Inhomogeneous Velocity Research Articles

Flow in linearly sheared two-dimensional foams: From bubble to bulk scale

We probe the flow of two-dimensional (2D) foams, consisting of a monolayer of bubbles sandwiched between a liquid bath and glass plate, as a function of driving rate, packing fraction, and degree of disorder. First, we find that bidisperse, disordered foams exhibit strongly rate-dependent and inhomogeneous (shear-banded) velocity profiles, while monodisperse ordered foams are also shear banded but essentially rate independent. Second, we adapt a simple model [E. Janiaud, D. Weaire, and S. Hutzler, Phys. Rev. Lett. 97, 038302 (2006)] based on balancing the averaged drag forces between the bubbles and the top plate F[over ]_{bw} and the averaged bubble-bubble drag forces F[over ]_{bb} by assuming that F[over ]_{bw} approximately v;{2/3} and F[over ]_{bb} approximately ( partial differential_{y}v);{beta} , where v and ( partial differential_{y}v) denote average bubble velocities and gradients. This model captures the observed rate-dependent flows for beta approximately 0.36 , and the rate independent flows for beta approximately 0.67 . Third, we perform independent rheological measurements of F[over ]_{bw} and F[over ]_{bb} , both for ordered and disordered systems, and find these to be fully consistent with the forms assumed in the simple model. Disorder thus leads to a modified effective exponent beta . Fourth, we vary the packing fraction phi of the foam over a substantial range and find that the flow profiles become increasingly shear banded when the foam is made wetter. Surprisingly, the model describes flow profiles and rate dependence over the whole range of packing fractions with the same power-law exponents-only a dimensionless number k that measures the ratio of the prefactors of the viscous drag laws is seen to vary with packing fraction. We find that k approximately (phi-phi_{c});{-1} , where phi_{c} approximately 0.84 corresponds to the 2D jamming density, and suggest that this scaling follows from the geometry of the deformed facets between bubbles in contact. Overall, our work shows that the presence of disorder qualitatively changes the effective bubble-bubble drag forces and suggests a route to rationalize aspects of the ubiquitous Herschel-Bulkley (power-law) rheology observed in a wide range of disordered materials.

New electrodynamic effects in transparent optical media

This paper presents a systematic theory of electrodynamic relativistic first-order effects in media with spatially inhomogeneous velocity. A geometrooptical approach is developed in terms of which the ray curvatures and changes of the polarization characteristics of the radiation as it passes through a continuous medium with inhomogeneous velocity are found. Nonreciprocal waveguides and lenses (that differ for opposite propagation directions) are demonstrated in a medium with transverse inhomogeneity of the velocity. Scattering (diffraction) of radiation at a localized velocity inhomogeneity is studied. The possibility of masking regions of space so that they become invisible is studied, and the influence of the motion of such a region is analyzed. The velocity inhomogeneity that appears when a region moves causes the radiation reflected from the boundary to appear and makes the inhomogeneity visible. A correct theory is constructed for the reflection of weak radiation from inhomogeneities induced by intense laser pulses in a fixed nonlinear medium and moving with the (group) velocity of light.

Estimation of the 2D crustal velocity structure in the Hidaka and Iburi Subprefectures, Hokkaido, Japan

Applying the iterative shooting/bisection technique for rapid forward modeling to the seismic explosion data, we could refine the crustal velocity structure model of the western part of the Hidaka collision zone, Hokkaido, Japan. We used only the precise P-wave first arrival data obtained by the Research Group for Explosion Seismology, which set up a 113.4-km-long profile in August 2000 along with 327 observation points and four shot points with TNT charges from 100 to 300 kg. We could estimate a two-dimensional inhomogeneous crustal velocity structure model with a velocity decrease in the eastern direction at a depth of 15.7 km, several portions of velocity reversals with depth and a low velocity anomaly proposed in previous studies. The root-mean-square of travel-time residuals was improved from 0.398 s for the previous structure model to 0.176 s for the present model with a reduction of 55.8%.

Shear banding or not in entangled DNA solutions depending on the level of entanglement

Entangled DNA solutions are ideal as a model system to examine nonlinear shear flow behavior. Even when the number of entanglements per chain, Z, is higher than 100, the solution is still soft enough with an elastic plateau modulus under 100Pa and is thus amenable to experimental study by commercial rotational rheometry without ambiguity and uncertainty. We have investigated nonlinear flow behavior of three entangled DNA solutions with Z=24, 60, and 156, respectively, using a combination of particle-tracking velocimetric (PTV) and conventional rheometric measurements. We explore questions such as (a) whether shear banding also occurs in moderately entangled solutions, (b) whether creep results in development of nonlinear velocity profile, (c) whether shear banding produced in startup shear and creep persists at long times in steady state, and (d) whether these entangled solutions exhibit homogeneous shear at the upper end of the stress plateau region. We found that the first DNA solution (Z=24) only shows transient weakly inhomogeneous shear and steady linear velocity profile. In the more entangled solutions (Z=60 and 156), shear banding is observed in startup rate- and stress-controlled shear in the shear thinning regime. Shear homogeneity eventually returns at the upper end of the stress plateau (shear thinning) regime.

$L^p$-stability estimates for the spatially inhomogeneous discrete velocity Boltzmann model

We present two a priori $L^p$-stability estimates to the discrete velocity Boltzmann models. In a close-to-global Maxwellian regime, we derive a local-in-time $L^2$-stability estimate using a macro-micro decomposition and dispersion estimates for smooth perturbations, and as a direct application, we establish that classical solutions in Kawashima's framework [22, 24] are uniformly $L^2$-stable. In a close-to-vacuum regime, we also obtain a local-in-time $L^p$-stability estimates for classical solutions near vacuum.

Interaction of electromagnetic waves with caustics in plasma flows

An electromagnetic wave (EMW) interacting with the moving singularity of the charged particle flux undergoes the reflection and absorption as well as frequency change due to Doppler effect and nonlinearity. The singularity corresponding to a caustic in plasma flow with inhomogeneous velocity can arise during the breaking of the finite amplitude Langmuir waves due to nonlinear effects. A systematic analysis of the wave-breaking regimes and caustics formation is presented and the EMW reflection coefficients are calculated.

A comparison of imaging conditions for wave-equation shot-profile migration

The application of a deconvolution imaging condition in wave-equation shot-profile migration is important to provide illumination compensation and amplitude recovery. Particularly if the aim is to successfully recover a measure of the medium reflectivity, an imaging condition that destroys amplitudes is unacceptable. We study a set of imaging conditions with illumination compensation. The imaging conditions are evaluated by the quality of the output amplitudes and artifacts produced. In numerical experiments using a vertically inhomogeneous velocity model, the best of all imaging conditions we tested is the one that divides the crosscorrelation of upgoing and downgoing wavefields by the autocorrelation of the downgoing wavefield, also known as the illumination map. In an application to Marmousi data, unconditional division by autocorrelation turned out to be unstable. Effective stabilization was achieved by smoothing the illumination map.

Anomalous transport of particles in plasma flow with strong inhomogeneous velocity shear

The temporal evolution of the drift modes and resulting anomalous transport are considered under the conditions of strong inhomogeneous flow shear [flow shear parameter dv0(r)∕dr is greater or comparable to the drift frequency] on the ground of the nonmodal approach with application to boundary regions of tokamaks. The nonmodal linear analysis of the effect of flow shear nonuniformity on the temporal evolution of the drift modes, performed on the base of the Hasegava–Wakatani model, has shown, that terms reflecting velocity profile curvature decay more rapidly with time, as compared with those containing only velocity shearing rate. Therefore, the linear effect of the flow shear nonuniformity appears to be subdominant and the long-time evolution of the drift modes is determined by more slowly damped shear rate contained terms. The anomalous transport of particles in shear flow due to nonmodal drift perturbations exhibits a subdiffusive behavior with the diffusion coefficient reducing in time as t−3.

Flow, Transport, and Reactions in a Thin Layer Flow Cell

The performance of fuel cells depends on the rate parameters of the kinetic reactions between the involved species, among other conditions. The determination of these parameters is crucial for the understanding of the functionality of fuel cells. Differential electrochemical mass spectroscopy in thin layer flow cells is used as a tool to gain improved understanding of the heterogeneous catalytic reactions taking place in fuel cell catalytic layers. In this paper, we focus on the description of thin layer cells by numerical models based on partial differential equations and the extraction of kinetics parameters by inverse modeling. For the model setup, various software tools are used. The simulation of laminar free flow is performed by the commercial code COMSOL. A finite volume code is used for the simulation of the reactive transport. The latter is coupled with a Levenberg–Marquardt algorithm for the determination of kinetic constants. Two designs of thin layer flow cells are considered: a cylindrical and a rectangular design. A drawback of the cylindrical cell design is the highly inhomogeneous velocity field leading to spatial variations of the conditions for electrode reactions. In contrast, the rectangular cell design shows a homogeneous flow field in the vicinity of the catalyst. The rectangular cell design has the additional advantage that flow is essentially two dimensional and can be computed analytically, which simplifies the numerical approach. The inverse modeling procedure is demonstrated for a hydrogen-carbon monoxide system.

Evaluation and interpretation of the effects of heterogeneous layers in an OBS/air-gun crustal structure study

We present a method for interpreting seismic records with arrivals and waveforms having characteristics which could be generated by extremely inhomogeneous velocity structures, such as non-typical oceanic crust, decollement at subduction zones, and seamounts in oceanic regions, by comparing them with synthetic waveforms. Recent extensive refraction and wide-angle reflection surveys in oceanic regions have provided us with a huge number of high-resolution and high-quality seismic records containing characteristic arrivals and waveforms, besides first arrivals and major reflected phases such as PmP. Some characteristic waveforms, with significant later reflected phases or anomalous amplitude decay with offset distance, are difficult to interpret using only a conventional interpretation method such as the traveltime tomographic inversion method. We find the best process for investigating such characteristic phases is to use an interactive interpretation method to compare observed data with synthetic waveforms, and calculate raypaths and traveltimes. This approach enables us to construct a reasonable structural model that includes all of the major characteristics of the observed waveforms. We present results here with some actual observed examples that might be of great help in the interpretation of such problematic phases. Our approach to the analysis of waveform characteristics is endorsed as an innovative method for constructing high-resolution and high-quality crustal structure models, not only in oceanic regions, but also in the continental regions.

Nonlinear Microrheology: Bulk Stresses versus Direct Interactions

In passive microrheology, the linear viscoelastic properties of complex fluids are inferred from the Brownian motion of colloidal tracer particles. Active (but gentle) forcing may also be used to obtain such linear-response information. More significant forcing may drive the material significantly out of equilibrium, thus potentially providing a window into the nonlinear response properties of the material. In leaving the linear-response regime, however, the theoretical underpinning for passive microrheology is lost, and a variety of issues arise. Most generally, what exactly can be measured, and how can such measurements be interpreted? Here we motivate and discuss a variety of theoretical issues facing the interpretation of active microrheology. First, in the continuum limit, the inhomogeneous velocity field around the probe gives rise to rheological inhomogeneities, whereupon an assumed generalized Stokes drag yields a weighted average of the viscosities around the probe rather than the (homogeneous) viscosity measured macroscopically. We then explicitly treat the material microstructure using a model system (a large colloidal probe pulled through a dilute suspension of small bath particles). We examine the different sources of stress upon the probe particle (e.g., direct probe-bath collisions as well as microstructural deformations within the bulk suspension) and discuss their analog (or lack thereof) in the corresponding macrorheological system. We discuss several crucial issues for the interpretation of nonlinear microrheology: (1) how to interpret the inhomogeneous and nonviscometric nature of the deformation field around the probe, (2) the distinction between direct and bulk stresses and their deconvolution, and (3) the (Lagrangian) time-dependent nature of the stress histories experienced by material elements as they advect past the probe. Having identified these issues, we briefly discuss adaptations of the basic technique to recover bulk rheology more faithfully. Whereas we specifically discuss a model colloidal suspension, we ultimately envision a technique capable of measuring the nonlinear rheology of general materials.

Surface coseismic gravity changes caused by dislocations in a 3-D heterogeneous earth

SUMMARY This study describes an examination of surface gravity changes caused by dislocations within a 3-D heterogeneous earth. This new theory is described using six independent dislocations: a vertical strike-slip, two vertical dip-slips perpendicular to each other, and three tensile openings on three perpendicular planes. A combination of the six independent dislocations is useful to compute coseismic gravity changes resulting from an arbitrary seismic source at an arbitrary position. Based on the 3-D lateral inhomogeneous P-wave velocity model, we deduce the 3-D density and S-wave velocity models using the relation of Karato. Finally, numerical computations are performed for a location south of Japan (30 ◦ N, 135 ◦ E). We calculate the coseismic gravity changes resulting from the six independent dislocations for source depths of 100, 300 and 637 km, respectively. Numerical results show that the maximum 3-D effect varies concomitantly with the dislocation type and the source depth. For seismic problems, the effect of elastic parameter μ is dominant.

Upper crust structure of eastern A’nyemaqên suture zone: Results of Barkam-Luqu-Gulang deep seismic sounding profile

Barkam-Luqu-Gulang deep seismic sounding profile runs from north of Sichuan Province to south of Gansu Province. It is located at the northeastern edge of Tibetan Plateau and crosses eastern A’nyemaqen suture zone. The upper crust structures around eastern A’nyemaqen suture zone and its adjacent area are reconstructed based on the arrival times of refracted Pg and Sg waves by using finite difference method, ray tracing inversion, time-term method and travel-time curve analysis. The results show that the depth variation of basement along profile is very strong as indicated by Pg and Sg waves. The basement rose in Zoige basin and depressed in eastern A’nyemaqen suture zone, and it gradually rose again northward and then depressed. The results also indicate that eastern A’nyemaqen suture zone behaves as inhomogeneous low velocity structures in the upper crust and is inclined toward the south. Hoh Sai Hu-Maqen fault, Wudu-Diebu fault and Zhouqu-Liangdang fault are characterized by low velocity distributions with various scales. The distinct variation in basement depth occurred near Hoh Sai Hu-Maqen fault and Zhouqu-Liangdang fault, which are main tectonic boundaries of A’nyemaqen suture zone. Wudu-Diebu fault, located at the depth variation zone of the basement, possibly has the same deep tectonic background with Zhouqu-Liangdang fault. The strongly depressed basement characterized by low velocity distribution and lateral inhomogeneity in A’nyemaqen suture zone implies crushed zone features under pinching action.

L-type Ca2+ channel mutations and T-wave alternans: a model study

A number of mutations have been linked to diseases for which the underlying mechanisms are poorly understood. An example is Timothy Syndrome (TS), a multisystem disorder that includes severe cardiac arrhythmias. Here we employ theoretical simulations to examine the effects of a TS mutation in the L-type Ca(2+) channel on cardiac dynamics over multiple scales, from a gene mutation to protein, cell, tissue, and finally the ECG, to connect a defective Ca(2+) channel to arrhythmia susceptibility. Our results indicate that 1) the TS mutation disrupts the rate-dependent dynamics in a single cardiac cell and promotes the development of alternans; 2) in coupled tissue, concordant alternans is observed at slower heart rates in mutant tissue than in normal tissue and, once initiated, rapidly degenerates into discordant alternans and conduction block; and 3) the ECG computed from mutant-simulated tissue exhibits prolonged QT intervals at physiological rates and with small increases in pacing rate, T-wave alternans, and alternating T-wave inversion. At the cellular level, enhanced Ca(2+) influx due to the TS mutation causes electrical instabilities. In tissue, the interplay between faulty Ca(2+) influx and steep action potential duration restitution causes arrhythmogenic discordant alternans. The prolongation of action potentials causes spatial dispersion of the Na(+) channel excitability, leading to inhomogeneous conduction velocity and large action potential spatial gradients. Our model simulations are consistent with the ECG patterns from TS patients, which suggest that the TS mutation is sufficient to cause the clinical phenotype and allows for the revelation of the complex interactions of currents underlying it.

Nonextensivity and the power-law distributions for the systems with self-gravitating long-range interactions

By a natural nonextensive generalization of the conservation of energy in the q-kinetic theory, we study the nonextensivity and the power-law distributions for the many-body systems with the self-gravitating long-range interactions. It is shown that the power-law distributions describe the long-range nature of the interactions and the non-local correlations within the self-gravitating system with the inhomogeneous velocity dispersion. A relation is established between the nonextensive parameter q and the measurable quantities of the self-gravitating system: the velocity dispersion and the mass density. Correspondingly, the nonextensive parameter q can be uniquely determined from the microscopic dynamical equation and thus the physical interpretation of q different from unity can be clearly presented. We derive a nonlinear differential equation for the radial density dependence of the self-gravitating system with the inhomogeneous velocity dispersion, which can correctly describe the density distribution for the dark matter in the above physical situation. We also apply this q-kinetic approach to analyze the nonextensivity of self-gravitating collisionless systems and self-gravitating gaseous dynamical systems, giving the power-law distributions the clear physical meaning.

Seismic modeling of gas chimneys

We propose a simple acoustic model explaining the main features of gas chimneys. The main elements of the model consist of gas diffusing from a connected fracture network and into the surrounding shale creating an inhomogeneous gas saturation. The gas saturation results in an inhomogeneous fluctuating compressional velocity field that distorts seismic waves. We model the fracture network by a random-walk process constrained by maximum fracture length and angle of the fracture with respect to the vertical. The gas saturation is computed from a simple analytical solution of the diffusion equation, and pressure-wave velocities are locally obtained assuming that mixing of shale and gas occurs on a scale much smaller than seismic wavelengths. Synthetic seismic sections are then computed using the resulting inhomogeneous velocity model and shown to give rise to similar deterioration in data quality as that found in data from real gas chimneys. Also, synthetic common-midpoint (CMP) gathers show the same distorted and attenuated traveltime curves as those obtained from a real data set. The model shows clearly that the features of gas chimneys change with geological time (a model parameter in our approach), the deterioration of seismic waves being smallest just after the creation of the gas chimney. It seems likely that at least some of the features of gas chimneys can be explained by a simple elastic model in combination with gas diffusion from a fracture network.

Optical Magnus effect in metamaterials fabricated from ferromagnetic microwires

In homogeneous negative phase velocity media, the Doppler and Cherenkov-Vavilov effects and the refraction and pressure of light are anomalous: they are inverse with respect to the corresponding effects in conventional media. Using the geometrical optics approximation, it is shown that the optical Magnus effect in inhomogeneous negative phase velocity media is also anomalous. The effect is demonstrated by considering a metamaterial consisting of parallel amorphous ferromagnetic microwires in a magnetic field. The metamaterial proves to be a left-handed one in the realistic region of the electromagnetic spectrum. The optical properties of such a left-handed medium can be controlled by the external magnetic field.

Uncertainties in indentation testing of articular cartilage: A fibril-reinforced poroviscoelastic study

Indentation testing provides a quantitative technique to evaluate mechanical characteristics of articular cartilage in situ and in vivo. Traditionally, analytical solutions proposed by Hayes et al. [Hayes WC, Keer LM, Herrmann G, Mockros LF. A mathematical analysis for indentation tests of articular cartilage. J Biomech 1972;5(5):541–51] have been applied for the analysis of indentation measurements, and due to their practicality, they have been used for clinical diagnostics. Using this approach, the elastic modulus is derived based on scaling factors which depend on cartilage thickness, indenter radius and Poisson's ratio, and the cartilage model is assumed isotropic and homogeneous, thereby greatly simplifying the true tissue characteristics. The aim was to investigate the validity of previous model assumptions for indentation testing. Fibril-reinforced poroviscoelastic cartilage (FRPVE) model including realistic tissue characteristics was used to simulate indentation tests. The effects of cartilage inhomogeneity, anisotropy, and indentation velocity on the indentation response were evaluated, and scaling factors from the FRPVE analysis were derived. Subsequently, the validity of scaling factors obtained using the traditional and the FRPVE analyses was studied by calculating indentation moduli for bovine cartilage samples, and comparing these values to those obtained experimentally in unconfined compression testing. Collagen architecture and compression velocity had significant effects on the indentation response. Isotropic elastic analysis gave significantly higher (30–107%) Young's moduli for indentation compared to unconfined compression testing. Modification of Hayes’ scaling factors by accounting for cartilage inhomogeneity and anisotropy improved the agreement of Young's moduli obtained for the two test configurations by 14–28%. These results emphasize the importance of realistic cartilage structure and mechanical properties in the indentation analysis. Although it is not possible to fully describe tissue inhomogeneity and anisotropy with just the Young's modulus and Poisson's ratio, accounting for inhomogeneity and anisotropy in these two parameters may help to improve the in vivo characterization of tissue using arthroscopic indentation testing.

The study and analysis of floating datum selection for rugged terrain

We analyze the characteristics of different floating datums for static corrections and discuss the methods for determining them. The effect of different floating datum corrections was studied using theoretical model experiments, resulting in the conclusion that the velocity obtained after the floating datum correction with the minimum static correction errors depends on the velocity of the layer below the low velocity layer (LVL) lower boundary and is not related to topographic relief and LVL structure. For the real data processing case, wave equation numerical model experiments were conducted which resulted in a new method for calculating objective functions based on the waveform and modifications to the calculation equation for minimum static correction errors to make the method suitable for real data static correction processing using inhomogeneous velocity models with lower velocity boundary relief. Real data processing results demonstrate the method’s superiority.

Results of theoretical and experimental studies of solar wind and active galactic nuclei on LFVN VLBI network using S2 recording system

We discuss the results of two sessions of observations at the Low-Frequency VLBI Network (LFVN), carried out in 1999 (INTAS99.4) and 2000 (INTAS00.3) at a wavelength of 18 cm using the S2 recording system and processed using the correlator system in Pentictone, Canada. In different configurations of the experiments on studying the solar wind and active galactic nuclei, the antennas at the following sites were employed: Medvezhji Ozera (RT-64, Special Engineering Bureau of Moscow Power Engineering Institute, Russia), Pushchino (RT-22, Pushchino Radio Astronomy Observatory, Russia), Hartebeesthoek (RT-25, South Africa), Noto (RT-32, Italy), Shanghai (RT-25, China), Pune (RT-45, India), Svetloe (RT-32, Institute of Applied Astronomy RAS, Russia). The work resulted in successful testing of the method of radio probing of the solar-wind plasma by radiation of extragalactic sources, supplemented with the method of radio interferometric reception. Spectral analysis of the obtained data allowed us to estimate the index of spatial spectrum of the electron number density.uctuations and the transfer velocity of the solar-wind inhomogeneities on the sounding path. We present and discuss the retrieved images of STA-102 quasar and the BL Lacertae object 1418+546 with millisecond angular resolution and demonstrate the results of modeling the structure of these sources.