Journal articles: 'Anisotroping'

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Ben Slimane, Mourad. "Anisotropic Two-Microlocal Spaces and Regularity." Journal of Function Spaces 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/505796.

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We defineD-u-anisotropic two-microlocal spaces by decay conditions on anisotropic wavelet coefficients on anyD-u-anisotropic wavelet basis ofL2(Rd). We prove that these spaces allow the characterizing of pointwise anisotropic Hölder regularity. We also prove an anisotropic wavelet criterion for anisotropic uniform regularity. We finally prove that both this criterion and anisotropicD-u-two-microlocal spaces are independent of the chosen anisotropicD-u-orthonormal wavelet basis.

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Xiong, Zonghou. "Electromagnetic fields of electric dipoles embedded in a stratified anisotropic earth." GEOPHYSICS 54, no. 12 (December 1989): 1643–46. http://dx.doi.org/10.1190/1.1442633.

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The anisotropy of electrical conductivity in earth formations may be caused by crystal anisotropies of minerals, as well as by minilayers which occur frequently in sedimentary environments. The effects of anisotropy on the propagation of electromagnetic (EM) fields have been studied by many geophysicists. For instance, Kong (1972) and Wait (1981) solved the EM propagation problem for vertically anisotropic layered earths; O’Brien and Morrison (1967), for a horizontally anisotropic multilayer half‐space; Chetayev (1960), as well as Reddy and Rankin (1971), for media of dipping anisotropies; and Al’tgauzen (1969), for more complicated anisotropic media with a tensor dielectric constant of five components.

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Badreddine, Houssem, and Khemais Saanouni. "On the full coupling of plastic anisotropy and anisotropic ductile damage under finite strains." International Journal of Damage Mechanics 26, no. 7 (March 3, 2016): 1080–123. http://dx.doi.org/10.1177/1056789516635729.

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In this work, thermodynamically consistent, non-associative and fully anisotropic elastoplastic constitutive equations strongly coupled with ductile anisotropic damage developed in previous work are used to study the responses of the proposed model under various simple and complex loading paths. First, the complete set of the fully coupled non-associative constitutive equations based on the rotated frame formulation (RFF) for finite strains is summarized and shortly discussed. Then, the effect of the rotating frame in the model response is analyzed on the light of typical loading paths. The influence of the induced plastic anisotropies on the evolution of the anisotropic ductile damage is investigated. Finally, the responses of the model for non-proportional loading paths are studied, compared and discussed with respect to the initial and induced anisotropies of the plastic flow and the ductile damage evolution as well as with respect to the rotating frame choice.

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Remazeilles, Mathieu, Andrea Ravenni, and Jens Chluba. "Leverage on small-scale primordial non-Gaussianity through cross-correlations between CMB E-mode and μ-distortion anisotropies." Monthly Notices of the Royal Astronomical Society 512, no. 1 (February 24, 2022): 455–70. http://dx.doi.org/10.1093/mnras/stac519.

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ABSTRACT Multifield inflation models and non-Bunch–Davies vacuum initial conditions both predict sizeable non-Gaussian primordial perturbations and anisotropic μ-type spectral distortions of the cosmic microwave background (CMB) blackbody. While CMB anisotropies allow us to probe non-Gaussianity at wavenumbers $k\simeq 0.05\, {\rm Mpc^{-1}}$, μ-distortion anisotropies are related to non-Gaussianity of primordial perturbation modes with much larger wavenumbers, $k\simeq 740\, {\rm Mpc^{-1}}$. Through cross-correlations between CMB and μ-distortion anisotropies, one can therefore shed light on the aforementioned inflation models. We investigate the ability of a future CMB satellite imager like LiteBIRD to measure μT and μE cross-power spectra between anisotropic μ-distortions and CMB temperature and E-mode polarization anisotropies in the presence of foregrounds, and derive LiteBIRD forecasts on ${f_{\rm NL}^\mu (k\simeq 740\, {\rm Mpc^{-1}})}$. We show that μE cross-correlations with CMB polarization provide more constraining power on $f_{\rm NL}^\mu$ than μT cross-correlations in the presence of foregrounds, and the joint combination of μT and μE observables adds further leverage to the detection of small-scale primordial non-Gaussianity. For multifield inflation, we find that LiteBIRD would detect ${f_{\rm NL}^\mu }=4500$ at 5σ significance after foreground removal, and achieve a minimum error of ${\sigma (f_{\rm NL}^\mu =0) \simeq 800}$ at 68 per cent CL by combining CMB temperature and polarization. Due to the huge dynamic range of wavenumbers between CMB and μ-distortion anisotropies, such large $f^\mu _{\rm NL}$ values would still be consistent with current CMB constraints in the case of very mild scale dependence of primordial non-Gaussianity. Anisotropic spectral distortions thus provide a new path, complementary to CMB B-modes, to probe inflation with LiteBIRD.

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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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CLAUSEL, M., and B. VEDEL. "EXPLICIT CONSTRUCTION OF OPERATOR SCALING GAUSSIAN RANDOM FIELDS." Fractals 19, no. 01 (March 2011): 101–11. http://dx.doi.org/10.1142/s0218348x11005208.

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We propose an explicit way to generate a large class of Operator scaling Gaussian random fields (OSGRF). Such fields are anisotropic generalizations of self-similar fields. More specifically, we are able to construct any Gaussian field belonging to this class with given Hurst index and exponent. Our construction provides — for simulations of texture as well as for detection of anisotropies in an image — a large class of models with controlled anisotropic geometries and structures.

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Castro, Caio Leandro Perdigão, José Jadsom Sampaio de Figueiredo, and Isadora Augusta Soares de Macedo. "COMPARING TWO APPROACHES ON THE ESTIMATIVE ANISOTROPIC PARAMETERSFROM WELL LOGS: AN APPLICATION ON THE NORNE FIELD DATASET." Revista Brasileira de Geofísica 36, no. 4 (December 21, 2018): 1. http://dx.doi.org/10.22564/rbgf.v36i4.1971.

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ABSTRACT. Estimating the elastic properties of the rocks in the subsurface is a task with many challenges. The main goal of this work is to estimate the Thomsen anisotropic parameters from the inversion of elastic stiffness coefficients using data from five wells of the Norne Field, located at Norway. We compare the results of these parameters with the Backus average, using Li’s empirical method. Further, aspect ratio and crack density are calculated from the results of the elastic stiffness coefficients. It is considered a transversely isotropic medium. The results from the two methods showed similarities in estimating anisotropic parameters, aspect ratio and fracture density. The anisotropy of the study area is weak with some regions with moderate anisotropy. Some patterns suggest the possibility of calculating the anisotropic parameters for the adjacent wells and interpolate values for use in seismic processing.Keywords: Transversally isotropic medium, well logs, Thomsen parameters, Backus AverageRESUMO. Estimar as propriedades elásticas das rochas em subsurperfície é uma tarefa com muitos desafios. O principal objetivo deste trabalho é estimar os parâmetros de anisotropia de Thomsen a partir da inversão dos coeficientes de rigidez elástica, utilizando dados de cinco diferentes poços do campo de Norne, localizado na Noruega. Comparamos os resultados obtidos para esses parâmetros com a média de Backus, usando o método empírico de Li. Em seguida, a razão de aspecto e a densidade de fratura foram calculadas a partir dos resultados dos coeficientes de rigidez elástica. O meio transversalmente isotrópico é considerado neste trabalho. Os resultados obtidos a partir dos dois métodos mostraram similaridades na estimativa dos parâmetros de anisotropia, razão de aspecto e densidade de fratura. A anisotropia da área de estudo é fraca com algumas regiões de anisotropia moderada. Alguns padrões encontrados sugerem a possibilidade de calcular os parâmetros de anisotropia para os poços vizinhos e interpolá-los para uso futuro no processamento sísmico.Palavras-chave: Meios transversalmente isotrópicos, perfis de poços, parâmetros de Thomsen, média de Backus 1UFPA,

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Heiba, Z. K., and Karimat El-Sayed. "Structural and anisotropic thermal expansion correlation of Li2ZrO3at different temperatures." Journal of Applied Crystallography 35, no. 5 (September 18, 2002): 634–36. http://dx.doi.org/10.1107/s0021889802011214.

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Structural and thermal expansion studies of Li2ZrO3were carried out by recording X-ray powder diffraction patterns at five temperatures, 82, 198, 300, 423 and 573 K. The Rietveld refinement method was used for the analysis. There were large anisotropic changes in the lattice parameters as a function of temperature, slight changes in the fractional coordinates of the different atoms, and anisotropic changes in the interatomic distances between the different cations. The correlation of these anisotropies with the structure is considered.

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Hood, J. A. "A simple method for decomposing fracture‐induced anisotropy." GEOPHYSICS 56, no. 8 (August 1991): 1275–79. http://dx.doi.org/10.1190/1.1443149.

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A heterogeneous mixture of isotropic elements may appear homogeneous and anisotropic when the scale of its fabric is smaller than the seismic wavelengths that measure it (Backus, 1962). These fabrics can result from thin layering or from oriented microcracks or fractures. In many situations the anisotropy is quite complex, resulting, for example, from fractures in previously anisotropic media. Since these anisotropies combine, the effect of each must be separated to permit the study of either the fractures or the preexisting anisotropy.

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Gudelev, V. G., L. P. Svirina, and Yu P. Zhurik. "Polarization Dynamical Phenomena in Gas Lasers with Weakly Anisotropic Cavities." International Journal of Bifurcation and Chaos 08, no. 05 (May 1998): 1025–32. http://dx.doi.org/10.1142/s0218127498000838.

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This paper presents the results of theoretical and experimental studies of a series of polarization dynamical phenomena in a single-mode standing-wave class-A laser with weakly anisotropic cavity at elliptically polarized eigenstates. The existence of spontaneous pulsations caused by the competition of active medium and empty cavity anisotropies is also proved.

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Yuan, Xiao, P. S. Riseborough, Eleonir Calegari, and Sergio Magalhaes. "Enhanced Spin Orbit Interaction in Actinides." Journal of Physics: Conference Series 2164, no. 1 (March 1, 2022): 012059. http://dx.doi.org/10.1088/1742-6596/2164/1/012059.

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Abstract We investigate the effect of many-body interactions on the spin-orbit coupling of anisotropic metals. We use the Underscreened Anderson Lattice Model that was proposed to describe actinide compounds. The Coulomb interactions induce off-diagonal correlations that enhance the components of the spin-orbit coupling. Modest values of the Coulomb interaction U can significantly enhance the spin-orbit coupling and effect the electronic spectrum. The enhancements are most pronounced for systems that are on the verge of magnetic instabilities. The enhancement is anisotropic in crystals with non-cubic symmetries and can lead to giant magnetic anisotropies in paramagnetic states.

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Pranowo, Waskito, and Sonny Winardhi. "Application of Velocity Variation with Angle (VVA) Method on an Anisotropic Model with Thomsen Delta Anisotropy Parameters." Jurnal Geofisika 16, no. 2 (September 19, 2018): 6. http://dx.doi.org/10.36435/jgf.v16i2.371.

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Anisotropic properties will influence seismic propagation, for example it will affect wave velocity. One of well-known anisotropi equation for Transversaly Isotropic media is weak anisotropy with Thomsen's notation. Supriyono [2011] tried to estimate all of these variables by using velocity variation with angle (VVA) attribute. This research uses synthetic data, which is CMP Gather to know limitations of VVA attribute, to identify the error values, and to determine the best indicator of anisotropic eect. This research also uses another analysis method, which is grid search inversion to estimate VP0. From this research, Both VVA and grid search invesion still produce signcant error. The effects which will appear because of anisotropic property's presence are hockey-stick and over NMO-stretching.

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López-Corredoira, Martín. "Wrinkles in the Galaxy." Symposium - International Astronomical Union 201 (2005): 482–83. http://dx.doi.org/10.1017/s007418090021677x.

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New calculations of the Galactic contribution to microwave background radiation anisotropies are carried out and a probable Galactic predominance over cosmological signals at large scales is explored for these frequencies. When we take into account a frequency-dependent contrast of molecular clouds with respect to the Galactic background of the diffuse interstellar medium, the anisotropic amplitude produced by Galactic dust is of the same order as that of the data from the observations. The frequency independence of anisotropies in the microwave range is not necessarily an argument against the Galactic predominance if we take into account an aditional rotational dust emission, for instance. This provides a basis for questioning the validity of considering negligible the Galactic contribution of the microwave background radiation anisotropies. Moreover, the size of the clouds is nearly coincident with that of the structures observed in the microwaves.

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Bouknia, Mohamed Lamine, Chemseddine Zebiri, Djamel Sayad, Issa Elfergani, Jonathan Rodriguez, Mohammad Alibakhshikenari, Raed A. Abd-Alhameed, Francisco Falcone, and Ernesto Limiti. "Theoretical Study of the Input Impedance and Electromagnetic Field Distribution of a Dipole Antenna Printed on an Electrical/Magnetic Uniaxial Anisotropic Substrate." Electronics 10, no. 9 (April 29, 2021): 1050. http://dx.doi.org/10.3390/electronics10091050.

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The present work considers the investigation of the effects of both electrical and magnetic uniaxial anisotropies on the input impedance, resonant length, and fields distribution of a dipole printed on an anisotropic grounded substrate. In this study, the associated integral equation, based on the derivation of the Green’s functions in the spectral domain, is numerically solved employing the method of moments. In order to validate the computing method and the evaluated calculation code, numerical results are compared with available data in the literature treating particular cases of electrical uniaxial anisotropy; reasonable agreements are reported. Novel results of the magnetic uniaxial anisotropy effects on the input impedance and the evaluated electromagnetic field are presented and discussed. This work will serve as a stepping stone for further works for a better understanding of the electromagnetic field behavior in complex anisotropic and bi-anisotropic media.

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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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Cleanthous, Galatia, Athanasios G. Georgiadis, and Morten Nielsen. "Fourier multipliers on anisotropic mixed-norm spaces of distributions." MATHEMATICA SCANDINAVICA 124, no. 2 (June 17, 2019): 289–304. http://dx.doi.org/10.7146/math.scand.a-113031.

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A new general Hörmander type condition involving anisotropies and mixed norms is introduced, and boundedness results for Fourier multipliers on anisotropic Besov and Triebel-Lizorkin spaces of distributions with mixed Lebesgue norms are obtained. As an application, the continuity of such operators is established on mixed Sobolev and Lebesgue spaces too. Some lifting properties and equivalent norms are obtained as well.

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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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Sharma, M. D. "Rayleigh wave at the surface of a general anisotropic poroelastic medium: derivation of real secular equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2211 (March 2018): 20170589. http://dx.doi.org/10.1098/rspa.2017.0589.

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A secular equation governs the propagation of Rayleigh wave at the surface of an anisotropic poroelastic medium. In the case of anisotropy with symmetry, this equation is obtained as a real irrational equation. But, in the absence of anisotropic symmetries, this secular equation is obtained as a complex irrational equation. True surface waves in non-dissipative materials decay only with depth. That means, propagation of Rayleigh wave in anisotropic poroelastic solid should be represented by a real phase velocity. In this study, the determinantal system leading to the complex secular equation is manipulated to obtain a transformed equation. Even for arbitrary (triclinic) anisotropy, this transformed equation remains real for the propagation of true surface waves. Such a real secular equation is obtained with the option of boundary pores being opened or sealed. A numerical example is solved to study the existence and propagation of Rayleigh waves in porous media for the top three (i.e. triclinic, monoclinic and orthorhombic) anisotropies.

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Strauss, R. D., J. P. van den Berg, and J. S. Rankin. "Cosmic-Ray Transport near the Sun." Astrophysical Journal 928, no. 1 (March 1, 2022): 22. http://dx.doi.org/10.3847/1538-4357/ac582a.

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Abstract The strongly diverging magnetic field lines in the very inner heliosphere, through the associated magnetic focusing/mirroring forces, can, potentially, lead to highly anisotropic galactic cosmic-ray distributions close to the Sun. Using a simplified analytical approach, validated by numerical simulations, we study the behavior of the galactic cosmic-ray distribution in this newly explored region of the heliosphere and find that significant anisotropies can be expected inside 0.2 au.

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Chen, Shutian, Zhengcao Li, and Zhengjun Zhang. "Fabrication and Optical Property of PeriodicSn1-xTixO2Nanostructures Patterned by the Polystyrene Microsphere Templates." Journal of Nanomaterials 2011 (2011): 1–7. http://dx.doi.org/10.1155/2011/510237.

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Regular arrays ofSn1-xTixO2nanostructures were fabricated by glancing angle sputter deposition onto self-assembled close-packed arrays of 200 nm diameter, 500 nm diameter, and 1 μm diameter polystyrene microspheres, respectively. The morphology of the nanostructures could be modulated by the variation of the sputtering power of Ti target and the size of polystyrene microspheres templates. Accordingly, the performance of reflection which was dependent on the morphology of nanostructures could be tuned by optimizing the parameters. The anisotropic morphology of nanoflakes achieved by adjusting the sputtering power of Ti target could generate the anisotropism of reflectance. With the increase of the PS sphere size, the anisotropism of nanostructures weakened; however, they exhibited excellent antireflection effects by creating a smaller gradient of refractive index.

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Yu, Jing, Yongmei Zhang, Yuhong Zhao, and Yue Ma. "Anisotropies in Elasticity, Sound Velocity, and Minimum Thermal Conductivity of Low Borides VxBy Compounds." Metals 11, no. 4 (April 1, 2021): 577. http://dx.doi.org/10.3390/met11040577.

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Anisotropies in the elasticity, sound velocity, and minimum thermal conductivity of low borides VB, V5B6, V3B4, and V2B3 are discussed using the first-principles calculations. The various elastic anisotropic indexes (AU, Acomp, and Ashear), three-dimensional (3D) surface contours, and their planar projections among different crystallographic planes of bulk modulus, shear modulus, and Young’s modulus are used to characterize elastic anisotropy. The bulk, shear, and Young’s moduli all show relatively strong degrees of anisotropy. With increased B content, the degree of anisotropy of the bulk modulus increases while those of the shear modulus and Young’s modulus decrease. The anisotropies of the sound velocity in the different planes show obvious differences. Meanwhile, the minimum thermal conductivity shows little dependence on crystallographic direction.

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Garemstani, Hamid, Dong Sheng Li, and Moe A. Khaleel. "Microstructure Sensitive Design and Quantitative Prediction of Effective Conductivity in Fuel Cell Design." Materials Science Forum 561-565 (October 2007): 315–18. http://dx.doi.org/10.4028/www.scientific.net/msf.561-565.315.

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Statistical continuum approach is used to predict effective conductivity of anisotropic random porous heterogeneous media using two-point correlation functions. Probability functions play a critical role in describing the statistical distribution of different constituents in a heterogeneous media. In this study a 3-dimensional two-point correlation function is utilized to characterize the anisotropic porous media of a Cathode materials to incorporate all the details of the microstructure. These correlation functions are then linked to the effective properties using homogenization relations. An anisotropioc Green’s function solution is used to solve the set of field equations. Examples in this study demonstrated how the model captured the anisotropy in effective conductivity of the random heterogeneous media. Predicted results showed the influence of microstructure on the effective conductivity tensor.

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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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Sarwar, Golam, and Jan-e. Alam. "Kinetic evolution and correlation of fluctuations in an expanding quark gluon plasma." International Journal of Modern Physics A 33, no. 08 (March 20, 2018): 1850040. http://dx.doi.org/10.1142/s0217751x18500409.

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Evolution of spatially anisotropic perturbation created in the system formed after Relativistic Heavy Ion Collisions has been studied. The microscopic evolution of the fluctuations has been examined within the ambit of Boltzmann Transport Equation (BTE) in a hydrodynamically expanding background. The expansion of the background composed of quark gluon plasma (QGP) is treated within the framework of relativistic hydrodynamics. Spatial anisotropic fluctuations with different geometries have been evolved through Boltzmann equation. It is observed that the trace of such fluctuation survives the evolution. Within the relaxation time approximation, analytical results have been obtained for the evolution of these anisotropies. Explicit relations between fluctuations and transport coefficients have been derived. The mixing of various Fourier (or k) modes of the perturbations during the evolution of the system has been explicitly demonstrated. This study is very useful in understanding the presumption that the measured anisotropies in the data from heavy ion collisions at relativistic energies imitate the initial state effects. The evolution of correlation function for the perturbation in pressure has been studied and shows that the initial correlation between two neighbouring points in real space evolves to a constant value at later time which gives rise to Dirac delta function for the correlation function in Fourier space. The power spectrum of the fluctuation in thermodynamic quantities (like temperature estimated in this work) can be connected to the fluctuation in transverse momentum of the thermal hadrons measured experimentally. The bulk viscous coefficient of the QGP has been estimated by using correlations of pressure fluctuation with the help of Green–Kubo relation. Angular power spectrum of the anisotropies has been estimated in the appendix.

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Allen, GW, RS Armstrong, MJ Aroney, RK Pierens, and KR Skamp. "Anisotropic Polarizabilities of Tin(IV)-Containing Groups." Australian Journal of Chemistry 39, no. 2 (1986): 221. http://dx.doi.org/10.1071/ch9860221.

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Electric birefringences , dipole moments and refractivities are reported for a series of organotin compounds. From these are deduced molecular polarizability anisotropies which, with data from Raman band intensities, can be dissected to give the anisotropic polarizabilities for component tin-containing groups. The results fit reasonably within a 'valence-optical' scheme of group polarizability additivity. Regular trends are observed in the directional polarizabilities of groups containing the Group 4b elements Si, Ge and Sn.

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Yuan, S. P., and R. M. C. So. "Turbulent rotating flow calculations: An assessment of two-equation anisotropic and Reynolds stress models." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 212, no. 3 (March 1, 1998): 193–212. http://dx.doi.org/10.1243/0954410981532270.

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The stress field in a rotating turbulent internal flow is highly anisotropic. This is true irrespective of whether the axis of rotation is aligned with or normal to the mean flow plane. Consequently, turbulent rotating flow is very difficult to model. This paper attempts to assess the relative merits of three different ways to account for stress anisotropies in a rotating flow. One is to assume an anisotropic stress tensor, another is to model the anisotropy of the dissipation rate tensor, while a third is to solve the stress transport equations directly. Two different near-wall two-equation models and one Reynolds stress closure are considered. All the models tested are asymptotically consistent near the wall. The predictions are compared with measurements and direct numerical simulation data. Calculations of turbulent flows with inlet swirl numbers up to 1.3, with and without a central recirculation, reveal that none of the anisotropic two-equation models tested is capable of replicating the mean velocity field at these swirl numbers. This investigation, therefore, indicates that neither the assumption of anisotropic stress tensor nor that of an anisotropic dissipation rate tensor is sufficient to model flows with medium to high rotation correctly. It is further found that, at very high rotation rates, even the Reynolds stress closure fails to predict accurately the extent of the central recirculation zone.

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Adams, Robert A. "Anisotropic Sobolev inequalities." Časopis pro pěstování matematiky 113, no. 3 (1988): 267–79. http://dx.doi.org/10.21136/cpm.1988.108786.

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Welemane, Hélène, Cristina Goidescu, Djimédo Kondo, Olivier Pantalé, and Moussa Karama. "Brittle Damage in Initially Anisotropic Materials: A Model Accounting for the Induced Anisotropy and Unilateral Effects." Applied Mechanics and Materials 784 (August 2015): 173–78. http://dx.doi.org/10.4028/www.scientific.net/amm.784.173.

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A new micromechanical modelling approach for brittle damage in initially orthotropic materials is presented. The proposed strain-based energy formulation allows to derive a fully anisotropic multilinear model for microcracked materials with arbitrary oriented defects. The thermodynamics framework provides a standard procedure for the damage evolution law. The new model explicitly accounts for the interaction between primary and induced anisotropies. Moreover, the very challenging issue of opening-closure effects (unilateral behavior) is addressed in this framework.

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LEUNG, KWAN-TAI. "FINITE-SIZE SCALING AT CRITICAL POINTS WITH SPATIAL ANISOTROPIES." International Journal of Modern Physics C 03, no. 02 (April 1992): 367–83. http://dx.doi.org/10.1142/s0129183192000294.

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We report some selected recent developments in the finite-size scaling theory of critical phenomena occurring in systems with strong spatial anisotropies. Such systems are characterized by correlation lengths divergent with different exponents (ν⊥, ν||) along different directions. Attention is focused on the driven diffusive lattice gas that exhibits a second order nonequilibrium phase transition. We present in detail the phenomenology and its comparison with computer simulation. Novel features of finite-size effects in anisotropic nonequilibrium systems are emphasized.

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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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Gander, Martin J., Laurence Halpern, Florence Hubert, and Stella Krell. "Optimized Schwarz methods with general Ventcell transmission conditions for fully anisotropic diffusion with discrete duality finite volume discretizations." Moroccan Journal of Pure and Applied Analysis 7, no. 2 (December 28, 2020): 182–213. http://dx.doi.org/10.2478/mjpaa-2021-0014.

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Abstract We introduce a new non-overlapping optimized Schwarz method for fully anisotropic diffusion problems. Optimized Schwarz methods take into account the underlying physical properties of the problem at hand in the transmission conditions, and are thus ideally suited for solving anisotropic diffusion problems. We first study the new method at the continuous level for two subdomains, prove its convergence for general transmission conditions of Ventcell type using energy estimates, and also derive convergence factors to determine the optimal choice of parameters in the transmission conditions. We then derive optimized Robin and Ventcell parameters at the continuous level for fully anisotropic diffusion, both for the case of unbounded and bounded domains. We next present a discretization of the algorithm using discrete duality finite volumes, which are ideally suited for fully anisotropic diffusion on very general meshes. We prove a new convergence result for the discretized optimized Schwarz method with two subdomains using energy estimates for general Ventcell transmission conditions. We finally study the convergence of the new optimized Schwarz method numerically using parameters obtained from the continuous analysis. We find that the predicted optimized parameters work very well in practice, and that for certain anisotropies which we characterize, our new bounded domain analysis is important.

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Mannion, Damien J., J. Scott McDonald, and Colin W. G. Clifford. "Orientation Anisotropies in Human Visual Cortex." Journal of Neurophysiology 103, no. 6 (June 2010): 3465–71. http://dx.doi.org/10.1152/jn.00190.2010.

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Representing the orientation of features in the visual image is a fundamental operation of the early cortical visual system. The nature of such representations can be informed by considering anisotropic distributions of response across the range of orientations. Here we used functional MRI to study modulations in the cortical activity elicited by observation of a sinusoidal grating that varied in orientation. We report a significant anisotropy in the measured blood-oxygen level-dependent activity within visual areas V1, V2, V3, and V3A/B in which horizontal orientations evoked a reduced response. These visual areas and hV4 showed a further anisotropy in which increased responses were observed for orientations that were radial to the point of fixation. We speculate that the anisotropies in cortical activity may be related to anisotropies in the prevalence and behavioral relevance of orientations in typical natural environments.

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Giani, Leonardo, Oliver F. Piattella, and Alexander Yu Kamenshchik. "Bianchi IX gravitational collapse of matter inhomogeneities." Journal of Cosmology and Astroparticle Physics 2022, no. 03 (March 1, 2022): 028. http://dx.doi.org/10.1088/1475-7516/2022/03/028.

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Abstract We investigate a model of gravitational collapse of matter inhomogeneities where the latter are modelled as Bianchi type IX (BIX) spacetimes. We found that this model contains, as limiting cases, both the standard spherical collapse model and the Zeldovich solution. We study how these models are affected by small anisotropies within the BIX potential. For the spherical collapse case, we found that the model is equivalent to a closed FLRW Universe filled with matter and two perfect fluids representing the anisotropic contributions. From the linear evolution up to the turnaround, the anisotropies effectively shift the value of the FLRW spatial curvature, because the fluids have effective Equation of State (EoS) parameters w ≈ -1/3. Then we estimate the impact of such anisotropies on the number density of haloes using the Press-Schechter formalism. If a fluid description of the anisotropies is still valid after virialization, the averaged over time EoS parameters are w ≈ 1/3. Using this and demanding hydrostatic equilibrium, we find a relation between the mass M, the average radius R and the pressure p of the virialized final structure. When we consider within the BIX ansatz small deviations from the Zeldovich solution, our qualitative analysis suggests that the so called pancakes exhibit oscillatory behavior, as would be expected in the case of a vacuum BIX spacetime.

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Orlando, Giorgio, P. Daniel Meerburg, and Subodh P. Patil. "Primordial tensor bispectra in μ-CMB cross-correlations." Journal of Cosmology and Astroparticle Physics 2022, no. 02 (February 1, 2022): 004. http://dx.doi.org/10.1088/1475-7516/2022/02/004.

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Abstract Cross-correlations between Cosmic Microwave Background (CMB) temperature and polarization anisotropies and μ-spectral distortions have been considered to measure (squeezed) primordial scalar bispectra in a range of scales inaccessible to primary CMB bispectra. In this work we address whether it is possible to constrain tensor non-Gaussianities with these cross-correlations. We find that only primordial tensor bispectra with statistical anisotropies leave distinct signatures, while isotropic tensor bispectra leave either vanishing or highly suppressed signatures. We discuss how the angular dependence of squeezed bispectra in terms of the short and long momenta determine the non-zero cross-correlations. We also discuss how these non-vanishing configurations are affected by the way in which primordial bispectra transform under parity. By employing the so-called BipoSH formalism to capture the observational effects of statistical anisotropies, we make Fisher-forecasts to assess the detection prospects from μ T, μ E and μ B cross-correlations. Observing statistical anisotropies in squeezed ⟨γγγ⟩ and ⟨γγζ⟩ bispectra is going to be challenging as the imprint of tensor perturbations on μ-distortions is subdominant to scalar perturbations, therefore requiring a large, independent amplification of the effect of tensor perturbations in the μ-epoch. In absence of such a mechanism, statistical anisotropies in squeezed ⟨ζζγ⟩ bispectrum are the most relevant sources of μ T, μ E and μ B cross-correlations. In particular, we point out that in anisotropic inflationary models where ⟨ζζζ⟩ leaves potentially observable signatures in μ T and μ E, the detection prospects of ⟨ζζγ⟩ from μ B are enhanced.

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35

Wang, Xun, Matthias Merkel, Leo B. Sutter, Gonca Erdemci-Tandogan, M. Lisa Manning, and Karen E. Kasza. "Anisotropy links cell shapes to tissue flow during convergent extension." Proceedings of the National Academy of Sciences 117, no. 24 (May 28, 2020): 13541–51. http://dx.doi.org/10.1073/pnas.1916418117.

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Within developing embryos, tissues flow and reorganize dramatically on timescales as short as minutes. This includes epithelial tissues, which often narrow and elongate in convergent extension movements due to anisotropies in external forces or in internal cell-generated forces. However, the mechanisms that allow or prevent tissue reorganization, especially in the presence of strongly anisotropic forces, remain unclear. We study this question in the converging and extendingDrosophilagermband epithelium, which displays planar-polarized myosin II and experiences anisotropic forces from neighboring tissues. We show that, in contrast to isotropic tissues, cell shape alone is not sufficient to predict the onset of rapid cell rearrangement. From theoretical considerations and vertex model simulations, we predict that in anisotropic tissues, two experimentally accessible metrics of cell patterns—the cell shape index and a cell alignment index—are required to determine whether an anisotropic tissue is in a solid-like or fluid-like state. We show that changes in cell shape and alignment over time in theDrosophilagermband predict the onset of rapid cell rearrangement in both wild-type andsnail twistmutant embryos, where our theoretical prediction is further improved when we also account for cell packing disorder. These findings suggest that convergent extension is associated with a transition to more fluid-like tissue behavior, which may help accommodate tissue-shape changes during rapid developmental events.

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Dhanasekaran, M. R., Sarit Kumar Das, and S. P. Venkateshan. "Natural Convection in a Cylindrical Enclosure Filled With Heat Generating Anisotropic Porous Medium." Journal of Heat Transfer 124, no. 1 (May 30, 2001): 203–7. http://dx.doi.org/10.1115/1.1418700.

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A numerical study has been made to analyze the effects of anisotropic permeability and thermal diffusivity on natural convection in a heat generating porous medium contained in a vertical cylindrical enclosure with isothermal wall and the top and bottom perfectly insulated surfaces. The results show that the anisotropies influence the flow field and heat transfer rate significantly. The non-dimensional maximum cavity temperature increases with increase in permeability ratio. For aspect ratio greater than or equal to two, the nondimensional maximum cavity temperature increases with an increase in the thermal diffusivity ratio. For aspect ratio equal to unity, there exists a critical value of thermal diffusivity ratio at which the maximum cavity temperature is a minimum. This critical value increases with an increase in the value of anisotropic permeability ratio. Based on a parametric study correlations for maximum cavity temperature and average Nusselt number are presented.

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Hoffelner, Daniel, Matthias Kundt, Annette M. Schmidt, Emmanuel Kentzinger, Philipp Bender, and Sabrina Disch. "Directing the orientational alignment of anisotropic magnetic nanoparticles using dynamic magnetic fields." Faraday Discussions 181 (2015): 449–61. http://dx.doi.org/10.1039/c4fd00242c.

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The structure-directing influence of static and dynamic, i.e. rotating, magnetic fields on the orientational alignment of spindle-type hematite particles with a high aspect ratio is investigated. Structural characterization using electron microscopy and small-angle X-ray scattering confirms a nearly collinear particle arrangement with orientation of the main particle axis either parallel or perpendicular to the substrate as directed by the magnetic field geometry. The combination of large structural and magnetocrystalline anisotropies results in significantly different, strongly anisotropic magnetic properties of the assemblies revealed by directional magnetization measurements.

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Satapathy, Pragnya, Pralay K. Santra, and S. Krishna Prasad. "Synergistic Path for Dual Anisotropic and Electrically Switchable Emission From a Nanocomposite of CsPbBr3 Quantum Cuboids and Nematic Liquid Crystal." Crystals 9, no. 8 (July 24, 2019): 378. http://dx.doi.org/10.3390/cryst9080378.

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We report photophysical properties of a nanocomposite consisting of perovskite quantum cuboids (QCs) formed by CsPbBr3 and a wide temperature range nematic liquid crystal. Contrary to observations made with conventional II-VI quantum dots dispersed in a liquid crystal, the used QCs form, under the influence of the nematic orientation, linear assemblies over macroscopic length scales evidenced by polarizing optical microscopy. Interestingly, the linear assembly is actually caused by such an anisotropic arrangement at the nm scale, as seen in TEM images. Thin films of the nanocomposite exhibiting this unique and fascinating character exhibit absorption and emission features, which are quite appealing. These include retention of the sharp bandwidth of emission characteristic of the native QCs and establishment of dual anisotropies, arising from the values being different along the director as well in the two directions orthogonal to it. We also present data on voltage-driven switching between one of the anisotropic limits.

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39

Antonelli, Marta, Alessandra Lanotte, and Andrea Mazzino. "Anisotropies and Universality of Buoyancy-Dominated Turbulent Fluctuations: A Large-Eddy Simulation Study." Journal of the Atmospheric Sciences 64, no. 7 (July 1, 2007): 2642–56. http://dx.doi.org/10.1175/jas3951.1.

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Abstract Turbulent fluctuations of both velocity and temperature fields, issuing from high-resolution large-eddy simulations, have been analyzed in convective boundary layers. The numerically simulated flows are strongly anisotropic at large scales: this is due both to the action of buoyancy and to the imposed geostrophic wind. Their relative weight is varied so that one experiment’s results are much more convective than the other. To properly disentangle anisotropic properties, the authors exploit both standard statistical indicators, like skewness coefficients, and the three-dimensional rotational group decomposition SO(3). Two main conclusions can be drawn. First, despite the strong anisotropies at large scales, isotropy is statistically recovered at scales much smaller than the large ones. Second, relevant statistical indicators of turbulence such as the scaling exponents, of both velocity and temperature fields, are remarkably close for the two experiments. Implications of these findings for the problem of subgrid-scale modeling are discussed.

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40

KRAUS, L. "LOCAL MAGNETIC ANISOTROPY AND MAGNETOANELASTIC EFFECT IN AMORPHOUS AND NANOCRYSTALLINE ALLOYS." International Journal of Modern Physics B 07, no. 01n03 (January 1993): 916–21. http://dx.doi.org/10.1142/s0217979293001979.

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Anelastic deformation of amorphous and nanocrystalline metals results in an anisotropic distribution of atomic pair bonds. This mechanism can lead to rather strong macroscopic magnetic anisotropy in some alloys. Experimental results show that the creep-induced magnetic anisotropy of amorphous and nanocrystalline Fe- and Co-based alloys essentially depends both on TM and metalloid elements. This is a clear evidence that the random local magnetic anisotropy in these materials is closely related to the details of electronic structure. Based on this conclusion a model of bond -orientational anisotropy taking into account the distribution of local anisotropies in TM-based alloys is proposed.

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41

Cesaroni, A., H. Kröner, and M. Novaga. "Anisotropic mean curvature flow of Lipschitz graphs and convergence to self-similar solutions." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 97. http://dx.doi.org/10.1051/cocv/2021096.

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We consider the anisotropic mean curvature flow of entire Lipschitz graphs. We prove existence and uniqueness of expanding self-similar solutions which are asymptotic to a prescribed cone, and we characterize the long time behavior of solutions, after suitable rescaling, when the initial datum is a sublinear perturbation of a cone. In the case of regular anisotropies, we prove the stability of self-similar solutions asymptotic to strictly mean convex cones, with respect to perturbations vanishing at infinity. We also show the stability of hyperplanes, with a proof which is novel also for the isotropic mean curvature flow.

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42

Shaaban, S. M., M. Lazar, P. H. Yoon, and S. Poedts. "Quasilinear approach of the cumulative whistler instability in fast solar wind: Constraints of electron temperature anisotropy." Astronomy & Astrophysics 627 (July 2019): A76. http://dx.doi.org/10.1051/0004-6361/201935515.

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Context. Solar outflows are a considerable source of free energy that accumulates in multiple forms such as beaming (or drifting) components, or temperature anisotropies, or both. However, kinetic anisotropies of plasma particles do not grow indefinitely and particle-particle collisions are not efficient enough to explain the observed limits of these anisotropies. Instead, self-generated wave instabilities can efficiently act to constrain kinetic anisotropies, but the existing approaches are simplified and do not provide satisfactory explanations. Thus, small deviations from isotropy shown by the electron temperature (T) in fast solar winds are not explained yet. Aims. This paper provides an advanced quasilinear description of the whistler instability driven by the anisotropic electrons in conditions typical for the fast solar winds. The enhanced whistler-like fluctuations may constrain the upper limits of temperature anisotropy A ≡ T⊥/T∥ > 1, where ⊥, ∥ are defined with respect to the magnetic field direction. Methods. We studied self-generated whistler instabilities, cumulatively driven by the temperature anisotropy and the relative (counter)drift of electron populations, for example, core and halo electrons. Recent studies have shown that quasi-stable states are not bounded by linear instability thresholds but an extended quasilinear approach is necessary to describe these quasi-stable states in this case. Results. Marginal conditions of stability are obtained from a quasilinear theory of cumulative whistler instability and approach the quasi-stable states of electron populations reported by the observations. The instability saturation is determined by the relaxation of both the temperature anisotropy and relative drift of electron populations.

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Nicula, Anabela, and Matthew R. Longo. "Perception of Tactile Distance on the Back." Perception 50, no. 8 (June 18, 2021): 677–89. http://dx.doi.org/10.1177/03010066211025384.

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The perceived distance between two touches is anisotropic on many parts of the body. Generally, tactile distances oriented across body width are perceived as larger than distances oriented along body length, though the magnitude of such biases differs substantially across the body. In this study, we investigated tactile distance perception on the back. Participants made verbal estimates of the perceived distance between pairs of touches oriented either across body width or along body length on (a) the left hand, (b) the left upper back, and (c) the left lower back. There were clear tactile distance anisotropies on the hand and upper back, with distances oriented across body width overestimated relative to those along body length/height, consistent with previous results. On the lower back, however, an anisotropy in exactly the opposite direction was found. These results provide further evidence that tactile distance anisotropies vary systematically across the body and suggest that the spatial representation of touch on the lower back may differ qualitatively from that on other regions of the body.

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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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Wu, Jie, Zuren Feng, and Zhigang Ren. "Improved structure-adaptive anisotropic filter based on a nonlinear structure tensor." Cybernetics and Information Technologies 14, no. 1 (March 1, 2014): 112–27. http://dx.doi.org/10.2478/cait-2014-0009.

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Abstract A variety of structure-adaptive filters are proposed to overcome the blurred effects of image structures caused by the classical Gaussian weighted mean filter. However, two major issues are needed to be dealt with carefully for structure-adaptive anisotropic filters. One is to properly construct the filter kernel and the other is to accurately estimate the orientation of the image structures. In this paper we propose to improve the structure-adaptive anisotropic filtering approach based on the nonlinear structure tensor (NLST) analysis technique. According to the anisotropism measurements of image structures, a new kernel construction method is designed to make the filter shape fine adapted to image features. Through the accurately estimated orientation of the image structures, the filter kernels are then properly aligned to perform the filtering process. Experimental results show that the proposed filter denoises the noisy images carefully and image features, such as corners and junctions are well preserved. Compared with some other known filters, the proposed filter obtains great improvements both in Mean Square Error (MSE) and visual quality.

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46

Ohlemacher, Crittenden J., and Gary R. Hamed. "Aging with Applied Strain of A Black-Filled Natural Rubber Vulcanizate. Part I: Network Changes." Rubber Chemistry and Technology 81, no. 4 (September 1, 2008): 650–70. http://dx.doi.org/10.5254/1.3548225.

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Abstract Black-filled natural rubber, with an inefficient sulfur cure, was aged at 90 °C and 110 °C under nitrogen, with and without applied strain. Samples aged under strain became “double networks” and retained a residual extension ratio. The crosslink density of samples passed through a maximum with increasing severity of aging. Presumably this arises because the thermally labile, polysulfidic crosslinks break, and new crosslinks of lower rank form, resulting in increased crosslink density; but, when aged at 110 °C, this is offset by chain scission and other main-chain modifications. For double networks, it is proposed that a second network, which tends to keep samples extended, is formed at the expense of crosslinks in the original, first network. Unaged and single network samples were isotropic in tensile behavior and only slightly anisotropic in swelling behavior. For double networks, swelling and tensile properties were anisotropic, and there was some evidence that parallel specimens have increased ability to strain-crystallize. The observed anisotropies in double networks are proposed to arise from the chain orientation that persisted after double network formation.

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Chernenko, Volodymyr A. "Concepts and Physical Phenomena in Magnetic Shape Memory Science." Advanced Materials Research 52 (June 2008): 3–14. http://dx.doi.org/10.4028/www.scientific.net/amr.52.3.

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The magnetically weakly anisotropic cubic Ni-Mn-Ga Heusler alloys exhibit martensitic transformation resulting in martensitic phases with elastically soft crystal lattices and strong magnetocrystalline anisotropies. The magnetic state of these martensites is coupled with a highly mobile twin structure through the ordinary magnetoelastic interactions giving rise to a giant magnetic-field-induced-strain effect. This effect is the key ingredient of a new scientific field. In the present article, the basic phenomena and concepts of this field, such as lattice instability, soft-mode behavior, electron concentration, ferromagnetic shape memory effect, magnetic-field-induced superelasticity, twinning strain-induced change of magnetization, and magnetoelastic mechanism of magnetostress are briefly reviewed.

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Krūminiene, I. "ANALYSIS OF ANISOTROPIC VARIOGRAM MODELS FOR PREDICTION OF THE CURONIAN LAGOON DATA." Mathematical Modelling and Analysis 11, no. 1 (March 31, 2006): 73–86. http://dx.doi.org/10.3846/13926292.2006.9637303.

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The anisotropy in particular environmental phenomena is detected when behavior of a physical process differs in different directions. In this paper geometric and zonal anisotropies are considered. Various methods of geostatistical analysis, also isotropic and geometrical anisotropic variogram models are compared and applied for the Curonian lagoon depth data. The results demonstrate that after robust estimation, i.e. elimination of outliers and after elimination of geometric anisotropy the precision of prediction and adequacy of models are much better. All computations have been performed by means of gstat, base and spatial packages of R system. Prediction results are compared with the results of research where outliers and geometric anisotropy were not eliminated.

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OWERRE, SOLOMON AKARAKA, and M. B. PARANJAPE. "QUANTUM-CLASSICAL PHASE TRANSITION OF THE ESCAPE RATE OF TWO-SUBLATTICE ANTIFERROMAGNETIC LARGE SPINS." International Journal of Modern Physics B 28, no. 03 (January 22, 2014): 1450008. http://dx.doi.org/10.1142/s0217979214500088.

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The Hamiltonian of a two-sublattice antiferromagnetic spins, with single (hard-axis) and double ion anisotropies described by [Formula: see text] is investigated using the method of effective potential. The problem is mapped to a single particle quantum-mechanical Hamiltonian in terms of the relative coordinate and reduced mass. We study the quantum-classical phase transition of the escape rate of this model. We show that the first-order phase transition for this model sets in at the critical value Jc = (Kc+Jz, c)/2 while for the anisotropic Heisenberg coupling [Formula: see text] we obtain Jc = (2Kc-Jz, c)/3. The phase diagrams of the transition are also studied.

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Brito, P., and M. Mechetti. "Determination of dipole moment values of anisotropic molecules using Brot's formalism." Canadian Journal of Chemistry 68, no. 9 (September 1, 1990): 1523–26. http://dx.doi.org/10.1139/v90-234.

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A method for the determination of dipole moment values based on Brot's theory is proposed. It takes into account the influence of the molecular anisotropies of shape and polarizability on the permittivity of a mixture. Starting from measurements performed on dilute solutions and from the knowledge of the molecular structure of some chlorinated derivatives of α-cyanostilbene and 1,3 derivatives of benzene, the best parameters of an ellipsoid used for the representation of a polar anisotropic molecule are determined. The dipole moments obtained, using benzene and tetrachloromethane as solvents, are finally compared to values from the literature. Keywords: dipole moment, Brot's formalism, molecular anisotropy.

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Journal articles on the topic 'Anisotroping'

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