models. The ensemble statistical methods developed and applied to NWP models aim at describing the inherent uncertainties of the meteorological model results. These uncertainties stem from e.g. limits in meteorological observations used to initialise meteorological forecast series. By perturbing e.g. the initial state of an NWP model run in agreement with the available observational data, an ensemble of meteorological forecasts is produced from which uncertainties in the various meteorological parameters are estimated, e.g. probabilities for rain. Corresponding ensembles of atmospheric dispersion can now be computed from which uncertainties of predicted radionuclide concentration and deposition patterns can be derived. (Author)

Variational Boussinesq model for strongly nonlinear dispersive waves

NARCIS (Netherlands)

Lawrence, C.; Adytia, D.; van Groesen, E.

2018-01-01

For wave tank, coastal and oceanic applications, a fully nonlinear Variational Boussinesq model with optimized dispersion is derived and a simple Finite Element implementation is described. Improving a previous weakly nonlinear version, high waves over flat and varying bottom are shown to be

Fractional vector calculus for fractional advection dispersion

Science.gov (United States)

Meerschaert, Mark M.; Mortensen, Jeff; Wheatcraft, Stephen W.

2006-07-01

We develop the basic tools of fractional vector calculus including a fractional derivative version of the gradient, divergence, and curl, and a fractional divergence theorem and Stokes theorem. These basic tools are then applied to provide a physical explanation for the fractional advection-dispersion equation for flow in heterogeneous porous media.

Chemical countermeasures: Dispersants overview of dispersant use (including application) and research issues

International Nuclear Information System (INIS)

Butler, J.N.

1992-01-01

I will attempt in twenty minutes to summarize the state of research on oil spill dispersants as I perceive it. The expertise I bring to this task includes 20 years of experience with the fate and effects of petroleum in the marine environment, including participation in the 1973 and 1981 NRC studies and three years as chairman of the NRC committee on oil spill dispersants. I More recently I served on a committee of the International Maritime Organization which reviewed the open-quotes Impact of oil and related chemicals and wastes on the marine environment.close quotes That report will be published this year. However, my statements in this paper are not made as a representative of either NRC or IMO. They are my own interpretation of scientific literature cited in the above reviews. Dispersants are chemical formulations, which include surface active agents, designed to decrease the interfacial tension between oil and water. Because the first attempts to disperse oil on a large scale, at the Torrey Canyon spill of 1967, used highly toxic degreasing agents, dispersants have an undeserved reputation for toxicity. In fact, for twenty years dispersant formulations have been developed with an emphasis on reducing their toxicity to marine life. The dispersal of oil in water has been documented in the laboratory by dozens of papers (see references in NRC 1989, pp 70-79), and in the field by dozens of studies (NRC 1989, pp 165- 193). The toxicity of commercial dispersant formulations (NRC 1989, pp 81-123) and dispersed oil (NRC 1989, pp 123-147) has been tested on a wide variety of marine organisms ranging from algae to salmonid fishes. The NRC review has been updated by the IMO/GESAMP (1992) study, but the conclusions remain unchanged

Dispersion in a bent-solenoid channel with symmetric focusing

Energy Technology Data Exchange (ETDEWEB)

Wang, Chun-xi [Argonne National Lab. (ANL), Argonne, IL (United States)

2001-08-21

Longitudinal ionization cooling of a muon beam is essential for muon colliders and will be useful for neutrino factories. Bent-solenoid channels with symmetric focusing has been considered for beam focusing and for generating the required dispersion in the ``emittance exchange'' scheme of longitudinal cooling. In this paper, we derive the Hamiltonian that governs the linear beam dynamics of a bent-solenoid channel, solve the single-particle dynamics, and give equations for determining the lattice functions, in particular, the dispersion functions.

Modeling the dispersal of spiny lobster (

NARCIS (Netherlands)

Whomersley, P.; van der Molen, J.; Holt, D.; Trundle, C.; Clark, S.; Fletcher, D.

2018-01-01

Knowledge of larval dispersal, population dynamics and connectivity in relation to the management and conservation of commercially important species is vital if existing fisheries are to remain sustainable into the future. Larval dispersal of the commercially exploited spiny lobster, Palinurus