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Journal articles on the topic 'Behaviour isotropy'
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1
Kim, J., and R. A. Antonia. "Isotropy of the small scales of turbulence at low Reynolds number." Journal of Fluid Mechanics 251 (June 1993): 219–38. http://dx.doi.org/10.1017/s0022112093003398.
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Spectral local isotropy tests are applied to direct numerical simulation data, mainly at the centreline of a fully developed turbulent channel flow. Despite the small Reynolds number of the simulation, the high-wavenumber behaviour of velocity and vorticity spectra is consistent with local isotropy. This consistency is verified by the relationship between streamwise wavenumber spectra and spanwise wavenumber spectra. The high-wavenumber behaviour of the pressure spectrum is also consistent with local isotropy and compares favourably with the calculation of Batchelor (1951), which assumes isotropy and joint normality of the velocity field at two points in space. The latter assumption is validated by the shape but not the magnitude of the quadruple correlation of the streamwise velocity fluctuation at small separations. There is only partial support for local spectral isotropy away from the centreline as the magnitude of the mean strain rate increases.
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SHAFI, H. S., and R. A. ANTONIA. "Small-scale characteristics of a turbulent boundary layer over a rough wall." Journal of Fluid Mechanics 342 (July 10, 1997): 263–93. http://dx.doi.org/10.1017/s0022112097005612.
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Measurements of the spanwise and wall-normal components of vorticity and their constituent velocity derivative fluctuations have been made in a turbulent boundary layer over a mesh-screen rough wall using a four-hot-wire vorticity probe. The measured spectra and variances of vorticity and velocity derivatives have been corrected for the effect of spatial resolution. The high-wavenumber behaviour of the spectra conforms closely with isotropy. Over most of the outer layer, the normalized magnitudes of the velocity derivative variances differ significantly from those over a smooth wall layer. The differences are such that the variances are much more nearly isotropic over the rough wall than on the smooth wall. This behaviour is consistent with earlier observations that the large-scale structure in this rough wall layer is more isotropic than that in a smooth wall layer. Isotropy-based approximations for the mean energy dissipation rate and mean enstrophy are consequently more reliable in this rough wall layer than in a smooth wall layer. In the outer layer, the vorticity variances are slightly larger than those over a smooth wall; reflecting structural differences between the two flows.
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Gautam, Rajeeb, and Ron CK Wong. "Transversely isotropic stiffness parameters and their measurement in Colorado shale." Canadian Geotechnical Journal 43, no. 12 (December 1, 2006): 1290–305. http://dx.doi.org/10.1139/t06-083.
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Drained stress path triaxial tests and confined torsion tests were conducted on Colorado shale core samples to investigate transversely isotropic stiffness parameters at small strain deformation. Nonlinear plastic behaviour occurred along the primary loading path even at strains less than 0.01%. Nonlinear, hysteric behaviour was only observed during the loading–unloading path. However, the shale material displayed transverse isotropy in deformation, and very small or nondetectable Poisson's ratios in vertical and horizontal directions. This special response alludes to the postulate that the Colorado shale could be approximated by a transversely isotropic elasticity model at small strain levels with negligible yielding.Key words: anisotropy, elasticity, stiffness, triaxial test, torsion test, shale.
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CHOI, KWING-SO, and JOHN L. LUMLEY. "The return to isotropy of homogeneous turbulence." Journal of Fluid Mechanics 436 (June 10, 2001): 59–84. http://dx.doi.org/10.1017/s002211200100386x.
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Three types of homogeneous anisotropic turbulence were produced by the plane distortion, axisymmetric expansion and axisymmetric contraction of grid-generated turbulence, and their behaviour in returning to isotropy was experimentally studied using hot-wire anemometry. It was found that the turbulence trajectory after the plane distortion was highly nonlinear, and did not follow Rotta's linear model in returning to isotropy. The turbulence wanted to become axisymmetric even more than it wanted to return to isotropy. In order to show the rate of return to isotropy of homogeneous turbulence, a map of the ratio of the characteristic time scale for the decay of turbulent kinetic energy to that of the return to isotropy was constructed. This demonstrated that the rate of return to isotropy was much lower for turbulence with a greater third invariant of the anisotropy tensor. The invariant technique was then applied to the experimental results to develop a new turbulence model for the return-to-isotropy term in the Reynolds stress equation which satisfied the realizability conditions. The effect of the Reynolds number on the rate of return to isotropy was also investigated and the results incorporated in the proposed model.
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ANTONIA, R. A., T. ZHOU, and Y. ZHU. "Three-component vorticity measurements in a turbulent grid flow." Journal of Fluid Mechanics 374 (November 10, 1998): 29–57. http://dx.doi.org/10.1017/s0022112098002547.
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All components of the fluctuating vorticity vector have been measured in decaying grid turbulence using a vorticity probe of relatively simple geometry (four X-probes, i.e. a total of eight hot wires). The data indicate that local isotropy is more closely satisfied than global isotropy, the r.m.s. vorticities being more nearly equal than the r.m.s. velocities. Two checks indicate that the performance of the probe is satisfactory. Firstly, the fully measured mean energy dissipation rate 〈ε〉 is in good agreement with the value inferred from the rate of decay of the mean turbulent energy 〈q2〉 in the quasi-homogeneous region; the isotropic mean energy dissipation rate 〈εiso〉 agrees closely with this value even though individual elements of 〈ε〉 indicate departures from isotropy. Secondly, the measured decay rate of the mean-square vorticity 〈ω2〉 is consistent with that of 〈q2〉 and in reasonable agreement with the isotropic form of the transport equation for 〈ω2〉. Although 〈ε〉≃〈εiso〉, there are discernible differences between the statistics of ε and εiso; in particular, εiso is poorly correlated with either ε or ω2. The behaviour of velocity increments has been examined over a narrow range of separations for which the third-order longitudinal velocity structure function is approximately linear. In this range, transverse velocity increments show larger departures than longitudinal increments from predictions of Kolmogorov (1941). The data indicate that this discrepancy is only partly associated with differences between statistics of locally averaged ε and ω2, the latter remaining more intermittent than the former across this range. It is more likely caused by a departure from isotropy due to the small value of Rλ, the Taylor microscale Reynolds number, in this experiment.
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Svendsen, Bob, and Kolumban Hutter. "A continuum approach for modelling induced anisotropy in glaciers and ice sheets." Annals of Glaciology 23 (1996): 262–69. http://dx.doi.org/10.3189/s0260305500013525.
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This paper presents a formulation of a continuum model for so-called (stress or deformation) induced anisotropy in natural ice which, unlike computer-based Taylor-type models, can be incorporated in numerical simulations of large ice masses to account for the effects of this process on the flow of these bodies in a physical fashion. To do this, we treat natural ice as a rigid-elastic, non-linear inelastic material which can develop transverse isotropic behaviour (accounting for the simplest kind of induced anisotropy in natural ice masses), where the degree of such anisotropy at each point is controlled by the distribution of crystal glide-plane orientations there. This distribution is described by a so-called orientation-distribution function, for which an evolution relation can be derived. The central constitutive assumption of this formulation relates this distribution to the “structure” tensor representing the transverse isotropy of the material. On the basis of this relation, the model predicts in particular isotropic (e.g. classical Glen’s flow-law type) behaviour at a given point when the distribution of crystal glide-plane orientations is uniform there.
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KANG, HYUNG SUK, and CHARLES MENEVEAU. "Passive scalar anisotropy in a heated turbulent wake: new observations and implications for large-eddy simulations." Journal of Fluid Mechanics 442 (August 24, 2001): 161–70. http://dx.doi.org/10.1017/s0022112001005225.
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The effects of passive scalar anisotropy on subgrid-scale (SGS) physics and modelling for large-eddy simulations are studied experimentally. Measurements are performed across a moderate Reynolds number wake flow generated by a heated cylinder, using an array of four X-wire and four cold-wire probes. By varying the separation distance among probes in the array, we obtain filtered and subgrid quantities at three different filter sizes. We compute several terms that comprise the subgrid dissipation tensor of kinetic energy and scalar variance and test for isotropic behaviour, as a function of filter scale. We find that whereas the kinetic energy dissipation tensor tends towards isotropy at small scales, the SGS scalar-variance dissipation remains anisotropic independent of filter scale. The eddy-diffusion model predicts isotropic behaviour, whereas the nonlinear (or tensor eddy diffusivity) model reproduces the correct trends, but overestimates the level of scalar dissipation anisotropy. These results provide some support for so-called mixed models but raise new questions about the causes of the observed anisotropy.
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Svendsen, Bob, and Kolumban Hutter. "A continuum approach for modelling induced anisotropy in glaciers and ice sheets." Annals of Glaciology 23 (1996): 262–69. http://dx.doi.org/10.1017/s0260305500013525.
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This paper presents a formulation of a continuum model for so-called (stress or deformation) induced anisotropy in natural ice which, unlike computer-based Taylor-type models, can be incorporated in numerical simulations of large ice masses to account for the effects of this process on the flow of these bodies in a physical fashion. To do this, we treat natural ice as a rigid-elastic, non-linear inelastic material which can develop transverse isotropic behaviour (accounting for the simplest kind of induced anisotropy in natural ice masses), where the degree of such anisotropy at each point is controlled by the distribution of crystal glide-plane orientations there. This distribution is described by a so-called orientation-distribution function, for which an evolution relation can be derived. The central constitutive assumption of this formulation relates this distribution to the “structure” tensor representing the transverse isotropy of the material. On the basis of this relation, the model predicts in particular isotropic (e.g. classical Glen’s flow-law type) behaviour at a given point when the distribution of crystal glide-plane orientations is uniform there.
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Jiménez-Morales, F., and J. J. Luque. "Collective behaviour in a cellular automaton and isotropy of the neighbourhood." Physica A: Statistical Mechanics and its Applications 212, no. 1-2 (December 1994): 118–22. http://dx.doi.org/10.1016/0378-4371(94)90141-4.
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Wandrol, Ivo, Karel Frydrýšek, and Daniel Čepica. "Analysis of the Influence of Thermal Loading on the Behaviour of the Earth’s Crust." Applied Sciences 13, no. 7 (March 29, 2023): 4367. http://dx.doi.org/10.3390/app13074367.
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The article focuses on the deformation and strain-stress analysis of the Earth’s crust under external thermal loading. More specifically, the influence of cyclic changes in the surface temperature field on the stress and displacement inside the crust over a two-year time span is investigated. The finite element program MSC.Marc Mentat was used to calculate the stresses and displacements. For practical analysis reasons, the Earth’s crust is simplified as a planar, piecewise homogeneous, isotropic model (plane strain), and time-varying temperature functions of illumination (thermal radiation) from the Sun are considered in the local isotropy sections of the model. Interaction between the Earth’s crust and mantle is defined by the Winkler elastic foundation. By applying a probabilistic approach (Monte Carlo Method), a new stochastic model of displacements and stresses and new information on crustal displacements relative to the Earth’s mantle were obtained. The results proved the heating influence of the Sun on the Earth’s crust and plate tectonics.
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Shokrieh, M. M., and M. Safarabadi. "Effect of fibre transverse isotropy on micro-residual stresses in polymeric composites." Journal of Strain Analysis for Engineering Design 46, no. 8 (August 13, 2011): 817–24. http://dx.doi.org/10.1177/0309324711416184.
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In this paper, the influence of transversely isotropic behaviour of the fibre on micro-residual stress fields is investigated. For this purpose, the energy method is utilized to predict the micro-structural stresses in polymer matrix composites under uniform thermal loads. The representative volume element (RVE) considered here includes a transversely isotropic fibre embedded in an isotropic polymer matrix. Based on the energy method, a three-dimensional closed-form solution for micro-residual stresses is obtained. The analytical results are evaluated with a finite element solution. The analysis shows that the transversely isotropic behaviour of the fibre greatly increases the fibre and matrix axial residual stresses in comparison with the isotropic fibre assumption. Fibre anisotropy has a significant effect on the interfacial shear stress distribution, in contrast with the interfacial radial stress field. Both the finite element solution and analytical method result in a similar behaviour for micro-residual stresses distribution along the fibre length. However, the finite element method cannot satisfy the stress-free condition for the residual shear stress at the fibre end due to the stress singularity.
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Negussey, D., and Y. P. Vaid. "Sand deformation under proportional loading." Canadian Geotechnical Journal 23, no. 2 (May 1, 1986): 155–63. http://dx.doi.org/10.1139/t86-025.
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A fundamental experimental study of sand behaviour under low stress ratio proportional loading wherein all strain components are contractant is presented. Experimentally observed behaviour under stress conditions of the triaxial test led to a coherent framework for representing proportional loading stress–strain response. The stress–strain relationship formulated incorporates relative density as an inherent independent state variable and does not require appeal to material isotropy. Key words: triaxial test, proportional loading, sand, relative density, energy density, stress increment, strain increment.
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Antonia, R. A., Y. Zhu, and H. S. Shafi. "Lateral vorticity measurements in a turbulent wake." Journal of Fluid Mechanics 323 (September 25, 1996): 173–200. http://dx.doi.org/10.1017/s0022112096000882.
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The accurate measurement of vorticity has proven difficult because of the difficulty of estimating spatial derivatives of velocity fluctuations reliably. A method is proposed for correcting the lateral vorticity spectrum measured using a four-wire probe. The attenuation of the measured spectrum increases as the wavenumber increases but does not vanish when the wavenumber is zero. Although the correction procedure assumes local isotropy, the major contributor to the high-wavenumber part of the vorticity spectrum is the streamwise derivative of the lateral velocity fluctuation, and the correction of this latter quantity does not depend on local isotropy. Satisfactory support for local isotropy is provided by the high-wavenumber parts of the velocity, velocity derivative and vorticity spectra measured on the centreline of a turbulent wake. Second- and fourth-order moments of vorticity show departures from local isotropy but the degree of departure seems unaffected by the turbulence Reynolds number Rλ. The vorticity probability density function is approximately exponential and has tails which stretch out to larger amplitudes as Rλ increases. The vorticity flatness factor, which is appreciably larger than the flatness factor of the streamwise velocity derivative, also increases with Rλ. When Rλ is sufficiently large for velocity structure functions to indicate a r2/3 inertial range, two-point longitudinal correlations of lateral vorticity fluctuations give encouraging support for the theoretical r−4/3 behaviour.
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NOKHODKAR, A. H. "APPLICATIONS OF SYSTEMS OF QUADRATIC FORMS TO GENERALISED QUADRATIC FORMS." Bulletin of the Australian Mathematical Society 102, no. 3 (February 13, 2020): 374–86. http://dx.doi.org/10.1017/s0004972720000106.
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A system of quadratic forms is associated to every generalised quadratic form over a division algebra with involution of the first kind in characteristic two. It is shown that this system determines the isotropy behaviour and the isometry class of generalised quadratic forms. An application of this construction to the Witt index of generalised quadratic forms is also given.
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Antonia, R. A., L. W. B. Browne, and D. A. Shah. "Characteristics of vorticity fluctuations in a turbulent wake." Journal of Fluid Mechanics 189 (April 1988): 349–65. http://dx.doi.org/10.1017/s0022112088001053.
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Measurements of the lateral components of the vorticity fluctuation have been made in the self-preserving turbulent wake of a circular cylinder. Each component was obtained separately using two X-wires separated in the appropriate lateral directions. The two velocity derivatives which make up the streamwise vorticity component were also determined but not simultaneously. An approximation to the streamwise vorticity was made from these measurements. Moments, probability density functions and spectra of the three vorticity components across the wake are presented and discussed. The high-wavenumber behaviour of the spectra is compared with calculations, based on local isotropy. Satisfactory agreement with the calculations is obtained for the lateral vorticity components over a significant high-wavenumber range. The approximated streamwise vorticity spectrum tends towards the isotropic calculation at very large wavenumbers.
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Vanderbauwhede, A. "Hopf bifurcation for equivariant conservative and time-reversible systems." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 116, no. 1-2 (1990): 103–28. http://dx.doi.org/10.1017/s0308210500031401.
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SynopsisWe study the bifurcation of small periodic solutions at a non-semi-simple 1:1-resonance in equivariant conservative or equivariant time-reversible systems. By using an equivariant Liapunov-Schmidt method and restricting to solutions with an appropriate isotropy, we reduce the problem to a scalar bifurcation equation. The analysis of this equation shows a bifurcation behaviour similar to that found for the Hamiltonian Hopf bifurcation.
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Antonia, R. A., and J. Mi. "Temperature dissipation in a turbulent round jet." Journal of Fluid Mechanics 250 (May 1993): 531–51. http://dx.doi.org/10.1017/s0022112093001557.
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Parallel cold wires were used to measure the temperature derivative, in each of the three spatial directions, in the self-preserving region of a turbulent round jet. The temperature derivative variances were inferred from the correlation method and from the temperature derivative spectra after correcting these for the effect of wire separation. Both methods yielded fully consistent results for the components of the average temperature dissipation: the radial and azimuthal values are nearly equal and only slightly larger than the axial component. The resulting departure from isotropy of the temperature dissipation is small, especially when compared with results in other free shear flows. The high-wavenumber behaviour of the corrected temperature derivative spectra conforms closely with isotropy on the jet axis but small departures occur away from the axis. Conditional averages, based on spatially coherent temperature jumps, indicate that, while the organized motion makes a significant contribution to the temperature variance, its contribution to the temperature-derivative variances is small.
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Sivathayalan, S., and Y. P. Vaid. "Truly undrained response of granular soils with no membrane-penetration effects." Canadian Geotechnical Journal 35, no. 5 (October 1, 1998): 730–39. http://dx.doi.org/10.1139/t98-048.
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Conventional and truly undrained behaviour of granular soils is compared by direct experimental measurements. The truly undrained behaviour was determined by compensation for membrane penetration induced volume changes, using a feedback controlled water injection system. A more reliable, nondestructive, specimen-specific method is presented to measure the magnitude of membrane penetration, for use in the injection routine. This new method, unlike the existing methods, does not make any assumptions regarding either the constitutive behaviour or isotropy of sands. It is shown that the truly undrained pore pressures predicted by correcting those observed in conventional undrained tests are too large, implying incorrect linkage between membrane penetration induced volume change and volumetric constitutive behaviour of the granular material. The sand which responds in a strain-hardening manner in conventional undrained loading may, in fact, be strain softening (liquefiable) when truly undrained, a matter of serious practical concern.Key words: sand, truly undrained behaviour, liquefaction, membrane penetration.
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Spurzem, R. "On Gravothermal Instability of Anisotropic Self-Gravitating Gas Spheres: Singular Equilibrium Solution." International Astronomical Union Colloquium 132 (1993): 241–53. http://dx.doi.org/10.1017/s0252921100066136.
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AbstractA reinvestigation of the linear perturbation theory is presented, which examines the hydrostatic readjustment of an isolated self-gravitating gas sphere to a redistribution of energy. The here presented model describes a stellar system by the common equations of gas in hydrostatic equilibrium but with the effect of the anisotropic velocity distribution on the pressure gradient. We take as equilibrium models the singular isothermal solution with and without anisotropy. The total variation of the Boltzmann entropy resulting from a perturbation of the system caused by a redistribution of heat (i.e. r.m.s. kinetic energy of the stars) is calculated for anisotropic solutions to first order as well as to second order for the isotropic equilibrium. The extremized eigenfunctions which represent the entropy and anisotropy perturbation functions, are determined analytically. They exhibit gravothermal behaviour in the central region where heat is removed. It is also found that the anisotropy readjusts non-thermally in the sense that the system departs from isotropy although the total entropy increases.
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Escobedo, Miguel, Stephane Mischler, and Manuel A. Valle. "Homogeneous Boltzmann equation in quantum relativistic kinetic theory." Electronic Journal of Differential Equations 1, Mon. 01-09 (January 20, 2003): 04. http://dx.doi.org/10.58997/ejde.mon.04.
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We consider some mathematical questions about Boltzmann equations for quantum particles, relativistic or non relativistic. Relevant particular cases such as Bose, Bose-Fermi, and photon-electron gases are studied. We also consider some simplifications such as the isotropy of the distribution functions and the asymptotic limits (systems where one of the species is at equilibrium). This gives rise to interesting mathematical questions from a physical point of view. New results are presented about the existence and long time behaviour of the solutions to some of these problems.
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CERUTTI, STEFANO, CHARLES MENEVEAU, and OMAR M. KNIO. "Spectral and hyper eddy viscosity in high-Reynolds-number turbulence." Journal of Fluid Mechanics 421 (October 25, 2000): 307–38. http://dx.doi.org/10.1017/s0022112000001671.
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For the purpose of studying the spectral properties of energy transfer between large and small scales in high-Reynolds-number turbulence, we measure the longitudinal subgrid-scale (SGS) dissipation spectrum, defined as the co-spectrum of the SGS stress and filtered strain-rate tensors. An array of four closely spaced X-wire probes enables us to approximate a two-dimensional box filter by averaging over different probe locations (cross-stream filtering) and in time (streamwise filtering using Taylor's hypothesis). We analyse data taken at the centreline of a cylinder wake at Reynolds numbers up to Rλ ∼ 450. Using the assumption of local isotropy, the longitudinal SGS stress and filtered strain-rate co-spectrum is transformed into a radial co-spectrum, which allows us to evaluate the spectral eddy viscosity, v(k, kΔ). In agreement with classical two-point closure predictions, for graded filters, the spectral eddy viscosity deduced from the box-filtered data decreases near the filter wavenumber kΔ. When using a spectral cutoff filter in the streamwise direction (with a box-filter in the cross-stream direction) a cusp behaviour near the filter scale is observed. In physical space, certain features of a wavenumber-dependent eddy viscosity can be approximated by a combination of a regular and a hyper-viscosity term. A hyper-viscous term is also suggested from considering equilibrium between production and SGS dissipation of resolved enstrophy. Assuming local isotropy, the dimensionless coefficient of the hyper-viscous term can be related to the skewness coefficient of filtered velocity gradients. The skewness is measured from the X-wire array and from direct numerical simulation of isotropic turbulence. The results show that the hyper-viscosity coefficient is negative for graded filters and positive for spectral filters. These trends are in agreement with the spectral eddy viscosity measured directly from the SGS stress–strain rate co-spectrum. The results provide significant support, now at high Reynolds numbers, for the ability of classical two-point closures to predict general trends of mean energy transfer in locally isotropic turbulence.
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Pavan, P. G., P. Pachera, C. Stecco, and A. N. Natali. "Constitutive Modeling of Time-Dependent Response of Human Plantar Aponeurosis." Computational and Mathematical Methods in Medicine 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/530242.
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The attention is focused on the viscoelastic behavior of human plantar aponeurosis tissue. At this purpose, stress relaxation tests were developed on samples taken from the plantar aponeurosis of frozen adult donors with age ranging from 67 to 78 years, imposing three levels of strain in the physiological range (4%, 6%, and 8%) and observing stress decay for 240 s. A viscohyperelastic fiber-reinforced constitutive model with transverse isotropy was assumed to describe the time-dependent behavior of the aponeurotic tissue. This model is consistent with the structural conformation of the tissue where collagen fibers are mainly aligned with the proximal-distal direction. Constitutive model fitting to experimental data was made by implementing a stochastic-deterministic procedure. The stress relaxation was found close to 40%, independently of the level of strain applied. The agreement between experimental data and numerical results confirms the suitability of the constitutive model to describe the viscoelastic behaviour of the plantar aponeurosis.
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Cohn, Daniel, Hani Younes, Eli Milgarter, and Gideon Uretzky. "Mechanical behaviour of isolated pericardium: species, isotropy, strain rate and collagenase effect on pericardial tissue." Clinical Materials 2, no. 2 (January 1987): 115–24. http://dx.doi.org/10.1016/0267-6605(87)90030-8.
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Yang, Kun, Lihao Zhao, and Helge I. Andersson. "Mean shear versus orientation isotropy: effects on inertialess spheroids’ rotation mode in wall turbulence." Journal of Fluid Mechanics 844 (April 12, 2018): 796–816. http://dx.doi.org/10.1017/jfm.2018.205.
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The orientation of spheroidal particles dispersed in a fluid flow is known to influence the particles’ rotation mode. Rod-like and disk-like particles orient themselves differently and accordingly also rotate differently. In order to explore the role of the deterministic factors, i.e. mean shear and vorticity anisotropy, on the orientational behaviour of inertialess tracer spheroids, we adopted a purpose-made Couette–Poiseuille flow simulated numerically by Yang et al. (Intl J. Heat Fluid Flow, vol. 63, 2017, pp. 14–27). Typical wall turbulence with streamwise-oriented streaky structures caused by the locally high mean shear rate was observed only at one of the walls. The absence of mean shear at the other wall gave rise to an atypical turbulence field. Over a relatively wide and quasi-homogeneous core region, a modest mean shear rate made the vorticity field anisotropic. In spite of the mean shear, rod-like tracers were spinning and disk-like spheroids were tumbling, just as in homogeneous isotropic turbulence. We explained this phenomenon by the isotropic particle orientation and concluded that zero mean shear is not necessary for rod spinning and disk tumbling. The orientation and rotation of the Lagrangian tracer spheroids near the high shear wall were almost indistinguishable from the well-known behaviour in turbulent channel flows. Near the opposite wall, where the mean shear was negligibly small, disk-like particles aligned preferentially in the wall-normal direction and rotated similarly as in the presence of high shear. Rod-like particles, on the contrary, aligned more randomly and accordingly rotated similarly as in the core region. These observations revealed that the degree of particle orientation anisotropy has a major impact on the particle rotation mode, whereas mean shear, irrespective of the actual shear rate, only plays a secondary role in particle rotation. Deduction of the eigenvectors of the left Cauchy–Green tensor showed that the preferential orientation of the tracer spheroids was caused by the alignment of rods and disks with the strongest Lagrangian stretching and compression directions, respectively. Lagrangian stretching/compression determines the particle orientations and the particle orientation affects the particle rotation mode.
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Gennaro, V. De, J. Canou, J. C. Dupla, and N. Benahmed. "Influence of loading path on the undrained behaviour of a medium loose sand." Canadian Geotechnical Journal 41, no. 1 (February 1, 2004): 166–80. http://dx.doi.org/10.1139/t03-082.
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The results of an experimental programme aimed at studying the undrained behaviour of Hostun sand are presented in this paper. Specific conditions concerning the initial relative density (medium loose arrangements) and the loading paths (compression and extension under monotonic and cyclic loadings) were considered in the test programme. Monotonic tests carried out in both drained and undrained conditions show a significant difference in behaviour between compression and extension. It is observed that, in undrained conditions, Hostun sand is weaker in extension than in compression. In compression, the material is stable (dilatant) and the phase-transformation state controls the mechanical behaviour. In extension, the experimental results show an unstable behaviour (contractant), with monotonic, liquefaction-induced instability in undrained conditions. The results of cyclic tests, carried out with one- and two-way stress reversals, show a good correlation with the results of monotonic tests. The loading path strongly influences the undrained mechanical behaviour of the sand, mainly by inducing liquefaction in extension. This situation suggests that differences in soil fabric, caused by the sample preparation technique (air pluviation), can influence the sand behaviour by inducing a significant contraction in extension. By further analysing the cyclic results, it is shown that, during unloading, the stress paths reflect the transverse isotropy (orthotropy) of the sand, with stiffer elastic characteristics in the vertical direction than in the horizontal direction.Key words: liquefaction, cyclic mobility, sands, triaxial test, anisotropy, loading path.
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Vašata, Daniel. "On long-range dependence of random measures." Advances in Applied Probability 48, no. 4 (December 2016): 1235–55. http://dx.doi.org/10.1017/apr.2016.72.
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AbstractThis paper deals with long-range dependence of random measures on ℝd. By examples, it is demonstrated that one must be careful in order to define it consistently. Therefore, we define long-range dependence by a rather specific second-order condition and provide an equivalent formulation involving the asymptotic behaviour of the Bartlett spectrum near the origin. Then it is shown that the defining condition may be formulated less strictly when the additional isotropy assumption holds. Finally, we present an example of a long-range dependent random measure based on the 0-level excursion set of a Gaussian random field for which the corresponding spectral density and its asymptotics are explicitly derived.
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Brassel, B. P., S. D. Maharaj, and G. Govender. "Analytical Models for Gravitating Radiating Systems." Advances in Mathematical Physics 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/274251.
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We analyse the gravitational behaviour of a relativistic heat conducting fluid in a shear-free spherically symmetric spacetime. We show that the isotropy of pressure is a consistency condition which realises a second order nonlinear ordinary differential equation with variable coefficients in the gravitational potentials. Several new classes of solutions are found to the governing equation by imposing various forms on one of the potentials. Interestingly, a complex transformation leads to an exact solution with only real metric functions. All solutions are written in terms of elementary functions. We demonstrate graphically that the fluid pressure, energy density, and heat flux are well behaved for the model, and the model is consistent with a core-envelope framework.
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Ruskov, Rusko, Joshua Combes, Klaus Mølmer, and Howard M. Wiseman. "Qubit purification speed-up for three complementary continuous measurements." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1979 (November 28, 2012): 5291–307. http://dx.doi.org/10.1098/rsta.2011.0516.
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We consider qubit purification under simultaneous continuous measurement of the three non-commuting qubit operators , , . The purification dynamics is quantified by (i) the average purification rate and (ii) the mean time of reaching a given level of purity, 1− ε . Under ideal measurements (detector efficiency η =1), we show in the first case an asymptotic mean purification speed-up of 4 when compared with a standard (classical) single-detector measurement. However, by the second measure—the mean time of first passage of the purity—the corresponding speed-up is only 2. We explain these speed-ups using the isotropy of the qubit evolution that provides an equivalence between the original measurement directions and three simultaneous measurements, one with an axis aligned along the Bloch vector and the other with axes in the two complementary directions. For inefficient detectors, η =1− δ <1, the mean time of first passage increases because qubit purification competes with an isotropic qubit dephasing. In the asymptotic high-purity limit ( ε , δ ≪1), we show that the increase possesses a scaling behaviour : is a function only of the ratio δ / ε . The increase is linear for small arguments, but becomes exponential for δ / ε large.
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Rabey, P. K., A. Wynn, and O. R. H. Buxton. "The kinematics of the reduced velocity gradient tensor in a fully developed turbulent free shear flow." Journal of Fluid Mechanics 767 (February 20, 2015): 627–58. http://dx.doi.org/10.1017/jfm.2015.60.
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AbstractThis paper examines the kinematic behaviour of the reduced velocity gradient tensor (VGT),$\tilde{\unicode[STIX]{x1D608}}_{ij}$, which is defined as a$2\times 2$block, from a single interrogation plane, of the full VGT$\unicode[STIX]{x1D608}_{ij}=\partial u_{i}/\partial x_{j}$. Direct numerical simulation data from the fully developed turbulent region of a nominally two-dimensional mixing layer are used in order to examine the extent to which information on the full VGT can be derived from the reduced VGT. It is shown that the reduced VGT is able to reveal significantly more information about regions of the flow in which strain rate is dominant over rotation. It is thus possible to use the assumptions of homogeneity and isotropy to place bounds on the first two statistical moments (and their covariance) of the eigenvalues of the reduced strain-rate tensor (the symmetric part of the reduced VGT) which in turn relate to the turbulent strain rates. These bounds are shown to be dependent upon the kurtosis of$\partial u_{1}/\partial x_{1}$and another variable defined from the constituents of the reduced VGT. The kurtosis is observed to be minimised on the centreline of the mixing layer and thus tighter bounds are possible at the centre of the mixing layer than at the periphery. Nevertheless, these bounds are observed to hold for the entirety of the mixing layer, despite departures from local isotropy. The interrogation plane from which the reduced VGT is formed is observed not to affect the joint probability density functions (p.d.f.s) between the strain-rate eigenvalues and the reduced strain-rate eigenvalues despite the fact that this shear flow has a significant mean shear in the cross-stream direction. Further, it is found that the projection of the eigenframe of the strain-rate tensor onto the interrogation plane of the reduced VGT is also independent of the plane that is chosen, validating the approach of bounding the full VGT using the assumption of local isotropy.
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Coscarella, F., N. Penna, S. Servidio, and R. Gaudio. "An experimental study on the anisotropic and intermittent behaviour of a turbulent flow over a rough bed." Journal of Physics: Conference Series 2293, no. 1 (June 1, 2022): 012001. http://dx.doi.org/10.1088/1742-6596/2293/1/012001.
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Abstract The flow field in open channels can be classified into different zones according to the velocity distribution. To explore the anisotropic and intermittent behaviour in the turbulent flow layers, an experimental study was performed using Particle Image Velocimetry (PIV) measurements in a hydraulic flume with rough bed. Specifically, the analysis has been focused on the two-dimensional (2D) high-order structure functions applied to the velocity data. It is demonstrated that the system spans from large-scale anisotropy, which is induced by the main shear of the boundary layer, to small-scale isotropy. Moreover, it is shown that the intermittency is more pronounced in the near-bed layer, where the flow is more populated by coherent whirling structures. In essence, both anisotropy and intermittency are proved to be important phenomena for natural bed rivers, since they affect the turbulence transport characteristics of the flow.
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Lethole, Ndanduleni, and Terrence Sibila. "Effect of Mn on the structural, energetic, electronic and elastic properties of ordered L10 FePt Alloy." MATEC Web of Conferences 406 (2024): 03017. https://doi.org/10.1051/matecconf/202440603017.
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This study performed systematic ternary substitution of Mn into the ordered L10 bulk FePt alloy to investigate its effect on structural, energetic, electronic and elastic behaviour at 0 K. Three ternary compositions were considered; namely Fe0.7Mn0.3Pt, Fe0.5Mn0.5Pt and Fe0.3Mn0.7Pt. Ab initio calculations based on the density functional theory (DFT) formalism were employed using the CATEP module within the Materials Studio program. The findings of this study showed that Mn substitution promotes thermodynamic stability and isotropy due to the decreased enthalpy of formation and universal anisotropy index. The Fe0.3Mn0.7Pt system was predicted to be the most favourable composition, due to less volume deviation from the pristine ordered FePt, the highest Debye temperature and the presence of a deep pseudo gap around the Fermi level.
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Duarte, Vannessa de J., Klaus Thoeni, Diego Garzón-Alvarado, and Miguel Cerrolaza. "A Simplified Scheme for Piezoelectric Anisotropic Analysis in Human Vertebrae Using Integral Methods." Mathematical Problems in Engineering 2018 (June 19, 2018): 1–8. http://dx.doi.org/10.1155/2018/2783867.
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This paper outlines a computational model for the analysis of the piezoelectric behaviour of the vertebral body remodelling process. Particular attention is paid to the algorithms for the simulation of the stress energy density for each point of the geometry and the distribution of the density in the bone. In addition, the model takes into account the piezoelectric effect and the anisotropy (transversal isotropy) of the bone. A model for internal anisotropic piezoelectric bone remodelling of a human vertebra is discussed in detail. The model consists of the implementation of an algorithm which includes the elastic and electric variables in a single equation using boundary element method. The presented results show a good agreement with biological data and the model does not include any electric additional charge.
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Bali, Raj, and Seema Saraf. "Creation Field Cosmological Model with Variable Cosmological Term (Λ) in Bianchi Type III Space-Time." Advances in High Energy Physics 2024 (April 5, 2024): 1–6. http://dx.doi.org/10.1155/2024/5901224.
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The paper is devoted to the study of cosmological models with time-varying cosmological term (Λ) in the presence of creation field in the framework of Bianchi type III space-time. To obtain deterministic model of the universe, we have assumed Λ∝1/R3, where R is the scale factor, for steady state cosmology and creation field, and shear (σ) is proportion to expansion (θ) which leads to B=Cn, where B and C are the metric potentials to explain small anisotropic behaviour of the universe and its isotropy. To obtain the results in terms of cosmic time t, we have assumed n=2. The model satisfies conservation equations, and creation field increases with time. The present model is free from singularity, has particle horizon, and provides a natural explanation for inflationary scenario and isotropization. Creation field and Einstein field equations are derived using principle of least action and Lagrangian formulation of variable cosmological term. For illustrative purposes, evolutionary behaviour of some cosmological parameters are shown graphically. The other physical aspects like accelerating behaviour of the model are also discussed. Thus, the model represents not only expanding universe but also accelerating which matches with the results of present-day observations.
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Djouadi, Inès, Richard Giot, Simon Raude, Sam Cuvilliez, François Laigle, and Roméo Fernandes. "Integration of Transverse Isotropy in the Instantaneous Behaviour of Geomaterials with Application to Numerical Modelling of Underground Structures." Geotechnical and Geological Engineering 38, no. 5 (May 25, 2020): 4917–38. http://dx.doi.org/10.1007/s10706-020-01336-z.
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Namdeo, Jitendra, S. K. Dubey, and Lobzang Dorji. "Dynamic Analysis of Isotropic Homogeneous Beams Using the Method of Initial Functions and Comparison with Classical Beam Theories and FEM." Complexity 2023 (December 9, 2023): 1–18. http://dx.doi.org/10.1155/2023/6636975.
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The main aim of this study is the dynamic analysis of isotropic homogeneous beams using the method of initial functions (MIFs) and comparison with classical beam theories and FEM. Also, this research employs the state space methodology, with a special emphasis on isotropy, to analyse simply supported beam systems. A mathematical model for the dynamic response of beams is constructed using the method of initial functions. The novelty of this study lies in its approach to dynamic analysis, where isotropic homogeneous beams are explored without making assumptions, thus ensuring increased precision using the method of initial functions. Importantly, the approach remains free from restrictive assumptions and relies solely on mathematical formulations, yielding results superior to classical beam theories such as Euler–Bernoulli, Timoshenko, and Rayleigh beam theories. In this work, the application of MIFs of various orders (4th, 6th, 8th, and 10th) to calculate natural frequencies is explored, enabling a thorough examination of the beam’s dynamic characteristics. In addition, parameters such as normal stresses, shear stresses, and deflections in different directions are considered to provide a comprehensive understanding of beam behaviour. To validate the findings, a detailed comparison with a finite element method (FEM) is conducted, achieving excellent agreement between the analytical results and FEM solutions. Furthermore, the influence of Poisson’s ratio (μ) on natural frequencies is investigated by varying its value from 0.18 to 0.30. The research also explores the deviation of plane stress values of the beam section from those estimated using the FEM for the corresponding components.
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SLEVIN, KEITH, and TARO NAGAO. "MAXIMUM ENTROPY MODELS OF TRANSPORT IN MESOSCOPIC WIRES." International Journal of Modern Physics B 09, no. 02 (January 20, 1995): 103–43. http://dx.doi.org/10.1142/s0217979295000070.
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We review the maximum entropy models for the probability distribution of the transfer matrix of a disordered mesoscopic wire. We relate this distribution to the zero temperature conductance of the wire using the Landauer formula and discuss the extent to which the maximum entropy models describe accurately the weak localisation effect and universal conductance fluctuations which occur in the diffusive regime. A detailed comparison between numerical simulations and the maximum entropy models is also presented. For “long” wires there is a crossover from diffusive to localised behaviour and we review the predictions of the maximum entropy models in this regime, chiefly the symmetry dependence of the localisation length and the log-normal distribution of the conductance. In conclusion we discuss the limitations of the maximum entropy models and in particular the property of isotropy.
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AFSAR, M. Z. "Asymptotic properties of the overall sound pressure level of subsonic jet flows using isotropy as a paradigm." Journal of Fluid Mechanics 664 (November 3, 2010): 510–39. http://dx.doi.org/10.1017/s0022112010003976.
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Measurements of subsonic air jets show that the peak noise usually occurs when observations are made at small angles to the jet axis. In this paper, we develop further understanding of the mathematical properties of this peak noise by analysing the properties of the overall sound pressure level with an acoustic analogy using isotropy as a paradigm for the turbulence. The analogy is based upon the hyperbolic conservation form of the Euler equations derived by Goldstein (Intl J. Aeroacoust., vol. 1, 2002, p. 1). The mean flow and the turbulence properties are defined by a Reynolds-averaged Navier–Stokes calculation, and we use Green's function based upon a parallel mean flow approximation. Our analysis in this paper shows that the jet noise spectrum can, in fact, be thought of as being composed of two terms, one that is significant at large observation angles and a second term that is especially dominant at small observation angles to the jet axis. This second term can account for the experimentally observed peak jet noise (Lush, J. Fluid Mech., vol. 46, 1971, p. 477) and was first identified by Goldstein (J. Fluid Mech., vol. 70, 1975, p. 595). We discuss the low-frequency asymptotic properties of this second term in order to understand its directional behaviour; we show, for example, that the sound power of this term is proportional to the square of the mean velocity gradient. We also show that this small-angle shear term does not exist if the instantaneous Reynolds stress source strength in the momentum equation itself is assumed to be isotropic for any value of time (as was done previously by Morris & Farrasat, AIAA J., vol. 40, 2002, p. 356). However, it will be significant if the auto-covariance of the Reynolds stress source, when integrated over the vector separation, is taken to be isotropic in all of its tensor suffixes. Although the analysis shows that the sound pressure of this small-angle shear term is sensitive to the statistical properties of the turbulence, this work provides a foundation for a mathematical description of the two-source model of jet noise.
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MOFFATT, H. K., and A. SELLIER. "Migration of an insulating particle under the action of uniform ambient electric and magnetic fields. Part 1. General theory." Journal of Fluid Mechanics 464 (August 10, 2002): 279–86. http://dx.doi.org/10.1017/s0022112002001131.
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The behaviour of an insulating particle suspended in a liquid metal and subject to the influence of locally uniform electric and magnetic fields (E, B) is considered. The electric field drives a current J which is perturbed by the presence of the particle, and the resulting Lorentz force drives a flow. It is assumed that both the Reynolds number and the Hartmann number based on particle size are small. If the particle is fixed, it experiences a force and couple that are each bilinear in J and B; if it is freely suspended, then it moves with translational velocity U and angular velocity Ω each similarly bilinear in J and B. The general form of these bilinear relationships is determined, with particular attention to three types of particle symmetry: (i) isotropy; (ii) axisymmetry; and (iii) orthotropy.
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Djenidi, L., and R. A. Antonia. "Transport equation for the mean turbulent energy dissipation rate in low- grid turbulence." Journal of Fluid Mechanics 747 (April 17, 2014): 288–315. http://dx.doi.org/10.1017/jfm.2014.157.
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AbstractA direct numerical simulation (DNS) based on the lattice Boltzmann method (LBM) is carried out in low-Reynolds-number grid turbulence to analyse the mean turbulent kinetic energy dissipation rate, $\overline{\epsilon }$, and its transport equation during decay. All the components of $\overline{\epsilon }$ and its transport equation terms are computed, providing for the first time the opportunity to assess the contribution of each term to the decay. The results indicate that although small departures from isotropy are observed in the components of $\overline{\epsilon }$ and its destruction term, there is sufficient compensation among the components for these two quantities to satisfy isotropy to a close approximation. A short distance downstream of the grid, the transport equation of $\overline{\epsilon }$ simplifies to its high-Reynolds-number homogeneous and isotropic form. The decay rate of $\overline{\epsilon }$ is governed by the imbalance between the production due to vortex stretching and the destruction caused by the action of viscosity, the latter becoming larger than the former as the distance from the grid increases. This imbalance, which is not constant during the decay as argued by Batchelor & Townsend (Proc. R. Soc. Lond. A, vol. 190, 1947, pp. 534–550), varies according to a power law of $x$, the distance downstream of the grid. The non-constancy implies a lack of dynamical similarity in the mechanisms controlling the transport of $\overline{\epsilon }$. This is consistent with the fact that the power-law-decay ($\overline{q^2} \sim x^n$) exponent $n$ is not equal to $-$1. It is actually close to $-$1.6, a value in keeping with the relatively low Reynolds number of the simulation. These results highlight the importance of the imbalance in establishing the value of $n$. The $\overline{\epsilon }$-transport equation is also analysed in relation to the power-law decay. The results show that the power-law exponent $n$ is controlled by the imbalance between production and destruction. Further, a relatively straightforward analysis provides information on the behaviour of $n$ during the entire decay process and an interesting theoretical result, which is yet to be confirmed, when $R_{\lambda } \rightarrow 0 $, namely, the destruction coefficient $G$ is constant and its value must lie between $15/7$ and $30/7$. These two limits encompass the predictions for the final period of decay by Batchelor & Townsend (1947) and Saffman (J. Fluid Mech., vol. 27, 1967, pp. 581–593).
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Alves Portela, F., G. Papadakis, and J. C. Vassilicos. "The turbulence cascade in the near wake of a square prism." Journal of Fluid Mechanics 825 (July 20, 2017): 315–52. http://dx.doi.org/10.1017/jfm.2017.390.
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We present a study of the turbulence cascade on the centreline of an inhomogeneous and anisotropic near-field turbulent wake generated by a square prism at a Reynolds number of$Re=3900$using the Kármán–Howarth–Monin–Hill equation. This is the fully generalised scale-by-scale energy balance which, unlike the Kármán–Howarth equation, does not require homogeneity or isotropy assumptions. Our data are obtained from a direct numerical simulation and therefore enable us to access all of the processes involved in this energy balance. A significant range of length scales exists where the orientation-averaged nonlinear interscale transfer rate is approximately constant and negative, indicating a forward turbulence cascade on average. This average cascade consists of coexisting forward and inverse cascade behaviours in different scale-space orientations. With increasing distance from the prism but within the near field of the wake, the orientation-averaged nonlinear interscale transfer rate tends to be approximately equal to minus the turbulence dissipation rate even though all of the inhomogeneity-related energy processes in the scale-by-scale energy balance are significant, if not equally important. We also find well-defined near$-5/3$energy spectra in the streamwise direction, in particular at a centreline position where the inverse cascade behaviour occurs for streamwise oriented length scales.
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Oktariena, Madaniya, W. Triyoso, Fatkhan, S. Sukmono, E. Septama, P. D. Wardaya, and B. S. Murdianto. "Evaluation of Depth Dependent Seismic Anisotropy within Limited Offset on Vertical Transverse Isotropy Media: Deep Water Reservoir Case Study." IOP Conference Series: Earth and Environmental Science 1437, no. 1 (December 1, 2024): 012011. https://doi.org/10.1088/1755-1315/1437/1/012011.
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Abstract Hydrocarbon bearing sediment in deep water reservoirs are uniquely characterized by the body of water being an additional weight on the top of vertical sedimentary layering. While large aerial extent of deep water reservoirs is known for their ability to contain substantial amount of reserves, they come with technical difficulties mainly in acquisition and imaging aspect. Deep water seismic imaging more often than not suffers from the hockey stick effect found in the long offset. At the same time, the presence of hockey stick in seismic long offset could be utilized as a tool to extract anisotropy information from seismic data. However, the deep target level requires a rather long offset in seismic data to be able in capturing a proper hockey stick condition. This research intends to evaluate seismic anisotropy behaviour in various depth level within a limited offset range instead of the commonly used very long offset. Seismic related anisotropy (η) is extracted from travel time error as a delta to the isotropic travel time. The extracted anisotropy η is to be plotted against several known VTI travel time approximation in order to identified the equation that most fitted to the deep water real data condition. Several depth levels are to be analysed as an attempt to capture depth related variation in multi reservoir scenarios. Observation is conducted on PMBG Seismic Gather around several well location as point of validation. The result shows indication of seismic anisotropy degree variation within progressed depth that could be concluded as depth dependant behaviour. The fact that the observed area has a typical character of weak anisotropy which only has a small impact on seismic data encourages a possibility to delineate anisotropy from seismic data with a certain treatment. Analysis on limited range offset seismic promotes the utilization of old vintage seismic data for seismic anisotropy extraction that contribute to the vision of using a new insight on the existing data as part of enhanced oil recovery strategies.
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Eaton-Evans, James, Janice M. Dulieu-Barton, Edward G. Little, and Ian A. Brown. "Factors Influencing the Suitability of Thermal Methods for Stress Analysis of NiTi Shape Memory Alloys." Applied Mechanics and Materials 13-14 (July 2008): 225–30. http://dx.doi.org/10.4028/www.scientific.net/amm.13-14.225.
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The material assumptions made to facilitate Thermoelastic Stress Analysis (TSA) are linear elasticity, material homogeneity and isotropy, and mechanical properties that are independent of temperature. The unusual shape memory and superelastic properties of near equiatomic NiTi alloys complicate the application of any experimental stress analysis technique, and in the case of TSA, make these assumptions invalid. This paper describes a detailed analysis conducted to characterise the material properties of NiTi shape memory alloys and to identify loading conditions suitable for quantitative stress analysis using TSA. The mechanical behaviour of the material in three distinct regions is considered and the suitability of each region for TSA is discussed. It is shown that the thermoelastic response is dependent on the mean stress when tested at room temperature in the pre-martensitic phase, due the presence of an intermediate R-phase. Theoretical calculations are used to confirm that this effect is related to the high temperature dependence of the material’s Young’s modulus.
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Ayvar, S. S., S. H. Hashemi, I. C. Howard, and J. R. Yates. "An Experimental and Finite Element Study of the Ductile Tearing Characteristics of High-Toughness Gas Pipeline Steel." Applied Mechanics and Materials 3-4 (August 2006): 259–66. http://dx.doi.org/10.4028/www.scientific.net/amm.3-4.259.
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This paper reports recent results from a set of experimental and computational studies of ductile flat fracture in modern gas pipeline steel. Experimental data from plain and notched cylindrical tensile bars and standard C(T) specimens together with damage mechanics theories have been used to capture the flat fracture characteristics of a gas pipeline steel of grade X100. The modelling was via finite element analysis using the Gurson-Tvergaard modified model (GTN) of ductile damage development. The assumption of effective material damage isotropy was sufficiently accurate to allow the transfer of data from the notched bars to predict, in a 2D model, the crack growth behaviour of the C(T) specimen. This was in spite of the considerable ovalisation of the bars at the end of their deformation. However, it was not possible to obtain similar accuracy with a 3D model of the C(T)test, even after a large number of attempts to adjust the values of the GTN parameters. This, and the anisotropic shape change in the tensile bars, suggests very strongly that the damage behaviour is so anisotropic that conventional models are not good enough for a full engineering description of the flat fracture behaviour. Suitable averaging (of shape) in the modelling of the notched bar data, and the companion averaging associated with the 2D model of the C(T) data provide a relatively fast way of transferring engineering data in the tests. There is a discussion of potential ways in which to incorporate 3D effects into the modelling for those purposes where the considerable increase in computational time (due to the microstructurally-sized finite elements needed to capture the damage behaviour) is acceptable in order to include through-thickness effects.
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Anssari-Benam, Afshin, Andrea Bucchi, Hazel R. C. Screen, and Sam L. Evans. "A transverse isotropic viscoelastic constitutive model for aortic valve tissue." Royal Society Open Science 4, no. 1 (January 2017): 160585. http://dx.doi.org/10.1098/rsos.160585.
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A new anisotropic viscoelastic model is developed for application to the aortic valve (AV). The directional dependency in the mechanical properties of the valve, arising from the predominantly circumferential alignment of collagen fibres, is accounted for in the form of transverse isotropy. The rate dependency of the valve's mechanical behaviour is considered to stem from the viscous ( η ) dissipative effects of the AV matrix, and is incorporated as an explicit function of the deformation rate ( λ ˙ ). Model (material) parameters were determined from uniaxial tensile deformation tests of porcine AV specimens at various deformation rates, by fitting the model to each experimental dataset. It is shown that the model provides an excellent fit to the experimental data across all different rates and satisfies the condition of strict local convexity. Based on the fitting results, a nonlinear relationship between η and λ ˙ is established, highlighting a ‘shear-thinning’ behaviour for the AV with increase in the deformation rate. Using the model and these outcomes, the stress–deformation curves of the AV tissue under physiological deformation rates in both the circumferential and radial directions are predicted and presented. To verify the predictive capabilities of the model, the stress–deformation curves of AV specimens at an intermediate deformation rate were estimated and validated against the experimental data at that rate, showing an excellent agreement. While the model is primarily developed for application to the AV, it may be applied without the loss of generality to other collagenous soft tissues possessing a similar structure, with a single preferred direction of embedded collagen fibres.
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Weinstock, Jerome. "Analytical theory of homogeneous mean shear turbulence." Journal of Fluid Mechanics 727 (June 20, 2013): 256–81. http://dx.doi.org/10.1017/jfm.2014.13.
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AbstractA compact nonlinear expression for the velocity spectra of homogeneous mean shear flow is derived by means of a simplified two-point closure. It applies to all scales and times. The derived equation can be viewed as a nonlinear extension of the linear, rapid-distortion-theory (RDT) equation. The principal simplification is to model the nonlinear pressure–strain rate as first-order in the spectral anisotropy: a spectral Rotta-equation. This simplified equation and its solution are expressed in terms of the RDT solution. That solution helps reveal the role of nonlinearity. An equation for the velocity spectrum is then obtained at all scales and times. A dominant characteristic predicted for nonlinear behaviour is that the turbulence energy grows exponentially with time, with the spectrum simultaneously moving to smaller and smaller wavenumbers. The nonlinear growth rate is determined. Other analytical predictions of the derived equation include: the conditions for self-similarity; local isotropy; various properties of mean shear flow, including characteristic energy, length and temporal growth scales; and a critique of perturbation theory. Comparisons are made with laboratory experiments and direct numerical simulations. Although the theory applies to all scales and times, including an exact expression for RDT, the calculations are focused on nonlinear behaviour at large times. Several approximations used in this work are examined.
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Nguyen, Khuong X., and Chenning Tong. "Investigation of subgrid-scale physics in the convective atmospheric surface layer using the budgets of the conditional mean subgrid-scale stress and temperature flux." Journal of Fluid Mechanics 772 (May 5, 2015): 295–329. http://dx.doi.org/10.1017/jfm.2015.171.
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The subgrid-scale (SGS) physics in the convective atmospheric surface layer is studied using the SGS stress and SGS scalar flux. We derive the budget equations for the conditional mean SGS stress and SGS temperature flux and show that, for transport-equation-based SGS models, the budget terms must be correctly predicted by the SGS model in order for large-eddy simulation (LES) to reproduce the resolvable-scale velocity and temperature probability density functions. Field data from the Advection Horizontal Array Turbulence Study, which notably includes measurements of the fluctuating pressure and the advection of the velocity and temperature fields, are then used to analyse the budget equations. The results reveal the complex behaviour of the dynamics of the convective atmospheric surface layer. The budgets of the conditional mean SGS shear stress and SGS temperature flux are an approximate balance between the conditional mean production and pressure destruction, with the latter causing return to isotropy. The budgets of the normal SGS stress components are more complex. For strongly convective surface layers, energy is redistributed from the (smaller) vertical to the (larger) horizontal stress components during downdrafts, resulting in generation of anisotropy by the conditional mean SGS pressure–strain-rate correlation; wall pressure reflections can also enhance the anisotropy. The conditional mean SGS pressure transport, meanwhile, is a significant source of energy during updrafts as a result of the near-wall pressure minima. The vertical advection also plays a significant role in the transfer of SGS energy. For weakly convective surface layers, pressure transport is small while the SGS pressure–strain-rate correlation reverts to its usual role of causing return to isotropy. The results of the present study, particularly for the conditional mean SGS pressure–strain-rate correlation, provide new insights into the SGS physics first educed in a recent analysis of the mean SGS budgets by Nguyen et al. (J. Fluid Mech., vol. 729, 2013, pp. 388–422) and have important implications for near-wall models utilizing SGS transport equations in the convective atmospheric surface layer.
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Carter, Douglas W., and Filippo Coletti. "Scale-to-scale anisotropy in homogeneous turbulence." Journal of Fluid Mechanics 827 (August 22, 2017): 250–84. http://dx.doi.org/10.1017/jfm.2017.496.
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We experimentally investigate scale-to-scale anisotropy from the integral to the dissipative scales in homogeneous turbulence. We employ an apparatus in which two facing arrays of randomly actuated air jets generate turbulence with negligible mean flow and shear, over a volume several times larger than the energy-containing eddy size. The Reynolds number based on the Taylor microscale is varied in the range$Re_{\unicode[STIX]{x1D706}}\approx 300{-}500$, while the axial-to-radial ratio of the root mean square velocity fluctuations ranges between 1.38 and 1.72. Two velocity components are measured by particle image velocimetry at varying resolutions, capturing from the integral to the Kolmogorov scales and yielding statistics up to sixth order. Over the inertial range, the scaling exponents of the velocity structure functions are found to differ not only between the longitudinal and transverse components, but also between the axial and radial directions of separation. At the dissipative scales, the moments of the velocity gradients indicate that departure from isotropy is, at the present Reynolds numbers, significant and more pronounced for stronger large-scale anisotropy. The generalized flatness factors of the longitudinal velocity differences tend towards isotropy as the separation is reduced from the inertial to the near-dissipative scales (down to about$10\unicode[STIX]{x1D702}$,$\unicode[STIX]{x1D702}$being the Kolmogorov length), but become more anisotropic for even smaller scales which are characterized by high intermittency. At the large scales, the direction of turbulence forcing is associated with a larger integral length, defined as the distance over which the velocity component in a given direction is spatially correlated. Because of anisotropy, the definition of the integral length is not trivial and may lead to dissimilar conclusions on the qualitative behaviour of the large scales and on the quantitative values of the normalized dissipation. Alternative definitions of these quantities are proposed to account for the anisotropy. Overall, these results highlight the importance of evaluating both the different velocity components and the different spatial directions across all scales of the flow.
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ZIKANOV, OLEG, and ANDRE THESS. "Direct numerical simulation of forced MHD turbulence at low magnetic Reynolds number." Journal of Fluid Mechanics 358 (March 10, 1998): 299–333. http://dx.doi.org/10.1017/s0022112097008239.
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The transformation of initially isotropic turbulent flow of electrically conducting incompressible viscous fluid under the influence of an imposed homogeneous magnetic field is investigated using direct numerical simulation. Under the assumption of large kinetic and small magnetic Reynolds numbers (magnetic Prandtl number Pm[Lt ]1) the quasi-static approximation is applied for the computation of the magnetic field fluctuations. The flow is assumed to be homogeneous and contained in a three-dimensional cubic box with periodic boundary conditions. Large-scale forcing is applied to maintain a statistically steady level of the flow energy. It is found that the pathway traversed by the flow transformation depends decisively on the magnetic interaction parameter (Stuart number). If the magnetic interaction number is small the flow remains three-dimensional and turbulent and no detectable deviation from isotropy is observed. In the case of a strong magnetic field (large magnetic interaction parameter) a rapid transformation to a purely two-dimensional steady state is obtained in agreement with earlier analytical and numerical results for decaying MHD turbulence. At intermediate values of the magnetic interaction parameter the system exhibits intermittent behaviour, characterized by organized quasi-two-dimensional evolution lasting several eddy-turnover times, which is interrupted by strong three-dimensional turbulent bursts. This result implies that the conventional picture of steady angular energy transfer in MHD turbulence must be refined. The spatial structure of the steady two-dimensional final flow obtained in the case of large magnetic interaction parameter is examined. It is found that due to the type of forcing and boundary conditions applied, this state always occurs in the form of a square periodic lattice of alternating vortices occupying the largest possible scale. The stability of this flow to three-dimensional perturbations is analysed using the energy stability method.
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Jiang, Hua-Long, Song-Hao Jia, Da-Wei Zhou, Chun-Ying Pu, Fei-Wu Zhang, and Shuai Zhang. "First-Principles Calculations of the Mechanical and Elastic Properties of 2Hc- and 2Ha-WS2/CrS2 Under Pressure." Zeitschrift für Naturforschung A 71, no. 6 (June 1, 2016): 517–24. http://dx.doi.org/10.1515/zna-2015-0517.
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AbstractBy utilizing the first-principles method, the pressure-induced effects on phase transition, mechanical stability, and elastic properties of WS2/CrS2 are investigated in the pressure range from 0 to 80 GPa. Transitions from 2Hc to 2Ha for WS2 and CrS2 are found to occur at 17.5 and 25 GPa, respectively. It is found that both 2Ha and 2Hc phases of WS2 and CrS2 meet the mechanical stability criteria up to 80 GPa, suggesting that those structures are mechanically stable. The bulk and shear modulus anisotropy of the two phases of WS2 and CrS2 decrease rapidly under pressure and, finally, trend to isotropy. With increasing pressure, the elastic moduli (Y, B, and G), sound velocities (vs, vp, vm), and Debye temperatures (Θ) of 2Ha and 2Hc of WS2 and CrS2 increase monotonously. Moreover, the Debye temperature (Θ) of 2Hc phase is higher than that of 2Ha phase for both WS2 and CrS2. The bulk, shear, and Young’s modulus, Poisson coefficient, and brittle/ductile behaviour are estimated. The percentages of anisotropy in compressibility and shear and the ratio of bulk to shear modulus (B/G) are also studied.
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Klimanek, P., and R. Kužel. "X-ray diffraction line broadening due to dislocations in non-cubic materials. I. General considerations and the case of elastic isotropy applied to hexagonal crystals." Journal of Applied Crystallography 21, no. 1 (February 1, 1988): 59–66. http://dx.doi.org/10.1107/s0021889887009580.
Full textAbstract:
Use is made of the theory of dislocation-induced X-ray diffraction line broadening in the form presented by Krivoglaz, Martynenko & Ryaboshapka [Fiz. Metall. Metalloved. (1983), 55, 5–171 to express the so-called orientation factors occurring in the relations of diffraction profile parameters (e.g. Fourier coefficients, line widths) in a form which systematically takes into account both the lattice geometry and the elastic behaviour of the scattering crystals. The formalism can be used, in principle, for any materials and types of dislocations. In the case of elastically isotropic media the orientation factors can be described by analytical expressions. The application of the formalism is demonstrated in some detail for various slip systems in hexagonal polycrystals with random orientation of grains.