Journal articles on the topic 'Anisotropic energy'
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Zhang, Chao, Xiangzhuang Kong, Xian Wang, Yanxia Du, and Guangming Xiao. "A Predicting Model for the Effective Thermal Conductivity of Anisotropic Open-Cell Foam." Energies 15, no. 16 (August 22, 2022): 6091. http://dx.doi.org/10.3390/en15166091.
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The structural anisotropy of open-cell foam leads to the anisotropy of effective thermal conductivity (ETC). To quantitatively analyze the effect of structural anisotropy on the anisotropy of ETC, a new predicting model for the ETC of anisotropic open-cell foam was proposed based on an anisotropy tetrakaidecahedron cell (ATC). Feret diameters in three orthogonal directions obtained by morphological analysis of real foam structures were used to characterize the anisotropy of ATC. To validate our proposed anisotropic model, the ETCs of real foam structures in three orthogonal directions predicted by it were compared with the numerical results, for which the structures of numerical models are reconstructed by X-ray computed tomography (X-CT). Using the present anisotropic model, the influences of the thermal conductivity ratio (TCR) and porosity of the foams on the anisotropic ratios of ETCs are also investigated. Results show that there is good consistency between the ETCs obtained by the anisotropic model and the numerical method. The maximum relative errors between them are 2.84% and 13.57% when TCRs are 10 and 100, respectively. The present anisotropic model can not only predict the ETCs in different orthogonal directions but also quantitatively predict the anisotropy of ETC. The anisotropies of the ETCs decrease with porosity because the proportion of the foam skeleton decreases. However, the anisotropies of ETCs increase with TCR, and there exist asymptotic values in anisotropic ratios of ETCs as TCR approaches infinity and they are equal to the relative Feret diameters in different orthogonal directions.
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Janhunen, P., A. Olsson, H. Laakso, and A. Vaivads. "Middle-energy electron anisotropies in the auroral region." Annales Geophysicae 22, no. 1 (January 1, 2004): 237–49. http://dx.doi.org/10.5194/angeo-22-237-2004.
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Abstract. Field-aligned anisotropic electron distribution functions of T∥ > T⊥ type are observed on auroral field lines at both low and high altitudes. We show that typically the anisotropy is limited to a certain range of energies, often below 1keV, although sometimes extending to slightly higher energies as well. Almost always there is simultaneously an isotropic electron distribution at higher energies. Often the anisotropies are up/down symmetrical, although cases with net upward or downward electron flow also occur. For a statistical analysis of the anisotropies we divide the energy range into low (below 100eV), middle (100eV–1keV) and high (above 1keV) energies and develop a measure of anisotropy expressed in density units. The statistical magnetic local time and invariant latitude distribution of the middle-energy anisotropies obeys that of the average auroral oval, whereas the distributions of the low and high energy anisotropies are more irregular. This suggests that it is specifically the middle-energy anisotropies that have something to do with auroral processes. The anisotropy magnitude decreases monotonically with altitude, as one would expect, because electrons have high mobility along the magnetic field and thus, the anisotropy properties spread rapidly to different altitudes. Key words. Magnetospheric physics (auroral phenomena). Space plasma physics (wave-particle interactions; changed particle motion and acceleration)
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Song, Honghua, Yixin Zhao, Yaodong Jiang, and Jiehao Wang. "Scale Effect on the Anisotropy of Acoustic Emission in Coal." Shock and Vibration 2018 (December 18, 2018): 1–11. http://dx.doi.org/10.1155/2018/8386428.
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Acoustic emission (AE) in coal is anisotropic. In this paper, we investigate the microstructure-related scale effect on the anisotropic AE feature in coal at unconfined loading process. A series of coal specimens were processed with diameters of 25 mm, 38 mm, 50 mm, and 75 mm (height to diameter ratio of 2) and anisotropic angles of 0°, 15°, 30°, 45°, 60°, and 90°. The cumulative AE counts and energy dissipation increase with the specimen size, while the energy dissipation per AE count behaves in the opposite way. This may result from the increasing amount of both preexisting discontinuities and cracks (volume/number) needed for specimen failure and the lower energy dissipation AE counts generated by them. The effect of microstructures on the anisotropies of AE weakens with the increasing specimen size. The TRFD and its anisotropy reduce as the specimen size increases, and the reduction of fractal dimension is most pronounced at the anisotropic angle of 45°. The correlation between TRFD and cumulative AE energy in the specimens with different sizes are separately consistent with the negative exponential equation proposed by Xie and Pariseau. With the specimen size gain, the reduction of the TRFD weakens with the increasing amount of cumulative absolute AE energy.
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Shaaban, S. M., and M. Lazar. "Whistler instabilities from the interplay of electron anisotropies in space plasmas: a quasi-linear approach." Monthly Notices of the Royal Astronomical Society 492, no. 3 (December 28, 2019): 3529–39. http://dx.doi.org/10.1093/mnras/stz3569.
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ABSTRACT Recent statistical studies of observational data unveil relevant correlations between whistler fluctuations and the anisotropic electron populations present in space plasmas, e.g. solar wind and planetary magnetospheres. Locally, whistlers can be excited by two sources of free energy associated with anisotropic electrons, i.e. temperature anisotropies and beaming populations carrying the heat flux. However, these two sources of free energy and the resulting instabilities are usually studied independently preventing a realistic interpretation of their interplay. This paper presents the results of a parametric quasi-linear study of the whistler instability cumulatively driven by two counter-drifting electron populations and their anisotropic temperatures. By comparison to individual regimes dominated either by beaming population or by temperature anisotropy, in a transitory regime the instability becomes highly conditioned by the effects of both these two sources of free energy. Cumulative effects stimulate the instability and enhance the resulting fluctuations, which interact with electrons and stimulate their diffusion in velocity space, leading to a faster and deeper relaxation of the beaming velocity associated with a core heating in perpendicular direction and a thermalization of the beaming electrons. In particular, the relaxation of temperature anisotropy to quasi-stable states below the thresholds conditions predicted by linear theory may explain the observations showing the accumulation of these states near the isotropy and equipartition of energy.
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Rocha, Daniel, Nicolay Tanushev, and Paul Sava. "Anisotropic elastic wavefield imaging using the energy norm." GEOPHYSICS 82, no. 3 (May 1, 2017): S225—S234. http://dx.doi.org/10.1190/geo2016-0424.1.
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Based on the energy conservation principle, we derive a scalar imaging condition for anisotropic elastic wavefield migration. Compared with conventional imaging conditions that correlate displacement components or potentials from source and receiver wavefields, the proposed imaging condition does not suffer from polarity reversal, which degrades the image quality after stacking over shots. Our imaging condition also accounts for the directionality of the wavefields in space and time, leading to the attenuation of backscattering artifacts, which commonly appear in elastic reverse time migration images in the presence of strong model contrasts. In addition, our new imaging condition does not require wave-mode decomposition, which demands significant additional cost for elastic wavefields in anisotropic media. To properly image structures, we rely on the anisotropy parameters used in migration, as one would do for any other imaging condition. Our imaging condition is suitable for arbitrary anisotropy. We show the successful application of the anisotropic energy imaging condition by performing numerical experiments on simple and complex geologic models. We compare its quality with conventional counterparts by simulating complex geologic settings with vertical or tilted transverse isotropy.
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Mishra, B., and S. K. Tripathy. "Anisotropic dark energy model with a hybrid scale factor." Modern Physics Letters A 30, no. 36 (November 3, 2015): 1550175. http://dx.doi.org/10.1142/s0217732315501758.
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Anisotropic dark energy model with dynamic pressure anisotropies along different spatial directions is constructed at the backdrop of a spatially homogeneous diagonal Bianchi type V (BV) spacetime in the framework of General Relativity. A time varying deceleration parameter generating a hybrid scale factor is considered to simulate a cosmic transition from early deceleration to late time acceleration. We found that the pressure anisotropies along the y- and z-axes evolve dynamically and continue along with the cosmic expansion without being subsided even at late times. The anisotropic pressure along the x-axis becomes equal to the mean fluid pressure. At a late phase of cosmic evolution, the model enters into a phantom region. From a statefinder diagnosis, it is found that the model overlaps with [Formula: see text] at late phase of cosmic time.
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MAK, M. K., PETER N. DOBSON, and T. HARKO. "EXACT MODELS FOR ANISOTROPIC RELATIVISTIC STARS." International Journal of Modern Physics D 11, no. 02 (February 2002): 207–21. http://dx.doi.org/10.1142/s0218271802001317.
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We present a class of exact solutions of the Einstein gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solution is represented in a closed integral form. The energy density and both radial and tangential pressure are finite and positive inside the anisotropic star. The energy density, radial pressure, pressure-density ratio and the adiabatic speed of sound are monotonically decreasing functions. Several stellar models with the anisotropy coefficient proportional to r2 are discussed, the values of the basic physical parameters of the star (radius, mass and red shift) and bound on anisotropy parameter is obtained.
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MOHAPATRA, RANJITA K., P. S. SAUMIA, and AJIT M. SRIVASTAVA. "ANALYZING FLOW ANISOTROPIES WITH EXCURSION SETS IN RELATIVISTIC HEAVY-ION COLLISIONS." Modern Physics Letters A 27, no. 29 (September 17, 2012): 1250168. http://dx.doi.org/10.1142/s0217732312501684.
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We show that flow anisotropies in relativistic heavy-ion collisions can be analyzed using a certain technique of shape analysis of excursion sets recently proposed by us for CMBR fluctuations to investigate anisotropic expansion history of the universe. The technique analyzes shapes (sizes) of patches above (below) certain threshold value for transverse energy/particle number (the excursion sets) as a function of the azimuthal angle and rapidity. Modeling flow by imparting extra anisotropic momentum to the momentum distribution of particles from HIJING, we compare the resulting distributions for excursion sets at two different azimuthal angles. Angles with maximum difference in the two distributions identify the event plane, and the magnitude of difference in the two distributions relates to the magnitude of momentum anisotropy, i.e. elliptic flow.
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Hossienkhani, H., V. Fayaz, and A. Jafari. "Energy conditions and modified gravity in anisotropic universe." Canadian Journal of Physics 96, no. 2 (February 2018): 225–32. http://dx.doi.org/10.1139/cjp-2017-0375.
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In this paper, energy conditions in a new [Formula: see text] modified gravity ([Formula: see text] and T represent the Gauss–Bonnet invariant and trace of the energy–momentum tensor, respectively) for anisotropic universe with perfect fluid are analyzed. In this model, we develop the general scheme for new [Formula: see text] modified gravity reconstruction from realistic anisotropic Bianchi type-I cosmology. Using de Sitter solution, the exact solutions of the field equations have been obtained. It is found that null and weak energy conditions are satisfied for the parameter range considered. As a result, the analyses show that the increase of anisotropy is attributed to the increase of weak energy condition.
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Burlakov, Victor M., and Alain Goriely. "Ligand-Assisted Growth of Nanowires from Solution." Applied Sciences 11, no. 16 (August 20, 2021): 7641. http://dx.doi.org/10.3390/app11167641.
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We consider the development of ligand-assisted growth processes for generating shape-anisotropic nanomaterials. Using statistical mechanics, we analyze the conditions under which ligand-assisted growth of shape-anisotropic crystalline nanomaterials from solution can take place. Depending on ligand-facet interaction energy and crystal facet area, molecular ligands can form compact layers on some facets leaving other facets free. The growth process is then restricted to free facets and may result in significant anisotropy in crystal shape. Our study uncovers the conditions for ligand-assisted growth of nanoplatelets and nanowires from isotropic or anisotropic seed nanocrystals of cuboid shape. We show that in contrast to nanoplatelets, ligand-assisted growth of nanowires requires certain anisotropy in the ligand-facet interaction energy.
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Shaaban, S. M., M. Lazar, R. A. López, and R. F. Wimmer-Schweingruber. "On the interplay of solar wind proton and electron instabilities: linear and quasi-linear approaches." Monthly Notices of the Royal Astronomical Society 503, no. 3 (March 31, 2021): 3134–44. http://dx.doi.org/10.1093/mnras/stab075.
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ABSTRACT Important efforts are currently being made to understand the so-called kinetic instabilities, driven by the anisotropy of different species of plasma particles present in the solar wind and terrestrial magnetosphere. These instabilities are fast enough to efficiently convert the free energy of plasma particles into enhanced (small-scale) fluctuations, with multiple implications, regulating the anisotropy of plasma particles. In this paper we use both linear and quasi-linear (QL) frameworks to describe complex unstable regimes, which realistically combine different temperature anisotropies of electrons and ions (protons). Thus various instabilities are parametrized, for example the proton and electron firehose, electromagnetic ion cyclotron and whistler instabilities, showing that their main linear properties are markedly altered by the interplay of anisotropic electrons and protons. Linear theory may predict the strong competition of two instabilities of different natures when their growth rates are comparable. In the QL phase, wave fluctuations grow and saturate at different levels and temporal scales, in comparison to results for the individual excitation of the proton or electron instabilities. In addition, the cumulative effects of the combined proton- and electron-induced fluctuations can markedly stimulate the relaxation of their temperature anisotropies. Only whistler fluctuations inhibit the efficiency of proton firehose fluctuations in the relaxation of anisotropic protons. These results offer valuable premises for further investigations in numerical simulations to decode the full spectrum of kinetic instabilities resulting from the interplay of anisotropic electrons and protons in space plasmas.
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Ashcheulov, Anatoly, Mykola Derevianchuk, and Dmytro Lavreniuk. "Anisotropic metadielectric converter." Electrical Engineering and Power Engineering, no. 4 (April 20, 2022): 18–27. http://dx.doi.org/10.15588/1607-6761-2021-4-2.
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Purpose. Investigation of the peculiarities of the electric field energy conversion by an anisotropic meta-medium with a negative value of the dielectric constant in one of the selected main crystallographic directions. Methodology. Research was carried out using methods of physical and mathematical modeling of anisotropic metadielectric converter; using methods to optimize the function of the dependence of the conversion factor m, anisotropic metadielectric converter, on the angle α between one of the crystallographic axes and the edge of the platinum a, at fixed anisotropy coefficients of metadielectric material. Findings. For the first time, the peculiarities of the electric field transformation by an anisotropic meta-medium with a negative value of the dielectric constant in one of the selected main crystallographic directions were studied. It is established that at the moment of application to the upper and lower faces of the anisotropic metadielectric plate, which is the basis of the anisotropic metadielectric converter, some potential difference leads to polarization of its volume and the emergence of both longitudinal and transverse components of the vortex electric field. This situation leads to axial folding of its internal field, which in turn causes the appearance of micro-vortices of the electric field, given by the expression , where - the circular time of rotation of the micro-vortex, and signs "+" and "-" - indicate the direction of its rotation. Such axial electric micro vortices are an efficient mechanism that pumps energy between the physical vacuum and, in our case, the anisotropic metadielectric plate of the transducer. The dependence of the transformation coefficient m of this medium on the value of anisotropy is analyzed. Studies have shown that in the interval the value of m is characterized by a negative value, and in the interval – positive, this allowed us to determine the areas of stable existence of different types of energy. The use of metadielectric material in comparison with the classical one is characterized by values of m>1. Note that in some cases there is an abnormal increase in the coefficient. Originality. Using the representations of vortex electrodynamics, the mechanism of energy interaction between the vortex electric field of an anisotropic metaenvironment and the physical vacuum is proposed. Practical value. A model of the original design of an anisotropic metadielectric converter is proposed. Areas of its practical use in the form of generators of electricity, heat and cold are determined, calculated expressions for their efficiency are in the range η = 0.5 ÷ 0.98, and the cooling temperature can reach the temperature of liquid helium.
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Rocha, Daniel, and Paul Sava. "Elastic least-squares reverse time migration using the energy norm." GEOPHYSICS 83, no. 3 (May 1, 2018): S237—S248. http://dx.doi.org/10.1190/geo2017-0465.1.
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Incorporating anisotropy and elasticity into least-squares migration is an important step toward recovering accurate amplitudes in seismic imaging. An efficient way to extract reflectivity information from anisotropic elastic wavefields exploits properties of the energy norm. We derive linearized modeling and migration operators based on the energy norm to perform anisotropic least-squares reverse time migration (LSRTM) describing subsurface reflectivity and correctly predicting observed data without costly decomposition of wave modes. Imaging operators based on the energy norm have no polarity reversal at normal incidence and remove backscattering artifacts caused by sharp interfaces in the earth model, thus accelerating convergence and generating images of higher quality when compared with images produced by conventional methods. With synthetic and field data experiments, we find that our elastic LSRTM method generates high-quality images that predict the data for arbitrary anisotropy, without the complexity of wave-mode decomposition and with a high convergence rate.
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Motoa-Manzano, Josué, J. Bayron Orjuela-Quintana, Thiago S. Pereira, and César A. Valenzuela-Toledo. "Anisotropic solid dark energy." Physics of the Dark Universe 32 (May 2021): 100806. http://dx.doi.org/10.1016/j.dark.2021.100806.
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Ghezzi, Cristian R. "Anisotropic dark energy stars." Astrophysics and Space Science 333, no. 2 (March 10, 2011): 437–47. http://dx.doi.org/10.1007/s10509-011-0663-4.
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CHAN, R., M. F. A. DA SILVA, and JAIME F. VILLAS DA ROCHA. "ON ANISOTROPIC DARK ENERGY." Modern Physics Letters A 24, no. 14 (May 10, 2009): 1137–46. http://dx.doi.org/10.1142/s0217732309028692.
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Since the discovery of accelerated expansion of the universe, it was necessary to introduce a new component of matter distribution called dark energy. The standard cosmological model considers isotropy of the pressure and assumes an equation of state p = ωρ, relating the pressure p and the energy density ρ. The interval of the parameter ω defines the kind of matter of the universe, related to the fulfillment, or not, of the energy conditions of the fluid. The recent interest in this kind of fluid with anisotropic pressure, in the scenario of the gravitational collapse and star formation, imposes a careful analysis of the energy conditions and the role of the components of the pressure. Here, in this work, we show an example where the classification of dark energy for isotropic pressure fluids is used incorrectly for anisotropic fluids. The correct classification and its consequences are presented.
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Sharif, M., and Shehrbano Ahmed. "Gravitationally decoupled non-static anisotropic spherical solutions." Modern Physics Letters A 36, no. 20 (June 28, 2021): 2150145. http://dx.doi.org/10.1142/s0217732321501455.
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This paper is devoted for the formulation of new anisotropic solutions for non-static spherically symmetric self-gravitating systems through gravitational decoupling technique. Initially, we add a gravitational source in the perfect matter distribution for inducing the effects of anisotropy in the considered model. We then decouple the field equations through minimal geometric deformation approach and derive three new anisotropic solutions. Among these, two anisotropic solutions are evaluated by applying specific constraints on anisotropic source and the third solution is obtained by employing the barotropic equation of state. The physical acceptability and stability of the anisotropic models are investigated through energy conditions and causality condition, respectively. We conclude that all the derived anisotropic solutions are physically viable as well as stable.
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Elliott, Jacob C., Andrea Arguelles, and Julianna Simon. "Histotripsy bubble dynamics in tendon and anisotropic gel phantoms." Journal of the Acoustical Society of America 151, no. 4 (April 2022): A31. http://dx.doi.org/10.1121/10.0010561.
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Collagenous, anisotropic tissues such as tendon have demonstrated resistance to liquefaction by histotripsy, despite the creation, oscillation, and collapse of bubbles verified using B-mode imaging. The objective of this work is to evaluate effects of anisotropy on bubble dynamics in tissue-mimicking hydrogels and compare to anisotropic tissues. Polyacrylamide, fibrin, and collagen hydrogels were fabricated; ex vivo bovine tendons were obtained. Sound speeds were measured in each axial direction to evaluate degree of anisotropy. Hydrogels and tendons were exposed to 1.5-MHz focused ultrasound with 10-ms pulses repeated at 1-Hz with p + =89 MPa, p − = 26 MPa. Cavitation activity was monitored with simultaneous high-speed photography and passive cavitation imaging using a Philips/ATL L7-4 transducer and Vantage® ultrasound system. Violent cavitation activity and fractionation was observed in polyacrylamide, collagen, and fibrin hydrogels with low degrees of anisotropy (<1.2); such behavior is unlike that of tendon. Dehydration of fibrin gels resulted in a 55% reduction in peak cavitation emission energy and a 260% increase in anisotropy compared to standard fibrin formulations. These gels demonstrated similar cavitation energy than tendon (within 4%) but 50% less anisotropy, indicating more hydrogel formulations should be explored to better mimic collagenous, anisotropic tissue. [Work supported by NIH R21EB027886.]
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PETUKHOV, A. V., and A. LIEBSCH. "SURFACE ANISOTROPY OF SECOND HARMONIC GENERATION AT Al(111)." Surface Review and Letters 01, no. 04 (December 1994): 521–23. http://dx.doi.org/10.1142/s0218625x94000576.
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We present results of the first calculation of the surface anisotropic contribution to second harmonic generation for a realistic metal surface. Although the anisotropic second-order response has its origin at the surface, the main contribution to the surface anisotropic parameter ξ has a remarkably large penetration depth. Moreover, the long-range oscillations of the anisotropic nonlinear surface current deep inside aluminum are found. The surface anisotropic secondorder polarizability ξ is in a good qualitative agreement with recent experimental data on clean Al(111) at ħω=1.17 eV. A resonant enhancement of the SHG anisotropy is predicted for ω and 2ω close to 1.5 eV—the energy gap in bulk aluminum along the [100] directions. A significant decrease of the surface anisotropic response in comparison with the isotropic one is found for ω≥1.5 eV.
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Wu, Honghong, Shiyong Huang, Xin Wang, Liping Yang, and Zhigang Yuan. "Influence of Intermittency on the Energy Transfer Rate of Solar Wind Turbulence." Astrophysical Journal Letters 958, no. 2 (November 27, 2023): L28. http://dx.doi.org/10.3847/2041-8213/ad0a68.
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Abstract The intermittency in the solar wind turbulence manifests itself in the anisotropic scaling due to the anisotropic spectral index and the intermittent level based on the extended P model. However, the influence of intermittency on the energy transfer rate remains unclear. Here we apply the partial variance of increments method to identify the intermittency for the magnetic field measurements in the fast solar wind from the Ulysses spacecraft. We distinguish the sampling direction using the angle θ RB between the local magnetic field and radial direction to study the anisotropy. We perform the multiorder structure function analyses and adopt the log-Poisson cascade model to describe the role of intermittency in the cascade process. We find that the anisotropy of the scaling becomes isotropic with a complete removal of intermittency. We compare explicitly the anisotropy of the energy transfer rate before and after removing the intermittency for the same interval for the first time. We find a distinct anisotropy with a cascade enhancement in the direction perpendicular to the local magnetic field. The removal of the intermittency greatly weakens the anisotropy by mainly reducing the perpendicular energy transfer rate. Our findings suggest that the intermittency effectively enhances the energy transfer rate, in particular in the perpendicular direction in the solar wind turbulence.
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Vladimirov, Ivaylo N., and Stefanie Reese. "Prediction of Springback in Unconstrained Bending by a Model for Evolving Elastic and Plastic Anisotropy." Key Engineering Materials 554-557 (June 2013): 2330–37. http://dx.doi.org/10.4028/www.scientific.net/kem.554-557.2330.
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Sheet metals exhibit anisotropic plastic behavior due to the large plastic deformations that occur during the rolling of the sheet and which induce texture and are responsible for the initial anisotropy. There exist various possibilities to introduce plastic anisotropy into the finite element modelling of sheet metal forming. The initial yield anisotropy can be incorporated either through an anisotropic yield surface or directly by means of a crystallographic texture model. Here, one basically differentiates between empirical and phenomenological anisotropic yield function equations, where the anisotropy coefficients can be obtained from mechanical tests, and texture-based models the coefficients of which are directly determined based on experimentally obtained orientation distributions. Another type of anisotropy that can be usually found in anisotropic materials is the elastic anisotropy. In metal plasticity one often considers the effect of elastic anisotropy significantly smaller than the effect of plastic anisotropy. Consequently, elastic isotropic expressions are often used for elastic stored energy functions with anisotropic yield criteria. However, the influence of elastic anisotropy in the elastoplastic behavior can be very important especially during elastic recovery processes during unloading after forming and springback. This research focuses, therefore, on the study of the influence of elastic anisotropy on the amount of springback in bending processes such as e.g. unconstrained bending. We discuss a finite strain material model for evolving elastic and plastic anisotropy combining nonlinear isotropic and kinematic hardening. The evolution of elastic anisotropy is described by representing the Helmholtz free energy as a function of a family of evolving structure tensors. In addition, plastic anisotropy is modelled via the dependence of the yield surface on the same family of structure tensors. Exploiting the dissipation inequality leads to the interesting result that all tensor-valued internal variables are symmetric. Thus, the integration of the evolution equations can be efficiently performed by means of an algorithm that automatically retains the symmetry of the internal variables in every time step. The material model has been implemented as a user material subroutine UMAT into the commercial finite element software ABAQUS/Standard and has been applied to the simulation of springback of unconstrained bending.
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Claudia T.S., Gracella, and Anto Sulaksono. "Anisotropic quark star and the energy conditions." Journal of Physics: Conference Series 2214, no. 1 (February 1, 2022): 012008. http://dx.doi.org/10.1088/1742-6596/2214/1/012008.
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Abstract One of the compact objects that are attractive for investigating their energy conditions is quark stars. The existence of radial and tangential pressure differences in quark stars can cause anisotropic effects on the stars. We focus on and examine the energy conditions of quark stars using the Einstein Field Equation Solution. The energy stability of an anisotropic quark star can be determined by evaluating the profile of the pressure and energy density of the star using the anisotropic EOS as an input. The used equation is the extended MIT Bag Model, which involves the constant B and interaction parameter a 4 and the corresponding parameters of anisotropic part. It is known that parameter a 4 affects the mass distribution of quark stars to be more anisotropic. This anisotropic pressure also affects the energy condition profile of the star. We find the energy state of an anisotropic quark star satisfies the energy state of an ideal fluid.
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MORGADO, W. A. M., M. M. DORIA, G. CARNEIRO, and I. G. DE OLIVEIRA. "VORTEX-LINE PHASE DIAGRAM FOR ANISOTROPIC SUPERCONDUCTORS." International Journal of Modern Physics B 16, no. 09 (April 10, 2002): 1307–26. http://dx.doi.org/10.1142/s0217979202010282.
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The zero-temperature vortex phase diagram for uniaxial anisotropic superconductors placed in an external magnetic field tilted with respect to the axis of anisotropy is studied for parameters typical of BSCCO and YBCO. The exact Gibbs free energy in the London approximation, using a self-energy expression with an anisotropic core cut-off, is minimized numerically, assuming only that the equilibrium vortex state is a vortex-line-lattice with a single vortex line per primitive unit cell. The numerical method is based on simulated annealing and uses a fast convergent series to calculate the energy of interaction between vortex lines. A phase diagram with three distinct phases is reported and the phases are characterized in detail. New results for values of the applied field close to the lower critical field are reported.
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JAIN, PANKAJ, MONINDER S. MODGIL, and JOHN P. RALSTON. "SEARCH FOR GLOBAL METRIC ANISOTROPY IN TYPE 1a SUPERNOVA DATA." Modern Physics Letters A 22, no. 16 (May 30, 2007): 1153–65. http://dx.doi.org/10.1142/s0217732307023389.
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We examine the Type 1a supernova data in order to determine if it shows any signal of large scale anisotropy. The anisotropy is modelled by an extended Gödel metric, which incorporates expansion along with rotation. The model is smoothly connected to the usual FRW type, while expressing anisotropic metric effects depending on certain parameters. We find no significant signal of anisotropy in the data. We obtain bounds on an anisotropic redshift versus magnitude relationship, and accompanying parameters of the Gödel–Obukhov metric.
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Yeung, P. K., James G. Brasseur, and Qunzhen Wang. "Dynamics of direct large-small scale couplings in coherently forced turbulence: concurrent physical- and Fourier-space views." Journal of Fluid Mechanics 283 (January 25, 1995): 43–95. http://dx.doi.org/10.1017/s0022112095002230.
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As discussed in a recent paper by Brasseur & Wei (1994), scale interactions in fully developed turbulence are of two basic types in the Fourier-spectral view. The cascade of energy from large to small scales is embedded within ‘local-to-non-local’ triadic interactions separated in scale by a decade or less. ‘Distant’ triadic interactions between widely disparate scales transfer negligible energy between the largest and smallest scales, but directly modify the structure of the smallest scales in relationship to the structure of the energy-dominated large scales. Whereas cascading interactions tend to isotropize the small scales as energy moves through spectral shells from low to high wavenumbers, distant interactions redistribute energy within spectral shells in a manner that leads to anisotropic redistributions of small-scale energy and phase in response to anisotropic structure in the large scales. To study the role of long-range interactions in small-scale dynamics, Yeung & Brasseur (1991) carried out a numerical experiment in which the marginally distant triads were purposely stimulated through a coherent narrow-band anisotropic forcing at the large scales readily interpretable in both the Fourier- and physical-space views. It was found that, after one eddy turnover time, the smallest scales rapidly became anisotropic as a direct consequence of the marginally distant triadic group in a manner consistent with the distant triadic equations. Because these asymptotic equations apply in the infinite Reynolds number limit, Yeung & Brasseur argued that the observed long-range effects should be applicable also at high Reynolds numbers.We continue the analysis of forced simulations in this study, focusing (i) on the detailed three-dimensional restructuring of the small scales as predicted by the asymptotic triadic equations, and (ii) on the relationship between Fourier- and physical-space evolution during forcing. We show that the three-dimensional restructuring of small-scale energy and vorticity in Fourier space from large-scale forcing is predicted in some detail by the distant triadic equations. We find that during forcing the distant interactions alter small-scale structure in two ways: energy is redistributed anisotropically within high-wavenumber spectral shells, and phase correlations are established at the small scales by the distant interactions. In the numerical experiments, the long-range interactions create two pairs of localized volumes of concentrated energy in three-dimensional Fourier space at high wavenumbers in which the Fourier modes are phase coupled. Each pair of locally phase-correlated volumes of Fourier modes separately corresponds to aligned vortex tubes in physical space in two orthogonal directions. We show that the dynamics of distant interactions in creating small-scale anisotropy may be described in physical space by differential advection and distortion of small-scale vorticity by the coherent large-scale energy-containing eddies, producing anisotropic alignment of small-scale vortex tubes.Scaling arguments indicate a disparity in timescale between distant triadic interactions and energy-cascading local-to-non-local interactions which increases with scale separation. Consequently, the small scales respond to forcing initially through the distant interactions. However, as energy cascades from the large-scale to the small-scale Fourier modes, the stimulated distant interactions become embedded within a sea of local-to-non-local energy cascading interactions which reduce (but do not eliminate) small-scale anisotropy at later times. We find that whereas the small-scale structure is still anisotropic at these later times, the second-order velocity moment tensor is insensitive to this anisotropy. Third-order moments, on the other hand, do detect the anisotropy. We conclude that whereas a single statistical measure of anisotropy can be used to indicate the presence of anisotropy, a null result in that measure does not necessarily imply that the signal is isotropic. The results indicate that non-equilibrium non-stationary turbulence is particularly sensitive to long-range interactions and deviations from local isotropy.
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Du, Senbei, Hui Li, Xiangrong Fu, and Zhaoming Gan. "Anisotropic Energy Transfer and Conversion in Magnetized Compressible Turbulence." Astrophysical Journal 948, no. 2 (May 1, 2023): 72. http://dx.doi.org/10.3847/1538-4357/acc5e9.
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Abstract We present a spatial filtering (or coarse-graining) analysis on 3D magnetized magnetohydrodynamic (MHD) turbulence simulations. The filtered compressible MHD formulae show transfer of kinetic and magnetic energies from large to small scales, as well as energy conversion between kinetic, magnetic, and thermal energies. The anisotropic filtering enables separate analyses of the energy flows perpendicular and parallel to the global mean magnetic field. Anisotropy in energy cascade is demonstrated by the larger perpendicular energy cascade rate and also the larger perpendicular wavenumbers associated with the peak energy transfer rate. We also find that the “inertial range” along the parallel (perpendicular) direction in the anisotropic energy cascade formulation is no longer strictly dissipation-free, because it includes the dissipation in the perpendicular (parallel) direction. A change in the driving force (kinetic only versus kinetic and magnetic) affects the energy conversion between kinetic and magnetic energies. While the compressibility of the driving force changes the partition of different channels of energy transfer and conversion, and also increases the total energy transfer rate, the global energy flow remains unaffected by compressibility qualitatively. Our analysis can be applied to multispacecraft observations of turbulence in the solar wind or a planetary magnetosphere.
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Nowicki, Michał, Roman Szewczyk, and Paweł Nowak. "Experimental Verification of Isotropic and Anisotropic Anhysteretic Magnetization Models." Materials 12, no. 9 (May 11, 2019): 1549. http://dx.doi.org/10.3390/ma12091549.
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The anhysteretic magnetization curve is the key element of modeling magnetic hysteresis loops. Despite the fact that it is intensively exploited, known models of anhysteretic curve have not been verified experimentally. This paper presents the validation of four anhysteretic curve models considering four different materials, including isotropic, such as Mn-Zn soft ferrite, as well as anisotropic amorphous and nanocrystalline alloys. The presented results indicate that only the model that considers anisotropic energy is valid for a wide set of modern magnetic materials. The most suitable of the verified models is the anisotropic extension function-based model, which considers uniaxial anisotropy.
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Ziaziulia P. A. and Malevich V. L. "Anisotropic photoconductivity excited in a semiconductor by two-frequency optical radiation." Technical Physics Letters 48, no. 11 (2022): 17. http://dx.doi.org/10.21883/tpl.2022.11.54881.19313.
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Anisotropic photoconductivity at a difference frequency, excited in a semiconductor by linearly polarized two-frequency optical radiation, is considered. The anisotropy of the photoconductivity arises due to the optical alignment of photoexcited electrons momenta and dependence of their effective mass and momentum relaxation time on energy. It is shown that the contribution of the anisotropic photoconductivity to the photocurrent at the difference frequency lying in the terahertz frequency range can be comparable with that of the isotropic photoconductivity. This effect can manifest itself in photoconductive antennae, devices used to generate terahertz radiation. Keywords: Anisotropic photoconductivity, photomixing, terahertz radiation, photoconductive antenna.
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Sharif, Muhammad, and Muhammad Gul. "Dynamics of Anisotropic Cylindrical Collapse in Energy-Momentum Squared Gravity." Physical Sciences Forum 2, no. 1 (March 19, 2021): 40. http://dx.doi.org/10.3390/ecu2021-09513.
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This paper deals with the dynamics of cylindrical collapse with anisotropic matter configuration in the context of energy-momentum squared gravity. This covariant generalization of general relativity allows the presence of T_abT^ab in the action of functional theory. Consequently, the relevant field equations are different from general relativity only in the presence of matter sources. In this theory, there is a maximum energy density and a minimum scale factor of the early universe. This means that there is a bounce at early times which avoids the presence of an early-time singularity. Moreover, this theory possesses a true sequence of cosmological eras. However, the cosmological constant does not play an important role in the early times and becomes important only after the matter-dominated era. In this theory, the “repulsive” nature of the cosmological constant plays a crucial role at early times in resolving the singularity. We formulate the corresponding field equations as well as junction conditions. We construct dynamical equations through the Misner–Sharp technique and examine the impact of energy-momentum squared gravity on the collapse rate. We develop a relation among fluid parameters, correction terms and Weyl scalar and examine the effects of anisotropy, effective matter variables and correction terms on the collapsing phenomenon. Due to the presence of anisotropic pressure, spacetime is no longer considered to be conformally flat. To obtain conformally flat spacetime, we neglect the impact of anisotropy and assume the isotropic matter distribution which yields homogeneity of the energy density and conformally flat spacetime. The hydrodynamical force determines the stability of the system and prevents the collapsing as well as expanding process for the constant energy-momentum squared gravity model. We conclude that positive correction terms and anisotropy provide the anti-gravitational behavior leading to the stability of self-gravitating objects and hence prevent the collapsing process.
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Jin, Juan, Jiandong Liu, Weidong Jiang, Wei Cheng, and Xiaowen Zhang. "Evolution of the Anisotropic Thermal Conductivity of Oil Shale with Temperature and Its Relationship with Anisotropic Pore Structure Evolution." Energies 15, no. 21 (October 28, 2022): 8021. http://dx.doi.org/10.3390/en15218021.
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Due to its sedimentary characteristics and natural fractures, oil shale shows anisotropy in heat transfer characteristics. Moreover, the anisotropic thermal conductivity will change with the temperature. This change in the anisotropic thermal conductivity coefficient affects the temperature field distribution and heating efficiency during the in situ electric heating pyrolysis of oil shale. Therefore, it is very important to study the evolution of the anisotropy thermal conductivity coefficient of oil shale with temperature. In this study, the variation of weight loss and the specific heat of an oil shale with temperature is investigated using a differential scanning calorimeter. The variation of the anisotropic pore and fracture structure of the oil shale with temperature is studied through CT scanning technology. The variation of the anisotropic thermal conductivity with temperature is studied through the hot disk method. Finally, the relationship between the change in the anisotropic heat conductivity of the oil shale and the evolution of the anisotropic pore and fracture structure is discussed. The results show that the mass loss of oil shale mainly occurs after 400 °C. The thermal conductivity of both perpendicular and parallel to bedding directions decreases linearly with the increase of temperature. The research results of this study can serve as an important reference in the study of the in situ pyrolysis of oil shale.
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Bhatti, Muhammad Zaeem-ul-Haq, M. Sharif, Z. Yousaf, and M. Ilyas. "Role of f(G,T) gravity on the evolution of relativistic stars." International Journal of Modern Physics D 27, no. 04 (March 2018): 1850044. http://dx.doi.org/10.1142/s021827181850044x.
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The aim of this paper is to explore some physically viable aspects for the possible emergence of compact stars in [Formula: see text] theory of gravity with some particular models, where [Formula: see text] and [Formula: see text] are Gauss–Bonnet invariant and trace of stress–energy tensor, respectively. We present basic formalism of this modified theory in the presence of anisotropic source. We explore some realistic aspects using the energy conditions with physical parameters. Three distinct known star models namely, [Formula: see text] [Formula: see text] and [Formula: see text], are used for this systematic investigation. The physical behavior of anisotropic stresses, energy density, energy conditions, measure of anisotropy and stability of compact stars are discussed through plots. We conclude that compactness at the core of a star model increases and energy conditions hold.
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Ts. ADZHEMYAN, L., M. HNATICH, D. HORVÁTH, and M. STEHLIK. "INFRARED PROPERTIES OF AN ANISOTROPICALLY DRIVEN MHD TURBULENCE." International Journal of Modern Physics B 09, no. 26 (November 30, 1995): 3401–19. http://dx.doi.org/10.1142/s0217979295001348.
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The model of anisotropic magnetohydrodynamic turbulence is investigated by the renormalization group approach. It is demonstrated that the inclusion of small anisotropy into the model leads to increasing of the Lorentz force influence. This effect is especially important in the kinetic regime in which the Kolmogorov spectrum of pulsation energy takes place. It is quite different from the isotropic case where the Lorentz force has no influence on large scale properties of magnetohydrodynamic turbulence, even if the external injection of energy is very intensive. Therefore, the magnetic field behaves like a passive admixture. In the anisotropic MHD, nonlinear interactions generate modified "anisotropic Lorentz forces". These forces are relevant for certain values of dimensionless parameter a, which describes the spectrum of the magnetic noise, and the magnetic field ceases to be a passive admixture. In particular, this statement is true for the most realistic value of a = 1 when the random magnetic force amplitude has the same dimensionality as the energy injection rate.
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Badreddine, Houssem, and Khemais Saanouni. "Advanced Anisotropic Damage Model Fully Coupled with Anisotropic Plasticity." Applied Mechanics and Materials 784 (August 2015): 153–60. http://dx.doi.org/10.4028/www.scientific.net/amm.784.153.
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In this work, a thermodynamically-consistent framework is used to formulate a non-associative finite strain anisotropic elastoplastic model fully coupled with anisotropic ductile damage. The finite strain assumption is considered using specific large strains kinematics based on multiplicative decomposition of the total transformation gradient and assuming a small elastic strains. The objectivity principle fulfillment is assumed using the well-known rotating frame formulation. The effective variables are defined to introduce the effect of the anisotropic damage on the other variables through the total energy equivalence assumption. The non-associative plasticity framework, for which equivalent stresses in yield function and in plastic potential are separately defined, allows better plastic anisotropy description. The evolution equations for overall dissipative phenomena are deduced from the generalized normality rule applied to the plastic potential while the consistency condition is still applied to the yield function. Applications are made to an RVE with generic material parameters by considering non-proportional loading paths. For each loading path the effect of the anisotropic plasticity on the damage evolution is studied in the context of finite strains.
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Matsumura, Takashi, Shoichi Tamura, and Pedro José Arrazola. "Cutting Force Prediction in Drilling of Anisotropic Materials." Key Engineering Materials 504-506 (February 2012): 1365–70. http://dx.doi.org/10.4028/www.scientific.net/kem.504-506.1365.
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The paper presents a predictive cutting force model in drilling of anisotropic materials. Three dimensional chip flow in drilling is interpreted as a piling up of the orthogonal cuttings in the planes containing the cutting velocities and the chip flow velocities. The cutting models in the chip flow are determined to calculate the cutting energy using the orthogonal cutting data. Then, the chip flow direction is determined to minimize the cutting energy. The cutting force can be predicted in the determined chip flow model. The cutting force with anisotropy in the material is modeled as the change in the shear stress on the shear plane. The shear stress changes with the rotation angle of the cutter. The cutting force prediction is verified in drilling of a titanium alloy. The anisotropic parameters are identified to minimize the model error between the measured and the predicted cutting forces. The periodical oscillation of the cutting force is also predicted by anisotropy in the shear stress.
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Yin, Peng-Fei, Sheng-Qi Yang, and Pathegama Gamage Ranjith. "Anisotropic Mechanical Behaviors of Shale Rock and Their Relation to Hydraulic Fracturing in a Shale Reservoir: A Review." Energies 17, no. 7 (April 7, 2024): 1761. http://dx.doi.org/10.3390/en17071761.
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Shale gas is an important supplement to the supply of natural gas resources and plays an important role on the world’s energy stage. The efficient implementation of hydraulic fracturing is the key issue in the exploration and exploitation of shale gas. The existence of bedding structure results in a distinct anisotropy of shale rock formation. The anisotropic behaviors of shale rock have important impacts on wellbore stability, hydraulic fracture propagation, and the formation of complex fracture networks. This paper briefly reviews previous work on the anisotropic mechanical properties of shale rock and their relation to hydraulic fracturing in shale reservoirs. In this paper, the research status of work addressing the lithological characteristics of shale rock is summarized first, particularly work considering the mineral constituent, which determines its physical and mechanical behavior in essence. Then the anisotropic physical and mechanical properties of shale specimens, including ultrasonic anisotropy, mechanical behavior under uniaxial and triaxial compression tests, and tensile property under the Brazilian test, are summarized, and the state of the literature on fracture toughness anisotropy is discussed. The concerns of anisotropic mechanical behavior under laboratory tests are emphasized in this paper, particularly the evaluation of shale brittleness based on mechanical characteristics, which is discussed in detail. Finally, further concerns such as the effects of bedding plane on hydraulic fracturing failure strength, crack propagation, and failure pattern are also drawn out. This review study will provide a better understanding of current research findings on the anisotropic mechanical properties of shale rock, which can provide insight into the shale anisotropy related to the fracture propagation of hydraulic fracturing in shale reservoirs.
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Li, Xing-Wang, Bing Zhou, Chao-Ying Bai, and Jian-Lu Wu. "Seismic complex ray tracing in 2D/3D viscoelastic anisotropic media by a modified shortest-path method." GEOPHYSICS 85, no. 6 (November 1, 2020): T331—T342. http://dx.doi.org/10.1190/geo2020-0113.1.
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In a viscoelastic anisotropic medium, velocity anisotropy and wave energy attenuation occur and are often observed in seismic data applications. Numerical investigation of seismic wave propagation in complex viscoelastic anisotropic media is very helpful in understanding seismic data and reconstructing subsurface structures. Seismic ray tracing is an effective means to study the propagation characteristics of high-frequency seismic waves. Unfortunately, most seismic ray-tracing methods and traveltime tomographic inversion algorithms only deal with elastic media and ignore the effect of viscoelasticity on the seismic raypath. We have developed a method to find the complex ray velocity that gives the seismic ray speed and attenuation in an arbitrary viscoelastic anisotropic medium, and we incorporate them with the modified shortest-path method to determine the raypath and calculate the real and imaginary traveltime (wave energy attenuation) simultaneously. We determine that the complex ray-tracing method is applicable to arbitrary 2D/3D viscoelastic anisotropic media in a complex geologic model and the computational errors of the real and imaginary traveltime are less than 0.36% and 0.59%, respectively. The numerical examples verify that the new method is an effective and powerful tool for accomplishing seismic complex ray tracing in heterogeneous viscoelastic anisotropic media.
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Vidyasagar, A., S. Krödel, and D. M. Kochmann. "Microstructural patterns with tunable mechanical anisotropy obtained by simulating anisotropic spinodal decomposition." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2218 (October 2018): 20180535. http://dx.doi.org/10.1098/rspa.2018.0535.
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The generation of mechanical metamaterials with tailored effective properties through carefully engineered microstructures requires avenues to predict optimal microstructural architectures. Phase separation in heterogeneous systems naturally produces complex microstructural patterns whose effective response depends on the underlying process of spinodal decomposition. During this process, anisotropy may arise due to advection, diffusive chemical gradients or crystallographic interface energy, leading to anisotropic patterns with strongly directional effective properties. We explore the link between anisotropic surface energies during spinodal decomposition, the resulting microstructures and, ultimately, the anisotropic elastic moduli of the resulting medium. We simulate the formation of anisotropic patterns within representative volume elements, using recently developed stabilized spectral techniques that circumvent further regularization, and present a powerful alternative to current numerical techniques. The interface morphology of representative phase-separated microstructures is shown to strongly depend on surface anisotropy. The effective elastic moduli of the thus-obtained porous media are identified by periodic homogenization, and directionality is demonstrated through elastic surfaces. Our approach not only improves upon numerical tools to simulate phase separation; it also offers an avenue to generate tailored microstructures with tunable resulting elastic anisotropy.
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Samec, Pierre, and J. P. Blangy. "Viscoelastic attenuation, anisotropy, and AVO." GEOPHYSICS 57, no. 3 (March 1992): 441–50. http://dx.doi.org/10.1190/1.1443258.
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The classical interpretation relating Amplitude Versus Offset (AVO) to Poisson’s ratio and other petrophysical properties is based on the assumptions of elasticity and isotropy. We extend this interpretation to a layered medium with anisotropic and/or viscoelastic properties, using a Fourier Pseudo‐Spectral method to solve the wave equation. Both viscoelasticity and anisotropy are key factors for the quantitative interpretation of AVO trends, because they contribute to the seismic energy partition at geological interfaces (the reflection coefficients), and because they continually induce propagation effects. We show that: 1) Reflection coefficients at an interface are strongly dependent on the elastic anisotropy of both the overlying and the underlying media. The AVO effect is further complicated by materials with viscoelastic properties. 2) Propagation effects are due to elastic anisotropic energy focusing and viscoelastic dissipation that distort the energy and phase distribution of the incident and reflected wavefronts. These two phenomena can be of the same order of magnitude as variations in reflection amplitudes with offset and can make it difficult to recover reflection coefficients along an interface from seismic data. In theory, they make the amplitude determination of a seismic event somewhat dependent on wavelet phase changes that occur continually as the wavefront propagates. In practice, they create anisotropic radiation patterns and differentially focus the seismic energy distribution along the wavefront. For these reasons, all detailed reservoir characterizations based on modeling and interpretation work should attempt to account for anisotropy and viscoelastic attenuation; this is not an easy task in the real world because of the difficulty in prescribing appropriate physical parameters.
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KAYA, TUNCER. "ELECTRONIC TRANSPORT IN ANISOTROPIC DISORDERED QUANTUM WIRE." International Journal of Modern Physics B 22, no. 06 (March 10, 2008): 683–96. http://dx.doi.org/10.1142/s0217979208038831.
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We have investigated the transport properties of anisotropic disordered quantum wire by the method of energy level statistics and transfer matrix method. We have found a general average conductance relation in terms of the anisotropy parameter t, disorder strength W, and the cross-sectional area, A, of the wire. From the available numerical data, we have also shown that the anisotropic correlation length ξt can be related to the isotropic correlation length ξ as ξt ≃ t2ξ, for L ≃ A and ξt ≃ tξ, for L ≫ A. Here, L is the length of the wire. In addition, anisotropic dependence of conductance fluctuation and conductance distribution have been studied to a certain extent.
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KOISO, Miyuki. "Geometry of Anisotropic Surface Energy." Proceedings of Mechanical Engineering Congress, Japan 2016 (2016): jikiin04. http://dx.doi.org/10.1299/jsmemecj.2016.jikiin04.
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Mota, D. F., J. R. Kristiansen, T. Koivisto, and N. E. Groeneboom. "Constraining dark energy anisotropic stress." Monthly Notices of the Royal Astronomical Society 382, no. 2 (December 1, 2007): 793–800. http://dx.doi.org/10.1111/j.1365-2966.2007.12413.x.
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Cheng, Qiang, and Tie Jun Cui. "Energy localization using anisotropic metamaterials." Physics Letters A 367, no. 4-5 (July 2007): 259–62. http://dx.doi.org/10.1016/j.physleta.2007.03.033.
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Keller, J., K. Scharnberg, and H. Monien. "Free energy of anisotropic superconductors." Physica C: Superconductivity 152, no. 4 (June 1988): 302–14. http://dx.doi.org/10.1016/0921-4534(88)90088-3.
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Beltrán Almeida, Juan P., Alejandro Guarnizo, Ryotaro Kase, Shinji Tsujikawa, and César A. Valenzuela-Toledo. "Anisotropic 2-form dark energy." Physics Letters B 793 (June 2019): 396–404. http://dx.doi.org/10.1016/j.physletb.2019.05.008.
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Das, Kanika, and Nawsad Ali. "Anisotropic charged dark energy star." Astrophysics and Space Science 356, no. 1 (December 5, 2014): 57–66. http://dx.doi.org/10.1007/s10509-014-2184-4.
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Sharif, M., and Sobia Sadiq. "Study of tilted anisotropic polytropes." International Journal of Modern Physics D 28, no. 03 (February 2019): 1950051. http://dx.doi.org/10.1142/s0218271819500512.
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The purpose of this paper is to construct spherically symmetric models for anisotropic matter configurations by imposing conformally flat conditions. This work is done for a relatively moving observer with matter using two types of polytropic equations of state. We evaluate the corresponding conservation equation, mass equation as well as energy constraints for both choices of equations of state. The conformal flatness is employed to find a specific form of anisotropy which aids study to spherical polytropic configurations. It is found that the first model satisfies all the energy conditions while the second model does not meet the dominant energy bound. It is also found that both models remain stable throughout the evolution.
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Grøn, Øyvind G. "Anisotropic Generalization of the ΛCDM Universe Model with Application to the Hubble Tension." Symmetry 16, no. 5 (May 5, 2024): 564. http://dx.doi.org/10.3390/sym16050564.
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I deduce an exact and analytic Bianchi type I solution of Einstein’s field equations, which generalizes the isotropic ΛCDM universe model to a corresponding model with anisotropic expansion. The main point of the article is to present the anisotropic generalization of the ΛCDM universe model in a way suitable for investigating how anisotropic expansion modifies observable properties of the ΛCDM universe model. Although such generalizations of the isotropic ΛCDM universe model have been considered earlier, they have never been presented in this form before. Several physical properties of the model are pointed out and compared with properties of special cases, such as the isotropic ΛCDM universe model. The solution is then used to investigate the Hubble tension. It has recently been suggested that the cosmic large-scale anisotropy may solve the Hubble tension. I consider those earlier suggestions and find that the formulae of these papers lead to the result that the anisotropy of the cosmic expansion is too small to solve the Hubble tension. Then, I investigate the problem in a new way, using the exact solution of the field equations. This gives the result that the cosmic expansion anisotropy is still too small to solve the Hubble tension in the general Bianchi type I universe with dust and LIVE (Lorentz Invariant Vacuum Energy with a constant energy density, which is represented by the cosmological constant) and anisotropic expansion in all three directions—even if one neglects the constraints coming from the requirement that the anisotropy should be sufficiently small so that it does not have any significant effect upon the results coming from the calculations of the comic nucleosynthesis during the first ten minutes of the universe. If this constraint is taken into account, the cosmic expansion anisotropy is much too small to solve the Hubble tension.
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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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Xue, Yibin, and Jianmin Qu. "On the Energy Release Rate of Elliptical Cracks in Anisotropic Elastic Media." Journal of Mechanics 19, no. 1 (March 2003): 233–39. http://dx.doi.org/10.1017/s1727719100004263.
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ABSTRACTThis brief note discusses some issues related to the calculation of energy release rate for elliptical cracks in anisotropic solids. By using the Stroh formalism, analytical expressions of the energy release rate are obtained for elliptical cracks in an unbounded anisotropic solid. Because of material anisotropy and geometric asymmetry of the crack, the local energy release rate varies along the crack front. The average energy release rate can be obtained by integrating the local energy release rate over the entire crack front. On the other hand, the total work done by the crack-surface traction on the entire crack opening displacement can be easily evaluated once the crack opening displacement is known. It is shown that the average energy release rate is equal to the rate of change per unit crack area increment of the work done by the external load on the crack opening displacement.
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Ta, Na, Muhammad Umer Bilal, Ines Häusler, Alaukik Saxena, Yueh-Yu Lin, Felix Schleifer, Michael Fleck, Uwe Glatzel, Birgit Skrotzki, and Reza Darvishi Kamachali. "Simulation of the θ′ Precipitation Process with Interfacial Anisotropy Effects in Al-Cu Alloys." Materials 14, no. 5 (March 8, 2021): 1280. http://dx.doi.org/10.3390/ma14051280.
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The effects of anisotropic interfacial properties and heterogeneous elasticity on the growth and ripening of plate-like θ′-phase (Al2Cu) in Al-1.69 at.% Cu alloy are studied. Multi-phase-field simulations are conducted and discussed in comparison with aging experiments. The precipitate/matrix interface is considered to be anisotropic in terms of its energy and mobility. We find that the additional incorporation of an anisotropic interfacial mobility in conjunction with the elastic anisotropy result in substantially larger aspect ratios of the precipitates closer to the experimental observations. The anisotropy of the interfacial energy shows comparably small effect on the precipitate’s aspect ratio but changes the interface’s shape at the rim. The effect of the chemo-mechanical coupling, i.e., the composition dependence of the elastic constants, is studied as well. We show that the inverse ripening phenomenon, recently evidenced for δ’ precipitates in Al-Li alloys (Park et al. Sci. Rep. 2019, 9, 3981), does not establish for the θ′ precipitates. This is because of the anisotropic stress fields built around the θ′ precipitates, stemming from the precipitate’s shape and the interaction among different variants of the θ′ precipitate, that disturb the chemo-mechanical effects. These results show that the chemo-mechanical effects on the precipitation ripening strongly depend on the degree of sphericity and elastic isotropy of the precipitate and matrix phases.