Nonlinear Solver Approaches for the Diffusive Wave Approximation to the Shallow Water Equations

NASA Astrophysics Data System (ADS)

Collier, N.; Knepley, M.

2015-12-01

The diffusive wave approximation to the shallow water equations (DSW) is a doubly-degenerate, nonlinear, parabolic partial differential equation used to model overland flows. Despite its challenges, the DSW equation has been extensively used to model the overland flow component of various integrated surface/subsurface models. The equation's complications become increasingly problematic when ponding occurs, a feature which becomes pervasive when solving on large domains with realistic terrain. In this talk I discuss the various forms and regularizations of the DSW equation and highlight their effect on the solvability of the nonlinear system. In addition to this analysis, I present results of a numerical study which tests the applicability of a class of composable nonlinear algebraic solvers recently added to the Portable, Extensible, Toolkit for Scientific Computation (PETSc).

Tidal waves within the thermosphere. [emphasizing wave dissipation and diffusion

NASA Technical Reports Server (NTRS)

Volland, H.; Mayr, H. G.

1974-01-01

The eigenfunctions of the atmosphere (the Hough functions within the lower atmosphere below about 100 km) change their structure and their propagation characteristics within the thermosphere due to dissipation effects such as heat conduction, viscosity, and ion drag. Wave dissipation can be parameterized to a first-order approximation by a complex frequency, the imaginary term of which simulates an effective ion drag force. It is shown how the equivalent depth, the attenuation, and the vertical wavelength of the predominant symmetric diurnal tidal modes change with height as functions of effective ion drag. The boundary conditions of tidal waves are discussed, and asymptotic solutions for the wave parameters like pressure, density, temperature, and wind generated by a heat input proportional to the mean pressure are given. Finally, diffusion effects upon the minor constituents within the thermosphere are described.

Electron Currents and Heating in the Ion Diffusion Region of Asymmetric Reconnection

NASA Technical Reports Server (NTRS)

Graham, D. B.; Khotyaintsev, Yu. V.; Norgren, C.; Vaivads, A.; Andre, M.; Lindqvist, P. A.; Marklund, G. T.; Ergun, R. E.; Paterson, W. R.; Gershman, D. J.;

Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory.

PubMed

Contini, D; Martelli, F; Zaccanti, G

1997-07-01

The diffusion approximation of the radiative transfer equation is a model used widely to describe photon migration in highly diffusing media and is an important matter in biological tissue optics. An analysis of the time-dependent diffusion equation together with its solutions for the slab geometry and for a semi-infinite diffusing medium are reported. These solutions, presented for both the time-dependent and the continuous wave source, account for the refractive index mismatch between the turbid medium and the surrounding medium. The results have been compared with those obtained when different boundary conditions were assumed. The comparison has shown that the effect of the refractive index mismatch cannot be disregarded. This effect is particularly important for the transmittance. The discussion of results also provides an analysis of the role of the absorption coefficient in the expression of the diffusion coefficient.

Quasilinear diffusion coefficients in a finite Larmor radius expansion for ion cyclotron heated plasmas

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

Lee, Jungpyo; Wright, John; Bertelli, Nicola

In this study, a reduced model of quasilinear velocity diffusion by a small Larmor radius approximation is derived to couple the Maxwell’s equations and the Fokker Planck equation self-consistently for the ion cyclotron range of frequency waves in a tokamak. The reduced model ensures the important properties of the full model by Kennel-Engelmann diffusion, such as diffusion directions, wave polarizations, and H-theorem. The kinetic energy change (Wdot ) is used to derive the reduced model diffusion coefficients for the fundamental damping (n = 1) and the second harmonic damping (n = 2) to the lowest order of the finite Larmormore » radius expansion. The quasilinear diffusion coefficients are implemented in a coupled code (TORIC-CQL3D) with the equivalent reduced model of the dielectric tensor. We also present the simulations of the ITER minority heating scenario, in which the reduced model is verified within the allowable errors from the full model results.« less

Quasilinear diffusion coefficients in a finite Larmor radius expansion for ion cyclotron heated plasmas

DOE PAGES

Lee, Jungpyo; Wright, John; Bertelli, Nicola; ...

2017-04-24

In this study, a reduced model of quasilinear velocity diffusion by a small Larmor radius approximation is derived to couple the Maxwell’s equations and the Fokker Planck equation self-consistently for the ion cyclotron range of frequency waves in a tokamak. The reduced model ensures the important properties of the full model by Kennel-Engelmann diffusion, such as diffusion directions, wave polarizations, and H-theorem. The kinetic energy change (Wdot ) is used to derive the reduced model diffusion coefficients for the fundamental damping (n = 1) and the second harmonic damping (n = 2) to the lowest order of the finite Larmormore » radius expansion. The quasilinear diffusion coefficients are implemented in a coupled code (TORIC-CQL3D) with the equivalent reduced model of the dielectric tensor. We also present the simulations of the ITER minority heating scenario, in which the reduced model is verified within the allowable errors from the full model results.« less

Diffusion approximation with polarization and resonance effects for the modelling of seismic waves in strongly scattering small-scale media

NASA Astrophysics Data System (ADS)

Margerin, Ludovic

2013-01-01

This paper presents an analytical study of the multiple scattering of seismic waves by a collection of randomly distributed point scatterers. The theory assumes that the energy envelopes are smooth, but does not require perturbations to be small, thereby allowing the modelling of strong, resonant scattering. The correlation tensor of seismic coda waves recorded at a three-component sensor is decomposed into a sum of eigenmodes of the elastodynamic multiple scattering (Bethe-Salpeter) equation. For a general moment tensor excitation, a total number of four modes is necessary to describe the transport of seismic waves polarization. Their spatio-temporal dependence is given in closed analytical form. Two additional modes transporting exclusively shear polarizations may be excited by antisymmetric moment tensor sources only. The general solution converges towards an equipartition mixture of diffusing P and S waves which allows the retrieval of the local Green's function from coda waves. The equipartition time is obtained analytically and the impact of absorption on Green's function reconstruction is discussed. The process of depolarization of multiply scattered waves and the resulting loss of information is illustrated for various seismic sources. It is shown that coda waves may be used to characterize the source mechanism up to lapse times of the order of a few mean free times only. In the case of resonant scatterers, a formula for the diffusivity of seismic waves incorporating the effect of energy entrapment inside the scatterers is obtained. Application of the theory to high-contrast media demonstrates that coda waves are more sensitive to slow rather than fast velocity anomalies by several orders of magnitude. Resonant scattering appears as an attractive physical phenomenon to explain the small values of the diffusion constant of seismic waves reported in volcanic areas.

Magnetospheric Multiscale Observations of Large-Amplitude Parallel, Electrostatic Waves Associated with Magnetic Reconnection at the Magnetopause

NASA Technical Reports Server (NTRS)

Ergun, R. E.; Holmes, J. C.; Goodrich, K. A.; Wilder, F. D.; Stawarz, J. E.; Eriksson, S.; Newman, D. L.; Schwartz, S. J.; Goldman, M. V.; Sturner, A. P.;

Unimolecular diffusion-mediated reactions with a nonrandom time-modulated absorbing barrier

NASA Technical Reports Server (NTRS)

Bashford, D.; Weaver, D. L.

1986-01-01

A diffusion-reaction model with time-dependent reactivity is formulated and applied to unimolecular reactions. The model is solved exactly numerically and approximately analytically for the unreacted fraction as a function of time. It is shown that the approximate analytical solution is valid even when the system is far from equilibrium, and when the reactivity probability is more complicated than a square-wave function of time. A discussion is also given of an approach to problems of this type using a stochastically fluctuating reactivity, and the first-passage time for a particular example is derived.

Application of a simplified calculation for full-wave microtremor H/ V spectral ratio based on the diffuse field approximation to identify underground velocity structures

NASA Astrophysics Data System (ADS)

Wu, Hao; Masaki, Kazuaki; Irikura, Kojiro; Sánchez-Sesma, Francisco José

2017-12-01

Under the diffuse field approximation, the full-wave (FW) microtremor H/ V spectral ratio ( H/ V) is modeled as the square root of the ratio of the sum of imaginary parts of the Green's function of the horizontal components to that of the vertical one. For a given layered medium, the FW H/ V can be well approximated with only surface waves (SW) H/ V of the "cap-layered" medium which consists of the given layered medium and a new larger velocity half-space (cap layer) at large depth. Because the contribution of surface waves can be simply obtained by the residue theorem, the computation of SW H/ V of cap-layered medium is faster than that of FW H/ V evaluated by discrete wavenumber method and contour integration method. The simplified computation of SW H/ V was then applied to identify the underground velocity structures at six KiK-net strong-motion stations. The inverted underground velocity structures were used to evaluate FW H/ Vs which were consistent with the SW H/ Vs of corresponding cap-layered media. The previous study on surface waves H/ Vs proposed with the distributed surface sources assumption and a fixed Rayleigh-to-Love waves amplitude ratio for horizontal motions showed a good agreement with the SW H/ Vs of our study. The consistency between observed and theoretical spectral ratios, such as the earthquake motions of H/ V spectral ratio and spectral ratio of horizontal motions between surface and bottom of borehole, indicated that the underground velocity structures identified from SW H/ V of cap-layered medium were well resolved by the new method.[Figure not available: see fulltext.

A model of recovering the parameters of fast nonlocal heat transport in magnetic fusion plasmas

NASA Astrophysics Data System (ADS)

Kukushkin, A. B.; Kulichenko, A. A.; Sdvizhenskii, P. A.; Sokolov, A. V.; Voloshinov, V. V.

2017-12-01

A model is elaborated for interpreting the initial stage of the fast nonlocal transport events, which exhibit immediate response, in the diffusion time scale, of the spatial profile of electron temperature to its local perturbation, while the net heat flux is directed opposite to ordinary diffusion (i.e. along the temperature gradient). We solve the inverse problem of recovering the kernel of the integral equation, which describes nonlocal (superdiffusive) transport of energy due to emission and absorption of electromagnetic (EM) waves with long free path and strong reflection from the vacuum vessel’s wall. To allow for the errors of experimental data, we use the method based on the regularized (in the framework of an ill-posed problem, using the parametric models) approximation of available experimental data. The model is applied to interpreting the data from stellarator LHD and tokamak TFTR. The EM wave transport is considered here in the single-group approximation, however the limitations of the physics model enable us to identify the spectral range of the EM waves which might be responsible for the observed phenomenon.

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

NASA Astrophysics Data System (ADS)

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

2015-07-01

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

Effect of field-aligned-beam in parallel diffusion of energetic particles in the Earth's foreshock

NASA Astrophysics Data System (ADS)

Matsukiyo, S.; Nakanishi, K.; Otsuka, F.; Kis, A.; Lemperger, I.; Hada, T.

2016-12-01

Diffusive shock acceleration (DSA) is one of the plausible acceleration mechanisms of cosmic rays. In the standard DSA model the partial density of the accelerated particles, diffused into upstream, exponentially decreases as the distance to the shock increases. Kis et al. (GRL, 31, L20801, 2004) examined the density gradients of energetic ions upstream of the bow shock with high accuracy by using Cluster data. They estimated the diffusion coefficients of energetic ions for the event in February 18, 2003 and showed that the obtained diffusion coefficients are significantly smaller than those estimated in the past statistical study. This implies that particle acceleration at the bow shock can be more efficient than considered before. Here, we focus on the effect of the field-aligned-beam (FAB) which is often observed in the foreshock, and examine how the FAB affects the efficiency of diffusion of the energetic ions by performing test particle simulations. The upstream turbulence is given by the superposition of parallel Alfven waves with power-law energy spectrum with random phase approximation. In the spectrum we further add a peak corresponding to the waves resonantly generated by the FAB. The dependence of the diffusion coefficient on the presence of the FAB as well as total energy of the turbulence, power-law index of the turbulence, and intensity of FAB oriented waves are discussed.

Analytical solution of reaction-diffusion equations for calcium wave propagation in a starburst amacrine cell.

PubMed

Poznanski, R R

2010-09-01

A reaction-diffusion model is presented to encapsulate calcium-induced calcium release (CICR) as a potential mechanism for somatofugal bias of dendritic calcium movement in starburst amacrine cells. Calcium dynamics involves a simple calcium extrusion (pump) and a buffering mechanism of calcium binding proteins homogeneously distributed over the plasma membrane of the endoplasmic reticulum within starburst amacrine cells. The system of reaction-diffusion equations in the excess buffer (or low calcium concentration) approximation are reformulated as a nonlinear Volterra integral equation which is solved analytically via a regular perturbation series expansion in response to calcium feedback from a continuously and uniformly distributed calcium sources. Calculation of luminal calcium diffusion in the absence of buffering enables a wave to travel at distances of 120 μm from the soma to distal tips of a starburst amacrine cell dendrite in 100 msec, yet in the presence of discretely distributed calcium-binding proteins it is unknown whether the propagating calcium wave-front in the somatofugal direction is further impeded by endogenous buffers. If so, this would indicate CICR to be an unlikely mechanism of retinal direction selectivity in starburst amacrine cells.

Physarum machines: encapsulating reaction-diffusion to compute spanning tree

NASA Astrophysics Data System (ADS)

Adamatzky, Andrew

2007-12-01

The Physarum machine is a biological computing device, which employs plasmodium of Physarum polycephalum as an unconventional computing substrate. A reaction-diffusion computer is a chemical computing device that computes by propagating diffusive or excitation wave fronts. Reaction-diffusion computers, despite being computationally universal machines, are unable to construct certain classes of proximity graphs without the assistance of an external computing device. I demonstrate that the problem can be solved if the reaction-diffusion system is enclosed in a membrane with few ‘growth points’, sites guiding the pattern propagation. Experimental approximation of spanning trees by P. polycephalum slime mold demonstrates the feasibility of the approach. Findings provided advance theory of reaction-diffusion computation by enriching it with ideas of slime mold computation.

Gravity Wave Mixing and Effective Diffusivity for Minor Chemical Constituents in the Mesosphere/Lower Thermosphere

NASA Astrophysics Data System (ADS)

Grygalashvyly, M.; Becker, E.; Sonnemann, G. R.

2012-06-01

The influence of gravity waves (GWs) on the distributions of minor chemical constituents in the mesosphere-lower thermosphere (MLT) is studied on the basis of the effective diffusivity concept. The mixing ratios of chemical species used for calculations of the effective diffusivity are obtained from numerical experiments with an off-line coupled model of the dynamics and chemistry abbreviated as KMCM-MECTM (Kuehlungsborn Mechanistic general Circulation Model—MEsospheric Chemistry-Transport Model). In our control simulation the MECTM is driven with the full dynamical fields from an annual cycle simulation with the KMCM, where mid-frequency GWs down to horizontal wavelengths of 350 km are resolved and their wave-mean flow interaction is self-consistently induced by an advanced turbulence model. A perturbation simulation with the MECTM is defined by eliminating all meso-scale variations with horizontal wavelengths shorter than 1000 km from the dynamical fields by means of spectral filtering before running the MECTM. The response of the MECTM to GWs perturbations reveals strong effects on the minor chemical constituents. We show by theoretical arguments and numerical diagnostics that GWs have direct, down-gradient mixing effects on all long-lived minor chemical species that possess a mean vertical gradient in the MLT. Introducing the term wave diffusion (WD) and showing that wave mixing yields approximately the same WD coefficient for different chemical constituents, we argue that it is a useful tool for diagnostic irreversible transport processes. We also present a detailed discussion of the gravity-wave mixing effects on the photochemistry and highlight the consequences for the general circulation of the MLT.

Beam-plasma instability in the presence of low-frequency turbulence. [during type 3 solar emission

NASA Technical Reports Server (NTRS)

Goldman, M. V.; Dubois, D. F.

1982-01-01

General equations are derived for a linear beam-plasma instability in the presence of low-frequency turbulence. Within a 'quasi-linear' statistical approximation, these equations contain Langmuir wave scattering, diffusion, resonant and nonresonant anomalous absorption, and a 'plasma laser' effect. It is proposed that naturally occurring density irregularities in the solar wind may stabilize the beam-unstable Langmuir waves which occur during type III solar emissions.

Invariance property of wave scattering through disordered media

PubMed Central

Pierrat, Romain; Ambichl, Philipp; Gigan, Sylvain; Haber, Alexander; Carminati, Rémi; Rotter, Stefan

2014-01-01

A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only on the system's boundary geometry and is thus unaffected by the value of the mean free path. Here we show that this result is rooted on a much deeper level than that of a random walk, which allows us to extend the reach of this universal invariance property beyond the diffusion approximation. Specifically, we demonstrate that an equivalent invariance relation also holds for the scattering of waves in resonant structures as well as in ballistic, chaotic or in Anderson localized systems. Our work unifies a number of specific observations made in quite diverse fields of science ranging from the movement of ants to nuclear scattering theory. Potential experimental realizations using light fields in disordered media are discussed. PMID:25425671

One step linear reconstruction method for continuous wave diffuse optical tomography

NASA Astrophysics Data System (ADS)

Ukhrowiyah, N.; Yasin, M.

2017-09-01

The method one step linear reconstruction method for continuous wave diffuse optical tomography is proposed and demonstrated for polyvinyl chloride based material and breast phantom. Approximation which used in this method is selecting regulation coefficient and evaluating the difference between two states that corresponding to the data acquired without and with a change in optical properties. This method is used to recovery of optical parameters from measured boundary data of light propagation in the object. The research is demonstrated by simulation and experimental data. Numerical object is used to produce simulation data. Chloride based material and breast phantom sample is used to produce experimental data. Comparisons of results between experiment and simulation data are conducted to validate the proposed method. The results of the reconstruction image which is produced by the one step linear reconstruction method show that the image reconstruction almost same as the original object. This approach provides a means of imaging that is sensitive to changes in optical properties, which may be particularly useful for functional imaging used continuous wave diffuse optical tomography of early diagnosis of breast cancer.

Avalanches, breathers, and flow reversal in a continuous Lorenz-96 model

NASA Astrophysics Data System (ADS)

Blender, R.; Wouters, J.; Lucarini, V.

2013-07-01

For the discrete model suggested by Lorenz in 1996, a one-dimensional long-wave approximation with nonlinear excitation and diffusion is derived. The model is energy conserving but non-Hamiltonian. In a low-order truncation, weak external forcing of the zonal mean flow induces avalanchelike breather solutions which cause reversal of the mean flow by a wave-mean flow interaction. The mechanism is an outburst-recharge process similar to avalanches in a sandpile model.

Diffusely scattered and transmitted elastic waves by random rough solid-solid interfaces using an elastodynamic Kirchhoff approximation

NASA Astrophysics Data System (ADS)

Shi, Fan; Lowe, Mike; Craster, Richard

2017-06-01

Elastic waves scattered by random rough interfaces separating two distinct media play an important role in modeling phonon scattering and impact upon thermal transport models, and are also integral to ultrasonic inspection. We introduce theoretical formulas for the diffuse field of elastic waves scattered by, and transmitted across, random rough solid-solid interfaces using the elastodynamic Kirchhoff approximation. The new formulas are validated by comparison with numerical Monte Carlo simulations, for a wide range of roughness (rms σ ≤λ /3 , correlation length λ0≥ wavelength λ ), demonstrating a significant improvement over the widely used small-perturbation approach, which is valid only for surfaces with small rms values. Physical analysis using the theoretical formulas derived here demonstrates that increasing the rms value leads to a considerable change of the scattering patterns for each mode. The roughness has different effects on the reflection and the transmission, with a strong dependence on the material properties. In the special case of a perfect match of the wave speed of the two solid media, the transmission is the same as the case for a flat interface. We pay particular attention to scattering in the specular direction, often used as an observable quantity, in terms of the roughness parameters, showing a peak at an intermediate value of rms; this rms value coincides with that predicted by the Rayleigh parameter.

Finite element modeling of light propagation in fruit under illumination of continuous-wave beam

USDA-ARS?s Scientific Manuscript database

Spatially-resolved spectroscopy provides a means for measuring the optical properties of biological tissues, based on analytical solutions to diffusion approximation for semi-infinite media under the normal illumination of infinitely small size light beam. The method is, however, prone to error in m...

Oxygenation level and hemoglobin concentration in experimental tumor estimated by diffuse optical spectroscopy

NASA Astrophysics Data System (ADS)

Orlova, A. G.; Kirillin, M. Yu.; Volovetsky, A. B.; Shilyagina, N. Yu.; Sergeeva, E. A.; Golubiatnikov, G. Yu.; Turchin, I. V.

2017-07-01

Using diffuse optical spectroscopy the level of oxygenation and hemoglobin concentration in experimental tumor in comparison with normal muscle tissue of mice have been studied. Subcutaneously growing SKBR-3 was used as a tumor model. Continuous wave fiber probe diffuse optical spectroscopy system was employed. Optical properties extraction approach was based on diffusion approximation. Decreased blood oxygen saturation level and increased total hemoglobin content were demonstrated in the neoplasm. The main reason of such differences between tumor and norm was significant elevation of deoxyhemoglobin concentration in SKBR-3. The method can be useful for diagnosis of tumors as well as for study of blood flow parameters of tumor models with different angiogenic properties.

Diffusion-driven fluid dynamics in ideal gases and plasmas

NASA Astrophysics Data System (ADS)

Vold, E. L.; Yin, L.; Taitano, W.; Molvig, K.; Albright, B. J.

2018-06-01

The classical transport theory based on Chapman-Enskog methods provides self-consistent approximations for the kinetic flux of mass, heat, and momentum in a fluid limit characterized with a small Knudsen number. The species mass fluxes relative to the center of mass, or "diffusive fluxes," are expressed as functions of known gradient quantities with kinetic coefficients evaluated using similar analyses for mixtures of gases or plasma components. The sum over species of the diffusive mass fluxes is constrained to be zero in the Lagrange frame, and thus results in a non-zero molar flux leading to a pressure perturbation. At an interface between two species initially in pressure equilibrium, the pressure perturbation driven by the diffusive molar flux induces a center of mass velocity directed from the species of greater atomic mass towards the lighter atomic mass species. As the ratio of the species particle masses increases, this center of mass velocity carries an increasingly greater portion of the mass across the interface and for a particle mass ratio greater than about two, the center of mass velocity carries more mass than the gradient driven diffusion flux. Early time transients across an interface between two species in a 1D plasma regime and initially in equilibrium are compared using three methods; a fluid code with closure in a classical transport approximation, a particle in cell simulation, and an implicit Fokker-Planck solver for the particle distribution functions. The early time transient phenomenology is shown to be similar in each of the computational simulation methods, including a pressure perturbation associated with the stationary "induced" component of the center of mass velocity which decays to pressure equilibrium during diffusion. At early times, the diffusive process generates pressure and velocity waves which propagate outward from the interface and are required to maintain momentum conservation. The energy in the outgoing waves dissipates as heat in viscous regions, and it is hypothesized that these diffusion driven waves may sustain fluctuations in less viscid finite domains after reflections from the boundaries. These fluid dynamic phenomena are similar in gases or plasmas and occur in flow transients with a moderate Knudsen number. The analysis and simulation results show how the kinetic flux, represented in the fluid transport closure, directly modifies the mass averaged flow described with the Euler equations.

Bounce- and MLT-averaged diffusion coefficients in a physics-based magnetic field geometry obtained from RAM-SCB for the March 17 2013 storm

DOE PAGES

Zhao, Lei; Yu, Yiqun; Delzanno, Gian Luca; ...

2015-04-01

Local acceleration via whistler wave and particle interaction plays a significant role in particle dynamics in the radiation belt. In this work we explore gyro-resonant wave-particle interaction and quasi-linear diffusion in different magnetic field configurations related to the March 17 2013 storm. We consider the Earth's magnetic dipole field as a reference and compare the results against non-dipole field configurations corresponding to quiet and stormy conditions. The latter are obtained with the ring current-atmosphere interactions model with a self-consistent magnetic field RAM-SCB, a code that models the Earth's ring current and provides a realistic modeling of the Earth's magnetic field.more » By applying quasi-linear theory, the bounce- and MLT-averaged electron pitch angle, mixed term, and energy diffusion coefficients are calculated for each magnetic field configuration. For radiation belt (~1 MeV) and ring current (~100 keV) electrons, it is shown that at some MLTs the bounce-averaged diffusion coefficients become rather insensitive to the details of the magnetic field configuration, while at other MLTs storm conditions can expand the range of equatorial pitch angles where gyro-resonant diffusion occurs and significantly enhance the diffusion rates. When MLT average is performed at drift shell L = 4.25 (a good approximation to drift average), the diffusion coefficients become quite independent of the magnetic field configuration for relativistic electrons, while the opposite is true for lower energy electrons. These results suggest that, at least for the March 17 2013 storm and for L ≲ 4.25, the commonly adopted dipole approximation of the Earth's magnetic field can be safely used for radiation belt electrons, while a realistic modeling of the magnetic field configuration is necessary to describe adequately the diffusion rates of ring current electrons.« less

Bounce- and MLT-averaged diffusion coefficients in a physics-based magnetic field geometry obtained from RAM-SCB for the March 17 2013 storm

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

Zhao, Lei; Yu, Yiqun; Delzanno, Gian Luca

Local acceleration via whistler wave and particle interaction plays a significant role in particle dynamics in the radiation belt. In this work we explore gyro-resonant wave-particle interaction and quasi-linear diffusion in different magnetic field configurations related to the March 17 2013 storm. We consider the Earth's magnetic dipole field as a reference and compare the results against non-dipole field configurations corresponding to quiet and stormy conditions. The latter are obtained with the ring current-atmosphere interactions model with a self-consistent magnetic field RAM-SCB, a code that models the Earth's ring current and provides a realistic modeling of the Earth's magnetic field.more » By applying quasi-linear theory, the bounce- and MLT-averaged electron pitch angle, mixed term, and energy diffusion coefficients are calculated for each magnetic field configuration. For radiation belt (~1 MeV) and ring current (~100 keV) electrons, it is shown that at some MLTs the bounce-averaged diffusion coefficients become rather insensitive to the details of the magnetic field configuration, while at other MLTs storm conditions can expand the range of equatorial pitch angles where gyro-resonant diffusion occurs and significantly enhance the diffusion rates. When MLT average is performed at drift shell L = 4.25 (a good approximation to drift average), the diffusion coefficients become quite independent of the magnetic field configuration for relativistic electrons, while the opposite is true for lower energy electrons. These results suggest that, at least for the March 17 2013 storm and for L ≲ 4.25, the commonly adopted dipole approximation of the Earth's magnetic field can be safely used for radiation belt electrons, while a realistic modeling of the magnetic field configuration is necessary to describe adequately the diffusion rates of ring current electrons.« less

Electron heating in quasi-perpendicular shocks - A Monte Carlo simulation

NASA Technical Reports Server (NTRS)

Veltri, Pierluigi; Mangeney, Andre; Scudder, Jack D.

1990-01-01

To study the problem of electron heating in quasi-perpendicular shocks, under the combined effects of 'reversible' motion, in the shock electric potential and magnetic field, and wave-particle interactions a diffusion equation was derived, in the drift (adiabatic) approximation and it was solved by using a Monte Carlo method. The results show that most of the observations can be explained within this framework. The simulation has also definitively shown that the electron parallel temperature is determined by the dc electromagnetic field and not by any wave particle induced heating. Wave-particle interactions are effective in smoothing out the large gradients in phase space produced by the 'reversible' motion of the electrons, thus producing a 'cooling' of the electrons. Some constraints on the wave-particle interaction process may be obtained from a detailed comparison between the simulation and observations. In particular, it appears that the adiabatic approximation must be violated in order to explain the observed evolution of the perpendicular temperature.

Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

NASA Astrophysics Data System (ADS)

Owolabi, Kolade M.

2018-03-01

In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

Building 1D resonance broadened quasilinear (RBQ) code for fast ions Alfvénic relaxations

NASA Astrophysics Data System (ADS)

Gorelenkov, Nikolai; Duarte, Vinicius; Berk, Herbert

2016-10-01

The performance of the burning plasma is limited by the confinement of superalfvenic fusion products, e.g. alpha particles, which are capable of resonating with the Alfvénic eigenmodes (AEs). The effect of AEs on fast ions is evaluated using a resonance line broadened diffusion coefficient. The interaction of fast ions and AEs is captured for cases where there are either isolated or overlapping modes. A new code RBQ1D is being built which constructs diffusion coefficients based on realistic eigenfunctions that are determined by the ideal MHD code NOVA. The wave particle interaction can be reduced to one-dimensional dynamics where for the Alfvénic modes typically the particle kinetic energy is nearly constant. Hence to a good approximation the Quasi-Linear (QL) diffusion equation only contains derivatives in the angular momentum. The diffusion equation is then one dimensional that is efficiently solved simultaneously for all particles with the equation for the evolution of the wave angular momentum. The evolution of fast ion constants of motion is governed by the QL diffusion equations which are adapted to find the ion distribution function.

Finite element modeling of light propagation in turbid media under illumination of a continuous-wave beam

USDA-ARS?s Scientific Manuscript database

Spatially-resolved spectroscopy provides a means for measuring the optical properties of biological tissues, based on analytical solutions to diffusion approximation for semi-infinite media under the normal illumination of infinitely small size light beam. The method is, however, prone to error in m...

Turbulent resistivity, diffusion and heating

NASA Technical Reports Server (NTRS)

Fried, B. D.; Kennel, C. F.; Mackenzie, K.; Coroniti, F. V.; Kindel, J. M.; Stenzel, R.; Taylor, R. J.; White, R.; Wong, A. Y.; Bernstein, W.

1971-01-01

Experimental and theoretical studies are reported on ion acoustic and ion cyclotron turbulence and their roles in anomalous resistivity, viscosity, diffusion and heating and in the structure of collisionless electrostatic shocks. Resistance due to ion acoustic turbulence has been observed in experiments with a streaming cesium plasma in which electron current, potential rise due to turbulent resistivity, spectrum of unstable ion acoustic waves, and associated electron heating were all measured directly. Kinetic theory calculations for an expanding, unstable plasma, give results in agreement with the experiment. In a strong magnetic field, with T sub e/T sub i approximately 1 and current densities typical for present Tokomaks, the plasma is stable to ion acoustic but unstable to current driven electrostatic ion cyclotron waves. Relevant characteristics of these waves are calculated and it is shown that for ion, beta greater than m sub e/m sub i, the electromagnetic ion cyclotron wave has a lower instability threshold than the electrostatic one. However, when ion acoustic turbulence is present experiments with double plasma devices show rapid anomalous heating of an ion beam streaming through a plasma.

Carbon diffusion in molten uranium: an ab initio molecular dynamics study

NASA Astrophysics Data System (ADS)

Garrett, Kerry E.; Abrecht, David G.; Kessler, Sean H.; Henson, Neil J.; Devanathan, Ram; Schwantes, Jon M.; Reilly, Dallas D.

2018-04-01

In this work we used ab initio molecular dynamics within the framework of density functional theory and the projector-augmented wave method to study carbon diffusion in liquid uranium at temperatures above 1600 K. The electronic interactions of carbon and uranium were described using the local density approximation (LDA). The self-diffusion of uranium based on this approach is compared with literature computational and experimental results for liquid uranium. The temperature dependence of carbon and uranium diffusion in the melt was evaluated by fitting the resulting diffusion coefficients to an Arrhenius relationship. We found that the LDA calculated activation energy for carbon was nearly twice that of uranium: 0.55 ± 0.03 eV for carbon compared to 0.32 ± 0.04 eV for uranium. Structural analysis of the liquid uranium-carbon system is also discussed.

Adsorbate Diffusion on Transition Metal Nanoparticles

DTIC Science & Technology

2015-01-01

different sizes and shapes using density functional theory calculations. We show that nanoparticles bind adsorbates more strongly than the...structure theoretical methods, a quantitative study with accurate density functional theory (DFT) calculations is still missing. Here, we perform a...functional theory . The projector augmented wave (PAW) potentials29,30 were used for electron- ion interactions and the generalized gradient approximation

The effects of noise on binocular rivalry waves: a stochastic neural field model

NASA Astrophysics Data System (ADS)

Webber, Matthew A.; Bressloff, Paul C.

2013-03-01

We analyze the effects of extrinsic noise on traveling waves of visual perception in a competitive neural field model of binocular rivalry. The model consists of two one-dimensional excitatory neural fields, whose activity variables represent the responses to left-eye and right-eye stimuli, respectively. The two networks mutually inhibit each other, and slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We first show how, in the absence of any noise, the system supports a propagating composite wave consisting of an invading activity front in one network co-moving with a retreating front in the other network. Using a separation of time scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how extrinsic noise in the activity variables leads to a diffusive-like displacement (wandering) of the composite wave from its uniformly translating position at long time scales, and fluctuations in the wave profile around its instantaneous position at short time scales. We use our analysis to calculate the first-passage-time distribution for a stochastic rivalry wave to travel a fixed distance, which we find to be given by an inverse Gaussian. Finally, we investigate the effects of noise in the depression variables, which under an adiabatic approximation lead to quenched disorder in the neural fields during propagation of a wave.

Modelling coupled turbulence - dissolved oxygen dynamics near the sediment-water interface under wind waves and sea swell.

PubMed

Chatelain, Mathieu; Guizien, Katell

2010-03-01

A one-dimensional vertical unsteady numerical model for diffusion-consumption of dissolved oxygen (DO) above and below the sediment-water interface was developed to investigate DO profile dynamics under wind waves and sea swell (high-frequency oscillatory flows with periods ranging from 2 to 30s). We tested a new approach to modelling DO profiles that coupled an oscillatory turbulent bottom boundary layer model with a Michaelis-Menten based consumption model. The flow regime controls both the mean value and the fluctuations of the oxygen mass transfer efficiency during a wave cycle, as expressed by the non-dimensional Sherwood number defined with the maximum shear velocity (Sh). The Sherwood number was found to be non-dependent on the sediment biogeochemical activity (mu). In the laminar regime, both cycle-averaged and variance of the Sherwood number are very low (Sh <0.05, VAR(Sh)<0.1%). In the turbulent regime, the cycle-averaged Sherwood number is larger (Sh approximately 0.2). The Sherwood number also has intra-wave cycle fluctuations that increase with the wave Reynolds number (VAR(Sh) up to 30%). Our computations show that DO mass transfer efficiency under high-frequency oscillatory flows in the turbulent regime are water-side controlled by: (a) the diffusion time across the diffusive boundary layer and (b) diffusive boundary layer dynamics during a wave cycle. As a result of these two processes, when the wave period decreases, the Sh minimum increases and the Sh maximum decreases. Sh values vary little, ranging from 0.17 to 0.23. For periods up to 30s, oxygen penetration depth into the sediment did not show any intra-wave fluctuations. Values for the laminar regime are small (

Interferometric Near-Infrared Spectroscopy (iNIRS) for determination of optical and dynamical properties of turbid media

PubMed Central

Borycki, Dawid; Kholiqov, Oybek; Chong, Shau Poh; Srinivasan, Vivek J.

2016-01-01

We introduce and implement interferometric near-infrared spectroscopy (iNIRS), which simultaneously extracts optical and dynamical properties of turbid media through analysis of a spectral interference fringe pattern. The spectral interference fringe pattern is measured using a Mach-Zehnder interferometer with a frequency-swept narrow linewidth laser. Fourier analysis of the detected signal is used to determine time-of-flight (TOF)-resolved intensity, which is then analyzed over time to yield TOF-resolved intensity autocorrelations. This approach enables quantification of optical properties, which is not possible in conventional, continuous-wave near-infrared spectroscopy (NIRS). Furthermore, iNIRS quantifies scatterer motion based on TOF-resolved autocorrelations, which is a feature inaccessible by well-established diffuse correlation spectroscopy (DCS) techniques. We prove this by determining TOF-resolved intensity and temporal autocorrelations for light transmitted through diffusive fluid phantoms with optical thicknesses of up to 55 reduced mean free paths (approximately 120 scattering events). The TOF-resolved intensity is used to determine optical properties with time-resolved diffusion theory, while the TOF-resolved intensity autocorrelations are used to determine dynamics with diffusing wave spectroscopy. iNIRS advances the capabilities of diffuse optical methods and is suitable for in vivo tissue characterization. Moreover, iNIRS combines NIRS and DCS capabilities into a single modality. PMID:26832264

Wave activity in the neighborhood of the bowshock of Mars

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

Sagdeev, R.Z.; Shapiro, V.D.; Shevchenko, V.I.

Plasma wave activity in the neighborhood of the Martial bow shock were measured for the first time by the Soviet spacecraft Phobos-2 in a wide frequency range from dc to 150 kHz. The wave activity varied in character as the spacecraft moved across different plasma regions: in the neighborhood of the Martian bow shock, inside the magnetosheath and in the tail region. In this paper the authors provide suggestions for the processes responsible for these plasma waves. The most interesting peculiarities of the wave activity around Mars is the sharp increase of wave intensity in the magnetosheath region. This increasemore » is attributed to two different physical mechanisms. High frequency waves are excited at the shock front due to currents flowing along the front; these ion acoustic waves are convected inside by the solar wind. The low frequency waves ({approximately}100 Hz) close to the inside boundary were, they believe, generated by heavy Martian ions diffusing through the planetopause into the magnetosheath.« less

Electrostatically confined nanoparticle interactions and dynamics.

PubMed

Eichmann, Shannon L; Anekal, Samartha G; Bevan, Michael A

2008-02-05

We report integrated evanescent wave and video microscopy measurements of three-dimensional trajectories of 50, 100, and 250 nm gold nanoparticles electrostatically confined between parallel planar glass surfaces separated by 350 and 600 nm silica colloid spacers. Equilibrium analyses of single and ensemble particle height distributions normal to the confining walls produce net electrostatic potentials in excellent agreement with theoretical predictions. Dynamic analyses indicate lateral particle diffusion coefficients approximately 30-50% smaller than expected from predictions including the effects of the equilibrium particle distribution within the gap and multibody hydrodynamic interactions with the confining walls. Consistent analyses of equilibrium and dynamic information in each measurement do not indicate any roles for particle heating or hydrodynamic slip at the particle or wall surfaces, which would both increase diffusivities. Instead, lower than expected diffusivities are speculated to arise from electroviscous effects enhanced by the relative extent (kappaa approximately 1-3) and overlap (kappah approximately 2-4) of electrostatic double layers on the particle and wall surfaces. These results demonstrate direct, quantitative measurements and a consistent interpretation of metal nanoparticle electrostatic interactions and dynamics in a confined geometry, which provides a basis for future similar measurements involving other colloidal forces and specific biomolecular interactions.

Analysis of nonlocal phonon thermal conductivity simulations showing the ballistic to diffusive crossover

NASA Astrophysics Data System (ADS)

Allen, Philip B.

2018-04-01

Simulations [e.g., X. W. Zhou et al., Phys. Rev. B 79, 115201 (2009), 10.1103/PhysRevB.79.115201] show nonlocal effects of the ballistic/diffusive crossover. The local temperature has nonlinear spatial variation not contained in the local Fourier law j ⃗(r ⃗) =-κ ∇ ⃗T (r ⃗) . The heat current j ⃗(r ⃗) depends not just on the local temperature gradient ∇ ⃗T (r ⃗) but also on temperatures at points r⃗' within phonon mean free paths, which can be micrometers long. This paper uses the Peierls-Boltzmann transport theory in nonlocal form to analyze the spatial variation Δ T (r ⃗) . The relaxation-time approximation (RTA) is used because the full solution is very challenging. Improved methods of extrapolation to obtain the bulk thermal conductivity κ are proposed. Callaway invented an approximate method of correcting RTA for the q ⃗ (phonon wave vector or crystal momentum) conservation of N (Normal as opposed to Umklapp) anharmonic collisions. This method is generalized to the nonlocal case where κ (k ⃗) depends on the wave vector of the current j ⃗(k ⃗) and temperature gradient i k ⃗Δ T (k ⃗) .

Generalized thermoelastic diffusive waves in heat conducting materials

NASA Astrophysics Data System (ADS)

Sharma, J. N.

2007-04-01

Keeping in view the applications of diffusion processes in geophysics and electronics industry, the aim of the present paper is to give a detail account of the plane harmonic generalized thermoelastic diffusive waves in heat conducting solids. According to the characteristic equation, three longitudinal waves namely, elastodiffusive (ED), mass diffusion (MD-mode) and thermodiffusive (TD-mode), can propagate in such solids in addition to transverse waves. The transverse waves get decoupled from rest of the fields and hence remain unaffected due to temperature change and mass diffusion effects. These waves travel without attenuation and dispersion. The other generalized thermoelastic diffusive waves are significantly influenced by the interacting fields and hence suffer both attenuation and dispersion. At low frequency mass diffusion and thermal waves do not exist but at high-frequency limits these waves propagate with infinite velocity being diffusive in character. Moreover, in the low-frequency regions, the disturbance is mainly dominant by mechanical process of transportation of energy and at high-frequency regions it is significantly dominated by a close to diffusive process (heat conduction or mass diffusion). Therefore, at low-frequency limits the waves like modes are identifiable with small amplitude waves in elastic materials that do not conduct heat. The general complex characteristic equation is solved by using irreducible case of Cardano's method with the help of DeMoivre's theorem in order to obtain phase speeds, attenuation coefficients and specific loss factor of energy dissipation of various modes. The propagation of waves in case of non-heat conducting solids is also discussed. Finally, the numerical solution is carried out for copper (solvent) and zinc (solute) materials and the obtained phase velocities, attenuation coefficients and specific loss factor of various thermoelastic diffusive waves are presented graphically.

Carbon diffusion in molten uranium: an ab initio molecular dynamics study

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

Garrett, Kerry E.; Abrecht, David G.; Kessler, Sean H.

In this work we used ab initio molecular dynamics (AIMD) within the framework of density functional theory (DFT) and the projector-augmented wave (PAW) method to study carbon diffusion in liquid uranium at temperatures above 1600 K. The electronic interactions of carbon and uranium were described using the local density approximation (LDA). The self-diffusion of uranium based on this approach is compared with literature computational and experimental results for liquid uranium. The temperature dependence of carbon and uranium diffusion in the melt was evaluated by fitting the resulting diffusion coefficients to an Arrhenius relationship. We found that the LDA calculated activationmore » energy for carbon was nearly twice that of uranium: 0.55±0.03 eV for carbon compared to 0.32±0.04 eV for uranium. Structural analysis of the liquid uranium-carbon system is also discussed.« less

SPATIAL DAMPING OF PROPAGATING KINK WAVES IN PROMINENCE THREADS

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

Soler, R.; Oliver, R.; Ballester, J. L., E-mail: roberto.soler@wis.kuleuven.be

Transverse oscillations and propagating waves are frequently observed in threads of solar prominences/filaments and have been interpreted as kink magnetohydrodynamic (MHD) modes. We investigate the spatial damping of propagating kink MHD waves in transversely nonuniform and partially ionized prominence threads. Resonant absorption and ion-neutral collisions (Cowling's diffusion) are the damping mechanisms taken into account. The dispersion relation of resonant kink waves in a partially ionized magnetic flux tube is numerically solved by considering prominence conditions. Analytical expressions of the wavelength and damping length as functions of the kink mode frequency are obtained in the thin tube and thin boundary approximations.more » For typically reported periods of thread oscillations, resonant absorption is an efficient mechanism for the kink mode spatial damping, while ion-neutral collisions have a minor role. Cowling's diffusion dominates both the propagation and damping for periods much shorter than those observed. Resonant absorption may explain the observed spatial damping of kink waves in prominence threads. The transverse inhomogeneity length scale of the threads can be estimated by comparing the observed wavelengths and damping lengths with the theoretically predicted values. However, the ignorance of the form of the density profile in the transversely nonuniform layer introduces inaccuracies in the determination of the inhomogeneity length scale.« less

Propagation and Breaking at High Altitudes of Gravity Waves Excited by Tropospheric Forcing

NASA Technical Reports Server (NTRS)

Prusa, Joseph M.; Smolarkiewicz, Piotr K.; Garcia, Rolando R.

1996-01-01

An anelastic approximation is used with a time-variable coordinate transformation to formulate a two-dimensional numerical model that describes the evolution of gravity waves. The model is solved using a semi-Lagrangian method with monotone (nonoscillatory) interpolation of all advected fields. The time-variable transformation is used to generate disturbances at the lower boundary that approximate the effect of a traveling line of thunderstorms (a squall line) or of flow over a broad topographic obstacle. The vertical propagation and breaking of the gravity wave field (under conditions typical of summer solstice) is illustrated for each of these cases. It is shown that the wave field at high altitudes is dominated by a single horizontal wavelength; which is not always related simply to the horizontal dimension of the source. The morphology of wave breaking depends on the horizontal wavelength; for sufficiently short waves, breaking involves roughly one half of the wavelength. In common with other studies, it is found that the breaking waves undergo "self-acceleration," such that the zonal-mean intrinsic frequency remains approximately constant in spite of large changes in the background wind. It is also shown that many of the features obtained in the calculations can be understood in terms of linear wave theory. In particular, linear theory provides insights into the wavelength of the waves that break at high altitudes, the onset and evolution of breaking. the horizontal extent of the breaking region and its position relative to the forcing, and the minimum and maximum altitudes where breaking occurs. Wave breaking ceases at the altitude where the background dissipation rate (which in our model is a proxy for molecular diffusion) becomes greater than the rate of dissipation due to wave breaking, This altitude, in effect, the model turbopause, is shown to depend on a relatively small number of parameters that characterize the waves and the background state.

Low-Frequency Oscillations and Transport Processes Induced by Multiscale Transverse Structures in the Polar Wind Outflow: A Three-Dimensional Simulation

NASA Technical Reports Server (NTRS)

Ganguli, Supriya B.; Gavrishchaka, Valeriy V.

1999-01-01

Multiscale transverse structures in the magnetic-field-aligned flows have been frequently observed in the auroral region by FAST and Freja satellites. A number of multiscale processes, such as broadband low-frequency oscillations and various cross-field transport effects are well correlated with these structures. To study these effects, we have used our three-dimensional multifluid model with multiscale transverse inhomogeneities in the initial velocity profile. Self-consistent-frequency mode driven by local transverse gradients in the generation of the low field-aligned ion flow and associated transport processes were simulated. Effects of particle interaction with the self-consistent time-dependent three-dimensional wave potential have been modeled using a distribution of test particles. For typical polar wind conditions it has been found that even large-scale (approximately 50 - 100 km) transverse inhomogeneities in the flow can generate low-frequency oscillations that lead to significant flow modifications, cross-field particle diffusion, and other transport effects. It has also been shown that even small-amplitude (approximately 10 - 20%) short-scale (approximately 10 km) modulations of the original large-scale flow profile significantly increases low-frequency mode generation and associated cross-field transport, not only at the local spatial scales imposed by the modulations but also on global scales. Note that this wave-induced cross-field transport is not included in any of the global numerical models of the ionosphere, ionosphere-thermosphere, or ionosphere-polar wind. The simulation results indicate that the wave-induced cross-field transport not only affects the ion outflow rates but also leads to a significant broadening of particle phase-space distribution and transverse particle diffusion.

Integrating flood modelling in a hydrological catchment model: flow approximations and spatial resolution.

NASA Astrophysics Data System (ADS)

van den Bout, Bastian; Jetten, Victor

2017-04-01

Within hydrological models, flow approximations are commonly used to reduce computation time. The validity of these approximations is strongly determined by flow height, flow velocity, the spatial resolution of the model, and by the manner in which flow routing is implemented. The assumptions of these approximations can furthermore limit emergent behavior, and influence flow behavior under space-time scaling. In this presentation, the validity and performance of the kinematic, diffusive and dynamic flow approximations are investigated for use in a catchment-based flood model. Particularly, the validity during flood events and for varying spatial resolutions is investigated. The OpenLISEM hydrological model is extended to implement these flow approximations and channel flooding based on dynamic flow. The kinematic routing uses a predefined converging flow network, the diffusive and dynamic routing uses a 2D flow solution over a DEM. The channel flow in all cases is a 1D kinematic wave approximation. The flow approximations are used to recreate measured discharge in three catchments of different size in China, Spain and Italy, among which is the hydrograph of the 2003 flood event in the Fella river basin (Italy). Furthermore, spatial resolutions are varied for the flood simulation in order to investigate the influence of spatial resolution on these flow approximations. Results show that the kinematic, diffusive and dynamic flow approximation provide least to highest accuracy, respectively, in recreating measured temporal variation of the discharge. Kinematic flow, which is commonly used in hydrological modelling, substantially over-estimates hydrological connectivity in the simulations with a spatial resolution of below 30 meters. Since spatial resolutions of models have strongly increased over the past decades, usage of routed kinematic flow should be reconsidered. In the case of flood events, spatial modelling of kinematic flow substantially over-estimates hydrological connectivity and flow concentration, leading to significant errors. The combination of diffusive or dynamic overland flow and dynamic channel flooding provides high accuracy in recreating the 2003 Fella river flood event. Finally, flow approximations substantially influenced the predictive potential of the (flash) flood model.

Light propagation in tissues with controlled optical properties

NASA Astrophysics Data System (ADS)

Tuchin, Valery V.; Maksimova, Irina L.; Zimnyakov, Dmitry A.; Kon, Irina L.; Mavlyutov, Albert H.; Mishin, Alexey A.

1997-10-01

Theoretical and computer modeling approaches, such as Mie theory, radiative transfer theory, diffusion wave correlation spectroscopy, and Monte Carlo simulation were used to analyze tissue optics during a process of optical clearing due to refractive index matching. Continuous wave transmittance and forward scattering measurement as well as intensity correlation experiments were used to monitor tissue structural and optical properties. As a control, tissue samples of the human sclera were taken. Osmotically active solutions, such as Trazograph, glucose, and polyethylene glycol, were used as chemicals. A characteristic time response of human scleral optical clearing the range 3 to 10 min was determined. The diffusion coefficients describing the permeability of the scleral samples to Trazograph were experimentally estimated; the average value was DT approximately equals (0.9 +/- 0.5) X 10-5 cm2/s. The results are general and can be used to describe many other fibrous tissues.

a Bounded Finite-Difference Discretization of a Two-Dimensional Diffusion Equation with Logistic Nonlinear Reaction

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

In the present manuscript, we introduce a finite-difference scheme to approximate solutions of the two-dimensional version of Fisher's equation from population dynamics, which is a model for which the existence of traveling-wave fronts bounded within (0,1) is a well-known fact. The method presented here is a nonstandard technique which, in the linear regime, approximates the solutions of the original model with a consistency of second order in space and first order in time. The theory of M-matrices is employed here in order to elucidate conditions under which the method is able to preserve the positivity and the boundedness of solutions. In fact, our main result establishes relatively flexible conditions under which the preservation of the positivity and the boundedness of new approximations is guaranteed. Some simulations of the propagation of a traveling-wave solution confirm the analytical results derived in this work; moreover, the experiments evince a good agreement between the numerical result and the analytical solutions.

Magnetospheric Multiscale Observations of an Ion Diffusion Region With Large Guide Field at the Magnetopause: Current System, Electron Heating, and Plasma Waves

NASA Astrophysics Data System (ADS)

Zhou, M.; Berchem, J.; Walker, R. J.; El-Alaoui, M.; Goldstein, M. L.; Lapenta, G.; Deng, X.; Li, J.; Le Contel, O.; Graham, D. B.; Lavraud, B.; Paterson, W. R.; Giles, B. L.; Burch, J. L.; Torbert, R. B.; Russell, C. T.; Strangeway, R. J.; Zhao, C.; Ergun, R. E.; Lindqvist, P.-A.; Marklund, G.

2018-03-01

We report Magnetospheric Multiscale (MMS) observations of a reconnecting current sheet in the presence of a weak density asymmetry with large guide field at the dayside magnetopause. An ion diffusion region (IDR) was detected associated with this current sheet. Parallel current dominated over the perpendicular current in the IDR, as found in previous studies of component reconnection. Electrons were preferentially heated parallel to the magnetic field within the IDR. The heating was manifested as a flattop distribution below 400 eV. Two types of electromagnetic electron whistler waves were observed within the regions where electrons were heated. One type of whistler wave was associated with nonlinear structures in E|| with amplitudes up to 20 mV/m. The other type was not associated with any structures in E||. Poynting fluxes of these two types of whistler waves were directed away from the X-line. We suggest that the nonlinear evolution of the oblique whistler waves gave rise to the solitary structures in E||. There was a perpendicular super-Alfvénic outflow jet that was carried by magnetized electrons. Intense electrostatic lower hybrid drift waves were localized in the current sheet center and were probably driven by the super-Alfvénic electron jet, the velocity of which was approximately equal to the diamagnetic drift of demagnetized ions. Our observations suggest that the guide field significantly modified the structures (Hall electromagnetic fields and current system) and wave properties in the IDR.

Diffusion by one wave and by many waves

NASA Astrophysics Data System (ADS)

Albert, J. M.

2010-03-01

Radiation belt electrons and chorus waves are an outstanding instance of the important role cyclotron resonant wave-particle interactions play in the magnetosphere. Chorus waves are particularly complex, often occurring with large amplitude, narrowband but drifting frequency and fine structure. Nevertheless, modeling their effect on radiation belt electrons with bounce-averaged broadband quasi-linear theory seems to yield reasonable results. It is known that coherent interactions with monochromatic waves can cause particle diffusion, as well as radically different phase bunching and phase trapping behavior. Here the two formulations of diffusion, while conceptually different, are shown to give identical diffusion coefficients, in the narrowband limit of quasi-linear theory. It is further shown that suitably averaging the monochromatic diffusion coefficients over frequency and wave normal angle parameters reproduces the full broadband quasi-linear results. This may account for the rather surprising success of quasi-linear theory in modeling radiation belt electrons undergoing diffusion by chorus waves.

Acoustic instability driven by cosmic-ray streaming

NASA Technical Reports Server (NTRS)

Begelman, Mitchell C.; Zweibel, Ellen G.

1994-01-01

We study the linear stability of compressional waves in a medium through which cosmic rays stream at the Alfven speed due to strong coupling with Alfven waves. Acoustic waves can be driven unstable by the cosmic-ray drift, provided that the streaming speed is sufficiently large compared to the thermal sound speed. Two effects can cause instability: (1) the heating of the thermal gas due to the damping of Alfven waves driven unstable by cosmic-ray streaming; and (2) phase shifts in the cosmic-ray pressure perturbation caused by the combination of cosmic-ray streaming and diffusion. The instability does not depend on the magnitude of the background cosmic-ray pressure gradient, and occurs whether or not cosmic-ray diffusion is important relative to streaming. When the cosmic-ray pressure is small compared to the gas pressure, or cosmic-ray diffusion is strong, the instability manifests itself as a weak overstability of slow magnetosonic waves. Larger cosmic-ray pressure gives rise to new hybrid modes, which can be strongly unstable in the limits of both weak and strong cosmic-ray diffusion and in the presence of thermal conduction. Parts of our analysis parallel earlier work by McKenzie & Webb (which were brought to our attention after this paper was accepted for publication), but our treatment of diffusive effects, thermal conduction, and nonlinearities represent significant extensions. Although the linear growth rate of instability is independent of the background cosmic-ray pressure gradient, the onset of nonlinear eff ects does depend on absolute value of DEL (vector differential operator) P(sub c). At the onset of nonlinearity the fractional amplitude of cosmic-ray pressure perturbations is delta P(sub C)/P(sub C) approximately (kL) (exp -1) much less than 1, where k is the wavenumber and L is the pressure scale height of the unperturbed cosmic rays. We speculate that the instability may lead to a mode of cosmic-ray transport in which plateaus of uniform cosmic-ray pressure are separated by either laminar or turbulent jumps in which the thermal gas is subject to intense heating.

A remark on the theory of measuring thermal diffusivity by the modified Angstrom's method. [in lunar samples

NASA Technical Reports Server (NTRS)

Horai, K.-I.

1981-01-01

A theory of the measurement of the thermal diffusivity of a sample by the modified Angstrom method is developed for the case in which radiative heat loss from the end surface of the sample is not negligible, and applied to measurements performed on lunar samples. Formulas allowing sample thermal diffusivity to be determined from the amplitude decay and phase lag of a temperature wave traveling through the sample are derived for a flat disk sample for which only heat loss from the end surface is important, and a sample of finite diameter and length for which heat loss through the end and side surfaces must be considered. It is noted that in the case of a flat disk, measurements at a single angular frequency of the temperature wave are sufficient, while the sample of finite diameter and length requires measurements at two discrete angular frequencies. Comparison of the values of the thermal diffusivities of two lunar samples of dimensions approximately 1 x 1 x 2 cm derived by the present methods and by the Angstrom theory for a finite bar reveals them to differ by not more than 5%, and indicates that more refined data are required as the measurement theory becomes more complicated.

Evaluation of a fast single-photon avalanche photodiode for measurement of early transmitted photons through diffusive media.

PubMed

Mu, Ying; Valim, Niksa; Niedre, Mark

2013-06-15

We tested the performance of a fast single-photon avalanche photodiode (SPAD) in measurement of early transmitted photons through diffusive media. In combination with a femtosecond titanium:sapphire laser, the overall instrument temporal response time was 59 ps. Using two experimental models, we showed that the SPAD allowed measurement of photon-density sensitivity functions that were approximately 65% narrower than the ungated continuous wave case at very early times. This exceeds the performance that we have previously achieved with photomultiplier-tube-based systems and approaches the theoretical maximum predicted by time-resolved Monte Carlo simulations.

THEMIS Observations of the Magnetopause Electron Diffusion Region: Large Amplitude Waves and Heated Electrons

NASA Technical Reports Server (NTRS)

Tang, Xiangwei; Cattell, Cynthia; Dombeck, John; Dai, Lei; Wilson, Lynn B. III; Breneman, Aaron; Hupack, Adam

2013-01-01

We present the first observations of large amplitude waves in a well-defined electron diffusion region based on the criteria described by Scudder et al at the subsolar magnetopause using data from one Time History of Events and Macroscale Interactions during Substorms (THEMIS) satellite. These waves identified as whistler mode waves, electrostatic solitary waves, lower hybrid waves, and electrostatic electron cyclotron waves, are observed in the same 12 s waveform capture and in association with signatures of active magnetic reconnection. The large amplitude waves in the electron diffusion region are coincident with abrupt increases in electron parallel temperature suggesting strong wave heating. The whistler mode waves, which are at the electron scale and which enable us to probe electron dynamics in the diffusion region were analyzed in detail. The energetic electrons (approx. 30 keV) within the electron diffusion region have anisotropic distributions with T(sub e(right angle))/T(sub e(parallel)) > 1 that may provide the free energy for the whistler mode waves. The energetic anisotropic electrons may be produced during the reconnection process. The whistler mode waves propagate away from the center of the "X-line" along magnetic field lines, suggesting that the electron diffusion region is a possible source region of the whistler mode waves.

Volume nanograting formation in laser-silica interaction as a result of the 1D plasma-resonance ionization instability

NASA Astrophysics Data System (ADS)

Gildenburg, V. B.; Pavlichenko, I. A.

2016-08-01

The initial stage of the small-scale ionization-induced instability developing inside the fused silica volume exposed to the femtosecond laser pulse is studied as a possible initial cause of the self-organized nanograting formation. We have calculated the spatial spectra of the instability with the electron-hole diffusion taken into account for the first time and have found that it results in the formation of some hybrid (diffusion-wave) 1D structure with the spatial period determined as the geometrical mean of the laser wavelength and characteristic diffusion length of the process considered. Near the threshold of the instability, this period occurs to be approximately equal to the laser half-wavelength in the silica, close to the one experimentally observed.

One-dimensional numerical study of charged particle trajectories in turbulent electrostatic wave fields

NASA Technical Reports Server (NTRS)

Graham, K. N.; Fejer, J. A.

1976-01-01

The paper describes a numerical simulation of electron trajectories in weak random electric fields under conditions that are approximately true for Langmuir waves whose wavelength is much longer than the Debye length. Two types of trajectory calculations were made: (1) the initial particle velocity was made equal to the mean phase velocity of the waves, or (2) it was equal to 0.7419 times the mean velocity of the waves, so that the initial velocity differed substantially from all phase velocities of the wave spectrum. When the autocorrelation time is much greater than the trapping time, the particle motion can change virtually instantaneously from one of three states - high-velocity, low-velocity, or trapped state - to another. The probability of instantaneous transition from a high- or low-velocity state becomes small when the difference between the particle velocity and the mean phase velocity of the waves becomes high in comparison to the trapping velocity. Diffusive motion becomes negligible under these conditions also.

Interaction of ring current and radiation belt protons with ducted plasmaspheric hiss. 1: Diffusion coefficients and timescales

NASA Technical Reports Server (NTRS)

Kozyra, J. U.; Rasmussen, C. E.; Miller, R. H.; Lyons, L. R.

1994-01-01

Protons that are convected into the inner magnetosphere in response to enhanced magnetic activity can resonate with ducted plasmaspheric hiss in the outer plasmasphere via an anomalous Doppler-shifted cyclotron resonance. Plasmaspheric hiss is a right-hand-polarized electromagnetic emission that is observed to fill the plasmasphere on a routine basis. When plasmaspheric hiss is confined within field-aligned ducts or guided along density gradients, wave normal angles remain largely below 45 deg. This allows resonant interactions with ions at typical ring current and radiation belt energies to take place. Such field-aligned ducts have been observed both within the plasmasphere and in regions outside of the plasmasphere. Wave intensities are estimated using statistical information from studies of detached plasma regions. Diffusion coefficients are presented for a range of L shells and proton energies for a fixed wave distribution. Harmonic resonances in the range N = +/-100 are considered in order to include interactions between hiss at 100 Hz to 2 kHz frequencies, and protons in the energy range between approximately 10 keV and 1000 keV. Diffusion timescales are estimated to be of the order of tens of days and comparable to or shorter than lifetimes for Coulomb decay and charge exchange losses over most of the energy and spatial ranges of interest.

Thermophotonic lock-in imaging of early demineralized and carious lesions in human teeth

NASA Astrophysics Data System (ADS)

Tabatabaei, Nima; Mandelis, Andreas; Amaechi, Bennett Tochukwu

2011-07-01

As an extension of frequency-domain photothermal radiometry, a novel dental-imaging modality, thermophotonic lock-in imaging (TPLI), is introduced. This methodology uses photothermal wave principles and is capable of detecting early carious lesions and cracks on occlusal and approximal surfaces as well as early caries induced by artificial demineralizing solutions. The increased light scattering and absorption within early carious lesions increases the thermal-wave amplitude and shifts the thermal-wave centroid, producing contrast between the carious lesion and the intact enamel in both amplitude and phase images. Samples with artificial and natural occlusal and approximal caries were examined in this study. Thermophotonic effective detection depth is controlled by the modulation frequency according to the well-known concept of thermal diffusion length. TPLI phase images are emissivity normalized and therefore insensitive to the presence of stains. Amplitude images, on the other hand, provide integrated information from deeper enamel regions. It is concluded that the results of our noninvasive, noncontacting imaging methodology exhibit higher sensitivity to very early demineralization than dental radiographs and are in agreement with the destructive transverse microradiography mineral density profiles.

Subcontinental-scale crustal velocity changes along the Pacific-North America plate boundary.

PubMed

Davis, J L; Wernicke, B P; Bisnath, S; Niemi, N A; Elósegui, P

2006-06-29

Transient tectonic deformation has long been noted within approximately 100 km of plate boundary fault zones and within active volcanic regions, but it is unknown whether transient motions also occur at larger scales within plates. Relatively localized transients are known to occur as both seismic and episodic aseismic events, and are generally ascribed to motions of magma bodies, aseismic creep on faults, or elastic or viscoelastic effects associated with earthquakes. However, triggering phenomena and systematic patterns of seismic strain release at subcontinental (approximately 1,000 km) scale along diffuse plate boundaries have long suggested that energy transfer occurs at larger scale. Such transfer appears to occur by the interaction of stresses induced by surface wave propagation and magma or groundwater in the crust, or from large-scale stress diffusion within the oceanic mantle in the decades following clusters of great earthquakes. Here we report geodetic evidence for a coherent, subcontinental-scale change in tectonic velocity along a diffuse approximately 1,000-km-wide deformation zone. Our observations are derived from continuous GPS (Global Positioning System) data collected over the past decade across the Basin and Range province, which absorbs approximately 25 per cent of Pacific-North America relative plate motion. The observed changes in site velocity define a sharp boundary near the centre of the province oriented roughly parallel to the north-northwest relative plate motion vector. We show that sites to the west of this boundary slowed relative to sites east of it by approximately 1 mm yr(-1) starting in late 1999.

Modeling of Outer Radiation Belt Electron Scattering due to Spatial and Spectral Properties of ULF Waves

NASA Astrophysics Data System (ADS)

Tornquist, Mattias

The research presented in this thesis covers wave-particle interactions for relativistic (0.5-10 MeV) electrons in Earth's outer radiation belt (r = 3-7 RE, or L-shells: L = 3-7) interacting with magnetospheric Pc-5 (ULF) waves. This dissertation focuses on ideal models for short and long term electron energy and radial position scattering caused by interactions with ULF waves. We use test particle simulations to investigate these wave-particle interactions with ideal wave and magnetic dipole fields. We demonstrate that the wave-particle phase can cause various patterns in phase space trajectories, i.e. local acceleration, and that for a global electron population, for all initial conditions accounted for, has a negligible net energy scattering. Working with GSM polar coordinates, the relevant wave field components are EL, Ephi and Bz, where we find that the maximum energy scattering is 3-10 times more effective for Ephi compared to EL in a magnetic dipole field with a realistic dayside compression amplitude. We also evaluate electron interactions with two coexisting waves for a set of small frequency separations and phases, where it is confirmed that multi-resonant transport is possible for overlapping resonances in phase space when the Chirikov criterion is met (stochasticity parameter K = 1). The electron energy scattering enhances with decreasing frequency separation, i.e. increasing K, and is also dependent on the phases of the waves. The global acceleration is non-zero, can be onset in about 1 hour and last for > 4 hours. The adiabatic wave-particle interaction discussed up to this point can be regarded as short-term scattering ( tau ˜ hours ). When the physical problem extends to longer time scales (tau ˜ days ) the process ceases to be adiabatic due to the introduction of stochastic element in the system and becomes a diffusive process. We show that any mode in a broadband spectrum can contribute to the total diffusion rate for a particular drift frequency within the spectral band via dynamic phases. Each mode contributes maximally at a phase reset frequency fr = 2.63fk, where fk is the mode frequency. We experiment with electron diffusion due to interaction with wave broadband spectra in MLT sectors and find the phase reset effect being strongest when there is no azimuthal wave vector (msec = 0) within the sector. DLL rapidly coheres to the local PSD as the wave number increases and, for example, at msec = 1.00+/-0.25 the effect of phase resets is only 10-30% as strong as for msec = 0. Since phase resets depend on particle drift frequencies when MLT sectors are involved, a consequence is that DLL must adjust as a function of L-shell as well. For example, from the local PSD as the sole contributor to diffusion Schulz and Lanzerotte (1979) has shown that DLL ˜ L6 , but we prove that the function becomes DLL ˜ L5 with some variations due to fd and MLT sector width. The final part of this dissertation evaluates a pre storm commencement event on November 7, 2004, when Earth's magnetopause was struck by a high-speed solar wind with a mostly northward component of interplanetary magnetic field. We obtained a global MHD field simulated by the OpenGGC model for the interval 17:00-18:40 in universal time from NASA's Community Coordinated Modeling Center. Global distribution plots of the electric and magnetic field PSD reveal strong ULF waves spanning the whole dayside sector. There are distinct electric field modes at approximately 0.9, 2.3 and 3.7-6.3 mHz within the dayside sector, which we then used in test-particle simulations and the variance calculations in order to evaluate the diffusion coefficients. To ensure diffusion by sufficient stochasticity, we run the event by repeating the interval 10 times in series for a total duration of 12 hours. For the wave electric fields, the predicted diffusion coefficient due to local PSD matches the outcome from simulated electron scattering at 0.9 and 2.3 mHz. The diffusion due to the wider frequency band at 3.7-6.3 mHz does not fit the PSD profile alone, and requires phase resets in non-resonant modes within the spectrum to yield an agreement between the calculations and the simulations. Furthermore, only msec = 1 provides the correct solution. We have thus demonstrated the importance in including both the MLT sector width and wave number as additional significant factors apart from the local PSD in determining the diffusion coefficient for a realistic wave field. (Abstract shortened by UMI.).

Simulation of propagation of the HPM in the low-pressure argon plasma

NASA Astrophysics Data System (ADS)

Zhigang, LI; Zhongcai, YUAN; Jiachun, WANG; Jiaming, SHI

2018-02-01

The propagation of the high-power microwave (HPM) with a frequency of 6 GHz in the low-pressure argon plasma was studied by the method of fluid approximation. The two-dimensional transmission model was built based on the wave equation, the electron drift-diffusion equations and the heavy species transport equations, which were solved by means of COMSOL Multiphysics software. The simulation results showed that the propagation characteristic of the HPM was closely related to the average electron density of the plasma. The attenuation of the transmitted wave increased nonlinearly with the electron density. Specifically, the growth of the attenuation slowed down as the electron density increased uniformly. In addition, the concrete transmission process of the HPM wave in the low-pressure argon plasma was given.

Scattering attenuation profile of the Moon: Implications for shallow moonquakes and the structure of the megaregolith

NASA Astrophysics Data System (ADS)

Gillet, K.; Margerin, L.; Calvet, M.; Monnereau, M.

2017-01-01

We report measurements of the attenuation of short period seismic waves in the Moon based on the quantitative analysis of envelope records of lunar quakes. Our dataset consists of waveforms corresponding to 62 events, including artificial and natural impacts, shallow moonquakes and deep moonquakes, recorded by the four seismometers deployed during Apollo missions 12, 14, 15 and 16. To quantify attenuation and distinguish between elastic (scattering) and inelastic (absorption) mechanisms we measure the time of arrival of the maximum of energy tmax and the coda quality factor Qc . The former is controlled by both scattering and absorption, while the latter is an excellent proxy for absorption. Consistent with the strong broadening of seismogram envelopes in the Moon, we employ diffusion theory in spherical geometry to model the propagation of seismic energy in depth-dependent scattering and absorbing media. To minimize the misfit between predicted and observed tmax for deep moonquakes and impacts, we employ a genetic algorithm and explore a large number of depth-dependent attenuation models quantified by the scattering quality factor Qsc or equivalently the wave diffusivity D, and the absorption quality factor Qi . The scattering and absorption profiles that best fit the data display very strong scattering attenuation (Qsc ≤ 10) or equivalently very low wave diffusivity (D ≈ 2 km2/s) in the first 10 km of the Moon. These values correspond to the most heterogeneous regions on Earth, namely volcanic areas. Below this surficial layer, the diffusivity rises very slowly up to a depth of approximately 80 km where Qsc and D exhibit an abrupt increase of about one order of magnitude. Below 100 km depth, Qsc increases rapidly up to approximately 2000 at a depth of about 150 km, a value similar to the one found in the Earth's mantle. By contrast, the absorption quality factor on the Moon Qi ≈ 2400 is about one order or magnitude larger than on Earth. Our results suggest the existence of an approximately 100 km thick megaregolith, which is much larger than what was previously thought. The rapid decrease of scattering attenuation below this depth is compatible with crack healing through viscoelastic mechanisms. Using our best attenuation model, we invert for the depth of shallow moonquakes based on the observed variation of tmax with epicentral distance. On average, they are found to originate from a depth of about 50 km ± 20 km, which suggests that these earthquakes are caused by the failure of deep faults in the brittle part of the Moon.

Coronal ``Wave'': Magnetic Footprint of a Coronal Mass Ejection?

NASA Astrophysics Data System (ADS)

Attrill, Gemma D. R.; Harra, Louise K.; van Driel-Gesztelyi, Lidia; Démoulin, Pascal

2007-02-01

We investigate the properties of two ``classical'' EUV Imaging Telescope (EIT) coronal waves. The two source regions of the associated coronal mass ejections (CMEs) possess opposite helicities, and the coronal waves display rotations in opposite senses. We observe deep core dimmings near the flare site and also widespread diffuse dimming, accompanying the expansion of the EIT wave. We also report a new property of these EIT waves, namely, that they display dual brightenings: persistent ones at the outermost edge of the core dimming regions and simultaneously diffuse brightenings constituting the leading edge of the coronal wave, surrounding the expanding diffuse dimmings. We show that such behavior is consistent with a diffuse EIT wave being the magnetic footprint of a CME. We propose a new mechanism where driven magnetic reconnections between the skirt of the expanding CME magnetic field and quiet-Sun magnetic loops generate the observed bright diffuse front. The dual brightenings and the widespread diffuse dimming are identified as innate characteristics of this process.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-01-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-06-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0. Furthermore, we prove the global existence and uniqueness of C^{α ,β }-solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1-space. The exponential convergence rate is also derived.

Anomalous plasma diffusion and the magnetopause boundary layer

NASA Technical Reports Server (NTRS)

Treumann, Rudolf A.; Labelle, James; Haerendel, Gerhard; Pottelette, Raymond

1992-01-01

An overview of the current state of anomalous diffusion research at the magnetopause and its role in the formation of the magnetopause boundary layer is presented. Plasma wave measurements in the boundary layer indicate that most of the relevant unstable wave modes contribute negligibly to the diffusion process at the magnetopause under magnetically undisturbed northward IMF conditions. The most promising instability is the lower hybrid drift instability, which may yield diffusion coefficients of the right order if the highest measured wave intensities are assumed. It is concluded that global stationary diffusion due to wave-particle interactions does not take place at the magnetopause. Microscopic wave-particle interaction and anomalous diffusion may contribute to locally break the MD frozen-in conditions and help in transporting large amounts of magnetosheath plasma across the magnetospheric boundary.

Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming

2017-12-01

In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.

Sharp-front wave of strong magnetic field diffusion in solid metal

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

Xiao, Bo; Gu, Zhuo-wei; Kan, Ming-xian

When a strong magnetic field diffuses into a solid metal, if the metal's resistance possesses an abrupt rise at some critical temperature and the magnetic field strength is above some critical value, the magnetic field will diffuse into the metal in the form of a sharp-front wave. Formulas for the critical conditions under which a sharp-front magnetic diffusion wave emerges and a formula for the wave-front velocity are derived in this work.

Nonlinear Landau damping in the ionosphere

NASA Technical Reports Server (NTRS)

Kiwamoto, Y.; Benson, R. F.

1978-01-01

A model is presented to explain the non-resonant waves which give rise to the diffuse resonance observed near 3/2 f sub H by the Alouette and ISIS topside sounders, where f sub H is the ambient electron cyclotron frequency. In a strictly linear analysis, these instability driven waves will decay due to Landau damping on a time scale much shorter than the observed time duration of the diffuse resonance. Calculations of the nonlinear wave particle coupling coefficients, however, indicate that the diffuse resonance wave can be maintained by the nonlinear Landau damping of the sounder stimulated 2f sub H wave. The time duration of the diffuse resonance is determined by the transit time of the instability generated and nonlinearly maintained diffuse resonance wave from the remote short lived hot region back to the antenna. The model is consistent with the Alouette/ISIS observations, and clearly demonstrates the existence of nonlinear wave-particle interactions in the ionosphere.

Models of inertial range spectra of interplanetary magnetohydrodynamic turbulence

NASA Technical Reports Server (NTRS)

Zhou, YE; Matthaeus, William H.

1990-01-01

A framework based on turbulence theory is presented to develop approximations for the local turbulence effects that are required in transport models. An approach based on Kolmogoroff-style dimensional analysis is presented as well as one based on a wave-number diffusion picture. Particular attention is given to the case of MHD turbulence with arbitrary cross helicity and with arbitrary ratios of the Alfven time scale and the nonlinear time scale.

An approximate theoretical treatment of ion transfer processes at asymmetric microscopic and nanoscopic liquid-liquid interfaces: Single and double potential pulse techniques

NASA Astrophysics Data System (ADS)

Molina, A.; Laborda, E.; Compton, R. G.

2014-03-01

Simple theory for the electrochemical study of reversible ion transfer processes at micro- and nano-liquid|liquid interfaces supported on a capillary is presented. Closed-form expressions are obtained for the response in normal pulse and differential double pulse voltammetries, which describe adequately the particular behaviour of these systems due to the ‘asymmetric’ ion diffusion inside and outside the capillary. The use of different potential pulse techniques for the determination of the formal potential and diffusion coefficients of the ion is examined. For this, very simple analytical expressions are presented for the half-wave potential in NPV and the peak potential in DDPV.

A Continuum Model of Actin Waves in Dictyostelium discoideum

PubMed Central

Khamviwath, Varunyu; Hu, Jifeng; Othmer, Hans G.

2013-01-01

Actin waves are complex dynamical patterns of the dendritic network of filamentous actin in eukaryotes. We developed a model of actin waves in PTEN-deficient Dictyostelium discoideum by deriving an approximation of the dynamics of discrete actin filaments and combining it with a signaling pathway that controls filament branching. This signaling pathway, together with the actin network, contains a positive feedback loop that drives the actin waves. Our model predicts the structure, composition, and dynamics of waves that are consistent with existing experimental evidence, as well as the biochemical dependence on various protein partners. Simulation suggests that actin waves are initiated when local actin network activity, caused by an independent process, exceeds a certain threshold. Moreover, diffusion of proteins that form a positive feedback loop with the actin network alone is sufficient for propagation of actin waves at the observed speed of . Decay of the wave back can be caused by scarcity of network components, and the shape of actin waves is highly dependent on the filament disassembly rate. The model allows retraction of actin waves and captures formation of new wave fronts in broken waves. Our results demonstrate that a delicate balance between a positive feedback, filament disassembly, and local availability of network components is essential for the complex dynamics of actin waves. PMID:23741312

Wave Augmented Diffuser for Centrifugal Compressor

NASA Technical Reports Server (NTRS)

Skoch, Gary J. (Inventor); Paxson, Daniel E. (Inventor)

2001-01-01

A wave augmented diffuser for a centrifugal compressor surrounds the outlet of an impeller that rotates on a drive shaft having an axis of rotation. The impeller brings flow in in an axial direction and imparts kinetic energy to the flow discharging it in radial and tangential directions. The flow is discharged into a plurality of circumferentially disposed wave chambers. The wave chambers are periodically opened and closed by a rotary valve such that the flow through the diffuser is unsteady. The valve includes a plurality of valve openings that are periodically brought into and out of fluid communication with the wave chambers. When the wave chambers are closed, a reflected compression wave moves upstream towards the diffuser bringing the flow into the wave chamber to rest. This action recovers the kinetic energy from the flow and limits any boundary layer growth. The flow is then discharged in an axial direction through an opening in the valve plate when the valve plate is rotated to an open position. The diffuser thus efficiently raises the static pressure of the fluid and discharges an axially directed flow at a radius that is predominantly below the maximum radius of the diffuser.

1D Resonance line Broadened Quasilinear (RBQ1D) code for fast ion Alfvenic relaxations and its validations

NASA Astrophysics Data System (ADS)

Gorelenkov, Nikolai; Duarte, Vinicius; Podesta, Mario

2017-10-01

The performance of the burning plasma can be limited by the requirements to confine the superalfvenic fusion products which are capable of resonating with the Alfvénic eigenmodes (AEs). The effect of AEs on fast ions is evaluated using the quasi-linear approach [Berk et al., Ph.Plasmas'96] generalized for this problem recently [Duarte et al., Ph.D.'17]. The generalization involves the resonance line broadened interaction regions with the diffusion coefficient prescribed to find the evolution of the velocity distribution function. The baseline eigenmode structures are found using the NOVA-K code perturbatively [Gorelenkov et al., Ph.Plasmas'99]. A RBQ1D code allowing the diffusion in radial direction is presented here. The wave particle interaction can be reduced to one-dimensional dynamics where for the Alfvénic modes typically the particle kinetic energy is nearly constant. Hence to a good approximation the Quasi-Linear (QL) diffusion equation only contains derivatives in the angular momentum. The diffusion equation is then one dimensional that is efficiently solved simultaneously for all particles with the equation for the evolution of the wave angular momentum. The RBQ1D is validated against recent DIIID results [Collins et al., PRL'16]. Supported by the US Department of Energy under DE-AC02-09CH11466.

Using Global Invariant Manifolds to Understand Metastability in the Burgers Equation With Small Viscosity

NASA Astrophysics Data System (ADS)

Beck, Margaret; Wayne, C. Eugene

2009-01-01

The large-time behavior of solutions to the Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability, which in the present context means that solutions spend a very long time near the family of solutions known as diffusive N-waves before finally converging to a stable self-similar diffusion wave. More precisely, it is shown that in terms of similarity, or scaling, variables in an algebraically weighted L^2 space, the self-similar diffusion waves correspond to a one-dimensional global center manifold of stationary solutions. Through each of these fixed points there exists a one-dimensional, global, attractive, invariant manifold corresponding to the diffusive N-waves. Thus, metastability corresponds to a fast transient in which solutions approach this metastable manifold of diffusive N-waves, followed by a slow decay along this manifold, and, finally, convergence to the self-similar diffusion wave.

Heating of the Interstellar Diffuse Ionized Gas via the Dissipation of Turbulence

NASA Astrophysics Data System (ADS)

Minter, Anthony H.; Spangler, Steven R.

1997-08-01

We have recently published observations that specify most of the turbulent and mean plasma characteristics for a region of the sky containing the interstellar diffuse ionized gas (DIG). These observations have provided virtually all of the information necessary to calculate the heating rate from dissipation of turbulence. We have calculated the turbulent dissipation heating rate employing two models for the interstellar turbulence. The first is a customary modeling as a superposition of magnetohydrodynamic waves. The second is a fluid-turbulence-like model based on the ideas of Higdon. This represents the first time that such calculations have been carried out with full and specific interstellar turbulence parameters. The wave model of interstellar turbulence encounters the severe difficulty that plausible estimates of heating by Landau damping exceed the radiative cooling capacity of the interstellar DIG by 3-4 orders of magnitude. Clearly interstellar turbulence does not behave like an ensemble of obliquely propagating fast magnetosonic waves. The heating rate due to two other wave dissipation mechanisms, ion-neutral collisional damping and the parametric decay instability, are comparable to the cooling capacity of the diffuse ionized medium. We find that the fluid-like turbulence model is an acceptable and realistic model of the turbulence in the interstellar medium once the effects of ion-neutral collisions are included in the model. This statement is contingent on an assumption that the dissipation of such turbulence because of Landau damping is several orders of magnitude less than that from an ensemble of obliquely propagating magnetosonic waves with the same energy density. Arguments as to why this may be the case are made in the paper. Rough parity between the turbulent heating rate and the radiative cooling rate in the DIG also depends on the hydrogen ionization fraction being in excess of 90% or on a model-dependent lower limit to the heating rate being approximately valid. We conclude that the dissipation of turbulence is capable of providing a substantial and perhaps major contribution to the energy budget of the diffuse ionized medium.

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

NASA Astrophysics Data System (ADS)

Henderson, Gregory Newell

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

Deploying dengue-suppressing Wolbachia : Robust models predict slow but effective spatial spread in Aedes aegypti.

PubMed

Turelli, Michael; Barton, Nicholas H

2017-06-01

A novel strategy for controlling the spread of arboviral diseases such as dengue, Zika and chikungunya is to transform mosquito populations with virus-suppressing Wolbachia. In general, Wolbachia transinfected into mosquitoes induce fitness costs through lower viability or fecundity. These maternally inherited bacteria also produce a frequency-dependent advantage for infected females by inducing cytoplasmic incompatibility (CI), which kills the embryos produced by uninfected females mated to infected males. These competing effects, a frequency-dependent advantage and frequency-independent costs, produce bistable Wolbachia frequency dynamics. Above a threshold frequency, denoted pˆ, CI drives fitness-decreasing Wolbachia transinfections through local populations; but below pˆ, infection frequencies tend to decline to zero. If pˆ is not too high, CI also drives spatial spread once infections become established over sufficiently large areas. We illustrate how simple models provide testable predictions concerning the spatial and temporal dynamics of Wolbachia introductions, focusing on rate of spatial spread, the shape of spreading waves, and the conditions for initiating spread from local introductions. First, we consider the robustness of diffusion-based predictions to incorporating two important features of wMel-Aedes aegypti biology that may be inconsistent with the diffusion approximations, namely fast local dynamics induced by complete CI (i.e., all embryos produced from incompatible crosses die) and long-tailed, non-Gaussian dispersal. With complete CI, our numerical analyses show that long-tailed dispersal changes wave-width predictions only slightly; but it can significantly reduce wave speed relative to the diffusion prediction; it also allows smaller local introductions to initiate spatial spread. Second, we use approximations for pˆ and dispersal distances to predict the outcome of 2013 releases of wMel-infected Aedes aegypti in Cairns, Australia, Third, we describe new data from Ae. aegypti populations near Cairns, Australia that demonstrate long-distance dispersal and provide an approximate lower bound on pˆ for wMel in northeastern Australia. Finally, we apply our analyses to produce operational guidelines for efficient transformation of vector populations over large areas. We demonstrate that even very slow spatial spread, on the order of 10-20 m/month (as predicted), can produce area-wide population transformation within a few years following initial releases covering about 20-30% of the target area. Copyright © 2017 Elsevier Inc. All rights reserved.

The Foggy EUV Corona and Coronal Heating by MHD Waves from Explosive Reconnection Events

NASA Technical Reports Server (NTRS)

Moore, Ron L.; Cirtain, Jonathan W.; Falconer, David A.

2008-01-01

In 0.5 arcsec/pixel TRACE coronal EUV images, the corona rooted in active regions that are at the limb and are not flaring is seen to consist of (1) a complex array of discrete loops and plumes embedded in (2) a diffuse ambient component that shows no fine structure and gradually fades with height. For each of two not-flaring active regions, found that the diffuse component is (1) approximately isothermal and hydrostatic and (2) emits well over half of the total EUV luminosity of the active-region corona. Here, from a TRACE Fe XII coronal image of another not-flaring active region, the large sunspot active region AR 10652 when it was at the west limb on 30 July 2004, we separate the diffuse component from the discrete loop component by spatial filtering, and find that the diffuse component has about 60% of the total luminosity. If under much higher spatial resolution than that of TRACE (e. g., the 0.1 arcsec/pixel resolution of the Hi-C sounding-rocket experiment proposed by J. W. Cirtain et al), most of the diffuse component remains diffuse rather being resolved into very narrow loops and plumes, this will raise the possibility that the EUV corona in active regions consists of two basically different but comparably luminous components: one being the set of discrete bright loops and plumes and the other being a truly diffuse component filling the space between the discrete loops and plumes. This dichotomy would imply that there are two different but comparably powerful coronal heating mechanisms operating in active regions, one for the distinct loops and plumes and another for the diffuse component. We present a scenario in which (1) each discrete bright loop or plume is a flux tube that was recently reconnected in a burst of reconnection, and (2) the diffuse component is heated by MHD waves that are generated by these reconnection events and by other fine-scale explosive reconnection events, most of which occur in and below the base of the corona where they are seen as UV explosive events, EUV blinkers, and type II spicules. These MHD waves propagate across field lines and dissipate, heating the plasma in the field between the bright loops and plumes.

Shock drift acceleration in the presence of waves

NASA Technical Reports Server (NTRS)

Decker, R. B.; Vlahos, L.

1985-01-01

Attention is given to the initial results of a model designed to study the modification of the scatter-free, shock drift acceleration of energetic test particles by wave activity in the vicinity of a quasi-perpendicular, fast-mode MHD shock. It is emphasized that the concept of magnetic moment conservation is a valid approximation only in the perpendicular and nearly perpendicular regimes, when the angle theta-Bn between the shock normal and the upstream magnetic field vector is in the range from 70 deg to 90 deg. The present investigation is concerned with one step in a program which is being developed to combine the shock drift and diffusive processes at a shock of arbitrary theta-Bn.

Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering in Outer RB

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Gamayunov, K. V.

2007-01-01

We present the equatorial and bounce average pitch angle diffusion coefficients for scattering of relativistic electrons by the H+ mode of EMIC waves. Both the model (prescribed) and self consistent distributions over the wave normal angle are considered. The main results of our calculation can be summarized as follows: First, in comparison with field aligned waves, the intermediate and highly oblique waves reduce the pitch angle range subject to diffusion, and strongly suppress the scattering rate for low energy electrons (E less than 2 MeV). Second, for electron energies greater than 5 MeV, the |n| = 1 resonances operate only in a narrow region at large pitch-angles, and despite their greatest contribution in case of field aligned waves, cannot cause electron diffusion into the loss cone. For those energies, oblique waves at |n| greater than 1 resonances are more effective, extending the range of pitch angle diffusion down to the loss cone boundary, and increasing diffusion at small pitch angles by orders of magnitude.

Electromagnetic Ion Cyclotron Waves in the Helium Branch Induced by Multiple Electromagnetic Ion Cyclotron Triggered Emissions

NASA Astrophysics Data System (ADS)

Shoji, M.; Omura, Y.; Grison, B.; Pickett, J. S.; Dandouras, I. S.; Engebretson, M. J.

2011-12-01

Electromagnetic ion cyclotron (EMIC) triggered emissions with rising tones between the H+ and He+ cyclotron frequencies were found in the inner magnetosphere by the recent Cluster observations. Another type of EMIC wave with a constant frequency is occasionally observed below the He+ cyclotron frequency after the multiple EMIC triggered emissions. We performed a self-consistent hybrid simulation with a one-dimensional cylindrical magnetic flux model approximating the dipole magnetic field of the Earth's inner magnetosphere. In the presence of energetic protons with a sufficient density and temperature anisotropy, multiple EMIC triggered emissions are reproduced due to the nonlinear wave growth mechanism of rising-tone chorus emissions, and a constant frequency wave in the He+ EMIC branch is subsequently generated. Through interaction with the multiple EMIC rising-tone emissions, the velocity distribution function of the energetic protons is strongly modified. Because of the pitch angle scattering of the protons, the gradient of the distribution in velocity phase space is enhanced along the diffusion curve of the He+ branch wave, resulting in the linear growth of the EMIC wave in the He+ branch.

Electromagnetic ion cyclotron waves in the helium branch induced by multiple electromagnetic ion cyclotron triggered emissions

NASA Astrophysics Data System (ADS)

Shoji, Masafumi; Omura, Yoshiharu; Grison, Benjamin; Pickett, Jolene; Dandouras, Iannis; Engebretson, Mark

2011-09-01

Electromagnetic ion cyclotron (EMIC) triggered emissions with rising tones between the H+ and He+ cyclotron frequencies were found in the inner magnetosphere by the recent Cluster observations. Another type of EMIC wave with a constant frequency is occasionally observed below the He+ cyclotron frequency after the multiple EMIC triggered emissions. We performed a self-consistent hybrid simulation with a one-dimensional cylindrical magnetic flux model approximating the dipole magnetic field of the Earth's inner magnetosphere. In the presence of energetic protons with a sufficient density and temperature anisotropy, multiple EMIC triggered emissions are reproduced due to the nonlinear wave growth mechanism of rising-tone chorus emissions, and a constant frequency wave in the He+ EMIC branch is subsequently generated. Through interaction with the multiple EMIC rising-tone emissions, the velocity distribution function of the energetic protons is strongly modified. Because of the pitch angle scattering of the protons, the gradient of the distribution in velocity phase space is enhanced along the diffusion curve of the He+ branch wave, resulting in the linear growth of the EMIC wave in the He+ branch.

Dissipation of ionospheric irregularities by wave-particle and collisional interactions

NASA Technical Reports Server (NTRS)

Bernhardt, P. A.; Pongratz, M. B.; Gray, S. P.; Thomsen, M. F.

1982-01-01

The nonlinear dissipation of plasma irregularities aligned parallel to an ambient magnetic field is studied numerically using a model which employs both wave-particle and collisional diffusion. A wave-particle diffusion coefficient derived from a local theory of the universal drift instability is used. This coefficient is effective in regions of nonzero plasma gradients and produces triangular-shaped irregularities with spectra which vary as f to the -4th, where f is the spatial frequency. Collisional diffusion acts rapidly on the vertices of the irregularities to reduce their amplitude. The simultaneous action of the two dissipative processes is more efficient than collisions acting alone. In this model, wave-particle diffusion mimics the forward cascade process of wave-wave coupling.

Fisher equation for anisotropic diffusion: simulating South American human dispersals.

PubMed

Martino, Luis A; Osella, Ana; Dorso, Claudio; Lanata, José L

2007-09-01

The Fisher equation is commonly used to model population dynamics. This equation allows describing reaction-diffusion processes, considering both population growth and diffusion mechanism. Some results have been reported about modeling human dispersion, always assuming isotropic diffusion. Nevertheless, it is well-known that dispersion depends not only on the characteristics of the habitats where individuals are but also on the properties of the places where they intend to move, then isotropic approaches cannot adequately reproduce the evolution of the wave of advance of populations. Solutions to a Fisher equation are difficult to obtain for complex geometries, moreover, when anisotropy has to be considered and so few studies have been conducted in this direction. With this scope in mind, we present in this paper a solution for a Fisher equation, introducing anisotropy. We apply a finite difference method using the Crank-Nicholson approximation and analyze the results as a function of the characteristic parameters. Finally, this methodology is applied to model South American human dispersal.

Delay-induced wave instabilities in single-species reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Otto, Andereas; Wang, Jian; Radons, Günter

2017-11-01

The Turing (wave) instability is only possible in reaction-diffusion systems with more than one (two) components. Motivated by the fact that a time delay increases the dimension of a system, we investigate the presence of diffusion-driven instabilities in single-species reaction-diffusion systems with delay. The stability of arbitrary one-component systems with a single discrete delay, with distributed delay, or with a variable delay is systematically analyzed. We show that a wave instability can appear from an equilibrium of single-species reaction-diffusion systems with fluctuating or distributed delay, which is not possible in similar systems with constant discrete delay or without delay. More precisely, we show by basic analytic arguments and by numerical simulations that fast asymmetric delay fluctuations or asymmetrically distributed delays can lead to wave instabilities in these systems. Examples, for the resulting traveling waves are shown for a Fisher-KPP equation with distributed delay in the reaction term. In addition, we have studied diffusion-induced instabilities from homogeneous periodic orbits in the same systems with variable delay, where the homogeneous periodic orbits are attracting resonant periodic solutions of the system without diffusion, i.e., periodic orbits of the Hutchinson equation with time-varying delay. If diffusion is introduced, standing waves can emerge whose temporal period is equal to the period of the variable delay.

Investigating Whistler Mode Wave Diffusion Coefficients at Mars

NASA Astrophysics Data System (ADS)

Shane, A. D.; Liemohn, M. W.; Xu, S.; Florie, C.

2017-12-01

Observations of electron pitch angle distributions have suggested collisions are not the only pitch angle scattering process occurring in the Martian ionosphere. This unknown scattering process is causing high energy electrons (>100 eV) to become isotropized. Whistler mode waves are one pitch angle scattering mechanism known to preferentially scatter high energy electrons in certain plasma regimes. The distribution of whistler mode wave diffusion coefficients are dependent on the background magnetic field strength and thermal electron density, as well as the frequency and wave normal angle of the wave. We have solved for the whistler mode wave diffusion coefficients using the quasi-linear diffusion equations and have integrated them into a superthermal electron transport (STET) model. Preliminary runs have produced results that qualitatively match the observed electron pitch angle distributions at Mars. We performed parametric sweeps over magnetic field, thermal electron density, wave frequency, and wave normal angle to understand the relationship between the plasma parameters and the diffusion coefficient distributions, but also to investigate what regimes whistler mode waves scatter only high energy electrons. Increasing the magnetic field strength and lowering the thermal electron density shifts the distribution of diffusion coefficients toward higher energies and lower pitch angles. We have created an algorithm to identify Mars Atmosphere Volatile and EvolutioN (MAVEN) observations of high energy isotropic pitch angle distributions in the Martian ionosphere. We are able to map these distributions at Mars, and compare the conditions under which these are observed at Mars with the results of our parametric sweeps. Lastly, we will also look at each term in the kinetic diffusion equation to determine if the energy and mixed diffusion coefficients are important enough to incorporate into STET as well.

Diffusive instabilities in a hyperbolic activator-inhibitor system with superdiffusion

NASA Astrophysics Data System (ADS)

Mvogo, Alain; Macías-Díaz, Jorge E.; Kofané, Timoléon Crépin

2018-03-01

We investigate analytically and numerically the conditions for wave instabilities in a hyperbolic activator-inhibitor system with species undergoing anomalous superdiffusion. In the present work, anomalous superdiffusion is modeled using the two-dimensional Weyl fractional operator, with derivative orders α ∈ [1,2]. We perform a linear stability analysis and derive the conditions for diffusion-driven wave instabilities. Emphasis is placed on the effect of the superdiffusion exponent α , the diffusion ratio d , and the inertial time τ . As the superdiffusive exponent increases, so does the wave number of the Turing instability. Opposite to the requirement for Turing instability, the activator needs to diffuse sufficiently faster than the inhibitor in order for the wave instability to occur. The critical wave number for wave instability decreases with the superdiffusive exponent and increases with the inertial time. The maximum value of the inertial time for a wave instability to occur in the system is τmax=3.6 . As one of the main results of this work, we conclude that both anomalous diffusion and inertial time influence strongly the conditions for wave instabilities in hyperbolic fractional reaction-diffusion systems. Some numerical simulations are conducted as evidence of the analytical predictions derived in this work.

Explicit approximations to estimate the perturbative diffusivity in the presence of convectivity and damping. I. Semi-infinite slab approximations

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

Berkel, M. van; Fellow of the Japan Society for the Promotion of Science; FOM Institute DIFFER-Dutch Institute for Fundamental Energy Research, Association EURATOM- FOM, Trilateral Euregio Cluster, PO Box 1207, 3430 BE Nieuwegein

2014-11-15

In this paper, a number of new approximations are introduced to estimate the perturbative diffusivity (χ), convectivity (V), and damping (τ) in cylindrical geometry. For this purpose, the harmonic components of heat waves induced by localized deposition of modulated power are used. The approximations are based on semi-infinite slab approximations of the heat equation. The main result is the approximation of χ under the influence of V and τ based on the phase of two harmonics making the estimate less sensitive to calibration errors. To understand why the slab approximations can estimate χ well in cylindrical geometry, the relationships betweenmore » heat transport models in slab and cylindrical geometry are studied. In addition, the relationship between amplitude and phase with respect to their derivatives, used to estimate χ, is discussed. The results are presented in terms of the relative error for the different derived approximations for different values of frequency, transport coefficients, and dimensionless radius. The approximations show a significant region in which χ, V, and τ can be estimated well, but also regions in which the error is large. Also, it is shown that some compensation is necessary to estimate V and τ in a cylindrical geometry. On the other hand, errors resulting from the simplified assumptions are also discussed showing that estimating realistic values for V and τ based on infinite domains will be difficult in practice. This paper is the first part (Part I) of a series of three papers. In Part II and Part III, cylindrical approximations based directly on semi-infinite cylindrical domain (outward propagating heat pulses) and inward propagating heat pulses in a cylindrical domain, respectively, will be treated.« less

Birth-jump processes and application to forest fire spotting.

PubMed

Hillen, T; Greese, B; Martin, J; de Vries, G

2015-01-01

Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly concentrated, we show that the integro-differential equation can be approximated by a reaction-diffusion equation, in which the proliferation rate contributes to both the diffusion term and the reaction term. We completely solve the corresponding critical domain size problem and the minimal wave speed problem. Birth-jump models can be applied in many areas in mathematical biology. We highlight an application of our results in the context of forest fire spread through spotting. We show that spotting increases the invasion speed of a forest fire front.

Plasma diffusion at the magnetopause - The case of lower hybrid drift waves

NASA Technical Reports Server (NTRS)

Treumann, R. A.; Labelle, J.; Pottelette, R.

1991-01-01

The diffusion expected from the quasi-linear theory of the lower hybrid drift instability at the earth's magnetopause is recalculated. The resulting diffusion coefficient is marginally large enough to explain the thickness of the boundary layer under quiet conditions, based on observational upper limits for the wave intensities. Thus, one possible model for the boundary layer could involve equilibrium between the diffusion arising from lower hybrid waves and various loss processes.

Coronal "wave": Magnetic Footprint Of A Cme?

NASA Astrophysics Data System (ADS)

Attrill, Gemma; Harra, L. K.; van Driel-Gesztelyi, L.; Demoulin, P.; Wuelser, J.

2007-05-01

We propose a new mechanism for the generation of "EUV coronal waves". This work is based on new analysis of data from SOHO/EIT, SOHO/MDI & STEREO/EUVI. Although first observed in 1997, the interpretation of coronal waves as flare-induced or CME-driven remains a debated topic. We investigate the properties of two "classical" SOHO/EIT coronal waves in detail. The source regions of the associated CMEs possess opposite helicities & the coronal waves display rotations in opposite senses. We observe deep dimmings near the flare site & also widespread diffuse dimming, accompanying the expansion of the EIT wave. We report a new property of these EIT waves, namely, that they display dual brightenings: persistent ones at the outermost edge of the core dimming regions & simultaneously diffuse brightenings constituting the leading edge of the coronal wave, surrounding the expanding diffuse dimmings. We show that such behaviour is consistent with a diffuse EIT wave being the magnetic footprint of a CME. We propose a new mechanism where driven magnetic reconnections between the skirt of the expanding CME & quiet-Sun magnetic loops generate the observed bright diffuse front. The dual brightenings & widespread diffuse dimming are identified as innate characteristics of this process. In addition we present some of the first analysis of a STEREO/EUVI limb coronal wave. We show how the evolution of the diffuse bright front & dimmings can be understood in terms of the model described above. We show that an apparently stationary part of the bright front can be understood in terms of magnetic interchange reconnections between the expanding CME & the "open" magnetic field of a low-latitude coronal hole. We use both the SOHO/EIT & STEREO/EUVI events to demonstrate that through successive reconnections, this new model provides a natural mechanism via which CMEs can become large-scale in the lower corona.

Diffusive Cosmic-Ray Acceleration at Shock Waves of Arbitrary Speed with Magnetostatic Turbulence. I. General Theory and Correct Nonrelativistic Speed Limit

NASA Astrophysics Data System (ADS)

Schlickeiser, R.; Oppotsch, J.

2017-12-01

The analytical theory of diffusive acceleration of cosmic rays at parallel stationary shock waves of arbitrary speed with magnetostatic turbulence is developed from first principles. The theory is based on the diffusion approximation to the gyrotropic cosmic-ray particle phase-space distribution functions in the respective rest frames of the up- and downstream medium. We derive the correct cosmic-ray jump conditions for the cosmic-ray current and density, and match the up- and downstream distribution functions at the position of the shock. It is essential to account for the different particle momentum coordinates in the up- and downstream media. Analytical expressions for the momentum spectra of shock-accelerated cosmic rays are calculated. These are valid for arbitrary shock speeds including relativistic shocks. The correctly taken limit for nonrelativistic shock speeds leads to a universal broken power-law momentum spectrum of accelerated particles with velocities well above the injection velocity threshold, where the universal power-law spectral index q≃ 2-{γ }1-4 is independent of the flow compression ratio r. For nonrelativistic shock speeds, we calculate for the first time the injection velocity threshold, settling the long-standing injection problem for nonrelativistic shock acceleration.

Passive Imaging in Nondiffuse Acoustic Wavefields

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

Mulargia, Francesco; Castellaro, Silvia

2008-05-30

A main property of diffuse acoustic wavefields is that, taken any two points, each of them can be seen as the source of waves and the other as the recording station. This property is shown to follow simply from array azimuthal selectivity and Huygens principle in a locally isotropic wavefield. Without time reversal, this property holds approximately also in anisotropic azimuthally uniform wavefields, implying much looser constraints for undistorted passive imaging than those required by a diffuse field. A notable example is the seismic noise field, which is generally nondiffuse, but is found to be compatible with a finite aperturemore » anisotropic uniform wavefield. The theoretical predictions were confirmed by an experiment on seismic noise in the mainland of Venice, Italy.« less

Relativistic electrons and whistlers in Jupiter's magnetosphere

NASA Technical Reports Server (NTRS)

Barbosa, D. D.; Coroniti, F. V.

1976-01-01

The paper examines some of the consequences of relativistic electrons in stably trapped equilibrium with parallel propagating whistlers in the inner magnetosphere of Jupiter. Approximate scaling laws for the stably trapped electron flux and equilibrium wave intensity are derived, and the equatorial growth rate for whistlers is determined. It is shown that fluxes are near the stably trapped limit, which suggests that whistler intensities may be high enough to cause significant diffusion of electrons, accounting for the observed reduction of phase space densities.

Banded Structures in Electron Pitch Angle Diffusion Coefficients from Resonant Wave Particle Interactions

NASA Technical Reports Server (NTRS)

Tripathi, A. K.; Singhal, R. P.; Khazanov, G. V.; Avanov, L. A.

2016-01-01

Electron pitch angle (D (alpha)) and momentum (D(pp)) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L = 4.6 and 6.8 for electron energies 10 keV. Landau (n = 0) resonance and cyclotron harmonic resonances n = +/-1, +/-2,...+/-5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (alpha) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusion coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n = +1 and n = +2. A major contribution to momentum diffusion coefficients appears from n = +2. However, the banded structures in D alpha and Dpp coefficients appear only in the profile of diffusion coefficients for n = +2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The Dpp diffusion coefficient for ECH waves is one to two orders smaller than D alpha coefficients. For chorus waves, Dpp coefficients are about an order of magnitude smaller than D alpha coefficients for the case n does not = 0. In case of Landau resonance, the values of Dpp coefficient are generally larger than the values of D alpha coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89 deg and harmonic resonances n = +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10 deg and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies (is) greater than1 keV, and for whistler mode chorus waves, structures appear for energies greater than 2 keV at L = 4.6 and above 200 eV for L = 6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.

Banded Structures in Electron Pitch Angle Diffusion Coefficients from Resonant Wave-Particle Interactions

NASA Technical Reports Server (NTRS)

Tripathi, A. K.; Singhal, R. P.; Khazanov, G. V.; Avanov, L. A.

2016-01-01

Electron pitch angle (D(sub (alpha alpha))) and momentum (D(sub pp)) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L=4.6 and 6.8 for electron energies less than or equal to 10 keV. Landau (n=0) resonance and cyclotron harmonic resonances n= +/- 1, +/-2, ... +/-5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (alpha) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusion coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n=+1 and n=+2. A major contribution to momentum diffusion coefficients appears from n=+2. However, the banded structures in D(sub alpha alpha) and D(sub pp) coefficients appear only in the profile of diffusion coefficients for n=+2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The D(sub pp) diffusion coefficient for ECH waves is one to two orders smaller than D(sub alpha alpha) coefficients. For chorus waves, D(sub pp) coefficients are about an order of magnitude smaller than D(sub alpha alpha) coefficients for the case n does not equal 0. In case of Landau resonance, the values of D(sub pp) coefficient are generally larger than the values of D(sub alpha alpha) coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89 deg and harmonic resonances n= +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10 deg and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies 1 greater than or equal to keV, and for whistler mode chorus waves, structures appear for energies greater than 2 keV at L=4.6 and above 200 eV for L=6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.

Diffusion, capture and recycling of SCAR/WAVE and Arp2/3 complexes observed in cells by single-molecule imaging.

PubMed

Millius, Arthur; Watanabe, Naoki; Weiner, Orion D

2012-03-01

The SCAR/WAVE complex drives lamellipodium formation by enhancing actin nucleation by the Arp2/3 complex. Phosphoinositides and Rac activate the SCAR/WAVE complex, but how SCAR/WAVE and Arp2/3 complexes converge at sites of nucleation is unknown. We analyzed the single-molecule dynamics of WAVE2 and p40 (subunits of the SCAR/WAVE and Arp2/3 complexes, respectively) in XTC cells. We observed lateral diffusion of both proteins and captured the transition of p40 from diffusion to network incorporation. These results suggest that a diffusive 2D search facilitates binding of the Arp2/3 complex to actin filaments necessary for nucleation. After nucleation, the Arp2/3 complex integrates into the actin network and undergoes retrograde flow, which results in its broad distribution throughout the lamellipodium. By contrast, the SCAR/WAVE complex is more restricted to the cell periphery. However, with single-molecule imaging, we also observed WAVE2 molecules undergoing retrograde motion. WAVE2 and p40 have nearly identical speeds, lifetimes and sites of network incorporation. Inhibition of actin retrograde flow does not prevent WAVE2 association and disassociation with the membrane but does inhibit WAVE2 removal from the actin cortex. Our results suggest that membrane binding and diffusion expedites the recruitment of nucleation factors to a nucleation site independent of actin assembly, but after network incorporation, ongoing actin polymerization facilitates recycling of SCAR/WAVE and Arp2/3 complexes.

Diffusion, capture and recycling of SCAR/WAVE and Arp2/3 complexes observed in cells by single-molecule imaging

PubMed Central

Millius, Arthur; Watanabe, Naoki; Weiner, Orion D.

2012-01-01

The SCAR/WAVE complex drives lamellipodium formation by enhancing actin nucleation by the Arp2/3 complex. Phosphoinositides and Rac activate the SCAR/WAVE complex, but how SCAR/WAVE and Arp2/3 complexes converge at sites of nucleation is unknown. We analyzed the single-molecule dynamics of WAVE2 and p40 (subunits of the SCAR/WAVE and Arp2/3 complexes, respectively) in XTC cells. We observed lateral diffusion of both proteins and captured the transition of p40 from diffusion to network incorporation. These results suggest that a diffusive 2D search facilitates binding of the Arp2/3 complex to actin filaments necessary for nucleation. After nucleation, the Arp2/3 complex integrates into the actin network and undergoes retrograde flow, which results in its broad distribution throughout the lamellipodium. By contrast, the SCAR/WAVE complex is more restricted to the cell periphery. However, with single-molecule imaging, we also observed WAVE2 molecules undergoing retrograde motion. WAVE2 and p40 have nearly identical speeds, lifetimes and sites of network incorporation. Inhibition of actin retrograde flow does not prevent WAVE2 association and disassociation with the membrane but does inhibit WAVE2 removal from the actin cortex. Our results suggest that membrane binding and diffusion expedites the recruitment of nucleation factors to a nucleation site independent of actin assembly, but after network incorporation, ongoing actin polymerization facilitates recycling of SCAR/WAVE and Arp2/3 complexes. PMID:22349699

Treatment of the polar coordinate singularity in axisymmetric wave propagation using high-order summation-by-parts operators on a staggered grid

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

Prochnow, Bo; O'Reilly, Ossian; Dunham, Eric M.

In this paper, we develop a high-order finite difference scheme for axisymmetric wave propagation in a cylindrical conduit filled with a viscous fluid. The scheme is provably stable, and overcomes the difficulty of the polar coordinate singularity in the radial component of the diffusion operator. The finite difference approximation satisfies the principle of summation-by-parts (SBP), which is used to establish stability using the energy method. To treat the coordinate singularity without losing the SBP property of the scheme, a staggered grid is introduced and quadrature rules with weights set to zero at the endpoints are considered. Finally, the accuracy ofmore » the scheme is studied both for a model problem with periodic boundary conditions at the ends of the conduit and its practical utility is demonstrated by modeling acoustic-gravity waves in a magmatic conduit.« less

Lee wave breaking region: the map of instability development scenarios

NASA Astrophysics Data System (ADS)

Yakovenko, S. N.

2017-10-01

Numerical study of a stably stratified flow above the two-dimensional cosine-shaped obstacle has been performed by DNS and LES. These methods were implemented to solve the three-dimensional Navier-Stokes equations in the Boussinesq approximation, together with by the scalar diffusion equation. The results of scanning in the wide ranges of physical parameters (Reynolds and Prandtl/Schmidt numbers relating to laboratory experiment cases and atmospheric or oceanic situations) are presented for instability and turbulence development scenarios in the overturning internal lee waves. The latter is generated by the obstacle in a flow with the constant inflow values of velocity and stable density gradient. Evolution of lee-wave breaking is explored by visualization of velocity and scalar (density) fields, and the analysis of spectra. Based on the numerical simulation results, the power-law dependence on Reynolds number is demonstrated for the wavelength of the most unstable perturbation.

Treatment of the polar coordinate singularity in axisymmetric wave propagation using high-order summation-by-parts operators on a staggered grid

DOE PAGES

Prochnow, Bo; O'Reilly, Ossian; Dunham, Eric M.; ...

2017-03-16

In this paper, we develop a high-order finite difference scheme for axisymmetric wave propagation in a cylindrical conduit filled with a viscous fluid. The scheme is provably stable, and overcomes the difficulty of the polar coordinate singularity in the radial component of the diffusion operator. The finite difference approximation satisfies the principle of summation-by-parts (SBP), which is used to establish stability using the energy method. To treat the coordinate singularity without losing the SBP property of the scheme, a staggered grid is introduced and quadrature rules with weights set to zero at the endpoints are considered. Finally, the accuracy ofmore » the scheme is studied both for a model problem with periodic boundary conditions at the ends of the conduit and its practical utility is demonstrated by modeling acoustic-gravity waves in a magmatic conduit.« less

A model for oscillations and pattern formation in protoplasmic droplets of Physarum polycephalum

NASA Astrophysics Data System (ADS)

Radszuweit, M.; Engel, H.; Bär, M.

2010-12-01

A mechano-chemical model for the spatiotemporal dynamics of free calcium and the thickness in protoplasmic droplets of the true slime mold Physarum polycephalum is derived starting from a physiologically detailed description of intracellular calcium oscillations proposed by Smith and Saldana (Biopys. J. 61, 368 (1992)). First, we have modified the Smith-Saldana model for the temporal calcium dynamics in order to reproduce the experimentally observed phase relation between calcium and mechanical tension oscillations. Then, we formulate a model for spatiotemporal dynamics by adding spatial coupling in the form of calcium diffusion and advection due to calcium-dependent mechanical contraction. In another step, the resulting reaction-diffusion model with mechanical coupling is simplified to a reaction-diffusion model with global coupling that approximates the mechanical part. We perform a bifurcation analysis of the local dynamics and observe a Hopf bifurcation upon increase of a biochemical activity parameter. The corresponding reaction-diffusion model with global coupling shows regular and chaotic spatiotemporal behaviour for parameters with oscillatory dynamics. In addition, we show that the global coupling leads to a long-wavelength instability even for parameters where the local dynamics possesses a stable spatially homogeneous steady state. This instability causes standing waves with a wavelength of twice the system size in one dimension. Simulations of the model in two dimensions are found to exhibit defect-mediated turbulence as well as various types of spiral wave patterns in qualitative agreement with earlier experimental observation by Takagi and Ueda (Physica D, 237, 420 (2008)).

Effects of pressure on the magnetic properties of FeO: A diffusion Monte Carlo study

NASA Astrophysics Data System (ADS)

Townsend, Joshua; Shulenburger, Luke; Mattsson, Thomas; Esler, Ken; Cohen, Ronald

While simple in terms of structure and composition, both experimental and computational investigations have demonstrated that FeO has a rich phase diagram of structural phase transformations, electronic spin transitions, insulator-metal transitions, and magnetic ordering transitions, due to the open-shell occupation of the Fe 3d electrons. We investigated the magnetic and electronic structures of FeO under ambient and high pressure conditions using diffusion Quantum Monte Carlo (QMC) within the fixed-node approximation. QMC techniques are especially well suited to the study of strongly correlated systems because they explicitly include correlation into the ground-state wave function. Here we report on the effects of the choice of trial wave function on the ambient pressure lattice distortion due to AFM ordering, as well as the equation of state, spin collapse, and metal-insulator transitions. Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE.

Quantum Landau damping in dipolar Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Mendonça, J. T.; Terças, H.; Gammal, A.

2018-06-01

We consider Landau damping of elementary excitations in Bose-Einstein condensates (BECs) with dipolar interactions. We discuss quantum and quasiclassical regimes of Landau damping. We use a generalized wave-kinetic description of BECs which, apart from the long-range dipolar interactions, also takes into account the quantum fluctuations and the finite-energy corrections to short-range interactions. Such a description is therefore more general than the usual mean-field approximation. The present wave-kinetic approach is well suited for the study of kinetic effects in BECs, such as those associated with Landau damping, atom trapping, and turbulent diffusion. The inclusion of quantum fluctuations and energy corrections changes the dispersion relation and the damping rates, leading to possible experimental signatures of these effects. Quantum Landau damping is described with generality, and particular examples of dipolar condensates in two and three dimensions are studied. The occurrence of roton-maxon excitations, and their relevance to Landau damping, are also considered in detail. The present approach is mainly based on a linear perturbative procedure, but the nonlinear regime of Landau damping, which includes atom trapping and atom diffusion, is also briefly discussed.

Theoretical aspects of tidal and planetary wave propagation at thermospheric heights

NASA Technical Reports Server (NTRS)

Volland, H.; Mayr, H. G.

1977-01-01

A simple semiquantitative model is presented which allows analytic solutions of tidal and planetary wave propagation at thermospheric heights. This model is based on perturbation approximation and mode separation. The effects of viscosity and heat conduction are parameterized by Rayleigh friction and Newtonian cooling. Because of this simplicity, one gains a clear physical insight into basic features of atmospheric wave propagation. In particular, we discuss the meridional structures of pressure and horizontal wind (the solutions of Laplace's equation) and their modification due to dissipative effects at thermospheric heights. Furthermore, we solve the equations governing the height structure of the wave modes and arrive at a very simple asymptotic solution valid in the upper part of the thermosphere. That 'system transfer function' of the thermosphere allows one to estimate immediately the reaction of the thermospheric wave mode parameters such as pressure, temperature, and winds to an external heat source of arbitrary temporal and spatial distribution. Finally, the diffusion effects of the minor constituents due to the global wind circulation are discussed, and some results of numerical calculations are presented.

Boundary mediated position control of traveling waves

NASA Astrophysics Data System (ADS)

Martens, Steffen; Ziepke, Alexander; Engel, Harald

Reaction control is an essential task in biological systems and chemical process industry. Often, the excitable medium supporting wave propagation exhibits an irregular shape and/or is limited in size. In particular, the analytic treatment of wave phenomena is notoriously difficult due to the spatial modulation of the domain's. Recently, we have provided a first systematic treatment by applying asymptotic perturbation analysis leading to an approximate description that involves a reduction of dimensionality; the 3D RD equation with spatially dependent NFBCs on the reactants reduces to a 1D reaction-diffusion-advection equation. Here, we present a novel method to control the position ϕ (t) of traveling waves in modulated domains according to a prespecified protocol of motion. Given this protocol, the ``optimal'' geometry of reactive domains Q (x) is found as the solution of the perturbatively derived equation of motion. Noteworthy, such a boundary control can be expressed in terms of the uncontrolled wave profile and its propagation velocity, rendering detailed knowledge of the reaction kinetics unnecessary. German Science Foundation DFG through the SFB 910 ''Control of Self-Organizing Nonlinear Systems''.

Osmotic forces and gap junctions in spreading depression: a computational model

NASA Technical Reports Server (NTRS)

Shapiro, B. E.

2001-01-01

In a computational model of spreading depression (SD), ionic movement through a neuronal syncytium of cells connected by gap junctions is described electrodiffusively. Simulations predict that SD will not occur unless cells are allowed to expand in response to osmotic pressure gradients and K+ is allowed to move through gap junctions. SD waves of [K+]out approximately 25 to approximately 60 mM moving at approximately 2 to approximately 18 mm/min are predicted over the range of parametric values reported in gray matter, with extracellular space decreasing up to approximately 50%. Predicted waveform shape is qualitatively similar to laboratory reports. The delayed-rectifier, NMDA, BK, and Na+ currents are predicted to facilitate SD, while SK and A-type K+ currents and glial activity impede SD. These predictions are consonant with recent findings that gap junction poisons block SD and support the theories that cytosolic diffusion via gap junctions and osmotic forces are important mechanisms underlying SD.

The effect of density fluctuations on electron cyclotron beam broadening and implications for ITER

NASA Astrophysics Data System (ADS)

Snicker, A.; Poli, E.; Maj, O.; Guidi, L.; Köhn, A.; Weber, H.; Conway, G.; Henderson, M.; Saibene, G.

2018-01-01

We present state-of-the-art computations of propagation and absorption of electron cyclotron waves, retaining the effects of scattering due to electron density fluctuations. In ITER, injected microwaves are foreseen to suppress neoclassical tearing modes (NTMs) by driving current at the q=2 and q=3/2 resonant surfaces. Scattering of the beam can spoil the good localization of the absorption and thus impair NTM control capabilities. A novel tool, the WKBeam code, has been employed here in order to investigate this issue. The code is a Monte Carlo solver for the wave kinetic equation and retains diffraction, full axisymmetric tokamak geometry, determination of the absorption profile and an integral form of the scattering operator which describes the effects of turbulent density fluctuations within the limits of the Born scattering approximation. The approach has been benchmarked against the paraxial WKB code TORBEAM and the full-wave code IPF-FDMC. In particular, the Born approximation is found to be valid for ITER parameters. In this paper, we show that the radiative transport of EC beams due to wave scattering in ITER is diffusive unlike in present experiments, thus causing up to a factor of 2-4 broadening in the absorption profile. However, the broadening depends strongly on the turbulence model assumed for the density fluctuations, which still has large uncertainties.

Electron pitch angle diffusion by electrostatic electron cyclotron harmonic waves: The origin of pancake distributions

NASA Astrophysics Data System (ADS)

Horne, Richard B.; Thorne, Richard M.

2000-03-01

It has been suggested that highly anisotropic electron pancake distributions are the result of pitch angle diffusion by electrostatic electron cyclotron harmonic (ECH) and whistler mode waves in the equatorial region. Here we present pitch angle diffusion rates for ECH wave spectra centered at different frequencies with respect to the electron gyrofrequency Ωe corresponding to spacecraft observations. The wave spectra are carefully mapped to the correct resonant electron velocities. We show that previous diffusion calculations of ECH waves at 1.5Ωe, driven by the loss cone instability, result in large diffusion rates confined to a small range of pitch angles near the loss cone and therefore cannot account for pancake distributions. However, when the wave spectrum is centered at higher frequencies in the band (>1.6Ωe), the diffusion rates become very small inside the loss cone, peak just outside, and remain large over a wide range of pitch angles up to 60° or more. When the upper hybrid resonance frequency ωUHR is several times Ωe, ECH waves excited in higher bands also contribute significantly to pitch angle diffusion outside the loss cone up to very large pitch angles. We suggest that ECH waves driven by a loss cone could form pancake distributions as they grow if the wave spectrum extends from the middle to the upper part of the first (and higher) gyroharmonic bands. Alternatively, we suggest that pancake distributions can be formed by outward propagation in a nonhomogeneous medium, so that resonant absorption occurs at higher frequencies between(n+12) and (n+1)Ωe in regions where waves are also growing locally at <=1.5Ωe. The calculated diffusion rates suggest that ECH waves with amplitudes of the order of 1 mV m-1 can form pancake distributions from an initially isotropic distribution on a timescale of a few hours. This is consistent with recent CRRES observations of ECH wave amplitudes following substorm injections near geostationary orbit and the timescales for pancake formation. Persistent but much weaker ECH waves can further intensify and maintain pancake distributions during magnetically quiet periods.

Diffusion Driven Combustion Waves in Porous Media

NASA Technical Reports Server (NTRS)

Aldushin, A. P.; Matkowsky, B. J.

2000-01-01

Filtration of gas containing oxidizer, to the reaction zone in a porous medium, due, e.g., to a buoyancy force or to an external pressure gradient, leads to the propagation of Filtration combustion (FC) waves. The exothermic reaction occurs between the fuel component of the solid matrix and the oxidizer. In this paper, we analyze the ability of a reaction wave to propagate in a porous medium without the aid of filtration. We find that one possible mechanism of propagation is that the wave is driven by diffusion of oxidizer from the environment. The solution of the combustion problem describing diffusion driven waves is similar to the solution of the Stefan problem describing the propagation of phase transition waves, in that the temperature on the interface between the burned and unburned regions is constant, the combustion wave is described by a similarity solution which is a function of the similarity variable x/square root of(t) and the wave velocity decays as 1/square root of(t). The difference between the two problems is that in the combustion problem the temperature is not prescribed, but rather, is determined as part of the solution. We will show that the length of samples in which such self-sustained combustion waves can occur, must exceed a critical value which strongly depends on the combustion temperature T(sub b). Smaller values of T(sub b) require longer sample lengths for diffusion driven combustion waves to exist. Because of their relatively small velocity, diffusion driven waves are considered to be relevant for the case of low heat losses, which occur for large diameter samples or in microgravity conditions, Another possible mechanism of porous medium combustion describes waves which propagate by consuming the oxidizer initially stored in the pores of the sample. This occurs for abnormally high pressure and gas density. In this case, uniformly propagating planar waves, which are kinetically controlled, can propagate, Diffusion of oxidizer decreases the wave velocity. In addition to the reaction and diffusion layers, the uniformly propagating wave structure includes a layer with a pressure gradient, where the gas motion is induced by the production or consumption of the gas in the reaction as well as by thermal expansion of the gas. The width of this zone determines the scale of the combustion wave in the porous medium.

Observation of High-Frequency Electrostatic Waves in the Vicinity of the Reconnection Ion Diffusion Region by the Spacecraft of the Magnetospheric Multiscale (MMS) Mission

NASA Technical Reports Server (NTRS)

Zhou, M.; Ashour-Abdalla, M.; Berchem, J.; Walker, R. J.; Liang, H.; El-Alaoui, M.; Goldstein, M. L.; Lindqvist, P.-A.; Marklund, G.; Khotyaintsev, Y. V.;

Response of radiation belt simulations to different radial diffusion coefficients

NASA Astrophysics Data System (ADS)

Drozdov, A.; Shprits, Y.; Subbotin, D.; Kellerman, A. C.

2013-12-01

Resonant interactions between Ultra Low Frequency (ULF) waves and relativistic electrons may violate the third adiabatic invariant of motion, which produces radial diffusion in the electron radiation belts. This process plays an important role in the formation and structure of the outer electron radiation belt and is important for electron acceleration and losses in that region. Two parameterizations of the resonant wave-particle interaction of electrons with ULF waves in the magnetosphere by Brautigam and Albert [2000] and Ozeke et al. [2012] are evaluated using the Versatile Electron Radiation Belt (VERB) diffusion code to estimate their relative effect on the radiation belt simulation. The period of investigation includes quiet time and storm time geomagnetic activity and is compared to data based on satellite observations. Our calculations take into account wave-particle interactions represented by radial diffusion transport, local acceleration, losses due to pitch-angle diffusion, and mixed diffusion. We show that the results of the 3D diffusion simulations depend on the assumed parametrization of waves. The differences between the simulations and potential missing physical mechanisms are discussed. References Brautigam, D. H., and J. M. Albert (2000), Radial diffusion analysis of outer radiation belt electrons during the October 9, 1990, magnetic storm, J. Geophys. Res., 105(A1), 291-309, doi:10.1029/1999JA900344 Ozeke, L. G., I. R. Mann, K. R. Murphy, I. J. Rae, D. K. Milling, S. R. Elkington, A. A. Chan, and H. J. Singer (2012), ULF wave derived radiation belt radial diffusion coefficients, J. Geophys. Res., 117, A04222, doi:10.1029/2011JA017463.

Response of radiation belt simulations to different radial diffusion coefficients for relativistic and ultra-relativistic electrons

NASA Astrophysics Data System (ADS)

Drozdov, Alexander; Mann, Ian; Baker, Daniel N.; Subbotin, Dmitriy; Ozeke, Louis; Shprits, Yuri; Kellerman, Adam

Two parameterizations of the resonant wave-particle interactions of electrons with ULF waves in the magnetosphere by Brautigam and Albert [2000] and Ozeke et al. [2012] are evaluated using the Versatile Electron Radiation Belt (VERB) diffusion code to estimate the effect of changing a diffusion coefficient on the radiation belt simulation. The period of investigation includes geomagnetically quiet and active time. The simulations take into account wave-particle interactions represented by radial diffusion transport, local acceleration, losses due to pitch-angle diffusion, and mixed diffusion. 1. Brautigam, D. H., and J. M. Albert (2000), Radial diffusion analysis of outer radiation belt electrons during the October 9, 1990, magnetic storm, J. Geophys. Res., 105(A1), 291-309, doi:10.1029/1999JA900344 2. Ozeke, L. G., I. R. Mann, K. R. Murphy, I. J. Rae, D. K. Milling, S. R. Elkington, A. A. Chan, and H. J. Singer (2012), ULF wave derived radiation belt radial diffusion coefficients, J. Geophys. Res., 117, A04222, doi:10.1029/2011JA017463.

Application of New Chorus Wave Model from Van Allen Probe Observations in Earth's Radiation Belt Modeling

NASA Astrophysics Data System (ADS)

Wang, D.; Shprits, Y.; Spasojevic, M.; Zhu, H.; Aseev, N.; Drozdov, A.; Kellerman, A. C.

2017-12-01

In situ satellite observations, theoretical studies and model simulations suggested that chorus waves play a significant role in the dynamic evolution of relativistic electrons in the Earth's radiation belts. In this study, we developed new wave frequency and amplitude models that depend on Magnetic Local Time (MLT)-, L-shell, latitude- and geomagnetic conditions indexed by Kp for upper-band and lower-band chorus waves using measurements from the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) instrument onboard the Van Allen Probes. Utilizing the quasi-linear full diffusion code, we calculated corresponding diffusion coefficients in each MLT sector (1 hour resolution) for upper-band and lower-band chorus waves according to the new developed wave models. Compared with former parameterizations of chorus waves, the new parameterizations result in differences in diffusion coefficients that depend on energy and pitch angle. Utilizing obtained diffusion coefficients, lifetime of energetic electrons is parameterized accordingly. In addition, to investigate effects of obtained diffusion coefficients in different MLT sectors and under different geomagnetic conditions, we performed simulations using four-dimensional Versatile Electron Radiation Belt simulations and validated results against observations.

Diffusion phenomenon for linear dissipative wave equations in an exterior domain

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

Generalized Sagdeev potential theory for shock waves modeling

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-05-01

In this paper, we develop an innovative approach to study the shock wave propagation using the Sagdeev potential method. We also present an analytical solution for Korteweg de Vries Burgers (KdVB) and modified KdVB equation families with a generalized form of the nonlinearity term which agrees well with the numerical one. The novelty of the current approach is that it is based on a simple analogy of the particle in a classical potential with the variable particle energy providing one with a deeper physical insight into the problem and can easily be extended to more complex physical situations. We find that the current method well describes both monotonic and oscillatory natures of the dispersive-diffusive shock structures in different viscous fluid configurations. It is particularly important that all essential parameters of the shock structure can be deduced directly from the Sagdeev potential in small and large potential approximation regimes. Using the new method, we find that supercnoidal waves can decay into either compressive or rarefactive shock waves depending on the initial wave amplitude. Current investigation provides a general platform to study a wide range of phenomena related to nonlinear wave damping and interactions in diverse fluids including plasmas.

The parallel-antiparallel signal difference in double-wave-vector diffusion-weighted MR at short mixing times: A phase evolution perspective

NASA Astrophysics Data System (ADS)

Finsterbusch, Jürgen

2011-01-01

Experiments with two diffusion weightings applied in direct succession in a single acquisition, so-called double- or two-wave-vector diffusion-weighting (DWV) experiments at short mixing times, have been shown to be a promising tool to estimate cell or compartment sizes, e.g. in living tissue. The basic theory for such experiments predicts that the signal decays for parallel and antiparallel wave vector orientations differ by a factor of three for small wave vectors. This seems to be surprising because in standard, single-wave-vector experiments the polarity of the diffusion weighting has no influence on the signal attenuation. Thus, the question how this difference can be understood more pictorially is often raised. In this rather educational manuscript, the phase evolution during a DWV experiment for simple geometries, e.g. diffusion between parallel, impermeable planes oriented perpendicular to the wave vectors, is considered step-by-step and demonstrates how the signal difference develops. Considering the populations of the phase distributions obtained, the factor of three between the signal decays which is predicted by the theory can be reproduced. Furthermore, the intermediate signal decay for orthogonal wave vector orientations can be derived when investigating diffusion in a box. Thus, the presented “phase gymnastics” approach may help to understand the signal modulation observed in DWV experiments at short mixing times.

The viscous lee wave problem and its implications for ocean modelling

NASA Astrophysics Data System (ADS)

Shakespeare, Callum J.; Hogg, Andrew McC.

2017-05-01

Ocean circulation models employ 'turbulent' viscosity and diffusivity to represent unresolved sub-gridscale processes such as breaking internal waves. Computational power has now advanced sufficiently to permit regional ocean circulation models to be run at sufficiently high (100 m-1 km) horizontal resolution to resolve a significant part of the internal wave spectrum. Here we develop theory for boundary generated internal waves in such models, and in particular, where the waves dissipate their energy. We focus specifically on the steady lee wave problem where stationary waves are generated by a large-scale flow acting across ocean bottom topography. We generalise the energy flux expressions of [Bell, T., 1975. Topographically generated internal waves in the open ocean. J. Geophys. Res. 80, 320-327] to include the effect of arbitrary viscosity and diffusivity. Applying these results for realistic parameter choices we show that in the present generation of models with O(1) m2s-1 horizontal viscosity/diffusivity boundary-generated waves will inevitably dissipate the majority of their energy within a few hundred metres of the boundary. This dissipation is a direct consequence of the artificially high viscosity/diffusivity, which is not always physically justified in numerical models. Hence, caution is necessary in comparing model results to ocean observations. Our theory further predicts that O(10-2) m2s-1 horizontal and O(10-4) m2s-1 vertical viscosity/diffusivity is required to achieve a qualitatively inviscid representation of internal wave dynamics in ocean models.

Diffusion in plasma: The Hall effect, compositional waves, and chemical spots

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

Urpin, V., E-mail: Vadim.urpin@uv.es

2017-03-15

Diffusion caused by a combined influence of the electric current and Hall effect is considered, and it is argued that such diffusion can form inhomogeneities of a chemical composition in plasma. The considered mechanism can be responsible for the formation of element spots in laboratory and astrophysical plasmas. This current-driven diffusion can be accompanied by propagation of a particular type of waves in which the impurity number density oscillates alone. These compositional waves exist if the magnetic pressure in plasma is much greater than the gas pressure.

The Fisher-KPP problem with doubly nonlinear diffusion

NASA Astrophysics Data System (ADS)

Audrito, Alessandro; Vázquez, Juan Luis

2017-12-01

The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it possesses a family of travelling waves that describe the asymptotic behaviour of a large class solutions 0 ≤ u (x , t) ≤ 1 of the problem posed in the real line. The existence of propagation waves with finite speed has been confirmed in some related models and disproved in others. We investigate here the corresponding theory when the linear diffusion is replaced by the "slow" doubly nonlinear diffusion and we find travelling waves that represent the wave propagation of more general solutions even when we extend the study to several space dimensions. A similar study is performed in the critical case that we call "pseudo-linear", i.e., when the operator is still nonlinear but has homogeneity one. With respect to the classical model and the "pseudo-linear" case, the "slow" travelling waves exhibit free boundaries.

Pitch-angle diffusion of electrons through growing and propagating along a magnetic field electromagnetic wave in Earth's radiation belts

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

Choi, C.-R., E-mail: crchoi@kaist.ac.kr; Dokgo, K.; Min, K.-W.

The diffusion of electrons via a linearly polarized, growing electromagnetic (EM) wave propagating along a uniform magnetic field is investigated. The diffusion of electrons that interact with the growing EM wave is investigated through the autocorrelation function of the parallel electron acceleration in several tens of electron gyration timescales, which is a relatively short time compared with the bounce time of electrons between two mirror points in Earth's radiation belts. Furthermore, the pitch-angle diffusion coefficient is derived for the resonant and non-resonant electrons, and the effect of the wave growth on the electron diffusion is discussed. The results can bemore » applied to other problems related to local acceleration or the heating of electrons in space plasmas, such as in the radiation belts.« less

Porous medium acoustics of wave-induced vorticity diffusion

NASA Astrophysics Data System (ADS)

Müller, T. M.; Sahay, P. N.

2011-02-01

A theory for attenuation and dispersion of elastic waves due to wave-induced generation of vorticity at pore-scale heterogeneities in a macroscopically homogeneous porous medium is developed. The diffusive part of the vorticity field associated with a viscous wave in the pore space—the so-called slow shear wave—is linked to the porous medium acoustics through incorporation of the fluid strain rate tensor of a Newtonian fluid in the poroelastic constitutive relations. The method of statistical smoothing is then used to derive dynamic-equivalent elastic wave velocities accounting for the conversion scattering process into the diffusive slow shear wave in the presence of randomly distributed pore-scale heterogeneities. The result is a simple model for wave attenuation and dispersion associated with the transition from viscosity- to inertia-dominated flow regime.

Conditions for supersonic bent Marshak waves

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

Xu, Qiang, E-mail: xuqiangxu@pku.edu.cn; Ren, Xiao-dong; Li, Jing

Supersonic radiation diffusion approximation is an useful method to study the radiation transportation. Considering the 2-d Marshak theory, and an invariable source temperature, conditions for supersonic radiation diffusion are proved to be coincident with that for radiant flux domination in the early time when √(ε)x{sub f}/L≪1. However, they are even tighter than conditions for radiant flux domination in the late time when √(ε)x{sub f}/L≫1, and can be expressed as M>4(1+ε/3)/3 and τ>1. A large Mach number requires the high temperature, while the large optical depth requires the low temperature. Only when the source temperature is in a proper region themore » supersonic diffusion conditions can be satisfied. Assuming a power-low (in temperature and density) opacity and internal energy, for a given density, the supersonic diffusion regions are given theoretically. The 2-d Marshak theory is proved to be able to bound the supersonic diffusion conditions in both high and low temperature regions, however, the 1-d theory only bounds it in low temperature region. Taking SiO{sub 2} and the Au, for example, these supersonic regions are shown numerically.« less

Effect of upstream ULF waves on the energetic ion diffusion at the earth's foreshock: Theory, Simulation, and Observations

NASA Astrophysics Data System (ADS)

Otsuka, F.; Matsukiyo, S.; Kis, A.; Hada, T.

2017-12-01

Spatial diffusion of energetic particles is an important problem not only from a fundamental physics point of view but also for its application to particle acceleration processes at astrophysical shocks. Quasi-linear theory can provide the spatial diffusion coefficient as a function of the wave turbulence spectrum. By assuming a simple power-law spectrum for the turbulence, the theory has been successfully applied to diffusion and acceleration of cosmic rays in the interplanetary and interstellar medium. Near the earth's foreshock, however, the wave spectrum often has an intense peak, presumably corresponding to the upstream ULF waves generated by the field-aligned beam (FAB). In this presentation, we numerically and theoretically discuss how the intense ULF peak in the wave spectrum modifies the spatial parallel diffusion of energetic ions. The turbulence is given as a superposition of non-propagating transverse MHD waves in the solar wind rest frame, and its spectrum is composed of a piecewise power-law spectrum with different power-law indices. The diffusion coefficients are then estimated by using the quasi-linear theory and test particle simulations. We find that the presence of the ULF peak produces a concave shape of the diffusion coefficient when it is plotted versus the ion energy. The results above are used to discuss the Cluster observations of the diffuse ions at the Earth's foreshock. Using the density gradients of the energetic ions detected by the Cluster spacecraft, we determine the e-folding distances, equivalently, the spatial diffusion coefficients, of ions with their energies from 10 to 32 keV. The observed e-folding distances are significantly smaller than those estimated in the past statistical studies. This suggests that the particle acceleration at the foreshock can be more efficient than considered before. Our test particle simulation explains well the small estimate of the e-folding distances, by using the observed wave turbulence spectrum near the shock.

DIFFUSE AURORA ON GANYMEDE DRIVEN BY ELECTROSTATIC WAVES

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

Singhal, R. P.; Tripathi, A. K.; Halder, S.

The role of electrostatic electron cyclotron harmonic (ECH) waves in producing diffuse auroral emission O i 1356 Å on Ganymede is investigated. Electron precipitation flux entering the atmosphere of Ganymede due to pitch-angle diffusion by ECH waves into the atmospheric loss-cone is calculated. The analytical yield spectrum approach for electron energy degradation in gases is used for calculating diffuse auroral intensities. It is found that calculated O i 1356 Å intensity resulting from the precipitation of magnetospheric electrons observed near Ganymede is insufficient to account for the observed diffuse auroral intensity. This is in agreement with estimates made in earliermore » works. Heating and acceleration of ambient electrons by ECH wave turbulence near the magnetic equator on the field line connecting Ganymede and Jupiter are considered. Two electron distribution functions are used to simulate the heating effect by ECH waves. Use of a Maxwellian distribution with temperature 100 eV can produce about 50–70 Rayleigh O i 1356 Å intensities, and the kappa distribution with characteristic energy 50 eV also gives rise to intensities with similar magnitude. Numerical experiments are performed to study the effect of ECH wave spectral intensity profile, ECH wave amplitude, and temperature/characteristic energy of electron distribution functions on the calculated diffuse auroral intensities. The proposed missions, joint NASA/ESA Jupiter Icy Moon Explorer and the present JUNO mission to Jupiter, would provide new data to constrain the ECH wave and other physical parameters near Ganymede. These should help confirm the findings of the present study.« less

Ultrasonic monitoring of spontaneous imbibition experiments: Precursory moisture diffusion effects ahead of water front

NASA Astrophysics Data System (ADS)

David, Christian; Sarout, Joël.; Dautriat, Jérémie; Pimienta, Lucas; Michée, Marie; Desrues, Mathilde; Barnes, Christophe

2017-07-01

Fluid substitution processes have been investigated in the laboratory on 14 carbonate and siliciclastic reservoir rock analogues through spontaneous imbibition experiments on vertical cylindrical specimens with simultaneous ultrasonic monitoring and imaging. The motivation of our study was to identify the seismic attributes of fluid substitution in reservoir rocks and to link them to physical processes. It is shown that (i) the P wave velocity either decreases or increases when the capillary front reaches the Fresnel clearance zone, (ii) the P wave amplitude is systematically impacted earlier than the velocity is, (iii) this precursory amplitude decrease occurs when the imbibition front is located outside of the Fresnel zone, and (iv) the relative variation of the P wave amplitude is always much larger than that of the P wave velocity. These results suggest that moisture diffuses into the pore space ahead of the water front. This postulate is further supported by a quantitative analysis of the time evolution of the observed P wave amplitudes. In a sense, P wave amplitude acts as a precursor of the arrival of the capillary front. This phenomenon is used to estimate the effective diffusivity of moisture in the tested rocks. The effective moisture diffusivity estimated from the ultrasonic data is strongly correlated with permeability: a power law with exponent 0.96 predicts permeability from ultrasonic monitoring within a factor 3 without noticeable bias. When the effective diffusivity is high, moisture diffusion affects ultrasonic P wave attributes even before the imbibition starts and impacts the P wave reflectivity as evidenced by the variations recorded in the waveform coda.

Gravitational-Wave and Neutrino Signals from Core-Collapse Supernovae with QCD Phase Transition

NASA Astrophysics Data System (ADS)

Zha, Shuai; Leung, Shing Chi; Lin, Lap Ming; Chu, Ming-Chung

Core-collapse supernovae (CCSNe) mark the catastrophic death of massive stars. We simulate CCSNe with a hybrid equations of state (EOS) containing a QCD (quantum chromodynamics) phase transition. The hybrid EOS incorporates the pure hadronic HShen EOS and the MIT Bag Model, with a Gibbs construction. Our two-dimensional hydrodynamics code includes a fifth-order shock capturing scheme WENO and models neutrino transport with the isotropic diffusion source approximation (IDSA). As the proto-neutron-star accretes matter and the core enters the mixed phase, a second collapse takes place due to softening of the EOS. We calculate the gravitational-wave (GW) and neutrino signals for this kind of CCSNe model. Future detection of these signals from CCSNe may help to constrain this scenario and the hybrid EOS.

Two-dimensional CFD modeling of wave rotor flow dynamics

NASA Technical Reports Server (NTRS)

Welch, Gerard E.; Chima, Rodrick V.

1994-01-01

A two-dimensional Navier-Stokes solver developed for detailed study of wave rotor flow dynamics is described. The CFD model is helping characterize important loss mechanisms within the wave rotor. The wave rotor stationary ports and the moving rotor passages are resolved on multiple computational grid blocks. The finite-volume form of the thin-layer Navier-Stokes equations with laminar viscosity are integrated in time using a four-stage Runge-Kutta scheme. Roe's approximate Riemann solution scheme or the computationally less expensive advection upstream splitting method (AUSM) flux-splitting scheme is used to effect upwind-differencing of the inviscid flux terms, using cell interface primitive variables set by MUSCL-type interpolation. The diffusion terms are central-differenced. The solver is validated using a steady shock/laminar boundary layer interaction problem and an unsteady, inviscid wave rotor passage gradual opening problem. A model inlet port/passage charging problem is simulated and key features of the unsteady wave rotor flow field are identified. Lastly, the medium pressure inlet port and high pressure outlet port portion of the NASA Lewis Research Center experimental divider cycle is simulated and computed results are compared with experimental measurements. The model accurately predicts the wave timing within the rotor passages and the distribution of flow variables in the stationary inlet port region.

Two-dimensional CFD modeling of wave rotor flow dynamics

NASA Technical Reports Server (NTRS)

Welch, Gerard E.; Chima, Rodrick V.

1993-01-01

A two-dimensional Navier-Stokes solver developed for detailed study of wave rotor flow dynamics is described. The CFD model is helping characterize important loss mechanisms within the wave rotor. The wave rotor stationary ports and the moving rotor passages are resolved on multiple computational grid blocks. The finite-volume form of the thin-layer Navier-Stokes equations with laminar viscosity are integrated in time using a four-stage Runge-Kutta scheme. The Roe approximate Riemann solution scheme or the computationally less expensive Advection Upstream Splitting Method (AUSM) flux-splitting scheme are used to effect upwind-differencing of the inviscid flux terms, using cell interface primitive variables set by MUSCL-type interpolation. The diffusion terms are central-differenced. The solver is validated using a steady shock/laminar boundary layer interaction problem and an unsteady, inviscid wave rotor passage gradual opening problem. A model inlet port/passage charging problem is simulated and key features of the unsteady wave rotor flow field are identified. Lastly, the medium pressure inlet port and high pressure outlet port portion of the NASA Lewis Research Center experimental divider cycle is simulated and computed results are compared with experimental measurements. The model accurately predicts the wave timing within the rotor passage and the distribution of flow variables in the stationary inlet port region.

Banded structures in electron pitch angle diffusion coefficients from resonant wave-particle interactions

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

Tripathi, A. K., E-mail: aktrip2001@yahoo.co.in; Singhal, R. P., E-mail: rpsiitbhu@yahoo.com; Khazanov, G. V., E-mail: George.V.Khazanov@nasa.gov

2016-04-15

Electron pitch angle (D{sub αα}) and momentum (D{sub pp}) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L = 4.6 and 6.8 for electron energies ≤10 keV. Landau (n = 0) resonance and cyclotron harmonic resonances n = ±1, ±2, … ±5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (α) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusionmore » coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n = +1 and n = +2. A major contribution to momentum diffusion coefficients appears from n = +2. However, the banded structures in D{sub αα} and D{sub pp} coefficients appear only in the profile of diffusion coefficients for n = +2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The D{sub pp} diffusion coefficient for ECH waves is one to two orders smaller than D{sub αα} coefficients. For chorus waves, D{sub pp} coefficients are about an order of magnitude smaller than D{sub αα} coefficients for the case n ≠ 0. In case of Landau resonance, the values of D{sub pp} coefficient are generally larger than the values of D{sub αα} coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89° and harmonic resonances n = +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10° and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies ≥1 keV, and for whistler mode chorus waves, structures appear for energies >2 keV at L = 4.6 and above 200 eV for L = 6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.« less

Wave Augmented Diffusers for Centrifugal Compressors

NASA Technical Reports Server (NTRS)

Paxson, Daniel E.; Skoch, Gary J.

1998-01-01

A conceptual device is introduced which would utilize unsteady wave motion to slow and turn flows in the diffuser section of a centrifugal compressor. The envisioned device would substantially reduce the size of conventional centrifugal diffusers by eliminating the relatively large ninety degree bend needed to turn the flow from the radial/tangential to the axial direction. The bend would be replaced by a wall and the flow would instead exit through a series of rotating ports located on a disk, adjacent to the diffuser hub, and fixed to the impeller shaft. The ports would generate both expansion and compression waves which would rapidly transition from the hub/shroud (axial) direction to the radial/tangential direction. The waves would in turn induce radial/tangential and axial flow. This paper presents a detailed description of the device. Simplified cycle analysis and performance results are presented which were obtained using a time accurate, quasi-one-dimensional CFD code with models for turning, port flow conditions, and losses due to wall shear stress. The results indicate that a periodic wave system can be established which yields diffuser performance comparable to a conventional diffuser. Discussion concerning feasibility, accuracy, and integration follow.

Modeling radiation belt electron dynamics during GEM challenge intervals with the DREAM3D diffusion model

NASA Astrophysics Data System (ADS)

Tu, Weichao; Cunningham, G. S.; Chen, Y.; Henderson, M. G.; Camporeale, E.; Reeves, G. D.

2013-10-01

a response to the Geospace Environment Modeling (GEM) "Global Radiation Belt Modeling Challenge," a 3D diffusion model is used to simulate the radiation belt electron dynamics during two intervals of the Combined Release and Radiation Effects Satellite (CRRES) mission, 15 August to 15 October 1990 and 1 February to 31 July 1991. The 3D diffusion model, developed as part of the Dynamic Radiation Environment Assimilation Model (DREAM) project, includes radial, pitch angle, and momentum diffusion and mixed pitch angle-momentum diffusion, which are driven by dynamic wave databases from the statistical CRRES wave data, including plasmaspheric hiss, lower-band, and upper-band chorus. By comparing the DREAM3D model outputs to the CRRES electron phase space density (PSD) data, we find that, with a data-driven boundary condition at Lmax = 5.5, the electron enhancements can generally be explained by radial diffusion, though additional local heating from chorus waves is required. Because the PSD reductions are included in the boundary condition at Lmax = 5.5, our model captures the fast electron dropouts over a large L range, producing better model performance compared to previous published results. Plasmaspheric hiss produces electron losses inside the plasmasphere, but the model still sometimes overestimates the PSD there. Test simulations using reduced radial diffusion coefficients or increased pitch angle diffusion coefficients inside the plasmasphere suggest that better wave models and more realistic radial diffusion coefficients, both inside and outside the plasmasphere, are needed to improve the model performance. Statistically, the results show that, with the data-driven outer boundary condition, including radial diffusion and plasmaspheric hiss is sufficient to model the electrons during geomagnetically quiet times, but to best capture the radiation belt variations during active times, pitch angle and momentum diffusion from chorus waves are required.

Multiphysics modeling of non-linear laser-matter interactions for optically active semiconductors

NASA Astrophysics Data System (ADS)

Kraczek, Brent; Kanp, Jaroslaw

Development of photonic devices for sensors and communications devices has been significantly enhanced by computational modeling. We present a new computational method for modelling laser propagation in optically-active semiconductors within the paraxial wave approximation (PWA). Light propagation is modeled using the Streamline-upwind/Petrov-Galerkin finite element method (FEM). Material response enters through the non-linear polarization, which serves as the right-hand side of the FEM calculation. Maxwell's equations for classical light propagation within the PWA can be written solely in terms of the electric field, producing a wave equation that is a form of the advection-diffusion-reaction equations (ADREs). This allows adaptation of the computational machinery developed for solving ADREs in fluid dynamics to light-propagation modeling. The non-linear polarization is incorporated using a flexible framework to enable the use of multiple methods for carrier-carrier interactions (e.g. relaxation-time-based or Monte Carlo) to enter through the non-linear polarization, as appropriate to the material type. We demonstrate using a simple carrier-carrier model approximating the response of GaN. Supported by ARL Materials Enterprise.

Sound waves and resonances in electron-hole plasma

NASA Astrophysics Data System (ADS)

Lucas, Andrew

2016-06-01

Inspired by the recent experimental signatures of relativistic hydrodynamics in graphene, we investigate theoretically the behavior of hydrodynamic sound modes in such quasirelativistic fluids near charge neutrality, within linear response. Locally driving an electron fluid at a resonant frequency to such a sound mode can lead to large increases in the electrical response at the edges of the sample, a signature, which cannot be explained using diffusive models of transport. We discuss the robustness of this signal to various effects, including electron-acoustic phonon coupling, disorder, and long-range Coulomb interactions. These long-range interactions convert the sound mode into a collective plasmonic mode at low frequencies unless the fluid is charge neutral. At the smallest frequencies, the response in a disordered fluid is quantitatively what is predicted by a "momentum relaxation time" approximation. However, this approximation fails at higher frequencies (which can be parametrically small), where the classical localization of sound waves cannot be neglected. Experimental observation of such resonances is a clear signature of relativistic hydrodynamics, and provides an upper bound on the viscosity of the electron-hole plasma.

Functional imaging of the human brain using a modular, fibre-less, high-density diffuse optical tomography system.

PubMed

Chitnis, Danial; Cooper, Robert J; Dempsey, Laura; Powell, Samuel; Quaggia, Simone; Highton, David; Elwell, Clare; Hebden, Jeremy C; Everdell, Nicholas L

2016-10-01

We present the first three-dimensional, functional images of the human brain to be obtained using a fibre-less, high-density diffuse optical tomography system. Our technology consists of independent, miniaturized, silicone-encapsulated DOT modules that can be placed directly on the scalp. Four of these modules were arranged to provide up to 128, dual-wavelength measurement channels over a scalp area of approximately 60 × 65 mm 2 . Using a series of motor-cortex stimulation experiments, we demonstrate that this system can obtain high-quality, continuous-wave measurements at source-detector separations ranging from 14 to 55 mm in adults, in the presence of hair. We identify robust haemodynamic response functions in 5 out of 5 subjects, and present diffuse optical tomography images that depict functional haemodynamic responses that are well-localized in all three dimensions at both the individual and group levels. This prototype modular system paves the way for a new generation of wearable, wireless, high-density optical neuroimaging technologies.

Toward real-time diffuse optical tomography: accelerating light propagation modeling employing parallel computing on GPU and CPU

NASA Astrophysics Data System (ADS)

Doulgerakis, Matthaios; Eggebrecht, Adam; Wojtkiewicz, Stanislaw; Culver, Joseph; Dehghani, Hamid

2017-12-01

Parameter recovery in diffuse optical tomography is a computationally expensive algorithm, especially when used for large and complex volumes, as in the case of human brain functional imaging. The modeling of light propagation, also known as the forward problem, is the computational bottleneck of the recovery algorithm, whereby the lack of a real-time solution is impeding practical and clinical applications. The objective of this work is the acceleration of the forward model, within a diffusion approximation-based finite-element modeling framework, employing parallelization to expedite the calculation of light propagation in realistic adult head models. The proposed methodology is applicable for modeling both continuous wave and frequency-domain systems with the results demonstrating a 10-fold speed increase when GPU architectures are available, while maintaining high accuracy. It is shown that, for a very high-resolution finite-element model of the adult human head with ˜600,000 nodes, consisting of heterogeneous layers, light propagation can be calculated at ˜0.25 s/excitation source.

Separating non-diffuse component from ambient seismic noise cross-correlation in southern California­­

NASA Astrophysics Data System (ADS)

Liu, X.; Beroza, G. C.; Nakata, N.

2017-12-01

Cross-correlation of fully diffuse wavefields provides Green's function between receivers, although the ambient noise field in the real world contains both diffuse and non-diffuse fields. The non-diffuse field potentially degrades the correlation functions. We attempt to blindly separate the diffuse and the non-diffuse components from cross-correlations of ambient seismic noise and analyze the potential bias caused by the non-diffuse components. We compute the 9-component noise cross-correlations for 17 stations in southern California. For the Rayleigh wave components, we assume that the cross-correlation of multiply scattered waves (diffuse component) is independent from the cross-correlation of ocean microseismic quasi-point source responses (non-diffuse component), and the cross-correlation function of ambient seismic data is the sum of both components. Thus we can blindly separate the non-diffuse component due to physical point sources and the more diffuse component due to cross-correlation of multiply scattered noise based on their statistical independence. We also perform beamforming over different frequency bands for the cross-correlations before and after the separation, and we find that the decomposed Rayleigh wave represents more coherent features among all Rayleigh wave polarization cross-correlation components. We show that after separating the non-diffuse component, the Frequency-Time Analysis results are less ambiguous. In addition, we estimate the bias in phase velocity on the raw cross-correlation data due to the non-diffuse component. We also apply this technique to a few borehole stations in Groningen, the Netherlands, to demonstrate its applicability in different instrument/geology settings.

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

NASA Astrophysics Data System (ADS)

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

2004-04-01

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

Simulation of energy-dependent electron diffusion processes in the Earth's outer radiation belt

DOE PAGES

Ma, Q.; Li, W.; Thorne, R. M.; ...

2016-04-28

The radial and local diffusion processes induced by various plasma waves govern the highly energetic electron dynamics in the Earth's radiation belts, causing distinct characteristics in electron distributions at various energies. In this study, we present our simulation results of the energetic electron evolution during a geomagnetic storm using the University of California, Los Angeles 3-D diffusion code. Following the plasma sheet electron injections, the electrons at different energy bands detected by the Magnetic Electron Ion Spectrometer (MagEIS) and Relativistic Electron Proton Telescope (REPT) instruments on board the Van Allen Probes exhibit a rapid enhancement followed by a slow diffusivemore » movement in differential energy fluxes, and the radial extent to which electrons can penetrate into depends on energy with closer penetration toward the Earth at lower energies than higher energies. We incorporate radial diffusion, local acceleration, and loss processes due to whistler mode wave observations to perform a 3-D diffusion simulation. Here, our simulation results demonstrate that chorus waves cause electron flux increase by more than 1 order of magnitude during the first 18 h, and the subsequent radial extents of the energetic electrons during the storm recovery phase are determined by the coupled radial diffusion and the pitch angle scattering by EMIC waves and plasmaspheric hiss. The radial diffusion caused by ULF waves and local plasma wave scattering are energy dependent, which lead to the observed electron flux variations with energy dependences. Lastly, this study suggests that plasma wave distributions in the inner magnetosphere are crucial for the energy-dependent intrusions of several hundred keV to several MeV electrons.« less

Low thermal diffusivity measurements of thin films using mirage technique

NASA Astrophysics Data System (ADS)

Wong, P. K.; Fung, P. C. W.; Tam, H. L.

1998-12-01

Mirage technique is proved to be powerful in measurements of thermal diffusivity. Its contactless nature makes it suitable for delicate samples such as thin films and single crystals. However, as the damping of the thermal wave profile increases progressively upon the decrease in thermal diffusivity of the medium, mirage technique becomes more difficult to be applied to low thermal diffusivity measurements. Moreover influences from substrate signals make analysis difficult when the samples are thermally thin. Recently a thermal-wave-coupling method for mirage signal analysis [P. K. Wong, P. C. W. Fung, H. L. Tam, and J. Gao, Phys. Rev. B 51, 523 (1995)] was reported for thermal diffusivity measurements of thin film down to 60 nm thick. In this article we apply the thermal-wave-coupling method to thin films of low thermal diffusivity, especially polymer films. A new lower limit of thermal diffusivity measurable by mirage technique has been reached.

Simulation of whistler waves excited in the presence of a cold plasma cloud - Implications for the CRRES mission. [Combined Release and Radiation Effects Satellite

NASA Technical Reports Server (NTRS)

Pritchett, P. L.; Schriver, D.; Ashour-Abdalla, M.

1991-01-01

A one-dimensional electromagnetic particle simulation model is constructed to study the excitation of whistler waves in the presence of a cold plasma cloud for conditions representative of those after the release of lithium in the inner plasma sheet during the Combined Release and Radiation Effect Satellite mission. The results indicate that a standing-wave pattern with discrete wave frequencies is formed within the cloud. The magnetic wave amplitude inside the cloud, which is limited by quasi-linear diffusion, is of the order of several nanoteslas. Assuming a magnetospheric loss cone of 5 deg, the observed pitch angle diffusion produced by the whistler waves is sufficient to put the electrons on strong diffusion.

3D radiation belt diffusion model results using new empirical models of whistler chorus and hiss

NASA Astrophysics Data System (ADS)

Cunningham, G.; Chen, Y.; Henderson, M. G.; Reeves, G. D.; Tu, W.

2012-12-01

3D diffusion codes model the energization, radial transport, and pitch angle scattering due to wave-particle interactions. Diffusion codes are powerful but are limited by the lack of knowledge of the spatial & temporal distribution of waves that drive the interactions for a specific event. We present results from the 3D DREAM model using diffusion coefficients driven by new, activity-dependent, statistical models of chorus and hiss waves. Most 3D codes parameterize the diffusion coefficients or wave amplitudes as functions of magnetic activity indices like Kp, AE, or Dst. These functional representations produce the average value of the wave intensities for a given level of magnetic activity; however, the variability of the wave population at a given activity level is lost with such a representation. Our 3D code makes use of the full sample distributions contained in a set of empirical wave databases (one database for each wave type, including plasmaspheric hiss, lower and upper hand chorus) that were recently produced by our team using CRRES and THEMIS observations. The wave databases store the full probability distribution of observed wave intensity binned by AE, MLT, MLAT and L*. In this presentation, we show results that make use of the wave intensity sample probability distributions for lower-band and upper-band chorus by sampling the distributions stochastically during a representative CRRES-era storm. The sampling of the wave intensity probability distributions produces a collection of possible evolutions of the phase space density, which quantifies the uncertainty in the model predictions caused by the uncertainty of the chorus wave amplitudes for a specific event. A significant issue is the determination of an appropriate model for the spatio-temporal correlations of the wave intensities, since the diffusion coefficients are computed as spatio-temporal averages of the waves over MLT, MLAT and L*. The spatiotemporal correlations cannot be inferred from the wave databases. In this study we use a temporal correlation of ~1 hour for the sampled wave intensities that is informed by the observed autocorrelation in the AE index, a spatial correlation length of ~100 km in the two directions perpendicular to the magnetic field, and a spatial correlation length of 5000 km in the direction parallel to the magnetic field, according to the work of Santolik et al (2003), who used multi-spacecraft measurements from Cluster to quantify the correlation length scales for equatorial chorus . We find that, despite the small correlation length scale for chorus, there remains significant variability in the model outcomes driven by variability in the chorus wave intensities.

Many-body calculations of low energy eigenstates in magnetic and periodic systems with self healing diffusion Monte Carlo: steps beyond the fixed-phase

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

Reboredo, Fernando A.

The self-healing diffusion Monte Carlo algorithm (SHDMC) [Reboredo, Hood and Kent, Phys. Rev. B {\\bf 79}, 195117 (2009), Reboredo, {\\it ibid.} {\\bf 80}, 125110 (2009)] is extended to study the ground and excited states of magnetic and periodic systems. A recursive optimization algorithm is derived from the time evolution of the mixed probability density. The mixed probability density is given by an ensemble of electronic configurations (walkers) with complex weight. This complex weigh allows the amplitude of the fix-node wave function to move away from the trial wave function phase. This novel approach is both a generalization of SHDMC andmore » the fixed-phase approximation [Ortiz, Ceperley and Martin Phys Rev. Lett. {\\bf 71}, 2777 (1993)]. When used recursively it improves simultaneously the node and phase. The algorithm is demonstrated to converge to the nearly exact solutions of model systems with periodic boundary conditions or applied magnetic fields. The method is also applied to obtain low energy excitations with magnetic field or periodic boundary conditions. The potential applications of this new method to study periodic, magnetic, and complex Hamiltonians are discussed.« less

Strong Pitch-Angle Diffusion of Ring Current Ions in Geomagnetic Storm-Associated Conditions

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Gamayunov, K. V.; Gallagher, D. L.; Spann, J. F.

2005-01-01

Do electromagnetic ion cyclotron (EMIC) waves cause strong pitch-angle diffusion of RC ions? This question is the primary motivation of this paper and has been affirmatively answered from the theoretical point of view. The materials that are presented in the Results section show clear evidence that strong pitch-angle diffusion takes place in the inner magnetosphere indicating an important role for the wave-particle interaction mechanism in the formation of RC ions and EMIC waves.

Generative complexity of Gray-Scott model

NASA Astrophysics Data System (ADS)

Adamatzky, Andrew

2018-03-01

In the Gray-Scott reaction-diffusion system one reactant is constantly fed in the system, another reactant is reproduced by consuming the supplied reactant and also converted to an inert product. The rate of feeding one reactant in the system and the rate of removing another reactant from the system determine configurations of concentration profiles: stripes, spots, waves. We calculate the generative complexity-a morphological complexity of concentration profiles grown from a point-wise perturbation of the medium-of the Gray-Scott system for a range of the feeding and removal rates. The morphological complexity is evaluated using Shannon entropy, Simpson diversity, approximation of Lempel-Ziv complexity, and expressivity (Shannon entropy divided by space-filling). We analyse behaviour of the systems with highest values of the generative morphological complexity and show that the Gray-Scott systems expressing highest levels of the complexity are composed of the wave-fragments (similar to wave-fragments in sub-excitable media) and travelling localisations (similar to quasi-dissipative solitons and gliders in Conway's Game of Life).

Microscale anechoic architecture: acoustic diffusers for ultra low power microparticle separation via traveling surface acoustic waves.

PubMed

Behrens, Jan; Langelier, Sean; Rezk, Amgad R; Lindner, Gerhard; Yeo, Leslie Y; Friend, James R

2015-01-07

We present a versatile and very low-power traveling SAW microfluidic sorting device able to displace and separate particles of different diameter in aqueous suspension; the travelling wave propagates through the fluid bulk and diffuses via a Schröder diffuser, adapted from its typical use in concert hall acoustics to be the smallest such diffuser to be suitable for microfluidics. The effective operating power range is two to three orders of magnitude less than current SAW devices, uniquely eliminating the need for amplifiers, and by using traveling waves to impart forces directly upon suspended microparticles, they can be separated by size.

Plasma diffusion at the magnetopause? The case of lower hybrid drift waves

NASA Technical Reports Server (NTRS)

Treumann, R. A.; Labelle, J.; Pottelette, R.; Gary, S. P.

1990-01-01

The diffusion expected from the quasilinear theory of the lower hybrid drift instability at the Earth's magnetopause is recalculated. The resulting diffusion coefficient is in principle just marginally large enough to explain the thickness of the boundary layer under quiet conditions, based on observational upper limits for the wave intensities. Thus, one possible model for the boundary layer could involve equilibrium between the diffusion arising from lower hybrid waves and various low processes. However, some recent data and simulations seems to indicate that the magnetopause is not consistent with such a soft diffusive equilibrium model. Furthermore, investigation of the nonlinear equations for the lower hybrid waves for magnetopause parameters indicates that the quasilinear state may never arise because coalescence to large wavelengths, followed by collapse once a critical wavelengths is reached, occur on a time scale faster than the quasilinear diffusion. In this case, an inhomogeneous boundary layer is to be expected. More simulations are required over longer time periods to explore whether this nonlinear evolution really takes place at the magnetopause.

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2006-01-01

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

Wave reflection in a reaction-diffusion system: breathing patterns and attenuation of the echo.

PubMed

Tsyganov, M A; Ivanitsky, G R; Zemskov, E P

2014-05-01

Formation and interaction of the one-dimensional excitation waves in a reaction-diffusion system with the piecewise linear reaction functions of the Tonnelier-Gerstner type are studied. We show that there exists a parameter region where the established regime of wave propagation depends on initial conditions. Wave phenomena with a complex behavior are found: (i) the reflection of waves at a growing distance (the remote reflection) upon their collision with each other or with no-flux boundaries and (ii) the periodic transformation of waves with the jumping from one regime of wave propagation to another (the periodic trigger wave).

Wave reflection in a reaction-diffusion system: Breathing patterns and attenuation of the echo

NASA Astrophysics Data System (ADS)

Tsyganov, M. A.; Ivanitsky, G. R.; Zemskov, E. P.

2014-05-01

Formation and interaction of the one-dimensional excitation waves in a reaction-diffusion system with the piecewise linear reaction functions of the Tonnelier-Gerstner type are studied. We show that there exists a parameter region where the established regime of wave propagation depends on initial conditions. Wave phenomena with a complex behavior are found: (i) the reflection of waves at a growing distance (the remote reflection) upon their collision with each other or with no-flux boundaries and (ii) the periodic transformation of waves with the jumping from one regime of wave propagation to another (the periodic trigger wave).

Inviscid spatial stability of a compressible mixing layer. II - The flame sheet model

NASA Technical Reports Server (NTRS)

Jackson, T. L.; Grosch, C. E.

1990-01-01

The results of an inviscid spatial calculation for a compressible reacting mixing layer are reported. The limit of infinitive activation energy is taken and the diffusion flame is approximated by a flame sheet. Results are reported for the phase speeds of the neutral waves and maximum growth rates of the unstable waves as a function of the parameters of the problem: the ratio of the temperature of the stationary stream to that of the moving stream, the Mach number of the moving streams, the heat release per unit mass fraction of the reactant, the equivalence ratio of the reaction, and the frequency of the disturbance. These results are compared to the phase speeds and growth rates of the corresponding nonreacting mixing layer. We show that the addition of combustion has important and complex effects on the flow stability.

Ray tracing study of rising tone EMIC-triggered emissions

NASA Astrophysics Data System (ADS)

Hanzelka, Miroslav; Santolík, Ondřej; Grison, Benjamin; Cornilleau-Wehrlin, Nicole

2017-04-01

ElectroMagnetic Ion Cyclotron (EMIC) triggered emissions have been subject of extensive theoretical and experimental research in last years. These emissions are characterized by high coherence values and a frequency range of 0.5 - 2.0 Hz, close to local helium gyrofrequency. We perform ray tracing case studies of rising tone EMIC-triggered emissions observed by the Cluster spacecraft in both nightside and dayside regions off the equatorial plane. By comparison of simulated and measured wave properties, namely wave vector orientation, group velocity, dispersion and ellipticity of polarization, we determine possible source locations. Diffusive equilibrium density model and other, semi-empirical models are used with ion composition inferred from cross-over frequencies. Ray tracing simulations are done in cold plasma approximation with inclusion of Landau and cyclotron damping. Various widths, locations and profiles of plasmapause are tested.

Boundary value problems for multi-term fractional differential equations

NASA Astrophysics Data System (ADS)

Daftardar-Gejji, Varsha; Bhalekar, Sachin

2008-09-01

Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.

Interface morphology of Mo/Si multilayer systems with varying Mo layer thickness studied by EUV diffuse scattering.

PubMed

Haase, Anton; Soltwisch, Victor; Braun, Stefan; Laubis, Christian; Scholze, Frank

2017-06-26

We investigate the influence of the Mo-layer thickness on the EUV reflectance of Mo/Si mirrors with a set of unpolished and interface-polished Mo/Si/C multilayer mirrors. The Mo-layer thickness is varied in the range from 1.7 nm to 3.05 nm. We use a novel combination of specular and diffuse intensity measurements to determine the interface roughness throughout the multilayer stack and do not rely on scanning probe measurements at the surface only. The combination of EUV and X-ray reflectivity measurements and near-normal incidence EUV diffuse scattering allows to reconstruct the Mo layer thicknesses and to determine the interface roughness power spectral density. The data analysis is conducted by applying a matrix method for the specular reflection and the distorted-wave Born approximation for diffuse scattering. We introduce the Markov-chain Monte Carlo method into the field in order to determine the respective confidence intervals for all reconstructed parameters. We unambiguously detect a threshold thickness for Mo in both sample sets where the specular reflectance goes through a local minimum correlated with a distinct increase in diffuse scatter. We attribute that to the known appearance of an amorphous-to-crystallization transition at a certain thickness threshold which is altered in our sample system by the polishing.

Accelerated ions and self-excited Alfvén waves at the Earth's bow shock

NASA Astrophysics Data System (ADS)

Berezhko, E. G.; Taneev, S. N.; Trattner, K. J.

2011-07-01

The diffuse energetic ion event and related Alfvén waves upstream of the Earth's bow shock, measured by AMPTE/IRM satellite on 29 September 1984, 06:42-07:22 UT, was studied using a self-consistent quasi-linear theory of ion diffusive shock acceleration and associated Alfvén wave generation. The wave energy density satisfies a wave kinetic equation, and the ion distribution function satisfies the diffusive transport equation. These coupled equations are solved numerically, and calculated ion and wave spectra are compared with observations. It is shown that calculated steady state ion and Alfvén wave spectra are established during the time period of about 1000 s. Alfvén waves excited by accelerated ions are confined within the frequency range (10-2 to 1) Hz, and their spectral peak with the wave amplitude δB ≈ B comparable to the interplanetary magnetic field value B corresponds to the frequency 2 × 10-2 Hz. The high-frequency part of the wave spectrum undergoes absorption by thermal protons. It is shown that the observed ion spectra and the associated Alfvén wave spectra are consistent with the theoretical prediction.

Spectrum of spin waves in cold polarized gases

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

Andreeva, T. L., E-mail: phdocandreeva@yandex.ru

2017-02-15

The spin dynamics of cold polarized gases are investigated using the Boltzmann equation. The dispersion relation for spin waves (transverse component of the magnetic moment) and the spin diffusion coefficient of the longitudinal component of the magnetic moment are calculated without using fitting parameters. The spin wave frequency and the diffusion coefficient for rubidium atoms are estimated numerically.

Many-body effects in the mobility and diffusivity of interstitial solute in a crystalline solid: The case of helium in BCC tungsten

NASA Astrophysics Data System (ADS)

Wen, Haohua; Semenov, A. A.; Woo, C. H.

2017-09-01

The many-body dynamics of a crystalline solid containing an interstitial solute atom (ISA) is usually interpreted within the one-particle approximation as a random walker hopping among trapping centers at periodic lattice sites. The corresponding mobility and diffusivity can be formulated based on the transition-state theory in the form of the Arrhenius law. Possible issues arising from the many-body nature of the dynamics may need to be understood and resolved both scientifically and technologically. Noting the congruence between the dynamics of the many-body and stochastic systems within the Mori-Zwanzig theory, we analyzed the dynamics of a model particle subjected to a saw-tooth potential in a noisy medium. The ISA mobility is found to be governed by two sources of dissipative friction: that which is produced by the scattering of lattice waves by the moving ISA (phonon wind), and that which is derived from the energy dissipation associated with overcoming the migration barrier screened by lattice waves (i.e., phonon screened). The many-body effect in both cases increases with temperature, so that the first component of the friction is important at high temperatures and the second component is important at low temperatures. A formulation built on this mechanistic structure of the dissipative friction requires the mobility and diffusivity to be expressed not only in terms of the migration enthalpy and entropy, but also of the phonon drag coefficient. As a test, the complex temperature dependence of the mobility and diffusivity of interstitial helium in BCC W obtained from molecular-dynamics simulation is very well reproduced.

An experimental investigation of compressible three-dimensional boundary layer flow in annular diffusers

NASA Technical Reports Server (NTRS)

Om, Deepak; Childs, Morris E.

1987-01-01

An experimental study is described in which detailed wall pressure measurements have been obtained for compressible three-dimensional unseparated boundary layer flow in annular diffusers with and without normal shock waves. Detailed mean flow-field data were also obtained for the diffuser flow without a shock wave. Two diffuser flows with shock waves were investigated. In one case, the normal shock existed over the complete annulus whereas in the second case, the shock existed over a part of the annulus. The data obtained can be used to validate computational codes for predicting such flow fields. The details of the flow field without the shock wave show flow reversal in the circumferential direction on both inner and outer surfaces. However, there is a lag in the flow reversal between the inner nad the outer surfaces. This is an interesting feature of this flow and should be a good test for the computational codes.

Diffusion in coastal and harbour zones, effects of Waves,Wind and Currents

NASA Astrophysics Data System (ADS)

Diez, M.; Redondo, J. M.

2009-04-01

As there are multiple processes at different scales that produce turbulent mixing in the ocean, thus giving a large variation of horizontal eddy diffusivities, we use a direct method to evaluate the influence of different ambient parameters such as wave height and wind on coastal dispersion. Measurements of the diffusivity are made by digital processing of images taken from from video recordings of the sea surface near the coast. The use of image analysis allows to estimate both spatial and temporal characteristics of wave fields, surface circulation and mixing in the surf zone, near Wave breakers and inside Harbours. The study of near-shore dispersion [1], with the added complexity of the interaction between wave fields, longshore currents, turbulence and beach morphology, needs detailed measurements of simple mixing processes to compare the respective influences of forcings at different scales. The measurements include simultaneous time series of waves, currents, wind velocities from the studied area. Cuantitative information from the video images is accomplished using the DigImage video processing system [3], and a frame grabber. The video may be controlled by the computer, allowing, remote control of the processing. Spectral analysis on the images has also used n order to estimate dominant wave periods as well as the dispersion relations of dominant instabilities. The measurements presented here consist mostly on the comarison of difussion coeficients measured by evaluating the spread of blobs of dye (milk) as well as by measuring the separation between different buoys released at the same time. We have used a techniques, developed by Bahia(1997), Diez(1998) and Bezerra(2000)[1-3] to study turbulent diffusion by means of digital processing of images taken from remote sensing and video recordings of the sea surface. The use of image analysis allows to measure variations of several decades in horizontal diffusivity values, the comparison of the diffusivities between different sites is not direct and a good understanding of the dominant mixing processes is needed. There is an increase of diffusivity with wave height but only for large Wave Reynolds numbers. Other important factors are wind speed and tidal currents. The horizontal diffusivity shows a marked anisotropy as a function of wave height and distance from the coast. The measurements were performed under a variety of weather conditions conditional sampling has been used to identify the different influences of the environmental agents on the actual effective horizontal diffusion[4]. [1] Bahia E. (1998) "Un estudio numerico experimental de la dispersion de contaminantes en aguas costeras, PhD Tesis UPC, Barcelona. [2] Bezerra M.O., (2000) "Diffusion de contaminantes en la costa. , PhD Tesis Uni. De Barcelona, Barcelona. [3] Diez M. (1998) "Estudio de la Hidrodinamica de la zona de rompientes mediante el analisis digital de imagenes. Master Thesis, UPC, Barcelona. [4] Artale V., Boffetta G., Celani A., Cencini M. and Vulpiani A., 1997, "Dispersion of passive tracers in closed basins: Beyond the diffusion coefficient", Physics of Fluids, vol 9, pp 3162-1997

Magnetic Field Line Random Walk in Arbitrarily Stretched Isotropic Turbulence

NASA Astrophysics Data System (ADS)

Wongpan, P.; Ruffolo, D.; Matthaeus, W. H.; Rowlands, G.

2006-12-01

Many types of space and laboratory plasmas involve turbulent fluctuations with an approximately uniform mean magnetic field B_0, and the field line random walk plays an important role in guiding particle motions. Much of the relevant literature concerns isotropic turbulence, and has mostly been perturbative, i.e., for small fluctuations, or based on numerical simulations for specific conditions. On the other hand, solar wind turbulence is apparently anisotropic, and has been modeled as a sum of idealized two-dimensional and one dimensional (slab) components, but with the deficiency of containing no oblique wave vectors. In the present work, we address the above issues with non-perturbative analytic calculations of diffusive field line random walks for unpolarized, arbitrarily stretched isotropic turbulence, including the limits of nearly one-dimensional (highly stretched) and nearly two-dimensional (highly squashed) turbulence. We develop implicit analytic formulae for the diffusion coefficients D_x and D_z, two coupled integral equations in which D_x and D_z appear inside 3-dimensional integrals over all k-space, are solved numerically with the aid of Mathematica routines for specific cases. We can vary the parameters B0 and β, the stretching along z for constant turbulent energy. Furthermore, we obtain analytic closed-form solutions in all extreme cases. We obtain 0.54 < D_z/D_x < 2, indicating an approximately isotropic random walk even for very anisotropic (unpolarized) turbulence, a surprising result. For a given β, the diffusion coefficient vs. B0 can be described by a Padé approximant. We find quasilinear behavior at high B0 and percolative behavior at low B_0. Partially supported by a Sritrangthong Scholarship from the Faculty of Science, Mahidol University; the Thailand Research Fund; NASA Grant NNG05GG83G; and Thailand's Commission for Higher Education.

Optical device for thermal diffusivity determination in liquids by reflection of a thermal wave

NASA Astrophysics Data System (ADS)

Sánchez-Pérez, C.; De León-Hernández, A.; García-Cadena, C.

2017-08-01

In this work, we present a device for determination of the thermal diffusivity using the oblique reflection of a thermal wave within a solid slab that is in contact with the medium to be characterized. By using the reflection near a critical angle under the assumption that thermal waves obey Snell's law of refraction with the square root of the thermal diffusivities, the unknown thermal diffusivity is obtained by simple formulae. Experimentally, the sensor response is measured using the photothermal beam deflection technique within a slab that results in a compact device with no contact of the laser probing beam with the sample. We describe the theoretical basis and provide experimental results to validate the proposed method. We determine the thermal diffusivity of tridistilled water and glycerin solutions with an error of less than 0.5%.

A new diffusion matrix for whistler mode chorus waves

NASA Astrophysics Data System (ADS)

Horne, Richard B.; Kersten, Tobias; Glauert, Sarah A.; Meredith, Nigel P.; Boscher, Daniel; Sicard-Piet, Angelica; Thorne, Richard M.; Li, Wen

2013-10-01

Global models of the Van Allen radiation belts usually include resonant wave-particle interactions as a diffusion process, but there is a large uncertainty over the diffusion rates. Here we present a new diffusion matrix for whistler mode chorus waves that can be used in such models. Data from seven satellites are used to construct 3536 power spectra for upper and lower band chorus for 1.5≤L∗≤10 MLT, magnetic latitude 0°≤|λm|≤60° and five levels of Kp. Five density models are also constructed from the data. Gaussian functions are fitted to the spectra and capture typically 90% of the wave power. The frequency maxima of the power spectra vary with L∗ and are typically lower than that used previously. Lower band chorus diffusion increases with geomagnetic activity and is largest between 21:00 and 12:00 MLT. Energy diffusion extends to a few megaelectron volts at large pitch angles >60° and at high energies exceeds pitch angle diffusion at the loss cone. Most electron diffusion occurs close to the geomagnetic equator (<12°). Pitch angle diffusion rates for lower band chorus increase with L∗ and are significant at L∗=8 even for low levels of geomagnetic activity, while upper band chorus is restricted to mainly L∗<6. The combined drift and bounce averaged diffusion rates for upper and lower band chorus extend from a few kiloelectron volts near the loss cone up to several megaelectron volts at large pitch angles indicating loss at low energies and net acceleration at high energies.

Wavenumber distribution in Hopf-wave instability: the reversible Selkov model of glycolytic oscillation.

PubMed

Dutt, Arun K

2005-09-22

We have investigated the short-wave instability due to Hopf bifurcation in a reaction-diffusion model of glycolytic oscillations. Very low values of the ratio d of the diffusion coefficient of the inhibitor (ATP) and that of the activator (ADP) do help to create short waves, whereas high values of the ratio d and the complexing reaction of the activator ADP reduces drastically the wave-instability domain, generating much longer wavelengths.

Analysis of pulse thermography using similarities between wave and diffusion propagation

NASA Astrophysics Data System (ADS)

Gershenson, M.

2017-05-01

Pulse thermography or thermal wave imaging are commonly used as nondestructive evaluation (NDE) method. While the technical aspect has evolve with time, theoretical interpretation is lagging. Interpretation is still using curved fitting on a log log scale. A new approach based directly on the governing differential equation is introduced. By using relationships between wave propagation and the diffusive propagation of thermal excitation, it is shown that one can transform from solutions in one type of propagation to the other. The method is based on the similarities between the Laplace transforms of the diffusion equation and the wave equation. For diffusive propagation we have the Laplace variable s to the first power, while for the wave propagation similar equations occur with s2. For discrete time the transformation between the domains is performed by multiplying the temperature data vector by a matrix. The transform is local. The performance of the techniques is tested on synthetic data. The application of common back projection techniques used in the processing of wave data is also demonstrated. The combined use of the transform and back projection makes it possible to improve both depth and lateral resolution of transient thermography.

Unmagnetized diffusion for azimuthally symmetric wave and particle distributions

NASA Technical Reports Server (NTRS)

Dusenbery, P. B.; Lyons, L. R.

1988-01-01

The quasi-linear diffusion of particles from resonant interactions with a spectrum of electrostatic waves is investigated theoretically, extending results obtained for no magnetic field and for strong magnetic fields to cases where the ambient magnetic field which organizes azimuthally symmetric wave and particle distributions does not have to be taken into consideration in evaluating the local interaction. The derivation of the governing equations is explained, and numerical results are presented in extensive graphs and characterized in detail. Slow-mode ion-acoustic waves are shown to be unstable under the plasma conditions studied, and the dependence of resonant-ion diffusion rates with pitch angle, speed, and the distribution of wave energy in wavenumber space is explored. The implications of the present findings for theoretical models of the earth bow shock and plasma-sheet boundary layer are indicated.

Experiment E89-044 of quasi-elastic diffusion 3He(e,e'p) at Jefferson Laboratory: Analyze cross sections of the two body breakup in parallel kinematics; Experience E89-044 de diffusion quasi-elastique 3he(e,e'p) au Jefferson Laboratory : analyse des sections efficaces de desintegration a deux corps en cinematique parallele (in French)

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

Penel-Nottaris, Emilie

2004-07-01

The Jefferson Lab Hall A experiment has measured the 3He(e,e'p) reaction cross sections. The separation of the longitudinal and transverse response functions for the two-body breakup reaction in parallel kinematics allows to study the bound proton electromagnetic properties in the 3He nucleus and the involved nuclear mechanisms beyond impulse approximation. Preliminary cross sections show some disagreement with theoretical predictions for the forward angles kinematics around 0 MeV/c missing momenta, and sensitivity to final state interactions and 3He wave functions for missing momenta of 300 MeV/c.

Linear and nonlinear susceptibilities from diffusion quantum Monte Carlo: application to periodic hydrogen chains.

PubMed

Umari, P; Marzari, Nicola

2009-09-07

We calculate the linear and nonlinear susceptibilities of periodic longitudinal chains of hydrogen dimers with different bond-length alternations using a diffusion quantum Monte Carlo approach. These quantities are derived from the changes in electronic polarization as a function of applied finite electric field--an approach we recently introduced and made possible by the use of a Berry-phase, many-body electric-enthalpy functional. Calculated susceptibilities and hypersusceptibilities are found to be in excellent agreement with the best estimates available from quantum chemistry--usually extrapolations to the infinite-chain limit of calculations for chains of finite length. It is found that while exchange effects dominate the proper description of the susceptibilities, second hypersusceptibilities are greatly affected by electronic correlations. We also assess how different approximations to the nodal surface of the many-body wave function affect the accuracy of the calculated susceptibilities.

Mirror instability and origin of morningside auroral structure

NASA Technical Reports Server (NTRS)

Chiu, Y. T.; Schulz, M.; Fennell, J. F.; Kishi, A. M.

1983-01-01

Auroral optical imagery shows marked differences between auroral features of the evening and morning sectors: the separation between diffuse and discrete auroras in the evening sector is not distinct in the morning sector, which is dominated by auroral patches and multiple banded structures aligned along some direction. Plasma distribution function signatures also show marked differences: downward electron beams and inverted-V signatures prefer the evening sector, while the electron spectra on the morning sector are similar to the diffuse aurora. A theory of morningside auroras consistent with these features was constructed. The theory is based on modulation of the growth rates of electron cyclotron waves by the mirror instability, which is in turn driven by inward-convected ions that have become anisotropic. This modulation produces alternating bands of enhanced and reduced electron precipitation which approximate the observed multiple auroral bands and patches of the morning sector.

There’s plenty of light at the bottom: statistics of photon penetration depth in random media

PubMed Central

Martelli, Fabrizio; Binzoni, Tiziano; Pifferi, Antonio; Spinelli, Lorenzo; Farina, Andrea; Torricelli, Alessandro

2016-01-01

We propose a comprehensive statistical approach describing the penetration depth of light in random media. The presented theory exploits the concept of probability density function f(z|ρ, t) for the maximum depth reached by the photons that are eventually re-emitted from the surface of the medium at distance ρ and time t. Analytical formulas for f, for the mean maximum depth 〈zmax〉 and for the mean average depth reached by the detected photons at the surface of a diffusive slab are derived within the framework of the diffusion approximation to the radiative transfer equation, both in the time domain and the continuous wave domain. Validation of the theory by means of comparisons with Monte Carlo simulations is also presented. The results are of interest for many research fields such as biomedical optics, advanced microscopy and disordered photonics. PMID:27256988

Method for using acoustic sounder categories to determine atmospheric stability

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

Schubert, J.F.

1979-01-01

Capabilities of the diffusion meteorologist have been expanded by the acoustic sounder, an economical tool for monitoring in real time the height of the mixed layer. The acoustic sounder continuously measures the rate of change in the height of the mixed layer which is an important parameter in calculating the transport and diffusion of radioactive and nonradioactive air pollutants. Continuous record of convective cells, gravity waves, inversions, and frontal systems permit analysis of the synoptic (analysis of stability in terms of simultaneous weather information) and complex (analysis of the stability of a single place by the relative frequencies of variousmore » stability types or groups of such types) stabilities of the local area. Sounder data obtained at the Savannah River Plant was compared on an hourly basis to data obtained at the WJBF-TV tower located approximately 20 km northwest of the acoustic sounder site.« less

CORSAIR Solar Energetic Particle Model

NASA Astrophysics Data System (ADS)

Sandroos, A.

2013-05-01

Acceleration of particles in coronal mass ejection (CME) driven shock waves is the most commonly accepted and best developed theory of the genesis of gradual solar energetic particle (SEP) events. The underlying acceleration mechanism is the diffusive shock acceleration (DSA). According to DSA, particles scatter from fluctuations present in the ambient magnetic field, which causes some particles to encounter the shock front repeatedly and to gain energy during each crossing. Currently STEREO and near-Earth spacecraft are providing valuable multi-point information on how SEP properties, such as composition and energy spectra, vary in longitude. Initial results have shown that longitude distributions of large CME-associated SEP events are much wider than reported in earlier studies. These findings have important consequences on SEP modeling. It is important to extend the present models into two or three spatial coordinates to properly take into account the effects of coronal and interplanetary (IP) magnetic geometry, and evolution of the CME and the associated shock, on the acceleration and transport of SEPs. We give a status update on CORSAIR project, which is an effort to develop a new self-consistent (total energy conserving) DSA acceleration model that is capable of modeling energetic particle acceleration and transport in IP space in two or three spatial dimensions. In the new model particles are propagated using guiding center approximation. Waves are modeled as (Lagrangian) wave packets propagating (anti)parallel to ambient magnetic field. Diffusion coefficients related to scattering from the waves are calculated using quasilinear theory. State of ambient plasma is obtained from an MHD simulation or by using idealized analytic models. CORSAIR is an extension to our earlier efforts to model the effects of magnetic geometry on SEP acceleration (Sandroos & Vainio, 2007,2009).

Non-ideal magnetohydrodynamics on a moving mesh

NASA Astrophysics Data System (ADS)

Marinacci, Federico; Vogelsberger, Mark; Kannan, Rahul; Mocz, Philip; Pakmor, Rüdiger; Springel, Volker

2018-05-01

In certain astrophysical systems, the commonly employed ideal magnetohydrodynamics (MHD) approximation breaks down. Here, we introduce novel explicit and implicit numerical schemes of ohmic resistivity terms in the moving-mesh code AREPO. We include these non-ideal terms for two MHD techniques: the Powell 8-wave formalism and a constrained transport scheme, which evolves the cell-centred magnetic vector potential. We test our implementation against problems of increasing complexity, such as one- and two-dimensional diffusion problems, and the evolution of progressive and stationary Alfvén waves. On these test problems, our implementation recovers the analytic solutions to second-order accuracy. As first applications, we investigate the tearing instability in magnetized plasmas and the gravitational collapse of a rotating magnetized gas cloud. In both systems, resistivity plays a key role. In the former case, it allows for the development of the tearing instability through reconnection of the magnetic field lines. In the latter, the adopted (constant) value of ohmic resistivity has an impact on both the gas distribution around the emerging protostar and the mass loading of magnetically driven outflows. Our new non-ideal MHD implementation opens up the possibility to study magneto-hydrodynamical systems on a moving mesh beyond the ideal MHD approximation.

Fluorescence and diffusive wave diffraction tomographic probes in turbid media

NASA Astrophysics Data System (ADS)

Li, Xingde

1998-10-01

Light transport over long distances in tissue-like highly scattering media is well approximated as a diffusive process. Diffusing photons can be used to detect, localize and characterize non-invasively optical inhomogeneities such as tumors and hematomas embedded in thick biological tissue. Most of the contrast relies on the endogenous optical property differences between the inhomogeneities and the surrounding media. Recently exogenous fluorescent contrast agents have been considered as a means to enhance the sensitivity and specificity for tumor detection. In the first part of the thesis (Chapter 2 and 3), a theoretical basis is established for modeling the transport, of fluorescent photons in highly scattering media. Fluorescent Diffuse Photon Density Waves (FDPDW) are used to describe the transport of fluorescent photons. A detailed analysis based upon a practical signal-to-noise model was used to access the utility of the fluorescent method. The analysis reveals that a small heterogeneity, embedded in deep tissue-like turbid media with biologically relevant parameters, and with a practically achievable 5-fold fluorophore concentration contrast, can be detected and localized when its radius is greater than 0.2 cm, and can be characterized when its radius is greater than 0.7 cm. In vivo and preliminary clinical studies demonstrate the feasibility of using FDPDW's for tumor diagnosis. Optical imaging with diffusing photons is challenging. Many of the imaging algorithms developed so far are either fundamentally incorrect as in the case of back- projection approach, or require a huge amount of computational resources and CPU time. In the second part of the thesis (Chapter 4), a fast, K-space diffraction tomographic imaging algorithm based upon spatial angular spectrum analysis is derived and applied. Absolute optical properties of thin inhomogeneities and relative optical properties of spatially extended inhomogeneities are reconstructed within a sub-second time scale. Phantom experiments have demonstrated the power of the K-space algorithm and preliminary clinical investigations have exhibited its potential for real time optical diagnosis and imaging of breast cancer.

Relationship of Topside Ionospheric Ion Outflows to Auroral Forms and Precipitations, Plasma Waves, and Convection Observed by POLAR

NASA Technical Reports Server (NTRS)

Hirahara, M.; Horwitz, J. L.; Moore, T. E.; Germany, G. A.; Spann, J. F.; Peterson, W. K.; Shelley, E. G.; Chandler, M. O.; Giles, B. L.; Craven, P. D.;

A technique to measure the thermal diffusivity of high Tc superconductors

NASA Technical Reports Server (NTRS)

Powers, Charles E.

1991-01-01

High T(sub c) superconducting electrical current leads and ground straps will be used in cryogenic coolers in future NASA Goddard Space Flight Center missions. These superconducting samples are long, thin leads with a typical diameter of two millimeters. A longitudinal method is developed to measure the thermal diffusivity of candidate materials for this application. This technique uses a peltier junction to supply an oscillatory heat wave into one end of a sample and will use low mass thermocouples to follow the heat wave along the sample. The thermal diffusivity is calculated using both the exponential decay of the heat wave and the phase shift to the wave. Measurements are performed in a cryostat between 10 K and room temperature.

Diffuse Optical Tomography for Brain Imaging: Continuous Wave Instrumentation and Linear Analysis Methods

NASA Astrophysics Data System (ADS)

Giacometti, Paolo; Diamond, Solomon G.

Diffuse optical tomography (DOT) is a functional brain imaging technique that measures cerebral blood oxygenation and blood volume changes. This technique is particularly useful in human neuroimaging measurements because of the coupling between neural and hemodynamic activity in the brain. DOT is a multichannel imaging extension of near-infrared spectroscopy (NIRS). NIRS uses laser sources and light detectors on the scalp to obtain noninvasive hemodynamic measurements from spectroscopic analysis of the remitted light. This review explains how NIRS data analysis is performed using a combination of the modified Beer-Lambert law (MBLL) and the diffusion approximation to the radiative transport equation (RTE). Laser diodes, photodiode detectors, and optical terminals that contact the scalp are the main components in most NIRS systems. Placing multiple sources and detectors over the surface of the scalp allows for tomographic reconstructions that extend the individual measurements of NIRS into DOT. Mathematically arranging the DOT measurements into a linear system of equations that can be inverted provides a way to obtain tomographic reconstructions of hemodynamics in the brain.

Toward real-time diffuse optical tomography: accelerating light propagation modeling employing parallel computing on GPU and CPU.

PubMed

Doulgerakis, Matthaios; Eggebrecht, Adam; Wojtkiewicz, Stanislaw; Culver, Joseph; Dehghani, Hamid

2017-12-01

Parameter recovery in diffuse optical tomography is a computationally expensive algorithm, especially when used for large and complex volumes, as in the case of human brain functional imaging. The modeling of light propagation, also known as the forward problem, is the computational bottleneck of the recovery algorithm, whereby the lack of a real-time solution is impeding practical and clinical applications. The objective of this work is the acceleration of the forward model, within a diffusion approximation-based finite-element modeling framework, employing parallelization to expedite the calculation of light propagation in realistic adult head models. The proposed methodology is applicable for modeling both continuous wave and frequency-domain systems with the results demonstrating a 10-fold speed increase when GPU architectures are available, while maintaining high accuracy. It is shown that, for a very high-resolution finite-element model of the adult human head with ∼600,000 nodes, consisting of heterogeneous layers, light propagation can be calculated at ∼0.25  s/excitation source. (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).

Diffusive wave in the low Mach limit for non-viscous and heat-conductive gas

NASA Astrophysics Data System (ADS)

Liu, Yechi

2018-06-01

The low Mach number limit for one-dimensional non-isentropic compressible Navier-Stokes system without viscosity is investigated, where the density and temperature have different asymptotic states at far fields. It is proved that the solution of the system converges to a nonlinear diffusion wave globally in time as Mach number goes to zero. It is remarked that the velocity of diffusion wave is proportional with the variation of temperature. Furthermore, it is shown that the solution of compressible Navier-Stokes system also has the same phenomenon when Mach number is suitably small.

Diffusing-wave polarimetry for tissue diagnostics

NASA Astrophysics Data System (ADS)

Macdonald, Callum; Doronin, Alexander; Peña, Adrian F.; Eccles, Michael; Meglinski, Igor

2014-03-01

We exploit the directional awareness of circularly and/or elliptically polarized light propagating within media which exhibit high numbers of scattering events. By tracking the Stokes vector of the detected light on the Poincaŕe sphere, we demonstrate its applicability for characterization of anisotropy of scattering. A phenomenological model is shown to have an excellent agreement with the experimental data and with the results obtained by the polarization tracking Monte Carlo model, developed in house. By analogy to diffusing-wave spectroscopy we call this approach diffusing-wave polarimetry, and illustrate its utility in probing cancerous and non-cancerous tissue samplesin vitro for diagnostic purposes.

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.

PubMed

Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q

2013-03-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION

PubMed Central

Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.

2013-01-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian. PMID:23772179

Forced sound transmission through a finite-sized single leaf panel subject to a point source excitation.

PubMed

Wang, Chong

2018-03-01

In the case of a point source in front of a panel, the wavefront of the incident wave is spherical. This paper discusses spherical sound waves transmitting through a finite sized panel. The forced sound transmission performance that predominates in the frequency range below the coincidence frequency is the focus. Given the point source located along the centerline of the panel, forced sound transmission coefficient is derived through introducing the sound radiation impedance for spherical incident waves. It is found that in addition to the panel mass, forced sound transmission loss also depends on the distance from the source to the panel as determined by the radiation impedance. Unlike the case of plane incident waves, sound transmission performance of a finite sized panel does not necessarily converge to that of an infinite panel, especially when the source is away from the panel. For practical applications, the normal incidence sound transmission loss expression of plane incident waves can be used if the distance between the source and panel d and the panel surface area S satisfy d/S>0.5. When d/S ≈0.1, the diffuse field sound transmission loss expression may be a good approximation. An empirical expression for d/S=0  is also given.

Breathing spiral waves in the chlorine dioxide-iodine-malonic acid reaction-diffusion system.

PubMed

Berenstein, Igal; Muñuzuri, Alberto P; Yang, Lingfa; Dolnik, Milos; Zhabotinsky, Anatol M; Epstein, Irving R

2008-08-01

Breathing spiral waves are observed in the oscillatory chlorine dioxide-iodine-malonic acid reaction-diffusion system. The breathing develops within established patterns of multiple spiral waves after the concentration of polyvinyl alcohol in the feeding chamber of a continuously fed, unstirred reactor is increased. The breathing period is determined by the period of bulk oscillations in the feeding chamber. Similar behavior is obtained in the Lengyel-Epstein model of this system, where small amplitude parametric forcing of spiral waves near the spiral wave frequency leads to the formation of breathing spiral waves in which the period of breathing is equal to the period of forcing.

A hybrid continuous-discrete method for stochastic reaction-diffusion processes.

PubMed

Lo, Wing-Cheong; Zheng, Likun; Nie, Qing

2016-09-01

Stochastic fluctuations in reaction-diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method.

Quantified Energy Dissipation Rates in the Terrestrial Bow Shock. 2; Waves and Dissipation

NASA Technical Reports Server (NTRS)

Wilson, L. B., III; Sibeck, D. G.; Breneman, A. W.; Le Contel, O.; Cully, C.; Turner, D. L.; Angelopoulos, V.; Malaspina, D. M.

2014-01-01

We present the first quantified measure of the energy dissipation rates, due to wave-particle interactions, in the transition region of the Earth's collision-less bow shock using data from the Time History of Events and Macro-Scale Interactions during Sub-Storms spacecraft. Our results show that wave-particle interactions can regulate the global structure and dominate the energy dissipation of collision-less shocks. In every bow shock crossing examined, we observed both low-frequency (less than 10 hertz) and high-frequency (approximately or greater than10 hertz) electromagnetic waves throughout the entire transition region and into the magnetosheath. The low-frequency waves were consistent with magnetosonic-whistler waves. The high-frequency waves were combinations of ion-acoustic waves, electron cyclotron drift instability driven waves, electrostatic solitary waves, and whistler mode waves. The high-frequency waves had the following: (1) peak amplitudes exceeding delta B approximately equal to 10 nanoteslas and delta E approximately equal to 300 millivolts per meter, though more typical values were delta B approximately equal to 0.1-1.0 nanoteslas and delta E approximately equal to 10-50 millivolts per meter (2) Poynting fluxes in excess of 2000 microWm(sup -2) (micro-waves per square meter) (typical values were approximately 1-10 microWm(sup -2) (micro-waves per square meter); (3) resistivities greater than 9000 omega meters; and (4) associated energy dissipation rates greater than 10 microWm(sup -3) (micro-waves per cubic meter). The dissipation rates due to wave-particle interactions exceeded rates necessary to explain the increase in entropy across the shock ramps for approximately 90 percent of the wave burst durations. For approximately 22 percent of these times, the wave-particle interactions needed to only be less than or equal to 0.1 percent efficient to balance the nonlinear wave steepening that produced the shock waves. These results show that wave-particle interactions have the capacity to regulate the global structure and dominate the energy dissipation of collision-less shocks.

Existence, Uniqueness and Asymptotic Stability of Time Periodic Traveling Waves for a Periodic Lotka-Volterra Competition System with Diffusion

PubMed Central

Zhao, Guangyu; Ruan, Shigui

2011-01-01

We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a periodic diffusive Lotka-Volterra competition system. Under certain conditions, we prove that there exists a maximal wave speed c* such that for each wave speed c ≤ c*, there is a time periodic traveling wave connecting two semi-trivial periodic solutions of the corresponding kinetic system. It is shown that such a traveling wave is unique modulo translation and is monotone with respect to its co-moving frame coordinate. We also show that the traveling wave solutions with wave speed c < c* are asymptotically stable in certain sense. In addition, we establish the nonexistence of time periodic traveling waves for nonzero speed c > c*. PMID:21572575

Inviscid spatial stability of a compressible mixing layer. Part 2: The flame sheet model

NASA Technical Reports Server (NTRS)

Jackson, T. L.; Grosch, C. E.

1989-01-01

The results of an inviscid spatial calculation for a compressible reacting mixing layer are reported. The limit of infinitive activation energy is taken and the diffusion flame is approximated by a flame sheet. Results are reported for the phase speeds of the neutral waves and maximum growth rates of the unstable waves as a function of the parameters of the problem: the ratio of the temperature of the stationary stream to that of the moving stream, the Mach number of the moving streams, the heat release per unit mass fraction of the reactant, the equivalence ratio of the reaction, and the frequency of the disturbance. These results are compared to the phase speeds and growth rates of the corresponding nonreacting mixing layer. We show that the addition of combustion has important, and complex effects on the flow stability.

Classical electromagnetic fields from quantum sources in heavy-ion collisions

NASA Astrophysics Data System (ADS)

Holliday, Robert; McCarty, Ryan; Peroutka, Balthazar; Tuchin, Kirill

2017-01-01

Electromagnetic fields are generated in high energy nuclear collisions by spectator valence protons. These fields are traditionally computed by integrating the Maxwell equations with point sources. One might expect that such an approach is valid at distances much larger than the proton size and thus such a classical approach should work well for almost the entire interaction region in the case of heavy nuclei. We argue that, in fact, the contrary is true: due to the quantum diffusion of the proton wave function, the classical approximation breaks down at distances of the order of the system size. We compute the electromagnetic field created by a charged particle described initially as a Gaussian wave packet of width 1 fm and evolving in vacuum according to the Klein-Gordon equation. We completely neglect the medium effects. We show that the dynamics, magnitude and even sign of the electromagnetic field created by classical and quantum sources are different.

Turbulence in the presence of internal waves in the bottom boundary layer of the California inner shelf

NASA Astrophysics Data System (ADS)

Allen, Rachel M.; Simeonov, Julian A.; Calantoni, Joseph; Stacey, Mark T.; Variano, Evan A.

2018-05-01

Turbulence measurements were collected in the bottom boundary layer of the California inner shelf near Point Sal, CA, for 2 months during summer 2015. The water column at Point Sal is stratified by temperature, and internal bores propagate through the region regularly. We collected velocity, temperature, and turbulence data on the inner shelf at a 30-m deep site. We estimated the turbulent shear production ( P), turbulent dissipation rate ( ɛ), and vertical diffusive transport ( T), to investigate the near-bed local turbulent kinetic energy (TKE) budget. We observed that the local TKE budget showed an approximate balance ( P ≈ ɛ) during the observational period, and that buoyancy generally did not affect the TKE balance. On a finer resolution timescale, we explored the balance between dissipation and models for production and observed that internal waves did not affect the balance in TKE at this depth.

Application of cosmic-ray shock theories to the Cygnus Loop - An alternative model

NASA Technical Reports Server (NTRS)

Boulares, Ahmed; Cox, Donald P.

1988-01-01

Steady state cosmic-ray shock models are investigated here in the light of observations of the Cygnus Loop supernova remnant. The predicted downstream temperature is derived for each model. The Cygnus Loop data and the application of the models to them, including wave dissipation, are presented. Heating rate and ionization fraction structures are provided along with an estimate of the cosmic-ray diffusion coefficient. It is found that the model of Voelk, Drury, and McKenzie (1984), in which the plasma waves are generated by the streaming instability of the cosmic rays and are dissipated into the gas, can be made consistent with some observed characteristics of the Cygnus Loop shocks. The model is used to deduce upstream densities and shock velocities and, compared to the usual pure gas shock interpretation, it is found that lower densities and approximately three times higher velocities are required.

ULF Waves and Diffusive Radial Transport of Charged Particles

NASA Astrophysics Data System (ADS)

Ali, Ashar Fawad

The Van Allen radiation belts contain highly energetic particles which interact with a variety of plasma and magnetohydrodynamic (MHD) waves. Waves in the ultra low-frequency (ULF) range play an important role in the loss and acceleration of energetic particles. Considering the geometry of the geomagnetic field, charged particles trapped in the inner magnetosphere undergo three distinct types of periodic motions; an adiabatic invariant is associated with each type of motion. The evolution of the phase space density of charged particles in the magnetosphere in the coordinate space of the three adiabatic invariants is modeled by the Fokker-Planck equation. If we assume that the first two adiabatic invariants are conserved while the third invariant is violated, then the general Fokker-Planck equation reduces to a radial diffusion equation with the radial diffusion coefficient quantifying the rate of the radial diffusion of charged particles, including contributions from perturbations in both the magnetic and the electric fields. This thesis investigates two unanswered questions about ULF wave-driven radial transport of charged particles. First, how important are the ULF fluctuations in the magnetic field compared with the ULF fluctuations in the electric field in driving the radial diffusion of charged particles in the Earth's inner magnetosphere? It has generally been accepted that magnetic field perturbations dominate over electric field perturbations, but several recently published studies suggest otherwise. Second, what is the distribution of ULF wave power in azimuth, and how does ULF wave power depend upon radial distance and the level of geomagnetic activity? Analytic treatments of the diffusion coefficients generally assume uniform distribution of power in azimuth, but in situ measurements suggest that this may not be the case. We used the magnetic field data from the Combined Release and Radiation Effects Satellite (CRRES) and the electric and the magnetic field data from the Radiation Belt Storm Probes (RBSP) to compute the electric and the magnetic component of the radial diffusion coefficient using the Fei et al. [2006] formulation. We conclude that contrary to prior notions, the electric component is dominant in driving radial diffusion of charged particles in the Earth's inner magnetosphere instead of the magnetic component. The electric component can be up to two orders of magnitude larger than the magnetic component. In addition, we see that ULF wave power in both the electric and the magnetic fields has a clear dependence on Kp with wave power decreasing as radial distance decreases. For both fields, the noon sectors generally contain more ULF wave power than the dawn, dusk, and the midnight magnetic local time (MLT) sectors. There is no significant difference between ULF wave power in the dawn, dusk, and the midnight sectors.

A NEW MODEL FOR MIXING BY DOUBLE-DIFFUSIVE CONVECTION (SEMI-CONVECTION). III. THERMAL AND COMPOSITIONAL TRANSPORT THROUGH NON-LAYERED ODDC

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

Moll, Ryan; Garaud, Pascale; Stellmach, Stephan, E-mail: rmoll@soe.ucsc.edu

2016-05-20

Oscillatory double-diffusive convection (ODDC; also known as semi-convection) refers to a type of double-diffusive instability that occurs in regions of planetary and stellar interiors that have a destabilizing thermal stratification and a stabilizing mean molecular weight stratification. In this series of papers, we use an extensive suite of three-dimensional (3D) numerical simulations to quantify the transport of heat and chemical species by ODDC. Rosenblum et al. first showed that ODDC can either spontaneously form layers that significantly enhance the transport of heat and chemical species compared to microscopic transport or remain in a state dominated by large-scale gravity waves, inmore » which there is a more modest enhancement of the turbulent transport rates. Subsequent studies in this series focused on identifying under what conditions layers form and quantifying transport through layered systems. Here we proceed to characterize transport through systems that are unstable to ODDC, but do not undergo spontaneous layer formation. We measure the thermal and compositional fluxes in non-layered ODDC from both two-dimensional (2D) and 3D numerical simulations, and show that 3D simulations are well approximated by similar simulations in a 2D domain. We find that the turbulent mixing rate in this regime is weak and can, to a first-level approximation, be neglected. We conclude by summarizing the findings of papers I through III into a single prescription for transport systems unstable to ODDC.« less

Nonlinear waves in reaction-diffusion systems: The effect of transport memory

NASA Astrophysics Data System (ADS)

Manne, K. K.; Hurd, A. J.; Kenkre, V. M.

2000-04-01

Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity.

Ultra-low-frequency wave-driven diffusion of radiation belt relativistic electrons

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

Su, Zhenpeng; Zhu, Hui; Xiao, Fuliang

The Van Allen radiation belts are typically two zones of energetic particles encircling the Earth separated by the slot region. How the outer radiation belt electrons are accelerated to relativistic energies remains an unanswered question. Recent studies have presented compelling evidence for the local acceleration by very-low-frequency (VLF) chorus waves. However, there has been a competing theory to the local acceleration, radial diffusion by ultra-low-frequency (ULF) waves, whose importance has not yet been determined definitively. Here we report a unique radiation belt event with intense ULF waves but no detectable VLF chorus waves. So, our results demonstrate that the ULFmore » waves moved the inner edge of the outer radiation belt earthward 0.3 Earth radii and enhanced the relativistic electron fluxes by up to one order of magnitude near the slot region within about 10 h, providing strong evidence for the radial diffusion of radiation belt relativistic electrons.« less

Ultra-low-frequency wave-driven diffusion of radiation belt relativistic electrons

DOE PAGES

Su, Zhenpeng; Zhu, Hui; Xiao, Fuliang; ...

2015-12-22

The Van Allen radiation belts are typically two zones of energetic particles encircling the Earth separated by the slot region. How the outer radiation belt electrons are accelerated to relativistic energies remains an unanswered question. Recent studies have presented compelling evidence for the local acceleration by very-low-frequency (VLF) chorus waves. However, there has been a competing theory to the local acceleration, radial diffusion by ultra-low-frequency (ULF) waves, whose importance has not yet been determined definitively. Here we report a unique radiation belt event with intense ULF waves but no detectable VLF chorus waves. So, our results demonstrate that the ULFmore » waves moved the inner edge of the outer radiation belt earthward 0.3 Earth radii and enhanced the relativistic electron fluxes by up to one order of magnitude near the slot region within about 10 h, providing strong evidence for the radial diffusion of radiation belt relativistic electrons.« less

Resonant scattering of energetic electrons in the outer radiation belt by HAARP-induced ELF/VLF waves

NASA Astrophysics Data System (ADS)

Chang, Shanshan; Zhu, Zhengping; Ni, Binbin; Cao, Xing; Luo, Weihua

2016-10-01

Several extremely low-frequency (ELF)/very low-frequency (VLF) wave generation experiments have been performed successfully at High-Frequency Active Auroral Research Program (HAARP) heating facility and the artificial ELF/VLF signals can leak into the outer radiation belt and contribute to resonant interactions with energetic electrons. Based on the artificial wave properties revealed by many of in situ observations, we implement test particle simulations to evaluate the effects of energetic electron resonant scattering driven by the HAARP-induced ELF/VLF waves. The results indicate that for both single-frequency/monotonic wave and multi-frequency/broadband waves, the behavior of each electron is stochastic while the averaged diffusion effect exhibits temporal linearity in the wave-particle interaction process. The computed local diffusion coefficients show that, the local pitch-angle scattering due to HARRP-induced single-frequency ELF/VLF whistlers with an amplitude of ∼10 pT can be intense near the loss cone with a rate of ∼10-2 rad2 s-1, suggesting the feasibility of HAARP-induced ELF/VLF waves for removal of outer radiation belt energetic electrons. In contrast, the energy diffusion of energetic electrons is relatively weak, which confirms that pitch-angle scattering by artificial ELF/VLF waves can dominantly lead to the precipitation of energetic electrons. Moreover, diffusion rates of the discrete, broadband waves, with the same amplitude of each discrete frequency as the monotonic waves, can be much larger, which suggests that it is feasible to trigger a reasonable broadband wave instead of the monotonic wave to achieve better performance of controlled precipitation of energetic electrons. Moreover, our test particle scattering simulation show good agreement with the predictions of the quasi-linear theory, confirming that both methods are applied to evaluate the effects of resonant interactions between radiation belt electrons and artificially generated discrete ELF/VLF waves.

Focusing of light energy inside a scattering medium by controlling the time-gated multiple light scattering

NASA Astrophysics Data System (ADS)

Jeong, Seungwon; Lee, Ye-Ryoung; Choi, Wonjun; Kang, Sungsam; Hong, Jin Hee; Park, Jin-Sung; Lim, Yong-Sik; Park, Hong-Gyu; Choi, Wonshik

2018-05-01

The efficient delivery of light energy is a prerequisite for the non-invasive imaging and stimulating of target objects embedded deep within a scattering medium. However, the injected waves experience random diffusion by multiple light scattering, and only a small fraction reaches the target object. Here, we present a method to counteract wave diffusion and to focus multiple-scattered waves at the deeply embedded target. To realize this, we experimentally inject light into the reflection eigenchannels of a specific flight time to preferably enhance the intensity of those multiple-scattered waves that have interacted with the target object. For targets that are too deep to be visible by optical imaging, we demonstrate a more than tenfold enhancement in light energy delivery in comparison with ordinary wave diffusion cases. This work will lay a foundation to enhance the working depth of imaging, sensing and light stimulation.

Azimuthal ULF Structure and Radial Transport of Charged Particles

NASA Astrophysics Data System (ADS)

Ali, A.; Elkington, S. R.

2015-12-01

The Van Allen radiation belts contain highly energetic particles which interact with a variety of plasma and MHD waves. Waves with frequencies in the ULF range are understood to play an important role in loss and acceleration of energetic particles. There is still much to be understood about the interaction between charged particles and ULF waves in the inner magnetosphere and how they influence particle diffusion. We investigate how ULF wave power distribution in azimuth affects radial diffusion of charged particles. Analytic treatments of the diffusion coefficients generally assume uniform distribution of power in azimuth but in situ measurements suggest otherwise. The power profiles obtained from in situ measurements will be used to conduct particle simulations to see how well do the simulated diffusion coefficients agree with diffusion coefficients estimated directly from in situ measurements. We also look at the ULF wave power distribution across different modes. In order to use in situ point measurements from spacecraft, it is typically assumed that all of the wave power exists in m=1 mode. How valid is this assumption? Do higher modes contain a major fraction of the total power? If yes, then under what conditions? One strategy is to use the obtained realistic azimuthal power profiles from in situ measurements (such as from the Van Allen Probes) to drive simulations and see how the power distributions across modes larger than one depends on parameters such as the level of geomagnetic activity.

Simulations of the stratocumulus-topped boundary layer with a third-order closure model

NASA Technical Reports Server (NTRS)

Moeng, C. H.; Randall, D. A.

1984-01-01

A third order closure model is proposed by Andre et al. (1982), in which the time rate of change terms, the relaxation and rapid effects for the pressure related terms, and the clipping approximation are included along with the quasi-normal closure, to study turbulence in a cloudy layer which is cooled radiatively from above. A spurious oscillation which is strongest near the inversion occurs. An analysis of the problem shows that the oscillation arises from the mean gradient and buoyancy terms of the triple moment equations; these terms are largest near the cloud top. The oscillation is physical, rather than computational. In nature the oscillation is effectively damped, by a mechanism which apparently is not included in our model. In the stably stratified layer just above the mixed layer top, turbulence can excite gravity waves, whose energy is radiated away. Because the closure assumption for the pressure terms does not take into account the transport of wave energy, the model generates spurious oscillations. Damping of the oscillations is possible by introducing diffusion terms into the triple moment equations. With a large enough choice for the diffusion coefficient, the oscillation is effectively eliminated. The results are quite sensitive to the ad hoc eddy coefficient.

Radial Diffusion Coefficients Using E and B Field Data from the Van Allen Probes: Comparison with the CRRES Study

NASA Astrophysics Data System (ADS)

Ali, A.; Elkington, S. R.; Malaspina, D.

2014-12-01

The Van Allen radiation belts contain highly energetic particles which interact with a variety of plasma and MHD waves. Waves with frequencies in the ULF range are understood to play an important role in loss and acceleration of energetic particles. We are investigating the contributions from perturbations in both the magnetic and the electric fields in driving radial diffusion of charged particles and wish to probe two unanswered questions about ULF wave driven radial transport. First, how important are the fluctuations in the magnetic field compared with the fluctuations in the electric field in driving radial diffusion? Second, how does ULF wave power distribution in azimuth affect radial diffusion? Analytic treatments of the diffusion coefficients generally assume uniform distribution of power in azimuth but in situ measurements suggest otherwise. We present results from a study using the electric and magnetic field measurements from the Van Allen Probes to estimate the radial diffusion coefficients as a function of L and Kp. During the lifetime of the RBSP mission to date, there has been a dearth of solar activity. This compels us to consider Kp as the only time and activity dependent parameter instead of solar wind velocity and pressure.

Studies of the phase gradient at the boundary of the phase diffusion equation, motivated by peculiar wave patterns of rhythmic contraction in the amoeboid movement of Physarum polycephalum

NASA Astrophysics Data System (ADS)

Iima, Makoto; Kori, Hiroshi; Nakagaki, Toshiyuki

2017-04-01

The boundary of a cell is the interface with its surroundings and plays a key role in controlling the cell movement adaptations to different environments. We propose a study of the boundary effects on the patterns and waves of the rhythmic contractions in plasmodia of Physarum polycephalum, a tractable model organism of the amoeboid type. Boundary effects are defined as the effects of both the boundary conditions and the boundary shape. The rhythmicity of contraction can be modulated by local stimulation of temperature, light and chemicals, and by local deformation of cell shape via mechanosensitive ion channels as well. First, we examined the effects of boundary cell shapes in the case of a special shape resembling a tadpole, while requiring that the natural frequency in the proximity of the boundary is slightly higher and uniform. The simulation model reproduced the approximate propagated wave, from the tail to the head, while the inward waves were observed only near the periphery of the head section of the tadpole-shape. A key finding was that the frequency of the rhythmic contractions depended on the local shape of cell boundary. This implies that the boundary conditions of the phase were not always homogeneous. To understand the dependency, we reduced the two-dimensional model into a one-dimensional continuum model with Neumann boundary conditions. Here, the boundary conditions reflect the frequency distribution at the boundary. We described the analytic solutions and calculated the relationship between the boundary conditions and the wave propagation for a one-dimensional model of the continuous oscillatory field and a discrete coupled oscillator system. The results obtained may not be limited to cell movement of Physarum, but may be applicable to the other physical systems since the analysis used a generic phase diffusion equation.

Phase transition of traveling waves in bacterial colony pattern

NASA Astrophysics Data System (ADS)

Wakano, Joe Yuichiro; Komoto, Atsushi; Yamaguchi, Yukio

2004-05-01

Depending on the growth condition, bacterial colonies can exhibit different morphologies. Many previous studies have used reaction diffusion equations to reproduce spatial patterns. They have revealed that nonlinear reaction term can produce diverse patterns as well as nonlinear diffusion coefficient. Typical reaction term consists of nutrient consumption, bacterial reproduction, and sporulation. Among them, the functional form of sporulation rate has not been biologically investigated. Here we report experimentally measured sporulation rate. Then, based on the result, a reaction diffusion model is proposed. One-dimensional simulation showed the existence of traveling wave solution. We study the wave form as a function of the initial nutrient concentration and find two distinct types of solution. Moreover, transition between them is very sharp, which is analogous to phase transition. The velocity of traveling wave also shows sharp transition in nonlinear diffusion model, which is consistent with the previous experimental result. The phenomenon can be explained by separatrix in reaction term dynamics. Results of two-dimensional simulation are also shown and discussed.

Broadband diffuse terahertz wave scattering by flexible metasurface with randomized phase distribution

PubMed Central

Zhang, Yin; Liang, Lanju; Yang, Jing; Feng, Yijun; Zhu, Bo; Zhao, Junming; Jiang, Tian; Jin, Biaobing; Liu, Weiwei

2016-01-01

Suppressing specular electromagnetic wave reflection or backward radar cross section is important and of broad interests in practical electromagnetic engineering. Here, we present a scheme to achieve broadband backward scattering reduction through diffuse terahertz wave reflection by a flexible metasurface. The diffuse scattering of terahertz wave is caused by the randomized reflection phase distribution on the metasurface, which consists of meta-particles of differently sized metallic patches arranged on top of a grounded polyimide substrate simply through a certain computer generated pseudorandom sequence. Both numerical simulations and experimental results demonstrate the ultralow specular reflection over a broad frequency band and wide angle of incidence due to the re-distribution of the incident energy into various directions. The diffuse scattering property is also polarization insensitive and can be well preserved when the flexible metasurface is conformably wrapped on a curved reflective object. The proposed design opens up a new route for specular reflection suppression, and may be applicable in stealth and other technology in the terahertz spectrum. PMID:27225031

Broadband diffuse terahertz wave scattering by flexible metasurface with randomized phase distribution.

PubMed

Zhang, Yin; Liang, Lanju; Yang, Jing; Feng, Yijun; Zhu, Bo; Zhao, Junming; Jiang, Tian; Jin, Biaobing; Liu, Weiwei

2016-05-26

Suppressing specular electromagnetic wave reflection or backward radar cross section is important and of broad interests in practical electromagnetic engineering. Here, we present a scheme to achieve broadband backward scattering reduction through diffuse terahertz wave reflection by a flexible metasurface. The diffuse scattering of terahertz wave is caused by the randomized reflection phase distribution on the metasurface, which consists of meta-particles of differently sized metallic patches arranged on top of a grounded polyimide substrate simply through a certain computer generated pseudorandom sequence. Both numerical simulations and experimental results demonstrate the ultralow specular reflection over a broad frequency band and wide angle of incidence due to the re-distribution of the incident energy into various directions. The diffuse scattering property is also polarization insensitive and can be well preserved when the flexible metasurface is conformably wrapped on a curved reflective object. The proposed design opens up a new route for specular reflection suppression, and may be applicable in stealth and other technology in the terahertz spectrum.

Application of advection-diffusion routing model to flood wave propagation: A case study on Big Piney River, Missouri USA

Treesearch

Yang Yang; Theodore A. Endreny; David J. Nowak

2016-01-01

Flood wave propagation modeling is of critical importance to advancing water resources management and protecting human life and property. In this study, we investigated how the advection-diffusion routing model performed in flood wave propagation on a 16 km long downstream section of the Big Piney River, MO. Model performance was based on gaging station data at the...

Investigation of the validity of quasilinear theory for electron Landau damping in a tokamak using a broad-band wave effect

DOE PAGES

Lee, Jungpyo; Bonoli, Paul; Wright, John

2011-01-01

The quasilinear diffusion coefficient assuming a constant magnetic field along the electron orbit is widely used to describe electron Landau damping of waves in a tokamak where the magnitude of the magnetic field varies on a flux surface. To understand the impact of violating the constant magnetic field assumption, we introduce the effect of a broad-bandwidth wave spectrum which has been used in the past to validate quasilinear theory for the fast decorrelation process between resonances. By the reevaluation of the diffusion coefficient through the level of the phase integral for the tokamak geometry with the broad-band wave effect included,more » we identify the three acceptable errors for the use of the quasilinear diffusion coefficient.« less

Dynamics of scroll waves with time-delay propagation in excitable media

NASA Astrophysics Data System (ADS)

Chen, Jiang-Xing; Xiao, Jie; Qiao, Li-Yan; Xu, Jiang-Rong

2018-06-01

Information transmission delay can be widely observed in various systems. Here, we study the dynamics of scroll waves with time-delay propagation among slices in excitable media. Weak time delay induces scroll waves to meander. Through increasing the time delay, we find a series of dynamical transitions. Firstly, the straight filament of a scroll wave becomes twisted. Then, the scroll wave breaks and forms interesting patterns. With long time delay, loosed scroll waves are maintained while their period are greatly decreased. Also, cylinder waves appears. The influences of diffusively coupling strength on the time-delay-induced scroll waves are studied. It is found that the critical time delay characterizing those transitions decreases as the coupling strength is increased. A phase diagram in the diffusive coupling-time delay plane is presented.

Cloaking through cancellation of diffusive wave scattering

PubMed Central

Chen, P. Y.; Guenneau, S.; Bağcı, H.; Salama, K. N.; Alù, A.

2016-01-01

A new cloaking mechanism, which makes enclosed objects invisible to diffusive photon density waves, is proposed. First, diffusive scattering from a basic core–shell geometry, which represents the cloaked structure, is studied. The conditions of scattering cancellation in a quasi-static scattering regime are derived. These allow for tailoring the diffusivity constant of the shell enclosing the object so that the fields scattered from the shell and the object cancel each other. This means that the photon flow outside the cloak behaves as if the cloaked object were not present. Diffusive light invisibility may have potential applications in hiding hot spots in infrared thermography or tissue imaging. PMID:27616925

Cloaking through cancellation of diffusive wave scattering

NASA Astrophysics Data System (ADS)

Farhat, M.; Chen, P. Y.; Guenneau, S.; Bağc, H.; Salama, K. N.; Alù, A.

2016-08-01

A new cloaking mechanism, which makes enclosed objects invisible to diffusive photon density waves, is proposed. First, diffusive scattering from a basic core-shell geometry, which represents the cloaked structure, is studied. The conditions of scattering cancellation in a quasi-static scattering regime are derived. These allow for tailoring the diffusivity constant of the shell enclosing the object so that the fields scattered from the shell and the object cancel each other. This means that the photon flow outside the cloak behaves as if the cloaked object were not present. Diffusive light invisibility may have potential applications in hiding hot spots in infrared thermography or tissue imaging.

Collision broadened resonance localization in tokamaks excited with ICRF waves

NASA Astrophysics Data System (ADS)

Kerbel, G. D.; McCoy, M. G.

1985-08-01

Advanced wave models used to evaluate ICRH in tokamaks typically use warm plasma theory and allow inhomogeneity in one dimension. The authors have developed a bounce-averaged Fokker-Planck quasilinear computational model which evolves the population of particles on more realistic orbits. Each wave-particle resonance has its own specific interaction amplitude within any given volume element. These data need only be generated once, and appropriately stored for efficient retrieval. The wave-particle resonant interaction then serves as a mechanism by which the diffusion of particle populations can proceed among neighboring orbits. Collisions affect the absorption of RF energy by two quite distinct processes: In addition to the usual relaxation towards the Maxwellian distribution creating velocity gradients which drive quasilinear diffusion, collisions also affect the wave-particle resonance through the mechanism of gyro-phase diffusion. The local specific spectral energy absorption rate is directly calculable once the orbit geometry and populations are determined. The code is constructed in such fashion as to accommodate wave propagation models which provide the wave spectral energy density on a poloidal cross-section. Information provided by the calculation includes the local absorption properties of the medium which can then be exploited to evolve the wave field.

Effect of turbulence on the dissipation of the space-charge wave in a bounded turbulent plasma column

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

Lee, Myoung-Jae; Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr; Department of Applied Physics and Department of Bionanotechnology, Hanyang University, Ansan, Kyunggi-Do 15588

The dispersion relation and the dissipation process of the space-charge wave propagating in a bounded plasma such as a cylindrical waveguide are investigated by employing the longitudinal dielectric permittivity that contains the diffusivity based on the Dupree theory of turbulent plasma. We derived the dispersion relation for space-charge wave in terms of the radius of cylindrical waveguide and the roots of the Bessel function of the first kind which appears as the boundary condition. We find that the wave frequency for a lower-order root of the Bessel function is higher than that of a higher-order root. We also find thatmore » the dissipation is greatest for the lowest-order root, but it is suppressed significantly as the order of the root increases. The wave frequency and the dissipation process are enhanced as the radius of cylindrical waveguide increases. However, they are always smaller than the case of bulk plasma. We find that the diffusivity of turbulent plasma would enhance the damping of space-charge waves, especially, in the range of small wave number. For a large wave number, the diffusivity has little effect on the damping.« less

Spin-diffusions and diffusive molecular dynamics

NASA Astrophysics Data System (ADS)

Farmer, Brittan; Luskin, Mitchell; Plecháč, Petr; Simpson, Gideon

2017-12-01

Metastable configurations in condensed matter typically fluctuate about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of classical molecular dynamics (MD) methods and has spurned the development of a host of approximate algorithms. One recently proposed method is diffusive MD which aims at integrating a system of ordinary differential equations describing the likelihood of occupancy by one of two species, in the case of a binary alloy, while quasistatically evolving the locations of the atoms. While diffusive MD has shown itself to be efficient and provide agreement with observations, it is fundamentally a model, with unclear connections to classical MD. In this work, we formulate a spin-diffusion stochastic process and show how it can be connected to diffusive MD. The spin-diffusion model couples a classical overdamped Langevin equation to a kinetic Monte Carlo model for exchange amongst the species of a binary alloy. Under suitable assumptions and approximations, spin-diffusion can be shown to lead to diffusive MD type models. The key assumptions and approximations include a well-defined time scale separation, a choice of spin-exchange rates, a low temperature approximation, and a mean field type approximation. We derive several models from different assumptions and show their relationship to diffusive MD. Differences and similarities amongst the models are explored in a simple test problem.

Defect imaging for plate-like structures using diffuse field.

PubMed

Hayashi, Takahiro

2018-04-01

Defect imaging utilizing a scanning laser source (SLS) technique produces images of defects in a plate-like structure, as well as spurious images occurring because of resonances and reverberations within the specimen. This study developed defect imaging by the SLS using diffuse field concepts to reduce the intensity of spurious images, by which the energy of flexural waves excited by laser can be estimated. The experimental results in the different frequency bandwidths of excitation waves and in specimens with different attenuation proved that clearer images of defects are obtained in broadband excitation using a chirp wave and in specimens with low attenuation, which produce diffuse fields easily.

A hybrid continuous-discrete method for stochastic reaction–diffusion processes

PubMed Central

Zheng, Likun; Nie, Qing

2016-01-01

Stochastic fluctuations in reaction–diffusion processes often have substantial effect on spatial and temporal dynamics of signal transductions in complex biological systems. One popular approach for simulating these processes is to divide the system into small spatial compartments assuming that molecules react only within the same compartment and jump between adjacent compartments driven by the diffusion. While the approach is convenient in terms of its implementation, its computational cost may become prohibitive when diffusive jumps occur significantly more frequently than reactions, as in the case of rapid diffusion. Here, we present a hybrid continuous-discrete method in which diffusion is simulated using continuous approximation while reactions are based on the Gillespie algorithm. Specifically, the diffusive jumps are approximated as continuous Gaussian random vectors with time-dependent means and covariances, allowing use of a large time step, even for rapid diffusion. By considering the correlation among diffusive jumps, the approximation is accurate for the second moment of the diffusion process. In addition, a criterion is obtained for identifying the region in which such diffusion approximation is required to enable adaptive calculations for better accuracy. Applications to a linear diffusion system and two nonlinear systems of morphogens demonstrate the effectiveness and benefits of the new hybrid method. PMID:27703710

A New Numerical Scheme for Cosmic-Ray Transport

NASA Astrophysics Data System (ADS)

Jiang, Yan-Fei; Oh, S. Peng

2018-02-01

Numerical solutions of the cosmic-ray (CR) magnetohydrodynamic equations are dogged by a powerful numerical instability, which arises from the constraint that CRs can only stream down their gradient. The standard cure is to regularize by adding artificial diffusion. Besides introducing ad hoc smoothing, this has a significant negative impact on either computational cost or complexity and parallel scalings. We describe a new numerical algorithm for CR transport, with close parallels to two-moment methods for radiative transfer under the reduced speed of light approximation. It stably and robustly handles CR streaming without any artificial diffusion. It allows for both isotropic and field-aligned CR streaming and diffusion, with arbitrary streaming and diffusion coefficients. CR transport is handled explicitly, while source terms are handled implicitly. The overall time step scales linearly with resolution (even when computing CR diffusion) and has a perfect parallel scaling. It is given by the standard Courant condition with respect to a constant maximum velocity over the entire simulation domain. The computational cost is comparable to that of solving the ideal MHD equation. We demonstrate the accuracy and stability of this new scheme with a wide variety of tests, including anisotropic streaming and diffusion tests, CR-modified shocks, CR-driven blast waves, and CR transport in multiphase media. The new algorithm opens doors to much more ambitious and hitherto intractable calculations of CR physics in galaxies and galaxy clusters. It can also be applied to other physical processes with similar mathematical structure, such as saturated, anisotropic heat conduction.

Low-energy ion acceleration at quasi-perpendicular shocks: Transverse diffusion

NASA Technical Reports Server (NTRS)

Giacalone, J.; Jokipii, J. R.

1995-01-01

The problem of ion injection and acceleration at quasi perpendicular shocks has been the subject of some debate over the past two decades. It is widely known that these shocks efficiently accelerate particles that are well in the high-energy tail of the distribution. However, the issue of injection, or the acceleration of low-energy ions, has yet to reach a consensus. The fundamental issue is whether there is enough diffusion normal to the magnetic field for the particles to remain near the shock. Since transverse diffusion is a physical process that is not well understood in space plasmas, this is an important, and difficult issue to address. In this report, we will investigate the ion injection problem by performing test particle orbit integrations using synthesized turbulent fields. These fields are fully three-dimensional so that transverse diffusion is possible (cross-field diffusion is not possible in geometries where the electromagnetic fields are less than three dimensional). The synthesized fields are produced by superimposing a three-dimensional wave field on a background field. For completeness, we will compare the results from this model with the more well-established theories, such as the diffusive approximation and scatter-free shock drift acceleration. We will also compare these results with other numerical simulation techniques such as the well known hybrid simulation, and other test-particle calculations in which the shock fields are specified to have less than three dimensions. We will also discuss some recent relevant observations and how these compare with our results.

Asymptotic analysis of dissipative waves with applications to their numerical simulation

NASA Technical Reports Server (NTRS)

Hagstrom, Thomas

1990-01-01

Various problems involving the interplay of asymptotics and numerics in the analysis of wave propagation in dissipative systems are studied. A general approach to the asymptotic analysis of linear, dissipative waves is developed. It was applied to the derivation of asymptotic boundary conditions for numerical solutions on unbounded domains. Applications include the Navier-Stokes equations. Multidimensional traveling wave solutions to reaction-diffusion equations are also considered. A preliminary numerical investigation of a thermo-diffusive model of flame propagation in a channel with heat loss at the walls is presented.

Autocrine signal transmission with extracellular ligand degradation

NASA Astrophysics Data System (ADS)

Muratov, C B; Posta, F; Shvartsman, S Y

2009-03-01

Traveling waves of cell signaling in epithelial layers orchestrate a number of important processes in developing and adult tissues. These waves can be mediated by positive feedback autocrine loops, a mode of cell signaling where binding of a diffusible extracellular ligand to a cell surface receptor can lead to further ligand release. We formulate and analyze a biophysical model that accounts for ligand-induced ligand release, extracellular ligand diffusion and ligand-receptor interaction. We focus on the case when the main mode for ligand degradation is extracellular and analyze the problem with the sharp threshold positive feedback nonlinearity. We derive expressions that link the speed of propagation and other characteristics of traveling waves to the parameters of the biophysical processes, such as diffusion rates, receptor expression level, etc. Analyzing the derived expressions we found that traveling waves in such systems can exhibit a number of unusual properties, e.g. non-monotonic dependence of the speed of propagation on ligand diffusivity. Our results for the fully developed traveling fronts can be used to analyze wave initiation from localized perturbations, a scenario that frequently arises in the in vitro models of epithelial wound healing, and guide future modeling studies of cell communication in epithelial layers.

Radar cross-section reduction based on an iterative fast Fourier transform optimized metasurface

NASA Astrophysics Data System (ADS)

Song, Yi-Chuan; Ding, Jun; Guo, Chen-Jiang; Ren, Yu-Hui; Zhang, Jia-Kai

2016-07-01

A novel polarization insensitive metasurface with over 25 dB monostatic radar cross-section (RCS) reduction is introduced. The proposed metasurface is comprised of carefully arranged unit cells with spatially varied dimension, which enables approximate uniform diffusion of incoming electromagnetic (EM) energy and reduces the threat from bistatic radar system. An iterative fast Fourier transform (FFT) method for conventional antenna array pattern synthesis is innovatively applied to find the best unit cell geometry parameter arrangement. Finally, a metasurface sample is fabricated and tested to validate RCS reduction behavior predicted by full wave simulation software Ansys HFSSTM and marvelous agreement is observed.

Spin effects induced by thermal perturbation in a normal metal/magnetic insulator system

NASA Astrophysics Data System (ADS)

Lyapilin, I. I.; Okorokov, M. S.; Ustinov, V. V.

2015-05-01

Using one of the methods of quantum nonequilibrium statistical physics, we have investigated the spin transport transverse to the normal metal/ferromagnetic insulator interface in hybrid nanostructures. An approximation of the effective parameters, when each of the interacting subsystems (electron spin, magnon, and phonon) is characterized by its own effective temperature, has been considered. The generalized Bloch equations which describe the spin-wave current propagation in the dielectric have been derived. Finally, two sides of the spin transport "coin" have been revealed: the diffusive nature of the magnon motion and magnon relaxation processes, responsible for the spin pumping, and the spin-torque effect.

Existence and exponential stability of traveling waves for delayed reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Hsu, Cheng-Hsiung; Yang, Tzi-Sheng; Yu, Zhixian

2018-03-01

The purpose of this work is to investigate the existence and exponential stability of traveling wave solutions for general delayed multi-component reaction-diffusion systems. Following the monotone iteration scheme via an explicit construction of a pair of upper and lower solutions, we first obtain the existence of monostable traveling wave solutions connecting two different equilibria. Then, applying the techniques of weighted energy method and comparison principle, we show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave solutions provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev space.

Real-time absorption and scattering characterization of slab-shaped turbid samples obtained by a combination of angular and spatially resolved measurements.

PubMed

Dam, Jan S; Yavari, Nazila; Sørensen, Søren; Andersson-Engels, Stefan

2005-07-10

We present a fast and accurate method for real-time determination of the absorption coefficient, the scattering coefficient, and the anisotropy factor of thin turbid samples by using simple continuous-wave noncoherent light sources. The three optical properties are extracted from recordings of angularly resolved transmittance in addition to spatially resolved diffuse reflectance and transmittance. The applied multivariate calibration and prediction techniques are based on multiple polynomial regression in combination with a Newton--Raphson algorithm. The numerical test results based on Monte Carlo simulations showed mean prediction errors of approximately 0.5% for all three optical properties within ranges typical for biological media. Preliminary experimental results are also presented yielding errors of approximately 5%. Thus the presented methods show a substantial potential for simultaneous absorption and scattering characterization of turbid media.

Temporal evolution of the Green's function reconstruction in the seismic coda

NASA Astrophysics Data System (ADS)

Clerc, V.; Roux, P.; Campillo, M.

2013-12-01

In presence of multiple scattering, the wavefield evolves towards an equipartitioned state, equivalent to ambient noise. CAMPILLO and PAUL (2003) reconstructed the surface wave part of the Green's function between three pairs of stations in Mexico. The data indicate that the time asymmetry between causal and acausal part of the Green's function is less pronounced when the correlation is performed in the later windows of the coda. These results on the correlation of diffuse waves provide another perspective on the reconstruction of Green function which is independent of the source distribution and which suggests that if the time of observation is long enough, a single source could be sufficient. The paper by ROUX et al. (2005) provides a theoretical frame for the reconstruction of the Green's function in a homogeneous middle. In a multiple scattering medium with a single source, scatterers behave as secondary sources according to the Huygens principle. Coda waves are relevant to multiple scattering, a regime which can be approximated by diffusion for long lapse times. We express the temporal evolution of the correlation function between two receivers as a function of the secondary sources. We are able to predict the effect of the persistence of the net flux of energy observed by CAMPILLO and PAUL (2003) in numerical simulations. This method is also effective in order to retrieve the scattering mean free path. We perform a partial reconstruction of the Green's function in a strongly scattering medium in numerical simulations. The prediction of the flux asymmetry allows defining the parts of the coda providing the same information as ambient noise cross correlation.

Weak rotating flow disturbances in a centrifugal compressor with a vaneless diffuser

NASA Technical Reports Server (NTRS)

Moore, F. K.

1988-01-01

A theory is presented to predict the occurrence of weak rotating waves in a centrifugal compression system with a vaneless diffuser. As in a previous study of axial systems, an undisturbed performance characteristic is assumed known. Following an inviscid analysis of the diffuser flow, conditions for a neutral rotating disturbance are found. The solution is shown to have two branches; one with fast rotation, the other with very slow rotation. The slow branch includes a dense set of resonant solutions. The resonance is a feature of the diffuser flow, and therefore such disturbances must be expected at the various resonant flow coefficients regardless of the compressor characteristic. Slow solutions seem limited to flow coefficients less than about 0.3, where third and fourth harmonics appear. Fast waves seem limited to a first harmonic. These fast and slow waves are described, and effects of diffuser-wall convergence, backward blade angles, and partial recovery of exit velocity head are assessed.

Control of transversal instabilities in reaction-diffusion systems

NASA Astrophysics Data System (ADS)

Totz, Sonja; Löber, Jakob; Totz, Jan Frederik; Engel, Harald

2018-05-01

In two-dimensional reaction-diffusion systems, local curvature perturbations on traveling waves are typically damped out and vanish. However, if the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated waves and to spreading spiral turbulence. Here, we propose a scheme to induce or inhibit these instabilities via a spatio-temporal feedback loop. In a piecewise-linear version of the FitzHugh–Nagumo model, transversal instabilities and spiral turbulence in the uncontrolled system are shown to be suppressed in the presence of control, thereby stabilizing plane wave propagation. Conversely, in numerical simulations with the modified Oregonator model for the photosensitive Belousov–Zhabotinsky reaction, which does not exhibit transversal instabilities on its own, we demonstrate the feasibility of inducing transversal instabilities and study the emerging wave patterns in a well-controlled manner.

On the Chemical Mixing Induced by Internal Gravity Waves

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

Rogers, T. M.; McElwaine, J. N.

Detailed modeling of stellar evolution requires a better understanding of the (magneto)hydrodynamic processes that mix chemical elements and transport angular momentum. Understanding these processes is crucial if we are to accurately interpret observations of chemical abundance anomalies, surface rotation measurements, and asteroseismic data. Here, we use two-dimensional hydrodynamic simulations of the generation and propagation of internal gravity waves in an intermediate-mass star to measure the chemical mixing induced by these waves. We show that such mixing can generally be treated as a diffusive process. We then show that the local diffusion coefficient does not depend on the local fluid velocity,more » but rather on the wave amplitude. We then use these findings to provide a simple parameterization for this diffusion, which can be incorporated into stellar evolution codes and tested against observations.« less

Fast Ion and Thermal Plasma Transport in Turbulent Waves in the Large Plasma Device (LAPD)

NASA Astrophysics Data System (ADS)

Zhou, Shu

2011-10-01

The transport of fast ions and thermal plasmas in electrostatic microturbulence is studied. Strong density and potential fluctuations (δn / n ~ δϕ / kTe ~ 0 . 5 , f ~5-50 kHz) are observed in the LAPD in density gradient regions produced by obstacles with slab or cylindrical geometry. Wave characteristics and the associated plasma transport are modified by driving sheared E ×B drift through biasing the obstacle, and by modification of the axial magnetic fields (Bz) and the plasma species. Cross-field plasma transport is suppressed with small bias and large Bz, and is enhanced with large bias and small Bz. Suppressed cross-field thermal transport coincides with a 180° phase shift between the density and potential fluctuations in the radial direction, while the enhanced thermal transport is associated with modes having low mode number (m = 1) and long radial correlation length. Large gyroradius lithium ions (ρfast /ρs ~ 10) orbit through the turbulent region. Scans with a collimated analyzer and with Langmuir probes give detailed profiles of the fast ion spatial-temporal distribution and of the fluctuating fields. Fast-ion transport decreases rapidly with increasing fast-ion gyroradius. Background waves with different scale lengths also alter the fast ion transport: Beam diffusion is smaller in waves with smaller structures (higher mode number); also, coherent waves with long correlation length cause less beam diffusion than turbulent waves. Experimental results agree well with gyro-averaging theory. When the fast ion interacts with the wave for most of a wave period, a transition from super-diffusive to sub-diffusive transport is observed, as predicted by diffusion theory. A Monte Carlo trajectory-following code simulates the interaction of the fast ions with the measured turbulent fields. Good agreement between observation and modeling is observed. Work funded by DOE and NSF and performed at the Basic Plasma Science Facility.

A modulation wave approach to the order hidden in disorder

PubMed Central

Withers, Ray

2015-01-01

The usefulness of a modulation wave approach to understanding and interpreting the highly structured continuous diffuse intensity distributions characteristic of the reciprocal spaces of the very large family of inherently flexible materials which exhibit ordered ‘disorder’ is pointed out. It is shown that both longer range order and truly short-range order are simultaneously encoded in highly structured diffuse intensity distributions. The long-range ordered crystal chemical rules giving rise to such diffuse distributions are highlighted, along with the existence and usefulness of systematic extinction conditions in these types of structured diffuse distributions. PMID:25610629

Signal information available for plume source tracking with and without surface waves and learning by undergraduates assisting with the research

NASA Astrophysics Data System (ADS)

Wiley, Megan Beth

Autonomous vehicles have had limited success in locating point sources of pollutants, chemicals, and other passive scalars. However, animals such as stomatopods, a mantis shrimp, track odor plumes easily for food, mates, and habitat. Laboratory experiments using Planar Laser Induced Fluorescence measured odor concentration downstream of a diffusive source with and without live stomatopods to investigate their source-tracking strategies in unidirectional and "wave-affected" (surface waves with a mean current) flows. Despite the dearth of signal, extreme temporal variation, and meandering plume centerline, the stomatopods were able to locate the source, especially in the wave-affected flow. Differences in the two plumes far from the source (>160 cm) appeared to help the animals in the wave-affected flow position themselves closer to the source (<70 cm) at times with relatively large amounts of odor and plume filaments of high concentration. At the height of the animals' antennules, the site of their primary chemosensors, the time-averaged Reynolds stresses in the two flows were approximately the same. The temporal variation in stresses over the wave cycle may be responsible for differences in the two plumes. The antennule height falls between a region of large peaks in Reynolds stress in phase with peaks in streamwise acceleration, and a lower region with a smaller Reynolds stress peak in phase with maximum shear during flow reversal. Six undergraduate students assisted with the research. We documented their daily activities and ideas on plume dispersion using open-ended interviews. Most of their time was spent on tasks that required no understanding of fluid mechanics, and there was little evidence of learning by participation in the RAship. One RA's conceptions of turbulence did change, but a group workshop seemed to support this learning more than the RAship. The documented conceptions could aid in curriculum design, since situating new information within current knowledge seems to deepen learning outcomes. The RAs' conceptions varied widely with some overlap of ideas. The interviews also showed that most RAs did not discuss molecular diffusion as part of the mixing process and some remembered information from course demonstrations, but applied them inappropriately to the interview questions.

Camera flash heating of a three-layer solid composite: An approximate solution

NASA Astrophysics Data System (ADS)

Jibrin, Sani; Moksin, Mohd Maarof; Husin, Mohd Shahril; Zakaria, Azmi; Hassan, Jumiah; Talib, Zainal Abidin

2014-03-01

Camera flash heating and the subsequent thermal wave propagation in a solid composite material is studied using the Laplace transform technique. Full-field rear surface temperature for a single-layer, two-layer and three-layer solid composites are obtained directly from the Laplace transform conversion tables as opposed to the tedious inversion process by integral transform method. This is achieved by first expressing the hyperbolic-transcendental equation in terms of negative exponentials of square root of s/α and expanded same in a series by the binomial theorem. Electrophoretic deposition (EPD) and dip coating processes were used to prepare three-layer solid composites consisting ZnO/Cu/ZnO and starch/Al/starch respectively. About 0.5ml of deionized water enclosed within an air-tight aluminium container serves as the third three layer sample (AL/water/AL). Thermal diffusivity experiments were carried out on all the three samples prepared. Using Scaled Levenberg-Marquardt algorithm, the approximate temperature curve for the three-layer solid composite is fitted with the corresponding experimental result. The agreement between the theoretical curve and the experimental data as well as that between the obtained thermal diffusivity values for the ZnO, aluminium and deionized water in this work and similar ones found in literature is found to be very good.

Superthermal Electron Magnetosphere-Ionosphere Coupling in the Diffuse Aurora in the Presence of ECH Waves

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Tripathi, A. K.; Singhal, R. P.; Himwich, Elizabeth; Glocer, A.; Sibeck, D. G.

2015-01-01

There are two main theories for the origin of the diffuse auroral electron precipitation: first, pitch angle scattering by electrostatic electron cyclotron harmonic (ECH) waves, and second, by whistler mode waves. Precipitating electrons initially injected from the plasma sheet to the loss cone via wave-particle interaction processes degrade in the atmosphere toward lower energies and produce secondary electrons via impact ionization of the neutral atmosphere. These secondary electrons can escape back to the magnetosphere, become trapped on closed magnetic field lines, and deposit their energy back to the inner magnetosphere. ECH and whistler mode waves can also move electrons in the opposite direction, from the loss cone into the trap zone, if the source of such electrons exists in conjugate ionospheres located at the same field lines as the trapped magnetospheric electron population. Such a situation exists in the simulation scenario of superthermal electron energy interplay in the region of diffuse aurora presented and discussed by Khazanov et al. (2014) and will be quantified in this paper by taking into account the interaction of secondary electrons with ECH waves.

Chemotaxis of artificial microswimmers in active density waves

NASA Astrophysics Data System (ADS)

Geiseler, Alexander; Hänggi, Peter; Marchesoni, Fabio; Mulhern, Colm; Savel'ev, Sergey

2016-07-01

Living microorganisms are capable of a tactic response to external stimuli by swimming toward or away from the stimulus source; they do so by adapting their tactic signal transduction pathways to the environment. Their self-motility thus allows them to swim against a traveling tactic wave, whereas a simple fore-rear asymmetry argument would suggest the opposite. Their biomimetic counterpart, the artificial microswimmers, also propel themselves by harvesting kinetic energy from an active medium, but, in contrast, lack the adaptive capacity. Here we investigate the transport of artificial swimmers subject to traveling active waves and show, by means of analytical and numerical methods, that self-propelled particles can actually diffuse in either direction with respect to the wave, depending on its speed and waveform. Moreover, chiral swimmers, which move along spiraling trajectories, may diffuse preferably in a direction perpendicular to the active wave. Such a variety of tactic responses is explained by the modulation of the swimmer's diffusion inside traveling active pulses.

Communication: Development of standing evanescent-wave fluorescence correlation spectroscopy and its application to the lateral diffusion of lipids in a supported lipid bilayer

NASA Astrophysics Data System (ADS)

Otosu, Takuhiro; Yamaguchi, Shoichi

2017-07-01

We present standing evanescent-wave fluorescence correlation spectroscopy (SEW-FCS). This technique utilizes the interference of two evanescent waves which generates a standing evanescent-wave. Fringe-pattern illumination created by a standing evanescent-wave enables us to measure the diffusion coefficients of molecules with a super-resolution corresponding to one fringe width. Because the fringe width can be reliably estimated by a simple procedure, utilization of fringes is beneficial to quantitatively analyze the slow diffusion of molecules in a supported lipid bilayer (SLB), a model biomembrane formed on a solid substrate, with the timescale relevant for reliable FCS analysis. Furthermore, comparison of the data between SEW-FCS and conventional total-internal reflection FCS, which can also be performed by the SEW-FCS instrument, effectively eliminates the artifact due to afterpulsing of the photodiode detector. The versatility of SEW-FCS is demonstrated by its application to various SLBs.

Sodium Lidar-observed Strong Inertia-gravity Wave Activities in the Mesopause Region over Fort Collins, Colorado (41 deg N, 105 deg W)

NASA Technical Reports Server (NTRS)

Li, Tao; She, C. -Y.; Liu, Han-Li; Leblanc, Thierry; McDermid, I. Stuart

2007-01-01

In December 2004, the Colorado State University sodium lidar system at Fort Collins, Colorado (41 deg N, 105 deg W), conducted an approximately 80-hour continuous campaign for the simultaneous observations of mesopause region sodium density, temperature, and zonal and meridional winds. This data set reveals the significant inertia-gravity wave activities with a period of approximately 18 hours, which are strong in both wind components since UT day 338 (second day of the campaign), and weak in temperature and sodium density. The considerable variability of wave activities was observed with both wind amplitudes growing up to approximately 40 m/s at 95-100 km in day 339 and then decreasing dramatically in day 340. We also found that the sodium density wave perturbation is correlated in phase with temperature perturbation below 90 km, and approximately 180 deg out of phase above. Applying the linear wave theory, we estimated the wave horizontal propagation direction, horizontal wavelength, and apparent horizontal phase speed to be approximately 25 deg south of west, approximately 1800 +/- 150 km, and approximately 28 +/- 2 m/s, respectively of wave intrinsic period, intrinsic phase speed, and vertical wavelength were also estimated. While the onset of enhanced inertia-gravity wave amplitude in the night of 338 was observed to be in coincidence with short-period gravity wave breaking via convective instability, the decrease of inertia-gravity wave amplitude after noon of day 339 was also observed to coincide with the development of atmospheric dynamical instability layers with downward phase progression clearly correlated with the 18-hour inertia-gravity wave, suggesting likely breaking of this inertia-gravity wave via dynamical (shear) instability.

Comparison of techniques for approximating ocean bottom topography in a wave-refraction computer model

NASA Technical Reports Server (NTRS)

Poole, L. R.

1975-01-01

A study of the effects of using different methods for approximating bottom topography in a wave-refraction computer model was conducted. Approximation techniques involving quadratic least squares, cubic least squares, and constrained bicubic polynomial interpolation were compared for computed wave patterns and parameters in the region of Saco Bay, Maine. Although substantial local differences can be attributed to use of the different approximation techniques, results indicated that overall computed wave patterns and parameter distributions were quite similar.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

NASA Astrophysics Data System (ADS)

Horowitz, Jordan M.

2015-07-01

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

PubMed

Horowitz, Jordan M

2015-07-28

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Standing waves, clustering, and phase waves in 1D simulations of kinetic relaxation oscillations in NO+NH 3 on Pt(1 0 0) coupled by diffusion

NASA Astrophysics Data System (ADS)

Uecker, Hannes

2004-04-01

The Lombardo-Imbihl-Fink (LFI) ODE model of the NO+NH 3 reaction on a Pt(1 0 0) surface shows stable relaxation oscillations with very sharp transitions for temperatures T between 404 and 433 K. Here we study numerically the effect of linear diffusive coupling of these oscillators in one spatial dimension. Depending on the parameters and initial conditions we find a rich variety of spatio-temporal patterns which we group into four main regimes: bulk oscillations (BOs), standing waves (SW), phase clusters (PC), and phase waves (PW). Two key ingredients for SW and PC are identified, namely the relaxation type of the ODE oscillations and a nonlocal (and nonglobal) coupling due to relatively fast diffusion of the kinetically slaved variables NH 3 and H. In particular, the latter replaces the global coupling through the gas phase used to obtain SW and PC in models of related surface reactions. The PW exist only under the assumption of (relatively) slow diffusion of NH 3 and H.

Multi-fluid Approach to High-frequency Waves in Plasmas. II. Small-amplitude Regime in Partially Ionized Media

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

Martínez-Gómez, David; Soler, Roberto; Terradas, Jaume, E-mail: david.martinez@uib.es

2017-03-01

The presence of neutral species in a plasma has been shown to greatly affect the properties of magnetohydrodynamic waves. For instance, the interaction between ions and neutrals through momentum transfer collisions causes the damping of Alfvén waves and alters their oscillation frequency and phase speed. When the collision frequencies are larger than the frequency of the waves, single-fluid magnetohydrodynamic approximations can accurately describe the effects of partial ionization, since there is a strong coupling between the various species. However, at higher frequencies, the single-fluid models are not applicable and more complex approaches are required. Here, we use a five-fluid modelmore » with three ionized and two neutral components, which takes into consideration Hall’s current and Ohm’s diffusion in addition to the friction due to collisions between different species. We apply our model to plasmas composed of hydrogen and helium, and allow the ionization degree to be arbitrary. By analyzing the corresponding dispersion relation and numerical simulations, we study the properties of small-amplitude perturbations. We discuss the effect of momentum transfer collisions on the ion-cyclotron resonances and compare the importance of magnetic resistivity, and ion–neutral and ion–ion collisions on the wave damping at various frequency ranges. Applications to partially ionized plasmas of the solar atmosphere are performed.« less

DREAM3D simulations of inner-belt dynamics

NASA Astrophysics Data System (ADS)

Cunningham, G.

2015-12-01

A 1973 paper by Lyons and Thorne explains the two-belt structure for electrons in the inner magnetosphere as a balance between inward radial diffusion and loss to the atmosphere due to pitch-angle scattering from Coulomb and VLF wave-particle interactions. In this paper, equilibrium solutions to a set of 1D radial diffusion equations, one for each value of the first invariant of motion, μ, were computed to produce the equilibrium structure. Each diffusion equation incorporated an L- and μ-dependent `lifetime' due to the Coulomb and wave-particle interactions. This model is appropriate under the assumption that radial diffusion is slow in comparison to pitch-angle scattering, and that there is no acceleration caused by the VLF wave-particle interactions. We have revisited this model using our DREAM3D 3D diffusion code, which allows the user to explicitly model the diffusion in pitch-angle and momentum rather than using a lifetime. We find that a) replacing the lifetimes with an explicit model of pitch-angle diffusion, thus allowing for coupling between radial and pitch-angle diffusion, affects the equilibrium structure, and b) over the long time scales needed to reach equilibrium, significant acceleration due to VLF wave particle interactions takes place due to the 'cross-terms' in pitch-angle and momentum and the sharp gradient in the equilibrium pitch-angle distributions. We also find that the equilibrium solutions are quite sensitive to various aspects of the physics model employed in the 1973 paper that can be improved, suggesting that additional work needs to be done to fully understand the equilibirum nature of the trapped electron radiation belts.

Relativistic Electron Precipitation: An Observational Study.

DTIC Science & Technology

1980-01-01

al., 1970). These so-called "n + 1/2" waves (- n + 1/2) are found throughout the magnetosphere outside the plasmapause (Kennel et al., 1970; Shaw and...diffusion scattering one requires 2 L D~ . LSD - z ~.(21) 73 where aL = loss cone pitch angle D SD = coefficient for strong diffusion. Equation (20) can be...with substitutions yields a fluctuating field wave amplitude for strong electron diffusion: a." 0- x(23) and 00for f= LSD (24) LRo LRo + For ions

Fokker-Planck electron diffusion caused by an obliquely propagating electromagnetic wave packet of narrow bandwidth

NASA Technical Reports Server (NTRS)

Hizanidis, Kyriakos

1989-01-01

The relativistic motion of electrons in an intense electromagnetic wave packet propagating obliquely to a uniform magnetic field is analytically studied on the basis of the Fokker-Planck-Kolmogorov (FPK) approach. The wavepacket consists of circularly polarized electron-cyclotron waves. The dynamical system in question is shown to be reducible to one with three degrees of freedom. Within the framework of the Hamiltonian analysis the nonlinear diffusion tensor is derived, and it is shown that this tensor can be separated into zeroth-, first-, and second-order parts with respect to the relative bandwidth. The zeroth-order part describes diffusive acceleration along lines of constant unperturbed Hamiltonian. The second-order part, which corresponds to the longest time scale, describes diffusion across those lines. A possible transport theory is outlined on the basis of this separation of the time scales.

Driven waves in a two-fluid plasma

NASA Astrophysics Data System (ADS)

Roberge, W. G.; Ciolek, Glenn E.

2007-12-01

We study the physics of wave propagation in a weakly ionized plasma, as it applies to the formation of multifluid, magnetohydrodynamics (MHD) shock waves. We model the plasma as separate charged and neutral fluids which are coupled by ion-neutral friction. At times much less than the ion-neutral drag time, the fluids are decoupled and so evolve independently. At later times, the evolution is determined by the large inertial mismatch between the charged and neutral particles. The neutral flow continues to evolve independently; the charged flow is driven by and slaved to the neutral flow by friction. We calculate this driven flow analytically by considering the special but realistic case where the charged fluid obeys linearized equations of motion. We carry out an extensive analysis of linear, driven, MHD waves. The physics of driven MHD waves is embodied in certain Green functions which describe wave propagation on short time-scales, ambipolar diffusion on long time-scales and transitional behaviour at intermediate times. By way of illustration, we give an approximate solution for the formation of a multifluid shock during the collision of two identical interstellar clouds. The collision produces forward and reverse J shocks in the neutral fluid and a transient in the charged fluid. The latter rapidly evolves into a pair of magnetic precursors on the J shocks, wherein the ions undergo force-free motion and the magnetic field grows monotonically with time. The flow appears to be self-similar at the time when linear analysis ceases to be valid.

Rock anelasticity due to patchy saturation and fabric heterogeneity: A double double-porosity model of wave propagation

NASA Astrophysics Data System (ADS)

Ba, Jing; Xu, Wenhao; Fu, Li-Yun; Carcione, José M.; Zhang, Lin

2017-03-01

Heterogeneity of rock's fabric can induce heterogeneous distribution of immiscible fluids in natural reservoirs, since the lithological variations (mainly permeability) may affect fluid migration in geological time scales, resulting in patchy saturation of fluids. Therefore, fabric and saturation inhomogeneities both affect wave propagation. To model the wave effects (attenuation and velocity dispersion), we introduce a double double-porosity model, where pores saturated with two different fluids overlap with pores having dissimilar compressibilities. The governing equations are derived by using Hamilton's principle based on the potential energy, kinetic energy, and dissipation functions, and the stiffness coefficients are determined by gedanken experiments, yielding one fast P wave and four slow Biot waves. Three examples are given, namely, muddy siltstones, clean dolomites, and tight sandstones, where fabric heterogeneities at three different spatial scales are analyzed in comparison with experimental data. In muddy siltstones, where intrapore clay and intergranular pores constitute a submicroscopic double-porosity structure, wave anelasticity mainly occurs in the frequency range (104-107 Hz), while in pure dolomites with microscopic heterogeneity of grain contacts and tight sandstones with mesoscopic heterogeneity of less consolidated sands, it occurs at 103-107 Hz and 101-103 Hz (seismic band), respectively. The predicted maximum quality factor of the fast compressional wave for the sandstone is the lowest (approximately 8), and that of the dolomite is the highest. The results of the diffusive slow waves are affected by the strong friction effects between solids and fluids. The model describes wave propagation in patchy-saturated rocks with fabric heterogeneity at different scales, and the relevant theoretical predictions agree well with the experimental data in fully and partially saturated rocks.

Diffusion of Intervention Effects: The Impact of a Family-Based Substance Use Prevention Program on Friends of Participants.

PubMed

Rulison, Kelly L; Feinberg, Mark; Gest, Scott D; Osgood, D Wayne

2015-10-01

We tested whether effects of the Strengthening Families Program for Youth 10-14 (SFP10-14) diffused from intervention participants to their friends. We also tested which program effects on participants accounted for diffusion. Data are from 5,449 students (51% female; mean initial age = 12.3 years) in the PROmoting School-community-university Partnerships to Enhance Resilience community intervention trial (2001-2006) who did not participate in SFP10-14 (i.e., nonparticipants). At each of five waves, students identified up to seven friends and self-reported past month drunkenness and cigarette use, substance use attitudes, parenting practices, and unsupervised time spent with friends. We computed two measures of indirect exposure to SFP10-14: total number of SFP-attending friends at each wave and cumulative proportion of SFP-attending friends averaged across the current and all previous post-intervention waves. Three years post-intervention, the odds of getting drunk (odds ratio = 1.4) and using cigarettes (odds ratio = 2.7) were higher among nonparticipants with zero SFP-attending friends compared with nonparticipants with three or more SFP-attending friends. Multilevel analyses also provided evidence of diffusion: nonparticipants with a higher cumulative proportion of SFP-attending friends at a given wave were less likely than their peers to use drugs at that wave. Effects from SFP10-14 primarily diffused through friendship networks by reducing the amount of unstructured socializing (unsupervised time that nonparticipants spent with friends), changing friends' substance use attitudes, and then changing nonparticipants' own substance use attitudes. Program developers should consider and test how interventions may facilitate diffusion to extend program reach and promote program sustainability. Copyright © 2015 Society for Adolescent Health and Medicine. Published by Elsevier Inc. All rights reserved.

Diffusion of Intervention Effects: The Impact of a Family-based Substance Use Prevention Program on Friends of Participants

PubMed Central

Rulison, Kelly L.; Feinberg, Mark; Gest, Scott D.; Osgood, D. Wayne

2015-01-01

Purpose We tested whether effects of the Strengthening Families Program for Youth 10–14 (SFP10–14) diffused from intervention participants to their friends. We also tested which program effects on participants accounted for diffusion. Methods Data are from 5,449 students (51% female; mean initial age=12.3 years) in the PROSPER community intervention trial (2001–2006) who did not participate in SFP10–14 (i.e., non-participants). At each of 5 waves, students identified up to 7 friends and self-reported past month drunkenness and cigarette use, substance use attitudes, parenting practices, and unsupervised time spent with friends. We computed two measures of indirect exposure to SFP10–14: total number of SFP-attending friends at each wave and cumulative proportion of SFP-attending friends averaged across the current and all previous post-intervention waves. Results Three years post-intervention, the odds of getting drunk (OR=1.4) and using cigarettes (OR=2.7) were higher among non-participants with 0 SFP-attending friends compared to non-participants with 3 or more SFP-attending friends. Multilevel analyses also provided evidence of diffusion: non-participants with a higher cumulative proportion of SFP-attending friends at a given wave were less likely than their peers to use drugs at that wave. Effects from SFP10–14 primarily diffused through friendship networks by reducing the amount of unstructured socializing (unsupervised time that non-participants spent with friends), changing friends’ substance use attitudes, and then changing non-participants’ own substance use attitudes. Conclusions Program developers should consider and test how interventions may facilitate diffusion to extend program reach and promote program sustainability. PMID:26210856

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

NASA Astrophysics Data System (ADS)

Schreiner, Cedric; Vainio, Rami; Spanier, Felix

2018-02-01

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

PAINeT: An object-oriented software package for simulations of flow-field, transport coefficients and flux terms in non-equilibrium gas mixture flows

NASA Astrophysics Data System (ADS)

Istomin, V. A.

2018-05-01

The software package Planet Atmosphere Investigator of Non-equilibrium Thermodynamics (PAINeT) has been devel-oped for studying the non-equilibrium effects associated with electronic excitation, chemical reactions and ionization. These studies are necessary for modeling process in shock tubes, in high enthalpy flows, in nozzles or jet engines, in combustion and explosion processes, in modern plasma-chemical and laser technologies. The advantages and possibilities of the package implementation are stated. Within the framework of the package implementation, based on kinetic theory approximations (one-temperature and state-to-state approaches), calculations are carried out, and the limits of applicability of a simplified description of shock-heated air flows and any other mixtures chosen by the user are given. Using kinetic theory algorithms, a numerical calculation of the heat fluxes and relaxation terms can be performed, which is necessary for further comparison of engineering simulation with experi-mental data. The influence of state-to-state distributions over electronic energy levels on the coefficients of thermal conductivity, diffusion, heat fluxes and diffusion velocities of the components of various gas mixtures behind shock waves is studied. Using the software package the accuracy of different approximations of the kinetic theory of gases is estimated. As an example state-resolved atomic ionized mixture of N/N+/O/O+/e- is considered. It is shown that state-resolved diffusion coefficients of neutral and ionized species vary from level to level. Comparing results of engineering applications with those given by PAINeT, recommendations for adequate models selection are proposed.

Li diffusion in epitaxial (11 $bar 2$ 0) ZnO thin films

NASA Astrophysics Data System (ADS)

Wu, P.; Zhong, J.; Emanetoglu, N. W.; Chen, Y.; Muthukumar, S.; Lu, Y.

2004-06-01

Zinc oxide (ZnO) possesses many interesting properties, such as a wide energy bandgap, large photoconductivity, and high excitonic binding energy. Chemical-vapor-deposition-grown ZnO films generally show n-type conductivity. A compensation doping process is needed to achieve piezoelectric ZnO, which is needed for surface acoustic wave (SAW), bulk acoustic wave, and micro-electromechanical system devices. In this work, a gas-phase diffusion process is developed to achieve piezoelectric (11bar 20) ZnO films. Comparative x-ray diffraction (XRD) and scanning electron microscopy (SEM) measurements confirmed that high crystal quality and good surface morphology were preserved after diffusion. Photoluminescence (PL) measurements show a broad band emission with a peak wavelength at ˜580 nm, which is associated with Li doping. The SAW, including both Rayleigh-wave and Love-wave modes, is achieved along different directions in piezoelectric (11bar 20) ZnO films grown on an r-plane sapphire substrate.

Properties of seismic absorption induced reflections

NASA Astrophysics Data System (ADS)

Zhao, Haixia; Gao, Jinghuai; Peng, Jigen

2018-05-01

Seismic reflections at an interface are often regarded as the variation of the acoustic impedance (product of seismic velocity and density) in a medium. In fact, they can also be generated due to the difference in absorption of the seismic energy. In this paper, we investigate the properties of such reflections. Based on the diffusive-viscous wave equation and elastic diffusive-viscous wave equation, we investigate the dependency of the reflection coefficients on frequency, and their variations with incident angles. Numerical results at a boundary due to absorption contrasts are compared with those resulted from acoustic impedance variation. It is found that, the reflection coefficients resulted from absorption depend significantly on the frequency especially at lower frequencies, but vary very slowly at small incident angles. At the higher frequencies, the reflection coefficients of diffusive-viscous wave and elastic diffusive-viscous wave are close to those of acoustic and elastic cases, respectively. On the other hand, the reflections caused by acoustic impedance variation are independent of frequency but vary distinctly with incident angles before the critical angle. We also investigate the difference between the seismograms generated in the two different media. The numerical results show that the amplitudes of these reflected waves are attenuated and their phases are shifted. However, the reflections obtained by acoustic impedance contrast, show no significant amplitude attenuation and phase shift.

Inward propagating chemical waves in Taylor vortices.

PubMed

Thompson, Barnaby W; Novak, Jan; Wilson, Mark C T; Britton, Melanie M; Taylor, Annette F

2010-04-01

Advection-reaction-diffusion (ARD) waves in the Belousov-Zhabotinsky reaction in steady Taylor-Couette vortices have been visualized using magnetic-resonance imaging and simulated using an adapted Oregonator model. We show how propagating wave behavior depends on the ratio of advective, chemical and diffusive time scales. In simulations, inward propagating spiral flamelets are observed at high Damköhler number (Da). At low Da, the reaction distributes itself over several vortices and then propagates inwards as contracting ring pulses--also observed experimentally.

Modeling of sedimentation and resuspension processes induced by intensive internal gravity waves in the coastal water systems with the use of the advection-diffusion equation for sediment concentration

NASA Astrophysics Data System (ADS)

Rouvinskaya, Ekaterina; Kurkin, Andrey; Kurkina, Oxana

2017-04-01

Intensive internal gravity waves influence bottom topography in the coastal zone. They induce substantial flows in the bottom layer that are essential for the formation of suspension and for the sediment transport. It is necessary to develop a mathematical model to predict the state of the seabed near the coastline to assess and ensure safety during the building and operation of the hydraulic engineering constructions. There are many models which are used to predict the impact of storm waves on the sediment transport processes. Such models for the impact of the tsunami waves are also actively developing. In recent years, the influence of intense internal waves on the sedimentation processes is also of a special interest. In this study we adapt one of such models, that is based on the advection-diffusion equation and allows to study processes of resuspension under the influence of internal gravity waves in the coastal zone, for solving the specific practical problems. During the numerical simulation precomputed velocity values are substituted in the advection - diffusion equation for sediment concentration at each time step and each node of the computational grid. Velocity values are obtained by the simulation of the internal waves' dynamics by using the IGW Research software package for numerical integration of fully nonlinear two-dimensional (vertical plane) system of equations of hydrodynamics of inviscid incompressible stratified fluid in the Boussinesq approximation bearing in mind the impact of barotropic tide. It is necessary to set the initial velocity and density distribution in the computational domain, bottom topography, as well as the value of the Coriolis parameter and, if necessary, the parameters of the tidal wave to carry out numerical calculations in the software package IGW Research. To initialize the background conditions of the numerical model we used data records obtained in the summer in the southern part of the shelf zone of Sakhalin Island from 1999 to 2003, provided by SakhNIRO, Russia. The process of assimilation of field data with numerical model is described in detail in our previous studies. It has been shown that process of suspension formation is quite intense for the investigated condition. Concentration of suspended particles significantly increases during the tide, especially on naturally uneven bottom relief as well as on the right boundary of the computational domain (near shoreline). Pronounced nepheloid layer is produced. Its thickness is about 5.6 m. At the phase of low tide, the process of suspension sediment production stops, and suspended particles are beginning to settle because of the small vertical velocities. Thickness of nepheloid layer is actively reduced. Obviously, this should lead to a change in the bottom relief. The presented results of research were obtained with the support of the Russian President's scholarship for young scientists and graduate students SP-2311.2016.5.

Modification of wave-cut and faulting-controlled landforms.

USGS Publications Warehouse

Hanks, T.C.; Bucknam, R.C.; Lajoie, K.R.; Wallace, R.E.

1984-01-01

From a casual observation that the form of degraded fault scarps resembles the error function, this investigation proceeds through an elementary diffusion equation representation of landform evolution to the application of the resulting equations to the modern topography of scarplike landforms. The value of K = 1 GKG (K = 'mass diffusivity'; 1 GKG = 1m2/ka) may be generally applicable as a good first approximation, to the modification of alluvial terranes within the semiarid regions of the western United States. The Lake Bonneville shoreline K is the basis for dating four sets of fault scarps in west-central Utah. The Drum Mountains fault scarps date at 3.6 to 5.7 ka BP. Fault scarps along the eastern base of the Fish Springs Range are very young, 3 ka BP. We estimate the age of fault scarps along the western flank of the Oquirrh Mountains to be 32 ka B.P. Fault scarps along the NE margin of the Sheeprock Mountains are even older, 53 ka BP. -from Authors

Statistical analysis of Hasegawa-Wakatani turbulence

NASA Astrophysics Data System (ADS)

Anderson, Johan; Hnat, Bogdan

2017-06-01

Resistive drift wave turbulence is a multipurpose paradigm that can be used to understand transport at the edge of fusion devices. The Hasegawa-Wakatani model captures the essential physics of drift turbulence while retaining the simplicity needed to gain a qualitative understanding of this process. We provide a theoretical interpretation of numerically generated probability density functions (PDFs) of intermittent events in Hasegawa-Wakatani turbulence with enforced equipartition of energy in large scale zonal flows, and small scale drift turbulence. We find that for a wide range of adiabatic index values, the stochastic component representing the small scale turbulent eddies of the flow, obtained from the autoregressive integrated moving average model, exhibits super-diffusive statistics, consistent with intermittent transport. The PDFs of large events (above one standard deviation) are well approximated by the Laplace distribution, while small events often exhibit a Gaussian character. Furthermore, there exists a strong influence of zonal flows, for example, via shearing and then viscous dissipation maintaining a sub-diffusive character of the fluxes.

Revisited Fisher's equation in a new outlook: A fractional derivative approach

NASA Astrophysics Data System (ADS)

Alquran, Marwan; Al-Khaled, Kamel; Sardar, Tridip; Chattopadhyay, Joydev

2015-11-01

The well-known Fisher equation with fractional derivative is considered to provide some characteristics of memory embedded into the system. The modified model is analyzed both analytically and numerically. A comparatively new technique residual power series method is used for finding approximate solutions of the modified Fisher model. A new technique combining Sinc-collocation and finite difference method is used for numerical study. The abundance of the bird species Phalacrocorax carbois considered as a test bed to validate the model outcome using estimated parameters. We conjecture non-diffusive and diffusive fractional Fisher equation represents the same dynamics in the interval (memory index, α ∈(0.8384 , 0.9986)). We also observe that when the value of memory index is close to zero, the solutions bifurcate and produce a wave-like pattern. We conclude that the survivability of the species increases for long range memory index. These findings are similar to Fisher observation and act in a similar fashion that advantageous genes do.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

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

Horowitz, Jordan M., E-mail: jordan.horowitz@umb.edu

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochasticmore » thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.« less

Integral approximations to classical diffusion and smoothed particle hydrodynamics

DOE PAGES

Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.

2014-12-31

The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary.more » The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. As a result, an immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.« less

Micro-heterogeneity and micro-rheological properties of high-viscosity barley beta-glucan solutions studied by diffusion wave spectroscopy (DWS)

USDA-ARS?s Scientific Manuscript database

Soluble fiber ß-glucan is one of the key dietary materials in healthy food products known for reducing serum cholesterol levels. The micro-structural heterogeneity and micro-rheology of high-viscosity barley ß-glucan solutions were investigated by the diffusing wave spectroscopy (DWS) technology. By...

Detection of the presence of Chlamydia trachomatis bacteria using diffusing wave spectroscopy with a small number of scatterers

NASA Astrophysics Data System (ADS)

Ulyanov, Sergey; Ulianova, Onega; Filonova, Nadezhda; Moiseeva, Yulia; Zaitsev, Sergey; Saltykov, Yury; Polyanina, Tatiana; Lyapina, Anna; Kalduzova, Irina; Larionova, Olga; Utz, Sergey; Feodorova, Valentina

2018-04-01

Theory of diffusing wave spectroscopy has been firstly adapted to the problem of rapid detection of Chlamydia trachomatis bacteria in blood samples of Chlamydia patients. Formula for correlation function of temporal fluctuations of speckle intensity is derived for the case of small number of scattering events. Dependence of bandwidth of spectrum on average number of scatterers is analyzed. Set-up for detection of the presence of C. trachomatis cells in aqueous suspension is designed. Good agreement between theoretical results and experimental data is shown. Possibility of detection of the presence of C. trachomatis cells in probing volume using diffusing wave spectroscopy with a small number of scatterers is successfully demonstrated for the first time.

Traveling wave solutions to a reaction-diffusion equation

NASA Astrophysics Data System (ADS)

Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y.

2009-07-01

In this paper, we restrict our attention to traveling wave solutions of a reaction-diffusion equation. Firstly we apply the Divisor Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to find a quasi-polynomial first integral of an explicit form to an equivalent autonomous system. Then through this first integral, we reduce the reaction-diffusion equation to a first-order integrable ordinary differential equation, and a class of traveling wave solutions is obtained accordingly. Comparisons with the existing results in the literature are also provided, which indicates that some analytical results in the literature contain errors. We clarify the errors and instead give a refined result in a simple and straightforward manner.

Transverse particle acceleration and diffusion in a planetary magnetic field

NASA Technical Reports Server (NTRS)

Barbosa, D. D.

1994-01-01

A general model of particle acceleration by plasma waves coupled with adiabatic radial diffusion in a planetary magnetic field is developed. The model assumes that a spectrum of lower hybird waves is present to resonantly accelerate ions transverse to the magnetic field. The steady state Green's function for the combined radial diffusion and wave acceleration equation is found in terms of a series expansion. The results provide a rigorous demonstration of how a quasi-Maxwellian distribution function is formed in the absence of particle collisons and elucidate the nature of turbulent heating of magnetospheric plasmas. The solution is applied to the magnetosphere of Neptune for which a number of examples are given illustrating how the spectrum of pickup N(+) ions from Triton evolves.

Neuronal calcium wave propagation varies with changes in endoplasmic reticulum parameters: a computer model

PubMed Central

Neymotin, Samuel A.; McDougal, Robert A.; Sherif, Mohamed A.; Fall, Christopher P.; Hines, Michael L.; Lytton, William W.

2015-01-01

Calcium (Ca2+) waves provide a complement to neuronal electrical signaling, forming a key part of a neuron’s second messenger system. We developed a reaction-diffusion model of an apical dendrite with diffusible inositol triphosphate (IP3), diffusible Ca2+, IP3 receptors (IP3Rs), endoplasmic reticulum (ER) Ca2+ leak, and ER pump (SERCA) on ER. Ca2+ is released from ER stores via IP3Rs upon binding of IP3 and Ca2+. This results in Ca2+-induced-Ca2+-release (CICR) and increases Ca2+ spread. At least two modes of Ca2+ wave spread have been suggested: a continuous mode based on presumed relative homogeneity of ER within the cell; and a pseudo-saltatory model where Ca2+ regeneration occurs at discrete points with diffusion between them. We compared the effects of three patterns of hypothesized IP3R distribution: 1. continuous homogeneous ER, 2. hotspots with increased IP3R density (IP3R hotspots), 3. areas of increased ER density (ER stacks). All three modes produced Ca2+ waves with velocities similar to those measured in vitro (~50–90µm /sec). Continuous ER showed high sensitivity to IP3R density increases, with time to onset reduced and speed increased. Increases in SERCA density resulted in opposite effects. The measures were sensitive to changes in density and spacing of IP3R hotspots and stacks. Increasing the apparent diffusion coefficient of Ca2+ substantially increased wave speed. An extended electrochemical model, including voltage gated calcium channels and AMPA synapses, demonstrated that membrane priming via AMPA stimulation enhances subsequent Ca2+ wave amplitude and duration. Our modeling suggests that pharmacological targeting of IP3Rs and SERCA could allow modulation of Ca2+ wave propagation in diseases where Ca2+ dysregulation has been implicated. PMID:25734493

Anomalous Diffusion Approximation of Risk Processes in Operational Risk of Non-Financial Corporations

NASA Astrophysics Data System (ADS)

Magdziarz, M.; Mista, P.; Weron, A.

2007-05-01

We introduce an approximation of the risk processes by anomalous diffusion. In the paper we consider the case, where the waiting times between successive occurrences of the claims belong to the domain of attraction of alpha -stable distribution. The relationship between the obtained approximation and the celebrated fractional diffusion equation is emphasised. We also establish upper bounds for the ruin probability in the considered model and give some numerical examples.

Results of a zonally truncated three-dimensional model of the Venus middle atmosphere

NASA Technical Reports Server (NTRS)

Newman, M.

1992-01-01

Although the equatorial rotational speed of the solid surface of Venus is only 4 m s(exp-1), the atmospheric rotational speed reaches a maximum of approximately 100 m s(exp-1) near the equatorial cloud top level (65 to 70 km). This phenomenon, known as superrotation, is the central dynamical problem of the Venus atmosphere. We report here the results of numerical simulations aimed at clarifying the mechanism for maintaining the equatorial cloud top rotation. Maintenance of an equatorial rotational speed maximum above the surface requires waves or eddies that systematically transport angular momentum against its zonal mean gradient. The zonally symmetric Hadley circulation is driven thermally and acts to reduce the rotational speed at the equatorial cloud top level; thus wave or eddy transport must counter this tendency as well as friction. Planetary waves arising from horizontal shear instability of the zonal flow (barotropic instability) could maintain the equatorial rotation by transporting angular momentum horizontally from midlatitudes toward the equator. Alternatively, vertically propagating waves could provide the required momentum source. The relative motion between the rotating atmosphere and the pattern of solar heating, which as a maximum where solar radiation is absorbed near the cloud tops, drives diurnal and semidiurnal thermal tides that propagate vertically away from the cloud top level. The effect of this wave propagation is to transport momentum toward the cloud top level at low latitudes and accelerate the mean zonal flow there. We employ a semispectral primitive equation model with a zonal mean flow and zonal wavenumbers 1 and 2. These waves correspond to the diurnal and semidiurnal tides, but they can also be excited by barotropic or baroclinic instability. Waves of higher wavenumbers and interactions between the waves are neglected. Symmetry about the equator is assumed, so the model applies to one hemisphere and covers the altitude range 30 to 110 km. Horizontal resolution is 1.5 deg latitude, and vertical resolution is 1.5 km. Solar and thermal infrared heating, based on Venus observations and calculations drive the model flow. Dissipation is accomplished mainly by Rayleigh friction, chosen to produce strong dissipation above 85 km in order to absorb upward propagating waves and limit extreme flow velocities there, yet to give very weak Rayleigh friction below 70 km; results in the cloud layer do not appear to be sensitive to the Rayleigh friction. The model also has weak vertical diffusion, and very weak horizontal diffusion, which has a smoothing effect on the flow only at the two grid points nearest the pole.

The effect of breaking gravity waves on the dynamics and chemistry of the mesosphere and lower thermosphere (invited review)

NASA Technical Reports Server (NTRS)

Garcia, R. R.

1986-01-01

The influence of breaking gravity waves on the dynamics and chemical composition of the 60 to 110 km region is investigated with a two dimensional model that includes a parameterization of gravity wave momentum deposition and diffusion. The dynamical model is described by Garcia and Solomon (1983) and Solomon and Garcia (1983) and includes a complete chemical scheme for the mesosphere and lower thermosphere. The parameterization of Lindzen (1981) is used to calculate the momentum deposited and the turbulent diffusion produced by the gravity waves. It is found that wave momentum deposition drives a very vigorous mean meridional circulation, produces a very cold summer mesopause and reverse the zonal wind jets above about 85 km. The seasonal variation of the turbulent diffusion coefficient is consistent with the behavior of mesospheric turbulences inferred from MST radar echoes. The large degree of consistency between model results and various types of dynamical and chemical data supports very strongly the hypothesis that breaking gravity waves play a major role in determining the zonally-averaged dynamical and chemical structure of the 60 to 110 km region of the atmosphere.

Monostable traveling waves for a time-periodic and delayed nonlocal reaction-diffusion equation

NASA Astrophysics Data System (ADS)

Li, Panxiao; Wu, Shi-Liang

2018-04-01

This paper is concerned with a time-periodic and delayed nonlocal reaction-diffusion population model with monostable nonlinearity. Under quasi-monotone or non-quasi-monotone assumptions, it is known that there exists a critical wave speed c_*>0 such that a periodic traveling wave exists if and only if the wave speed is above c_*. In this paper, we first prove the uniqueness of non-critical periodic traveling waves regardless of whether the model is quasi-monotone or not. Further, in the quasi-monotone case, we establish the exponential stability of non-critical periodic traveling fronts. Finally, we illustrate the main results by discussing two types of death and birth functions arising from population biology.

Selection of intracellular calcium patterns in a model with clustered Ca2+ release channels

NASA Astrophysics Data System (ADS)

Shuai, J. W.; Jung, P.

2003-03-01

A two-dimensional model is proposed for intracellular Ca2+ waves, which incorporates both the discrete nature of Ca2+ release sites in the endoplasmic reticulum membrane and the stochastic dynamics of the clustered inositol 1,4,5-triphosphate (IP3) receptors. Depending on the Ca2+ diffusion coefficient and concentration of IP3, various spontaneous Ca2+ patterns, such as calcium puffs, local waves, abortive waves, global oscillation, and tide waves, can be observed. We further investigate the speed of the global waves as a function of the IP3 concentration and the Ca2+ diffusion coefficient and under what conditions the spatially averaged Ca2+ response can be described by a simple set of ordinary differential equations.

Air-sea fluxes of momentum and mass in the presence of wind waves

NASA Astrophysics Data System (ADS)

Zülicke, Christoph

2010-05-01

An air-sea interaction model (ASIM) is developed including the effect of wind waves on momentum and mass transfer. This includes the derivation of profiles of dissipation rate, flow speed and concentration from a certain height to a certain depth. Simplified assumptions on the turbulent closure, skin - bulk matching and the spectral wave model allow for an analytic treatment. Particular emphasis was put on the inclusion of primary (gravity) waves and secondary (capillary-gravity) waves. The model was tuned to match wall-flow theory and data on wave height and slope. Growing waves reduce the air-side turbulent stress and lead to an increasing drag coefficient. In the sea, breaking waves inject turbulent kinetic energy and accelerate the transfer. Cross-reference with data on wave-related momentum and energy flux, dissipation rate and transfer velocity was sufficient. The evaluation of ASIM allowed for the analytical calculation of bulk formulae for the wind-dependent gas transfer velocity including information on the air-side momentum transfer (drag coefficient) and the sea-side gas transfer (Dalton number). The following regimes have been identified: the smooth waveless regime with a transfer velocity proportional to (wind) × (diffusion)2-3, the primary wave regime with a wind speed dependence proportional to (wind)1-4 × (diffusion)1-2-(waveage)1-4 and the secondary wave regime including a more-than-linear wind speed dependence like (wind)15-8 × (diffusion)1-2 × (waveage)5-8. These findings complete the current understanding of air-sea interaction for medium winds between 2 and 20 m s^-1.

Two-dimensional wave patterns of spreading depolarization: Retracting, re-entrant, and stationary waves

NASA Astrophysics Data System (ADS)

Dahlem, Markus A.; Graf, Rudolf; Strong, Anthony J.; Dreier, Jens P.; Dahlem, Yuliya A.; Sieber, Michaela; Hanke, Wolfgang; Podoll, Klaus; Schöll, Eckehard

2010-06-01

We present spatio-temporal characteristics of spreading depolarizations (SD) in two experimental systems: retracting SD wave segments observed with intrinsic optical signals in chicken retina, and spontaneously occurring re-entrant SD waves that repeatedly spread across gyrencephalic feline cortex observed by laser speckle flowmetry. A mathematical framework of reaction-diffusion systems with augmented transmission capabilities is developed to explain the emergence and transitions between these patterns. Our prediction is that the observed patterns are reaction-diffusion patterns controlled and modulated by weak nonlocal coupling such as long-range, time-delayed, and global coupling. The described spatio-temporal characteristics of SD are of important clinical relevance under conditions of migraine and stroke. In stroke, the emergence of re-entrant SD waves is believed to worsen outcome. In migraine, retracting SD wave segments cause neurological symptoms and transitions to stationary SD wave patterns may cause persistent symptoms without evidence from noninvasive imaging of infarction.

The OPGT/MJS plasma wave science team

NASA Technical Reports Server (NTRS)

Scarf, F. L.

1972-01-01

Some properties of a model magnetosphere for Saturn were studied in order to determine the bounds that can be set on surface field strength and trapped particle population. The primary observational constraint was that nonthermal radiation similar to the Jovian radio emissions must be undetectable from Earth. It is argued that for a Saturn surface field of approximately one gauss, particles that are energized as they diffuse in from the magnetopause with conservation of magnetic moment will produce synchrotron radiation levels that are undetectable at a range of 9.5 AU. The plasma instabilities that heat the oncoming wind particles at the bow shock and others that can limit the stably-trapped flux levels are also discussed.

Using MLT Composition Observations to Evaluate Transport in a Comprehensive High Top Model

NASA Astrophysics Data System (ADS)

Smith, A. K.

2016-12-01

Gravity waves play an outsized role in the MLT: driving the mean meridional circulation, exerting a large degree of control over the mean winds and seasonal variations in temperature, and leading to diffusive vertical transport of heat and trace species. These waves are represented using a parameterization in the NCAR Whole Atmosphere Community Climate Model (WACCM), as in many other GCMs. To evaluate their impact, we need to consider not just the mean temperature and wind but the distributions of trace species that are affected by advection due to resolved winds and waves and diffusion associated with gravity wave dissipation. The responses of chemical species to changes in the gravity wave forcing are complex and sometimes unexpected. Transport and diffusion simultaneously affect all species and the heat and momentum budgets; subsequent interactions, and the strong dependence of reaction rates on temperature, affect the net impact of transport on the composition. In evaluating the model, we evaluate the simulations using a range of available observations of composition, including O, O3, CO, CO2, NO, NO2, OH, and H2O.

Modeling of Wave Spectrum and Wave Breaking Statistics Based on Balance Equation

NASA Astrophysics Data System (ADS)

Irisov, V.

2012-12-01

Surface roughness and foam coverage are the parameters determining microwave emissivity of sea surface in a wide range of wind. Existing empirical wave spectra are not associated with wave breaking statistics although physically they are closely related. We propose a model of sea surface based on the balance of three terms: wind input, dissipation, and nonlinear wave-wave interaction. It provides an insight on wave generation, interaction, and dissipation - very important parameters for understanding of wave development under changing oceanic and atmospheric conditions. The wind input term is the best known among all three. For our analysis we assume a wind input term as it was proposed by Plant [1982] and consider modification necessary to do to account for proper interaction of long fast waves with wind. For long gravity waves (longer than 15-30 cm) the dissipation term can be related to the wave breaking with whitecaps, as it was shown by Kudryavtsev et al. [2003], so we assume the cubic dependence of dissipation term on wind. It implies certain limitations on the spectrum shape. The most difficult is to estimate the term describing nonlinear wave-wave interaction. Hasselmann [1962] and Zakharov [1999] developed theory of 4-wave interaction, but the resulting equation requires at least 3-fold integration over wavenumbers at each time step of integration of balance equation, which makes it difficult for direct numerical modeling. It is desirable to use an approximation of wave-wave interaction term, which preserves wave action, energy, and momentum, and can be easily estimated during time integration of balance equation. Zakharov and Pushkarev [1999] proposed the diffusion approximation of the wave interaction term and showed that it can be used for estimate of wave spectrum. We believe their assumption that wave-wave interaction is the dominant factor in forming the wave spectrum does not agree with the observations made by Hwang and Sletten [2008]. Finally we consider modifications of the model equation, which can be done to describe gravity-capillary and capillary waves. An obvious correction is to add viscous dissipation. A little less obvious is a transition from 4-wave to 3-wave interaction. The model allows one to include easily generation of parasitic capillary waves as it was proposed by Kudryavtsev et al. [2003]. A modification of dissipation term can explain an "overshoot" phenomenon observed in JONSWAP spectrum. These examples demonstrate that the proposed model is quite flexible and can be used to account for various physical phenomena. The resulting balance equation is easy to integrate using a personal computer and necessity of its numerical solution is paid by the model flexibility and better physical background compared with empirical spectra. References Hasselmann, K., J. Fluid Mech., 12, pp.481-500, 1962. Hwang, P., and M. Sletten, J. Geophys. Res., 113, doi:10.1029/2007JC004277, 2008. Kudryavtsev, V., et al., J. Geophys. Res., 108 (C3), doi:10.1029/2001JC001003, 2003. Plant, W. J., J. Geophys. Res., vol. 87, pp. 1961-1967, 1982. Zakharov, V., and A. Pushkarev, Nonlinear Processes in Geophysics, 6, pp.1-10, 1999. Zakharov, V., Eur. J. Mech. B/Fluids, 18, pp.327-344, 1999.

Retina imaging system with adaptive optics for the eye with or without myopia

NASA Astrophysics Data System (ADS)

Li, Chao; Xia, Mingliang; Jiang, Baoguang; Mu, Quanquan; Chen, Shaoyuan; Xuan, Li

2009-04-01

An adaptive optics system for the retina imaging is introduced in the paper. It can be applied to the eye with myopia from 0 to 6 diopters without any adjustment of the system. A high-resolution liquid crystal on silicon (LCOS) device is used as the wave-front corrector. The aberration is detected by a Shack-Harmann wave-front sensor (HASO) that has a Root Mean Square (RMS) measurement accuracy of λ/100 ( λ = 0.633 μm). And an equivalent scale model eye is constructed with a short focal length lens (˜18 mm) and a diffuse reflection object (paper screen) as the retina. By changing the distance between the paper screen and the lens, we simulate the eye with larger diopters than 5 and the depth of field. The RMS value both before and after correction is obtained by the wave-front sensor. After correction, the system reaches the diffraction-limited resolution approximately 230 cycles/mm at the object space. It is proved that if the myopia is smaller than 6 diopters and the depth of field is between -40 and +50 mm, the system can correct the aberration very well.

Generalized extended Navier-Stokes theory: multiscale spin relaxation in molecular fluids.

PubMed

Hansen, J S

2013-09-01

This paper studies the relaxation of the molecular spin angular velocity in the framework of generalized extended Navier-Stokes theory. Using molecular dynamics simulations, it is shown that for uncharged diatomic molecules the relaxation time decreases with increasing molecular moment of inertia per unit mass. In the regime of large moment of inertia the fast relaxation is wave-vector independent and dominated by the coupling between spin and the fluid streaming velocity, whereas for small inertia the relaxation is slow and spin diffusion plays a significant role. The fast wave-vector-independent relaxation is also observed for highly packed systems. The transverse and longitudinal spin modes have, to a good approximation, identical relaxation, indicating that the longitudinal and transverse spin viscosities have same value. The relaxation is also shown to be isomorphic invariant. Finally, the effect of the coupling in the zero frequency and wave-vector limit is quantified by a characteristic length scale; if the system dimension is comparable to this length the coupling must be included into the fluid dynamical description. It is found that the length scale is independent of moment of inertia but dependent on the state point.

On the Linearly-Balanced Kinetic Energy Spectrum

NASA Technical Reports Server (NTRS)

Lu, Huei,-Iin; Robertson, F. R.

1999-01-01

It is well known that the earth's atmospheric motion can generally be characterized by the two dimensional quasi-geostrophic approximation, in which the constraints on global integrals of kinetic energy, entrophy and potential vorticity play very important roles in redistributing the wave energy among different scales of motion. Assuming the hypothesis of Kolmogrov's local isotropy, derived a -3 power law of the equilibrium two-dimensional kinetic energy spectrum that entails constant vorticity and zero energy flows from the energy-containing wave number up to the viscous cutoff. In his three dimensional quasi-geostrophic theory, showed that the spectrum function of the vertical scale turbulence - expressible in terms of the available potential energy - possesses the same power law as the two dimensional kinetic energy spectrum. As the slope of kinetic energy spectrum in the inertial range is theoretically related to the predictability of the synoptic scales (Lorenz, 1969), many general circulation models includes a horizontal diffusion to provide reasonable kinetic energy spectra, although the actual power law exhibited in the atmospheric general circulation is controversial. Note that in either the atmospheric modeling or the observational analyses, the proper choice of wave number Index to represent the turbulence scale Is the degree of the Legendre polynomial.

Evidence of negative-index refraction in nonlinear chemical waves.

PubMed

Yuan, Xujin; Wang, Hongli; Ouyang, Qi

2011-05-06

The negative index of refraction of nonlinear chemical waves has become a recent focus in nonlinear dynamics researches. Theoretical analysis and computer simulations have predicted that the negative index of refraction can occur on the interface between antiwaves and normal waves in a reaction-diffusion (RD) system. However, no experimental evidence has been found so far. In this Letter, we report our experimental design in searching for such a phenomenon in a chlorite-iodide-malonic acid (CIMA) reaction. Our experimental results demonstrate that competition between waves and antiwaves at their interface determines the fate of the wave interaction. The negative index of refraction was only observed when the oscillation frequency of a normal wave is significantly smaller than that of the antiwave. All experimental results were supported by simulations using the Lengyel-Epstein RD model which describes the CIMA reaction-diffusion system.

Convective instability and boundary driven oscillations in a reaction-diffusion-advection model

NASA Astrophysics Data System (ADS)

Vidal-Henriquez, Estefania; Zykov, Vladimir; Bodenschatz, Eberhard; Gholami, Azam

2017-10-01

In a reaction-diffusion-advection system, with a convectively unstable regime, a perturbation creates a wave train that is advected downstream and eventually leaves the system. We show that the convective instability coexists with a local absolute instability when a fixed boundary condition upstream is imposed. This boundary induced instability acts as a continuous wave source, creating a local periodic excitation near the boundary, which initiates waves travelling both up and downstream. To confirm this, we performed analytical analysis and numerical simulations of a modified Martiel-Goldbeter reaction-diffusion model with the addition of an advection term. We provide a quantitative description of the wave packet appearing in the convectively unstable regime, which we found to be in excellent agreement with the numerical simulations. We characterize this new instability and show that in the limit of high advection speed, it is suppressed. This type of instability can be expected for reaction-diffusion systems that present both a convective instability and an excitable regime. In particular, it can be relevant to understand the signaling mechanism of the social amoeba Dictyostelium discoideum that may experience fluid flows in its natural habitat.

Flow regimes for fluid injection into a confined porous medium

DOE PAGES

Zheng, Zhong; Guo, Bo; Christov, Ivan C.; ...

2015-02-24

We report theoretical and numerical studies of the flow behaviour when a fluid is injected into a confined porous medium saturated with another fluid of different density and viscosity. For a two-dimensional configuration with point source injection, a nonlinear convection–diffusion equation is derived to describe the time evolution of the fluid–fluid interface. In the early time period, the fluid motion is mainly driven by the buoyancy force and the governing equation is reduced to a nonlinear diffusion equation with a well-known self-similar solution. In the late time period, the fluid flow is mainly driven by the injection, and the governingmore » equation is approximated by a nonlinear hyperbolic equation that determines the global spreading rate; a shock solution is obtained when the injected fluid is more viscous than the displaced fluid, whereas a rarefaction wave solution is found when the injected fluid is less viscous. In the late time period, we also obtain analytical solutions including the diffusive term associated with the buoyancy effects (for an injected fluid with a viscosity higher than or equal to that of the displaced fluid), which provide the structure of the moving front. Numerical simulations of the convection–diffusion equation are performed; the various analytical solutions are verified as appropriate asymptotic limits, and the transition processes between the individual limits are demonstrated.« less

Symmetric rotating-wave approximation for the generalized single-mode spin-boson system

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

Albert, Victor V.; Scholes, Gregory D.; Brumer, Paul

2011-10-15

The single-mode spin-boson model exhibits behavior not included in the rotating-wave approximation (RWA) in the ultra and deep-strong coupling regimes, where counter-rotating contributions become important. We introduce a symmetric rotating-wave approximation that treats rotating and counter-rotating terms equally, preserves the invariances of the Hamiltonian with respect to its parameters, and reproduces several qualitative features of the spin-boson spectrum not present in the original rotating-wave approximation both off-resonance and at deep-strong coupling. The symmetric rotating-wave approximation allows for the treatment of certain ultra- and deep-strong coupling regimes with similar accuracy and mathematical simplicity as does the RWA in the weak-coupling regime.more » Additionally, we symmetrize the generalized form of the rotating-wave approximation to obtain the same qualitative correspondence with the addition of improved quantitative agreement with the exact numerical results. The method is readily extended to higher accuracy if needed. Finally, we introduce the two-photon parity operator for the two-photon Rabi Hamiltonian and obtain its generalized symmetric rotating-wave approximation. The existence of this operator reveals a parity symmetry similar to that in the Rabi Hamiltonian as well as another symmetry that is unique to the two-photon case, providing insight into the mathematical structure of the two-photon spectrum, significantly simplifying the numerics, and revealing some interesting dynamical properties.« less

Amplitude equations for breathing spiral waves in a forced reaction-diffusion system

NASA Astrophysics Data System (ADS)

Ghosh, Pushpita; Ray, Deb Shankar

2011-09-01

Based on a multiple scale analysis of a forced reaction-diffusion system leading to amplitude equations, we explain the existence of spiral wave and its photo-induced spatiotemporal behavior in chlorine dioxide-iodine-malonic acid system. When the photo-illumination intensity is modulated, breathing of spiral is observed in which the period of breathing is identical to the period of forcing. We have also derived the condition for breakup and suppression of spiral wave by periodic illumination. The numerical simulations agree well with our analytical treatment.

Determination of rock-sample anisotropy from P- and S-wave traveltime inversion

NASA Astrophysics Data System (ADS)

Pšenčík, Ivan; Růžek, Bohuslav; Lokajíček, Tomáš; Svitek, Tomáš

2018-04-01

We determine anisotropy of a rock sample from laboratory measurements of P- and S-wave traveltimes using weak-anisotropy approximation and parametri-zation of the medium by a special set of anisotropy parameters. For the traveltime inversion we use first-order velocity expressions in the weak-anisotropy approximation, which allow to deal with P and S waves separately. Each wave is described by 15 anisotropy parameters, 9 of which are common for both waves. The parameters allow an approximate construction of separate P- or common S-wave phase-velocity surfaces. Common S wave concept is used to simplify the treatment of S waves. In order to obtain all 21 anisotropy parameters, P- and S-wave traveltimes must be inverted jointly. The proposed inversion scheme has several advantages. As a consequence of the use of weak-anisotropy approximation and assumed homogeneity of the rock sample, equations used for the inversion are linear. Thus the inversion procedure is non-iterative. In the approximation used, phase and ray velocities are equal in their magnitude and direction. Thus analysis whether the measured velocity is the ray or phase velocity is unnecessary. Another advantage of the proposed inversion scheme is that, thanks to the use of the common S-wave concept, it does not require identification of S-wave modes. It is sufficient to know the two S-wave traveltimes without specification, to which S-wave mode they belong. The inversion procedure is tested first on synthetic traveltimes and then used for the inversion of traveltimes measured in laboratory. In both cases, we perform first the inversion of P-wave traveltimes alone and then joint inversion of P- and S-wave traveltimes, and compare the results.

Revisiting the time until fixation of a neutral mutant in a finite population - A coalescent theory approach.

PubMed

Greenbaum, Gili

2015-09-07

Evaluation of the time scale of the fixation of neutral mutations is crucial to the theoretical understanding of the role of neutral mutations in evolution. Diffusion approximations of the Wright-Fisher model are most often used to derive analytic formulations of genetic drift, as well as for the time scales of the fixation of neutral mutations. These approximations require a set of assumptions, most notably that genetic drift is a stochastic process in a continuous allele-frequency space, an assumption appropriate for large populations. Here equivalent approximations are derived using a coalescent theory approach which relies on a different set of assumptions than the diffusion approach, and adopts a discrete allele-frequency space. Solutions for the mean and variance of the time to fixation of a neutral mutation derived from the two approaches converge for large populations but slightly differ for small populations. A Markov chain analysis of the Wright-Fisher model for small populations is used to evaluate the solutions obtained, showing that both the mean and the variance are better approximated by the coalescent approach. The coalescence approximation represents a tighter upper-bound for the mean time to fixation than the diffusion approximation, while the diffusion approximation and coalescence approximation form an upper and lower bound, respectively, for the variance. The converging solutions and the small deviations of the two approaches strongly validate the use of diffusion approximations, but suggest that coalescent theory can provide more accurate approximations for small populations. Copyright © 2015 Elsevier Ltd. All rights reserved.

The equilibrium-diffusion limit for radiation hydrodynamics

DOE PAGES

Ferguson, J. M.; Morel, J. E.; Lowrie, R.

2017-07-27

The equilibrium-diffusion approximation (EDA) is used to describe certain radiation-hydrodynamic (RH) environments. When this is done the RH equations reduce to a simplified set of equations. The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibrium-diffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both first-order accurate with transport corrections occurring at second order. Having established the EDA’s first-order accuracy we then analyze the grey nonequilibrium-diffusion approximation and the grey Eddington approximation and show that they both preserve this first-order accuracy.more » Further, these approximations preserve the EDA’s first-order accuracy when made in either the comoving-frame (CMF) or the lab-frame (LF). And while analyzing the Eddington approximation, we found that the CMF and LF radiation-source equations are equivalent when neglecting O(β 2) terms and compared in the LF. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this first-order accuracy will not retain the correct equilibrium-diffusion solutions. As a practical example, we show that nonequilibrium-diffusion radiative-shock solutions devolve to equilibrium-diffusion solutions when the asymptotic parameter is small.« less

Galactic civilizations: Population dynamics and interstellar diffusion

NASA Technical Reports Server (NTRS)

Newman, W. I.; Sagan, C.

1978-01-01

The interstellar diffusion of galactic civilizations is reexamined by potential theory; both numerical and analytical solutions are derived for the nonlinear partial differential equations which specify a range of relevant models, drawn from blast wave physics, soil science, and, especially, population biology. An essential feature of these models is that, for all civilizations, population growth must be limited by the carrying capacity of the environment. Dispersal is fundamentally a diffusion process; a density-dependent diffusivity describes interstellar emigration. Two models are considered: the first describing zero population growth (ZPG), and the second which also includes local growth and saturation of a planetary population, and for which an asymptotic traveling wave solution is found.

Quasisolitons in self-diffusive excitable systems, or Why asymmetric diffusivity obeys the Second Law

PubMed Central

Biktashev, V. N.; Tsyganov, M. A.

2016-01-01

Solitons, defined as nonlinear waves which can reflect from boundaries or transmit through each other, are found in conservative, fully integrable systems. Similar phenomena, dubbed quasi-solitons, have been observed also in dissipative, “excitable” systems, either at finely tuned parameters (near a bifurcation) or in systems with cross-diffusion. Here we demonstrate that quasi-solitons can be robustly observed in excitable systems with excitable kinetics and with self-diffusion only. This includes quasi-solitons of fixed shape (like KdV solitons) or envelope quasi-solitons (like NLS solitons). This can happen in systems with more than two components, and can be explained by effective cross-diffusion, which emerges via adiabatic elimination of a fast but diffusing component. We describe here a reduction procedure can be used for the search of complicated wave regimes in multi-component, stiff systems by studying simplified, soft systems. PMID:27491430

Modeling cell-cycle synchronization during embryogenesis in Xenopus laevis

NASA Astrophysics Data System (ADS)

McIsaac, R. Scott; Huang, K. C.; Sengupta, Anirvan; Wingreen, Ned

2010-03-01

A widely conserved aspect of embryogenesis is the ability to synchronize nuclear divisions post-fertilization. How is synchronization achieved? Given a typical protein diffusion constant of 10 μm^2sec, and an embryo length of 1mm, it would take diffusion many hours to propagate a signal across the embryo. Therefore, synchrony cannot be attained by diffusion alone. We hypothesize that known autocatalytic reactions of cell-cycle components make the embryo an ``active medium'' in which waves propagate much faster than diffusion, enforcing synchrony. We report on robust spatial synchronization of components of the core cell cycle circuit based on a mathematical model previously determined by in vitro experiments. In vivo, synchronized divisions are preceded by a rapid calcium wave that sweeps across the embryo. Experimental evidence supports the hypothesis that increases in transient calcium levels lead to derepression of a negative feedback loop, allowing cell divisions to start. Preliminary results indicate a novel relationship between the speed of the initial calcium wave and the ability to achieve synchronous cell divisions.

Rossby wave activity in a two-dimensional model - Closure for wave driving and meridional eddy diffusivity

NASA Technical Reports Server (NTRS)

Hitchman, Matthew H.; Brasseur, Guy

1988-01-01

A parameterization of the effects of Rossby waves in the middle atmosphere is proposed for use in two-dimensional models. By adding an equation for conservation of Rossby wave activity, closure is obtained for the meridional eddy fluxes and body force due to Rossby waves. Rossby wave activity is produced in a climatological fashion at the tropopause, is advected by a group velocity which is determined solely by model zonal winds, and is absorbed where it converges. Absorption of Rossby wave activity causes both an easterly torque and an irreversible mixing of potential vorticity, represented by the meridional eddy diffusivity, K(yy). The distribution of Rossby wave driving determines the distribution of K(yy), which is applied to all of the chemical constituents. This provides a self-consistent coupling of the wave activity with the winds, tracer distributions and the radiative field. Typical winter stratospheric values for K(yy) of 2 million sq m/sec are obtained. Poleward tracer advection is enhanced and meridional tracer gradients are reduced where Rossby wave activity is absorbed in the model.

Tensor Based Representation and Analysis of Diffusion-Weighted Magnetic Resonance Images

ERIC Educational Resources Information Center

Barmpoutis, Angelos

2009-01-01

Cartesian tensor bases have been widely used to model spherical functions. In medical imaging, tensors of various orders can approximate the diffusivity function at each voxel of a diffusion-weighted MRI data set. This approximation produces tensor-valued datasets that contain information about the underlying local structure of the scanned tissue.…

Exact diffusion constant in a lattice-gas wind-tree model on a Bethe lattice

NASA Astrophysics Data System (ADS)

Zhang, Guihua; Percus, J. K.

1992-02-01

Kong and Cohen [Phys. Rev. B 40, 4838 (1989)] obtained the diffusion constant of a lattice-gas wind-tree model in the Boltzmann approximation. The result is consistent with computer simulations for low tree concentration. In this Brief Report we find the exact diffusion constant of the model on a Bethe lattice, which turns out to be identical with the Kong-Cohen and Gunn-Ortuño results. Our interpretation is that the Boltzmann approximation is exact for this type of diffusion on a Bethe lattice in the same sense that the Bethe-Peierls approximation is exact for the Ising model on a Bethe lattice.

Self-organized behavior of modeled shoreline shapes

NASA Astrophysics Data System (ADS)

Ashton, A.; Murray, A. B.

2003-04-01

Whenever waves approach a coast and break at oblique angles, they drive a current along the shore. This current, along with wave-induced sediment suspension, transports relatively large amounts of sediment, affecting the shape and evolution of a coastline. Traditionally, researchers have assumed that alongshore sediment transport will diffuse, or smooth, bumps along a shoreline. Recent research, however, shows that when the angle between wave crests in deep water and the shoreline is sufficiently high (greater than approximately 45 degrees), a shoreline is unstable. Linear stability analysis does not predict that this instability will cause a preferred wavelength of shoreline perturbation growth or that organized patterns will emerge. However, a simple numerical model of shoreline change shows those when there is a predominance of high angle waves approaching a shoreline, finite-amplitude features will develop that interact with each other and increase in wavelength over time, translating in the direction of net alongshore sediment transport. Some of these simulated features resemble naturally occurring shoreline features, such as 'alongshore sandwaves', 'ords', 'cuspate spits', and 'cuspate forelands'. By varying two wave climate parameters, one describing the relative dominance of waves approaching at high angles and the other controlling the signs of the approach angle of incoming waves (i.e., the asymmetry of waves approaching from the right vs. the left), we investigate how the attributes of the input wave climate determine the aspect ratio and characteristic form of the simulated features. Varying these two parameters also affects the wavelength of the initially fastest growing perturbation. By tracking the average wavelength of simulated features, which increases over time for all simulations, we show that more complicated phenomena, such as rapid period doubling, can dominate simulated shoreline evolution. These rich behaviors result from large-scale emergent interactions. Although the wave distribution determines the character of shoreline features, their specific configuration and evolution is sensitively dependant on both initial conditions and the stochastic sequencing of wave approach angles.

Comparison of the Radiative Two-Flux and Diffusion Approximations

NASA Technical Reports Server (NTRS)

Spuckler, Charles M.

2006-01-01

Approximate solutions are sometimes used to determine the heat transfer and temperatures in a semitransparent material in which conduction and thermal radiation are acting. A comparison of the Milne-Eddington two-flux approximation and the diffusion approximation for combined conduction and radiation heat transfer in a ceramic material was preformed to determine the accuracy of the diffusion solution. A plane gray semitransparent layer without a substrate and a non-gray semitransparent plane layer on an opaque substrate were considered. For the plane gray layer the material is semitransparent for all wavelengths and the scattering and absorption coefficients do not vary with wavelength. For the non-gray plane layer the material is semitransparent with constant absorption and scattering coefficients up to a specified wavelength. At higher wavelengths the non-gray plane layer is assumed to be opaque. The layers are heated on one side and cooled on the other by diffuse radiation and convection. The scattering and absorption coefficients were varied. The error in the diffusion approximation compared to the Milne-Eddington two flux approximation was obtained as a function of scattering coefficient and absorption coefficient. The percent difference in interface temperatures and heat flux through the layer obtained using the Milne-Eddington two-flux and diffusion approximations are presented as a function of scattering coefficient and absorption coefficient. The largest errors occur for high scattering and low absorption except for the back surface temperature of the plane gray layer where the error is also larger at low scattering and low absorption. It is shown that the accuracy of the diffusion approximation can be improved for some scattering and absorption conditions if a reflectance obtained from a Kubelka-Munk type two flux theory is used instead of a reflection obtained from the Fresnel equation. The Kubelka-Munk reflectance accounts for surface reflection and radiation scattered back by internal scattering sites while the Fresnel reflection only accounts for surface reflections.

Mode-converted diffuse ultrasonic backscatter.

PubMed

Hu, Ping; Kube, Christopher M; Koester, Lucas W; Turner, Joseph A

2013-08-01

Diffuse ultrasonic backscatter describes the scattering of elastic waves from interfaces within heterogeneous materials. Previously, theoretical models have been developed for the diffuse backscatter of longitudinal-to-longitudinal (L-L) wave scattering within polycrystalline materials. Following a similar formalism, a mode-conversion scattering model is presented here to quantify the component of an incident longitudinal wave that scatters and is converted to a transverse (shear) wave within a polycrystalline sample. The model is then used to fit experimental measurements associated with a pitch-catch transducer configuration performed using a sample of 1040 steel. From these measurements, an average material correlation length is determined. This value is found to be in agreement with results from L-L scattering measurements and is on the order of the grain size as determined from optical micrographs. Mode-converted ultrasonic backscatter is influenced much less by the front-wall reflection than an L-L measurement and it provides additional microstructural information that is not accessible in any other manner.

Notch-mediated lateral inhibition regulates proneural wave propagation when combined with EGF-mediated reaction diffusion

PubMed Central

Sato, Makoto; Yasugi, Tetsuo; Minami, Yoshiaki; Miura, Takashi; Nagayama, Masaharu

2016-01-01

Notch-mediated lateral inhibition regulates binary cell fate choice, resulting in salt and pepper patterns during various developmental processes. However, how Notch signaling behaves in combination with other signaling systems remains elusive. The wave of differentiation in the Drosophila visual center or “proneural wave” accompanies Notch activity that is propagated without the formation of a salt and pepper pattern, implying that Notch does not form a feedback loop of lateral inhibition during this process. However, mathematical modeling and genetic analysis clearly showed that Notch-mediated lateral inhibition is implemented within the proneural wave. Because partial reduction in EGF signaling causes the formation of the salt and pepper pattern, it is most likely that EGF diffusion cancels salt and pepper pattern formation in silico and in vivo. Moreover, the combination of Notch-mediated lateral inhibition and EGF-mediated reaction diffusion enables a function of Notch signaling that regulates propagation of the wave of differentiation. PMID:27535937

Solar Wind Strahl Broadening by Self-Generated Plasma Waves

NASA Technical Reports Server (NTRS)

Pavan, J.; Vinas, A. F.; Yoon, P. H.; Ziebell, L. F.; Gaelzer, R.

2013-01-01

This Letter reports on the results of numerical simulations which may provide a possible explanation for the strahl broadening during quiet solar conditions. The relevant processes involved in the broadening are due to kinetic quasi-linear wave-particle interaction. Making use of static analytical electron distribution in an inhomogeneous field, it is found that self-generated electrostatic waves at the plasma frequency, i.e., Langmuir waves, are capable of scattering the strahl component, resulting in energy and pitch-angle diffusion that broadens its velocity distribution significantly. The present theoretical results provide an alternative or complementary explanation to the usual whistler diffusion scenario, suggesting that self-induced electrostatic waves at the plasma frequency might play a key role in broadening the solar wind strahl during quiet solar conditions.

Position-dependent radiative transfer as a tool for studying Anderson localization: Delay time, time-reversal and coherent backscattering

NASA Astrophysics Data System (ADS)

van Tiggelen, B. A.; Skipetrov, S. E.; Page, J. H.

2017-05-01

Previous work has established that the localized regime of wave transport in open media is characterized by a position-dependent diffusion coefficient. In this work we study how the concept of position-dependent diffusion affects the delay time, the transverse confinement, the coherent backscattering, and the time reversal of waves. Definitions of energy transport velocity of localized waves are proposed. We start with a phenomenological model of radiative transfer and then present a novel perturbational approach based on the self-consistent theory of localization. The latter allows us to obtain results relevant for realistic experiments in disordered quasi-1D wave guides and 3D slabs.

Parameterization of planetary wave breaking in the middle atmosphere

NASA Technical Reports Server (NTRS)

Garcia, Rolando R.

1991-01-01

A parameterization of planetary wave breaking in the middle atmosphere has been developed and tested in a numerical model which includes governing equations for a single wave and the zonal-mean state. The parameterization is based on the assumption that wave breaking represents a steady-state equilibrium between the flux of wave activity and its dissipation by nonlinear processes, and that the latter can be represented as linear damping of the primary wave. With this and the additional assumption that the effect of breaking is to prevent further amplitude growth, the required dissipation rate is readily obtained from the steady-state equation for wave activity; diffusivity coefficients then follow from the dissipation rate. The assumptions made in the derivation are equivalent to those commonly used in parameterizations for gravity wave breaking, but the formulation in terms of wave activity helps highlight the central role of the wave group velocity in determining the dissipation rate. Comparison of model results with nonlinear calculations of wave breaking and with diagnostic determinations of stratospheric diffusion coefficients reveals remarkably good agreement, and suggests that the parameterization could be useful for simulating inexpensively, but realistically, the effects of planetary wave transport.

Fixed node diffusion Monte Carlo using a genetic algorithm: a study of the CO-(4)He(N) complex, N = 1…10.

PubMed

Ramilowski, Jordan A; Farrelly, David

2012-06-14

The diffusion Monte Carlo (DMC) method is a widely used algorithm for computing both ground and excited states of many-particle systems; for states without nodes the algorithm is numerically exact. In the presence of nodes approximations must be introduced, for example, the fixed-node approximation. Recently we have developed a genetic algorithm (GA) based approach which allows the computation of nodal surfaces on-the-fly [Ramilowski and Farrelly, Phys. Chem. Chem. Phys., 2010, 12, 12450]. Here GA-DMC is applied to the computation of rovibrational states of CO-(4)He(N) complexes with N≤ 10. These complexes have been the subject of recent high resolution microwave and millimeter-wave studies which traced the onset of microscopic superfluidity in a doped (4)He droplet, one atom at a time, up to N = 10 [Surin et al., Phys. Rev. Lett., 2008, 101, 233401; Raston et al., Phys. Chem. Chem. Phys., 2010, 12, 8260]. The frequencies of the a-type (microwave) series, which correlate with end-over-end rotation in the CO-(4)He dimer, decrease from N = 1 to 3 and then smoothly increase. This signifies the transition from a molecular complex to a quantum solvated system. The frequencies of the b-type (millimeter-wave) series, which evolves from free rotation of the rigid CO molecule, initially increase from N = 0 to N∼ 6 before starting to decrease with increasing N. An interesting feature of the b-type series, originally observed in the high resolution infra-red (IR) experiments of Tang and McKellar [J. Chem. Phys., 2003, 119, 754] is that, for N = 7, two lines are observed. The GA-DMC algorithm is found to be in good agreement with experimental results and possibly detects the small (∼0.7 cm(-1)) splitting in the b-series line at N = 7. Advantages and disadvantages of GA-DMC are discussed.

Numerical Tests and Properties of Waves in Radiating Fluids

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

Johnson, B M; Klein, R I

2009-09-03

We discuss the properties of an analytical solution for waves in radiating fluids, with a view towards its implementation as a quantitative test of radiation hydrodynamics codes. A homogeneous radiating fluid in local thermodynamic equilibrium is periodically driven at the boundary of a one-dimensional domain, and the solution describes the propagation of the waves thus excited. Two modes are excited for a given driving frequency, generally referred to as a radiative acoustic wave and a radiative diffusion wave. While the analytical solution is well known, several features are highlighted here that require care during its numerical implementation. We compare themore » solution in a wide range of parameter space to a numerical integration with a Lagrangian radiation hydrodynamics code. Our most significant observation is that flux-limited diffusion does not preserve causality for waves on a homogeneous background.« less

Magnetospheric Multiscale observations of large-amplitude, parallel, electrostatic waves associated with magnetic reconnection at the magnetopause

NASA Astrophysics Data System (ADS)

Ergun, R. E.; Holmes, J. C.; Goodrich, K. A.; Wilder, F. D.; Stawarz, J. E.; Eriksson, S.; Newman, D. L.; Schwartz, S. J.; Goldman, M. V.; Sturner, A. P.; Malaspina, D. M.; Usanova, M. E.; Torbert, R. B.; Argall, M.; Lindqvist, P.-A.; Khotyaintsev, Y.; Burch, J. L.; Strangeway, R. J.; Russell, C. T.; Pollock, C. J.; Giles, B. L.; Dorelli, J. J. C.; Avanov, L.; Hesse, M.; Chen, L. J.; Lavraud, B.; Le Contel, O.; Retino, A.; Phan, T. D.; Eastwood, J. P.; Oieroset, M.; Drake, J.; Shay, M. A.; Cassak, P. A.; Nakamura, R.; Zhou, M.; Ashour-Abdalla, M.; André, M.

2016-06-01

We report observations from the Magnetospheric Multiscale satellites of large-amplitude, parallel, electrostatic waves associated with magnetic reconnection at the Earth's magnetopause. The observed waves have parallel electric fields (E||) with amplitudes on the order of 100 mV/m and display nonlinear characteristics that suggest a possible net E||. These waves are observed within the ion diffusion region and adjacent to (within several electron skin depths) the electron diffusion region. They are in or near the magnetosphere side current layer. Simulation results support that the strong electrostatic linear and nonlinear wave activities appear to be driven by a two stream instability, which is a consequence of mixing cold (<10 eV) plasma in the magnetosphere with warm (~100 eV) plasma from the magnetosheath on a freshly reconnected magnetic field line. The frequent observation of these waves suggests that cold plasma is often present near the magnetopause.

Dispersion relation in oscillatory reaction-diffusion systems with self-consistent flow in true slime mold.

PubMed

Yamada, H; Nakagaki, T; Baker, R E; Maini, P K

2007-06-01

In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals. The basic nature of this wave behaviour is not well-understood because, to date, an important effect has been neglected, namely, the shuttle streaming of protoplasm which accompanies the biochemical rhythms. Here we study the effects of self-consistent flow on the wave behaviour of oscillatory reaction-diffusion models proposed for the Physarum plasmodium, by means of numerical simulation for the dispersion relation and weakly nonlinear analysis for derivation of the phase equation. We conclude that the flow term is able to increase the speed of phase waves (similar to elongation of wave length). We compare the theoretical consequences with real waves observed in the organism and also point out the physiological roles of these effects on control mechanisms of intracellular communication.

Application of a planetary wave breaking parameterization to stratospheric circulation statistics

NASA Technical Reports Server (NTRS)

Randel, William J.; Garcia, Rolando R.

1994-01-01

The planetary wave parameterization scheme developed recently by Garcia is applied to statospheric circulation statistics derived from 12 years of National Meteorological Center operational stratospheric analyses. From the data a planetary wave breaking criterion (based on the ratio of the eddy to zonal mean meridional potential vorticity (PV) gradients), a wave damping rate, and a meridional diffusion coefficient are calculated. The equatorward flank of the polar night jet during winter is identified as a wave breaking region from the observed PV gradients; the region moves poleward with season, covering all high latitudes in spring. Derived damping rates maximize in the subtropical upper stratosphere (the 'surf zone'), with damping time scales of 3-4 days. Maximum diffusion coefficients follow the spatial patterns of the wave breaking criterion, with magnitudes comparable to prior published estimates. Overall, the observed results agree well with the parameterized calculations of Garcia.

A phase space approach to wave propagation with dispersion.

PubMed

Ben-Benjamin, Jonathan S; Cohen, Leon; Loughlin, Patrick J

2015-08-01

A phase space approximation method for linear dispersive wave propagation with arbitrary initial conditions is developed. The results expand on a previous approximation in terms of the Wigner distribution of a single mode. In contrast to this previously considered single-mode case, the approximation presented here is for the full wave and is obtained by a different approach. This solution requires one to obtain (i) the initial modal functions from the given initial wave, and (ii) the initial cross-Wigner distribution between different modal functions. The full wave is the sum of modal functions. The approximation is obtained for general linear wave equations by transforming the equations to phase space, and then solving in the new domain. It is shown that each modal function of the wave satisfies a Schrödinger-type equation where the equivalent "Hamiltonian" operator is the dispersion relation corresponding to the mode and where the wavenumber is replaced by the wavenumber operator. Application to the beam equation is considered to illustrate the approach.

Computing the Dynamic Response of a Stratified Elastic Half Space Using Diffuse Field Theory

NASA Astrophysics Data System (ADS)

Sanchez-Sesma, F. J.; Perton, M.; Molina Villegas, J. C.

2015-12-01

The analytical solution for the dynamic response of an elastic half-space for a normal point load at the free surface is due to Lamb (1904). For a tangential force, we have Chaós (1960) formulae. For an arbitrary load at any depth within a stratified elastic half space, the resulting elastic field can be given in the same fashion, by using an integral representation in the radial wavenumber domain. Typically, computations use discrete wave number (DWN) formalism and Fourier analysis allows for solution in space and time domain. Experimentally, these elastic Greeńs functions might be retrieved from ambient vibrations correlations when assuming a diffuse field. In fact, the field could not be totally diffuse and only parts of the Green's functions, associated to surface or body waves, are retrieved. In this communication, we explore the computation of Green functions for a layered media on top of a half-space using a set of equipartitioned elastic plane waves. Our formalism includes body and surface waves (Rayleigh and Love waves). These latter waves correspond to the classical representations in terms of normal modes in the asymptotic case of large separation distance between source and receiver. This approach allows computing Green's functions faster than DWN and separating the surface and body wave contributions in order to better represent Green's function experimentally retrieved.

Solitary-wave solutions of the Benjamin equation

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

Albert, J.P.; Bona, J.L.; Restrepo, J.M.

1999-10-01

Considered here is a model equation put forward by Benjamin that governs approximately the evolution of waves on the interface of a two-fluid system in which surface-tension effects cannot be ignored. The principal focus is the traveling-wave solutions called solitary waves, and three aspects will be investigated. A constructive proof of the existence of these waves together with a proof of their stability is developed. Continuation methods are used to generate a scheme capable of numerically approximating these solitary waves. The computer-generated approximations reveal detailed aspects of the structure of these waves. They are symmetric about their crests, but unlikemore » the classical Korteqeg-de Vries solitary waves, they feature a finite number of oscillations. The derivation of the equation is also revisited to get an idea of whether or not these oscillatory waves might actually occur in a natural setting.« less

Diapycnal diffusivity in the core and oxycline of the tropical North Atlantic oxygen minimum zone

NASA Astrophysics Data System (ADS)

Köllner, Manuela; Visbeck, Martin; Tanhua, Toste; Fischer, Tim

2016-08-01

Diapycnal diffusivity estimates from two Tracer Release Experiments (TREs) and microstructure measurements in the oxycline and core of the oxygen minimum zone (OMZ) in the Eastern Tropical North Atlantic (ETNA) are compared. For the first time, two TREs within the same area at different depths were realized: the Guinea Upwelling Tracer Release Experiment (GUTRE) initiated in 2008 in the oxycline at approximately 320 m depth, and the Oxygen Supply Tracer Release Experiment (OSTRE) initiated in 2012 in the core of the OMZ at approximately 410 m depth. The mean diapycnal diffusivity Dz was found to be insignificantly smaller in the OMZ core with (1.06 ± 0.24) × 10- 5 m2 s- 1 compared to (1.11 ± 0.22) × 10- 5 m2 s- 1 90 m shallower in the oxycline. Unexpectedly, GUTRE tracer was detected during two of the OSTRE surveys which showed that the estimated diapycnal diffusivity from GUTRE over a time period of seven years was within the uncertainty of the previous estimates over a time period of three years. The results are consistent with the Dz estimates from microstructure measurements and demonstrate that Dz does not vary significantly vertically in the OMZ within the depth range of 200-600 m and does not change with time. The presence of a seamount chain in the vicinity of the GUTRE injection region did not cause enhanced Dz compared to the smoother bottom topography of the OSTRE injection region, although the analysis of vertical shear spectra from ship ADCP data showed elevated internal wave energy level in the seamount vicinity. However, the two tracer patches covered increasingly overlapping areas with time and thus spatially integrated increasingly similar fields of local diffusivity, as well as the difference in local stratification counteracted the influence of roughness on Dz. For both experiments no significant vertical displacements of the tracer were observed, thus diapycnal upwelling within the ETNA OMZ is below the uncertainty level of 5 m yr- 1.

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

Dechant, Lawrence J.

Wave packet analysis provides a connection between linear small disturbance theory and subsequent nonlinear turbulent spot flow behavior. The traditional association between linear stability analysis and nonlinear wave form is developed via the method of stationary phase whereby asymptotic (simplified) mean flow solutions are used to estimate dispersion behavior and stationary phase approximation are used to invert the associated Fourier transform. The resulting process typically requires nonlinear algebraic equations inversions that can be best performed numerically, which partially mitigates the value of the approximation as compared to a more complete, e.g. DNS or linear/nonlinear adjoint methods. To obtain a simpler,more » closed-form analytical result, the complete packet solution is modeled via approximate amplitude (linear convected kinematic wave initial value problem) and local sinusoidal (wave equation) expressions. Significantly, the initial value for the kinematic wave transport expression follows from a separable variable coefficient approximation to the linearized pressure fluctuation Poisson expression. The resulting amplitude solution, while approximate in nature, nonetheless, appears to mimic many of the global features, e.g. transitional flow intermittency and pressure fluctuation magnitude behavior. A low wave number wave packet models also recover meaningful auto-correlation and low frequency spectral behaviors.« less

Quantitative analysis of seismic fault zone waves in the rupture zone of the 1992 Landers, California, earthquake: Evidence for a shallow trapping structure

USGS Publications Warehouse

Peng, Z.; Ben-Zion, Y.; Michael, A.J.; Zhu, L.

2003-01-01

We analyse quantitatively a waveform data set of 238 earthquakes recorded by a dense seismic array across and along the rupture zone of the 1992 Landers earthquake. A grid-search method with station delay corrections is used to locate events that do not have catalogue locations. The quality of fault zone trapped waves generated by each event is determined from the ratios of seismic energy in time windows corresponding to trapped waves and direct S waves at stations close to and off the fault zone. Approximately 70 per cent of the events with S-P times of less than 2 s, including many clearly off the fault, produce considerable trapped wave energy. This distribution is in marked contrast with previous claims that trapped waves are generated only by sources close to or inside the Landers rupture zone. The time difference between the S arrival and trapped waves group does not grow systematically with increasing hypocentral distance and depth. The dispersion measured from the trapped waves is weak. These results imply that the seismic trapping structure at the Landers rupture zone is shallow and does not extend continuously along-strike by more than a few kilometres. Synthetic waveform modelling indicates that the fault zone waveguide has depth of approximately 2-4 km, a width of approximately 200 m, an S-wave velocity reduction relative to the host rock of approximately 30-40 per cent and an S-wave attenuation coefficient of approximately 20-30. The fault zone waveguide north of the array appears to be shallower and weaker than that south of the array. The waveform modelling also indicates that the seismic trapping structure below the array is centred approximately 100 m east of the surface break.

Dependence of radiation belt simulations to assumed radial diffusion rates

NASA Astrophysics Data System (ADS)

Drozdov, A.; Shprits, Y.; Aseev, N.; Kellerman, A. C.; Reeves, G. D.

2017-12-01

Radial diffusion is one of the dominant physical mechanisms that drives acceleration and loss of the radiation belt electrons due to wave-particle interaction with ultra low frequency (ULF) waves, which makes it very important for radiation belt modeling and forecasting. We investigate the sensitivity of several parameterizations of the radial diffusion including Brautigam and Albert [2000], Ozeke et al. [2014] and Ali et al. [2016] on long-term radiation belt modeling using the Versatile Electron Radiation Belt (VERB). Following previous studies, we first perform 1-D radial diffusion simulations. To take into account effects of local acceleration and loss, we perform additional 3-D simulations, including pitch-angle, energy and mixed diffusion. The obtained result demonstrates that the inclusion of local acceleration and pitch-angle diffusion can provide a negative feedback effect, such that the result is largely indistinguishable between simulations conducted with different radial diffusion parameterizations. We also perform a number of sensitivity tests by multiplying radial diffusion rates by constant factors and show that such an approach leads to unrealistic predictions of radiation belt dynamics.

Ocean Wave Studies with Applications to Ocean Modeling and Improvement of Satellite Altimeter Measurements

NASA Technical Reports Server (NTRS)

Glazman, Roman E.

1999-01-01

Combining analysis of satellite data (altimeter, scatterometer, high-resolution visible and infrared images, etc.) with mathematical modeling of non-linear wave processes, we investigate various ocean wave fields (on scales from capillary to planetary), their role in ocean dynamics and turbulent transport (of heat and biogeochemical quantities), and their effects on satellite altimeter measuring accuracy. In 1998 my attention was focused on long internal gravity waves (10 to 1000 km), known also as baroclinic inertia-gravity (BIG) waves. We found these waves to be a major factor of altimeter measurements "noise," resulting in a greater uncertainty [up to 10 cm in terms of sea surface height (SSH) amplitude] in the measured SSH signal than that caused by the sea state bias variations (up to 5 cm or so). This effect still remains largely overlooked by the satellite altimeter community. Our studies of BIG waves address not only their influence on altimeter measurements but also their role in global ocean dynamics and in transport and turbulent diffusion of biogeochemical quantities. In particular, in collaboration with Prof Peter Weichman, Caltech, we developed a theory of turbulent diffusion caused by wave motions of most general nature. Applied to the problem of horizontal turbulent diffusion in the ocean, the theory yielded the effective diffusion coefficient as a function of BIG wave parameters obtainable from satellite altimeter data. This effort, begun in 1997, has been successfully completed in 1998. We also developed a theory that relates spatial fluctuations of scalar fields (such as sea surface temperature, chlorophyll concentration, drifting ice concentration, etc.) to statistical characteristics of BIG waves obtainable from altimeter measurements. A manuscript is in the final stages of preparation. In order to verify the theoretical predictions and apply them to observations, we are now analyzing Sea-viewing Wide Field of view Sensor (SeaWiFS) and Field of view Sensor (SeaWiFS) and Advanced Very High-Resolution Radiometer (AVHRR) data on sea surface temperature (SST) and chlorophyll concentration jointly with TOPEX/POSEIDON data on SSH variations.

Modeling Wind Wave Evolution from Deep to Shallow Water

DTIC Science & Technology

2012-09-30

WORK COMPLETED Development of a Lumped Quadruplet Approximation ( LQA ) A scalable parameterization of non-linear four-wave interactions is being...what we refer to as the Lumped Quadruplet Approximation ( LQA ), in which discrete contributions on the locus are treated as individual wave number...includes inhomogeneous wave fields, but is compatible with the action balance generally used in operational wave models. RESULTS Development LQA

Multi-dimensional Core-Collapse Supernova Simulations with Neutrino Transport

NASA Astrophysics Data System (ADS)

Pan, Kuo-Chuan; Liebendörfer, Matthias; Hempel, Matthias; Thielemann, Friedrich-Karl

We present multi-dimensional core-collapse supernova simulations using the Isotropic Diffusion Source Approximation (IDSA) for the neutrino transport and a modified potential for general relativity in two different supernova codes: FLASH and ELEPHANT. Due to the complexity of the core-collapse supernova explosion mechanism, simulations require not only high-performance computers and the exploitation of GPUs, but also sophisticated approximations to capture the essential microphysics. We demonstrate that the IDSA is an elegant and efficient neutrino radiation transfer scheme, which is portable to multiple hydrodynamics codes and fast enough to investigate long-term evolutions in two and three dimensions. Simulations with a 40 solar mass progenitor are presented in both FLASH (1D and 2D) and ELEPHANT (3D) as an extreme test condition. It is found that the black hole formation time is delayed in multiple dimensions and we argue that the strong standing accretion shock instability before black hole formation will lead to strong gravitational waves.

Fast-to-Alfvén Mode Conversion in the Presence of Ambipolar Diffusion

NASA Astrophysics Data System (ADS)

Cally, Paul S.; Khomenko, Elena

2018-03-01

It is known that fast magnetohydrodynamic waves partially convert to upward and/or downward propagating Alfvén waves in a stratified atmosphere where Alfvén speed increases with height. This happens around the fast wave reflection height, where the fast wave’s horizontal phase speed equals the Alfvén speed (in a low-β plasma). Typically, this takes place in the mid to upper solar chromosphere for low-frequency waves in the few-millihertz band. However, this region is weakly ionized and thus susceptible to nonideal MHD processes. In this article, we explore how ambipolar diffusion in a zero-β plasma affects fast waves injected from below. Classical ambipolar diffusion is far too weak to have any significant influence at these low frequencies, but if enhanced by turbulence (in the quiet-Sun chromosphere but not in sunspot umbrae) or the production of sufficiently small-scale structure, can substantially absorb waves for turbulent ambipolar Reynolds numbers of around 20 or less. In that case, it is found that the mode conversion process is not qualitatively altered from the ideal case, though conversion to Alfvén waves is reduced because the fast wave flux reaching the conversion region is degraded. It is also found that any upward propagating Alfvén waves generated in this process are almost immune to further ambipolar attenuation, thereby reducing local ambipolar heating compared to cases without mode conversion. In that sense, mode conversion provides a form of “Alfvén cooling.”

Plasma Waves and Structures Associated with Magnetic Reconnection

NASA Astrophysics Data System (ADS)

Ergun, R.; Wilder, F. D.; Ahmadi, N.; Goodrich, K.; Holmes, J.; Newman, D. L.; Burch, J.; Torbert, R. B.; Le Contel, O.; Giles, B. L.; Strangeway, R. J.; Lindqvist, P. A.

2017-12-01

Space observations of magnetic reconnection indicate a variety of plasma wave modes and structures in the vicinity of the electron diffusion region including electromagnetic whistler waves, quasi-electrostatic whistler waves, electron phase-space holes, double layers, electron acoustic waves, lower hybrid waves, upper hybrid waves, and electromagnetic drift waves. These waves and plasma structures are seen in magnetotail reconnection and subsolar reconnection. The MMS mission has the unique ability to unequivocally identify the electron diffusion region and distinguish waves in the EDR from those in the extended separatrix. Such a distinction is critical since some of the observed waves may be involved the reconnection process while others may result from subsequent or associated events and do not directly influence the reconnection process. For example, some of the largest amplitude (> 100 mV/m) electrostatic waves have been identified as electron acoustic waves and upper hybrid waves. These waves are likely generated as a result of reconnection and do not appear to strongly influence the reconnection process. On the other hand, large-amplitude electrostatic whistler waves have been observed very near the X-line, are seen in simulations, and may be participating in reconnection physics. Electromagnetic drift waves almost always appear in cases of asymmetric reconnection and may lead to a more turbulent process. We summarize wave observations by MMS and discuss the relative their possible role in magnetic reconnection physics, concentrating on recent magnetotail observations.

Behavioral and electrophysiological auditory processing measures in traumatic brain injury after acoustically controlled auditory training: a long-term study

PubMed Central

Figueiredo, Carolina Calsolari; de Andrade, Adriana Neves; Marangoni-Castan, Andréa Tortosa; Gil, Daniela; Suriano, Italo Capraro

2015-01-01

ABSTRACT Objective To investigate the long-term efficacy of acoustically controlled auditory training in adults after tarumatic brain injury. Methods A total of six audioogically normal individuals aged between 20 and 37 years were studied. They suffered severe traumatic brain injury with diffuse axional lesion and underwent an acoustically controlled auditory training program approximately one year before. The results obtained in the behavioral and electrophysiological evaluation of auditory processing immediately after acoustically controlled auditory training were compared to reassessment findings, one year later. Results Quantitative analysis of auditory brainsteim response showed increased absolute latency of all waves and interpeak intervals, bilaterraly, when comparing both evaluations. Moreover, increased amplitude of all waves, and the wave V amplitude was statistically significant for the right ear, and wave III for the left ear. As to P3, decreased latency and increased amplitude were found for both ears in reassessment. The previous and current behavioral assessment showed similar results, except for the staggered spondaic words in the left ear and the amount of errors on the dichotic consonant-vowel test. Conclusion The acoustically controlled auditory training was effective in the long run, since better latency and amplitude results were observed in the electrophysiological evaluation, in addition to stability of behavioral measures after one-year training. PMID:26676270

A novel model of photothermal diffusion (PTD) for polymer nano-composite semiconducting of thin circular plate

NASA Astrophysics Data System (ADS)

Lotfy, Kh.

2018-05-01

In this article, theoretical discussions for a novel mathematical-physical Photothermal diffusion (PTD) model in the generalized thermoelasticity theory with photothermal processes and chemical action are introduced. The mean idea of this model depends on the interaction between quasi-particles (plasma waves) that depends on the kind of the used materials, the mechanical forces acting on the surface, the generalized thermo and mass diffusion (due to coupling of temperature fields with thermal waves and chemical potential) and the elastic waves. The one dimensional Laplace transforms is used to obtain the exact solution for some physical and chemical quantities for a thin circular plate of a semiconducting polymer nanocomposite such as silicon (Si). New variables are deduced and discussed. The obtained results of the physical quantities are presented analytically and illustrated graphically with some important applications.

Delay-induced Turing-like waves for one-species reaction-diffusion model on a network

NASA Astrophysics Data System (ADS)

Petit, Julien; Carletti, Timoteo; Asllani, Malbor; Fanelli, Duccio

2015-09-01

A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous perturbation. These are generalized Turing-like waves that materialize in a single-species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time-delayed differential equations. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz network and with the inclusion of the delay.

Mathematical analysis of thermal diffusion shock waves

NASA Astrophysics Data System (ADS)

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

2005-10-01

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

Amplitude equations for breathing spiral waves in a forced reaction-diffusion system.

PubMed

Ghosh, Pushpita; Ray, Deb Shankar

2011-09-14

Based on a multiple scale analysis of a forced reaction-diffusion system leading to amplitude equations, we explain the existence of spiral wave and its photo-induced spatiotemporal behavior in chlorine dioxide-iodine-malonic acid system. When the photo-illumination intensity is modulated, breathing of spiral is observed in which the period of breathing is identical to the period of forcing. We have also derived the condition for breakup and suppression of spiral wave by periodic illumination. The numerical simulations agree well with our analytical treatment. © 2011 American Institute of Physics

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth.

PubMed

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

Coarse-graining and hybrid methods for efficient simulation of stochastic multi-scale models of tumour growth

NASA Astrophysics Data System (ADS)

de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás

2017-12-01

The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of front, which cannot be accounted for by the coarse-grained model. Such fluctuations have non-trivial effects on the wave velocity. Beyond the development of a new hybrid method, we thus conclude that birth-rate fluctuations are central to a quantitatively accurate description of invasive phenomena such as tumour growth.

The alpha channeling effect

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

Fisch, N. J.

2015-12-10

Alpha particles born through fusion reactions in a tokamak reactor tend to slow down on electrons, but that could take up to hundreds of milliseconds. Before that happens, the energy in these alpha particles can destabilize on collisionless timescales toroidal Alfven modes and other waves, in a way deleterious to energy confinement. However, it has been speculated that this energy might be instead be channeled into useful energy, so as to heat fuel ions or to drive current. Such a channeling needs to be catalyzed by waves Waves can produce diffusion in energy of the alpha particles in a waymore » that is strictly coupled to diffusion in space. If these diffusion paths in energy-position space point from high energy in the center to low energy on the periphery, then alpha particles will be cooled while forced to the periphery. The energy from the alpha particles is absorbed by the wave. The amplified wave can then heat ions or drive current. This process or paradigm for extracting alpha particle energy collisionlessly has been called alpha channeling. While the effect is speculative, the upside potential for economical fusion is immense. The paradigm also operates more generally in other contexts of magnetically confined plasma.« less

The alpha channeling effect

NASA Astrophysics Data System (ADS)

Fisch, N. J.

2015-12-01

Alpha particles born through fusion reactions in a tokamak reactor tend to slow down on electrons, but that could take up to hundreds of milliseconds. Before that happens, the energy in these alpha particles can destabilize on collisionless timescales toroidal Alfven modes and other waves, in a way deleterious to energy confinement. However, it has been speculated that this energy might be instead be channeled into useful energy, so as to heat fuel ions or to drive current. Such a channeling needs to be catalyzed by waves Waves can produce diffusion in energy of the alpha particles in a way that is strictly coupled to diffusion in space. If these diffusion paths in energy-position space point from high energy in the center to low energy on the periphery, then alpha particles will be cooled while forced to the periphery. The energy from the alpha particles is absorbed by the wave. The amplified wave can then heat ions or drive current. This process or paradigm for extracting alpha particle energy collisionlessly has been called alpha channeling. While the effect is speculative, the upside potential for economical fusion is immense. The paradigm also operates more generally in other contexts of magnetically confined plasma.

Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering

NASA Technical Reports Server (NTRS)

Gamayunov, K. V.; Khazanov, G. V.

2006-01-01

The flux level of outer-zone relativistic electrons (above 1 MeV) is extremely variable during geomagnetic storms, and controlled by a competition between acceleration and loss. Precipitation of these electrons due to resonant pitch-angle scattering by electromagnetic ion cyclotron (EMIC) waves is considered one of the major loss mechanisms. This mechanism was suggested in early theoretical studies more than three decades ago. However, direct experimental evidence of the wave role in relativistic electrons precipitation is difficult to obtain because of lack of concurrent measurements of precipitating electrons at low altitudes and the waves in a magnetically conjugate equatorial region. Recently, the data from balloon-borne X-ray instruments provided indirect but strong evidence on an efficiency of the EMIC wave induced loss for the outer-zone relativistic electrons. These observations stimulated theoretical studies that, particularly, demonstrated that EMIC wave induced pitch-angle diffusion of MeV electrons can operate in the strong diffusion limit and this mechanism can compete with relativistic electron depletion caused by the Dst effect during the initial and main phases of storm. Although an effectiveness of relativistic electron scattering by EMIC waves depends strongly on the wave spectral properties, the most favorable assumptions regarding wave characteristics has been made in all previous theoretical studies. Particularly, only quasi field-aligned EMIC waves have been considered as a driver for relativistic electron loss. At the same time, there is growing experimental and theoretical evidence that these waves can be highly oblique; EMIC wave energy can occupy not only the region of generation, i.e. the region of small wave normal angles, but also the entire wave normal angle region, and even only the region near 90 degrees. The latter can dramatically change he effectiveness of relativistic electron scattering by EMIC waves. In the present study, we calculate the pitch-angle diffusion coefficients using the typical wave normal distributions obtained from our self-consistent ring current-EMIC wave model, and try to quantify the effect of EMIC wave normal angle characteristics on relativistic electron scattering.

Non-Additive Voltametric Currents From a Mixture of Two, Three and Four Redox-Active Compounds and Electroanalytical Implications

NASA Technical Reports Server (NTRS)

Dass, Amala; Oh, Woon Su; Gao, Xue-Rong; Rawashdeh, Abdel M.; Leventis, Nicholas

2004-01-01

We have published recently the effect of dissimilar diffusion coefficients on the size of the voltammetric waves from a mixture of two redox-active compounds. Similarly, at the potential range where three redox-active species, decamethylferrocene (dMeFc), ferrocene (Fc) and N-methylphenothiazine (MePTZ), are oxidized simultaneously with rates controlled by linear diffusion, electrogenerated radicals diffusing outwards from the electrode react with the original species diffusing towards the electrode from the bulk; thus, Fc(+) reacts with dMeFc producing Fc and dMeFc(+), while MePTZ(+) reacts both with dMeFc producing MePTZ and dMeFc(+), and with Fc producing MePTZ and Fc(+). These reactions replace dMeFc with Fc at the second plateau, and both dMeFc and Fc with MePTZ at the third plateau. Since the diffusion coefficients of the three species are not equal, the mass-transfer limited currents of the second and the third oxidation wave plateaus change by approx. 10%. Numerical simulations of the experimental voltamograms support this mechanism. Similar results were also obtained for a mixture of four redoxactive compounds. The implications of this non-additive nature of currents on: (a) the use of internal voltammetric standards for quantitative analysis of a mixture of redox-active compounds; and, (b) the half wave potentials (E1/2) of the 2nd, 3rd and 4th waves for qualitative analysis, will be discussed.

Facilitation of cytosolic calcium wave propagation by local calcium uptake into the sarcoplasmic reticulum in cardiac myocytes.

PubMed

Maxwell, Joshua T; Blatter, Lothar A

2012-12-01

The widely accepted paradigm for cytosolic Ca(2+) wave propagation postulates a 'fire-diffuse-fire' mechanism where local Ca(2+)-induced Ca(2+) release (CICR) from the sarcoplasmic reticulum (SR) via ryanodine receptor (RyR) Ca(2+) release channels diffuses towards and activates neighbouring release sites, resulting in a propagating Ca(2+) wave. A recent challenge to this paradigm proposed the requirement for an intra-SR 'sensitization' Ca(2+) wave that precedes the cytosolic Ca(2+) wave and primes RyRs from the luminal side to CICR. Here, we tested this hypothesis experimentally with direct simultaneous measurements of cytosolic ([Ca(2+)](i); rhod-2) and intra-SR ([Ca(2+)](SR); fluo-5N) calcium signals during wave propagation in rabbit ventricular myocytes, using high resolution fluorescence confocal imaging. The increase in [Ca(2+)](i) at the wave front preceded depletion of the SR at each point along the calcium wave front, while during this latency period a transient increase of [Ca(2+)](SR) was observed. This transient elevation of [Ca(2+)](SR) could be identified at individual release junctions and depended on the activity of the sarco-endoplasmic reticulum Ca(2+)-ATPase (SERCA). Increased SERCA activity (β-adrenergic stimulation with 1 μM isoproterenol (isoprenaline)) decreased the latency period and increased the amplitude of the transient elevation of [Ca(2+)](SR), whereas inhibition of SERCA (3 μM cyclopiazonic acid) had the opposite effect. In conclusion, the data provide experimental evidence that local Ca(2+) uptake by SERCA into the SR facilitates the propagation of cytosolic Ca(2+) waves via luminal sensitization of the RyR, and supports a novel paradigm of a 'fire-diffuse-uptake-fire' mechanism for Ca(2+) wave propagation in cardiac myocytes.

Facilitation of cytosolic calcium wave propagation by local calcium uptake into the sarcoplasmic reticulum in cardiac myocytes

PubMed Central

Maxwell, Joshua T; Blatter, Lothar A

2012-01-01

The widely accepted paradigm for cytosolic Ca2+ wave propagation postulates a ‘fire-diffuse-fire’ mechanism where local Ca2+-induced Ca2+ release (CICR) from the sarcoplasmic reticulum (SR) via ryanodine receptor (RyR) Ca2+ release channels diffuses towards and activates neighbouring release sites, resulting in a propagating Ca2+ wave. A recent challenge to this paradigm proposed the requirement for an intra-SR ‘sensitization’ Ca2+ wave that precedes the cytosolic Ca2+ wave and primes RyRs from the luminal side to CICR. Here, we tested this hypothesis experimentally with direct simultaneous measurements of cytosolic ([Ca2+]i; rhod-2) and intra-SR ([Ca2+]SR; fluo-5N) calcium signals during wave propagation in rabbit ventricular myocytes, using high resolution fluorescence confocal imaging. The increase in [Ca2+]i at the wave front preceded depletion of the SR at each point along the calcium wave front, while during this latency period a transient increase of [Ca2+]SR was observed. This transient elevation of [Ca2+]SR could be identified at individual release junctions and depended on the activity of the sarco-endoplasmic reticulum Ca2+-ATPase (SERCA). Increased SERCA activity (β-adrenergic stimulation with 1 μm isoproterenol (isoprenaline)) decreased the latency period and increased the amplitude of the transient elevation of [Ca2+]SR, whereas inhibition of SERCA (3 μm cyclopiazonic acid) had the opposite effect. In conclusion, the data provide experimental evidence that local Ca2+ uptake by SERCA into the SR facilitates the propagation of cytosolic Ca2+ waves via luminal sensitization of the RyR, and supports a novel paradigm of a ‘fire-diffuse-uptake-fire’ mechanism for Ca2+ wave propagation in cardiac myocytes. PMID:22988145

The Organization as a Filter of Institutional Diffusion

ERIC Educational Resources Information Center

Penuel, William R.; Frank, Kenneth A.; Sun, Min; Kim, Chong Min; Singleton, Corrine

2013-01-01

Background/Context: Institutional theories sometimes characterize the normative influence of institutions as diffusing like waves and as exerting uniform pressures on individuals. This article contributes to a growing literature on the microfoundations of institutions, investigating how intraorganizational networks mediate the diffusion of…

Reducing injection loss in drill strings

DOEpatents

Drumheller, Douglas S.

2004-09-14

A system and method for transferring wave energy into or out of a periodic structure having a characteristic wave impedance profile at a prime frequency, the characteristic wave impedance profile comprising a real portion and an imaginary portion, comprising: locating one or more energy transfer elements each having a wave impedance at the prime frequency approximately equal to the real portion of the characteristic wave impedance at one or more points on the periodic structure with the imaginary portion approximately equaling zero; and employing the one or more energy transfer elements to transfer wave energy into or out of the periodic structure. The energy transfer may be repeaters. Quarter-wave transformers can be provided at one or more points on the periodic structure with the imaginary portion approximately equaling zero to transmit waves across one or more discontinuities. A terminator can be employed for cancellation of waves. The invention substantially eliminates reflections of the wave energy at the prime frequency by joints between sections of the periodic structure.

Pitch Angle Scattering of Upgoing Electron Beams in Jupiter's Polar Regions by Whistler Mode Waves

NASA Astrophysics Data System (ADS)

Elliott, S. S.; Gurnett, D. A.; Kurth, W. S.; Clark, G.; Mauk, B. H.; Bolton, S. J.; Connerney, J. E. P.; Levin, S. M.

2018-02-01

The Juno spacecraft's Jupiter Energetic-particle Detector Instrument has observed field-aligned, unidirectional (upgoing) electron beams throughout most of Jupiter's entire polar cap region. The Waves instrument detected intense broadband whistler mode emissions occurring in the same region. In this paper, we investigate the pitch angle scattering of the upgoing electron beams due to interactions with the whistler mode waves. Profiles of intensity versus pitch angle for electron beams ranging from 2.53 to 7.22 Jovian radii show inconsistencies with the expected adiabatic invariant motion of the electrons. It is believed that the observed whistler mode waves perturb the electron motion and scatter them away from the magnetic field line. The diffusion equation has been solved by using diffusion coefficients which depend on the magnetic intensity of the whistler mode waves.

The complex fluid dynamics of simple diffusion

NASA Astrophysics Data System (ADS)

Vold, Erik

2017-11-01

Diffusion as the mass transport process responsible for mixing fluids at the atomic level is often underestimated in its complexity. An initial discontinuity between two species of different atomic masses exhibits a mass density discontinuity under isothermal pressure equilibrium implying equal species molar densities. The self-consistent kinetic transport processes across such an interface leads to a zero sum of mass flux relative to the center of mass and so diffusion alone cannot relax an initially stationary mass discontinuity nor broaden the density profile at the interface. The diffusive mixing leads to a molar imbalance which drives a center of mass velocity which moves the heavier species toward the lighter species leading to the interfacial density relaxation. Simultaneously, the species non-zero molar flux modifies the pressure profile in a transient wave and in a local perturbation. The resulting center of mass velocity has two components; one, associated with the divergence of the flow, persists in the diffusive mixing region throughout the diffusive mixing process, and two, travelling waves at the front of the pressure perturbations propagate away from the mixing region. The momentum in these waves is necessary to maintain momentum conservation in the center of mass frame. Thus, in a number of ways, the diffusive mixing provides feedback into the small scale advective motions. Numerical methods which diffuse all species assuming P-T equilibrium may not recover the subtle dynamics of mass transport at an interface. Work performed by the LANS, LLC, under USDOE Contract No. DE-AC52-06NA25396, funded by the (ASC) Program.

The Radiation Belt Electron Scattering by Magnetosonic Wave: Dependence on Key Parameters

NASA Astrophysics Data System (ADS)

Lei, Mingda; Xie, Lun; Li, Jinxing; Pu, Zuyin; Fu, Suiyan; Ni, Binbin; Hua, Man; Chen, Lunjin; Li, Wen

2017-12-01

Magnetosonic (MS) waves have been found capable of creating radiation belt electron butterfly distributions in the inner magnetosphere. To investigate the physical nature of the interactions between radiation belt electrons and MS waves, and to explore a preferential condition for MS waves to scatter electrons efficiently, we performed a comprehensive parametric study of MS wave-electron interactions using test particle simulations. The diffusion coefficients simulated by varying the MS wave frequency show that the scattering effect of MS waves is frequency insensitive at low harmonics (f < 20 fcp), which has great implications on modeling the electron scattering caused by MS waves with harmonic structures. The electron scattering caused by MS waves is very sensitive to wave normal angles, and MS waves with off 90° wave normal angles scatter electrons more efficiently. By simulating the diffusion coefficients and the electron phase space density evolution at different L shells under different plasma environment circumstances, we find that MS waves can readily produce electron butterfly distributions in the inner part of the plasmasphere where the ratio of electron plasma-to-gyrofrequency (fpe/fce) is large, while they may essentially form a two-peak distribution outside the plasmapause and in the inner radiation belt where fpe/fce is small.

Short-Path Statistics and the Diffusion Approximation

NASA Astrophysics Data System (ADS)

Blanco, Stéphane; Fournier, Richard

2006-12-01

In the field of first return time statistics in bounded domains, short paths may be defined as those paths for which the diffusion approximation is inappropriate. This is at the origin of numerous open questions concerning the characterization of residence time distributions. We show here how general integral constraints can be derived that make it possible to address short-path statistics indirectly by application of the diffusion approximation to long paths. Application to the moments of the distribution at the low-Knudsen limit leads to simple practical results and novel physical pictures.

Nonlinear theory of diffusive acceleration of particles by shock waves

NASA Astrophysics Data System (ADS)

Malkov, M. A.; Drury, L. O'C.

2001-04-01

Among the various acceleration mechanisms which have been suggested as responsible for the nonthermal particle spectra and associated radiation observed in many astrophysical and space physics environments, diffusive shock acceleration appears to be the most successful. We review the current theoretical understanding of this process, from the basic ideas of how a shock energizes a few reactionless particles to the advanced nonlinear approaches treating the shock and accelerated particles as a symbiotic self-organizing system. By means of direct solution of the nonlinear problem we set the limit to the test-particle approximation and demonstrate the fundamental role of nonlinearity in shocks of astrophysical size and lifetime. We study the bifurcation of this system, proceeding from the hydrodynamic to kinetic description under a realistic condition of Bohm diffusivity. We emphasize the importance of collective plasma phenomena for the global flow structure and acceleration efficiency by considering the injection process, an initial stage of acceleration and, the related aspects of the physics of collisionless shocks. We calculate the injection rate for different shock parameters and different species. This, together with differential acceleration resulting from nonlinear large-scale modification, determines the chemical composition of accelerated particles. The review concentrates on theoretical and analytical aspects but our strategic goal is to link the fundamental theoretical ideas with the rapidly growing wealth of observational data.

Determination of diffusivities in the Rustler Formation from exploratory-shaft construction at the Waste Isolation Pilot Plant in southeastern New Mexico

USGS Publications Warehouse

Stevens, Ken; Beyeler, Walt

1985-01-01

The construction of an exploratory shaft 12 feet in diameter into the Salado Formation (repository horizon for transuranic waste material) at the Waste Isolation Pilot Plant site in southeastern New Mexico affected water-levels in water-bearing zones above the repository horizon. By reading the construction history of the exploratory shaft, an approximation of construction-generated hydraulic stresses at the shaft was made. The magnitude of the construction-generated stresses was calibrated using the hydrographs from one hydrologic test pad. Whereas flow rates from the Magenta Dolomite and Culebra Dolomite Members in the Rustler Formation into the exploratory shaft were unknown, the ratio of transmissivity to storage (diffusivity) was determined by mathematically simulating the aquifers and the hydrologic stresses with flood-wave-response digital model. These results indicate that the Magenta Dolomite and Culebra Dolomite Members of the Rustler Formation can be modeled as homogeneous, isotropic, and confined water-bearing zones. One simple and consistent explanation, but by no means the only explanation, of the lack of a single diffusivity value in the Culebra aquifer is that the open-hole observation wells at the hydrologic test pads dampen the amplitude of water-level changes. (USGS)

Microscopic diffusion and hydrodynamic interactions of hemoglobin in red blood cells.

PubMed

Doster, Wolfgang; Longeville, Stéphane

2007-08-15

The cytoplasm of red blood cells is congested with the oxygen storage protein hemoglobin occupying a quarter of the cell volume. The high protein concentration leads to a reduced mobility; the self-diffusion coefficient of hemoglobin in blood cells is six times lower than in dilute solution. This effect is generally assigned to excluded volume effects in crowded media. However, the collective or gradient diffusion coefficient of hemoglobin is only weakly dependent on concentration, suggesting the compensation of osmotic and friction forces. This would exclude hydrodynamic interactions, which are of dynamic origin and do not contribute to the osmotic pressure. Hydrodynamic coupling between protein molecules is dominant at short time- and length scales before direct interactions are fully established. Employing neutron spin-echo-spectroscopy, we study hemoglobin diffusion on a nanosecond timescale and protein displacements on the scale of a few nanometers. A time- and wave-vector dependent diffusion coefficient is found, suggesting the crossover of self- and collective diffusion. Moreover, a wave-vector dependent friction function is derived, which is a characteristic feature of hydrodynamic interactions. The wave-vector and concentration dependence of the long-time self-diffusion coefficient of hemoglobin agree qualitatively with theoretical results on hydrodynamics in hard spheres suspensions. Quantitative agreement requires us to adjust the volume fraction by including part of the hydration shell: Proteins exhibit a larger surface/volume ratio compared to standard colloids of much larger size. It is concluded that hydrodynamic and not direct interactions dominate long-range molecular transport at high concentration.

Wave failure at strong coupling in intracellular C a2 + signaling system with clustered channels

NASA Astrophysics Data System (ADS)

Li, Xiang; Wu, Yuning; Gao, Xuejuan; Cai, Meichun; Shuai, Jianwei

2018-01-01

As an important intracellular signal, C a2 + ions control diverse cellular functions. In this paper, we discuss the C a2 + signaling with a two-dimensional model in which the inositol 1,4,5-trisphosphate (I P3 ) receptor channels are distributed in clusters on the endoplasmic reticulum membrane. The wave failure at large C a2 + diffusion coupling is discussed in detail in the model. We show that with varying model parameters the wave failure is a robust behavior with either deterministic or stochastic channel dynamics. We suggest that the wave failure should be a general behavior in inhomogeneous diffusing systems with clustered excitable regions and may occur in biological C a2 + signaling systems.

Statistical study of ULF wave occurrence in the dayside magnetosphere

NASA Technical Reports Server (NTRS)

Cao, M.; Mcpherron, R. L.; Russell, C. T.

1994-01-01

Ultralow-frequency (ULF) waves are observed almost everywhere in the dayside magnetosphere. The mechanism by which these waves are generated and transformed in the dayside magnetosphere is still not understood. Here we report a statistical study of these waves based on magnetic field data from the International Sun-Earth Explorer 1 (ISEE 1) spacecraft. Data from the first traversal of the spacecraft through the entire dayside magnetosphere have been examined to determine the spatial distribution of wave occurrence. Successive 20-min segments of data were transformed to a field-aligned coordinate system. The parallel component was detrended and all three components of the field spectrally analyzed. Wave occurrence was defined by the presence of significant peaks in the power spectra. Wave events were categorized by three wave frequency bands: Pc 3 with T approximately 10-45 s; Pc 4 with T approximately 45-150 s; the short-period part of the Pc 5 wave band with T approximately 150-324 s. Properties of the spectral peaks were then entered into a data base. The data base was next sorted to determine the spatial occurrence pattern for the waves. Our results show that Pc 3 waves most frequently occur just outside synchronous orbit and are approximately centered on local noon. Pc 4 waves have a similar distribution with its peak further out. Pc 5 waves have high occurrence rate at the two flanks of the magnetosphere. Peaks in spectra obtained near the magnetopause are less clearly defined than those deeper in the magnetosphere.

Fast penetration of megagauss fields into metallic conductors

NASA Astrophysics Data System (ADS)

Schnitzer, Ory

2014-08-01

Megagauss magnetic-field penetration into a conducting material is studied via a simplified but representative model, wherein the magnetic-diffusion equation is coupled with a thermal-energy balance. The specific scenario considered is that of a prescribed magnetic field rising (in proportion to an arbitrary power r of time) at the surface of a conducting half-space whose electric conductivity is assumed proportional to an arbitrary inverse power γ of temperature. We employ a systematic asymptotic scheme in which the case of a strong surface field corresponds to a singular asymptotic limit. In this limit, the highly magnetized and hot "skin" terminates at a distinct propagating wave-front. Employing the method of matched asymptotic expansions, we find self-similar solutions of the magnetized region which match a narrow boundary-layer region about the advancing wave front. The rapidly decaying magnetic-field profile in the latter region is also self similar; when scaled by the instantaneous propagation speed, its shape is time-invariant, depending only on the parameter γ. The analysis furnishes a simple asymptotic formula for the skin-depth (i.e., the wave-front position), which substantially generalizes existing approximations. It scales with the power γr + 1/2 of time and the power γ of field strength, and is much larger than the field-independent skin depth predicted by an athermal model. The formula further involves a dimensionless O(1) pre-factor which depends on r and γ. It is determined by solving a nonlinear eigenvalue problem governing the magnetized region. Another main result of the analysis, apparently unprecedented, is an asymptotic formula for the magnitude of the current-density peak characterizing the wave-front region. Complementary to these systematic results, we provide a closed-form but ad hoc generalization of the theory approximately applicable to arbitrary monotonically rising surface fields. Our results are in excellent agreement with numerical simulations of the model, and compare favourably with detailed magnetohydrodynamic simulations reported in the literature.

Wave-Current Conditions and Navigation Safety at an Inlet Entrance

DTIC Science & Technology

2015-06-26

effects of physical processes. Wave simulations with refraction, shoaling, and breaking provide estimates of wave-related parameters of interest to...summer and winter months and to better understand the cause- effect relationship between navigability conditions at Tillamook Inlet and characteristics of...the Coriolis force, wind stress, wave stress, bottom stress, vegetation flow drag, bottom friction, wave roller, and turbulent diffusion. Governing

Photoacoustic, Photothermal, and Diffusion-Wave Sciences in the Twenty-First Century: Triumphs of the Past Set the Trends for the Future

NASA Astrophysics Data System (ADS)

Mandelis, Andreas

2012-11-01

A handful of early breakthroughs in photoacoustic science and engineering since its modern-day (scientific) renaissance in the 1970s has defined directions in the development of the photoacoustic, photothermal, and diffusion-wave fields in the past 40 years that have shaped modern day developments and have led to an impressive range of vibrant and unique technologies in the third millennium (technological renaissance). A power-point presentation on the ICPPP-16 opening plenary talk focuses on the historical roots of what I perceive to be some of today's most successful and unique technologies, while readily acknowledging the impossibility to be all inclusive. It can be found under the url: http://cadift.mie.utoronto.ca/History_of_Photoacoustics-Photothermics.ppt. The thematic areas in question include historical reviews selected among the following topics: Piezoelectric photoacoustic microscopy (PAM) which, along with early gas-phase PA spectroscopic studies of biomaterials such as blood haemoglobin and progress in the physics of photon diffusion waves, has led to the modern-day explosion in biomedical photoacoustic imaging technologies with future trends for photoacoustic and ultrasound co-registered imagers; Thermoreflectance, piezoelectric, and gas-phase PA imaging of semiconductors which, along with developments in photocarrier diffusion wave physics, led to photocarrier radiometry, nanolayer diagnostics, carrierographic imaging of optoelectronic materials, and devices with industrial trends in solar cell inspection and control; Photoacoustic gas-phase and infrared radiometric probing and scanning imaging NDE which led to lock-in thermography and have spawned industrial and biomedical technologies; Thermal-wave interferometry and the quest for thermal coherence which led to thermal-wave cavities, the thermal-wave radar, and derivative depth profiling technologies, and, very recently, thermal coherence tomography. This review is meant to be a growing public record of work in progress, with new materials in the given thematic areas and other thematic areas being added as more information on the rich history of the field becomes available. Direct inputs to the author by the broader photoacoustic, photothermal, and diffusion-wave community are solicited and strongly encouraged to ensure that all landmark and seminal work that shaped the state of the science and art in the field receives fair and deserving exposure and the historical review becomes truly representative and comprehensive.

Influence of doping on thermal diffusivity of single crystals used in photonics: measurements based on thermal wave methods.

PubMed

Bodzenta, Jerzy; Kaźmierczak-Bałata, Anna; Wokulska, Krystyna B; Kucytowski, Jacek; Łukasiewicz, Tadeusz; Hofman, Władysław

2009-03-01

Three crystals used in solid-state lasers, namely, yttrium aluminum garnet (YAG), yttrium orthovanadate (YVO(4)), and gadolinium calcium oxoborate (GdCOB), were investigated to determine the influence of dopants on their thermal diffusivity. The thermal diffusivity was measured by thermal wave method with a signal detection based on mirage effect. The YAG crystals were doped with Yb or V, the YVO(4) with Nd or Ca and Tm, and the GdCOB crystals contained Nd or Yb. In all cases, the doping caused a decrease in thermal diffusivity. The analysis of complementary measurements of ultrasound velocity changes caused by dopants leads to the conclusion that impurities create phonon scattering centers. This additional scattering reduces the phonon mean free path and accordingly results in the decrease of the thermal diffusivity of the crystal. The influence of doping on lattice parameters was investigated, additionally.

Direct Measurement of Wave Kernels in Time-Distance Helioseismology

NASA Technical Reports Server (NTRS)

Duvall, T. L., Jr.

2006-01-01

Solar f-mode waves are surface-gravity waves which propagate horizontally in a thin layer near the photosphere with a dispersion relation approximately that of deep water waves. At the power maximum near 3 mHz, the wavelength of 5 Mm is large enough for various wave scattering properties to be observable. Gizon and Birch (2002,ApJ,571,966)h ave calculated kernels, in the Born approximation, for the sensitivity of wave travel times to local changes in damping rate and source strength. In this work, using isolated small magnetic features as approximate point-sourc'e scatterers, such a kernel has been measured. The observed kernel contains similar features to a theoretical damping kernel but not for a source kernel. A full understanding of the effect of small magnetic features on the waves will require more detailed modeling.

Resonant scattering of energetic electrons in the plasmasphere by monotonic whistler-mode waves artificially generated by ionospheric modification

NASA Astrophysics Data System (ADS)

Chang, S. S.; Ni, B. B.; Bortnik, J.; Zhou, C.; Zhao, Z. Y.; Li, J. X.; Gu, X. D.

2014-05-01

Modulated high-frequency (HF) heating of the ionosphere provides a feasible means of artificially generating extremely low-frequency (ELF)/very low-frequency (VLF) whistler waves, which can leak into the inner magnetosphere and contribute to resonant interactions with high-energy electrons in the plasmasphere. By ray tracing the magnetospheric propagation of ELF/VLF emissions artificially generated at low-invariant latitudes, we evaluate the relativistic electron resonant energies along the ray paths and show that propagating artificial ELF/VLF waves can resonate with electrons from ~ 100 keV to ~ 10 MeV. We further implement test particle simulations to investigate the effects of resonant scattering of energetic electrons due to triggered monotonic/single-frequency ELF/VLF waves. The results indicate that within the period of a resonance timescale, changes in electron pitch angle and kinetic energy are stochastic, and the overall effect is cumulative, that is, the changes averaged over all test electrons increase monotonically with time. The localized rates of wave-induced pitch-angle scattering and momentum diffusion in the plasmasphere are analyzed in detail for artificially generated ELF/VLF whistlers with an observable in situ amplitude of ~ 10 pT. While the local momentum diffusion of relativistic electrons is small, with a rate of < 10-7 s-1, the local pitch-angle scattering can be intense near the loss cone with a rate of ~ 10-4 s-1. Our investigation further supports the feasibility of artificial triggering of ELF/VLF whistler waves for removal of high-energy electrons at lower L shells within the plasmasphere. Moreover, our test particle simulation results show quantitatively good agreement with quasi-linear diffusion coefficients, confirming the applicability of both methods to evaluate the resonant diffusion effect of artificial generated ELF/VLF whistlers.

Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations

NASA Astrophysics Data System (ADS)

Zhang, Linghai

2017-10-01

The main purposes of this paper are to accomplish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations ut =uxx + α [ βH (u - θ) - u ] - w, wt = ε (u - γw) and to establish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ], under different conditions on the model constants. To establish the bifurcation for the system, we will study the existence and instability of a standing pulse solution if 0 < 2 (1 + αγ) θ < αβγ; the existence and stability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and γ2 ε > 1; the existence and instability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and 0 <γ2 ε < 1; the existence and instability of an upside down standing pulse solution if 0 < (1 + αγ) θ < αβγ < 2 (1 + αγ) θ. To establish the bifurcation for the scalar equation, we will study the existence and stability of a traveling wave front as well as the existence and instability of a standing pulse solution if 0 < 2 θ < β; the existence and stability of two standing wave fronts if 2 θ = β; the existence and stability of a traveling wave front as well as the existence and instability of an upside down standing pulse solution if 0 < θ < β < 2 θ. By the way, we will also study the existence and stability of a traveling wave back of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ] -w0, where w0 = α (β - 2 θ) > 0 is a positive constant, if 0 < 2 θ < β. To achieve the main goals, we will make complete use of the special structures of the model equations and we will construct Evans functions and apply them to study the eigenvalues and eigenfunctions of several eigenvalue problems associated with several linear differential operators. It turns out that a complex number λ0 is an eigenvalue of the linear differential operator, if and only if λ0 is a zero of the Evans function. The stability, instability and bifurcations of the nonlinear waves follow from the zeros of the Evans functions. A very important motivation to study the existence, stability, instability and bifurcations of the nonlinear waves is to study the existence and stability/instability of infinitely many fast/slow multiple traveling pulse solutions of the nonlinear system of reaction diffusion equations. The existence and stability of infinitely many fast multiple traveling pulse solutions are of great interests in mathematical neuroscience.

On singlet s-wave electron-hydrogen scattering.

NASA Technical Reports Server (NTRS)

Madan, R. N.

1973-01-01

Discussion of various zeroth-order approximations to s-wave scattering of electrons by hydrogen atoms below the first excitation threshold. The formalism previously developed by the author (1967, 1968) is applied to Feshbach operators to derive integro-differential equations, with the optical-potential set equal to zero, for the singlet and triplet cases. Phase shifts of s-wave scattering are computed in the zeroth-order approximation of the Feshbach operator method and in the static-exchange approximation. It is found that the convergence of numerical computations is faster in the former approximation than in the latter.

Different approach to the modeling of nonfree particle diffusion

NASA Astrophysics Data System (ADS)

Buhl, Niels

2018-03-01

A new approach to the modeling of nonfree particle diffusion is presented. The approach uses a general setup based on geometric graphs (networks of curves), which means that particle diffusion in anything from arrays of barriers and pore networks to general geometric domains can be considered and that the (free random walk) central limit theorem can be generalized to cover also the nonfree case. The latter gives rise to a continuum-limit description of the diffusive motion where the effect of partially absorbing barriers is accounted for in a natural and non-Markovian way that, in contrast to the traditional approach, quantifies the absorptivity of a barrier in terms of a dimensionless parameter in the range 0 to 1. The generalized theorem gives two general analytic expressions for the continuum-limit propagator: an infinite sum of Gaussians and an infinite sum of plane waves. These expressions entail the known method-of-images and Laplace eigenfunction expansions as special cases and show how the presence of partially absorbing barriers can lead to phenomena such as line splitting and band gap formation in the plane wave wave-number spectrum.

Distorted-wave methods for electron capture in ion-atom collisions

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

Burgdoerfer, J.; Taulbjerg, K.

1986-05-01

Distorted-wave methods for electron capture are discussed with emphasis on the surface term in the T matrix and on the properties of the associated integral equations. The surface term is generally nonvanishing if the distorted waves are sufficiently accurate to include parts of the considered physical process. Two examples are considered in detail. If distorted waves of the strong-potential Born-approximation (SPB) type are employed the surface term supplies the first-Born-approximation part of the T matrix. The surface term is shown to vanish in the continuum-distorted-wave (CDW) method. The integral kernel is in either case free of the dangerous disconnected termsmore » discussed by Greider and Dodd but the CDW theory is peculiar in the sense that its first-order approximation (CDW1) excludes a specific on-shell portion of the double-scattering term that is closely connected with the classical Thomas process. The latter is described by the second-order term in the CDW series. The distorted-wave Born approximation with SPB waves is shown to be free of divergences. In the limit of asymmetric collisions the DWB suggests a modification of the SPB approximation to avoid the divergence problem recently identified by Dewangan and Eichler.« less

Diffuse reflectance relations based on diffusion dipole theory for large absorption and reduced scattering

NASA Astrophysics Data System (ADS)

Bremmer, Rolf H.; van Gemert, Martin J. C.; Faber, Dirk J.; van Leeuwen, Ton G.; Aalders, Maurice C. G.

2013-08-01

Diffuse reflectance spectra are used to determine the optical properties of biological samples. In medicine and forensic science, the turbid objects under study often possess large absorption and/or scattering properties. However, data analysis is frequently based on the diffusion approximation to the radiative transfer equation, implying that it is limited to tissues where the reduced scattering coefficient dominates over the absorption coefficient. Nevertheless, up to absorption coefficients of 20 m at reduced scattering coefficients of 1 and 11.5 mm-1, we observed excellent agreement (r2=0.994) between reflectance measurements of phantoms and the diffuse reflectance equation proposed by Zonios et al. [Appl. Opt. 38, 6628-6637 (1999)], derived as an approximation to one of the diffusion dipole equations of Farrell et al. [Med. Phys. 19, 879-888 (1992)]. However, two parameters were fitted to all phantom experiments, including strongly absorbing samples, implying that the reflectance equation differs from diffusion theory. Yet, the exact diffusion dipole approximation at high reduced scattering and absorption also showed agreement with the phantom measurements. The mathematical structure of the diffuse reflectance relation used, derived by Zonios et al. [Appl. Opt. 38, 6628-6637 (1999)], explains this observation. In conclusion, diffuse reflectance relations derived as an approximation to the diffusion dipole theory of Farrell et al. can analyze reflectance ratios accurately, even for much larger absorption than reduced scattering coefficients. This allows calibration of fiber-probe set-ups so that the object's diffuse reflectance can be related to its absorption even when large. These findings will greatly expand the application of diffuse reflection spectroscopy. In medicine, it may allow the use of blue/green wavelengths and measurements on whole blood, and in forensic science, it may allow inclusion of objects such as blood stains and cloth at crime scenes.

Counterstreaming beams and flat-top electron distributions observed with Langmuir, Whistler, and compressional Alfvén waves in earth's magnetic tail.

PubMed

Teste, Alexandra; Parks, George K

2009-02-20

Relevant new clues to wave-particle interactions have been obtained in Earth's plasma sheet (PS). The plasma measurements made on Cluster spacecraft show that broadband (approximately 2-6 kHz) electrostatic emissions, in the PS boundary layer, are associated with cold counterstreaming electrons flowing at 5-12x10(3) km s(-1) through hot Maxwellian plasma. In the current sheet (CS), electromagnetic whistler mode waves (approximately 10-80 Hz) and compressional Alfvén waves (<2 Hz) are detected with flat-topped electron distributions whose cutoff speeds are approximately 15-17x10(3) km s(-1). These waves are damped in the central CS where |B|

Evaluation of the oblique detonation wave ramjet

NASA Technical Reports Server (NTRS)

Morrison, R. B.

1978-01-01

The potential performance of oblique detonation wave ramjets is analyzed in terms of multishock diffusion, oblique detonation waves, and heat release. Results are presented in terms of thrust coefficients and specific impulses for a range of flight Mach numbers of 6 to 16.

Reaction-diffusion waves in neuronal tissue and the window of cortical excitability

NASA Astrophysics Data System (ADS)

Dahlem, M. A.; Müller, S. C.

2004-07-01

Spreading depression (SD) is a dynamic wave phenomenon occurring in all gray matter regions of the central nervous systems (CNS). It is characterized by a sudden breakdown of neuronal activity and accompanied by a massive influx and efflux of ions across the membrane of neurons. The retina is a constituent of the CNS in which one can easily observe the dynamic behavior of the SD wave fronts, because SD changes the optical properties of the tissue. There is ample evidence that SD belongs to the self-organization processes due to the coupling of reaction with diffusion in excitable medium. It is assumed that the occurrence of SD is associated with some neurological symptoms of migraine with aura. A frequently reported aura symptom is a traveling visual blind region (scotoma) with a preceding figure of scintillating line segments. The characteristic form and development of the scotoma suggests that the underlying phenomenon is a wave propagating through the primary visual cortex, most likely the cortical spreading depression. In this article we discuss similarities between SD waves and the migraine aura on the basis of properties of reaction-diffusion waves known from other excitable media. In particular, the propagation velocities, the shape and the dynamics of the waves are compared with each other. We find that the assumption of the neuronal tissue to be in a state of only weak excitability explains some properties of the migraine aura, such as the confined appearance and its propagation with a stable velocity.

Epileptic encephalopathy with continuous spike-waves during sleep: the need for transition from childhood to adulthood medical care appears to be related to etiology.

PubMed

de Saint-Martin, Anne; Rudolf, Gabrielle; Seegmuller, Caroline; Valenti-Hirsch, Maria Paola; Hirsch, Edouard

2014-08-01

Epileptic encephalopathy with continuous diffuse spike-waves during slow-wave sleep (ECSWS) presents clinically with infrequent nocturnal focal seizures, atypical absences related to secondary bilateral synchrony, negative myoclonia, and atonic and rare generalized tonic-clonic seizures. The unique electroencephalography (EEG) pattern found in ECSWS consists of continuous, diffuse, bilateral spike-waves during slow-wave sleep. Despite the eventual disappearance of clinical seizures and EEG abnormalities by adolescence, the prognosis is guarded in most cases because of neuropsychological and behavioral deficits. ECSWS has a heterogeneous etiology (genetic, structural, and unknown). Because epilepsy and electroencephalography (EEG) abnormalities in epileptic encephalopathy with continuous diffuse spike-waves during slow-wave sleep (ECSWS) are self-limited and age related, the need for ongoing medical care and transition to adult care might be questioned. For adolescents in whom etiology remains unknown (possibly genetic) and who experience the disappearance of seizures and EEG abnormalities, there is rarely need for long-term neurologic follow-up, because often a relatively normal cognitive and social evolution follows. However, the majority of patients with structural and possibly "genetic syndromic" etiologies will have persistent cognitive deficits and will need suitable socioeducative care. Therefore, the transition process in ECSWS will depend mainly on etiology and its related features (epileptic active phase duration, and cognitive and behavioral evolution) and revolve around neuropsychological and social support rather than medical and pharmacologic follow-up. Wiley Periodicals, Inc. © 2014 International League Against Epilepsy.

Exact Markov chain and approximate diffusion solution for haploid genetic drift with one-way mutation.

PubMed

Hössjer, Ola; Tyvand, Peder A; Miloh, Touvia

2016-02-01

The classical Kimura solution of the diffusion equation is investigated for a haploid random mating (Wright-Fisher) model, with one-way mutations and initial-value specified by the founder population. The validity of the transient diffusion solution is checked by exact Markov chain computations, using a Jordan decomposition of the transition matrix. The conclusion is that the one-way diffusion model mostly works well, although the rate of convergence depends on the initial allele frequency and the mutation rate. The diffusion approximation is poor for mutation rates so low that the non-fixation boundary is regular. When this happens we perturb the diffusion solution around the non-fixation boundary and obtain a more accurate approximation that takes quasi-fixation of the mutant allele into account. The main application is to quantify how fast a specific genetic variant of the infinite alleles model is lost. We also discuss extensions of the quasi-fixation approach to other models with small mutation rates. Copyright © 2015 Elsevier Inc. All rights reserved.

Radial transport of radiation belt electrons in kinetic field-line resonances

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

Chaston, Christopher C.; Bonnell, J. W.; Wygant, J. R.

A representative case study from the Van Allen Probes during a geomagnetic storm recovery phase reveals enhanced electron fluxes at intermediate pitch angles over energies from ~100 keV to 5 MeV coincident with broadband low-frequency electromagnetic waves. The statistical properties of these waves are used to build a model for radial diffusion via drift-bounce resonances in kinetic Alfvén eigenmodes/kinetic field-line resonances. Estimated diffusion coefficients indicate timescales for radial transport on the order of hours in storm time events at energies from <100 keV to MeVs over equatorial pitch angles from the edge of the loss cone to nearly perpendicular tomore » the geomagnetic field. In conclusion, the correlation of kinetic resonances with electron depletions and enhancements during storm main phase and recovery, and the rapid diffusion these waves drive, suggests that they may modulate the outer radiation belt.« less

Radial transport of radiation belt electrons in kinetic field-line resonances

DOE PAGES

Chaston, Christopher C.; Bonnell, J. W.; Wygant, J. R.; ...

2017-07-25

A representative case study from the Van Allen Probes during a geomagnetic storm recovery phase reveals enhanced electron fluxes at intermediate pitch angles over energies from ~100 keV to 5 MeV coincident with broadband low-frequency electromagnetic waves. The statistical properties of these waves are used to build a model for radial diffusion via drift-bounce resonances in kinetic Alfvén eigenmodes/kinetic field-line resonances. Estimated diffusion coefficients indicate timescales for radial transport on the order of hours in storm time events at energies from <100 keV to MeVs over equatorial pitch angles from the edge of the loss cone to nearly perpendicular tomore » the geomagnetic field. In conclusion, the correlation of kinetic resonances with electron depletions and enhancements during storm main phase and recovery, and the rapid diffusion these waves drive, suggests that they may modulate the outer radiation belt.« less

Dynamics of Mesoscale Magnetic Field in Diffusive Shock Acceleration

NASA Astrophysics Data System (ADS)

Diamond, P. H.; Malkov, M. A.

2007-01-01

We present a theory for the generation of mesoscale (krg<<1, where rg is the cosmic-ray gyroradius) magnetic fields during diffusive shock acceleration. The decay or modulational instability of resonantly excited Alfvén waves scattering off ambient density perturbations in the shock environment naturally generates larger scale fields. For a broad spectrum of perturbations, the physical mechanism of energy transfer is random refraction, represented by the diffusion of Alfvén wave packets in k-space. The scattering field can be produced directly by the decay instability or by the Drury instability, a hydrodynamic instability driven by the cosmic-ray pressure gradient. This process is of interest to acceleration since it generates waves of longer wavelength, and so enables the confinement and acceleration of higher energy particles. This process also limits the intensity of resonantly generated turbulent magnetic fields on rg scales.

Liquid Aluminum: Atomic diffusion and viscosity from ab initio molecular dynamics

PubMed Central

Jakse, Noel; Pasturel, Alain

2013-01-01

We present a study of dynamic properties of liquid aluminum using density-functional theory within the local-density (LDA) and generalized gradient (GGA) approximations. We determine the temperature dependence of the self-diffusion coefficient as well the viscosity using direct methods. Comparisons with experimental data favor the LDA approximation to compute dynamic properties of liquid aluminum. We show that the GGA approximation induce more important backscattering effects due to an enhancement of the icosahedral short range order (ISRO) that impact directly dynamic properties like the self-diffusion coefficient. All these results are then used to test the Stokes-Einstein relation and the universal scaling law relating the diffusion coefficient and the excess entropy of a liquid. PMID:24190311

A new nonlinear diffusion formalism in a magnetized plasma - Application to space physics and astrophysics

NASA Technical Reports Server (NTRS)

Karimbadi, H.; Krauss-Varban, D.

1992-01-01

A novel diffusion formalism that takes into account the finite width of resonances is presented. The resonance diagram technique is shown to reproduce the details of the particle orbits very accurately, and can be used to determine the acceleration/scattering in the presence of a given wave spectrum. Ways in which the nonlinear orbits can be incorporated into the diffusion equation are shown. The resulting diffusion equation is an extension of the Q-L theory to cases where the waves have large amplitudes and/or are coherent. This new equation does not have a gap at 90 deg in cases where the individual orbits can cross the gap. The conditions under which the resonance gap at 90-deg pitch angle exits are also examined.

Anomalous diffusion in a dynamical optical lattice

NASA Astrophysics Data System (ADS)

Zheng, Wei; Cooper, Nigel R.

2018-02-01

Motivated by experimental progress in strongly coupled atom-photon systems in optical cavities, we study theoretically the quantum dynamics of atoms coupled to a one-dimensional dynamical optical lattice. The dynamical lattice is chosen to have a period that is incommensurate with that of an underlying static lattice, leading to a dynamical version of the Aubry-André model which can cause localization of single-particle wave functions. We show that atomic wave packets in this dynamical lattice generically spread via anomalous diffusion, which can be tuned between superdiffusive and subdiffusive regimes. This anomalous diffusion arises from an interplay between Anderson localization and quantum fluctuations of the cavity field.

Ion precipitation from the inner plasma sheet due to stochastic diffusion

NASA Technical Reports Server (NTRS)

Zelenyi, L.; Galeev, A.; Kennel, C. F.

1990-01-01

Plasma sheet ions do not conserve their first adiabatic invariant when the magnetic field is appreciably tail-like. They do conserve a different adiabatic invariant but only to linear, rather than exponential, accuracy in the appropriate small parameter. Thus significant stochastic diffusion can occur for particles crossing the separatrix dividing the segments of orbits on which the particles cross and do not cross the tail midplane. Such ions can escape the plasma sheet and precipitate into the atmosphere. Stochastic scattering is strongest from those field lines where the ion's Larmor period in the normal component of the neutral sheet magnetic field approximately equals its bounce period. By comparing the rates of stochastic ion loss and convection in the tail, it is possible to estimate the location and thickness of the inner edge of the ion plasma sheet created by stochastic ion loss. Ions of different masses precipitate into the atmosphere at slightly different locations. Since wave particle interactions are not needed, this precipitation will always occur and should be particularly evident during quiet geomagnetic conditions, when it is less likely to be masked by other precipitation mechanisms.

Measuring Thermal Diffusivity Of A High-Tc Superconductor

NASA Technical Reports Server (NTRS)

Powers, Charles E.; Oh, Gloria; Leidecker, Henning

1992-01-01

Technique for measuring thermal diffusivity of superconductor of high critical temperature based on Angstrom's temperature-wave method. Peltier junction generates temperature oscillations, which propagate with attenuation up specimen. Thermal diffusivity of specimen calculated from distance between thermocouples and amplitudes and phases of oscillatory components of thermocouple readings.

The Microtremor H/V Spectral Ratio: The Physical Basis of the Diffuse Field Assumption

NASA Astrophysics Data System (ADS)

Sanchez-Sesma, F. J.

2016-12-01

The microtremor H/V spectral ratio (MHVSR) is popular to obtain the dominant frequency at a site. Despite the success of MHVSR some controversy arose regarding its physical basis. One approach is the Diffuse Field Assumption, DFA. It is then assumed that noise diffuse features come from multiple scattering within the medium. According to theory, the average of the autocorrelation is proportional to directional energy density (DED) and to the imaginary part of the Green's function for same source and receiver. Then, the square of MHVSR is a ratio of DEDs which, in a horizontally layered system, is 2xImG11/ImG33, where ImG11 and ImG33 are the imaginary parts of Green's functions for horizontal and vertical components. This has physical implications that emerge from the duality DED-force, implicit in the DFA. Consider a surface force at a half-space. The radiated energy is carried away by various wave types and the proportions of each one are precisely the fractions of the energy densities of a diffuse elastic wave field at the free surface. Thus, some properties of applied forces are also characteristics of DEDs. For example, consider a Poisson solid. For a normal point load, 67 per cent of energy is carried away by Rayleigh waves. For the tangential case, it is less well known that, 77 per cent of energy goes as shear waves. In a full space, 92 per cent of the energy is emitted as shear waves. The horizontal DED at the half-space surface implies significant emission of down-going shear waves that explains the curious stair-like resonance spectrum of ImG11. Both ImG11 and ImG33 grow linearly versus frequency and this represents wave emission. For a layered medium, besides wave emission, the ensuing variations correspond to reflected waves. For high frequencies, ImG33 depends on the properties of the top layer. Reflected body waves are very small and Rayleigh waves behave in the top layer as in a kind of mini half-space. From HVSR one can invert the velocity model using the DFA. It is possible to compute efficiently the imaginary part of the Green's functions from the integrals along the radial wavenumber k. This can be made using either the Bouchon DWN method or the Cauchy residue theorem to get the pole contributions of Rayleigh and Love surface waves in the k complex plane. This allows separating the contributions of each wave type.

Nonlinear Acoustic Waves Generated by Surface Disturbances and Their Effects on Lower Thermospheric Composition

NASA Astrophysics Data System (ADS)

Pineyro, B.; Snively, J. B.

2017-12-01

Recent 1D and 2D nonlinear atmospheric models have provided important insight into acoustic waves generated by seismic events, which may steepen into shocks or saw-tooth trains while also dissipating strongly in the thermosphere [e.g., Chum et al., JGR, 121, 2016; Zettergren et al., JGR, 122, 2017]. Although they have yield results that agree with with observations of ionospheric perturbations, dynamical models for the diffusive and stratified lower thermosphere [e.g., Snively and Pasko, JGR, 113, 2008] often use single gas approximations with height-dependent physical properties (e.g. mean molecular weight, specific heats) that do not vary with time (fixed composition). This approximation is simpler and less computationally expensive than a true multi-fluid model, yet captures the important physical transition between molecular and atomic gases in the lower thermosphere. Models with time-dependent composition and properties have been shown to outperform commonly used models with fixed properties; these time-dependent effects have been included in a one-gas model by adding an advection equation for the molecular weight, finding closer agreement to a true binary-gas model [Walterscheid and Hickey, JGR, 106, 2001 and JGR, 117, 2012]. Here, a one-dimensional nonlinear mass fraction approach to multi-constituent gas modeling, motivated by the results of Walterscheid and Hickey [2001, 2012], is presented. The finite volume method of Bale et al. [SIAM JSC, 24, 2002] is implemented in Clawpack [http://www.clawpack.org; LeVeque, 2002] with a Riemann Solver to solve the Euler Equations including multiple species, defined by their mass fractions, as they undergo advection. Viscous dissipation and thermal conduction are applied via a fractional step method. The model is validated with shock tube problems for two species, and then applied to investigate propagating nonlinear acoustic waves from ground to thermosphere, such as following the 2011 Tohoku Earthquake [e.g., Zettergren et al., 2017] and rocket launches [Mabie et al., GRL, 43, 2016]. The limits of applicability are investigated for vertically propagating acoustic waves near the cut-off frequency, and for simulations of steepening waves at finite spatial resolution [Sabatini et al., JASA, 140, 2016].

Ion radial diffusion in an electrostatic impulse model for stormtime ring current formation

NASA Technical Reports Server (NTRS)

Chen, Margaret W.; Schulz, Michael; Lyons, Larry R.; Gorney, David J.

1992-01-01

Guiding-center simulations of stormtime transport of ring-current and radiation-belt ions having first adiabatic invariants mu is approximately greater than 15 MeV/G (E is approximately greater than 165 keV at L is approximately 3) are surprisingly well described (typically within a factor of approximately less than 4) by the quasilinear theory of radial diffusion. This holds even for the case of an individual model storm characterized by substorm-associated impulses in the convection electric field, provided that the actual spectrum of the electric field is incorporated in the quasilinear theory. Correction of the quasilinear diffusion coefficient D(sub LL)(sup ql) for drift-resonance broadening (so as to define D(sub LL)(sup ql)) reduced the typical discrepancy with the diffusion coefficients D(sub LL)(sup sim) deduced from guiding-center simulations of representative-particle trajectories to a factor of approximately 3. The typical discrepancy was reduced to a factor of approximately 1.4 by averaging D(sub LL)(sup sim), D(sub LL)(sup ql), and D(sub LL)(sup rb) over an ensemble of model storms characterized by different (but statistically equivalent) sets of substorm-onset times.

A space-time discretization procedure for wave propagation problems

NASA Technical Reports Server (NTRS)

Davis, Sanford

1989-01-01

Higher order compact algorithms are developed for the numerical simulation of wave propagation by using the concept of a discrete dispersion relation. The dispersion relation is the imprint of any linear operator in space-time. The discrete dispersion relation is derived from the continuous dispersion relation by examining the process by which locally plane waves propagate through a chosen grid. The exponential structure of the discrete dispersion relation suggests an efficient splitting of convective and diffusive terms for dissipative waves. Fourth- and eighth-order convection schemes are examined that involve only three or five spatial grid points. These algorithms are subject to the same restrictions that govern the use of dispersion relations in the constructions of asymptotic expansions to nonlinear evolution equations. A new eighth-order scheme is developed that is exact for Courant numbers of 1, 2, 3, and 4. Examples are given of a pulse and step wave with a small amount of physical diffusion.

Stability of wave processes in a rotating electrically conducting fluid

NASA Astrophysics Data System (ADS)

Peregudin, S. I.; Peregudina, E. S.; Kholodova, S. E.

2018-05-01

The paper puts forward a mathematical model of dynamics of spatial large-scale motions in a rotating layer of electrically conducting incompressible perfect fluid of variable depth with due account of dissipative effects. The resulting boundary-value problem is reduced to a vector system of partial differential equations for any values of the Reynolds number. Theoretical analysis of the so-obtained analytical solution reveals the effect of the magnetic field diffusion on the stability of the wave mode — namely, with the removed external magnetic field, the diffusion of the magnetic field promotes its damping. Besides, a criterion of stability of a wave mode is obtained.

Cloaks for suppression or enhancement of scattering of diffuse photon density waves

NASA Astrophysics Data System (ADS)

Renthlei, Lalruatfela; Ramakrishna, S. Anantha; Wanare, Harshawardhan

2018-07-01

Enhancement of wave-like characteristics of heavily damped diffuse photon density waves in a random medium by amplification can induce strongly localised resonances. These resonances can be used to either suppress or enhance scattering from an inhomogeneity in the random medium by cloaking the inhomogeneous region by a shell of random medium with the correct levels of absorption or amplification. A spherical core-shell structure consisting of a shell of a random amplifying medium is shown to enhance or suppress specific resonant modes. A shell with an absorbing random medium is also shown to suppress scattering which can also be used for cloaking the core region.

Convection in a colloidal suspension in a closed horizontal cell

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

Smorodin, B. L., E-mail: bsmorodin@yandex.ru; Cherepanov, I. N.

2015-02-15

The experimentally detected [1] oscillatory regimes of convection in a colloidal suspension of nanoparticles with a large anomalous thermal diffusivity in a closed horizontal cell heated from below have been simulated numerically. The concentration inhomogeneity near the vertical cavity boundaries arising from the interaction of thermal-diffusion separation and convective mixing has been proven to serve as a source of oscillatory regimes (traveling waves). The dependence of the Rayleigh number at the boundary of existence of the traveling-wave regime on the aspect ratio of the closed cavity has been established. The spatial characteristics of the emerging traveling waves have been determined.

Radial diffusion of relativistic electrons into the radiation belt slot region during the 2003 Halloween geomagnetic storms

NASA Astrophysics Data System (ADS)

Loto'Aniu, T. M.; Mann, I. R.; Ozeke, L. G.; Chan, A. A.; Dent, Z. C.; Milling, D. K.

2006-04-01

A study was undertaken to estimate the radial diffusion timescale, τLL, for relativistic electrons (2-6 MeV) to diffuse into the slot region due to drift-resonance with Pc5 ULF waves (2-10 mHz) on 29 October 2003. Large amplitude ULF waves were observed by ground-based magnetometer arrays to penetrate deep into the slot region (L ≃ 2-3) starting at 0600 UT and maximising (˜200 nT p-p) between 0930-1630 UT. Around the same time, the SAMPEX PET instrument measured an over two orders of magnitude increase in relativistic (2-6 MeV) electron flux levels in ˜24 hours within the slot region. The ground-based D-component magnetic power spectral densities (PSDδB) for 29 October were estimated for six latitudinally spaced ground stations covering L ˜ 2.3-4.3 for an observed ULF wave with central frequency ˜4 mHz. The PSDδB values were used to calculate the in situ equatorial poloidal wave electric field power spectral densities (PSDδEm) using a standing Alfvén wave model. The radial diffusion coefficients, DLL, were estimated using the PSDδEm values. The fastest τLL were 3-5 hours at L > 4, while τLL initially increased with decreasing L-value below L ≃ 4; peaking at L ≃ 3 with τLL ˜ 12-24 hours with PSDδEm estimated using a wave frequency bandwidth between Δf = 1 mHz and Δf = 2.5 mHz. The τLL over the L-range L ˜ 2.3-3.3 were consistent with the timescales observed by SAMPEX for the increase in relativistic fluxes in the slot region on 29 October. The authors believe that this is the first example of the ULF wave drift-resonance with relativistic electrons explaining a radiation belt slot region filling event.

Physics of the diffusion region in the Magnetospheric Multiscale era

NASA Astrophysics Data System (ADS)

Chen, L. J.; Hesse, M.; Wang, S.; Ergun, R.; Bessho, N.; Burch, J. L.; Giles, B. L.; Torbert, R. B.; Gershman, D. J.; Wilson, L. B., III; Dorelli, J.; Pollock, C. J.; Moore, T. E.; Lavraud, B.; Strangeway, R. J.; Russell, C. T.; Khotyaintsev, Y. V.; Le Contel, O.; Avanov, L. A.

2016-12-01

Encounters of reconnection diffusion regions by the Magnetospheric Multiscale (MMS) mission during its first magnetopause scan are studied in combination with theories and simulations. The goal is to understand by first-principles how stored magnetic energy is converted into plasma thermal and bulk flow energies via particle energization, mixing and interaction with waves. The magnetosheath population having much higher density than the magnetospheric plasma is an outstanding narrator for and participant in the magnetospheric part of the diffusion region. For reconnection with negligible guide fields, the accelerated magnetosheath population (for both electrons and ions) is cyclotron turned by the reconnected magnetic field to form outflow jets, and then gyrotropized downstream. Wave fluctuations are reduced in the central electron diffusion region (EDR) and do not dominate the energy conversion there. For an event with a significant guide field to magnetize the electrons, wave fluctuations at the lower hybrid frequency dominate the energy conversion in the EDR, and the fastest electron outflow is established dominantly by a strong perpendicular electric field via the ExB flow in one exhaust and by time-of-flight effects along with parallel electric field acceleration in the other. Whether the above features are common threads to magnetopause reconnection diffusion regions is a question to be further examined.

Spatial dispersion effects upon local excitation of extrinsic plasmons in a graphene micro-disk

NASA Astrophysics Data System (ADS)

Mencarelli, D.; Bellucci, S.; Sindona, A.; Pierantoni, L.

2015-11-01

Excitation of surface plasmon waves in extrinsic graphene is studied using a full-wave electromagnetic field solver as analysis engine. Particular emphasis is placed on the role played by spatial dispersion due to the finite size of the two-dimensional material at the micro-scale. A simple instructive set up is considered where the near field of a wire antenna is held at sub-micrometric distance from a disk-shaped graphene patch. The key-input of the simulation is the graphene conductivity tensor at terahertz frequencies, being modeled by the Boltzmann transport equation for the valence and conduction electrons at the Dirac points (where a linear wave-vector dependence of the band energies is assumed). The conductivity equation is worked out in different levels of approximations, based on the relaxation time ansatz with an additional constraint for particle number conservation. Both drift and diffusion currents are shown to significantly contribute to the spatially dispersive anisotropic features of micro-scale graphene. More generally, spatial dispersion effects are predicted to influence not only plasmon propagation free of external sources, but also typical scanning probe microscopy configurations. The paper sets the focus on plasmon excitation phenomena induced by near field probes, being a central issue for the design of optical devices and photonic circuits.

Oscillatory fluid flow in deformable tubes: Implications for pore-scale hydromechanics from comparing experimental observations with theoretical predictions.

PubMed

Kurzeja, Patrick; Steeb, Holger; Strutz, Marc A; Renner, Jörg

2016-12-01

Oscillatory flow of four fluids (air, water, two aqueous sodium-tungstate solutions) was excited at frequencies up to 250 Hz in tubes of two materials (steel, silicone) covering a wide range in length, diameter, and thickness. The hydrodynamical response was characterized by phase shift and amplitude ratio between pressures in an upstream (pressure excitation) and a downstream reservoir connected by the tubes. The resulting standing flow waves reflect viscosity-controlled diffusive behavior and inertia-controlled wave behavior for oscillation frequencies relatively low and high compared to Biot's critical frequency, respectively. Rigid-tube theories correspond well with the experimental results for steel tubes filled with air or water. The wave modes observed for silicone tubes filled with the rather incompressible liquids or air, however, require accounting for the solid's shear and bulk modulus to correctly predict speed of pressure propagation and deformation mode. The shear mode may be responsible for significant macroscopic attenuation in porous materials with effective frame-shear moduli lower than the bulk modulus of the pore fluid. Despite notable effects of the ratio of densities and of acoustic and shear velocity of fluid and solid, Biot's frequency remains an approximate indicator of the transition from the viscosity to the inertia controlled regime.

The narrow pulse approximation and long length scale determination in xenon gas diffusion NMR studies of model porous media

NASA Technical Reports Server (NTRS)

Mair, R. W.; Sen, P. N.; Hurlimann, M. D.; Patz, S.; Cory, D. G.; Walsworth, R. L.

2002-01-01

We report a systematic study of xenon gas diffusion NMR in simple model porous media, random packs of mono-sized glass beads, and focus on three specific areas peculiar to gas-phase diffusion. These topics are: (i) diffusion of spins on the order of the pore dimensions during the application of the diffusion encoding gradient pulses in a PGSE experiment (breakdown of the narrow pulse approximation and imperfect background gradient cancellation), (ii) the ability to derive long length scale structural information, and (iii) effects of finite sample size. We find that the time-dependent diffusion coefficient, D(t), of the imbibed xenon gas at short diffusion times in small beads is significantly affected by the gas pressure. In particular, as expected, we find smaller deviations between measured D(t) and theoretical predictions as the gas pressure is increased, resulting from reduced diffusion during the application of the gradient pulse. The deviations are then completely removed when water D(t) is observed in the same samples. The use of gas also allows us to probe D(t) over a wide range of length scales and observe the long time asymptotic limit which is proportional to the inverse tortuosity of the sample, as well as the diffusion distance where this limit takes effect (approximately 1-1.5 bead diameters). The Pade approximation can be used as a reference for expected xenon D(t) data between the short and the long time limits, allowing us to explore deviations from the expected behavior at intermediate times as a result of finite sample size effects. Finally, the application of the Pade interpolation between the long and the short time asymptotic limits yields a fitted length scale (the Pade length), which is found to be approximately 0.13b for all bead packs, where b is the bead diameter. c. 2002 Elsevier Sciences (USA).

The narrow pulse approximation and long length scale determination in xenon gas diffusion NMR studies of model porous media.

PubMed

Mair, R W; Sen, P N; Hürlimann, M D; Patz, S; Cory, D G; Walsworth, R L

2002-06-01

We report a systematic study of xenon gas diffusion NMR in simple model porous media, random packs of mono-sized glass beads, and focus on three specific areas peculiar to gas-phase diffusion. These topics are: (i) diffusion of spins on the order of the pore dimensions during the application of the diffusion encoding gradient pulses in a PGSE experiment (breakdown of the narrow pulse approximation and imperfect background gradient cancellation), (ii) the ability to derive long length scale structural information, and (iii) effects of finite sample size. We find that the time-dependent diffusion coefficient, D(t), of the imbibed xenon gas at short diffusion times in small beads is significantly affected by the gas pressure. In particular, as expected, we find smaller deviations between measured D(t) and theoretical predictions as the gas pressure is increased, resulting from reduced diffusion during the application of the gradient pulse. The deviations are then completely removed when water D(t) is observed in the same samples. The use of gas also allows us to probe D(t) over a wide range of length scales and observe the long time asymptotic limit which is proportional to the inverse tortuosity of the sample, as well as the diffusion distance where this limit takes effect (approximately 1-1.5 bead diameters). The Padé approximation can be used as a reference for expected xenon D(t) data between the short and the long time limits, allowing us to explore deviations from the expected behavior at intermediate times as a result of finite sample size effects. Finally, the application of the Padé interpolation between the long and the short time asymptotic limits yields a fitted length scale (the Padé length), which is found to be approximately 0.13b for all bead packs, where b is the bead diameter. c. 2002 Elsevier Sciences (USA).

Generation of Z mode radiation by diffuse auroral electron precipitation

NASA Astrophysics Data System (ADS)

Dusenbery, P. B.; Lyons, L. R.

1985-03-01

The generation of Z mode waves by diffuse auroral electron precipitation is investigated assuming that a loss cone exists in the upgoing portion of the distribution due to electron interactions with the atmosphere. The waves are generated at frequencies above, but very near, the local electron cyclotron frequency omega(e) and at wave normal angles larger than 90 deg. In agreement with Hewitt et al. (1983), the group velocity is directed downward in regions where the ratio of the upper hybrid frequency omega(pe) to Omega(e) is less than 0.5, so that Z mode waves excited above a satellite propagate toward it and away from the upper hybrid resonance. Z mode waves are excited in a frequency band between Omega(e) and about 1.02 Omega(e), and with maximum growth rates of about 0.001 Omega(e). The amplification length is about 100 km, which allows Z mode waves to grow to the intensities observed by high-altitude satellites.

Generation of Z mode radiation by diffuse auroral electron precipitation

NASA Technical Reports Server (NTRS)

Dusenbery, P. B.; Lyons, L. R.

1985-01-01

The generation of Z mode waves by diffuse auroral electron precipitation is investigated assuming that a loss cone exists in the upgoing portion of the distribution due to electron interactions with the atmosphere. The waves are generated at frequencies above, but very near, the local electron cyclotron frequency omega(e) and at wave normal angles larger than 90 deg. In agreement with Hewitt et al. (1983), the group velocity is directed downward in regions where the ratio of the upper hybrid frequency omega(pe) to Omega(e) is less than 0.5, so that Z mode waves excited above a satellite propagate toward it and away from the upper hybrid resonance. Z mode waves are excited in a frequency band between Omega(e) and about 1.02 Omega(e), and with maximum growth rates of about 0.001 Omega(e). The amplification length is about 100 km, which allows Z mode waves to grow to the intensities observed by high-altitude satellites.

Determination of the rotational diffusion tensor of macromolecules in solution from nmr relaxation data with a combination of exact and approximate methods--application to the determination of interdomain orientation in multidomain proteins.

PubMed

Ghose, R; Fushman, D; Cowburn, D

2001-04-01

In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand. Copyright 2001 Academic Press.

Determination of the Rotational Diffusion Tensor of Macromolecules in Solution from NMR Relaxation Data with a Combination of Exact and Approximate Methods—Application to the Determination of Interdomain Orientation in Multidomain Proteins

NASA Astrophysics Data System (ADS)

Ghose, Ranajeet; Fushman, David; Cowburn, David

2001-04-01

In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand.

Approximate non-linear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-03-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-waves scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform (GRT). After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic non-linear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P-wave and S-wave information.

Phase-Shifted Based Numerical Method for Modeling Frequency-Dependent Effects on Seismic Reflections

NASA Astrophysics Data System (ADS)

Chen, Xuehua; Qi, Yingkai; He, Xilei; He, Zhenhua; Chen, Hui

2016-08-01

The significant velocity dispersion and attenuation has often been observed when seismic waves propagate in fluid-saturated porous rocks. Both the magnitude and variation features of the velocity dispersion and attenuation are frequency-dependent and related closely to the physical properties of the fluid-saturated porous rocks. To explore the effects of frequency-dependent dispersion and attenuation on the seismic responses, in this work, we present a numerical method for seismic data modeling based on the diffusive and viscous wave equation (DVWE), which introduces the poroelastic theory and takes into account diffusive and viscous attenuation in diffusive-viscous-theory. We derive a phase-shift wave extrapolation algorithm in frequencywavenumber domain for implementing the DVWE-based simulation method that can handle the simultaneous lateral variations in velocity, diffusive coefficient and viscosity. Then, we design a distributary channels model in which a hydrocarbon-saturated sand reservoir is embedded in one of the channels. Next, we calculated the synthetic seismic data to analytically and comparatively illustrate the seismic frequency-dependent behaviors related to the hydrocarbon-saturated reservoir, by employing DVWE-based and conventional acoustic wave equation (AWE) based method, respectively. The results of the synthetic seismic data delineate the intrinsic energy loss, phase delay, lower instantaneous dominant frequency and narrower bandwidth due to the frequency-dependent dispersion and attenuation when seismic wave travels through the hydrocarbon-saturated reservoir. The numerical modeling method is expected to contribute to improve the understanding of the features and mechanism of the seismic frequency-dependent effects resulted from the hydrocarbon-saturated porous rocks.

Symmetric Positive 4th Order Tensors & Their Estimation from Diffusion Weighted MRI⋆

PubMed Central

Barmpoutis, Angelos; Jian, Bing; Vemuri, Baba C.; Shepherd, Timothy M.

2009-01-01

In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing a 2nd order tensor has been commonly used to approximate the diffusivity function at each lattice point of the DW-MRI data. It is now well known that this 2nd-order approximation fails to approximate complex local tissue structures, such as fibers crossings. In this paper we employ a 4th order symmetric positive semi-definite (PSD) tensor approximation to represent the diffusivity function and present a novel technique to estimate these tensors from the DW-MRI data guaranteeing the PSD property. There have been several published articles in literature on higher order tensor approximations of the diffusivity function but none of them guarantee the positive semi-definite constraint, which is a fundamental constraint since negative values of the diffusivity coefficients are not meaningful. In our methods, we parameterize the 4th order tensors as a sum of squares of quadratic forms by using the so called Gram matrix method from linear algebra and its relation to the Hilbert’s theorem on ternary quartics. This parametric representation is then used in a nonlinear-least squares formulation to estimate the PSD tensors of order 4 from the data. We define a metric for the higher-order tensors and employ it for regularization across the lattice. Finally, performance of this model is depicted on synthetic data as well as real DW-MRI from an isolated rat hippocampus. PMID:17633709

Effect of Upstream ULF Waves on the Energetic Ion Diffusion at the Earth's Foreshock. I. Theory and Simulation

NASA Astrophysics Data System (ADS)

Otsuka, Fumiko; Matsukiyo, Shuichi; Kis, Arpad; Nakanishi, Kento; Hada, Tohru

2018-02-01

Field-aligned diffusion of energetic ions in the Earth’s foreshock is investigated by using the quasi-linear theory (QLT) and test particle simulation. Non-propagating MHD turbulence in the solar wind rest frame is assumed to be purely transverse with respect to the background field. We use a turbulence model based on a multi-power-law spectrum including an intense peak that corresponds to upstream ULF waves resonantly generated by the field-aligned beam (FAB). The presence of the ULF peak produces a concave shape of the diffusion coefficient when it is plotted versus the ion energy. The QLT including the effect of the ULF wave explains the simulation result well, when the energy density of the turbulent magnetic field is 1% of that of the background magnetic field and the power-law index of the wave spectrum is less than 2. The numerically obtained e-folding distances from 10 to 32 keV ions match with the observational values in the event discussed in the companion paper, which contains an intense ULF peak in the spectra generated by the FAB. Evolution of the power spectrum of the ULF waves when approaching the shock significantly affects the energy dependence of the e-folding distance.

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

Wolfram, Phillip J.; Ringler, Todd D.

Meridional diffusivity is assessed in this paper for a baroclinically unstable jet in a high-latitudeIdealized Circumpolar Current (ICC) using the Model for Prediction Across Scales-Ocean (MPAS-O) and the online Lagrangian In-situ Global High-performance particle Tracking (LIGHT) diagnostic via space-time dispersion of particle clusters over 120 monthly realizations of O(10 6) particles on 11 potential density surfaces. Diffusivity in the jet reaches values of O(6000 m 2 s -1) and is largest near the critical layer supporting mixing suppression and critical layer theory. Values in the vicinity of the shelf break are suppressed to O(100 m 2 s -1) due tomore » the presence of westward slope front currents. Diffusivity attenuates less rapidly with depth in the jet than both eddy velocity and kinetic energy scalings would suggest. Removal of the mean flow via high-pass filtering shifts the nonlinear parameter (ratio of the eddy velocity to eddy phase speed) into the linear wave regime by increasing the eddy phase speed via the depth-mean flow. Low-pass filtering, in contrast, quantifies the effect of mean shear. Diffusivity is decomposed into mean flow shear, linear waves, and the residual nonhomogeneous turbulence components, where turbulence dominates and eddy-produced filamentation strained by background mean shear enhances mixing, accounting for ≥ 80% of the total diffusivity relative to mean shear [O(100 m 2 s -1)], linear waves [O(1000 m 2 s -1)], and undecomposed full diffusivity [O(6000 m 2 s -1)]. Finally, diffusivity parameterizations accounting for both the nonhomogeneous turbulence residual and depth variability are needed.« less

Statistics of multiply scattered broadband terahertz pulses.

PubMed

Pearce, Jeremy; Jian, Zhongping; Mittleman, Daniel M

2003-07-25

We describe the first measurements of the diffusion of broadband single-cycle optical pulses through a highly scattering medium. Using terahertz time-domain spectroscopy, we measure the electric field of a multiply scattered wave with a time resolution shorter than one optical cycle. This time-domain measurement provides information on the statistics of both the amplitude and phase distributions of the diffusive wave. We develop a theoretical description, suitable for broadband radiation, which adequately describes the experimental results.

Wave and pseudo-diffusion equations from squeezed states

NASA Technical Reports Server (NTRS)

Daboul, Jamil

1993-01-01

We show that the probability distributions P(sub n)(q,p;y) := the absolute value squared of (n(p,q;y), which are obtained from squeezed states, obey an interesting partial differential equation, to which we give two intuitive interpretations: as a wave equation in one space dimension; and as a pseudo-diffusion equation. We also study the corresponding Wehrl entropies S(sub n)(y), and we show that they have minima at zero squeezing, y = 0.

Hydrodynamic theory of diffusion in two-temperature multicomponent plasmas

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

Ramshaw, J.D.; Chang, C.H.

Detailed numerical simulations of multicomponent plasmas require tractable expressions for species diffusion fluxes, which must be consistent with the given plasma current density J{sub q} to preserve local charge neutrality. The common situation in which J{sub q} = 0 is referred to as ambipolar diffusion. The use of formal kinetic theory in this context leads to results of formidable complexity. We derive simple tractable approximations for the diffusion fluxes in two-temperature multicomponent plasmas by means of a generalization of the hydrodynamical approach used by Maxwell, Stefan, Furry, and Williams. The resulting diffusion fluxes obey generalized Stefan-Maxwell equations that contain drivingmore » forces corresponding to ordinary, forced, pressure, and thermal diffusion. The ordinary diffusion fluxes are driven by gradients in pressure fractions rather than mole fractions. Simplifications due to the small electron mass are systematically exploited and lead to a general expression for the ambipolar electric field in the limit of infinite electrical conductivity. We present a self-consistent effective binary diffusion approximation for the diffusion fluxes. This approximation is well suited to numerical implementation and is currently in use in our LAVA computer code for simulating multicomponent thermal plasmas. Applications to date include a successful simulation of demixing effects in an argon-helium plasma jet, for which selected computational results are presented. Generalizations of the diffusion theory to finite electrical conductivity and nonzero magnetic field are currently in progress.« less

Explicit Global Simulation of Gravity Waves up to the Lower Thermosphere

NASA Astrophysics Data System (ADS)

Becker, E.

2016-12-01

At least for short-term simulations, middle atmosphere general circulation models (GCMs) can be run with sufficiently high resolution in order to describe a good part of the gravity wave spectrum explicitly. Nevertheless, the parameterization of unresolved dynamical scales remains an issue, especially when the scales of parameterized gravity waves (GWs) and resolved GWs become comparable. In addition, turbulent diffusion must always be parameterized along with other subgrid-scale dynamics. A practical solution to the combined closure problem for GWs and turbulent diffusion is to dispense with a parameterization of GWs, apply a high spatial resolution, and to represent the unresolved scales by a macro-turbulent diffusion scheme that gives rise to wave damping in a self-consistent fashion. This is the approach of a few GCMs that extend from the surface to the lower thermosphere and simulate a realistic GW drag and summer-to-winter-pole residual circulation in the upper mesosphere. In this study we describe a new version of the Kuehlungsborn Mechanistic general Circulation Model (KMCM), which includes explicit (though idealized) computations of radiative transfer and the tropospheric moisture cycle. Particular emphasis is spent on 1) the turbulent diffusion scheme, 2) the attenuation of resolved GWs at critical levels, 3) the generation of GWs in the middle atmosphere from body forces, and 4) GW-tidal interactions (including the energy deposition of GWs and tides).

Density waves in Saturn's rings

NASA Technical Reports Server (NTRS)

Cuzzi, J. N.; Lissauer, J. J.; Shu, F. H.

1981-01-01

Certain radial brightness variations in the outer Cassini division of Saturn's rings may be spiral density waves driven by Saturn's large moon Iapetus, in which case a value of approximately 16 g/sq cm for the surface density is calculated in the region where the waves are seen. The kinematic viscosity in the same region is approximately 170 sq cm/s and the vertical scale height of the ring is estimated to be a maximum of approximately 40 m.

A theoretical formulation of wave-vortex interactions

NASA Technical Reports Server (NTRS)

Wu, J. Z.; Wu, J. M.

1989-01-01

A unified theoretical formulation for wave-vortex interaction, designated the '(omega, Pi) framework,' is presented. Based on the orthogonal decomposition of fluid dynamic interactions, the formulation can be used to study a variety of problems, including the interaction of a longitudinal (acoustic) wave and/or transverse (vortical) wave with a main vortex flow. Moreover, the formulation permits a unified treatment of wave-vortex interaction at various approximate levels, where the normal 'piston' process and tangential 'rubbing' process can be approximated dfferently.

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

NASA Astrophysics Data System (ADS)

Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

2018-03-01

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

Many-Body Theory of Proton-Generated Point Defects for Losses of Electron Energy and Photons in Quantum Wells

NASA Astrophysics Data System (ADS)

Huang, Danhong; Iurov, Andrii; Gao, Fei; Gumbs, Godfrey; Cardimona, D. A.

2018-02-01

The effects of point defects on the loss of either energies of ballistic electron beams or incident photons are studied by using a many-body theory in a multi-quantum-well system. This theory includes the defect-induced vertex correction to a bare polarization function of electrons within the ladder approximation, and the intralayer and interlayer screening of defect-electron interactions is also taken into account in the random-phase approximation. The numerical results of defect effects on both energy-loss and optical-absorption spectra are presented and analyzed for various defect densities, numbers of quantum wells, and wave vectors. The diffusion-reaction equation is employed for calculating distributions of point defects in a layered structure. For completeness, the production rate for Frenkel-pair defects and their initial concentration are obtained based on atomic-level molecular-dynamics simulations. By combining the defect-effect, diffusion-reaction, and molecular-dynamics models with an available space-weather-forecast model, it will be possible in the future to enable specific designing for electronic and optoelectronic quantum devices that will be operated in space with radiation-hardening protection and, therefore, effectively extend the lifetime of these satellite onboard electronic and optoelectronic devices. Specifically, this theory can lead to a better characterization of quantum-well photodetectors not only for high quantum efficiency and low dark current density but also for radiation tolerance or mitigating the effects of the radiation.

COMPARISON OF IMPLICIT SCHEMES TO SOLVE EQUATIONS OF RADIATION HYDRODYNAMICS WITH A FLUX-LIMITED DIFFUSION APPROXIMATION: NEWTON–RAPHSON, OPERATOR SPLITTING, AND LINEARIZATION

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

Tetsu, Hiroyuki; Nakamoto, Taishi, E-mail: h.tetsu@geo.titech.ac.jp

Radiation is an important process of energy transport, a force, and a basis for synthetic observations, so radiation hydrodynamics (RHD) calculations have occupied an important place in astrophysics. However, although the progress in computational technology is remarkable, their high numerical cost is still a persistent problem. In this work, we compare the following schemes used to solve the nonlinear simultaneous equations of an RHD algorithm with the flux-limited diffusion approximation: the Newton–Raphson (NR) method, operator splitting, and linearization (LIN), from the perspective of the computational cost involved. For operator splitting, in addition to the traditional simple operator splitting (SOS) scheme,more » we examined the scheme developed by Douglas and Rachford (DROS). We solve three test problems (the thermal relaxation mode, the relaxation and the propagation of linear waves, and radiating shock) using these schemes and then compare their dependence on the time step size. As a result, we find the conditions of the time step size necessary for adopting each scheme. The LIN scheme is superior to other schemes if the ratio of radiation pressure to gas pressure is sufficiently low. On the other hand, DROS can be the most efficient scheme if the ratio is high. Although the NR scheme can be adopted independently of the regime, especially in a problem that involves optically thin regions, the convergence tends to be worse. In all cases, SOS is not practical.« less

Evolution of Binary Supermassive Black Holes in Rotating Nuclei

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

Rasskazov, Alexander; Merritt, David

The interaction of a binary supermassive black hole with stars in a galactic nucleus can result in changes to all the elements of the binary’s orbit, including the angles that define its orientation. If the nucleus is rotating, the orientation changes can be large, causing large changes in the binary’s orbital eccentricity as well. We present a general treatment of this problem based on the Fokker–Planck equation for f , defined as the probability distribution for the binary’s orbital elements. First- and second-order diffusion coefficients are derived for the orbital elements of the binary using numerical scattering experiments, and analyticmore » approximations are presented for some of these coefficients. Solutions of the Fokker–Planck equation are then derived under various assumptions about the initial rotational state of the nucleus and the binary hardening rate. We find that the evolution of the orbital elements can become qualitatively different when we introduce nuclear rotation: (1) the orientation of the binary’s orbit evolves toward alignment with the plane of rotation of the nucleus and (2) binary orbital eccentricity decreases for aligned binaries and increases for counteraligned ones. We find that the diffusive (random-walk) component of a binary’s evolution is small in nuclei with non-negligible rotation, and we derive the time-evolution equations for the semimajor axis, eccentricity, and inclination in that approximation. The aforementioned effects could influence gravitational wave production as well as the relative orientation of host galaxies and radio jets.« less

Homogenization of Electromagnetic and Seismic Wavefields for Joint Inverse Modeling

NASA Astrophysics Data System (ADS)

Newman, G. A.; Commer, M.; Petrov, P.; Um, E. S.

2011-12-01

A significant obstacle in developing a robust joint imaging technology exploiting seismic and electromagnetic (EM) wave fields is the resolution at which these different geophysical measurements sense the subsurface. Imaging of seismic reflection data is an order of magnitude finer in resolution and scale compared to images produced with EM data. A consistent joint image of the subsurface geophysical attributes (velocity, electrical conductivity) requires/demands the different geophysical data types be similar in their resolution of the subsurface. The superior resolution of seismic data results from the fact that the energy propagates as a wave, while propagation of EM energy is diffusive and attenuates with distance. On the other hand, the complexity of the seismic wave field can be a significant problem due to high reflectivity of the subsurface and the generation of multiple scattering events. While seismic wave fields have been very useful in mapping the subsurface for energy resources, too much scattering and too many reflections can lead to difficulties in imaging and interpreting seismic data. To overcome these obstacles a formulation for joint imaging of seismic and EM wave fields is introduced, where each data type is matched in resolution. In order to accomplish this, seismic data are first transformed into the Laplace-Fourier Domain, which changes the modeling of the seismic wave field from wave propagation to diffusion. Though high frequency information (reflectivity) is lost with this transformation, several benefits follow: (1) seismic and EM data can be easily matched in resolution, governed by the same physics of diffusion, (2) standard least squares inversion works well with diffusive type problems including both transformed seismic and EM, (3) joint imaging of seismic and EM data may produce better starting velocity models critical for successful reverse time migration or full waveform imaging of seismic data (non transformed) and (4) possibilities to image across multiple scale lengths, incorporating different types of geophysical data and attributes in the process. Important numerical details of 3D seismic wave field simulation in the Laplace-Fourier domain for both acoustic and elastic cases will also be discussed.

Quantitative Characterization of the Microstructure and Transport Properties of Biopolymer Networks

PubMed Central

Jiao, Yang; Torquato, Salvatore

2012-01-01

Biopolymer networks are of fundamental importance to many biological processes in normal and tumorous tissues. In this paper, we employ the panoply of theoretical and simulation techniques developed for characterizing heterogeneous materials to quantify the microstructure and effective diffusive transport properties (diffusion coefficient De and mean survival time τ) of collagen type I networks at various collagen concentrations. In particular, we compute the pore-size probability density function P(δ) for the networks and present a variety of analytical estimates of the effective diffusion coefficient De for finite-sized diffusing particles, including the low-density approximation, the Ogston approximation, and the Torquato approximation. The Hashin-Strikman upper bound on the effective diffusion coefficient De and the pore-size lower bound on the mean survival time τ are used as benchmarks to test our analytical approximations and numerical results. Moreover, we generalize the efficient first-passage-time techniques for Brownian-motion simulations in suspensions of spheres to the case of fiber networks and compute the associated effective diffusion coefficient De as well as the mean survival time τ, which is related to nuclear magnetic resonance (NMR) relaxation times. Our numerical results for De are in excellent agreement with analytical results for simple network microstructures, such as periodic arrays of parallel cylinders. Specifically, the Torquato approximation provides the most accurate estimates of De for all collagen concentrations among all of the analytical approximations we consider. We formulate a universal curve for τ for the networks at different collagen concentrations, extending the work of Yeong and Torquato [J. Chem. Phys. 106, 8814 (1997)]. We apply rigorous cross-property relations to estimate the effective bulk modulus of collagen networks from a knowledge of the effective diffusion coefficient computed here. The use of cross-property relations to link other physical properties to the transport properties of collagen networks is also discussed. PMID:22683739

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

ERIC Educational Resources Information Center

McDaniel, Suzanne T.

1979-01-01

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

Approximate nonlinear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-07-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-wave scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform. After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic nonlinear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P- and S-wave information.

Arterial Wave Reflection and Aortic Valve Calcification in an Elderly Community-Based Cohort

PubMed Central

Sera, Fusako; Russo, Cesare; Iwata, Shinichi; Jin, Zhezhen; Rundek, Tatjana; Elkind, Mitchell S.V.; Homma, Shunichi; Sacco, Ralph L.; Di Tullio, Marco R.

2015-01-01

Background Aortic valve calcification (AVC) without stenosis is common in the elderly, is associated with cardiovascular morbidity and mortality, and may progress to aortic valve stenosis. Arterial stiffness and pulse wave reflection are important components of proximal aortic hemodynamics, but their relationship with AVC is not established. Methods To investigate the relationship of arterial wave reflection and stiffness with AVC, pulse wave analysis and AVC evaluation by echocardiography were performed in 867 participants from the Cardiovascular Abnormalities and Brain Lesions (CABL) study. Participants were divided into 4 categories based on the severity and extent of AVC: 1) none or mild focal AVC; 2) mild diffuse AVC; 3) moderate-severe focal AVC; and 4) moderate-severe diffuse AVC. Central blood pressures and pulse pressure, total arterial compliance, augmentation index, and time to wave reflection were assessed using applanation tonometry. Results Indicators of arterial stiffness and wave reflection were significantly associated with AVC severity, except for central systolic and diastolic pressures and time to reflection. After adjustment for pertinent covariates (age, sex, race/ethnicity, and eGFR), only augmentation pressure (P = .02) and augmentation index (P = .002) were associated with the severity of AVC. Multivariable logistic regression analysis revealed that augmentation pressure (odds ratio per mmHg = 1.14; 95% confidence interval, 1.02–1.27; P = .02) and augmentation index (odds ratio per percentage point = 1.07; 95% confidence interval, 1.01–1.13; P = .02) were associated with an increase risk of moderate-severe diffuse AVC, even when central blood pressure value was included in the same model. Conclusions Arterial wave reflection is associated with AVC severity, independent of blood pressure values. Increased contribution of wave reflection to central blood pressure could be involved in the process leading to AVC. PMID:25600036

Middle Atmosphere Program. Handbook for MAP, volume 20

NASA Technical Reports Server (NTRS)

Bowhill, S. A. (Editor); Edwards, B. (Editor)

1986-01-01

Various topics related to investigations of the middle atmosphere are discussed. Numerical weather prediction, performance characteristics of weather profiling radars, determination of gravity wave and turbulence parameters, case studies of gravity-wave propagation, turbulence and diffusion due to gravity waves, the climatology of gravity waves, mesosphere-stratosphere-troposphere radar, antenna arrays, and data management techniques are among the topics discussed.

Thermal diffusivity and nuclear spin relaxation: a continuous wave free precession NMR study.

PubMed

Venâncio, Tiago; Engelsberg, Mario; Azeredo, Rodrigo B V; Colnago, Luiz A

2006-07-01

Continuous wave free precession (CWFP) nuclear magnetic resonance is capable of yielding quantitative and easily obtainable information concerning the kinetics of processes that change the relaxation rates of the nuclear spins through the action of some external agent. In the present application, heat flow from a natural rubber sample to a liquid nitrogen thermal bath caused a large temperature gradient leading to a non-equilibrium temperature distribution. The ensuing local changes in the relaxation rates could be monitored by the decay of the CWFP signals and, from the decays, it was possible to ascertain the prevalence of a diffusive process and to obtain an average value for the thermal diffusivity.

Analysis of Flame Extinguishment and Height in Low Frequency Acoustically Excited Methane Jet Diffusion Flame

NASA Astrophysics Data System (ADS)

Zong, Ruowen; Kang, Ruxue; Liu, Chen; Zhang, Zhiyang; Zhi, Youran

2018-01-01

The exploration of microgravity conditions in space is increasing and existing fire extinguishing technology is often inadequate for fire safety in this special environment. As a result, improving the efficiency of portable extinguishers is of growing importance. In this work, a visual study of the effects on methane jet diffusion flames by low frequency sound waves is conducted to assess the extinguishing ability of sound waves. With a small-scale sound wave extinguishing bench, the extinguishing ability of certain frequencies of sound waves are identified, and the response of the flame height is observed and analyzed. Results show that the flame structure changes with disturbance due to low frequency sound waves of 60-100 Hz, and quenches at effective frequencies in the range of 60-90 Hz. In this range, 60 Hz is considered to be the quick extinguishing frequency, while 70-90 Hz is the stable extinguishing frequency range. For a fixed frequency, the flame height decreases with sound pressure level (SPL). The flame height exhibits the greatest sensitivity to the 60 Hz acoustic waves, and the least to the 100 Hz acoustic waves. The flame height decreases almost identically with disturbance by 70-90 Hz acoustic waves.

Analysis of Flame Extinguishment and Height in Low Frequency Acoustically Excited Methane Jet Diffusion Flame

NASA Astrophysics Data System (ADS)

Zong, Ruowen; Kang, Ruxue; Liu, Chen; Zhang, Zhiyang; Zhi, Youran

2018-05-01

The exploration of microgravity conditions in space is increasing and existing fire extinguishing technology is often inadequate for fire safety in this special environment. As a result, improving the efficiency of portable extinguishers is of growing importance. In this work, a visual study of the effects on methane jet diffusion flames by low frequency sound waves is conducted to assess the extinguishing ability of sound waves. With a small-scale sound wave extinguishing bench, the extinguishing ability of certain frequencies of sound waves are identified, and the response of the flame height is observed and analyzed. Results show that the flame structure changes with disturbance due to low frequency sound waves of 60-100 Hz, and quenches at effective frequencies in the range of 60-90 Hz. In this range, 60 Hz is considered to be the quick extinguishing frequency, while 70-90 Hz is the stable extinguishing frequency range. For a fixed frequency, the flame height decreases with sound pressure level (SPL). The flame height exhibits the greatest sensitivity to the 60 Hz acoustic waves, and the least to the 100 Hz acoustic waves. The flame height decreases almost identically with disturbance by 70-90 Hz acoustic waves.

Method and basis set dependence of anharmonic ground state nuclear wave functions and zero-point energies: application to SSSH.

PubMed

Kolmann, Stephen J; Jordan, Meredith J T

2010-02-07

One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol(-1) at the CCSD(T)/6-31G* level of theory, has a 4 kJ mol(-1) dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol(-1) lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol(-1) lower in energy at the CCSD(T)/6-31G* level of theory. Ideally, for sub-kJ mol(-1) thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.

Method and basis set dependence of anharmonic ground state nuclear wave functions and zero-point energies: Application to SSSH

NASA Astrophysics Data System (ADS)

Kolmann, Stephen J.; Jordan, Meredith J. T.

2010-02-01

One of the largest remaining errors in thermochemical calculations is the determination of the zero-point energy (ZPE). The fully coupled, anharmonic ZPE and ground state nuclear wave function of the SSSH radical are calculated using quantum diffusion Monte Carlo on interpolated potential energy surfaces (PESs) constructed using a variety of method and basis set combinations. The ZPE of SSSH, which is approximately 29 kJ mol-1 at the CCSD(T)/6-31G∗ level of theory, has a 4 kJ mol-1 dependence on the treatment of electron correlation. The anharmonic ZPEs are consistently 0.3 kJ mol-1 lower in energy than the harmonic ZPEs calculated at the Hartree-Fock and MP2 levels of theory, and 0.7 kJ mol-1 lower in energy at the CCSD(T)/6-31G∗ level of theory. Ideally, for sub-kJ mol-1 thermochemical accuracy, ZPEs should be calculated using correlated methods with as big a basis set as practicable. The ground state nuclear wave function of SSSH also has significant method and basis set dependence. The analysis of the nuclear wave function indicates that SSSH is localized to a single symmetry equivalent global minimum, despite having sufficient ZPE to be delocalized over both minima. As part of this work, modifications to the interpolated PES construction scheme of Collins and co-workers are presented.

Geometry of a naked singularity created by standing waves near a Schwarzschild horizon, and its application to the binary black hole problem

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

Mandel, Ilya

The most promising way to compute the gravitational waves emitted by binary black holes (BBHs) in their last dozen orbits, where post-Newtonian techniques fail, is a quasistationary approximation introduced by Detweiler and being pursued by Price and others. In this approximation the outgoing gravitational waves at infinity and downgoing gravitational waves at the holes' horizons are replaced by standing waves so as to guarantee that the spacetime has a helical Killing vector field. Because the horizon generators will not, in general, be tidally locked to the holes' orbital motion, the standing waves will destroy the horizons, converting the black holesmore » into naked singularities that resemble black holes down to near the horizon radius. This paper uses a spherically symmetric, scalar-field model problem to explore in detail the following BBH issues: (i) The destruction of a horizon by the standing waves. (ii) The accuracy with which the resulting naked singularity resembles a black hole. (iii) The conversion of the standing-wave spacetime (with a destroyed horizon) into a spacetime with downgoing waves by the addition of a 'radiation-reaction field'. (iv) The accuracy with which the resulting downgoing waves agree with the downgoing waves of a true black-hole spacetime (with horizon). The model problem used to study these issues consists of a Schwarzschild black hole endowed with spherical standing waves of a scalar field, whose wave frequency and near-horizon energy density are chosen to match those of the standing gravitational waves of the BBH quasistationary approximation. It is found that the spacetime metric of the singular, standing-wave spacetime, and its radiation-reaction-field-constructed downgoing waves are quite close to those for a Schwarzschild black hole with downgoing waves--sufficiently close to make the BBH quasistationary approximation look promising for non-tidally-locked black holes.« less

Implications of pressure diffusion for shock waves

NASA Technical Reports Server (NTRS)

Ram, Ram Bachan

1989-01-01

The report deals with the possible implications of pressure diffusion for shocks in one dimensional traveling waves in an ideal gas. From this new hypothesis all aspects of such shocks can be calculated except shock thickness. Unlike conventional shock theory, the concept of entropy is not needed or used. Our analysis shows that temperature rises near a shock, which is of course an experimental fact; however, it also predicts that very close to a shock, density increases faster than pressure. In other words, a shock itself is cold.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

John porter lecture: waves of protest--direct action, deliberation, and diffusion.

PubMed

Wood, Lesley

2015-02-01

The book Direct Action, Deliberation and Diffusion: Collective Action After the WTO Protests in Seattle argues that the process of diffusion is dependent on social processes in the receiving context. The most important in social movements is an egalitarian and reflexive deliberation among diverse actors. The book traces the direct action tactics associated with the Seattle protests against the World Trade Organization in 1999 and how these spread to activists in Toronto and New York City. It shows how the structure of the political field, racial and class inequalities, identity boundaries, and organizational and conversational dynamics limited deliberation among activists, and thus limited the diffusion of the Seattle tactics. By constraining the spread of the Seattle tactics, this slowed the global justice movement's wave of protest. In this paper, I explore the application of and implications of this model of protest tactic diffusion to the recent Idle No More mobilizations. © 2015 Canadian Sociological Association/La Société canadienne de sociologie.

TiO2 as diffusion barrier at Co/Alq3 interface studied by x-ray standing wave technique

NASA Astrophysics Data System (ADS)

Phatak Londhe, Vaishali; Gupta, A.; Ponpandian, N.; Kumar, D.; Reddy, V. R.

2018-06-01

Nano-scale diffusion at the interfaces in organic spin valve thin films plays a vital role in controlling the performance of magneto-electronic devices. In the present work, it is shown that a thin layer of titanium dioxide at the interface of Co/Alq3 can act as a good diffusion barrier. The buried interfaces of Co/Alq3/Co organic spin valve thin film has been studied using x-ray standing waves technique. A planar waveguide is formed with Alq3 layer forming the cavity and Co layers as the walls of the waveguide. Precise information about diffusion of Co into Alq3 is obtained through excitation of the waveguide modes. It is found that the top Co layer diffuses deep into the Alq3 resulting in incorporation of 3.1% Co in the Alq3 layer. Insertion of a 1.7 nm thick barrier layer of TiO2 at Co/Alq3 interface results in a drastic reduction in the diffusion of Co into Alq3 to a value of only 0.4%. This suggests a better performance of organic spin valve with diffusion barrier of TiO2.

Quasilinear diffusion operator for wave-particle interactions in inhomogeneous magnetic fields

NASA Astrophysics Data System (ADS)

Catto, P. J.; Lee, J.; Ram, A. K.

2017-10-01

The Kennel-Engelmann quasilinear diffusion operator for wave-particle interactions is for plasmas in a uniform magnetic field. The operator is not suitable for fusion devices with inhomogeneous magnetic fields. Using drift kinetic and high frequency gyrokinetic equations for the particle distribution function, we have derived a quasilinear operator which includes magnetic drifts. The operator applies to RF waves in any frequency range and is particularly relevant for minority ion heating. In order to obtain a physically meaningful operator, the first order correction to the particle's magnetic moment has to be retained. Consequently, the gyrokinetic change of variables has to be retained to a higher order than usual. We then determine the perturbed distribution function from the gyrokinetic equation using a novel technique that solves the kinetic equation explicitly for certain parts of the function. The final form of the diffusion operator is compact and completely expressed in terms of the drift kinetic variables. It is not transit averaged and retains the full poloidal angle variation without any Fourier decomposition. The quasilinear diffusion operator reduces to the Kennel-Engelmann operator for uniform magnetic fields. Supported by DoE Grant DE-FG02-91ER-54109.

A millimeter-wave tunneladder TWT

NASA Technical Reports Server (NTRS)

Wilson, D.

1988-01-01

A millimeter-wave traveling wave tube (TWT) was developed using a dispersive, high-impedance forward wave interaction structure based on a ladder, with non-space-harmonic interaction, for a tube with high gain per inch and high efficiency. The 'TunneLadder' interaction structure combines ladder properties modified to accommodate Pierce gun beam optics in a radially magnetized PM focusing structure. The development involved the fabrication of chemically milled, shaped ladders diffusion brazed to diamond cubes which are in turn active diffusion brazed to each ridge of a doubly ridged waveguide. Cold-test data, representing the (omega)(beta) and and impedance characteristics of the modified ladder circuit, were used in small and large-signal computer programs to predict TWT gain and efficiency. The structural design emphasizes ruggedness and reliability. Actual data from tested tubes verify the predicted performance while providing broader bandwidth than expected.

Adsorption of oxygen on low-index surfaces of the TiAl{sub 3} alloy

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

Latyshev, A. M.; Bakulin, A. V.; Kulkova, S. E., E-mail: kulkova@ms.tsc.ru

Method of the projector augmented waves in the plane-wave basis within the generalized-gradient approximation for the exchange-correlation functional has been used to study oxygen adsorption on (001), (100), and (110) low-index surfaces of the TiAl{sub 3} alloy. It has been established that the sites that are most energetically preferred for the adsorption of oxygen are hollow (H) positions on the (001) surface and bridge (B) positions on the (110) and (100) surfaces. Structural and electronic factors that define their energy preference have been discussed. Changes in the atomic and electronic structure of subsurface layers that occur as the oxygen concentrationmore » increases to three monolayers have been analyzed. It has been shown that the formation of chemical bonds of oxygen with both components of the alloy leads to the appearance of states that are split-off from the bottoms of their valence bands, which is accompanied by the formation of a forbidden gap at the Fermi level and by a weakening of the Ti–Al metallic bonds in the alloy. On the Al-terminated (001) and (110) surfaces, the oxidation of aluminum dominates over that of titanium. On the whole, the binding energy of oxygen on the low-index surfaces with a mixed termination is higher than that at the aluminum-terminated surface. The calculation of the diffusion of oxygen in the TiAl{sub 3} alloy has shown that the lowest barriers correspond to the diffusion between tetrahedral positions in the (001) plane; the diffusion of oxygen in the [001] direction occurs through octahedral and tetrahedral positions. An increase in the concentration of aluminum in the alloy favors a reduction in the height of the energy barriers as compared to the corresponding barriers in the γ-TiAl alloy.« less

Transport of secondary electrons and reactive species in ion tracks

NASA Astrophysics Data System (ADS)

Surdutovich, Eugene; Solov'yov, Andrey V.

2015-08-01

The transport of reactive species brought about by ions traversing tissue-like medium is analysed analytically. Secondary electrons ejected by ions are capable of ionizing other molecules; the transport of these generations of electrons is studied using the random walk approximation until these electrons remain ballistic. Then, the distribution of solvated electrons produced as a result of interaction of low-energy electrons with water molecules is obtained. The radial distribution of energy loss by ions and secondary electrons to the medium yields the initial radial dose distribution, which can be used as initial conditions for the predicted shock waves. The formation, diffusion, and chemical evolution of hydroxyl radicals in liquid water are studied as well. COST Action Nano-IBCT: Nano-scale Processes Behind Ion-Beam Cancer Therapy.

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

NASA Astrophysics Data System (ADS)

Marston, Philip L.

2004-05-01

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

Approximation solution of Schrodinger equation for Q-deformed Rosen-Morse using supersymmetry quantum mechanics (SUSY QM)

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

Alemgadmi, Khaled I. K., E-mail: azozkied@yahoo.com; Suparmi; Cari

2015-09-30

The approximate analytical solution of Schrodinger equation for Q-Deformed Rosen-Morse potential was investigated using Supersymmetry Quantum Mechanics (SUSY QM) method. The approximate bound state energy is given in the closed form and the corresponding approximate wave function for arbitrary l-state given for ground state wave function. The first excited state obtained using upper operator and ground state wave function. The special case is given for the ground state in various number of q. The existence of Rosen-Morse potential reduce energy spectra of system. The larger value of q, the smaller energy spectra of system.

Direct pair production in heavy-ion--atom collisions

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

Anholt, R.; Jakubassa-Amundsen, D.H.; Amundsen, P.A.

1983-02-01

Direct pair production in approx.5-MeV/amu heavy-ion--atom collisions with uranium target atoms is calculated with the plane-wave Born approximation and the semiclassical approximation. Briggs's approximation is used to obtain the electron and positron wave functions. Since pair production involves high momentum transfer q from the moving projectile to the vacuum, use is made of a high-q approximation to greatly simplify the numerical computations. Coulomb deflection of the projectile, the effect of finite nuclear size on the elec- tronic wave functions, and the energy loss by the projectile exciting the pair are all taken into account in these calculations.

On ballooning instability in current sheets

NASA Astrophysics Data System (ADS)

Leonovich, Anatoliy; Kozlov, Daniil

2015-06-01

The problem of instability of the magnetotail current sheet to azimuthally small-scale Alfvén and slow magnetosonic (SMS) waves is solved. The solutions describe unstable oscillations in the presence of a current sheet and correspond to the region of stretched closed field lines of the magnetotail. The spectra of eigen-frequencies of several basic harmonics of standing Alfvén and SMS waves are found in the local and WKB approximation, which are compared. It is shown that the oscillation properties obtained in these approximations differ radically. In the local approximation, the Alfvén waves are stable in the entire range of magnetic shells. SMS waves go into the aperiodic instability regime (the regime of the "ballooning" instability), on magnetic shells crossing the current sheet. In the WKB approximation, both the Alfvén and SMS oscillations go into an unstable regime with a non-zero real part of their eigen-frequency, on magnetic shells crossing the current sheet. The structure of azimuthally small-scale Alfvén waves across magnetic shells is determined.

A novel CFS-PML boundary condition for transient electromagnetic simulation using a fictitious wave domain method

NASA Astrophysics Data System (ADS)

Hu, Yanpu; Egbert, Gary; Ji, Yanju; Fang, Guangyou

2017-01-01

In this study, we apply fictitious wave domain (FWD) methods, based on the correspondence principle for the wave and diffusion fields, to finite difference (FD) modeling of transient electromagnetic (TEM) diffusion problems for geophysical applications. A novel complex frequency shifted perfectly matched layer (PML) boundary condition is adapted to the FWD to truncate the computational domain, with the maximum electromagnetic wave propagation velocity in the FWD used to set the absorbing parameters for the boundary layers. Using domains of varying spatial extent we demonstrate that these boundary conditions offer significant improvements over simpler PML approaches, which can result in spurious reflections and large errors in the FWD solutions, especially for low frequencies and late times. In our development, resistive air layers are directly included in the FWD, allowing simulation of TEM responses in the presence of topography, as is commonly encountered in geophysical applications. We compare responses obtained by our new FD-FWD approach and with the spectral Lanczos decomposition method on 3-D resistivity models of varying complexity. The comparisons demonstrate that our absorbing boundary condition in FWD for the TEM diffusion problems works well even in complex high-contrast conductivity models.

Influence of temperature on linear stability in buoyancy-driven fingering of reaction-diffusion fronts.

PubMed

Levitán, D; D'Onofrio, A

2012-09-01

A vertical Hele-Shaw cell was used to study the influence of temperature on Rayleigh-Taylor instabilities on reaction-diffusion fronts. The propagation of the chemical front can thus be observed, and experimental results can be obtained via image treatment. A chemical front produced by the coupling between molecular diffusion and the auto-catalysis of the chlorite-tetrathionate reaction, descends through the cell, consuming the reactants below while the product is formed above. Buoyancy-driven instabilities are formed due to the density difference between reactants and products, and the front takes a fingering pattern, whose growth rate has temperature dependence. In this study, the effect of temperature on the linear regime of the instability (that is, when the effects of such instability start to appear) was analyzed. To measure the instability, Fourier transform analysis is performed, in order to obtain the different wave numbers and their power as a function of time. Thus, the growth rate for each wave number and the most unstable wave number is obtained for each of the temperatures under study. Based on repeated experiments, a decrease in the growth rate for the most unstable wave number can be observed with the increase of temperature.

Frequency-constant Q, unity and disorder

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

Hargreaves, N.D.

1995-12-31

In exploration geophysics we obtain information about the earth by observing its response to different types of applied force. The response can cover the full range of possible Q values (where Q, the quality factor, is a measure of energy dissipation), from close to infinity in the case of deep crustal seismic to close to 0 in the case of many electromagnetic methods. When Q is frequency-constant, however, the various types of response have a common scaling behavior and can be described as being self-affine. The wave-equation then takes on a generalised form, changing from the standard wave-equation at Qmore » = {infinity} to the diffusion equation at Q = 0, via lossy, diffusive, propagation at intermediate Q values. Solutions of this wave-diffusion equation at any particular Q value can be converted to an equivalent set of results for any other Q value. In particular it is possible to convert from diffusive to wave propagation by a mapping from Q < {infinity} to Q = {infinity}. In the context of seismic sounding this is equivalent to applying inverse Q-filtering; in a more general context the mapping integrates different geophysical observations by referencing them to the common result at Q = {infinity}. The self-affinity of the observations for frequency-constant Q is an expression of scale invariance in the fundamental physical properties of the medium of propagation, this being the case whether the mechanism of diffusive propagation is scattering of intrinsic attenuation. Scale invariance, or fractal scaling, is a general property of disordered systems; the assumption of frequency-constant Q not only implies a unity between different geophysical observations, but also suggests that it is the disordered nature of the earth`s sub-surface that is the unifying factor.« less

Gravitational waves from vacuum first-order phase transitions: From the envelope to the lattice

NASA Astrophysics Data System (ADS)

Cutting, Daniel; Hindmarsh, Mark; Weir, David J.

2018-06-01

We conduct large scale numerical simulations of gravitational wave production at a first-order vacuum phase transition. We find a power law for the gravitational wave power spectrum at high wave number which falls off as k-1.5 rather than the k-1 produced by the envelope approximation. The peak of the power spectrum is shifted to slightly lower wave numbers from that of the envelope approximation. The envelope approximation reproduces our results for the peak power less well, agreeing only to within an order of magnitude. After the bubbles finish colliding, the scalar field oscillates around the true vacuum. An additional feature is produced in the UV of the gravitational wave power spectrum, and this continues to grow linearly until the end of our simulation. The additional feature peaks at a length scale close to the bubble wall thickness and is shown to have a negligible contribution to the energy in gravitational waves, providing the scalar field mass is much smaller than the Planck mass.

Fast Approximations of the Rotational Diffusion Tensor and their Application to Structural Assembly of Molecular Complexes

PubMed Central

Berlin, Konstantin; O’Leary, Dianne P.; Fushman, David

2011-01-01

We present and evaluate a rigid-body, deterministic, molecular docking method, called ELMDOCK, that relies solely on the three-dimensional structure of the individual components and the overall rotational diffusion tensor of the complex, obtained from nuclear spin-relaxation measurements. We also introduce a docking method, called ELMPATIDOCK, derived from ELMDOCK and based on the new concept of combining the shape-related restraints from rotational diffusion with those from residual dipolar couplings, along with ambiguous contact/interface-related restraints obtained from chemical shift perturbations. ELMDOCK and ELMPATIDOCK use two novel approximations of the molecular rotational diffusion tensor that allow computationally efficient docking. We show that these approximations are accurate enough to properly dock the two components of a complex without the need to recompute the diffusion tensor at each iteration step. We analyze the accuracy, robustness, and efficiency of these methods using synthetic relaxation data for a large variety of protein-protein complexes. We also test our method on three protein systems for which the structure of the complex and experimental relaxation data are available, and analyze the effect of flexible unstructured tails on the outcome of docking. Additionally, we describe a method for integrating the new approximation methods into the existing docking approaches that use the rotational diffusion tensor as a restraint. The results show that the proposed docking method is robust against experimental errors in the relaxation data or structural rearrangements upon complex formation and is computationally more efficient than current methods. The developed approximations are accurate enough to be used in structure refinement protocols. PMID:21604302

Theoretical studies of floating-reference method for NIR blood glucose sensing

NASA Astrophysics Data System (ADS)

Shi, Zhenzhi; Yang, Yue; Zhao, Huijuan; Chen, Wenliang; Liu, Rong; Xu, Kexin

2011-03-01

Non-invasive blood glucose monitoring using NIR light has been suffered from the variety of optical background that is mainly caused by the change of human body, such as the change of temperature, water concentration, and so on. In order to eliminate these internal influence and external interference a so called floating-reference method has been proposed to provide an internal reference. From the analysis of the diffuse reflectance spectrum, a position has been found where diffuse reflection of light is not sensitive to the glucose concentrations. Our previous work has proved the existence of reference position using diffusion equation. However, since glucose monitoring generally use the NIR light in region of 1000-2000nm, diffusion equation is not valid because of the high absorption coefficient and small source-detector separations. In this paper, steady-state high-order approximate model is used to further investigate the existence of the floating reference position in semi-infinite medium. Based on the analysis of different optical parameters on the impact of spatially resolved reflectance of light, we find that the existence of the floating-reference position is the result of the interaction of optical parameters. Comparing to the results of Monte Carlo simulation, the applicable region of diffusion approximation and higher-order approximation for the calculation of floating-reference position is discussed at the wavelength of 1000nm-1800nm, using the intralipid solution of different concentrations. The results indicate that when the reduced albedo is greater than 0.93, diffusion approximation results are more close to simulation results, otherwise the high order approximation is more applicable.

Fast approximations of the rotational diffusion tensor and their application to structural assembly of molecular complexes.

PubMed

Berlin, Konstantin; O'Leary, Dianne P; Fushman, David

2011-07-01

We present and evaluate a rigid-body, deterministic, molecular docking method, called ELMDOCK, that relies solely on the three-dimensional structure of the individual components and the overall rotational diffusion tensor of the complex, obtained from nuclear spin-relaxation measurements. We also introduce a docking method, called ELMPATIDOCK, derived from ELMDOCK and based on the new concept of combining the shape-related restraints from rotational diffusion with those from residual dipolar couplings, along with ambiguous contact/interface-related restraints obtained from chemical shift perturbations. ELMDOCK and ELMPATIDOCK use two novel approximations of the molecular rotational diffusion tensor that allow computationally efficient docking. We show that these approximations are accurate enough to properly dock the two components of a complex without the need to recompute the diffusion tensor at each iteration step. We analyze the accuracy, robustness, and efficiency of these methods using synthetic relaxation data for a large variety of protein-protein complexes. We also test our method on three protein systems for which the structure of the complex and experimental relaxation data are available, and analyze the effect of flexible unstructured tails on the outcome of docking. Additionally, we describe a method for integrating the new approximation methods into the existing docking approaches that use the rotational diffusion tensor as a restraint. The results show that the proposed docking method is robust against experimental errors in the relaxation data or structural rearrangements upon complex formation and is computationally more efficient than current methods. The developed approximations are accurate enough to be used in structure refinement protocols. Copyright © 2011 Wiley-Liss, Inc.

Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation

NASA Astrophysics Data System (ADS)

Kilcrease, D. P.; Brookes, S.

2013-12-01

The modeling of NLTE plasmas requires the solution of population rate equations to determine the populations of the various atomic levels relevant to a particular problem. The equations require many cross sections for excitation, de-excitation, ionization and recombination. A simple and computational fast way to calculate electron collisional excitation cross-sections for ions is by using the plane-wave Born approximation. This is essentially a high-energy approximation and the cross section suffers from the unphysical problem of going to zero near threshold. Various remedies for this problem have been employed with varying degrees of success. We present a correction procedure for the Born cross-sections that employs the Elwert-Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a cross-section similar to that from using the more time consuming Coulomb Born approximation. We compare this new approximation with other, often employed correction procedures. We also look at some further modifications to our Born Elwert procedure and its combination with Y.K. Kim's correction of the Coulomb Born approximation for singly charged ions that more accurately approximate convergent close coupling calculations.

Quantitative model of diffuse speckle contrast analysis for flow measurement.

PubMed

Liu, Jialin; Zhang, Hongchao; Lu, Jian; Ni, Xiaowu; Shen, Zhonghua

2017-07-01

Diffuse speckle contrast analysis (DSCA) is a noninvasive optical technique capable of monitoring deep tissue blood flow. However, a detailed study of the speckle contrast model for DSCA has yet to be presented. We deduced the theoretical relationship between speckle contrast and exposure time and further simplified it to a linear approximation model. The feasibility of this linear model was validated by the liquid phantoms which demonstrated that the slope of this linear approximation was able to rapidly determine the Brownian diffusion coefficient of the turbid media at multiple distances using multiexposure speckle imaging. Furthermore, we have theoretically quantified the influence of optical property on the measurements of the Brownian diffusion coefficient which was a consequence of the fact that the slope of this linear approximation was demonstrated to be equal to the inverse of correlation time of the speckle.

Remodelling of cellular excitation (reaction) and intercellular coupling (diffusion) by chronic atrial fibrillation represented by a reaction-diffusion system

NASA Astrophysics Data System (ADS)

Zhang, Henggui; Garratt, Clifford J.; Kharche, Sanjay; Holden, Arun V.

2009-06-01

Human atrial tissue is an excitable system, in which myocytes are excitable elements, and cell-to-cell electrotonic interactions are via diffusive interactions of cell membrane potentials. We developed a family of excitable system models for human atrium at cellular, tissue and anatomical levels for both normal and chronic atrial fibrillation (AF) conditions. The effects of AF-induced remodelling of cell membrane ionic channels (reaction kinetics) and intercellular gap junctional coupling (diffusion) on atrial excitability, conduction of excitation waves and dynamics of re-entrant excitation waves are quantified. Both ionic channel and gap junctional coupling remodelling have rate dependent effects on atrial propagation. Membrane channel conductance remodelling allows the propagation of activity at higher rates than those sustained in normal tissue or in tissue with gap junctional remodelling alone. Membrane channel conductance remodelling is essential for the propagation of activity at rates higher than 300/min as seen in AF. Spatially heterogeneous gap junction coupling remodelling increased the risk of conduction block, an essential factor for the genesis of re-entry. In 2D and 3D anatomical models, the dynamical behaviours of re-entrant excitation waves are also altered by membrane channel modelling. This study provides insights to understand the pro-arrhythmic effects of AF-induced reaction and diffusion remodelling in atrial tissue.

Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes.

PubMed

Barrenechea, Gabriel R; Burman, Erik; Karakatsani, Fotini

2017-01-01

For the case of approximation of convection-diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.

Velocity relaxation of a particle in a confined compressible fluid

NASA Astrophysics Data System (ADS)

Tatsumi, Rei; Yamamoto, Ryoichi

2013-05-01

The velocity relaxation of an impulsively forced spherical particle in a fluid confined by two parallel plane walls is studied using a direct numerical simulation approach. During the relaxation process, the momentum of the particle is transmitted in the ambient fluid by viscous diffusion and sound wave propagation, and the fluid flow accompanied by each mechanism has a different character and affects the particle motion differently. Because of the bounding walls, viscous diffusion is hampered, and the accompanying shear flow is gradually diminished. However, the sound wave is repeatedly reflected and spreads diffusely. As a result, the particle motion is governed by the sound wave and backtracks differently in a bulk fluid. The time when the backtracking of the particle occurs changes non-monotonically with respect to the compressibility factor ɛ = ν/ac and is minimized at the characteristic compressibility factor. This factor depends on the wall spacing, and the dependence is different at small and large wall spacing regions based on the different mechanisms causing the backtracking.

Effects of Drift-Shell Splitting by Chorus Waves on Radiation Belt Electrons

NASA Astrophysics Data System (ADS)

Chan, A. A.; Zheng, L.; O'Brien, T. P., III; Tu, W.; Cunningham, G.; Elkington, S. R.; Albert, J.

2015-12-01

Drift shell splitting in the radiation belts breaks all three adiabatic invariants of charged particle motion via pitch angle scattering, and produces new diffusion terms that fully populate the diffusion tensor in the Fokker-Planck equation. Based on the stochastic differential equation method, the Radbelt Electron Model (REM) simulation code allows us to solve such a fully three-dimensional Fokker-Planck equation, and to elucidate the sources and transport mechanisms behind the phase space density variations. REM has been used to perform simulations with an empirical initial phase space density followed by a seed electron injection, with a Tsyganenko 1989 magnetic field model, and with chorus wave and ULF wave diffusion models. Our simulation results show that adding drift shell splitting changes the phase space location of the source to smaller L shells, which typically reduces local electron energization (compared to neglecting drift-shell splitting effects). Simulation results with and without drift-shell splitting effects are compared with Van Allen Probe measurements.

Origin of Diffusion in Hamiltonian Dynamics

NASA Astrophysics Data System (ADS)

Benisti, Didier

1996-11-01

Without making any kind of ``loss of memory'' hypothesis, a diffusion equation is derived for the Hamiltonian dynamics defined by H = p^2 / 2 + A summ = -M^M \\cos (q - mt + \\varphi_m), where the \\varphi_m's are fixed random phases. The key point of the derivation is a property of locality for the waves inducing transport. Using perturbation theory, it is shown that only waves whose phase velocities meet the condition mid v_\\varphi - p (t) mid <= α A^2/3, where α is a constant close to 5, play a relevant role for the statistical properties of the dynamics. This implies that, at each time, a particle can be considered as being acted upon only by these nearby waves. Thus, after a shift of momentum of 2 α A^2/3, a particle feels the influence of different waves, with different phases \\varphi_m's, from the ones it initially experienced. Because the phases \\varphi_m's are random, a shift of momentum of 2 α A^2/3 then corresponds to the visit of a dynamical system independent from the previous one. This is what is regarded as being the cause of diffusion. Following this idea, one can predict that the force decorrelation, respectively the Gaussianity of the momentum distribution function, is well established after an average change of momentum close to 2 α A^2/3, respectively 4 α A^2/3. These predictions are in total agreement with the results of the numerical computations. Finally, a careful investigation of the initial behavior of < Δ p^2 (t) > enables one to prove the convergence of the diffusion coefficient to its quasilinear value when the amplitude A of the waves goes to infinity. The author gratefully acknowledges the collaboration of Dominique Escande, under whose supervision this work was carried out.

Reconciling phase diffusion and Hartree-Fock approximation in condensate systems

NASA Astrophysics Data System (ADS)

Giorgi, Gian Luca; de Pasquale, Ferdinando

2012-01-01

Despite the weakly interacting regime, the physics of Bose-Einstein condensates is widely affected by particle-particle interactions. They determine quantum phase diffusion, which is known to be the main cause of loss of coherence. Studying a simple model of two interacting Bose systems, we show how to predict the appearance of phase diffusion beyond the Bogoliubov approximation, providing a self-consistent treatment in the framework of a generalized Hartree-Fock-Bogoliubov perturbation theory.

Fluctuations in diffusion processes in microgravity.

PubMed

Mazzoni, Stefano; Cerbino, Roberto; Vailati, Alberto; Giglio, Marzio

2006-09-01

It has been shown recently that diffusion processes exhibit giant nonequilibrium fluctuations (NEFs). That is, the diffusing fronts display corrugations whose length scale ranges from the molecular to the macroscopic one. The amplitude of the NEF diverges following a power law behavior proportional to q(-4) (where q is the wave vector). However, fluctuations of wave number smaller than a critical "rolloff" wave vector are quenched by the presence of gravity. It is therefore expected that in microgravity conditions, the amplitude of the NEF should be boosted by the absence of the buoyancy-driven restoring force. This may affect any diffusion process performed in microgravity, such as the crystallization of a protein solution induced by the diffusion of a salt buffer. The aim of GRADFLEX (GRAdient-Driven FLuctuation EXperiment), a joint project of ESA and NASA, is to investigate the presence of NEFs arising in a diffusion process under microgravity conditions. The project consists of two experiments. One is carried out by UNIMI (University of Milan) and INFM (Istituto Nazionale per la Fisica della Materia) and is focused on NEF in a concentration diffusion process. The other experiment is performed by UCSB (University of California at Santa Barbara) concerning temperature NEF in a simple fluid. In the UNIMI part of the GRADFLEX experimental setup, NEFs are induced in a binary mixture by means of the Soret effect. The diagnostic method is an all-optical quantitative shadowgraph technique. The power spectrum of the induced NEFs is obtained by the processing of the shadowgraph images. A detailed description of the experimental apparatus as well as the ground-based experimental results is presented here for the UNIMI-INFM experiment. The GRADFLEX payload is scheduled to fly on the FOTON M3 capsule in April 2007.

Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

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

Morgan, R. V.; Likhachev, O. A.; Jacobs, J. W.

Theory and experiments are reported that explore the behaviour of the Rayleigh–Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order ofmore » $$1000g_{0}$$, where$$g_{0}$$is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duffet al. (Phys. Fluids, vol. 5, 1962, pp. 417–425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh–Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162–178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duffet al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a$$1/k^{2}$$decay in growth rates as$$k\\rightarrow \\infty$$for large-wavenumber perturbations.« less

Quantifying residual, eddy, and mean flow effects on mixing in an idealized circumpolar current

DOE PAGES

Wolfram, Phillip J.; Ringler, Todd D.

2017-07-13

Meridional diffusivity is assessed in this paper for a baroclinically unstable jet in a high-latitudeIdealized Circumpolar Current (ICC) using the Model for Prediction Across Scales-Ocean (MPAS-O) and the online Lagrangian In-situ Global High-performance particle Tracking (LIGHT) diagnostic via space-time dispersion of particle clusters over 120 monthly realizations of O(10 6) particles on 11 potential density surfaces. Diffusivity in the jet reaches values of O(6000 m 2 s -1) and is largest near the critical layer supporting mixing suppression and critical layer theory. Values in the vicinity of the shelf break are suppressed to O(100 m 2 s -1) due tomore » the presence of westward slope front currents. Diffusivity attenuates less rapidly with depth in the jet than both eddy velocity and kinetic energy scalings would suggest. Removal of the mean flow via high-pass filtering shifts the nonlinear parameter (ratio of the eddy velocity to eddy phase speed) into the linear wave regime by increasing the eddy phase speed via the depth-mean flow. Low-pass filtering, in contrast, quantifies the effect of mean shear. Diffusivity is decomposed into mean flow shear, linear waves, and the residual nonhomogeneous turbulence components, where turbulence dominates and eddy-produced filamentation strained by background mean shear enhances mixing, accounting for ≥ 80% of the total diffusivity relative to mean shear [O(100 m 2 s -1)], linear waves [O(1000 m 2 s -1)], and undecomposed full diffusivity [O(6000 m 2 s -1)]. Finally, diffusivity parameterizations accounting for both the nonhomogeneous turbulence residual and depth variability are needed.« less

Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory

DOE PAGES

Morgan, R. V.; Likhachev, O. A.; Jacobs, J. W.

2016-02-15

Theory and experiments are reported that explore the behaviour of the Rayleigh–Taylor instability initiated with a diffuse interface. Experiments are performed in which an interface between two gases of differing density is made unstable by acceleration generated by a rarefaction wave. Well-controlled, diffuse, two-dimensional and three-dimensional, single-mode perturbations are generated by oscillating the gases either side to side, or vertically for the three-dimensional perturbations. The puncturing of a diaphragm separating a vacuum tank beneath the test section generates a rarefaction wave that travels upwards and accelerates the interface downwards. This rarefaction wave generates a large, but non-constant, acceleration of the order ofmore » $$1000g_{0}$$, where$$g_{0}$$is the acceleration due to gravity. Initial interface thicknesses are measured using a Rayleigh scattering diagnostic and the instability is visualized using planar laser-induced Mie scattering. Growth rates agree well with theoretical values, and with the inviscid, dynamic diffusion model of Duffet al. (Phys. Fluids, vol. 5, 1962, pp. 417–425) when diffusion thickness is accounted for, and the acceleration is weighted using inviscid Rayleigh–Taylor theory. The linear stability formulation of Chandrasekhar (Proc. Camb. Phil. Soc., vol. 51, 1955, pp. 162–178) is solved numerically with an error function diffusion profile using the Riccati method. This technique exhibits good agreement with the dynamic diffusion model of Duffet al. for small wavenumbers, but produces larger growth rates for large-wavenumber perturbations. Asymptotic analysis shows a$$1/k^{2}$$decay in growth rates as$$k\\rightarrow \\infty$$for large-wavenumber perturbations.« less

Comparison of fluid neutral models for one-dimensional plasma edge modeling with a finite volume solution of the Boltzmann equation

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

Horsten, N., E-mail: niels.horsten@kuleuven.be; Baelmans, M.; Dekeyser, W.

2016-01-15

We derive fluid neutral approximations for a simplified 1D edge plasma model, suitable to study the neutral behavior close to the target of a nuclear fusion divertor, and compare its solutions to the solution of the corresponding kinetic Boltzmann equation. The plasma is considered as a fixed background extracted from a detached 2D simulation. We show that the Maxwellian equilibrium distribution is already obtained very close to the target, justifying the use of a fluid approximation. We compare three fluid neutral models: (i) a diffusion model; (ii) a pressure-diffusion model (i.e., a combination of a continuity and momentum equation) assumingmore » equal neutral and ion temperatures; and (iii) the pressure-diffusion model coupled to a neutral energy equation taking into account temperature differences between neutrals and ions. Partial reflection of neutrals reaching the boundaries is included in both the kinetic and fluid models. We propose two methods to obtain an incident neutral flux boundary condition for the fluid models: one based on a diffusion approximation and the other assuming a truncated Chapman-Enskog distribution. The pressure-diffusion model predicts the plasma sources very well. The diffusion boundary condition gives slightly better results overall. Although including an energy equation still improves the results, the assumption of equal ion and neutral temperature already gives a very good approximation.« less

Babcock-Leighton solar dynamo: the role of downward pumping and the equatorward propagation of activity

NASA Astrophysics Data System (ADS)

Karak, Bidya Binay; Cameron, Robert

2016-05-01

We investigate the role of downward magnetic pumping near the surface using a kinematic Babcock-Leighton model. We find that the pumping causes the poloidal field to become predominately radial in the near-surface shear layer. This allows the negative radial shear in the near-surface layer to effectively act on the radial field to produce a toroidal field. Consequently, we observe a clear equatorward migration of the toroidal field at low latitudes even when there is no meridional flow in the deep CZ. We show a case where the period of a dynamo wave solution is approximately 11 years. Flux transport models are also shown with periods close to 11 years. Both the dynamo wave and flux transport dynamo are thus able to reproduce some of the observed features of solar cycle. The main difference between the two types of dynamo is the value of $\\alpha$ required to produce dynamo action. In both types of dynamo, the surface meridional flow helps to advect and build the polar field in high latitudes, while in flux transport dynamo the equatorward flow near the bottom of CZ advects toroidal field to cause the equatorward migration in butterfly wings and this advection makes the dynamo easier by transporting strong toroidal field to low latitudes where $\\alpha$ effect works. Another conclusion of our study is that the magnetic pumping suppresses the diffusion of fields through the photospheric surface which helps to achieve the 11-year dynamo cycle at a moderately larger value of magnetic diffusivity than has previously been used.

Permeabilization and recovery of the stratum corneum in vivo: the synergy of photomechanical waves and sodium lauryl sulfate.

PubMed

Lee, S; McAuliffe, D J; Kollias, N; Flotte, T J; Doukas, A G

2001-01-01

Photomechanical waves render the stratum corneum permeable and allow macromolecules to diffuse into the epidermis and dermis. The aim of this study was to investigate the combined action of photomechanical waves and sodium lauryl sulfate, an anionic surfactant, for transdermal delivery. A single photomechanical wave was applied to the skin of rats in the presence of sodium lauryl sulfate. The sodium lauryl sulfate solution was removed and aqueous solutions of rhodamine-B dextran (40 kDa molecular weight) were applied to the skin at time points 2, 30, and 60 minutes post-exposure. The presence of rhodamine-B dextran in the skin was measured by fluorescence emission spectroscopy in vivo and fluorescence microscopy of frozen biopsies. The use of sodium lauryl sulfate delayed the recovery of the stratum corneum barrier and extended the time available for the diffusion of dextran through it. The combination of photomechanical waves and surfactants can enhance transdermal drug delivery. Copyright 2001 Wiley-Liss, Inc.

Wave Phenomena in Reaction-Diffusion Systems

NASA Astrophysics Data System (ADS)

Steinbock, Oliver; Engel, Harald

2013-12-01

Pattern formation in excitable and oscillatory reaction-diffusion systems provides intriguing examples for the emergence of macroscopic order from molecular reaction events and Brownian motion. Here we review recent results on several aspects of excitation waves including anomalous dispersion, vortex pinning, and three-dimensional scroll waves. Anomalies in the speed-wavelength dependence of pulse trains include nonmonotonic behavior, bistability, and velocity gaps. We further report on the hysteresis effects during the pinning-depinning transition of twodimensional spiral waves. The pinning of three-dimensional scroll waves shows even richer dynamic complexity, partly due to the possibility of geometric and topological mismatches between the unexcitable, pinning heterogeneities and the one-dimensional rotation backbone of the vortex. As examples we present results on the pinning of scroll rings to spherical, C-shaped, and genus-2-type heterogeneities. We also review the main results of several experimental studies employing the Belousov-Zhabotinsky reaction and briefly discuss the biomedical relevance of this research especially in the context of cardiology.

Electromagnetic and electrostatic emissions at the cusp-magnetosphere interface during substorms

NASA Technical Reports Server (NTRS)

Curtis, S. A.; Fairfield, D. H.; Wu, C. S.

1979-01-01

Strongly peaked electrostatic emissions near 10.0 kHz and electromagnetic emissions near 0.56 kHz have been observed by the VLF wave detector on board Imp 6 on crossings from the earth's magnetosphere into the polar cusp during the occurrence of large magnetospheric substorms. The electrostatic emissions were observed to be closely confined to the cusp-magnetosphere interface. The electromagnetic emissions were of somewhat broader spatial extent and were seen on higher-latitude field lines within the cusp. Using these plasma wave observations and additional information provided by plasma, magnetometer and particle measurements made simultaneously on Imp 6, theories are constructed to explain each of the two classes of emission. The electromagnetic waves are modeled as whistlers, and the electrostatic waves as electron-cyclotron harmonics. The resulting growth rates predict power spectra similar to those observed for both emission classes. The electrostatic waves may play a significant role via enhanced diffusion in the relaxation of the sharp substorm time cusp-magnetosphere boundary to a more diffuse quiet time boundary.

Core-Collapse Supernovae Explored by Multi-D Boltzmann Hydrodynamic Simulations

NASA Astrophysics Data System (ADS)

Sumiyoshi, Kohsuke; Nagakura, Hiroki; Iwakami, Wakana; Furusawa, Shun; Matsufuru, Hideo; Imakura, Akira; Yamada, Shoichi

We report the latest results of numerical simulations of core-collapse supernovae by solving multi-D neutrino-radiation hydrodynamics with Boltzmann equations. One of the longstanding issues of the explosion mechanism of supernovae has been uncertainty in the approximations of the neutrino transfer in multi-D such as the diffusion approximation and ray-by-ray method. The neutrino transfer is essential, together with 2D/3D hydrodynamical instabilities, to evaluate the neutrino heating behind the shock wave for successful explosions and to predict the neutrino burst signals. We tackled this difficult problem by utilizing our solver of the 6D Boltzmann equation for neutrinos in 3D space and 3D neutrino momentum space coupled with multi-D hydrodynamics adding special and general relativistic extensions. We have performed a set of 2D core-collapse simulations from 11M ⊙ and 15M ⊙ stars on K-computer in Japan by following long-term evolution over 400 ms after bounce to reveal the outcome from the full Boltzmann hydrodynamic simulations with a sophisticated equation of state with multi-nuclear species and updated rates for electron captures on nuclei.

Towards Simulating a Realistic Planetary Seismic Wavefield: The Contribution of the Megaregolith and Low-Velocity Waveguides

NASA Technical Reports Server (NTRS)

Schmerr, Nicholas C.; Weber, Renee C.; Lin, Pei-Ying Patty; Thorne, Michael Scott; Garnero, Ed J.

2011-01-01

Lunar seismograms are distinctly different from their terrestrial counterparts. The Apollo lunar seismometers recorded moonquakes without distinct P- or S-wave arrivals; instead waves arrive as a diffuse coda that decays over several hours making the identification of body waves difficult. The unusual character of the lunar seismic wavefield is generally tied to properties of the megaregolith: it consists of highly fractured and broken crustal rock, the result of extensive bombardment of the Moon. The megaregolith extends several kilometers into the lunar crust, possibly into the mantle in some regions, and is covered by a thin coating of fine-scale dust. These materials possess very low seismic velocities that strongly scatter the seismic wavefield at high frequencies. Directly modeling the effects of the megaregolith to simulate an accurate lunar seismic wavefield is a challenging computational problem, owing to the inherent 3-D nature of the problem and the high frequencies (greater than 1 Hz) required. Here we focus on modeling the long duration code, studying the effects of the low velocities found in the megaregolith. We produce synthetic seismograms using 1-D slowness integration methodologies, GEMINI and reflectivity, and a 3-D Cartesian finite difference code, Wave Propagation Program, to study the effect of thin layers of low velocity on the surface of a planet. These codes allow us generate seismograms with dominant frequencies of approximately 1 Hz. For background lunar seismic structure we explore several models, including the recent model of Weber et al., Science, 2011. We also investigate variations in megaregolithic thickness, velocity, attenuation, and seismogram frequency content. Our results are compared to the Apollo seismic dataset, using both a cross correlation technique and integrated envelope approach to investigate coda decay. We find our new high frequency results strongly support the hypothesis that the long duration of the lunar seismic codes is generated by the presence of the low velocity megaregolith, and that the diffuse arrivals are a combination of scattered energy and multiple reverberations within this layer. The 3-D modeling indicates the extreme surface topography of the Moon adds only a small contribution to scattering effects, though local geology may play a larger role. We also study the effects of the megaregolith on core reflected and converted phases and other body waves. Our analysis indicates detection of core interacting arrivals with a polarization filter technique is robust and lends the possibility of detecting other body waves from the Moon.

Finite Larmor radius effects on weak turbulence transport

NASA Astrophysics Data System (ADS)

Kryukov, N.; Martinell, J. J.

2018-06-01

Transport of test particles in two-dimensional weak turbulence with waves propagating along the poloidal direction is studied using a reduced model. Finite Larmor radius (FLR) effects are included by gyroaveraging over one particle orbit. For low wave amplitudes the motion is mostly regular with particles trapped in the potential wells. As the amplitude increases the trajectories become chaotic and the Larmor radius modifies the orbits. For a thermal distribution of Finite Larmor radii the particle distribution function (PDF) is Gaussian for small th$ (thermal gyroradius) but becomes non-Gaussian for large th$ . However, the time scaling of transport is diffusive, as characterized by a linear dependence of the variance of the PDF with time. An explanation for this behaviour is presented that provides an expression for an effective diffusion coefficient and reproduces the numerical results for large wave amplitudes which implies generalized chaos. When a shear flow is added in the direction of wave propagation, a modified model is obtained that produces free-streaming particle trajectories in addition to trapped ones; these contribute to ballistic transport for low wave amplitude but produce super-ballistic transport in the chaotic regime. As in the previous case, the PDF is Gaussian for low th$ becoming non-Gaussian as it increases. The perpendicular transport presents the same behaviour as in the case with no flow but the diffusion is faster in the presence of the flow.

A Three-Wave Model of the Stratosphere with Coupled Dynamics, Radiation and Photochemistry. Appendix M

NASA Technical Reports Server (NTRS)

Shia, Run-Lie; Zhou, Shuntai; Ko, Malcolm K. W.; Sze, Nien-Dak; Salstein, David; Cady-Pereira, Karen

1997-01-01

A zonal mean chemistry transport model (2-D CTM) coupled with a semi-spectral dynamical model is used to simulate the distributions of trace gases in the present day atmosphere. The zonal-mean and eddy equations for the velocity and the geopotential height are solved in the semi-spectral dynamical model. The residual mean circulation is derived from these dynamical variables and used to advect the chemical species in the 2- D CTM. Based on a linearized wave transport equation, the eddy diffusion coefficients for chemical tracers are expressed in terms of the amplitude, frequency and growth rate of dynamical waves; local chemical loss rates; and a time constant parameterizing small scale mixing. The contributions to eddy flux are from the time varying wave amplitude (transient eddy), chemical reactions (chemical eddy) and small scale mixing. In spite of the high truncation in the dynamical module (only three longest waves are resolved), the model has simulated many observed characteristics of stratospheric dynamics and distribution of chemical species including ozone. Compared with the values commonly used in 2-D CTMs, the eddy diffusion coefficients for chemical species calculated in this model are smaller, especially in the subtropics. It is also found that the chemical eddy diffusion has only a small effects in determining the distribution of most slow species, including ozone in the stratosphere.

Proceedings of the International Conference "Quantum Optics IV" Jaszowiec, Poland, June 17-24, 1997. Volume 93, Number 1

DTIC Science & Technology

1998-01-01

and creation operators of the radiation mode of frequency win. The interaction (in the rotating wave approximation ) is described by Am =• x10)(1llat...based on a series of approx- imations [such as the rotating wave approximation (RWA) and the "pole" approxi- mation (PA)] validity of which is...possibly, the oscillating dependencies ti(eo) and r(eo) arise when and because one does not use the rotating - wave and pole approximations inherently present

Fokker-Planck description of electron and photon transport in homogeneous media

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

Akcasu, A.Z.; Holloway, J.P.

1997-06-01

Starting from a Fokker-Planck description of particle transport, which is valid when the scattering is forwardly peaked and the energy change in scattering is small, we systematically obtain an approximate diffusionlike equation for the particle density by eliminating the direction variable {bold {cflx {Omega}}} with an elimination scheme based on Zwanzig{close_quote}s projection operator formalism in the interaction representation. The elimination procedure closely follows one described by Grigolini and Marchesoni [in {ital Memory Function Approaches to Stochastic Problems in Condensed Matter}, edited by Myron W. Evans, Paolo Grigolini, and Guiseppe P. Parravicini, Advances in Physical Chemistry, Vol. 62 (Wiley-Interscience, New York,more » 1985), Chap. II, p. 29], but with a different projection operator. The resulting diffusion equation is correct up to the second order in the coupling operator between the particle direction and position variable. The diffusion coefficients and mobility in the resulting diffusion equation depend on the initial distribution of the particles in direction and on the path length traveled by the particles. The full solution is obtained for a monoenergetic and monodirectional pulsed point source of particles in an infinite homogeneous medium. This solution is used to study the penetration and the transverse and longitudinal spread of the particles as they are transported through the medium. Application to diffusive wave spectroscopy in calculating the path-length distribution of photons, as well as application to dose calculations in tissue due to an electron beam are mentioned. {copyright} {ital 1997} {ital The American Physical Society}« less

Quantum dark soliton: Nonperturbative diffusion of phase and position

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

Dziarmaga, J.

2004-12-01

The dark soliton solution of the Gross-Pitaevskii equation in one dimension has two parameters that do not change the energy of the solution: the global phase of the condensate wave function and the position of the soliton. These degeneracies appear in the Bogoliubov theory as Bogoliubov modes with zero frequencies and zero norms. These 'zero modes' cannot be quantized as the usual Bogoliubov quasiparticle harmonic oscillators. They must be treated in a nonperturbative way. In this paper I develop a nonperturbative theory of zero modes. This theory provides a nonperturbative description of quantum phase diffusion and quantum diffusion of solitonmore » position. An initially well localized wave packet for soliton position is predicted to disperse beyond the width of the soliton.« less

Two species drag/diffusion model for energetic particle driven modes

NASA Astrophysics Data System (ADS)

Aslanyan, V.; Sharapov, S. E.; Spong, D. A.; Porkolab, M.

2017-12-01

A nonlinear bump-on-tail model for the growth and saturation of energetic particle driven plasma waves has been extended to include two populations of fast particles—one dominated by dynamical friction at the resonance and the other by velocity space diffusion. The resulting temporal evolution of the wave amplitude and frequency depends on the relative weight of the two populations. The two species model is applied to burning plasma with drag-dominated alpha particles and diffusion-dominated ICRH accelerated minority ions, showing the stabilization of bursting modes. The model also suggests an explanation for the recent observations on the TJ-II stellarator, where Alfvén Eigenmodes transition between steady state and bursting as the magnetic configuration varied.

Aeroacoustic directivity via wave-packet analysis of mean or base flows

NASA Astrophysics Data System (ADS)

Edstrand, Adam; Schmid, Peter; Cattafesta, Louis

2017-11-01

Noise pollution is an ever-increasing problem in society, and knowledge of the directivity patterns of the sound radiation is required for prediction and control. Directivity is frequently determined through costly numerical simulations of the flow field combined with an acoustic analogy. We introduce a new computationally efficient method of finding directivity for a given mean or base flow field using wave-packet analysis (Trefethen, PRSA 2005). Wave-packet analysis approximates the eigenvalue spectrum with spectral accuracy by modeling the eigenfunctions as wave packets. With the wave packets determined, we then follow the method of Obrist (JFM, 2009), which uses Lighthill's acoustic analogy to determine the far-field sound radiation and directivity of wave-packet modes. We apply this method to a canonical jet flow (Gudmundsson and Colonius, JFM 2011) and determine the directivity of potentially unstable wave packets. Furthermore, we generalize the method to consider a three-dimensional flow field of a trailing vortex wake. In summary, we approximate the disturbances as wave packets and extract the directivity from the wave-packet approximation in a fraction of the time of standard aeroacoustic solvers. ONR Grant N00014-15-1-2403.

Nonlinear Schroedinger Approximations for Partial Differential Equations with Quadratic and Quasilinear Terms

NASA Astrophysics Data System (ADS)

Cummings, Patrick

We consider the approximation of solutions of two complicated, physical systems via the nonlinear Schrodinger equation (NLS). In particular, we discuss the evolution of wave packets and long waves in two physical models. Due to the complicated nature of the equations governing many physical systems and the in-depth knowledge we have for solutions of the nonlinear Schrodinger equation, it is advantageous to use approximation results of this kind to model these physical systems. The approximations are simple enough that we can use them to understand the qualitative and quantitative behavior of the solutions, and by justifying them we can show that the behavior of the approximation captures the behavior of solutions to the original equation, at least for long, but finite time. We first consider a model of the water wave equations which can be approximated by wave packets using the NLS equation. We discuss a new proof that both simplifies and strengthens previous justification results of Schneider and Wayne. Rather than using analytic norms, as was done by Schneider and Wayne, we construct a modified energy functional so that the approximation holds for the full interval of existence of the approximate NLS solution as opposed to a subinterval (as is seen in the analytic case). Furthermore, the proof avoids problems associated with inverting the normal form transform by working with a modified energy functional motivated by Craig and Hunter et al. We then consider the Klein-Gordon-Zakharov system and prove a long wave approximation result. In this case there is a non-trivial resonance that cannot be eliminated via a normal form transform. By combining the normal form transform for small Fourier modes and using analytic norms elsewhere, we can get a justification result on the order 1 over epsilon squared time scale.

Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics.

PubMed

Strehl, Robert; Ilie, Silvana

2015-12-21

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated on three benchmarking systems, with special focus on approximation accuracy and efficiency.

Analyzing signal attenuation in PFG anomalous diffusion via a non-Gaussian phase distribution approximation approach by fractional derivatives.

PubMed

Lin, Guoxing

2016-11-21

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) techniques have been increasingly used to study anomalous diffusion in nuclear magnetic resonance and magnetic resonance imaging. However, the interpretation of PFG anomalous diffusion is complicated. Moreover, the exact signal attenuation expression including the finite gradient pulse width effect has not been obtained based on fractional derivatives for PFG anomalous diffusion. In this paper, a new method, a Mainardi-Luchko-Pagnini (MLP) phase distribution approximation, is proposed to describe PFG fractional diffusion. MLP phase distribution is a non-Gaussian phase distribution. From the fractional derivative model, both the probability density function (PDF) of a spin in real space and the PDF of the spin's accumulating phase shift in virtual phase space are MLP distributions. The MLP phase distribution leads to a Mittag-Leffler function based PFG signal attenuation, which differs significantly from the exponential attenuation for normal diffusion and from the stretched exponential attenuation for fractional diffusion based on the fractal derivative model. A complete signal attenuation expression E α (-D f b α,β * ) including the finite gradient pulse width effect was obtained and it can handle all three types of PFG fractional diffusions. The result was also extended in a straightforward way to give a signal attenuation expression of fractional diffusion in PFG intramolecular multiple quantum coherence experiments, which has an n β dependence upon the order of coherence which is different from the familiar n 2 dependence in normal diffusion. The results obtained in this study are in agreement with the results from the literature. The results in this paper provide a set of new, convenient approximation formalisms to interpret complex PFG fractional diffusion experiments.

Fractional Ablative Laser Followed by Transdermal Acoustic Pressure Wave Device to Enhance the Drug Delivery of Aminolevulinic Acid: In Vivo Fluorescence Microscopy Study.

PubMed

Waibel, Jill S; Rudnick, Ashley; Nousari, Carlos; Bhanusali, Dhaval G

2016-01-01

Topical drug delivery is the foundation of all dermatological therapy. Laser-assisted drug delivery (LAD) using fractional ablative laser is an evolving modality that may allow for a greater precise depth of penetration by existing topical medications, as well as more efficient transcutaneous delivery of large drug molecules. Additional studies need to be performed using energy-driven methods that may enhance drug delivery in a synergistic manner. Processes such as iontophoresis, electroporation, sonophoresis, and the use of photomechanical waves aid in penetration. This study evaluated in vivo if there is increased efficacy of fractional CO2 ablative laser with immediate acoustic pressure wave device. Five patients were treated and biopsied at 4 treatment sites: 1) topically applied aminolevulinic acid (ALA) alone; 2) fractional ablative CO2 laser and topical ALA alone; 3) fractional ablative CO2 laser and transdermal acoustic pressure wave device delivery system; and 4) topical ALA with transdermal delivery system. The comparison of the difference in the magnitude of diffusion with both lateral spread of ALA and depth diffusion of ALA was measured by fluorescence microscopy. For fractional ablative CO2 laser, ALA, and transdermal acoustic pressure wave device, the protoporphyrin IX lateral fluorescence was 0.024 mm on average vs 0.0084 mm for fractional ablative CO2 laser and ALA alone. The diffusion for the acoustic pressure wave device was an order of magnitude greater. We found that our combined approach of fractional ablative CO2 laser paired with the transdermal acoustic pressure wave device increased the depth of penetration of ALA.

Renormalization of the diffusion tensor for high-frequency, electromagnetic modes

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

Litwin, C.; Sudan, R.N.

The resonance broadening theory is used to derive the diffusion tensor for resonant particles in a spectrum of electromagnetic modes propagating parallel to the magnetic field. The magnetic trapping limit for saturation of wave amplitudes is discussed.

Cookbook asymptotics for spiral and scroll waves in excitable media.

PubMed

Margerit, Daniel; Barkley, Dwight

2002-09-01

Algebraic formulas predicting the frequencies and shapes of waves in a reaction-diffusion model of excitable media are presented in the form of four recipes. The formulas themselves are based on a detailed asymptotic analysis (published elsewhere) of the model equations at leading order and first order in the asymptotic parameter. The importance of the first order contribution is stressed throughout, beginning with a discussion of the Fife limit, Fife scaling, and Fife regime. Recipes are given for spiral waves and detailed comparisons are presented between the asymptotic predictions and the solutions of the full reaction-diffusion equations. Recipes for twisted scroll waves with straight filaments are given and again comparisons are shown. The connection between the asymptotic results and filament dynamics is discussed, and one of the previously unknown coefficients in the theory of filament dynamics is evaluated in terms of its asymptotic expansion. (c) 2002 American Institute of Physics.

Multi-spectral Metasurface for Different Functional Control of Reflection Waves.

PubMed

Huang, Cheng; Pan, Wenbo; Ma, Xiaoliang; Luo, Xiangang

2016-03-22

Metasurface have recently generated much interest due to its strong manipulation of electromagnetic wave and its easy fabrication compared to bulky metamaterial. Here, we propose the design of a multi-spectral metasurface that can achieve beam deflection and broadband diffusion simultaneously at two different frequency bands. The metasurface is composed of two-layered metallic patterns backed by a metallic ground plane. The top-layer metasurface utilizes the cross-line structures with two different dimensions for producing 0 and π reflection phase response, while the bottom-layer metasurface is realized by a topological morphing of the I-shaped patterns for creating the gradient phase distribution. The whole metasurface is demonstrated to independently control the reflected waves to realize different functions at two bands when illuminated by a normal linear-polarized wave. Both simulation and experimental results show that the beam deflection is achieved at K-band with broadband diffusion at X-Ku band.

Cookbook asymptotics for spiral and scroll waves in excitable media

NASA Astrophysics Data System (ADS)

Margerit, Daniel; Barkley, Dwight

2002-09-01

Algebraic formulas predicting the frequencies and shapes of waves in a reaction-diffusion model of excitable media are presented in the form of four recipes. The formulas themselves are based on a detailed asymptotic analysis (published elsewhere) of the model equations at leading order and first order in the asymptotic parameter. The importance of the first order contribution is stressed throughout, beginning with a discussion of the Fife limit, Fife scaling, and Fife regime. Recipes are given for spiral waves and detailed comparisons are presented between the asymptotic predictions and the solutions of the full reaction-diffusion equations. Recipes for twisted scroll waves with straight filaments are given and again comparisons are shown. The connection between the asymptotic results and filament dynamics is discussed, and one of the previously unknown coefficients in the theory of filament dynamics is evaluated in terms of its asymptotic expansion.

Multi-spectral Metasurface for Different Functional Control of Reflection Waves

PubMed Central

Huang, Cheng; Pan, Wenbo; Ma, Xiaoliang; Luo, Xiangang

2016-01-01

Metasurface have recently generated much interest due to its strong manipulation of electromagnetic wave and its easy fabrication compared to bulky metamaterial. Here, we propose the design of a multi-spectral metasurface that can achieve beam deflection and broadband diffusion simultaneously at two different frequency bands. The metasurface is composed of two-layered metallic patterns backed by a metallic ground plane. The top-layer metasurface utilizes the cross-line structures with two different dimensions for producing 0 and π reflection phase response, while the bottom-layer metasurface is realized by a topological morphing of the I-shaped patterns for creating the gradient phase distribution. The whole metasurface is demonstrated to independently control the reflected waves to realize different functions at two bands when illuminated by a normal linear-polarized wave. Both simulation and experimental results show that the beam deflection is achieved at K-band with broadband diffusion at X-Ku band. PMID:27001206

Stochastic fire-diffuse-fire model with realistic cluster dynamics.

PubMed

Calabrese, Ana; Fraiman, Daniel; Zysman, Daniel; Ponce Dawson, Silvina

2010-09-01

Living organisms use waves that propagate through excitable media to transport information. Ca2+ waves are a paradigmatic example of this type of processes. A large hierarchy of Ca2+ signals that range from localized release events to global waves has been observed in Xenopus laevis oocytes. In these cells, Ca2+ release occurs trough inositol 1,4,5-trisphosphate receptors (IP3Rs) which are organized in clusters of channels located on the membrane of the endoplasmic reticulum. In this article we construct a stochastic model for a cluster of IP3R 's that replicates the experimental observations reported in [D. Fraiman, Biophys. J. 90, 3897 (2006)]. We then couple this phenomenological cluster model with a reaction-diffusion equation, so as to have a discrete stochastic model for calcium dynamics. The model we propose describes the transition regimes between isolated release and steadily propagating waves as the IP3 concentration is increased.

Influence of lattice vibrations on the field driven electronic transport in chains with correlated disorder

NASA Astrophysics Data System (ADS)

da Silva, L. D.; Sales, M. O.; Ranciaro Neto, A.; Lyra, M. L.; de Moura, F. A. B. F.

2016-12-01

We investigate electronic transport in a one-dimensional model with four different types of atoms and long-ranged correlated disorder. The latter was attained by choosing an adequate distribution of on-site energies. The wave-packet dynamics is followed by taking into account effects due to a static electric field and electron-phonon coupling. In the absence of electron-phonon coupling, the competition between correlated disorder and the static electric field promotes the occurrence of wave-packet oscillations in the regime of strong correlations. When the electron-lattice coupling is switched on, phonon scattering degrades the Bloch oscillations. For weak electron-phonon couplings, a coherent oscillatory-like dynamics of the wave-packet centroid persists for short periods of time. For strong couplings the wave-packet acquires a diffusive-like displacement and spreading. A slower sub-diffusive spreading takes place in the regime of weak correlations.

Gas exchange across the air-sea interface

NASA Astrophysics Data System (ADS)

Hasse, L.; Liss, P. S.

1980-10-01

The physics of gas exchange at the air-sea interface are reviewed. In order to describe the transfer of gases in the liquid near the boundary, a molecular plus eddy diffusivity concept is used, which has been found useful for smooth flow over solid surfaces. From consideration of the boundary conditions, a similar dependence of eddy diffusivity on distance from the interface can be derived for the flow beneath a gas/liquid interface, at least in the absence of waves. The influence of waves is then discussed. It is evident from scale considerations that the effect of gravity waves is small. It is known from wind tunnel work that capillary waves enhance gas transfer considerably. The existing hypotheses are apparently not sufficient to explain the observations. Examination of field data is even more frustrating since the data do not show the expected increase of gas exchange with wind speed.

Skin welding using pulsed laser radiation and a dye

NASA Astrophysics Data System (ADS)

Fried, Nathaniel M.; Walsh, Joseph T., Jr.

1998-07-01

Previous skin welding studies have used continuous wave (CW) delivery of radiation. However, heat diffusion during irradiation prevents strong welds from being achieved without creating large zones of thermal damage to surrounding tissue. This damage may prevent normal wound healing. Strong welds and minimal thermal damage can be achieved by introducing a dye and delivering the radiation in a pulsed mode. Two-cm-long, full-thickness incisions were made in guinea pig skin. India ink was used as an absorber, and egg white albumin was used as an adhesive. A 5-mm-diameter spot of CW, 1.06-micrometer Nd:YAG laser radiation was scanned over the weld site, producing 100 millisecond pulses. The cooling time between scans and number of scans was varied. Thermal damage zones were measured using a transmission polarizing microscope to identify birefringence changes in tissue. Tensile strengths were measured using a tensiometer. For pulsed welding and long cooling times, weld strengths of 2.4 kg/cm2 were measured, and thermal damage to the epidermis was limited to approximately 500 micrometers. With CW welding, comparable weld strengths resulted in approximately 2700 micrometer of thermal damage. CW laser radiation weld strengths were only 0.6 kg/cm2 when thermal damage in the epidermis was limited to approximately 500 micrometers.

Fluctuations uncover a distinct class of traveling waves

PubMed Central

Korolev, Kirill S.

2018-01-01

Epidemics, flame propagation, and cardiac rhythms are classic examples of reaction–diffusion waves that describe a switch from one alternative state to another. Only two types of waves are known: pulled, driven by the leading edge, and pushed, driven by the bulk of the wave. Here, we report a distinct class of semipushed waves for which both the bulk and the leading edge contribute to the dynamics. These hybrid waves have the kinetics of pushed waves, but exhibit giant fluctuations similar to pulled waves. The transitions between pulled, semipushed, and fully pushed waves occur at universal ratios of the wave velocity to the Fisher velocity. We derive these results in the context of a species invading a new habitat by examining front diffusion, rate of diversity loss, and fluctuation-induced corrections to the expansion velocity. All three quantities decrease as a power law of the population density with the same exponent. We analytically calculate this exponent, taking into account the fluctuations in the shape of the wave front. For fully pushed waves, the exponent is −1, consistent with the central limit theorem. In semipushed waves, however, the fluctuations average out much more slowly, and the exponent approaches 0 toward the transition to pulled waves. As a result, a rapid loss of genetic diversity and large fluctuations in the position of the front occur, even for populations with cooperative growth and other forms of an Allee effect. The evolutionary outcome of spatial spreading in such populations could therefore be less predictable than previously thought. PMID:29610340

Fluctuations uncover a distinct class of traveling waves.

PubMed

Birzu, Gabriel; Hallatschek, Oskar; Korolev, Kirill S

2018-04-17

Epidemics, flame propagation, and cardiac rhythms are classic examples of reaction-diffusion waves that describe a switch from one alternative state to another. Only two types of waves are known: pulled, driven by the leading edge, and pushed, driven by the bulk of the wave. Here, we report a distinct class of semipushed waves for which both the bulk and the leading edge contribute to the dynamics. These hybrid waves have the kinetics of pushed waves, but exhibit giant fluctuations similar to pulled waves. The transitions between pulled, semipushed, and fully pushed waves occur at universal ratios of the wave velocity to the Fisher velocity. We derive these results in the context of a species invading a new habitat by examining front diffusion, rate of diversity loss, and fluctuation-induced corrections to the expansion velocity. All three quantities decrease as a power law of the population density with the same exponent. We analytically calculate this exponent, taking into account the fluctuations in the shape of the wave front. For fully pushed waves, the exponent is -1, consistent with the central limit theorem. In semipushed waves, however, the fluctuations average out much more slowly, and the exponent approaches 0 toward the transition to pulled waves. As a result, a rapid loss of genetic diversity and large fluctuations in the position of the front occur, even for populations with cooperative growth and other forms of an Allee effect. The evolutionary outcome of spatial spreading in such populations could therefore be less predictable than previously thought. Copyright © 2018 the Author(s). Published by PNAS.

The arbitrary order mixed mimetic finite difference method for the diffusion equation

DOE PAGES

Gyrya, Vitaliy; Lipnikov, Konstantin; Manzini, Gianmarco

2016-05-01

Here, we propose an arbitrary-order accurate mimetic finite difference (MFD) method for the approximation of diffusion problems in mixed form on unstructured polygonal and polyhedral meshes. As usual in the mimetic numerical technology, the method satisfies local consistency and stability conditions, which determines the accuracy and the well-posedness of the resulting approximation. The method also requires the definition of a high-order discrete divergence operator that is the discrete analog of the divergence operator and is acting on the degrees of freedom. The new family of mimetic methods is proved theoretically to be convergent and optimal error estimates for flux andmore » scalar variable are derived from the convergence analysis. A numerical experiment confirms the high-order accuracy of the method in solving diffusion problems with variable diffusion tensor. It is worth mentioning that the approximation of the scalar variable presents a superconvergence effect.« less

Stability of planar traveling waves in a Keller-Segel equation on an infinite strip domain

NASA Astrophysics Data System (ADS)

Chae, Myeongju; Choi, Kyudong; Kang, Kyungkeun; Lee, Jihoon

2018-07-01

We consider a simplified model of tumor angiogenesis, described by a Keller-Segel equation on the two dimensional domain (x , y) ∈ R ×Sλ where Sλ is the circle of perimeter λ. It is known that the system allows planar traveling wave solutions of an invading type. In case that λ is sufficiently small, we establish the nonlinear stability of traveling wave solutions in the absence of chemical diffusion if the initial perturbation is sufficiently small in some weighted Sobolev space. When chemical diffusion is present, it can be shown that the system is linearly stable. Lastly, we prove that any solution with our front condition eventually becomes planar under certain regularity conditions.

Reduced xenon diffusion for quantitative lung study--the role of SF(6)

NASA Technical Reports Server (NTRS)

Mair, R. W.; Hoffmann, D.; Sheth, S. A.; Wong, G. P.; Butler, J. P.; Patz, S.; Topulos, G. P.; Walsworth, R. L.

2000-01-01

The large diffusion coefficients of gases result in significant spin motion during the application of gradient pulses that typically last a few milliseconds in most NMR experiments. In restricted environments, such as the lung, this rapid gas diffusion can lead to violations of the narrow pulse approximation, a basic assumption of the standard Stejskal-Tanner NMR method of diffusion measurement. We therefore investigated the effect of a common, biologically inert buffer gas, sulfur hexafluoride (SF(6)), on (129)Xe NMR and diffusion. We found that the contribution of SF(6) to (129)Xe T(1) relaxation in a 1:1 xenon/oxygen mixture is negligible up to 2 bar of SF(6) at standard temperature. We also measured the contribution of SF(6) gas to (129)Xe T(2) relaxation, and found it to scale inversely with pressure, with this contribution approximately equal to 1 s for 1 bar SF(6) pressure and standard temperature. Finally, we found the coefficient of (129)Xe diffusion through SF(6) to be approximately 4.6 x 10(-6) m(2)s(-1) for 1 bar pressure of SF(6) and standard temperature, which is only 1.2 times smaller than the (129)Xe self diffusion coefficient for 1 bar (129)Xe pressure and standard temperature. From these measurements we conclude that SF(6) will not sufficiently reduce (129)Xe diffusion to allow accurate surface-area/volume ratio measurements in human alveoli using time-dependent gas diffusion NMR.

Limits of Wave Runup and Corresponding Beach-Profile Change from Large-Scale Laboratory Data

DTIC Science & Technology

2010-01-01

A nearly vertical scarp developed after 40 min of wave action, with the upper limit of beach change identified at the toe of the dune scarp. and...change UL was found to approximately equal the vertical excursion of total wave runup, Rtw. An exception was runs where beach or dune scarps were...approximately equal the vertical excursion of total wave runup, Rtw. An exception was runs where beach or dune scarps were produced, which substantially limit the

Two tandem queues with general renewal input. 2: Asymptotic expansions for the diffusion model

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

Knessl, C.; Tier, C.

1999-10-01

In Part 1 the authors formulated and solved a diffusion model for two tandem queues with exponential servers and general renewal arrivals. They thus obtained the easy traffic diffusion approximation to the steady state joint queue length distribution for this network. Here they study asymptotic and numerical properties of the diffusion approximation. In particular, analytical expressions are obtained for the tail probabilities. Both the joint distribution of the two queues and the marginal distribution of the second queue are considered. They also give numerical illustrations of how this marginal is affected by changes in the arrival and service processes.

Multiple Light Scattering Probes of Soft Materials

NASA Astrophysics Data System (ADS)

Scheffold, Frank

2007-02-01

I will discuss both static and dynamic properties of diffuse waves. In practical applications the optical properties of colloidal systems play an important role, for example in commercial products such as sunscreen lotions, food (drinks), coatings but also in medicine for example in cataract formation (eye lens turbidity). It is thus of importance to know the key parameters governing optical turbidity from the single to the multiple scattering regime. Temporal fluctuations of multiply scattered light are studied with photon correlation spectroscopy (Diffusing Wave Spectroscopy). This DWS method and its various implementations will be treated.

Ion-Scale Structure in Mercury's Magnetopause Reconnection Diffusion Region

NASA Technical Reports Server (NTRS)

Gershman, Daniel J.; Dorelli, John C.; DiBraccio, Gina A.; Raines, Jim M.; Slavin, James A.; Poh, Gangkai; Zurbuchen, Thomas H.

2016-01-01

The strength and time dependence of the electric field in a magnetopause diffusion region relate to the rate of magnetic reconnection between the solar wind and a planetary magnetic field. Here we use approximately 150 milliseconds measurements of energetic electrons from the Mercury Surface, Space Environment, GEochemistry, and Ranging (MESSENGER) spacecraft observed over Mercury's dayside polar cap boundary (PCB) to infer such small-scale changes in magnetic topology and reconnection rates. We provide the first direct measurement of open magnetic topology in flux transfer events at Mercury, structures thought to account for a significant portion of the open magnetic flux transport throughout the magnetosphere. In addition, variations in PCB latitude likely correspond to intermittent bursts of approximately 0.3 to 3 millivolts per meter reconnection electric fields separated by approximately 5 to10 seconds, resulting in average and peak normalized dayside reconnection rates of approximately 0.02 and approximately 0.2, respectively. These data demonstrate that structure in the magnetopause diffusion region at Mercury occurs at the smallest ion scales relevant to reconnection physics.

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

NASA Technical Reports Server (NTRS)

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

1985-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1985-01-01

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

Ionospheric disturbances detected by high-resolution GPS-TEC observations after an earthquake and a tornado

NASA Astrophysics Data System (ADS)

Tsugawa, Takuya; Otsuka, Yuichi; Saito, Akinori; Ishii, Mamoru; Nishioka, Michi

Ionospheric disturbances following the 2011 Tohoku earthquake and the 2013 Moore tornado were observed by high-resolution GPS total electron content (TEC) observations using dense GPS receiver networks. After the 2011 Tohoku earthquake, concentric waves with short propagation distance propagated in the radial direction in the propagation velocity of 3,457, 783, 423 m/s for the first, second, third peak, respectively. Following these waves, concentric waves with long propagation distance appeared to propagate at the velocity of 138-288 m/s. In the vicinity of the epicenter, sudden TEC depletions and short-period oscillations with a period of approximately 4 minutes were also observed. The center of these ionospheric variations, termed the "ionospheric epicenter", corresponded to the tsunami source. Comparing to the results of a numerical simulation using non-hydrostatic compressible atmosphere-ionosphere model, the first peak of circular wave would be caused by the acoustic waves generated from the propagating Rayleigh wave. The second and third waves would be caused by atmospheric gravity waves excited in the lower ionosphere due to the acoustic wave propagations from the tsunami source. The fourth and following waves are considered to be caused by the atmospheric gravity waves induced by the wavefronts of traveling tsunami. After the EF5 tornado hit Moore, Oklahoma, USA, on 20 May 2013, clear concentric waves and short-period oscillations were observed. These concentric waves were non-dispersive waves with a horizontal wavelength of approximately 120 km and a period of approximately 13 minutes. They were observed for more than seven hours throughout North America. TEC oscillations with a period of approximately 4 minutes were also observed in the south of Moore for more than eight hours. Comparison between the GPS-TEC observations and the infrared cloud images from the GOES satellite indicates that the concentric waves and the short-period oscillations would be caused by supercell-induced atmospheric gravity waves and acoustic resonances, respectively. In this presentation, we will introduce the observational results of these ionospheric disturbances and discuss about the mechanism of concentric waves and short-period oscillations observed in both events.

Capillary fluctuations of surface steps: An atomistic simulation study for the model Cu(111) system

NASA Astrophysics Data System (ADS)

Freitas, Rodrigo; Frolov, Timofey; Asta, Mark

2017-10-01

Molecular dynamics (MD) simulations are employed to investigate the capillary fluctuations of steps on the surface of a model metal system. The fluctuation spectrum, characterized by the wave number (k ) dependence of the mean squared capillary-wave amplitudes and associated relaxation times, is calculated for 〈110 〉 and 〈112 〉 steps on the {111 } surface of elemental copper near the melting temperature of the classical potential model considered. Step stiffnesses are derived from the MD results, yielding values from the largest system sizes of (37 ±1 ) meV/A ˚ for the different line orientations, implying that the stiffness is isotropic within the statistical precision of the calculations. The fluctuation lifetimes are found to vary by approximately four orders of magnitude over the range of wave numbers investigated, displaying a k dependence consistent with kinetics governed by step-edge mediated diffusion. The values for step stiffness derived from these simulations are compared to step free energies for the same system and temperature obtained in a recent MD-based thermodynamic-integration (TI) study [Freitas, Frolov, and Asta, Phys. Rev. B 95, 155444 (2017), 10.1103/PhysRevB.95.155444]. Results from the capillary-fluctuation analysis and TI calculations yield statistically significant differences that are discussed within the framework of statistical-mechanical theories for configurational contributions to step free energies.

Correction of the near threshold behavior of electron collisional excitation cross-sections in the plane-wave Born approximation

DOE PAGES

Kilcrease, D. P.; Brookes, S.

2013-08-19

The modeling of NLTE plasmas requires the solution of population rate equations to determine the populations of the various atomic levels relevant to a particular problem. The equations require many cross sections for excitation, de-excitation, ionization and recombination. Additionally, a simple and computational fast way to calculate electron collisional excitation cross-sections for ions is by using the plane-wave Born approximation. This is essentially a high-energy approximation and the cross section suffers from the unphysical problem of going to zero near threshold. Various remedies for this problem have been employed with varying degrees of success. We present a correction procedure formore » the Born cross-sections that employs the Elwert–Sommerfeld factor to correct for the use of plane waves instead of Coulomb waves in an attempt to produce a cross-section similar to that from using the more time consuming Coulomb Born approximation. We compare this new approximation with other, often employed correction procedures. Furthermore, we also look at some further modifications to our Born Elwert procedure and its combination with Y.K. Kim's correction of the Coulomb Born approximation for singly charged ions that more accurately approximate convergent close coupling calculations.« less

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity

DOE PAGES

Cerbino, Roberto; Sun, Yifei; Donev, Aleksandar; ...

2015-09-30

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. Here in this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion inmore » microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer.« less

Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity

PubMed Central

Cerbino, Roberto; Sun, Yifei; Donev, Aleksandar; Vailati, Alberto

2015-01-01

Diffusion processes are widespread in biological and chemical systems, where they play a fundamental role in the exchange of substances at the cellular level and in determining the rate of chemical reactions. Recently, the classical picture that portrays diffusion as random uncorrelated motion of molecules has been revised, when it was shown that giant non-equilibrium fluctuations develop during diffusion processes. Under microgravity conditions and at steady-state, non-equilibrium fluctuations exhibit scale invariance and their size is only limited by the boundaries of the system. In this work, we investigate the onset of non-equilibrium concentration fluctuations induced by thermophoretic diffusion in microgravity, a regime not accessible to analytical calculations but of great relevance for the understanding of several natural and technological processes. A combination of state of the art simulations and experiments allows us to attain a fully quantitative description of the development of fluctuations during transient diffusion in microgravity. Both experiments and simulations show that during the onset the fluctuations exhibit scale invariance at large wave vectors. In a broader range of wave vectors simulations predict a spinodal-like growth of fluctuations, where the amplitude and length-scale of the dominant mode are determined by the thickness of the diffuse layer. PMID:26419420