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Journal articles on the topic 'Anisotropic surface energy'

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Published: 1 June 2024

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1

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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2

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.
3

Koiso, Miyuki. "Uniqueness of Closed Equilibrium Hypersurfaces for Anisotropic Surface Energy and Application to a Capillary Problem." Mathematical and Computational Applications 24, no. 4 (October 10, 2019): 88. http://dx.doi.org/10.3390/mca24040088.

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We study a variational problem for hypersurfaces in the Euclidean space with an anisotropic surface energy. An anisotropic surface energy is the integral of an energy density that depends on the surface normal over the considered hypersurface, which was introduced to model the surface tension of a small crystal. The purpose of this paper is two-fold. First, we give uniqueness and nonuniqueness results for closed equilibria under weaker assumptions on the regularity of both considered hypersurfaces and the anisotropic surface energy density than previous works and apply the results to the anisotropic mean curvature flow. This part is an announcement of two forthcoming papers by the author. Second, we give a new uniqueness result for stable anisotropic capillary surfaces in a wedge in the three-dimensional Euclidean space.
4

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.
5

Lamichhane, Shobha Kanta. "Experimental investigation on anisotropic surface properties of crystalline silicon." BIBECHANA 8 (January 15, 2012): 59–66. http://dx.doi.org/10.3126/bibechana.v8i0.4828.

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Anisotropic etching of silicon has been studied by wet potassium hydroxide (KOH) etchant with its variation of temperature and concentration. Results presented here are temperature dependent etch rate along the crystallographic orientations. The etching rate of the (111) surface family is of prime importance for microfabrication. However, the experimental values of the corresponding etch rate are often scattered and the etching mechanism of (111) remains unclear. Etching and activation energy are found to be consistently favorable with the thermal agitation for a given crystal plane. Study demonstrate that the contribution of microscopic activation energy that effectively controls the etching process. Such a strong anisotropy in KOH allows us a precious control of lateral dimensions of the silicon microstructure.Keywords: microfabrication; activation energy; concentration; anisotropy; crystal planeDOI: http://dx.doi.org/10.3126/bibechana.v8i0.4828 BIBECHANA 8 (2012) 59-66
6

HE, L., Y. W. LIU, W. J. TONG, J. G. LIN, and X. F. WANG. "SURFACE ENERGY ENGINEERING OF Cu SURFACE BY STRAIN: FIRST-PRINCIPLES CALCULATIONS." Surface Review and Letters 20, no. 06 (December 2013): 1350054. http://dx.doi.org/10.1142/s0218625x13500546.

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Surface energies of strained Cu surfaces were studied systematically using first-principles methods. Results showed that the strain-stabilization of Cu surface was anisotropic and strongly related to the strain distribution. This strain-induced approach could be used as an effective way to engineer the surface energies of metals.
7

KRZYSZTON, T. "SURFACE BARRIER IN THE MIXED STATE OF ANISOTROPIC SUPERCONDUCTOR." Modern Physics Letters B 07, no. 12 (May 20, 1993): 841–47. http://dx.doi.org/10.1142/s0217984993000837.

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In the framework of London theory, the problem of equilibrium between magnetic flux density in the anisotropic superconductor and the applied external magnetic field is studied. The Gibbs free energy of a fluxoid in the presence of magnetic flux density in the sample is calculated. As a result, critical entry and exit fields are calculated and their dependence upon the angle which makes anisotropy axis and the direction of an external magnetic field.
8

Rofouie, P., Z. Wang, and A. D. Rey. "Two-wavelength wrinkling patterns in helicoidal plywood surfaces: imprinting energy landscapes onto geometric landscapes." Soft Matter 14, no. 25 (2018): 5180–85. http://dx.doi.org/10.1039/c8sm01022f.

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We present a model to investigate the formation of two-length scale surface patterns in biological and synthetic anisotropic soft matter materials through the high order interaction of anisotropic interfacial tension and capillarity at their free surfaces.
9

Wang, Ziheng, Phillip Servio, and Alejandro D. Rey. "Complex Nanowrinkling in Chiral Liquid Crystal Surfaces: From Shaping Mechanisms to Geometric Statistics." Nanomaterials 12, no. 9 (May 4, 2022): 1555. http://dx.doi.org/10.3390/nano12091555.

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Surface wrinkling is closely linked to a significant number of surface functionalities such as wetting, structural colour, tribology, frictions, biological growth and more. Given its ubiquity in nature’s surfaces and that most material formation processes are driven by self-assembly and self-organization and many are formed by fibrous composites or analogues of liquid crystals, in this work, we extend our previous theory and modeling work on in silico biomimicking nanowrinkling using chiral liquid crystal surface physics by including higher-order anisotropic surface tension nonlinearities. The modeling is based on a compact liquid crystal shape equation containing anisotropic capillary pressures, whose solution predicts a superposition of uniaxial, equibiaxial and biaxial egg carton surfaces with amplitudes dictated by material anchoring energy parameters and by the symmetry of the liquid crystal orientation field. The numerical solutions are validated by analytical solutions. The blending and interaction of egg carton surfaces create surface reliefs whose amplitudes depend on the highest nonlinearity and whose morphology depends on the anchoring coefficient ratio. Targeting specific wrinkling patterns is realized by selecting trajectories on an appropriate parametric space. Finally, given its importance in surface functionalities and applications, the geometric statistics of the patterns up to the fourth order are characterized and connected to the parametric anchoring energy space. We show how to minimize and/or maximize skewness and kurtosis by specific changes in the surface energy anisotropy. Taken together, this paper presents a theory and simulation platform for the design of nano-wrinkled surfaces with targeted surface roughness metrics generated by internal capillary pressures, of interest in the development of biomimetic multifunctional surfaces.
10

Wheeler, A. A., and G. B. McFadden. "A ξ-vector formulation of anisotropic phase-field models: 3D asymptotics." European Journal of Applied Mathematics 7, no. 4 (August 1996): 367–81. http://dx.doi.org/10.1017/s0956792500002424.

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In this paper we present a new formulation of a large class of phase-field models, which describe solidification of a pure material and allow for both surface energy and interface kinetic anisotropy, in terms of the Hoffman–Cahn ξ-vector. The ξ-vector has previously been used in the context of sharp interface models, where it provides an elegant tool for the representation and analysis of interfaces with anisotropic surface energy. We show that the usual gradient-energy formulations of anisotropic phase-field models are expressed in a natural way in terms of the ξ-vector when appropriately interpreted. We use this new formulation of the phase-field equations to provide a concise derivation of the Gibbs–Thomson–Herring equation in the sharp-interface limit in three dimensions.
11

TAYLOR, J. E., and J. W. CAHN. "A Cusp Singularity in Surfaces That Minimize an Anisotropic Surface Energy." Science 233, no. 4763 (August 1, 1986): 548–51. http://dx.doi.org/10.1126/science.233.4763.548.

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12

Wu, Sheng Yun, Jhong-Yi Ji, and Po-Hsun Shih. "Surface Magnetic Anisotropic Energy Gap in Cu2O Nanoparticles." Japanese Journal of Applied Physics 47, no. 1 (January 22, 2008): 706–11. http://dx.doi.org/10.1143/jjap.47.706.

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13

Hesketh, Peter J., Chishein Ju, Sanjay Gowda, Elmer Zanoria, and Steven Danyluk. "Surface Free Energy Model of Silicon Anisotropic Etching." Journal of The Electrochemical Society 140, no. 4 (April 1, 1993): 1080–85. http://dx.doi.org/10.1149/1.2056201.

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14

Jung Jung, Soon, Tarek Lutz, and John J. Boland. "Anisotropic etching induced by surface energy driven agglomeration." Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films 29, no. 5 (September 2011): 051403. http://dx.doi.org/10.1116/1.3626795.

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15

Hwang, S. K., and H. T. Han. "Anisotropic surface energy reduction of Zr by chemisorption." Journal of Nuclear Materials 161, no. 2 (February 1989): 175–81. http://dx.doi.org/10.1016/0022-3115(89)90480-7.

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16

Ciftja, Orion. "Variation of the elliptical Fermi surface for a two-dimensional electron gas with anisotropic mass." Journal of Physics: Conference Series 2164, no. 1 (March 1, 2022): 012023. http://dx.doi.org/10.1088/1742-6596/2164/1/012023.

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Abstract We consider a two-dimensional electron gas in the thermodynamic (bulk) limit. It is assumed that the system consists of fully spin-polarized (spinless) electrons with anisotropic mass. We study the variation of the shape of the expected elliptical Fermi surface as a function of the density of the system in presence of such form of internal anisotropy. To this effect, we calculate the energy of the system as well as the optimum ellipticity of the Fermi surface for two possible liquid states. One corresponds to the standard system with circular Fermi surface while the second one represents a liquid anisotropic phase with a tunable elliptical deformation of the Fermi surface that includes the state that minimizes the kinetic energy. The results obtained shed light on several possible scenarios that may arise in such a system. The competition between opposing tendencies of the kinetic energy and potential energy may lead to the stabilization of liquid phases where the optimal elliptical deformation of the Fermi surface is non-obvious and depends on the density as well as an array of other factors related to the specific values of various parameters that characterize the system.
17

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.
18

Shen, Xianda, Giuseppe Buscarnera, and Fengshou Zhang. "Anisotropic Breakage Mechanics for cemented granular materials." IOP Conference Series: Earth and Environmental Science 1330, no. 1 (May 1, 2024): 012049. http://dx.doi.org/10.1088/1755-1315/1330/1/012049.

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Abstract The anisotropy of granular geomaterials is sensitive to their fabric, which exhibits anisotropic mechanical properties as a function of deposition history, microscopic fabric, and loading paths. Here, a new fabric-enriched continuum breakage model is proposed to examine the relation between elastic and inelastic anisotropy in granular materials and cemented granular materials. A microstructure model is first implemented in the framework of fabric-enriched continuum breakage mechanics (F-CBM), where the anisotropic behaviour prior to yielding is introduced through a symmetric second-order fabric tensor embedded in the expression of the elastic energy potential. The anisotropic strain energy storage prior to grain crushing leads to the rotation and distortion of the yield surface of cemented granular materials. Parametric analyses are performed to assess the overall capability of the model to characterize the anisotropic inelastic processes in cemented granular. It is shown that the proposed model can accurately predict the strong correlation between anisotropic elasticity and breakage-damage processes in cemented granular materials. When damage involving the skeleton is the dominant inelastic process, the size of the elastic domain contracts and the material exhibits augmented brittleness with the disintegration of cement. While breakage processes are predicted to dominate the response of lightly cemented granular materials resulting in hardening behaviour. This work can be further extended to dynamically capture the anisotropic response of cemented granular materials with water-sensitive mineral constituents by accounting for the evolution of microstructural anisotropy.
19

Koiso, Miyuki. "Stable anisotropic capillary hypersurfaces in a wedge." Mathematics in Engineering 5, no. 2 (2022): 1–22. http://dx.doi.org/10.3934/mine.2023029.

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<abstract><p>We study a variational problem for hypersurfaces in a wedge in the Euclidean space. Our wedge is bounded by a finitely many hyperplanes passing a common point. The total energy of each hypersurface is the sum of its anisotropic surface energy and the wetting energy of the planar domain bounded by the boundary of the considered hypersurface. An anisotropic surface energy is a generalization of the surface area which was introduced to model the surface tension of a small crystal. We show an existence and uniqueness result of local minimizers of the total energy among hypersurfaces enclosing the same volume. Our result is new even when the special case where the surface energy is the surface area.</p></abstract>
20

GAO, Zhi-yong, Wei SUN, and Yue-hua HU. "Mineral cleavage nature and surface energy: Anisotropic surface broken bonds consideration." Transactions of Nonferrous Metals Society of China 24, no. 9 (September 2014): 2930–37. http://dx.doi.org/10.1016/s1003-6326(14)63428-2.

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21

Luo, Y. K., and R. S. Qin. "Description of Surface Energy Anisotropy for BCC Metals." Advanced Materials Research 922 (May 2014): 446–51. http://dx.doi.org/10.4028/www.scientific.net/amr.922.446.

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Surface energy anisotropy (SEA) has long been a hot topic in interface science as it has an important role in the interface/surface behaviours for crystalline phases. Most studies aim to determine the numerical values of the anisotropic surface energy in some particular orientations, but few investigate the whole orientation-dependent trend, or the morphology of the polar plot. The present work propose descriptions for SEA of both body centred cubic (BCC) and face centred cubic (FCC) metals by considering the interactions between an atom and its 1st, 2nd and 3rd nearest neighbouring (NN) atoms. The expression makes use of only three coefficients K1, K2 and K3 which are correspondent to the contribution of 1st, 2nd and 3rd NN interactions respectively. This allows estimation of surface energy for all crystallographic orientations if the values for (111), (100) and (110) orientations are provided. Matching of our model with modified analytical embedded-atom method (MAEAM) results demonstrates less than 0.5% average relative error. We also construct the polar plots of BCC metals based on our model and compare them with some other models.
22

Li, Mengyuan, and Qihuai Liu. "Periodic orbits of the spatial anisotropic Kepler problem with anisotropic perturbations." Electronic Journal of Differential Equations 2021, no. 01-104 (July 8, 2021): 63. http://dx.doi.org/10.58997/ejde.2021.63.

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In this article, we study the periodic orbits of the spatial anisotropic Kepler problem with anisotropic perturbations on each negative energy surface, where the perturbations are homogeneous functions of arbitrary integer degree p. By choosing the different ranges of a parameter &beta;, we show that there exist at least 6 periodic solutions for \(p>1\), while there exist at least 2 periodic solutions for \(p\le1\) on each negative energy surface. The proofs of main results are based on symplectic Delaunay coordinates, residue theorem, and averaging theory. For more information see https://ejde.math.txstate.edu/Volumes/2021/63/abstr.html
23

Garg, S. K., D. P. Datta, J. Ghatak, I. Thakur, K. Khare, D. Kanjilal, and T. Som. "Tunable wettability of Si through surface energy engineering by nanopatterning." RSC Advances 6, no. 54 (2016): 48550–57. http://dx.doi.org/10.1039/c6ra04906k.

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24

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.
25

Siegel, M. "Evolution of material voids for highly anisotropic surface energy." Journal of the Mechanics and Physics of Solids 52, no. 6 (June 2004): 1319–53. http://dx.doi.org/10.1016/j.jmps.2003.11.003.

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26

Sharif, M., and Sobia Sadiq. "Conformally flat polytropes for anisotropic cylindrical geometry." Canadian Journal of Physics 93, no. 12 (December 2015): 1583–87. http://dx.doi.org/10.1139/cjp-2015-0352.

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In this paper, we study cylindrically symmetric anisotropic matter distribution satisfying two polytropic equations of state. The corresponding Lane–Emden equations are constructed and the energy conditions are checked. We evaluate a particular expression for anisotropy by using the conformally flat condition, which helps in the study of polytropic models. The graphical analysis of surface gravitational potential indicates the increasing behavior of model compactness. Finally, we conclude that one of the obtained models is physically viable.
27

Eremeyev, V. A. "Strongly anisotropic surface elasticity and antiplane surface waves." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2162 (November 25, 2019): 20190100. http://dx.doi.org/10.1098/rsta.2019.0100.

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Within the new model of surface elasticity, the propagation of anti-plane surface waves is discussed. For the proposed model, the surface strain energy depends on surface stretching and on changing of curvature along a preferred direction. From the continuum mechanics point of view, the model describes finite deformations of an elastic solid with an elastic membrane attached on its boundary reinforced by a family of aligned elastic long flexible beams. Physically, the model was motivated by deformations of surface coatings consisting of aligned bar-like elements as in the case of hyperbolic metasurfaces. Using the least action variational principle, we derive the dynamic boundary conditions. The linearized boundary-value problem is also presented. In order to demonstrate the peculiarities of the problem, the dispersion relations for surface anti-plane waves are analysed. We have shown that the bending stiffness changes essentially the dispersion relation and conditions of anti-plane surface wave propagation. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 2)’.
28

SU, C. W., S. C. CHANG, and Y. C. CHANG. "MAGNETO-OPTIC FARADAY EFFECT ON SPIN ANISOTROPIC Co ULTRATHIN FILMS AND POST-NITRIDIZATION ON ZnO(002) CRYSTAL." SPIN 02, no. 04 (December 2012): 1250017. http://dx.doi.org/10.1142/s2010324712500178.

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Perpendicular magnetic anisotropy in the initial growth of epitaxial in-plane anisotropic Co ultrathin films on the ZnO (002) crystal surface was discovered. The critical thickness of weak spin reorientation transition phenomenon in deposition process from in-plane to out-of-plane magnetic anisotropy is around 2 nm. Ultrathin 1.2 nm Co film was stabilized by post-irradiation of low-energy N ions from the observation of hysteresis loop transforming from an S-shape soft magnetic state to a square hard magnetic state. The addition of N affected the magnetic behavior. The time-dependent nitridization process was observed using Auger electron spectroscopy. Magneto-optical Faraday effect measurements were used to observe the magnetic properties of high-transmission Co/ZnO (002) and Co–N/ZnO (002) surface. A strong polar magneto-optic Faraday effect was dominated in the 2.0–4.0 nm Co/ZnO (002) surfaces. From the N+ implantation that reduces the corresponding coercivity, a hexagonal c-axis lattice structure of Co with a preferred perpendicular anisotropy on the ZnO (002) surface may be explained.
29

Bigozha, O. D., A. Zh Seitmuratov, L. U. Taimuratova, B. K. Kazbekova, and Z. K. Aimaganbetova. "Longitudinal magnetoresistance of uniaxially deformed n-type silicon." Bulletin of the Karaganda University. "Physics" Series 106, no. 2 (June 30, 2022): 111–16. http://dx.doi.org/10.31489/2022ph1/111-116.

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The study of Galvano-magnetic effects (as well as tensoeffects) in silicon under extreme conditions allows not only to identify the mechanisms of these effects but also to identify the possibility of creating gaussmeters, infrared detectors, sensitive strain gauges, amplifiers and generators of a wide frequency range. The reliability of the mechanism of negative magnetoresistance was verified using uniaxial elastic deformation of the studied crystals. Uniaxial deformation excludes interline transitions of electrons, as a result of which negative magnetoresistance disappears with an increase in uniaxial pressure. When cubic symmetry is violated, anisotropic phenomena occur in such crystals. The multipath of the isoenergetic surface of the bottom of the silicon conduction band causes anisotropies of the effective mass and relaxation time, which are associated with the features of the transfer phenomenon. In particular, magnetoresistance (piezoresistance), which is the most sensitive to the anisotropy of the iso energy surface. The influence of the latter on magnetoresistance is most clearly revealed in the region of strong magnetic fields, where the magnetoresistance is saturated since the longitudinal magnetoresistance is entirely due to the anisotropy of electron mobility.
30

Bigozha, O. D., A. Zh Seitmuratov, L. U. Taimuratova, B. K. Kazbekova, and Z. K. Aimaganbetova. "Longitudinal magnetoresistance of uniaxially deformed n-type silicon." Bulletin of the Karaganda University "Physics Series" 106, no. 2 (June 30, 2022): 111–16. http://dx.doi.org/10.31489/2022ph2/111-116.

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The study of Galvano-magnetic effects (as well as tensoeffects) in silicon under extreme conditions allows not only to identify the mechanisms of these effects but also to identify the possibility of creating gaussmeters, infrared detectors, sensitive strain gauges, amplifiers and generators of a wide frequency range. The reliability of the mechanism of negative magnetoresistance was verified using uniaxial elastic deformation of the studied crystals. Uniaxial deformation excludes interline transitions of electrons, as a result of which negative magnetoresistance disappears with an increase in uniaxial pressure. When cubic symmetry is violated, anisotropic phenomena occur in such crystals. The multipath of the isoenergetic surface of the bottom of the silicon conduction band causes anisotropies of the effective mass and relaxation time, which are associated with the features of the transfer phenomenon. In particular, magnetoresistance (piezoresistance), which is the most sensitive to the anisotropy of the iso energy surface. The influence of the latter on magnetoresistance is most clearly revealed in the region of strong magnetic fields, where the magnetoresistance is saturated since the longitudinal magnetoresistance is entirely due to the anisotropy of electron mobility.
31

Gentsar, P. O., M. V. Vuichyk, and A. V. Stronski. "Impact of a surface on the electro-reflectance spectra of n-Si(110) and their polarization anisotropy." Physics and Chemistry of Solid State 21, no. 3 (September 30, 2020): 440–44. http://dx.doi.org/10.15330/pcss.21.3.440-444.

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The electro-reflectance spectra, including their polarization dependencies were analyzed for n-Si(110) in the energy range of 2.9-3.8 eV. Based on the optical anisotropy of electro-optical effect, two contributions originated from a surface, (isotropic part relates to the linear electro-optical effect which inherent for (110) surface) and bulk, (anisotropic part relates to the Franz–Keldysh effect) were identified and separated. The presence of such extreme is explained by the zero value of the electron wave function on the surface and (or) the structure gettering of the free carriers.
32

Emelianova, N., I. V. Fialkovsky, and N. Khusnutdinov. "Casimir effect for biaxial anisotropic plates with surface conductivity." Modern Physics Letters A 35, no. 03 (January 16, 2020): 2040012. http://dx.doi.org/10.1142/s021773232040012x.

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The Casimir energy is constructed for a system consisting of two semi-infinite slabs of anisotropic material. Each of them is characterized by bulk complex dielectric permittivity tensor and surface conductivity on the free boundary. We found general form of the scattering matrix and Fresnel coefficients for each part of the system by solving Maxwell equations in the anisotropic media.
33

MUKHOPADHYAY, INDRANIL, and A. ROY CHOWDHURY. "ANISOTROPIC AFFINE ALGEBRA AND ANISOTROPIC WZW MODEL." Modern Physics Letters A 10, no. 20 (June 28, 1995): 1441–48. http://dx.doi.org/10.1142/s0217732395001551.

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Invariant action for a new kind of (anisotropic) WZW model has been constructed using the co-adjoint orbit approach and the affine anistropic algebra suggested by Sidorenko. The Alekseev-Shatashvili type of equation is used to construct the corresponding symplectic form. The present model is similar in many aspects to the WZW model on a Riemann surface.
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KYRIAKOPOULOS, E. "FAMILY OF ROTATING ANISOTROPIC FLUID SOLUTIONS WHICH MATCH TO KERR'S SOLUTION." International Journal of Modern Physics D 22, no. 07 (June 2013): 1350051. http://dx.doi.org/10.1142/s021827181350051x.

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We present a family of exact rotating anisotropic fluid solutions, which satisfy all energy conditions for certain values of their parameters. The components of the Ricci tensor Rμν the eigenvalues of the tensor [Formula: see text] and the energy–momentum tensor Tμν of the solutions are given explicitly. All members of the family have the ring singularity of Kerr's solution and most of them have one or two more singularities. The solutions can be matched to the solution of Kerr on three closed surfaces, which for proper values of the parameters of the solutions approximate oblate spheroids. All matching surfaces are thin shells. For some values of a constant the surface density in one of them is positive everywhere and in this surface and in its interior all energy conditions are satisfied.
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Łysko, Jan M. "Anisotropic etching of the silicon crystal-surface free energy model." Materials Science in Semiconductor Processing 6, no. 4 (August 2003): 235–41. http://dx.doi.org/10.1016/j.mssp.2003.09.003.

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Burger, Martin. "Numerical simulation of anisotropic surface diffusion with curvature-dependent energy." Journal of Computational Physics 203, no. 2 (March 2005): 602–25. http://dx.doi.org/10.1016/j.jcp.2004.08.024.

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Gurski, K. F., and G. B. McFadden. "The effect of anisotropic surface energy on the Rayleigh instability." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 459, no. 2038 (October 8, 2003): 2575–98. http://dx.doi.org/10.1098/rspa.2003.1144.

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Koike, Naoyuki. "A holonomy invariant anisotropic surface energy in a Riemannian manifold." Differential Geometry and its Applications 44 (February 2016): 98–121. http://dx.doi.org/10.1016/j.difgeo.2015.11.003.

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SHEN, LIAN, and DICK K. P. YUE. "Large-eddy simulation of free-surface turbulence." Journal of Fluid Mechanics 440 (August 10, 2001): 75–116. http://dx.doi.org/10.1017/s0022112001004669.

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In this paper we investigate the large-eddy simulation (LES) of the interaction between a turbulent shear flow and a free surface at low Froude numbers. The benchmark flow field is first solved by using direct numerical simulations (DNS) of the Navier–Stokes equations at fine (1282 × 192 grid) resolution, while the LES is performed at coarse resolution. Analysis of the ensemble of 25 DNS datasets shows that the amount of energy transferred from the grid scales to the subgrid scales (SGS) reduces significantly as the free surface is approached. This is a result of energy backscatter associated with the fluid vertical motions. Conditional averaging reveals that the energy backscatter occurs at the splat regions of coherent hairpin vortex structures as they connect to the free surface. The free-surface region is highly anisotropic at all length scales while the energy backscatter is carried out by the horizontal components of the SGS stress only. The physical insights obtained here are essential to the efficacious SGS modelling of LES for free-surface turbulence. In the LES, the SGS contribution to the Dirichlet pressure free-surface boundary condition is modelled with a dynamic form of the Yoshizawa (1986) expression, while the SGS flux that appears in the kinematic boundary condition is modelled by a dynamic scale-similarity model. For the SGS stress, we first examine the existing dynamic Smagorinsky model (DSM), which is found to capture the free-surface turbulence structure only roughly. Based on the special physics of free-surface turbulence, we propose two new SGS models: a dynamic free-surface function model (DFFM) and a dynamic anisotropic selective model (DASM). The DFFM correctly represents the reduction of the Smagorinsky coefficient near the surface and is found to capture the surface layer more accurately. The DASM takes into account both the anisotropy nature of free-surface turbulence and the dependence of energy backscatter on specific coherent vorticity mechanisms, and is found to produce substantially better surface signature statistics. Finally, we show that the combination of the new DFFM and DASM with a dynamic scale-similarity model further improves the results.
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Guseynov, Sharif E., and Jekaterina V. Aleksejeva. "MODELLING AND INVESTIGATION OF THE DEPENDENCE OF SUPERHYDROPHOBIC PROPERTIES OF NANOSURFACES ON THE TOPOLOGY OF MICROCHANNELS." ENVIRONMENT. TECHNOLOGIES. RESOURCES. Proceedings of the International Scientific and Practical Conference 3 (June 20, 2019): 52. http://dx.doi.org/10.17770/etr2019vol3.4171.

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In the Cassie-Baxter state anisotropic superhydrophobic surfaces have high lubricating properties. Such superhydrophobic surfaces are used in medical implants, aircraft industry, vortex bioreactors etc. In spite of the fact that quantitative understanding of fluid dynamics on anisotropic superhydrophobic surfaces has been broadened substantially for last several years, there still are some unsolved problems in this field. This work investigates dynamics of a liquid on unidirectional superhydrophobic surfaces in the Cassie-Baxter state, when surface texture is filled with gas and, consequently, the liquid virtually is located on some kind of an air cushion. Energy of the interphase boundary liquid-gas is much smaller than energy of the interphase boundary solid-liquid, that is why the contact angle at wetting such surfaces differs a lot from the Young contact angle and depends on contact area ratio of liquid-gas and liquid-solid in visible contact of liquid and surface. Considering difference in energy obtained if we slightly shift the three-phase contact line, expression for macroscopic equilibrium contact angle, which describes the Cassie-Baxter state, can be deduced. In the work the design formula for computing local-slip length profiles of liquid on the considered superhydrophobic surfaces is obtained.
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Mighani, Saied, Carl H. Sondergeld, and Chandra S. Rai. "Observations of Tensile Fracturing of Anisotropic Rocks." SPE Journal 21, no. 04 (August 15, 2016): 1289–301. http://dx.doi.org/10.2118/2014-1934272-pa.

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Summary Hydraulic fracturing is crucial to hydrocarbon recovery from resource plays and is essential to exploitation of geothermal energy. This process creates new tensile fractures and reactivates existing natural fractures, forming a highly conductive stimulated-reservoir volume (SRV) around the borehole. Although this process has been extensively studied and modeled for isotropic rock, only a limited number of studies have been performed for anisotropic rocks, such as shales, gneisses, and foliated granites. The fracturing process of anisotropic rocks such as shales is examined in this study. We divide the rock anisotropy into two anisotropic groups: conventional and veined. Two members of the conventional first group are Lyons sandstone, a brittle, quartz-dominated, low-porosity and -permeability, anisotropic (11%) material; and pyrophyllite, a monomineralic-clay-rich, strongly anisotropic (19%) metamorphic rock similar chemically and mechanically to shale with extremely low porosity and permeability. The second group consists of a suite of natural shale samples (18% anisotropy) from the Wolfcamp formation containing mineralized veins. Fracture initiation and propagation are studied during Brazilian tests. Strain gauges and acoustic-emission (AE) sensors record the deformation leading to and during failure. Scanning-electron-microscope (SEM) imaging and surface profilometry are used to study the post-failure fracture system and failed surface topology. Post-fracture permeability is measured as a function of effective stress. The influence of anisotropy on fracturing is investigated by rotating the sample-fabric direction relative to the loading axis through increments of 15°. The rock microstructure, lamination, and brittleness control the activation of the layers. Lyons sandstone shows a wide brittle fracture with larger process zone with twice as much layer activation at lower stress levels than pyrophyllite. The fracturing process in veined shale is, however, a coupled function of rock fabric and mineral veins. The veins easily activate at 15° orientation with respect to the loading axis at stress levels of 30% of the unveined-failure load. The resulting unpropped fracture has enhanced permeability by orders of magnitude. We suggest that fracturing from a deviated well reduces the breakdown pressure significantly (compared with a vertical well) and activates a large number of veins with enhanced conductivity without the need for excessive proppant.
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Govender, M., R. S. Bogadi, D. B. Lortan, and S. D. Maharaj. "Radiating collapse in the presence of anisotropic stresses." International Journal of Modern Physics D 25, no. 03 (March 2016): 1650037. http://dx.doi.org/10.1142/s0218271816500371.

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In this paper, we investigate the effect of anisotropic stresses (radial and tangential pressures being unequal) for a collapsing fluid sphere dissipating energy in the form of radial flux. The collapse starts from an initial static sphere described by the Bowers and Liang solution and proceeds until the time of formation of the horizon. We find that the surface redshift increases as the stellar fluid moves away from isotropy. We explicitly show that the formation of the horizon is delayed in the presence of anisotropy. The evolution of the temperature profiles is investigated by employing a causal heat transport equation of the Maxwell–Cattaneo form. Both the Eckart and causal temperatures are enhanced by anisotropy at each interior point of the stellar configuration.
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Ren, Shaoting, Evan S. Miles, Li Jia, Massimo Menenti, Marin Kneib, Pascal Buri, Michael J. McCarthy, Thomas E. Shaw, Wei Yang, and Francesca Pellicciotti. "Anisotropy Parameterization Development and Evaluation for Glacier Surface Albedo Retrieval from Satellite Observations." Remote Sensing 13, no. 9 (April 28, 2021): 1714. http://dx.doi.org/10.3390/rs13091714.

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Glacier albedo determines the net shortwave radiation absorbed at the glacier surface and plays a crucial role in glacier energy and mass balance. Remote sensing techniques are efficient means to retrieve glacier surface albedo over large and inaccessible areas and to study its variability. However, corrections of anisotropic reflectance of glacier surface have been established for specific shortwave bands only, such as Landsat 5 Thematic Mapper (L5/TM) band 2 and band 4, which is a major limitation of current retrievals of glacier broadband albedo. In this study, we calibrated and evaluated four anisotropy correction models for glacier snow and ice, applicable to visible, near-infrared and shortwave-infrared wavelengths using airborne datasets of Bidirectional Reflectance Distribution Function (BRDF). We then tested the ability of the best-performing anisotropy correction model, referred to from here on as the ‘updated model’, to retrieve albedo from L5/TM, Landsat 8 Operational Land Imager (L8/OLI) and Moderate Resolution Imaging Spectroradiometer (MODIS) imagery, and evaluated these results with field measurements collected on eight glaciers around the world. Our results show that the updated model: (1) can accurately estimate anisotropic factors of reflectance for snow and ice surfaces; (2) generally performs better than prior approaches for L8/OLI albedo retrieval but is not appropriate for L5/TM; (3) generally retrieves MODIS albedo better than the MODIS standard albedo product (MCD43A3) in both absolute values and glacier albedo temporal evolution, i.e., exhibiting both fewer gaps and better agreement with field observations. As the updated model enables anisotropy correction of a maximum of 10 multispectral bands and is implemented in Google Earth Engine (GEE), it is promising for observing and analyzing glacier albedo at large spatial scales.
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Stiperski, Ivana, Marcelo Chamecki, and Marc Calaf. "Anisotropy of Unstably Stratified Near-Surface Turbulence." Boundary-Layer Meteorology 180, no. 3 (June 15, 2021): 363–84. http://dx.doi.org/10.1007/s10546-021-00634-0.

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AbstractClassic Monin–Obukov similarity scaling states that in a stationary, horizontally homogeneous flow, in the absence of subsidence, turbulence is dictated by the balance between shear production and buoyancy production/destruction, whose ratio is characterized by a single universal scaling parameter. An evident breakdown in scaling is observed though, through large scatter in traditional scaling relations for the horizontal velocity variances under unstable stratification, or more generally in complex flow conditions. This breakdown suggests the existence of processes other than local shear and buoyancy that modulate near-surface turbulence. Recent studies on the role of anisotropy in similarity scaling have shown that anisotropy, even if calculated locally, may encode the information about these missing processes. We therefore examine the possible processes that govern the degree of anisotropy in convective conditions. We first use the reduced turbulence-kinetic-energy budget to show that anisotropy in convective conditions cannot be uniquely described by a balance of buoyancy and shear production and dissipation, but that other terms in the budget play an important role. Subsequently, we identify a ratio of local time scales that acts as a proxy for the anisotropic state of convective turbulence. This ratio can be used to formulate a new non-dimensional group. Results show that building on this approach the role of anisotropy in scaling relations over complex terrain can be placed into a more generalized framework.
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Li, Haifeng, Wei Wang, Yajun Cao, and Shifan Liu. "Phase-Field Modeling Fracture in Anisotropic Materials." Advances in Civil Engineering 2021 (July 30, 2021): 1–13. http://dx.doi.org/10.1155/2021/4313755.

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The phase-field method is a widely used technique to simulate crack initiation, propagation, and coalescence without the need to trace the fracture surface. In the phase-field theory, the energy to create a fracture surface per unit area is equal to the critical energy release rate. Therefore, the precise definition of the crack-driving part is the key to simulate crack propagation. In this work, we propose a modified phase-field model to capture the complex crack propagation, in which the elastic strain energy is decomposed into volumetric-deviatoric energy parts. Because of the volumetric-deviatoric energy split, we introduce a novel form of the crack-driving energy to simulate mixed-mode fracture. Furthermore, a new degradation function is proposed to simulate crack processes in brittle materials with different degradation rates. The proposed model is implemented by a staggered algorithm and to validate the performance of the phase-field modelling, and several numerical examples are constructed under plane strain condition. All the presented examples demonstrate the capability of the proposed approach in solving problems of brittle fracture propagation.
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Fiedler, Thomas, Graeme E. Murch, Timo Bernthaler, and Irina V. Belova. "Numerical Characterization of Anisotropic Heat Sink Composites." Materials Science Forum 654-656 (June 2010): 1500–1503. http://dx.doi.org/10.4028/www.scientific.net/msf.654-656.1500.

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This work addresses the numerical analysis of anisotropic composite structures for thermal energy storage and temperature stabilization. The basic idea of heat sink composites is the combination of metallic matrices for fast energy transfer with phase change materials for thermal energy storage. Anisotropic matrices, such as lotus-type structures, allow for increased control of the thermal energy flow, without the necessity of additional thermal insulation. As an example, thermal energy can be directed towards a surface cooled by convection and excess energy is stored in the phase-change material. Computed tomography data of copper lotus-type material is used for the generation of the numerical calculation models. Due to its particular meso-structure, this material is characterised by strongly anisotropic properties. The void space of this cellular metal is filled with the phase-change material paraffin in order to enhance the energy storage capacity. A recently extended Lattice Monte Carlo method is used to evaluate the anisotropic thermal properties of these promising materials.
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Stölken, J. S., and A. M. Glaeser. "The morphological evolution of cylindrical rods with anisotropic surface free energy via surface diffusion." Scripta Metallurgica et Materialia 27, no. 4 (August 1992): 449–54. http://dx.doi.org/10.1016/0956-716x(92)90209-w.

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Ji, Jie, Kangnan Meng, Pin Li, and Zongbao Shen. "Fabrication of biomimetic anisotropic crescent-shaped microstructured surfaces by laser shock imprinting." Materials Science-Poland 41, no. 3 (September 1, 2023): 140–58. http://dx.doi.org/10.2478/msp-2023-0039.

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Abstract The crescent-shaped microstructure bionic to the slip zone of the slippery zone of the carnivorous plant genus Nepenthes was fabricated on the surface of copper foil by laser shock imprinting (LSI). The microstructure of crescent-shaped grooves was initially fabricated on the surface of the micro-mold by etching, and then the microstructure was replicated on the surface of copper foil through plastic deformation under laser shock loading. Increasing the laser shock energy or the number of shocks can increase the degree of replication of the crescent-shaped microstructure, the height of the crescent-shaped microstructure, and the contact angle of water droplets on the surface. The wettability of the surface of the crescent microstructure is anisotropic and increases with an increase in offset distance. The anisotropy of the crescent-shaped microstructure causes the solid–liquid contact line in the direction of the bottom of the arc to become a long and approximately straight line. According to the rule that controlling LSI processing parameters can fabricate surfaces with different heights and wettability, a gradient wetting surface consisting of crescent-shaped microstructures was designed to achieve the directional spreading of droplets. By altering the distribution of crescent-shaped microstructures, a type-I flow channel with the ability to limit the spreading range of water droplets was fabricated.
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Bartolomé, Juan, E. Bartolomé, V. V. Eremenko, V. V. Ibulaev, Valentyna Sirenko, and Yu T. Petrusenko. "Magnetic Anisotropy in 2H-NbSe2 Electron Irradiated Single Crystals." Solid State Phenomena 152-153 (April 2009): 470–73. http://dx.doi.org/10.4028/www.scientific.net/ssp.152-153.470.

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The anisotropic magnetic properties of the metallic layered compound with hexagonal crystal structure 2H-NbSe2 are investigated as a function of their dependence on high-energy electron irradiation. Pauli paramagnetism of free electrons is shown to dominate the magnetic susceptibility, P. The anisotropy is related to spin-orbit effects on the hybridized electronic states. Irradiation affects the density of states at the Fermi surface, increasing both P and the anisotropy. Below a threshold temperature, TS=54 K, the paramagnetic contribution, which increases with the dose, is ascribed to dangling bonds, nanotubes and nanorods generated by irradiation.
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Zhang, Lin, Raymond Barrett, Peter Cloetens, Carsten Detlefs, and Manuel Sanchez del Rio. "Anisotropic elasticity of silicon and its application to the modelling of X-ray optics." Journal of Synchrotron Radiation 21, no. 3 (April 4, 2014): 507–17. http://dx.doi.org/10.1107/s1600577514004962.

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The crystal lattice of single-crystal silicon gives rise to anisotropic elasticity. The stiffness and compliance coefficient matrix depend on crystal orientation and, consequently, Young's modulus, the shear modulus and Poisson's ratio as well. Computer codes (in Matlab and Python) have been developed to calculate these anisotropic elasticity parameters for a silicon crystal in any orientation. These codes facilitate the evaluation of these anisotropy effects in silicon for applications such as microelectronics, microelectromechanical systems and X-ray optics. For mechanically bent X-ray optics, it is shown that the silicon crystal orientation is an important factor which may significantly influence the optics design and manufacturing phase. Choosing the appropriate crystal orientation can both lead to improved performance whilst lowering mechanical bending stresses. The thermal deformation of the crystal depends on Poisson's ratio. For an isotropic constant Poisson's ratio, ν, the thermal deformation (RMS slope) is proportional to (1 + ν). For a cubic anisotropic material, the thermal deformation of the X-ray optics can be approximately simulated by using the average of ν12and ν13as an effective isotropic Poisson's ratio, where the direction 1 is normal to the optic surface, and the directions 2 and 3 are two normal orthogonal directions parallel to the optical surface. This average is independent of the direction in the optical surface (the crystal plane) for Si(100), Si(110) and Si(111). Using the effective isotropic Poisson's ratio for these orientations leads to an error in thermal deformation smaller than 5.5%.

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