Showing papers on "Isotropy published in 2013"
TL;DR: In this paper, a higher-order shear deformation theory for modeling functionally graded plates accounting for extensibility in the thickness direction is derived, and the explicit governing equations and boundary conditions are obtained using the principle of virtual displacements under Carrera's Unified Formulation.
Abstract: In this paper the authors derive a higher-order shear deformation theory for modeling functionally graded plates accounting for extensibility in the thickness direction. The explicit governing equations and boundary conditions are obtained using the principle of virtual displacements under Carrera’s Unified Formulation. The static and eigenproblems are solved by collocation with radial basis functions. The efficiency of the present approach is assessed with numerical results including deflection, stresses, free vibration, and buckling of functionally graded isotropic plates and functionally graded sandwich plates.
435 citations
TL;DR: Hyperelastic models of transversely isotropic tissues such as white matter should include contributions of both the I4 and I5 strain pseudo-invariants, and behavior in the small strain regime can usefully guide the choice and initial parameterization of more general material models of white matter.
Abstract: White matter in the brain is structurally anisotropic, consisting largely of bundles of aligned, myelin-sheathed axonal fibers. White matter is believed to be mechanically anisotropic as well. Specifically, transverse isotropy is expected locally, with the plane of isotropy normal to the local mean fiber direction. Suitable material models involve strain energy density functions that depend on the I 4 and I 5 pseudo-invariants of the Cauchy–Green strain tensor to account for the effects of relatively stiff fibers. The pseudo-invariant I 4 is the square of the stretch ratio in the fiber direction; I 5 contains contributions of shear strain in planes parallel to the fiber axis. Most, if not all, published models of white matter depend on I 4 but not on I 5 . Here, we explore the small strain limits of these models in the context of experimental measurements that probe these dependencies. Models in which strain energy depends on I 4 but not I 5 can capture differences in Young's (tensile) moduli, but will not exhibit differences in shear moduli for loading parallel and normal to the mean direction of axons. We show experimentally, using a combination of shear and asymmetric indentation tests, that white matter does exhibit such differences in both tensile and shear moduli. Indentation tests were interpreted through inverse fitting of finite element models in the limit of small strains. Results highlight that: (1) hyperelastic models of transversely isotropic tissues such as white matter should include contributions of both the I 4 and I 5 strain pseudo-invariants; and (2) behavior in the small strain regime can usefully guide the choice and initial parameterization of more general material models of white matter.
245 citations
TL;DR: The experimental realization of an isotropic complete photonic band gap (PBG) in a 2D disordered dielectric structure and realization of functional defects in this unique class of materials demonstrate their potential as building blocks for precise manipulation of photons in planar optical microcircuits and has implications for disordered acoustic and electronic band gap materials.
Abstract: Recently, disordered photonic media and random textured surfaces have attracted increasing attention as strong light diffusers with broadband and wide-angle properties. We report the experimental realization of an isotropic complete photonic band gap (PBG) in a 2D disordered dielectric structure. This structure is designed by a constrained optimization method, which combines advantages of both isotropy due to disorder and controlled scattering properties due to low-density fluctuations (hyperuniformity) and uniform local topology. Our experiments use a modular design composed of Al2O3 walls and cylinders arranged in a hyperuniform disordered network. We observe a complete PBG in the microwave region, in good agreement with theoretical simulations, and show that the intrinsic isotropy of this unique class of PBG materials enables remarkable design freedom, including the realization of waveguides with arbitrary bending angles impossible in photonic crystals. This experimental verification of a complete PBG and realization of functional defects in this unique class of materials demonstrate their potential as building blocks for precise manipulation of photons in planar optical microcircuits and has implications for disordered acoustic and electronic band gap materials.
198 citations
TL;DR: In this paper, the anisotropic nature of solar wind magnetic turbulence fluctuations is investigated scale by scale using high cadence in situ magnetic field measurements from the Cluster and ACE spacecraft missions.
Abstract: The anisotropic nature of solar wind magnetic turbulence fluctuations is investigated scale by scale using high cadence in situ magnetic field measurements from the Cluster and ACE spacecraft missions. The data span five decades in scales from the inertial range to the electron Larmor radius. In contrast to the inertial range, there is a successive increase toward isotropy between parallel and transverse power at scales below the ion Larmor radius, with isotropy being achieved at the electron Larmor radius. In the context of wave-mediated theories of turbulence, we show that this enhancement in magnetic fluctuations parallel to the local mean background field is qualitatively consistent with the magnetic compressibility signature of kinetic Alfven wave solutions of the linearized Vlasov equation. More generally, we discuss how these results may arise naturally due to the prominent role of the Hall term at sub-ion Larmor scales. Furthermore, computing higher-order statistics, we show that the full statistical signature of the fluctuations at scales below the ion Larmor radius is that of a single isotropic globally scale-invariant process distinct from the anisotropic statistics of the inertial range.
193 citations
TL;DR: In this article, it was shown that the nonlinear interplay between surface osmotic flows and solute advection can produce spontaneous and self-sustained motion of isotropic particles.
Abstract: Suspended colloidal particles interacting chemically with a solute can self-propel by autophoretic motion when they are asymmetrically patterned (Janus colloids). Here we demonstrate theoretically that such anisotropy is not necessary for locomotion and that the nonlinear interplay between surface osmotic flows and solute advection can produce spontaneous and self-sustained motion of isotropic particles. Solving the classical autophoretic framework for isotropic particles, we show that, for given material properties, there exists a critical particle size (or Peclet number) above which spontaneous symmetry-breaking and autophoretic motion occur. A hierarchy of instabilities is further identified for quantized critical Peclet numbers.
169 citations
TL;DR: In this article, a numerical procedure based on computation of the scattering patterns of the different parameters to assess the sensitivity of the seismic data to different parameterizations of vertical transverse isotropic media in the acoustic approximation is presented.
Abstract: In most geologic environments, accounting for anisotropy is necessary to perform acoustic full waveform inversion (FWI) of wide-azimuth and wide-aperture seismic data because of the potential dependence of wave speeds on the direction of the wave propagation. In the framework of multiparameter FWI, the subsurface parameterization controls the influence of the different parameter classes on the modeled seismic data as a function of the scattering angle and hence the resolution with which the parameters can be reconstructed and the potential trade-off between different parameters. We have evaluated a numerical procedure based on computation of the scattering patterns of the different parameters to assess the sensitivity of the seismic data to different parameterizations of vertical transverse isotropic media in the acoustic approximation. Among the different categories we have tested, a monoparametric FWI was found for imaging one wave speed with a broad wavenumber content, keeping the Thomsen param...
161 citations
TL;DR: In this article, a higher-order shear and normal deformation theory for the bending and free vibration analysis of sandwich plates with functionally graded isotropic face sheets is developed, which accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor.
Abstract: In this paper, a new higher-order shear and normal deformation theory for the bending and free vibration analysis of sandwich plates with functionally graded isotropic face sheets is developed. The number of unknown functions involved in the present theory is only five, as against six or more in case of other shear and normal deformation theories. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. The boundary conditions for the plate are assumed to be simply supported in all edges and in the static analysis, the plate is assumed to be subjected to a sinusoidally distributed load. Both symmetric and non-symmetric sandwich plates are considered. The equations of motion are obtained using Hamilton’s principle. Numerical results of present theory are compared with three-dimensional elasticity solutions and other higher-order theories reported in the literature. ...
153 citations
TL;DR: In this article, a coarse-grained model for steady-state granular flows was proposed, where the macroscopic fields involved density, velocity, granular temperature, as well as strain-rate, stress, and fabric structure tensors.
Abstract: Dry, frictional, steady-state granular flows down an inclined, rough surface are studied with discrete particle simulations. From this exemplary flow situation, macroscopic fields, consistent with the conservation laws of continuum theory, are obtained from microscopic data by time-averaging and spatial smoothing (coarse-graining). Two distinct coarse-graining length scale ranges are identified, where the fields are almost independent of the smoothing length w. The smaller, sub-particle length scale, w ≪ d, resolves layers in the flow near the base boundary that cause oscillations in the macroscopic fields. The larger, particle length scale, w ≈ d, leads to smooth stress and density fields, but the kinetic stress becomes scale-dependent; however, this scale-dependence can be quantified and removed. The macroscopic fields involve density, velocity, granular temperature, as well as strain-rate, stress, and fabric (structure) tensors. Due to the plane strain flow, each tensor can be expressed in an inherently anisotropic form with only four objective, coordinate frame invariant variables. For example, the stress is decomposed as: (i) the isotropic pressure, (ii) the “anisotropy” of the deviatoric stress, i.e., the ratio of deviatoric stress (norm) and pressure, (iii) the anisotropic stress distribution between the principal directions, and (iv) the orientation of its eigensystem. The strain rate tensor sets the reference system, and each objective stress (and fabric) variable can then be related, via discrete particle simulations, to the inertial number, I. This represents the plane strain special case of a general, local, and objective constitutive model. The resulting model is compared to existing theories and clearly displays small, but significant deviations from more simplified theories in all variables – on both the different length scales.
149 citations
TL;DR: In this article, the authors report mechanical properties of single-layer hexagonal boron-nitride (h-BN) and its band structures tuned by straining by using the density functional theory calculations.
Abstract: Current interest in two-dimensional materials extends from graphene to others systems such as single-layer hexagonal boron-nitride (h-BN), for the possibility of making heterogeneous structures. Here, we report mechanical properties of h-BN and its band structures tuned by straining by using the density functional theory calculations. Young’s modulus and bending rigidity for h-BN are isotropic; its failure strength and failure strain show strong anisotropy. A small fraction of antisite defects in h-BN can largely decrease its mechanical properties. We reveal that strain can tune single-layer h-BN from an insulator to a semiconductor.
143 citations
TL;DR: In this article, the effect of inclusions geometry, volume fraction, and properties contrast on the effective thermal conductivity and elastic modulus of isotropic random two-phase composite materials with low fillers content was analyzed.
Abstract: In this study, finite element, Mori–Tanaka and strong contrast modeling are carried out for the prediction of the effective thermal conductivity and elastic modulus of isotropic random two-phase composite materials with low fillers content. Effects of inclusions geometry (shape), volume fraction (1% and 3%) and properties contrast on the effective thermal conductivity and elastic modulus are analyzed. Our results show that finite element method could capture more details in the prediction of effective properties of the composite materials. On the other hand, Mori–Tanaka method is shown to be a fast as well as a valid alternative for the finite element modeling within a limited range of fillers geometries. Our results reveal that the strong contrast method based on statistical two-point correlation functions could not accurately describe the inclusions geometry effects.
143 citations
TL;DR: In this paper, anisotropic heterogeneous geotechnical fields are characterized using random field theory, in which five basic patterns of material anisotropy are simulated including isotropy, trans...
Abstract: In this study, anisotropic heterogeneous geotechnical fields are characterized using random field theory, in which five basic patterns of material anisotropy are simulated including isotropy, trans...
TL;DR: In this article, the influence of strong external magnetic fields on gluonic and fermionic observables in the QCD vacuum at zero and nonzero temperatures, via lattice simulations with N_f = 1+1+1 staggered quarks of physical masses, was studied.
Abstract: We study the influence of strong external magnetic fields on gluonic and fermionic observables in the QCD vacuum at zero and nonzero temperatures, via lattice simulations with N_f=1+1+1 staggered quarks of physical masses. The gluonic action density is found to undergo magnetic catalysis at low temperatures and inverse magnetic catalysis near and above the transition temperature, similar to the quark condensate. Moreover, the gluonic action develops an anisotropy: the chromo-magnetic field parallel to the external field is enhanced, while the chromo-electric field in this direction is suppressed. We demonstrate that the same hierarchy is obtained using the Euler-Heisenberg effective action. Conversely, the topological charge density correlator does not reveal a significant anisotropy up to magnetic fields eB~1 GeV^2. Furthermore, we show that the pressure remains isotropic even for nonzero magnetic fields, if it is defined through a compression of the system at fixed external field. In contrast, if the flux of the field is kept fixed during the compression -- which is the situation realized in the lattice simulation -- the pressure develops an anisotropy. We estimate the quark and gluonic contributions to this anisotropy, and relate them to the magnetization of the QCD vacuum. After performing electric charge renormalization, we obtain an estimate for the magnetization, which indicates that QCD is paramagnetic.
TL;DR: In this paper, the authors derived exact solutions of static wormholes in f(T) gravity by considering independent cases of the pressure components including isotropic and anisotropic pressure.
Abstract: In this paper, we derive some new exact solutions of static wormholes in f(T) gravity. We discuss independent cases of the pressure components including isotropic and anisotropic pressure. Lastly we consider radial pressure satisfying a barotropic equation of state. We also check the behavior of null energy condition (NEC) for each case and observe that it is violated for the anisotropic case, while it is satisfied for isotropic and barotropic cases.
TL;DR: The first experimental demonstration of a TE-polarization photonic band gap (PBG) in a 2D isotropic hyperuniform disordered solid (HUDS) made of dielectric media with a dielectrics index contrast of 1.6:1 is reported.
Abstract: We report the first experimental demonstration of a TE-polarization photonic band gap (PBG) in a 2D isotropic hyperuniform disordered solid (HUDS) made of dielectric media with a dielectric index contrast of 1.6:1, very low for PBG formation. The solid is composed of a connected network of dielectric walls enclosing air-filled cells. Direct comparison with photonic crystals and quasicrystals permitted us to investigate band-gap properties as a function of increasing rotational isotropy. We present results from numerical simulations proving that the PBG observed experimentally for HUDS at low index contrast has zero density of states. The PBG is associated with the energy difference between complementary resonant modes above and below the gap, with the field predominantly concentrated in the air or in the dielectric. The intrinsic isotropy of HUDS may offer unprecedented flexibilities and freedom in applications (i. e. defect architecture design) not limited by crystalline symmetries.
TL;DR: The present model can be used for free vibration analysis of single-walled carbon nanotubes with essential, natural and nonlinear boundary conditions.
TL;DR: The electron diffusion region during magnetic reconnection lies in different regimes depending on the pressure anisotropy, which is regulated by the properties of thermal electron orbits as discussed by the authors, and it offers an explanation for recent spacecraft observations.
Abstract: The electron diffusion region during magnetic reconnection lies in different regimes depending on the pressure anisotropy, which is regulated by the properties of thermal electron orbits. In kinetic simulations at the weakest guide fields, pitch angle mixing in velocity space causes the outflow electron pressure to become nearly isotropic. Above a threshold guide field that depends on a range of parameters, including the normalized electron pressure and the ion-to-electron mass ratio, electron pressure anisotropy develops in the exhaust and supports extended current layers. This new regime with electron current sheets extending to the system size is also reproduced by fluid simulations with an anisotropic closure for the electron pressure. It offers an explanation for recent spacecraft observations.
TL;DR: The paper describes a particle-resolved simulation method for turbulent flow laden with finite size particles based on the multiple-relaxation-time lattice Boltzmann equation and the resulting code is found to be computationally efficient with a good scalability.
Abstract: The paper describes a particle-resolved simulation method for turbulent flow laden with finite size particles. The method is based on the multiple-relaxation-time lattice Boltzmann equation. The no-slip boundary condition on the moving particle boundaries is handled by a second-order interpolated bounce-back scheme. The populations at a newly converted fluid lattice node are constructed by the equilibrium distribution with non-equilibrium corrections. MPI implementation details are described and the resulting code is found to be computationally efficient with a good scalability. The method is first validated using unsteady sedimentation of a single particle and sedimentation of a random suspension. It is then applied to a decaying isotropic turbulence laden with particles of Kolmogorov to Taylor microscale sizes. At a given particle volume fraction, the dynamics of the particle-laden flow is found to depend mainly on the effective particle surface area and particle Stokes number. The presence of finite-size inertial particles enhances dissipation at small scales while reducing kinetic energy at large scales. This is in accordance with related studies. The normalized pivot wavenumber is found to not only depend on the particle size, but also on the ratio of particle size to flow scales and particle-to-fluid density ratio.
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08 May 2013
TL;DR: The failure theory for isotropic materials failure behavior for fiber composite laminates is described in this article, where the authors define yield stress and failure stress (strength) for fiber composites.
Abstract: 1 The perspective on failure and direction of approach 2 History, conditions, and requirements 3 Isotropic baselines 4 The failure theory for isotropic materials 5 Isotropic materials failure behavior 6 Experimental and theoretical evaluation 7 Isotropic materials failure examples 8 The ductile/brittle transition for isotropic materials 9 Defining yield stress and failure stress (strength) 10 Fracture mechanics 11 Anisotropic, unidirectional fiber composites failure 12 Anisotropic, fiber composite laminates failure 13 Micromechanics failure analysis 14 Nanomechanics failure analysis 15 Damage, cumulative damage, creep, and fatigue failure 16 Probabilistic failure and probabilistic life prediction
TL;DR: In this article, an efficient domain decomposition method is proposed for solving the free, harmonic and transient vibrations of isotropic and composite cylindrical shells subjected to various combinations of classical and non-classical boundary conditions.
TL;DR: In this paper, a model of the FGM beams is first put forward by using on physical neutral surface and high-order shear deformation theory, and material properties are assumed to be temperature dependent and vary along the thickness.
TL;DR: In this paper, it was shown that a necessary consequence of this reduced form of the strain energy function is that the infinitesimal shear moduli are identical, an assumption that is not supported by experimental data.
Abstract: Skeletal muscles, ligaments and tendons are typically assumed to be incompressible, transversely isotropic, non-linearly hyperelastic materials. If one adopts the phenomenological approach to modelling, then the corresponding strain-energy function can be represented as an arbitrary function of two invariants of the Cauchy–Green strain tensors, representing the isotropic contribution, and two pseudo-invariants, representing the anisotropic contribution. For mathematical convenience, dependence on one of these pseudo-invariants is usually dropped. It will be shown here that a necessary consequence of this reduced form of the strain-energy function is that the infinitesimal shear moduli are identical, an assumption that is not supported by experimental data. It will also be shown that a further consequence is that two out of the three shearing modes are identical over the full range of deformation. The conclusion is that transversely isotropic biological, soft tissue must be modelled using both anisotropic invariants.
TL;DR: In this article, a general formalism to model polytropic Newtonian stars with anisotropic pressure was proposed and a heuristic model based on an ansatz was adopted to obtain anisotropic matter solutions from known solutions for isotropic matter.
Abstract: We set up the general formalism to model polytropic Newtonian stars with anisotropic pressure. We obtain the corresponding Lane-Emden equation. A heuristic model based on an ansatz to obtain anisotropic matter solutions from known solutions for isotropic matter is adopted to illustrate the effects of the pressure anisotropy on the structure of the star. In particular, we calculate the Chandrasekhar mass for a white dwarf. It is clearly displayed how the Chandrasekhar mass limit changes depending on the anisotropy. Prospective astrophysical applications of the proposed approach are discussed.
TL;DR: In this paper, the macroscopic response and stability of a new type of magnetorheological elastomer (MRE) under combined in-plane mechanical and magnetic loading by means of the finite-strain homogenization framework and partial decoupling approximation was analyzed.
Abstract: This paper is concerned with the development of constitutive models for a class of magnetoelastic composites consisting of stiff, aligned cylindrical fibers of a magnetizable material that are embedded firmly in a soft elastomeric matrix. The fibers have elliptical cross section and their (transverse) in-plane axes are also aligned, but their distribution is random and characterized by “elliptical” two-point correlations. Estimates are obtained for the macroscopic response and stability of this new type of magnetorheological elastomer (MRE) under combined in-plane mechanical and magnetic loading by means of the finite-strain homogenization framework and “partial decoupling approximation” of Ponte Castaneda and Galipeau (2011) . The resulting macroscopic magnetoelastic constitutive model accounts for the microstructure of the composite and its evolution under finite strains and rotations, as well as for the nonlinear magnetic behavior of the fibers, including the effect of magnetic saturation. When the loading directions are not aligned with the fiber axes, the model predicts magnetic and mechanical torques on the fibers, leading to their in-plane rotation, which is found to have significant effects on the coupled magnetoelastic response of the composite, including the possible development of macroscopic torques on a given finite-size sample of the composite. To eliminate these macroscopic torques, while maintaining the advantageous effects of the fiber rotations, we also investigate the response of a laminated composite consisting of plus/minus orientations of the fibers relative to the layering direction, and subjected to magnetic and mechanical loadings along the layering direction. The results for the actuation tractions, magnetostrictive strain and magnetoelastic moduli demonstrate that the microstructure of these laminated MRE samples can be designed optimally for significantly enhanced magnetoelastic effects. In particular, the actuation tractions and magnetostrictive strains can be made several times larger than the corresponding tractions and strains for isotropic MREs with spherical (circular) particles.
TL;DR: In this article, the authors present a dynamical analysis of the photometry and three-dimensional kinematics of ω Cen, 47 Tuc, and M15, by means of a recently introduced family of self-consistent axisymmetric rotating models.
Abstract: Internal rotation is thought to play a major role in the dynamics of some globular clusters. However, in only a few cases has internal rotation been studied by the quantitative application of realistic and physically justified global models. Here, we present a dynamical analysis of the photometry and three-dimensional kinematics of ω Cen, 47 Tuc, and M15, by means of a recently introduced family of self-consistent axisymmetric rotating models. The three clusters, characterized by different relaxation conditions, show evidence of differential rotation and deviations from sphericity. The combination of line-of-sight velocities and proper motions allows us to determine their internal dynamics, predict their morphology, and estimate their dynamical distance. The well-relaxed cluster 47 Tuc is interpreted very well by our model; internal rotation is found to explain the observed morphology. For M15, we provide a global model in good agreement with the data, including the central behavior of the rotation profile and the shape of the ellipticity profile. For the partially relaxed cluster ω Cen, the selected model reproduces the complex three-dimensional kinematics; in particular, the observed anisotropy profile, characterized by a transition from isotropy to weakly radial anisotropy and then to tangential anisotropy in the outer parts. The discrepancy found for the steep central gradient in the observed line-of-sight velocity dispersion profile and for the ellipticity profile is ascribed to the condition of only partial relaxation of this cluster and the interplay between rotation and radial anisotropy.
TL;DR: In this article, a modified linear forcing method is proposed to reduce the oscillatory nature of spectral space velocity field forcing in numerical simulations of isotropic turbulence, which has the advantages of being less memory intensive, less computationally expensive, and more easily extended to variable density simulations.
Abstract: As an alternative to spectral space velocity field forcing techniques commonly used in simulation studies of isotropic turbulence,Lundgren [Linearly forced isotropic turbulence,” in Annual Research Briefs (Center for Turbulence Research, Stanford, 2003), pp. 461–473] proposed and Rosales and Meneveau [“Linear forcing in numerical simulations of isotropic turbulence: Physical space implementations and convergence properties,” Phys. Fluids17, 095106 (2005)] validated a physical space forcing method termed “linear forcing.” Linear forcing has the advantages of being less memory intensive, less computationally expensive, and more easily extended to variable density simulations. However, this forcing method generates turbulent statistics that are highly oscillatory, requiring extended simulation run times to attain time-invariant properties. A slight modification of the forcing term is proposed, and it is shown to reduce this oscillatory nature without altering the turbulent physics.
TL;DR: In this paper, a consistent theory is developed for size-dependent piezoelectricity in dielectric solids, which shows that electric polarization can be generated as the result of coupling to the mean curvature tensor.
TL;DR: In this article, the authors investigated the transfer properties of energy and helicity fluctuations in fully developed homogeneous and isotropic turbulence by changing the nature of the nonlinear Navier-Stokes terms.
Abstract: We investigate the transfer properties of energy and helicity fluctuations in fully developed homogeneous and isotropic turbulence by changing the nature of the nonlinear Navier–Stokes terms. We perform a surgery of all possible interactions, by keeping only those triads that have sign-definite helicity content. In order to do this, we apply an exact decomposition of the velocity field in a helical Fourier basis, as first proposed by Constantin & Majda (Commun. Math. Phys, vol. 115, 1988, p. 435) and exploited in great detail by Waleffe (Phys. Fluids A, vol. 4, 1992, p. 350), and we evolve the Navier–Stokes dynamics keeping only those velocity components carrying a well-defined (positive or negative) helicity. The resulting dynamics preserves translational and rotational symmetries but not mirror invariance. We give clear evidence that this three-dimensional homogeneous and isotropic chiral turbulence is characterized by a stationary inverse energy cascade with a spectrum and by a direct helicity cascade with a spectrum . Our results are important to highlight the dynamics and statistics of those subsets of all possible Navier–Stokes interactions responsible for reversal events in the energy-flux properties, and demonstrate that the presence of an inverse energy cascade is not necessarily connected to a two-dimensionalization of the flow. We further comment on the possible relevance of such findings to flows of geophysical interest under rotations and in thin layers. Finally we propose other innovative numerical experiments that can be achieved by using a similar decimation of degrees of freedom.
TL;DR: In this paper, an incremental variational principle for the increments in strain and internal variables in materials governed by two potentials is derived, together with the variational method of Ponte Castaneda (1992) and a linear comparison composite (LCC) at each time step, approximating in a variational sense the original problem.
TL;DR: In this article, rates of convergence of their finitely truncated Karhunen-Lo-ve expansions in terms of the covariance spectrum are established, and algorithmic aspects of fast sample generation via fast Fourier transforms on the sphere are indicated.
Abstract: Isotropic Gaussian random fields on the sphere are characterized by Karhunen-Lo\`{e}ve expansions with respect to the spherical harmonic functions and the angular power spectrum The smoothness of the covariance is connected to the decay of the angular power spectrum and the relation to sample H\"{o}lder continuity and sample differentiability of the random fields is discussed Rates of convergence of their finitely truncated Karhunen-Lo\`{e}ve expansions in terms of the covariance spectrum are established, and algorithmic aspects of fast sample generation via fast Fourier transforms on the sphere are indicated The relevance of the results on sample regularity for isotropic Gaussian random fields and the corresponding lognormal random fields on the sphere for several models from environmental sciences is indicated Finally, the stochastic heat equation on the sphere driven by additive, isotropic Wiener noise is considered, and strong convergence rates for spectral discretizations based on the spherical harmonic functions are proven
TL;DR: In this paper, the authors proposed a method to design isotropic periodic microstructures of cellular materials using the bidirectional evolutionary structural optimization (BESO) technique to determine the optimal distribution of material phase within the periodic base cell.
Abstract: The aim of this study was to design isotropic periodic microstructures of cellular materials using the bidirectional evolutionary structural optimization (BESO) technique. The goal was to determine the optimal distribution of material phase within the periodic base cell. Maximizing bulk modulus or shear modulus was selected as the objective of the material design subject to an isotropy constraint and a volume constraint. The effective properties of the material were found using the homogenization method based on finite element analyses of the base cell. The proposed BESO procedure utilizes the gradient-based sensitivity method to impose the isotropy constraint and gradually evolve the microstructures of cellular materials to an optimum. Numerical examples show the computational efficiency of the approach. A series of new and interesting microstructures of isotropic cellular materials that maximize the bulk or shear modulus have been found and presented. The methodology can be extended to incorporate other...