Anisotropic Situations Research Articles

Reliability analysis of stability against piping and sliding in diversion dams, considering four cutoff wall configurations

The stability against piping and sliding, which is subject to numerous sources of uncertainty, is of great importance in the design of diversion dams. In this study, the performance of four cutoff wall configurations, including a single wall and two walls with half the length of the single wall, was evaluated stochastically using the random finite element method. The Cholesky decomposition technique in conjunction with three types of Auto-Correlation Function (ACF) was employed to generate numerous random fields. The results indicate that the probabilities of failure related to different cutoff wall configurations are similar, considering isotropic hydraulic conductivity. However, there are noticeable differences between the probabilities of failure of these configurations in anisotropic situations. Moreover, the use of a single cutoff wall on the upstream face of an impervious blanket provides the lowest probability of failure for piping. In addition, the exponential ACF ends up with greater exit hydraulic gradients than the second-order Markov and binary noise ACFs. In addition, the sliding stability of the ordinary and earthquake load combinations was examined stochastically using random field theory and Monte Carlo Simulation (MCS). The probability of failure appears to increase with an increase in the autocorrelation distance.

Shear viscosity in an anisotropic unitary Fermi gas

We consider a system consisting of a strongly interacting, ultracold unitary Fermi gas under harmonic confinement. Our analysis suggests the possibility of experimentally studying, in this system, an anisotropic shear viscosity tensor driven by the anisotropy in the trapping potential. In particular, we suggest that this experimental setup could mimic some features of anisotropic geometries that have recently been studied for strongly coupled field theories which have a dual gravitational description. Results using the AdS/CFT (anti-de Sitter/conformal field theory correspondence) in these theories show that in systems with a background linear potential, certain viscosity components can be made much smaller than the entropy density, parametrically violating the bound proposed by Kovtun, Son, and Starinets (KSS). This intuition, along with results from a Boltzmann analysis that we perform, suggests that a violation of the KSS bound can perhaps occur in the unitary Fermi gas system when it is subjected to a suitable anisotropic trapping potential which may be approximated to be linear in a suitable range of parameters. We give a concrete proposal for an experimental setup where an anisotropic shear viscosity tensor may arise. In such situations, it may also be possible to observe a reduction in the spin-1 component of the shear viscosity from its lowest value observed so far in ultracold Fermi gases. In extreme anisotropic situations, the reduction may be enough to reduce the shear viscosity to entropy ratio below the proposed KSS bound, although this regime is difficult to analyze in a theoretically controlled manner.

Impacts of Streambed Heterogeneity and Anisotropy on Residence Time of Hyporheic Zone

The hyporheic zone (HZ), which is the region beneath or alongside a streambed, plays an important role in the stream's ecology. The duration that a water molecule or a solute remains within the HZ, or residence time (RT), is one of the most common metrics used to evaluate the function of the HZ. The RT is greatly influenced by the streambed's hydraulic conductivity (K), which is intrinsically difficult to characterize due to its heterogeneity and anisotropy. Many laboratory and numerical studies of the HZ have simplified the streambed K to a constant, thus producing RT values that may differ from those gathered from the field. Some studies have considered the heterogeneity of the HZ, but very few have accounted for anisotropy or the natural K distributions typically found in real streambeds. This study developed numerical models in MODFLOW to examine the influence of heterogeneity and anisotropy, and that of the natural K distribution in a streambed, on the RT of the HZ. Heterogeneity and anisotropy were both found to shorten the mean and median RTs while increasing the range of the RTs. Moreover, heterogeneous K fields arranged in a more orderly pattern had longer RTs than those with random K distributions. These results could facilitate the design of streambed K values and distributions to achieve the desired RT during river restoration. They could also assist the translation of results from the more commonly considered homogeneous and/or isotropic conditions into heterogeneous and anisotropic field situations.

Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models.

Spin models are the prime example of simplified many-body Hamiltonians used to model complex, strongly correlated real-world materials. However, despite the simplified character of such models, their dynamics often cannot be simulated exactly on classical computers when the number of particles exceeds a few tens. For this reason, quantum simulation of spin Hamiltonians using the tools of atomic and molecular physics has become a very active field over the past years, using ultracold atoms or molecules in optical lattices, or trapped ions. All of these approaches have their own strengths and limitations. Here we report an alternative platform for the study of spin systems, using individual atoms trapped in tunable two-dimensional arrays of optical microtraps with arbitrary geometries, where filling fractions range from 60 to 100 per cent. When excited to high-energy Rydberg D states, the atoms undergo strong interactions whose anisotropic character opens the way to simulating exotic matter. We illustrate the versatility of our system by studying the dynamics of a quantum Ising-like spin-1/2 system in a transverse field with up to 30 spins, for a variety of geometries in one and two dimensions, and for a wide range of interaction strengths. For geometries where the anisotropy is expected to have small effects on the dynamics, we find excellent agreement with ab initio simulations of the spin-1/2 system, while for strongly anisotropic situations the multilevel structure of the D states has a measurable influence. Our findings establish arrays of single Rydberg atoms as a versatile platform for the study of quantum magnetism.

Investigation of Mechanical Properties of Magneto-Rheological Ethylene Propylene Diene Monomer and Natural Rubber Type Synthetic Rubbers for Both Isotropic and Anisotropic Situations

Manyeto-reolojik (MR) malzemeler dis manyetik alan uygulamalariyla tersinir ve hizli bir sekilde kontrol edilebilen reolojik ozelliklere sahip akilli(smart) malzeme sinifindandir. Gelisen teknoloji kosullari goz onune alindiginda kaucuk turu akilli malzemeler manyeto-reolojik etkilerle beraber daha fonksiyonel bir kullanima sahip olmustur. Bu calismada, manyeto-reolojik Etilen Propilen Dien Monomer (EPDM) ve Dogal Kaucuk (NR) turu sentetik kaucuklarin izotrop ve anizotrop durumda tek eksenli yukleme altindaki mekanik ozelliklerinin incelenmesi amaclanmistir. Bu tur kompozit malzemeler geleneksel sicak kalip sistemi yardimiyla izotrop (homojen) ve anizotrop (hizalanmis) olarak ferromanyetik toz ilave edilerek ve manyetik alan uygulanarak elde edilmistir. Elde edilen kompozit malzemelere manyetik alanin etkisi incelenmistir. Calismada EPDM sentetik kaucuk malzemesinin aksine NR kaucugunun akilli malzeme ozelligine daha yatkin oldugu gozlemlenmistir.

Can gravitation anisotropy be detected by pendulum experiments?

After some 170 years of Foucault pendulum experiments, the linear theory fails to quantitatively explain the results of any honest meticulous experiment. The pendulum motion usually degenerates into elliptical orbits after a few minutes. Moreover, unexplained discrepancies up to ± 20% in precession velocity are not uncommon. They are mostly regarded as a consequence of the elliptic motion of the bob associated with suspension anisotropy or as a lack of care in starting the pendulum motion. Over some 130 years, an impressive amount of talented physicists, engineers and mathematicians have contributed to a better partial understanding of the pendulum behaviour. In this work, the concept of biresonance is introduced to represent the motion of the spherical pendulum. It is shown that biresonance can be represented graphically by the isomorphism of the Poincare sphere. This new representation of the pendulum motion greatly clarifies its natural response to various anisotropic situations, including Airy precession. Anomalous observations in pendulum experiments by Allais are analyzed. These findings suggest that a pendulum placed within a mass distribution such as the earth, the moon and the sun should be treated as an interior problem, which can better be addressed by Santilli's new theory of gravitation than by those of Newton and Einstein.

Limiting observations for planar free-boundaries governed by isotropic-anisotropic singular diffusions, upper bounds for the limits

In this paper, variational inclusions of Euler--Lagrange types, governed by two-dimensional isotropic-anisotropic singular diffusions, are considered. On that basis, we focus on the geometric structures of free boundaries where anisotropic conditions tend to isotropic. In this light, a limit-set of special piecewise-constant solutions will be presented. The objective in this paper is to give some observations on the upper bounds of the limit set with geometric characterizations. As a consequence, it will be shown that the isotropic free boundaries, as in the limit set, consist of a finite number of $ C^{1,1} $-Jordan curves, and these have certain geometric connections with the approaching anisotropic situations. Observations for the lower bounds will be studied in the sequel to this paper.

Receiver-coupling effects in seismic waveform inversions

Seismic waveform-inversion offers opportunities for detailed characterization of the subsurface. However, its full potential can only be exploited when any systematic source and receiver effects are either carefully avoided or appropriately accounted for during the inversions. Repeated crosshole measurements in the Mont Terri (Switzerland) underground laboratory have revealed that receiver coupling may significantly affect the seismic waveforms. More seriously, coupling conditions may vary during the course of a monitoring experiment. To address this problem, we have developed a novel scheme that estimates medium properties, frequency-dependent source functions, and frequency-dependent receiver-coupling factors. We demonstrate the efficacy of the new scheme via a synthetic 2D crosshole experiment in which realistic receiver-coupling factors are incorporated. Because determination of medium parameters and estimation of source functions and receiver-coupling factors are largely separated, the method can be easily adapted to any other waveform-inversion problem, including elastic, anisotropic, 2.5D, or 3D situations.

Nonabelian plasma instabilities in Bjorken expansion

Plasma instabilities are parametrically the dominant nonequilibrium dynamics of a weakly coupled quark-gluon plasma. In recent years the time evolution of the corresponding collective colour fields has been studied in stationary anisotropic situations. Here I report on recent numerical results on the time evolution of the most unstable modes in a longitudinally expanding plasma as they grow from small rapidity fluctuations to amplitudes where non-Abelian self-interactions become important.

Selective Smoothed Finite Element Method

The paper examines three selective schemes for the smoothed finite element method (SFEM) which was formulated by incorporating a cell-wise strain smoothing operation into the standard compatible finite element method (FEM). These selective SFEM schemes were formulated based on three selective integration FEM schemes with similar properties found between the number of smoothing cells in the SFEM and the number of Gaussian integration points in the FEM. Both scheme 1 and scheme 2 are free of nearly incompressible locking, but scheme 2 is more general and gives better results than scheme 1. In addition, scheme 2 can be applied to anisotropic and nonlinear situations, while scheme 1 can only be applied to isotropic and linear situations. Scheme 3 is free of shear locking. This scheme can be applied to plate and shell problems. Results of the numerical study show that the selective SFEM schemes give more accurate results than the FEM schemes.

The generalized triphasic correspondence principle for simultaneous determination of the mechanical properties and proteoglycan content of articular cartilage by indentation

The triphasic mixture theory has been used to describe the mechanical and physicochemical behaviors of articular cartilage under some specialized loading conditions. However, the mathematical complexities of this theory have limited its applications for theoretical analyses of experimental studies and models for predicting cartilage and other biological tissues’ deformational behaviors. A generalized correspondence principle has been established in the present study, and this principle shows that the equilibrium deformational behavior of a charged-hydrated material under loading is identical to that of an elastic medium without charge. A set of explicit formulas has been derived to correlate the mechanical properties of an equivalent material with the intrinsic elastic moduli, fixed charge density and free-ion concentration within the cartilage tissue. The validity of these formulas is independent of the deformation state of the elastic solid matrix under an infinitesimal strain. Therefore they can be employed for any loading conditions, such as confined or unconfined compression, tension, and indentation tests, etc. In the current study, the fixed charge density of bovine cartilage is determined from the indentation creep data using this generalized correspondence principle. The proteoglycan content results were then compared with those from biochemical assay, yielding a linear regression slope of 1.034. Additionally a correspondence principle within a framework of cubic symmetry and a bilinear response in tension-compression (the conewise linear elasticity model) has also been developed to demonstrate the potential application of current methodology for inhomogeneous, anisotropic and nonlinear situations.

Anisotropic Analysis of Some Gaussian Models

Although the classical Fractional Brownian Motion is often used to describe porosity, it is not adapted to anisotropic situations. In the present work, we study a class of Gaussian fields with stationary increments and “spectral density.” They present asymptotic self-similarity properties and are good candidates to model a homogeneous anisotropic material, or its radiographic images. Unfortunately, the paths of all Gaussian fields with stationary increments have the same apparent regularity in all directions (except at most one). Hence we propose here a procedure to recover anisotropy from one realization: computing averages over all the hyperplanes which are orthogonal to a fixed direction, we get a process whose Holder regularity depends explicitly on the asymptotic behavior of the spectral density in this direction.

Renormalization-group picture of the Lifshitz critical behavior

New field theoretic renormalization group methods are developed to describe in a unified fashion the critical exponents of an m-fold Lifshitz point at the two-loop order in the anisotropic (m not equal to d) and isotropic (m=d close to 8) situations. The general theory is illustrated for the N-vector phi^4 model describing a d-dimensional system. A new regularization and renormalization procedure is presented for both types of Lifshitz behavior. The anisotropic cases are formulated with two independent renormalization group transformations. The description of the isotropic behavior requires only one type of renormalization group transformation. We point out the conceptual advantages implicit in this picture and show how this framework is related to other previous renormalization group treatments for the Lifshitz problem. The Feynman diagrams of arbitrary loop-order can be performed analytically provided these integrals are considered to be homogeneous functions of the external momenta scales. The anisotropic universality class (N,d,m) reduces easily to the Ising-like (N,d) when m=0. We show that the isotropic universality class (N,m) when m is close to 8 cannot be obtained from the anisotropic one in the limit d --> m near 8. The exponents for the uniaxial case d=3, N=m=1 are in good agreement with recent Monte Carlo simulations for the ANNNI model.

Particle-in-cell simulation study on halo formation in anisotropic beams

In a recent paper (M. Ikegami, Nucl. Instr. and Meth. A 435 (1999) 284), we investigated halo formation processes in transversely anisotropic beams based on the particle–core model. The effect of simultaneous excitation of two normal modes of core oscillation, i.e., high- and low-frequency modes, was examined. In the present study, self-consistent particle simulations are performed to confirm the results obtained in the particle–core analysis. In these simulations, it is confirmed that the particle–core analysis can predict the halo extent accurately even in anisotropic situations. Furthermore, we find that the halo intensity is enhanced in some cases where two normal modes of core oscillation are simultaneously excited as expected in the particle–core analysis. This result is of practical importance because pure high-frequency mode oscillation has frequently been assumed in preceding halo studies. The dependence of halo intensity on the 2:1 fixed point locations is also discussed.

Particle–core analysis of beam halo formation in anisotropic beams

We have derived a method to apply the particle–core analysis to coasting beams executing general envelope oscillation which is a superposition of two normal modes. Applying this method to transversely isotropic and anisotropic beams, the effects of simultaneous excitation of two normal modes on halo development mechanism have been explored. We find that, in isotropic cases with the same emittance and external focusing strength in the two transverse directions, single-particle motion exhibits strong chaosity in wide parameter space due to the resonance overlap of two 2:1 particle–core resonances. The strong chaosity is expected to result in an increase of halo intensity enhancing the chance for the particles to gain excess energy through resonant interaction with the core. Of particular importance is the result that the resonance overlap can be avoided by introducing appropriate anisotropy provided that the beam density is lower than a certain threshold. The avoidance of the resonance overlap suppresses chaosity in single-particle motion, which strongly suggests that halo intensity can be reduced in anisotropic situations by choosing appropriate parameters such as beam density and external focusing force strength. This gives us a practical criterion to choose parameters in designing a high-intensity ion synchrotron and storage ring.

Correlation functions in isotropic and anisotropic turbulence: the role of the symmetry group.

The theory of fully developed turbulence is usually considered in an idealized homogeneous and isotropic state. Real turbulent flows exhibit the effects of anisotropic forcing. The analysis of correlation functions and structure functions in isotropic and anisotropic situations is facilitated and made rational when performed in terms of the irreducible representations of the relevant symmetry group which is the group of all rotations SO(3). In this paper we first consider the needed general theory, and explain why we expect different (universal) scaling exponents in the different sectors of the symmetry group. We exemplify the theory context of isotropic turbulence (for third order tensorial structure functions) and in weakly anisotropic turbulence (for the second order structure function). The utility of the resulting expressions for the analysis of experimental data is demonstrated in the context of high Reynolds number measurements of turbulence in the atmosphere.

A numerical study of anisotropic, low Reynolds number, free surface flow for ice sheet modeling

Few ice sheet flow models have been developed that solve the complete set of mechanical equations. Until now, these models were limited to isotropic conditions. We present here a two‐dimensional, finite difference method capable of solving the equations for the steady flow of a viscous, incompressible, anisotropic fluid with a free surface under isothermal conditions. It is not a standard method, especially with respect to the time discretization of the numerical scheme, and converges for very low Reynolds numbers. This method is applied here to the planar flow of anisotropic ice over flat or irregular bedrock, with no‐slip boundary conditions at the ice‐bedrock interface. The results are presented here for Newtonian behavior in the vicinity of an ice divide. The ice is assumed to be isotropic at the ice sheet surface, with continuous and prescribed development of anisotropy with increasing depth. Going from isotropic to anisotropic situations, our results indicate that the free surface becomes flatter and the shear strain rates larger and more concentrated near the bedrock. The flow is less sensitive to variations of the bedrock topography in the anisotropic case than in the isotropic case. Furthermore, a new phenomenon appears in the anisotropic case: the partial stagnation of ice in the holes of the bedrock. These effects have significant consequences when dating the ice. The isochrones obtained in the anisotropic case are flatter and the anisotropic ice is more than 10% younger above the bumps and more than 100% older within the holes than for the isotropic ice.

Percolation on anisotropic media, the Bethe lattice revisited. Application to fracture networks

Abstract. A bond-percolation model based on the Bethe Lattice is presented. This model handles anisotropic and multiscale situations where, typically, the bond probability is non unique and depends on the sites it connects. The model is governed by a set of non-linear equations which are solved numerically. As a result, the structure of the network is obtained: strengths of the backbone, dead-end roads and finite clusters. Percolation thresholds and cluster sizes are also obtained. Application to fissured media is presented and random simulations of 3D distributions of fractures show the good accuracy of the model.

Kinetic and thermodynamic properties of a convecting plasma in a two‐dimensional dipole field

Charged particle guiding center motion is considered in the magnetic field of a two‐dimensional (“line”) dipole on which is superimposed a small, static, perpendicular electric field. The parallel equation of motion is that of a simple harmonic oscillator for cos θ, the cosine of magnetic colatitude θ. Equations for the perpendicular electric and magnetic drifts are derived as well as their bounce‐averaged forms. The latter are solved to yield a bounce‐averaged guiding center trajectory, which is the same as that obtained from conservation of magnetic moment µ, longitudinal invariant J, and total (kinetic plus electrostatic) energy K. The algebraic simplicity of the trajectory equations is also manifest in the forms of the invariants. An interesting result is that guiding centers drift in such a way that they preserve the values of their equatorial pitch angles and (equivalently) mirror latitudes. The most general Maxwellian form of the equilibrium one‐particle distribution function f is constructed from the invariants, and spatially varying density and pressure moments, parallel and perpendicular to the magnetic field, are identified. Much of the paper deals with the more restricted problem in which f is specified as a bi‐Maxwellian over a straight line of finite length in the equatorial plane of the dipole and perpendicular to field lines. This might be thought of as specifying a cross‐tail ion injection source; our formalism then describes the subsequent spatial development. The distribution away from the source is a scaled bi‐Maxwellian but one that is cut off at large and small kinetic energies, which depend on position. Density and pressure components are reduced from the values they would have if the total content of individual flux tubes convected intact. The equatorial and meridional variations of density and pressure components are examined and compared systematically for the isotropic and highly anisotropic situations. There appears to be little qualitative difference due to anisotropy. An anisotropy measure is defined, and its spatial variation determined as a signature of possible MHD instability. Extreme values are found, larger than at the source, but the plasma beta in such regions is probably so low as to render the effect inconsequential energetically. Finally, the possible consequence of “nonadiabatic” pressure profiles on electrostatic interchanges is considered, and a boundary delineating stabilizing and destabilizing regions determined.

Spatial distribution of magnetization in the anisotropic Co(H2O)2+ 6 ion from polarized neutron diffraction

In a polarized neutron diffraction experiment on the magnetically highly anisotropic ammonium cobalt Tutton salt (ND4)2Co(SO4)2·6D2O, 70 and 22 flipping ratios were measured in the hk0 and h01 zones respectively. These, and the underlying magnetization distribution around Co, more closely resemble those predicted by a model with a cubic crystal field with CoO6 axes, than those predicted from a generally orientated ellipsoidal crystal field, even though the latter provides a good fit to ESR and magnetic susceptibility data. However, all the real space magnetization distributions are substantially isotropic. For an examination of covalence as the experimental objective, these results indicate that a suitably scaled spin-only model for the magnetization distribution on the metal may suffice, even in highly anisotropic situations where a large orbital moment is present, such as the present case.