K 〈x, θ〉2dx = LK ∀θ ∈ Sn−1 where LK is a constant independent of θ, which is called the isotropy constant of K. Here 〈·, ·〉 denotes the standard scalar product in R. It is well known that for every convex body K ∈ R there exists an affine map T such that TK is isotropic. Furthermore, K and TK are both isotropic if and only if T is an orthogonal transformation. In this case the isotropy constant...

Some useful information is known about the fundamental domain for certain Hilbert modular groups. The six nonequivalent points with nontrivial isotropy in the fundamental domains under the action of the modular group for Q( √ 5), Q( √ 2), and Q( √ 3) have been determined previously by Gundlach. In finding these points, use was made of the exact size of the isotropy groups. Here we show that the...

[1] We present a multiple step procedure for joint modeling of surface wave group velocity dispersion curves and teleseismic receiver functions for lithospheric velocity structure. The method relies on an initial grid search for a simple crustal structure, followed by a formal iterative inversion, an additional grid search for shear wave velocity in the mantle, and finally, forward modeling of ...

It is well known that Landau's phenomenological description' of a continuous phase transition is very useful in classifying syminetry changes which can take place during such a transition. A good illustrative example is given by Lyubarskii. The procedure can be summarized as follows: (1) Find the space group 6 of the high-symmetry phase of a physical system (crystal, alloy, etc.) and the irredu...

A Hele-Shaw cell is a device used to study fluid flow between two parallel plates separated by small gap. The governing equation of within Darcy's law, which also describes through porous medium. In this work, we derive generalization law starting from three-dimensional with parity-broken viscosity tensor no isotropy. We discuss the observable effects parity-odd fluids in various physical setup...

The significant influence of transverse isotropy on mechanical behaviours soil has long been recognised, but it is still difficult to capture well under 3D stress conditions. In this study, a method establishing non-orthogonal elastoplastic (NOEP) constitutive models for transversely isotropic (TI-soil) proposed. effect considered by extending the characteristic with fabric tensor TI-soil. exte...

[1] Shear waves that traverse the lowermost mantle exhibit polarization anomalies and waveform complexities that indicate the presence of complex velocity structure above the core-mantle boundary. Synthetic seismograms for horizontally and vertically polarized shear waves (SH and SV, respectively) are computed using the reflectivity method for structures with low-velocity sheets (‘‘lamellae’’),...