Construction of a central extension of a Lie group from its class of symplectic cohomology

Bargmann’s group is a central extension of Galilei group motivated by quantum-theoretical considerations. Bargmann’s work suggests that one of the reasons of the failure of naïve attemps to construct actions on quantum wave functions has a cohomologic origin. It is this point, we develop in the context of Lie groups with symplectic actions. Studying the co-adjoint representation of a central extension of a group G$G$, we highlight the link between the extension cocycles and the symplectic cocycles of G$G$. Also, each extension coboundary corresponds to a symplectic coboundary. Finally, we emphasize the condition to be satisfied by the extension cocycle for the class of symplectic cohomology of the extension being null. The method is illustrated by application to Physics.     

Huge fluctuations in weight measurements at the bottom of a two-dimensional vertical sheet of grains

Weight measurements at the bottom of a quasi-2D vertical sheet of static cohesionless grains are carried out. The grains are held between two coaxial cylinders. This peculiar setup allows us to set either periodic or fixed lateral boundary conditions. Huge relative fluctuations in weight measurements appear in case of fixed lateral walls. This may be related to some indetermination in the mobilization state of friction forces on lateral walls. This argument would hold for any piling, but would lead to huge fluctuations in 2D systems only, because of averaging effects in 3D.     

Experimental evidence of spontaneous symmetry breaking in intracavity type II second-harmonic generation with triple resonance

We describe a spontaneous symmetry-breaking phenomenon between the intensities of the ordinary and extraordinary components of the fundamental field in intracavity type II harmonic generation. It is based on a triply resonant cavity containing a type II chi(2) crystal pumped at fundamental frequency omega0. The pump beam generates a second-harmonic mode at frequency 2omega0 that acts as a pump for frequency-degenerate type II parametric downconversion. Under operating conditions symmetric with respect to the ordinary and extraordinary components of the fundamental wave, we show a breaking of the symmetry of the intensities of these two waves.     

Effect of epitaxial strain on the spontaneous polarization of thin film ferroelectrics

Epitaxial strain can substantially enhance the spontaneous polarizations and Curie temperatures of ferroelectric thin films compared to the corresponding bulk materials. In this Letter we use first principles calculations to calculate the effect of epitaxial strain on the spontaneous polarization of the ferroelectrics , , and , and the multiferroic material . We show that the epitaxial strain dependence of the polarization varies considerably for the different systems, and in some cases is, in fact, very small. We discuss possible reasons for this different behavior and show that the effect of epitaxial strain can easily be understood in terms of the piezoelectric and elastic constants of the unstrained materials. Our results provide a computational tool for the quantitative prediction of strain behavior in ferroelectric thin films.     

Comment on the analysis of angle-dependent X-ray magnetic circular dichroism in systems with reduced dimensionality

The magnetic dipole term T appearing in the X-ray magnetic circular dichroism (XMCD) spin sum rule can be eliminated from the analysis within the spin sum rule by angle-dependent XMCD spectroscopy if the effects of spin–orbit coupling are small so that T_x+T_y+T_z≈0. It is shown by the ab initio electron theory for the extreme case of a low-dimensional system, i.e., for a free-standing monatomic Co wire that this relation is strongly violated, indicating that the determination of T by the angle-dependent XMCD is possibly not very reliable for low-dimensional magnetic systems.     

Diffusion approximation for billiards with totally accommodating scatterers

We study the 2D motion of independent point particles colliding with a periodic array of circular obstacles. The interaction between the particles and the obstacles is described by a total accommodation reflection law. Assuming that the array of scatterers has finite horizon, the density of particles is approximated by the solution of a diffusion equation in the long-time and large-scale regime. The proof relies on a multiscale asymptotics and gives the order of approximation.     

Improvement of kinetics,yield, and colloidal stability of biogenic gold nanoparticles using living cells of <Emphasis Type="Italic">Euglena gracilis</Emphasis> microalga

Recent years have witnessed a boom in the biosynthesis of a large variety of nanomaterials using different biological resources among which algae-based entities have been gaining much more attention within the community of material scientists worldwide. In our previously published findings, we explored some factors that governed the biofabrication of gold nanoparticles using living cultures of microalgae, such as the utilized microalgal genera, the phylum they belong to, and the impact of tetrachloroauric acid concentrations on the ability of these strains to perform the biosynthesis of gold nanoparticles once in contact with these cations. As a follow-up, we present in this paper an improvement of the features of bioproduced gold colloids using living cells of Euglena gracilis microalga when this species is grown under either mixotrophic or autotrophic conditions, i.e., exposed to light and grown in an organic carbon-enriched culture medium versus under autotrophic conditions. As an outcome to this alteration, the growth rate of this photosynthetic microorganism is multiplied 7–8 times when grown under mixotrophic conditions compared to autotrophic ones. Therefore, the yield, the kinetics, and the colloidal stability of the biosynthesized gold nanoparticles are dramatically enhanced. Moreover, the shape and the size of the as-produced nano-objects via this biological method are affected. In addition to round-shaped gold nanoparticles, particular shapes, such as triangles and hexagons, appear. These findings add up to the amassed knowledge toward the design of photobioreactors for the scalable and sustainable production of interesting nanomaterials.     

Relaxation effects in the quantification of fat using gradient echo imaging

Quantification of fat has been investigated using images acquired from multiple gradient echoes. The evolution of the signal with echo time and flip angle was measured in phantoms of known fat and water composition and in 21 research subjects with fatty liver. Data were compared to different models of the signal equation, in which each model makes different assumptions about the T1 and/or T2* relaxation effects. A range of T1, T2*, fat fraction and number of echoes was investigated to cover situations of relevance to clinical imaging. Results indicate that quantification is most accurate at low flip angles (to minimize T1 effects) with a small number of echoes (to minimize spectral broadening effects). At short echo times, the spectral broadening effects manifest as a short apparent T2 for the fat component.     

Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier–Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e^|k|/k_d{{{\rm e}^{|k|/k_{\rm d}}}} at high wavenumbers |k|. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e^{-C(k/k_d) ln(|k|/k_d)}{{{\rm e}^{-C(k/k_{\rm d})\,{\rm ln}(|k|/k_{\rm d})}}} for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C _* = 1/ ln 2. The same behavior with a universal constant C _* is conjectured for the Navier–Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier–Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.