Advection of a passive vector field by the Gaussian velocity field with finite correlations in time

Using the field theoretic renormalization group technique the model of a passive vector field advected by an incompressible turbulent flow is investigated up to the second order of the perturbation theory (two-loop approximation). The turbulent environment is given by statistical fluctuations of the velocity field that has a Gaussian distribution with zero mean and defined noise with finite correlations in time. Two-loop analysis of all possible scaling regimes in general d-dimensional space is done in the plane of exponents ? ? η, where ? characterizes the energy spectrum of the velocity field in the inertial range E ∝ k ^{1 ? 2ε}, and η is related to the correlation time at the wave number k which is scaled as k ^{?2 + η}. It is shown that the scaling regimes of the present model of vector advection have essentially different properties than the scaling regimes of the corresponding model of passively advected scalar quantity. The results demonstrate the fact that within the present model of passively advected vector field the internal tensor structure of the advected field can have nontrivial impact on the diffusion processes deep inside in the inertial interval of given turbulent flow.     

Structural and transport properties of Sn–Mg alloys

In this work, the structural and transport properties of Mg-doped Sn-based alloys have been investigated. The temperature-dependent transport and structural properties of Sn–Mg alloys were investigated for five different samples (Pure Sn, Sn-1.0 wt% Mg, Sn-2.0 wt% Mg, Sn-6.0 wt% Mg and Pure Mg). Scanning electron microscopy (SEM), X-ray diffraction and energy dispersive X-ray analysis measurements were carried out in order to clarify the structural properties of the samples. It was found that the samples had tetragonal crystal symmetry, except for pure Mg which had hexagonal crystal symmetry. We also found that the cell parameters changed slightly with the addition of Mg element. The SEM micrographs of the samples showed that they had smooth surfaces with a clear grain boundary. The electrical and thermal conductivity of the samples were measured by four-point probe and the radial heat flow method, respectively. The electrical resistivity of the samples increased almost linearly with the increasing temperature. The thermal conductivity values ranged between 0.60 and 1.00 W/Km, while they decreased slightly with temperature and increased with Mg composition. The thermal conductivity values of the alloys were in between the values of pure Sn and Mg. The thermal conductivity results of the alloys were compared with other available results, and a good agreement was seen between the results. In addition, the temperature coefficients of electrical resistivity and thermal conductivity were determined; these were independent of the composition of the alloying elements.     

Isomorphisms of spaces with large distortion

Let K and S be locally compact Hausdorff spaces and let X be a strictly convex Banach space of finite dimension at least 2. In this paper, we prove that if there exists an isomorphism T from onto satisfying then K and S are homeomorphic. Here denotes the Schäffer constant of X. Even for the classical cases , and , this result is the X‐valued Banach–Stone theorem via isomorphism with the largest distortion that is known so far, namely . On the other hand, it is well known that this result is not true for , even though K and S are compact Hausdorff spaces.     

Landauer–Büttiker and Thouless Conductance

In the independent electron approximation, the average (energy/charge/entropy) current flowing through a finite sample \({\mathcal{S}}\) connected to two electronic reservoirs can be computed by scattering theoretic arguments which lead to the famous Landauer–Büttiker formula. Another well known formula has been proposed by Thouless on the basis of a scaling argument. The Thouless formula relates the conductance of the sample to the width of the spectral bands of the infinite crystal obtained by periodic juxtaposition of \({\mathcal{S}}\). In this spirit, we define Landauer–Büttiker crystalline currents by extending the Landauer–Büttiker formula to a setup where the sample \({\mathcal{S}}\) is replaced by a periodic structure whose unit cell is \({\mathcal{S}}\). We argue that these crystalline currents are closely related to the Thouless currents. For example, the crystalline heat current is bounded above by the Thouless heat current, and this bound saturates iff the coupling between the reservoirs and the sample is reflectionless. Our analysis leads to a rigorous derivation of the Thouless formula from the first principles of quantum statistical mechanics.     

Large Deviations from a Stationary Measure for a Class of Dissipative PDEs with Random Kicks

We study a class of dissipative PDEs perturbed by a bounded random kick force. It is assumed that the random force is nondegenerate, so that the Markov process obtained by the restriction of solutions to integer times has a unique stationary measure. The main result of the paper is a large deviations principle for occupation measures of the Markov process in question. The proof is based on Kifer's large‐deviation criterion, a coupling argument for Markov processes, and an abstract result on large‐time asymptotic for generalized Markov semigroups.© 2015 Wiley Periodicals, Inc.     

Asymmetric deformation of bubble shape: cause or effect of vortex-shedding?

Two perpendicular projections of rising bubbles were observed in counter-current downstream diverging flow. Evidently, the bubbles did not enter the boundary layer at the channel wall and a plug liquid flow assumption was acceptable in our experimental equipment. This confirmed that the experiment was appropriate for simulation of bubble rises in a quiescent liquid column. Recent data obtained by a high-speed camera permitted recording over a period of 60 s. Image analysis by a tailor-made program provided a time-series of quantities related to the position, size, and shape of bubbles. In addition to determination of the aspect ratio of the equivalent oblate ellipsoid, deviation from this shape was investigated in respect of the difference between the bubble’s centre of mass and the geometrical centre of bubble projection. Autocorrelation of the data indicated that the bubble inclination oscillated harmonically with a frequency of 5–10 Hz; cross correlation showed that the horizontal shift of the centre of mass, as well as the horizontal velocity, increased with increasing bubble inclination, and the vertical shift of the centre of mass increased with an increases in the absolute value of the bubble inclination. There is no significant phase shift in the oscillation of these quantities. The bulky bottom side of the bubbles is in accordance with the model of bubble oscillation induced by instability of the equilibrium of gravity and surface tension forces. The oscillation frequency dependence on surface forces (Eötvös number) is evident, while viscosity does not play a significant role in low-viscosity liquids. Therefore, vortex-shedding is more likely to be an effect of the oscillation and not its cause.     

Application of very weak formulation on homogenization of boundary value problems in porous media

Czechoslovak Mathematical Journal - The goal of this paper is to present a different approach to the homogenization of the Dirichlet boundary value problem in porous medium. Unlike the standard...     

Conformal Galilei algebras,symmetric polynomials and singular vectors

We classify and explicitly describe homomorphisms of Verma modules for conformal Galilei algebras \({\mathfrak {cga}}_\ell (d,\mathbb {C})\) with \(d=1\) for any integer value \(\ell \in {\mathbb {N}}\). The homomorphisms are uniquely determined by singular vectors as solutions of certain differential operators of flag type and identified with specific polynomials arising as coefficients in the expansion of a parametric family of symmetric polynomials into power sum symmetric polynomials.     

Theoretical and experimental study of the nanoparticle-driven blue phase stabilisation

We have studied theoretically and experimentally the effects of various types of nanoparticles (NPs) on the temperature stability range [Formula: see text] T (BP) of liquid-crystalline (LC) blue phases. Using a mesoscopic Landau-de Gennes type approach we obtain that the defect core replacement (DCR) mechanism yields in the diluted regime [Formula: see text] T (BP)(x) [Formula: see text] 1/(1 - xb) , where x stands for the concentration of NPs and b is a constant. Our calculations suggest that the DCR mechanism is efficient if a local NP environment resembles the core structure of disclinations, which represent the characteristic property of BP structures. These predictions are in line with high-resolution ac calorimetry and optical polarising microscopy experiments using the CE8 LC and CdSe or aerosil NPs. In mixtures with CdSe NPs of 3.5nm diameter and hydrophobic coating the BPIII stability range has been extended up to 20K. On the contrary, the effect of aerosil silica nanoparticles of 7.0nm diameter and hydrophilic coating is very weak.