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GARCIA-SCHWARZ, G., M. BERCOVICI, L. A. MARSHALL, and J. G. SANTIAGO. "Sample dispersion in isotachophoresis." Journal of Fluid Mechanics 679 (May 12, 2011): 455–75. http://dx.doi.org/10.1017/jfm.2011.139.
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We present an analytical, numerical and experimental study of advective dispersion in isotachophoresis (ITP). We analyse the dynamics of the concentration field of a focused analyte in peak mode ITP. The analyte distribution is subject to electromigration, diffusion and advective dispersion. Advective dispersion results from strong internal pressure gradients caused by non-uniform electro-osmotic flow (EOF). Analyte dispersion strongly affects the sensitivity and resolution of ITP-based assays. We perform axisymmetric time-dependent numerical simulations of fluid flow, diffusion and electromigration. We find that analyte properties contribute greatly to dispersion in ITP. Analytes with mobility values near those of the trailing (TE) or leading electrolyte (LE) show greater penetration into the TE or LE, respectively. Local pressure gradients in the TE and LE then locally disperse these zones of analyte penetration. Based on these observations, we develop a one-dimensional analytical model of the focused sample zone. We treat the LE, TE and LE–TE interface regions separately and, in each, assume a local Taylor–Aris-type effective dispersion coefficient. We also performed well-controlled experiments in circular capillaries, which we use to validate our simulations and analytical model. Our model allows for fast and accurate prediction of the area-averaged sample distribution based on known parameters including species mobilities, EO mobility, applied current density and channel dimensions. This model elucidates the fundamental mechanisms underlying analyte advective dispersion in ITP and can be used to optimize detector placement in detection-based assays.
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Chen, G. Q., and L. Zeng. "Taylor dispersion in a packed tube." Communications in Nonlinear Science and Numerical Simulation 14, no. 5 (May 2009): 2215–21. http://dx.doi.org/10.1016/j.cnsns.2008.07.018.
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Rubinstein, I., and B. Zaltzman. "Convective diffusive mixing in concentration polarization: from Taylor dispersion to surface convection." Journal of Fluid Mechanics 728 (July 8, 2013): 239–78. http://dx.doi.org/10.1017/jfm.2013.276.
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AbstractWe analyse the steady-state convection–diffusion mixing of a solute by a creeping circulatory flow in a long sealed rectangular two-dimensional channel with impermeable sidewalls and fixed different solute concentrations at the two opposite edges. Solution circulation is due to a constant velocity slip along the sidewalls and a back flow along the channel axis. This simple model distils the essence of circulation in concentration polarization of an electrolyte solution under a DC electric current in a micro-channel sealed by an ion-selective element (a nano-channel or a cation exchange membrane). It is observed that in the slow circulation regime (small $Pe$ numbers) the solute flux through the channel is governed by the Taylor–Aris dispersion mechanism, i.e. the flux is driven by the cross-sectional average axial concentration gradient, whereas upon increase in $Pe$ this mechanism fails. The general question addressed is where the system goes after the breakdown of the Taylor–Aris dispersion regime. In order to find out the answer, the following specific questions have to be addressed. (1) How does the Taylor–Aris dispersion mechanism break down upon increase in $Pe$? (2) Why does it break down? (3) What is the role of the channel aspect ratio in this breakdown? The answers to these questions are obtained through analysing a hierarchy of suitable auxiliary model problems, including the unidirectional zero discharge channel flow and the circulatory analogue of plane-parallel Couette flow, for which most of the analysis is done. They may be summarized as follows. Upon increase in circulation velocity, the Taylor–Aris dispersion mechanism fails due to the formation of lateral non-uniformities of longitudinal solute concentration gradient driving the dispersion flux. These non-uniformities accumulate in protrusion-like disturbances of the solute concentration (wall fingers) emerging near the channel sidewall at the flow exit from the edge. Wall fingers propagate along the sidewalls with increase in $Pe$ and eventually reach the opposite channel edges, transforming into narrow surface convection layers. These layers, together with the edge diffusion layers, form a closed mass transport pattern carrying most of the mass flux through the channel with the bulk largely excluded from the transport. The formation of this pattern finalizes the transition from Taylor–Aris dispersion to the surface convection regime. For large circulation velocities, concentration distribution in the surface convection layers attains an oscillatory spiral structure reminiscent of thermal waves in heat conduction.
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Al Mukahal, F. H. H., B. R. Duffy, and S. K. Wilson. "Advection and Taylor–Aris dispersion in rivulet flow." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2207 (November 2017): 20170524. http://dx.doi.org/10.1098/rspa.2017.0524.
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Motivated by the need for a better understanding of the transport of solutes in microfluidic flows with free surfaces, the advection and dispersion of a passive solute in steady unidirectional flow of a thin uniform rivulet on an inclined planar substrate driven by gravity and/or a uniform longitudinal surface shear stress are analysed. Firstly, we describe the short-time advection of both an initially semi-infinite and an initially finite slug of solute of uniform concentration. Secondly, we describe the long-time Taylor–Aris dispersion of an initially finite slug of solute. In particular, we obtain the general expression for the effective diffusivity for Taylor–Aris dispersion in such a rivulet, and discuss in detail its different interpretations in the special case of a rivulet on a vertical substrate.
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Jordan, P. M., and C. Feuillade. "A note on Love's equation with damping." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2071 (February 21, 2006): 2063–76. http://dx.doi.org/10.1098/rspa.2006.1674.
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The dynamic propagation of a Heaviside input signal in a semi-infinite, dissipative/dispersive medium is considered. The exact solution to this problem, which corresponds to Stokes' first problem of fluid mechanics, is obtained and analysed using integral transform methods. Special/limiting cases are noted and numerical methods are used to illustrate the analytical findings. Specifically, the following results are presented: (i) critical values of the dispersion coefficient are noted and examined; (ii) for large values of time, the solution exhibits Taylor shock-like behaviour; (iii) the half-peak point of the Taylor shock exhibits a phase shift that depends on the dispersion coefficient. Lastly, links to other fields are noted and some associated mathematical relations are presented.
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Beck, Margaret, Osman Chaudhary, and C. Eugene Wayne. "Rigorous Justification of Taylor Dispersion via Center Manifolds and Hypocoercivity." Archive for Rational Mechanics and Analysis 235, no. 2 (August 7, 2019): 1105–49. http://dx.doi.org/10.1007/s00205-019-01440-2.
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Brenner, H., A. Nadim, and S. Haber. "Long-time molecular diffusion, sedimentation and Taylor dispersion of a fluctuating cluster of interacting Brownian particles." Journal of Fluid Mechanics 183 (October 1987): 511–42. http://dx.doi.org/10.1017/s002211208700274x.
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Generalized Taylor dispersion theory, incorporating so-called coupling effects, is used to calculate the transport properties of a single deformable ‘chain’ composed of hydrodynamically interacting rigid Brownian particles bound together by internal potentials and moving through an unbounded quiescent viscous fluid. The individual rigid particles comprising the flexible chain or cluster may each be of arbitrary shape, size and density, and are supposed ‘joined’ together to form the chain by a configuration-dependent internal potential V. Each particle separately undergoes translational and rotational Brownian motions; together, their relative motions give rise to a conformational or vibrational Brownian motion of the chain (in addition to a translational motion of the chain as a whole). Sufficient time is allowed for all accessible chain configurations to be sampled many times in consequence of this internal Brownian motion. As a result, an internal equilibrium Boltzmann probabilistic distribution of conformations derived from V effectively obtains.In contrast with prior analyses of such chain transport phenomena, no ad hoc preaveraging hypotheses are invoked to effect the averaging of the input conformation-specific hydrodynamic mobility data. Rather, the calculation is effected rigorously within the usual (quasi-static) context of configuration-specific Stokes-Einstein equations.Explicit numerical calculations serving to illustrate the general scheme are performed only for the simplest case, namely dumb-bells composed of identically sized spheres connected by a slack tether. In this context it is pointed out that prior calculations of flexible-body transport phenomena have failed to explicitly recognize the existence of a Taylor dispersion contribution to the long-time diffusivity of sedimenting deformable bodies. This fluctuation phenomenon is compounded of shape-sedimentation dispersion (arising as a consequence of the intrinsic geometrical anisotropy of the object) and size-sedimentation dispersion (arising from fluctuations in the instantaneous ‘size’ of the object). Whereas shape dispersion exists even for rigid objects, size dispersion is manifested only by flexible bodies. These two Taylor dispersion mechanisms are relevant to interpreting the non-equilibrium sedimentation-diffusion properties of monodisperse polymer molecules in solutions or suspensions.
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Feng, Shirani, and Inglis. "Droplets for Sampling and Transport of Chemical Signals in Biosensing: A Review." Biosensors 9, no. 2 (June 20, 2019): 80. http://dx.doi.org/10.3390/bios9020080.
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The chemical, temporal, and spatial resolution of chemical signals that are sampled and transported with continuous flow is limited because of Taylor dispersion. Droplets have been used to solve this problem by digitizing chemical signals into discrete segments that can be transported for a long distance or a long time without loss of chemical, temporal or spatial precision. In this review, we describe Taylor dispersion, sampling theory, and Laplace pressure, and give examples of sampling probes that have used droplets to sample or/and transport fluid from a continuous medium, such as cell culture or nerve tissue, for external analysis. The examples are categorized, as follows: (1) Aqueous-phase sampling with downstream droplet formation; (2) preformed droplets for sampling; and (3) droplets formed near the analyte source. Finally, strategies for downstream sample recovery for conventional analysis are described.
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El-Dib, Yusry O. "Nonlinear hydrodynamic Rayleigh—Taylor instability of viscous magnetic fluids: effect of a tangential magnetic field." Journal of Plasma Physics 51, no. 1 (February 1994): 1–11. http://dx.doi.org/10.1017/s0022377800017359.
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The nonlinear Rayleigh—Taylor instability of viscous magnetic fluids is considered under the influence of gravity and surface tension in the presence of a constant tangential magnetic field. The method of multiple-scales expansion is employed. A nonlinear Schrödinger equation with complex coefficients is imposed from the solvability conditions and used to analyse the stability of the system. A quadratic dispersion relation with complex coefficients is obtained. The Hurwitz criterion for a quadratic polynomial with complex coefficients is used to control the stability of the system. It is found that an increase in the viscosity increases the extent of the stable region in the presence of a magnetic field. Finally it is shown that the magnetic permeability of the fluid affects the stability conditions.
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Froitzheim, A., S. Merbold, and C. Egbers. "Velocity profiles, flow structures and scalings in a wide-gap turbulent Taylor–Couette flow." Journal of Fluid Mechanics 831 (October 13, 2017): 330–57. http://dx.doi.org/10.1017/jfm.2017.634.
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Fully turbulent Taylor–Couette flow between independently rotating cylinders is investigated experimentally in a wide-gap configuration ($\unicode[STIX]{x1D702}=0.5$) around the maximum transport of angular momentum. In that regime turbulent Taylor vortices are present inside the gap, leading to a pronounced axial dependence of the flow. To account for this dependence, we measure the radial and azimuthal velocity components in horizontal planes at different cylinder heights using particle image velocimetry. The ratio of angular velocities of the cylinder walls $\unicode[STIX]{x1D707}$, where the torque maximum appears, is located in the low counter-rotating regime ($\unicode[STIX]{x1D707}_{max}(\unicode[STIX]{x1D702}=0.5)=-0.2$). This point coincides with the smallest radial gradient of angular velocity in the bulk and the detachment of the neutral surface from the outer cylinder wall, where the azimuthal velocity component vanishes. The structure of the flow is further revealed by decomposing the flow field into its large-scale and turbulent contributions. Applying this decomposition to the kinetic energy, we can analyse the formation process of the turbulent Taylor vortices in more detail. Starting at pure inner cylinder rotation, the vortices are formed and strengthened until $\unicode[STIX]{x1D707}=-0.2$ quite continuously, while they break down rapidly for higher counter-rotation. The same picture is shown by the decomposed Nusselt number, and the range of rotation ratios, where turbulent Taylor vortices can exist, shrinks strongly in comparison to investigations at much lower shear Reynolds numbers. Moreover, we analyse the scaling of the Nusselt number and the wind Reynolds number with the shear Reynolds number, finding a communal transition at approximately $Re_{S}\approx 10^{5}$ from classical to ultimate turbulence with a transitional regime lasting at least up to $Re_{S}\geqslant 2\times 10^{5}$. Including the axial dispersion of the flow into the calculation of the wind amplitude, we can also investigate the wind Reynolds number as a function of the rotation ratio $\unicode[STIX]{x1D707}$, finding a maximum in the low counter-rotating regime slightly larger than $\unicode[STIX]{x1D707}_{max}$. Based on our study it becomes clear that the investigation of counter-rotating Taylor–Couette flows strongly requires an axial exploration of the flow.
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Yan, Hongyong, Lei Yang, Xiang-Yang Li, and Hong Liu. "Acoustic VTI Modeling Using an Optimal Time-Space Domain Finite-Difference Scheme." Journal of Computational Acoustics 24, no. 04 (December 2016): 1650016. http://dx.doi.org/10.1142/s0218396x16500168.
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Finite-difference (FD) schemes have been used widely for solving wave equations in seismic exploration. However, the conventional FD schemes hardly guarantee high accuracy at both small and large wavenumbers. In this paper, we propose an optimal time-space domain FD scheme for acoustic vertical transversely isotropic (VTI) wave modeling. The optimal FD coefficients for the second-order spatial derivatives are derived by approaching the time-space domain dispersion relation of acoustic VTI wave equations with the combination of the Taylor-series expansion and the sampling interpolation. We perform numerical dispersion analyses and acoustic VTI modeling using the optimal time-space domain FD scheme. The numerical dispersion analyses show that the optimal FD scheme has smaller dispersion than the conventional FD scheme at large wavenumbers, and also preserves high accuracy at small wavenumbers. The acoustic VTI modeling examples also demonstrate that the optimal time-space domain FD scheme has greater accuracy compared with the conventional time-space domain FD scheme for the same modeling parameters.
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Gou, J. N., R. H. Zeng, C. Wang, and Y. B. Sun. "Analytical model for viscous and elastic Rayleigh–Taylor instabilities in convergent geometries at static interfaces." AIP Advances 12, no. 7 (July 1, 2022): 075217. http://dx.doi.org/10.1063/5.0096383.
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Great attention has been attracted to study the viscous and elastic Rayleigh–Taylor instability in convergent geometries, especially for their low mode asymmetries that behave distinctively from the planar counterparts. However, most analyses have focused on the instability at static interfaces that excludes the studies of the Bell–Plesset effects and the elastic–plastic transition since they involve too complex mathematics. Herein, we perform detailed analyses on the dispersion relations by applying the viscous and elastic potential flow method to obtain their approximate growth rates compared with the exact ones to demonstrate: (i) The approximate growth rates based on potential flow method generally coincide with the exact ones. (ii) An alternative expression is proposed to overcome the discrepancy for the low mode asymmetries at fluid/fluid interface. (iii) Extra care must be taken in solids since the maximum discrepancies occur at the n = 1 mode and at the mode proximate to the cutoff. This analytical method of great simplicity is essential to describe the dynamic interface by including the overall motion of the interface based on the static construction, while the exact analysis involves too complex mathematics to be extended by including the Bell–Plesset effects and the elastic–plastic properties. To sum up, the approximate analytical dispersion relations derived in convergent geometries, have the potential for dealing with dynamic interfaces where Bell–Plesset effects are combined with elastic–plastic transition.
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Gallegos Orozco, Veronica, Audel Santos Beltrán, Miriam Santos Beltrán, Hansel Medrano Prieto, Carmen Gallegos Orozco, and Ivanovich Estrada Guel. "Effect on Microstructure and Hardness of Reinforcement in Al–Cu with Al4C3 Nanocomposites." Metals 11, no. 8 (July 28, 2021): 1203. http://dx.doi.org/10.3390/met11081203.
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By superposition, the individual strengthening mechanisms via hardness analyses and the particle dispersion contribution to strengthening were estimated for Al–C and Al–C–Cu composites and pure Al. An evident contribution to hardening due to the density of dislocations was observed for all samples; the presence of relatively high-density values was the result of the difference in the coefficients of thermal expansion (CTE) between the matrix and the reinforced particles when the composites were subjected to the sintering process. However, for the Al–C–Cu composites, the dispersion of the particles had an important effect on the strengthening. For the Al–C–Cu composites, the maximum increase in microhardness was ~210% compared to the pure Al sample processed under the same conditions. The crystallite size and dislocation density contribution to strengthening were calculated using the Langford–Cohen and Taylor equations from the microstructural analysis, respectively. The estimated microhardness values had a good correlation with the experimental. According to the results, the Cu content is responsible for integrating and dispersing the Al4C3 phase. The proposed mathematical equation includes the combined effect of the content of C and Cu (in weight percent). The composites were fabricated following a powder metallurgical route complemented with the mechanical alloying (MA) process. Microstructural analyses were carried out through X-ray analyses coupled with a convolutional multiple whole profile (CMWP) fitting program to determine the crystallite size and dislocation density.
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BEC, J., L. BIFERALE, A. S. LANOTTE, A. SCAGLIARINI, and F. TOSCHI. "Turbulent pair dispersion of inertial particles." Journal of Fluid Mechanics 645 (February 9, 2010): 497–528. http://dx.doi.org/10.1017/s0022112009992783.
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The relative dispersion of pairs of inertial point particles in incompressible, homogeneous and isotropic three-dimensional turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number Reλ ~ 200 and Reλ ~ 400, corresponding to resolutions of 5123 and 20483 grid points, respectively. The evolution of both heavy and light particle pairs is analysed by varying the particle Stokes number and the fluid-to-particle density ratio. For particles much heavier than the fluid, the range of available Stokes numbers is St ∈ [0.1 : 70], while for light particles the Stokes numbers span the range St ∈ [0.1 : 3] and the density ratio is varied up to the limit of vanishing particle density. For heavy particles, it is found that turbulent dispersion is schematically governed by two temporal regimes. The first is dominated by the presence, at large Stokes numbers, of small-scale caustics in the particle velocity statistics, and it lasts until heavy particle velocities have relaxed towards the underlying flow velocities. At such large scales, a second regime starts where heavy particles separate as tracers' particles would do. As a consequence, at increasing inertia, a larger transient stage is observed, and the Richardson diffusion of simple tracers is recovered only at large times and large scales. These features also arise from a statistical closure of the equation of motion for heavy particle separation that is proposed and is supported by the numerical results. In the case of light particles with high density ratio, strong small-scale clustering leads to a considerable fraction of pairs that do not separate at all, although the mean separation increases with time. This effect strongly alters the shape of the probability density function of light particle separations.
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Wang, Bo, Xijin Luo, Qinghong Sheng, and Zhijun Yan. "The Effect of Martian Ionospheric Dispersion on SAR Imaging." Space: Science & Technology 2022 (July 26, 2022): 1–13. http://dx.doi.org/10.34133/2022/9860932.
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When passing through the ionosphere, the high-frequency (HF) pulse signal of the Mars Exploration Radar is affected by the dispersion effect error, which results in signal attenuation and time delay and brings about a phase advance in such a way that the echo cannot be matched and filtered. In this paper, a high-order phase model is built to overcome the above problems and enable echo matching and filtering. Most studies on the dispersion effect approximate the additional phase after the effect, assuming that the ionosphere is a thin-layer structure. In this paper, an effective model for the HF waveband is constructed to analyze the change of signal propagation paths in the ionosphere. The additional phase is expanded in a Taylor series and retained these expansions as high-order terms to calculate the cumulative additional phase along the path. We show the range-offset variables of signal frequency, bandwidth, and electron density, simulate the effects of the ionosphere under different conditions, and conclude that the model can effectively estimate Mars without considering the effects of magnetic fields and anomalous solar activity and the effect of the ionosphere on synthetic aperture radar (SAR) echoes. The results obtained using ray tracing calculations are different from those obtained by simplifying assumptions, and we can simulate the Martian ionospheric effects by the former.
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Caslavska, Jitka, Richard A. Mosher, and Wolfgang Thormann. "Impact of Taylor-Aris diffusivity on analyte and system zone dispersion in CZE assessed by computer simulation and experimental validation." ELECTROPHORESIS 36, no. 14 (May 20, 2015): 1529–38. http://dx.doi.org/10.1002/elps.201500034.
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Zhou, Chengyao, Wei Wu, Pengyuan Sun, Wenjie Yin, and Xiangyang Li. "The Combined Compact Difference Scheme Applied to Shear-Wave Reverse-Time Migration." Applied Sciences 12, no. 14 (July 12, 2022): 7047. http://dx.doi.org/10.3390/app12147047.
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In this paper, the combined compact difference scheme (CCD) and the combined supercompact difference scheme (CSCD) are used in the numerical simulation of the shear-wave equation. According to the Taylor series expansion and shear-wave equation, the fourth-order discrete scheme of the displacement field is established; then, the CCD and CSCD schemes are used to calculate the spatial derivative of the displacement field. Additionally, the accuracy, dispersion, and stability of the CCD and CSCD are analyzed, and numerical simulation analyses are carried out using 1D uniform models. Lastly, based on the processing of artificial boundary reflection using PML boundary conditions, shear-wave reverse-time migrations are carried out using synthetic data. The results show that (1) CCD and CSCD have smaller truncation errors, higher simulation precision, and lower numerical dispersion than other normal difference schemes; (2) CCD and CSCD can use the coarse grid and larger time step to calculate, with less memory and high computational efficiency; (3) finally, the result of the shear-wave reverse-time migration of the 2D synthetic data model show that the reverse-time migration imaging is clear, and the proposed method for shear-wave reverse-time migration is practical and effective.
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Chikwendu, S. C., and G. U. Ojiakor. "Slow-zone model for longitudinal dispersion in two-dimensional shear flows." Journal of Fluid Mechanics 152 (March 1985): 15–38. http://dx.doi.org/10.1017/s0022112085000544.
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A two-zone model is proposed for the longitudinal dispersion of contaminants in two-dimensional turbulent flow in open channels – a fast zone in the upper region of the flow, and a slow zone nearer to the bottom. The usual one-dimensional dispersion approach (Elder 1959) is used in each zone, but with different flow speeds U1 and U2 and dispersion coefficients D1 and D2 in the fast and slow zones respectively. However, turbulent vertical mixing is allowed at the interface between the two zones, with a small vertical diffusivity ε. This leads to a pair of coupled, linear, one-dimensional dispersion equations, which are solved by Fourier transformation. The Fourier-inversion integrals are analysed using two different methods.In the first method asymptotically valid expressions are found using the saddle-point method. The resulting cross-sectional average concentration consists of a leading Gaussian distribution followed by a trailing Gaussian distribution. The trailing Gaussian cloud disperses (longitudinally) faster than the leading one, and this gives the long tail observed in most dispersion experiments. Significantly the peak value of the average concentration is found to decay exponentially with time at a rate which is close to the rate observed by Sullivan (1971) in the early stage of the dispersion process. The solution is useful for fairly small times, and both the calculated value of D1 and the predicted bulk concentration distribution are in meaningful agreement with the experimental and simulation data of Sullivan (1971).In the second method an exact solution is found in the form of a convolution integral for the case D1 = D2 = D0. Explicit expressions which are valid for small times and for large times from the release of contaminant are found. For small times this exact solution confirms the basic results obtained by the saddle-point method. For large times the exact solution gives a contaminant concentration which approaches a Gaussian distribution travelling with the bulk speed as predicted by the Taylor model. The overall longitudinal dispersion coefficient at large times, D(∞), consists of the diffusivity D0 plus a contribution D[ell ](∞) which depends entirely on the vertical mixing. D(∞) is in good agreement with Chatwin's (1971) interpretation of Fischer's (1966) experimental data.
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Weisberg, Joel M. "The Galactic Electron Density Distribution." International Astronomical Union Colloquium 160 (1996): 447–54. http://dx.doi.org/10.1017/s025292110004207x.
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AbstractPulsars are excellent probes of the galactic free electron layer. Interstellar dispersion and scattering measurably affect the observed pulsar signals, thereby providing information on the distribution and density of the free electrons causing these phenomena.Primary calibration of galactic electron density models is achieved through adjusting their parameters to fit the observed dispersion of pulsars having independently measured distances. The distances are determined via kinematic analyses of HI absorption spectra, through angular or timing parallax measurements, and from associations with other objects of known distances.The models have become steadily more refined as the body of data upon which they are based has grown. Independent distance measurements continue to accrue. The discovery of pulsars in globular clusters provided high latitude lines of sight for probing the z-distribution (Reynolds 1989). Additional calibration has been provided through incorporation of interstellar scattering measurements into the modelling process (Cordeset al. 1991). Individual spiral arms are now explicitly modelled (Taylor & Cordes 1993).While great progress has been achieved with these models, there are still uncertainties in modelling the electron density of the local region and the inner Galaxy, and in the z–distribution of the electron layer. Currently anticipated observations will help to resolve some of these issues.
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García-Martínez, L., M. Rosete-Aguilar, and J. Garduño-Mejía. "Characterization of ultrashort pulses in the focal region of refractive systems." Acta Universitaria 23 (December 6, 2013): 3–6. http://dx.doi.org/10.15174/au.2013.552.
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In this work we analyze the spatio-temporal intensity of sub-20 fs pulses with a carrier wavelength of 810 nm along the optical axis of low numerical aperture achromatic and apochromatic doublets designed in the IR region by using the scalar diffraction theory. The diffraction integral is solved by expanding the wave number around the carrier frequency of the pulse in a Taylor series up to third order, and then the integral over the frequencies is solved by using the Gauss-Legendre quadrature method. We will show that the third-order group velocity dispersion (GVD) is not negligible for 10 fs pulses at 810 nm propagating through the low numerical aperture doublets, and its effect is more important than the propagation time difference (PTD). For sub-20 fs pulses, these two effects make the use of a pulse shaper necessary to correct for second and higher-order GVD terms and also the use of apochromatic optics to correct the PTD effect.
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Sun, Y. B., J. N. Gou, and R. H. Zeng. "Rayleigh–Taylor and Richtmyer–Meshkov instabilities in the presence of an inclined magnetic field." Physics of Plasmas 29, no. 7 (July 2022): 072104. http://dx.doi.org/10.1063/5.0091639.
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A unified and analytical model is developed to study the effects of an inclined magnetic field on magneto-Rayleigh–Taylor (MRT) and magneto-Richtmyer–Meshkov (MRM) instabilities in ideal magnetohydrodynamics. Unlike either a horizontal or a vertical magnetic field is present, the decay modes possess decaying and oscillation behaviors together. The vorticity transportation is analyzed. The dispersion relations are derived, and some interesting phenomena are observed. For a small R that represents the ratio of the magnetic field strength, or equivalently, the inclination θ, the growth rate of MRT instabilities resembles the case when a vertical magnetic field is present. For a large R, the growth rate resembles to the case when a horizontal magnetic field exists. The maximum growth rate becomes strongly dependent on At instead of on R. Furthermore, analytical expression is obtained for the MRM instability by using the impulsive accelerated model. The decaying and oscillating rates of the perturbed amplitude are explicitly related to θ. For two limiting cases, with either the vertical or the horizontal magnetic field existing, our results retrieve previous one of the theoretical analyses and numerical simulations. Generally, the asymptotic amplitude becomes independent of the wave number of the initial perturbation in the MRM instability. These findings regarding magneto-hydrodynamic interfacial instabilities in an inclined magnetic field could provide physical insights for magnetically driven targets and astrophysical observations. This analytical model is easily expanded to investigate the effects of finite thickness of magnetic slab and sheared magnetic field in relevant to high-energy-density physics and to astrophysics.
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Xu, Shigang, Yang Liu, Zhiming Ren, and Hongyu Zhou. "Time-space-domain temporal high-order staggered-grid finite-difference schemes by combining orthogonality and pyramid stencils for 3D elastic-wave propagation." GEOPHYSICS 84, no. 4 (July 1, 2019): T259—T282. http://dx.doi.org/10.1190/geo2018-0551.1.
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The presently available staggered-grid finite-difference (SGFD) schemes for the 3D first-order elastic-wave equation can only achieve high-order spatial accuracy, but they exhibit second-order temporal accuracy. Therefore, the commonly used SGFD methods may suffer from visible temporal dispersion and even instability when relatively large time steps are involved. To increase the temporal accuracy and stability, we have developed a novel time-space-domain high-order SGFD stencil, characterized by ([Formula: see text])th-order spatial and ([Formula: see text])th-order temporal accuracies ([Formula: see text]), to numerically solve the 3D first-order elastic-wave equation. The core idea of this new stencil is to use a double-pyramid stencil with an operator length parameter [Formula: see text] together with the conventional second-order SGFD to approximate the temporal derivatives. At the same time, the spatial derivatives are discretized by the orthogonality stencil with an operator length parameter [Formula: see text]. We derive the time-space-domain dispersion relation of this new stencil and determine finite-difference (FD) coefficients using the Taylor-series expansion. In addition, we further optimize the spatial FD coefficients by using a least-squares (LS) algorithm to minimize the time-space-domain dispersion relation. To create accurate and reasonable P-, S-, and converted wavefields, we introduce the 3D wavefield-separation technique into our temporal high-order SGFD schemes. The decoupled P- and S-wavefields are extrapolated by using the P- and S-wave dispersion-relation-based FD coefficients, respectively. Moreover, we design an adaptive variable-length operator scheme, including operators [Formula: see text] and [Formula: see text], to reduce the extra computational cost arising from adopting this new stencil. Dispersion and stability analyses indicate that our new methods have higher accuracy and better stability than the conventional ones. Using several 3D modeling examples, we demonstrate that our SGFD schemes can yield greater temporal accuracy on the premise of guaranteeing high-order spatial accuracy. Through effectively combining our new stencil, LS-based optimization, large time step, variable-length operator, and graphic processing unit, the computational efficiency can be significantly improved for the 3D case.
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Vadivukkarasan, M., and Mahesh V. Panchagnula. "Combined Rayleigh–Taylor and Kelvin–Helmholtz instabilities on an annular liquid sheet." Journal of Fluid Mechanics 812 (December 22, 2016): 152–77. http://dx.doi.org/10.1017/jfm.2016.784.
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This paper describes the three-dimensional destabilization characteristics of an annular liquid sheet when subjected to the combined action of Rayleigh–Taylor (RT) and Kelvin–Helmholtz (KH) instability mechanisms. The stability characteristics are studied using temporal linear stability analysis and by assuming that the fluids are incompressible, immiscible and inviscid. Surface tension is also taken into account at both the interfaces. Linearized equations governing the growth of instability amplitude have been derived. These equations involve time-varying coefficients and have been analysed using two approaches – direct numerical time integration and frozen-flow approximation. From the direct numerical time integration, we show that the time-varying coefficients evolve on a slow time scale in comparison with the amplitude growth. Therefore, we justify the use of the frozen-flow approximation and derive a closed-form dispersion relation from the appropriate governing equations and boundary conditions. The effect of flow conditions and fluid properties is investigated by introducing dimensionless numbers such as Bond number ($Bo$), inner and outer Weber numbers ($We_{i}$, $We_{o}$) and inner and outer density ratios ($Q_{i}$, $Q_{o}$). We show that four instability modes are possible – Taylor, sinuous, flute and helical. It is observed that the choice of instability mode is influenced by a combination of both $Bo$ as well as $We_{i}$ and $We_{o}$. However, the instability length scale calculated from the most unstable wavenumbers is primarily a function of $Bo$. We show a regime map in the $Bo,We_{i},We_{o}$ parameter space to identify regions where the system is susceptible to three-dimensional helical modes. Finally, we show an optimal partitioning of a given total energy ($\unicode[STIX]{x1D701}$) into acceleration-induced and shear-induced instability mechanisms in order to achieve a minimum instability length scale (${\mathcal{L}}_{m}^{\ast }$). We show that it is beneficial to introduce at least 90 % of the total energy into acceleration induced RT instability mechanism. In addition, we show that when the RT mechanism is invoked to destabilize an annular liquid sheet, ${\mathcal{L}}_{m}^{\ast }\sim \unicode[STIX]{x1D701}^{-3/5}$.
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Chazel, F., M. Benoit, A. Ern, and S. Piperno. "A double-layer Boussinesq-type model for highly nonlinear and dispersive waves." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2108 (May 27, 2009): 2319–46. http://dx.doi.org/10.1098/rspa.2008.0508.
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We derive and analyse, in the framework of the mild-slope approximation, a new double-layer Boussinesq-type model that is linearly and nonlinearly accurate up to deep water. Assuming the flow to be irrotational, we formulate the problem in terms of the velocity potential, thereby lowering the number of unknowns. The model derivation combines two approaches, namely the method proposed by Agnon et al. ( Agnon et al. 1999 J. Fluid Mech. 399 , 319–333) and enhanced by Madsen et al. ( Madsen et al. 2003 Proc. R. Soc. Lond. A 459 , 1075–1104), which consists of constructing infinite-series Taylor solutions to the Laplace equation, to truncate them at a finite order and to use Padé approximants, and the double-layer approach of Lynett & Liu ( Lynett & Liu 2004 a Proc. R. Soc. Lond. A 460 , 2637–2669), which allows lowering the order of derivatives. We formulate the model in terms of a static Dirichlet–Neumann operator translated from the free surface to the still-water level, and we derive an approximate inverse of this operator that can be built once and for all. The final model consists of only four equations both in one and two horizontal dimensions, and includes only second-order derivatives, which is a major improvement in comparison with so-called high-order Boussinesq models. A linear analysis of the model is performed, and its properties are optimized using a free parameter determining the position of the interface between the two layers. Excellent dispersion and shoaling properties are obtained, allowing the model to be applied up to the deep-water value k h =10. Finally, numerical simulations are performed to quantify the nonlinear behaviour of the model, and the results exhibit a nonlinear range of validity reaching at least k h =3π.
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Mehta, Chander Bhan. "Magneto-rotatory compressible couple-stress fluid heated from below in porous medium." Studia Geotechnica et Mechanica 38, no. 1 (March 1, 2016): 55–63. http://dx.doi.org/10.1515/sgem-2016-0006.
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Abstract The study is aimed at analysing thermal convection in a compressible couple stress fluid in a porous medium in the presence of rotation and magnetic field. After linearizing the relevant equations, the perturbation equations are analysed in terms of normal modes. A dispersion relation governing the effects of rotation, magnetic field, couple stress parameter and medium permeability have been examined. For a stationary convection, the rotation postpones the onset of convection in a couple stress fluid heated from below in a porous medium in the presence of a magnetic field. Whereas, the magnetic field and couple stress postpones and hastens the onset of convection in the presence of rotation and the medium permeability hastens and postpones the onset of convection with conditions on Taylor number. Further the oscillatory modes are introduced due to the presence of rotation and the magnetic field which were non-existent in their absence, and hence the principle of exchange stands valid. The sufficient conditions for nonexistence of over stability are also obtained.
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Lawrence, J. J., W. Coenen, A. L. Sánchez, G. Pawlak, C. Martínez-Bazán, V. Haughton, and J. C. Lasheras. "On the dispersion of a drug delivered intrathecally in the spinal canal." Journal of Fluid Mechanics 861 (December 27, 2018): 679–720. http://dx.doi.org/10.1017/jfm.2018.937.
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This paper investigates the transport of a solute carried by the cerebrospinal fluid (CSF) in the spinal canal. The analysis is motivated by the need for a better understanding of drug dispersion in connection with intrathecal drug delivery (ITDD), a medical procedure used for treatment of some cancers, infections and pain, involving the delivery of the drug to the central nervous system by direct injection into the CSF via the lumbar route. The description accounts for the CSF motion in the spinal canal, described in our recent publication (Sánchez et al., J. Fluid Mech., vol. 841, 2018, pp. 203–227). The Eulerian velocity field includes an oscillatory component with angular frequency $\unicode[STIX]{x1D714}$, equal to that of the cardiac cycle, and associated tidal volumes that are a factor $\unicode[STIX]{x1D700}\ll 1$ smaller than the total CSF volume in the spinal canal, with the small velocity corrections resulting from convective acceleration providing a steady-streaming component with characteristic residence times of order $\unicode[STIX]{x1D700}^{-2}\unicode[STIX]{x1D714}^{-1}\gg \unicode[STIX]{x1D714}^{-1}$. An asymptotic analysis for $\unicode[STIX]{x1D700}\ll 1$ accounting for the two time scales $\unicode[STIX]{x1D714}^{-1}$ and $\unicode[STIX]{x1D700}^{-2}\unicode[STIX]{x1D714}^{-1}$ is used to investigate the prevailing drug-dispersion mechanisms and their dependence on the solute diffusivity, measured by the Schmidt number $S$. Convective transport driven by the time-averaged Lagrangian velocity, obtained as the sum of the Eulerian steady-streaming velocity and the Stokes-drift velocity associated with the non-uniform pulsating flow, is found to be important for all values of $S$. By way of contrast, shear-enhanced Taylor dispersion, which is important for values of $S$ of order unity, is shown to be negligibly small for the large values $S\sim \unicode[STIX]{x1D700}^{-2}\gg 1$ corresponding to the molecular diffusivities of all ITDD drugs. Results for a model geometry indicate that a simplified equation derived in the intermediate limit $1\ll S\ll \unicode[STIX]{x1D700}^{-2}$ provides sufficient accuracy under most conditions, and therefore could constitute an attractive reduced model for future quantitative analyses of drug dispersion in the spinal canal. The results can be used to quantify dependences of the drug-dispersion rate on the frequency and amplitude of the pulsation of the intracranial pressure, the compliance and specific geometry of the spinal canal and the molecular diffusivity of the drug.
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Clausse, A., K. Chetty, J. Buchanan, R. Ram, and M. Lopez de Bertodano. "Kinematic stability and simulations of the variational two-fluid model for slug flow." Physics of Fluids 34, no. 4 (April 2022): 043301. http://dx.doi.org/10.1063/5.0086196.
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The two-fluid short-wave theory (TF-SWT) mode of the one-dimensional two-fluid model (TFM) [A. Clausse and M. Lopez de Bertodano, “Natural modes of the two-fluid model of two-phase flow,” Phys. Fluids 33, 033324 (2021)] showed that the incompressible kinematic and Kelvin–Helmholtz instabilities are the source of the long-standing ill-posed question. Here, the stability of the short wave mode is analyzed to obtain an unstable incompressible well-posed TFM for vertical slug flow, where inertial coupling and drag play the key role. Then, a computational method is implemented to perform non-linear simulations of slug waves. Linear stability analyses, i.e., characteristics and dispersion, of a variational TF-SWT for vertical slug flows are presented. The current TFM is constituted with a lumped-parameter model of inertial coupling between the Taylor bubble and the liquid. A characteristic analysis shows that this conservative model is parabolic, and it provides a base upon which other models can be constructed, including short-wave damping mechanisms, like vortex dynamics. The dispersion analysis shows that depending on the interfacial drag, the problem can be kinematic unstable. A new kinematic condition in terms of the inertial coupling and the interfacial drag is derived that is consistent with previous theoretical and experimental results. The material waves, which are predicted by linear stability theory, then develop into nonlinear slug waveforms that are captured by the numerical simulations. These and the horizontal stratified flow waves of previous research illustrate the TFM capability to model interfacial structures that behave like waves. Otherwise, when the physics of the TF-SWT waves is ignored, the model is ill-posed.
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Bragg, Andrew D. "Analysis of the forward and backward in time pair-separation probability density functions for inertial particles in isotropic turbulence." Journal of Fluid Mechanics 830 (September 29, 2017): 63–92. http://dx.doi.org/10.1017/jfm.2017.586.
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In this paper we investigate, using theory and direct numerical simulations (DNS), the forward in time (FIT) and backward in time (BIT) probability density functions (PDFs) of the separation of inertial particle pairs in isotropic turbulence. In agreement with our earlier study (Bragg et al., Phys. Fluids, vol. 28, 2016, 013305), where we compared the FIT and BIT mean-square separations, we find that inertial particles separate much faster BIT than FIT, with the strength of the irreversibility depending upon the final/initial separation of the particle pair and their Stokes number $St$. However, we also find that the irreversibility shows up in subtle ways in the behaviour of the full PDF that it does not in the mean-square separation. In the theory, we derive new predictions, including a prediction for the BIT/FIT PDF for $St\geqslant O(1)$, and for final/initial separations in the dissipation regime. The prediction shows how caustics in the particle relative velocities in the dissipation range affect the scaling of the pair-separation PDF, leading to a PDF with an algebraically decaying tail. The predicted functional behaviour of the PDFs is universal, in that it does not depend upon the level of intermittency in the underlying turbulence. We also analyse the pair-separation PDFs for fluid particles at short times, and construct theoretical predictions using the multifractal formalism to describe the fluid relative velocity distributions. The theoretical and numerical results both suggest that the extreme events in the inertial particle-pair dispersion at the small scales are dominated by their non-local interaction with the turbulent velocity field, rather than due to the strong dissipation range intermittency of the turbulence itself. In fact, our theoretical results predict that for final/initial separations in the dissipation range, when $St\gtrsim 1$, the tails of the pair-separation PDFs decay faster as the Taylor Reynolds number $Re_{\unicode[STIX]{x1D706}}$ is increased, the opposite of what would be expected for fluid particles.
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Yang, Lei, Hongyong Yan, and Hong Liu. "Optimal staggered-grid finite-difference schemes based on the minimax approximation method with the Remez algorithm." GEOPHYSICS 82, no. 1 (January 1, 2017): T27—T42. http://dx.doi.org/10.1190/geo2016-0171.1.
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Finite-difference (FD) schemes, especially staggered-grid FD (SFD) schemes, have been widely implemented for wave extrapolation in numerical modeling, whereas the conventional approach to compute the SFD coefficients is based on the Taylor-series expansion (TE) method, which leads to unignorable great errors at large wavenumbers in the solution of wave equations. We have developed new optimal explicit SFD (ESFD) and implicit SFD (ISFD) schemes based on the minimax approximation (MA) method with a Remez algorithm to enhance the numerical modeling accuracy. Starting from the wavenumber dispersion relations, we derived the optimal ESFD and ISFD coefficients by using the MA method to construct the objective functions, and solve the objective functions with the Remez algorithm. We adopt the MA-based ESFD and ISFD coefficients to solve the spatial derivatives of the elastic-wave equations and perform numerical modeling. Numerical analyses indicated that the MA-based ESFD and ISFD schemes can overcome the disadvantages of conventional methods by improving the numerical accuracy at large wavenumbers. Numerical modeling examples determined that under the same discretizations, the MA-based ESFD and ISFD schemes lead to greater accuracy compared with the corresponding conventional ESFD or ISFD scheme, whereas under the same numerical precision, the shorter operator length can be adopted for the MA-based ESFD and ISFD schemes, so that the computation time is further decreased.
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Van den Broeck, C. "Taylor dispersion revisited." Physica A: Statistical Mechanics and its Applications 168, no. 2 (October 1990): 677–96. http://dx.doi.org/10.1016/0378-4371(90)90023-l.
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Lubis, Iman, and Zairihan Abdul Halim. "A Review of Factors that influence Equity Premium Literature: A Mini-Review Approach." International Journal of Finance, Economics and Business 1, no. 1 (March 31, 2022): 18–42. http://dx.doi.org/10.56225/ijfeb.v1i1.2.
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The equity premium (market risk premium) is one of the most crucial a basis for consideration of asset allocation and is one of the centers of asset pricing. Numerous previous researches have examined the factors that predict the size of the premium equity (excess return risk asset less risk-free assets). The premium equity size is why investors choose risky investments (stocks) over non-risk investments (saving products). This study aims to comprehend the predictor of the equity premium. This study was designed using qualitative approaches by reviewing several relevant pieces of literature. A total of 49 articles were collected from Science Direct, Wiley online library, and Taylor & Francis. The results indicated that oil price negatively affects the equity premium, especially during recessions and gold bars or coins. The economic policy uncertainty and return dispersion have negative relationships in China and others but not in U.S. commodities. Economic indicators have failed to predict equity premium in recession but have power with nonparametric tests in bullish markets. Technical indicators are better than economic indicators for predicting equity premium. The policy implication of this review article is the finding of trends in researching premium equity using predictive regression and structured predictive input that focuses more on the U.S. than on emerging markets, and none of the models have reached past 80 percent. Future research should make models analyze technical indicators and news by adding asymmetry, grouping based on equity and commodity distribution, time and profitability, and dynamic and macro models in emerging markets.
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Mangeney, A., C. Lacombe, M. Maksimovic, A. A. Samsonov, N. Cornilleau-Wehrlin, C. C. Harvey, J. M. Bosqued, and P. Trávníček. "Cluster observations in the magnetosheath – Part 1: Anisotropies of the wave vector distribution of the turbulence at electron scales." Annales Geophysicae 24, no. 12 (December 21, 2006): 3507–21. http://dx.doi.org/10.5194/angeo-24-3507-2006.
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Abstract. We analyse the power spectral density δB2 and δE2 of the magnetic and electric fluctuations measured by Cluster 1 (Rumba) in the magnetosheath during 23 h, on four different days. The frequency range of the STAFF Spectral Analyser (f=8 Hz to 4 kHz) extends from about the lower hybrid frequency, i.e. the electromagnetic (e.m.) range, up to about 10 times the proton plasma frequency, i.e. the electrostatic (e.s.) range. In the e.m. range, we do not consider the whistler waves, which are not always observed, but rather the underlying, more permanent fluctuations. In this e.m. range, δB2 (at 10 Hz) increases strongly while the local angle ΘBV between the magnetic field B and the flow velocity V increases from 0° to 90°. This behaviour, also observed in the solar wind at lower frequencies, is due to the Doppler effect. It can be modelled if we assume that, for the scales ranging from kc/ωpe≃0.3 to 30 (c/ωpe is the electron inertial length), the intensity of the e.m. fluctuations for a wave number k (i) varies like k−ν with ν>≃3, (ii) peaks for wave vectors k perpendicular to B like |sinθkB|µ with µ>≃100. The shape of the observed variations of δB2 with f and with ΘBV implies that the permanent fluctuations, at these scales, statistically do not obey the dispersion relation for fast/whistler waves or for kinetic Alfvén waves: the fluctuations have a vanishing frequency in the plasma frame, i.e. their phase velocity is negligible with respect to V (Taylor hypothesis). The electrostatic waves around 1 kHz behave differently: δE2 is minimum for ΘBV>≃90°. This can be modelled, still with the Doppler effect, if we assume that, for the scales ranging from k λDe>≃0.1 to 1 (λDe is the Debye length), the intensity of the e.s. fluctuations (i) varies like k−ν with ν>≃4, (ii) peaks for k parallel to B like |cosθkB|µ with µ>≃100. These e.s. fluctuations may have a vanishing frequency in the plasma frame, or may be ion acoustic waves. Our observations imply that the e.m. frequencies observed in the magnetosheath result from the Doppler shift of a spatial turbulence frozen in the plasma, and that the intensity of the turbulent k spectrum is strongly anisotropic, for both e.m. and e.s. fluctuations. We conclude that the turbulence has strongly anisotropic k distributions, on scales ranging from kc/ωpe≃0.3 (50 km) to kλDe≃1 (30 m), i.e. at electron scales, smaller than the Cluster separation.
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Chen, Leixing, and Derek G. Leaist. "Multicomponent Taylor Dispersion Coefficients." Journal of Solution Chemistry 43, no. 12 (November 21, 2014): 2224–37. http://dx.doi.org/10.1007/s10953-014-0268-y.
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Taladriz-Blanco, Patricia, Barbara Rothen-Rutishauser, Alke Petri-Fink, and Sandor Balog. "Precision of Taylor Dispersion." Analytical Chemistry 91, no. 15 (June 27, 2019): 9946–51. http://dx.doi.org/10.1021/acs.analchem.9b01679.
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Camacho, J. "Thermodynamic functions for Taylor dispersion." Physical Review E 48, no. 3 (September 1, 1993): 1844–49. http://dx.doi.org/10.1103/physreve.48.1844.
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Huiqian, Yang, Nam-Trung Nguyen, and Xiaoyang Huang. "Micromixer based on Taylor dispersion." Journal of Physics: Conference Series 34 (April 1, 2006): 136–41. http://dx.doi.org/10.1088/1742-6596/34/1/023.
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SHAPIRO, M., and P. M. ADLER. "TAYLOR DISPERSION OF MULTICOMPONENT SOLUTES." Chemical Engineering Communications 148-150, no. 1 (June 1996): 183–219. http://dx.doi.org/10.1080/00986449608936515.
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Compte, Albert, and Juan Camacho. "Lévy statistics in Taylor dispersion." Physical Review E 56, no. 5 (November 1, 1997): 5445–49. http://dx.doi.org/10.1103/physreve.56.5445.
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Cottet, Hervé, Jean-Philippe Biron, and Michel Martin. "Taylor Dispersion Analysis of Mixtures." Analytical Chemistry 79, no. 23 (December 2007): 9066–73. http://dx.doi.org/10.1021/ac071018w.
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Rosencrans, Steve. "Taylor Dispersion in Curved Channels." SIAM Journal on Applied Mathematics 57, no. 5 (October 1997): 1216–41. http://dx.doi.org/10.1137/s003613999426990x.
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Huber, David E., and Juan G. Santiago. "Ballistic dispersion in temperature gradient focusing." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2091 (December 18, 2007): 595–612. http://dx.doi.org/10.1098/rspa.2007.0161.
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Molecular dispersion is caused by both molecular diffusion and non-uniform bulk fluid motion. While the Taylor–Aris dispersion regime is the most familiar regime in microfluidic systems, an oft-overlooked regime is that of purely kinematic (or ballistic) dispersion. In most microfluidic systems, this dispersion regime is transient and quickly gives way to Taylor–Aris dispersion. In electrophoretic focusing methods such as temperature gradient focusing (TGF), however, the characteristic time scales for dispersion are fixed, and focused peaks may never reach the Taylor limit. In this situation, generalized Taylor dispersion analysis is not applicable. A heuristic model is developed here which accounts for both molecular diffusion and advective dispersion across all dispersion regimes, from pure diffusion to Taylor dispersion to pure advection. This model is compared to results from TGF experiments and accurately captures both the initial decrease and subsequent increase in peak widths as electric field strength increases. The results of this combined analytical and experimental study provide a useful tool for estimation of dispersion and optimization of TGF systems.
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Piva, M., A. Calvo, A. Aguirre, G. Callegari, S. Gabbanelli, M. Rosen, and J. E. Wesfreid. "Hydrodynamical Dispersion in Taylor-Couette Cells." Journal de Physique III 7, no. 4 (April 1997): 895–908. http://dx.doi.org/10.1051/jp3:1997164.
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Camacho, J. "Thermodynamics of Taylor dispersion: Constitutive equations." Physical Review E 47, no. 2 (February 1, 1993): 1049–53. http://dx.doi.org/10.1103/physreve.47.1049.
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Camacho, J. "Purely global model for Taylor dispersion." Physical Review E 48, no. 1 (July 1, 1993): 310–21. http://dx.doi.org/10.1103/physreve.48.310.
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IOSILEVSKII, G., and H. BRENNER. "TAYLOR DISPERSION IN DISCRETE REACTIVE MIXTURES." Chemical Engineering Communications 133, no. 1 (March 1995): 53–91. http://dx.doi.org/10.1080/00986449508936311.
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Haresnape, A. McD, E. A. Harris, and P. McN Hill. "Taylor laminar dispersion in human airways." Respiration Physiology 59, no. 2 (February 1985): 131–41. http://dx.doi.org/10.1016/0034-5687(85)90002-7.
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Li, Gang, Ping Wang, Wei-Quan Jiang, Li Zeng, Zhi Li, and G. Q. Chen. "Taylor dispersion in wind-driven current." Journal of Hydrology 555 (December 2017): 697–707. http://dx.doi.org/10.1016/j.jhydrol.2017.10.063.
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Shapiro, Michael, and Howard Brenner. "Chemically reactive generalized Taylor dispersion phenomena." AIChE Journal 33, no. 7 (July 1987): 1155–67. http://dx.doi.org/10.1002/aic.690330710.
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Vikhansky, A., and W. Wang. "Taylor dispersion in finite-length capillaries." Chemical Engineering Science 66, no. 4 (February 2011): 642–49. http://dx.doi.org/10.1016/j.ces.2010.11.019.
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Moore, Christine M. V., and Charles L. Cooney. "Axial dispersion in Taylor-Couette flow." AIChE Journal 41, no. 3 (March 1995): 723–27. http://dx.doi.org/10.1002/aic.690410329.
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