Existence results for a fourth order partial differential equation arising in condensed matter physics

We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation whose nonlinearity is the determinant of the Hessian matrix of the solution. We consider this model in a bounded domain of the real plane and study its stationary solutions both when the geometry of this domain is arbitrary and when it is the unit ball and the solution is radially symmetric. We also consider the initial-boundary value problem for the full parabolic equation. We summarize our results on existence of solutions in these cases and propose an open problem related to the existence of self-similar solutions.Comment: To appear in Mathematica Bohemic

Non-uniform carrier density in Cd3_3As2_2 evidenced by optical spectroscopy

We report the detailed optical properties of Cd$_3$As$_2$ crystals in a wide parameter space: temperature, magnetic field, carrier concentration and crystal orientation. We investigate high-quality crystals synthesized by three different techniques. In all the studied samples, independently of how they were prepared and how they were treated before the optical experiments, our data indicate conspicuous fluctuations in the carrier density (up to 30%). These charge puddles have a characteristic scale of 100 $\mu$m, they become more pronounced at low temperatures, and possibly, they become enhanced by the presence of crystal twinning. The Drude response is characterized by very small scattering rates ($\sim 1$ meV) for as-grown samples. Mechanical treatment, such as cutting or polishing, influences the optical properties of single crystals, by increasing the Drude scattering rate and also modifying the high frequency optical response. Magneto-reflectivity and Kerr rotation are consistent with electron-like charge carriers and a spatially non-uniform carrier density.Comment: Accepted in Physical Review

THE FORAGE UTILIZATION OF WINTER PEA-CEREAL MIXTURE IN AGRICULTURE LOW-INPUT SYSTEM

Abstract HAKL, J., BRANT, V., MÁŠKOVÁ, K., NECKÁŘ, K., PIVEC, J.: The forage utilization of winter pea-cereal mixture in agriculture low-input system. Acta univ. agric. et silvic. Mendel. Brun., 2011, LIX, No. 5, pp. 47-52 The aim of this paper is to evaluate the forage utilization of winter catch crop in relation to yield and mixture composition. In 2006-2009, the plot experiment with winter pea in mixtures with rye and triticale was conducted under completely randomized design with four replicates. The productivity of mixture was above 10 t.ha −1 whilst the signifi cantly lowest value was observed for pea monoculture. The rye represented the most productive component in mixture but it achieved lower forage quality in comparison with triticale. The ratio of pea varied from 7 to 38 % in dependence on year and companion cereal. The triticale mixture provided higher ratio in comparison with rye and signifi cant diff erences between rye varieties were also detected. The quality of mixture was depended mainly on ratio of crops in the mixture. The ratio of pea signifi cantly increased crude protein content in mixture according to linear regression where crude protein = 9.56 + 0.11* weight percentage pea ratio (P < 0.000, R 2 = 0.89). Quality of pea forage was also infl uenced by companion crop where pea in mixture with rye achieved signifi cantly lower quality. The amount of weeds was highest in the pea monoculture and lowest in mixture with rye

Magneto-optical signature of massless Kane electrons in Cd3As2

We report on optical reflectivity experiments performed on Cd3As2 over a broad range of photon energies and magnetic fields. The observed response clearly indicates the presence of 3D massless charge carriers. The specific cyclotron resonance absorption in the quantum limit implies that we are probing massless Kane electrons rather than symmetry-protected 3D Dirac particles. The latter may appear at a smaller energy scale and are not directly observed in our infrared experiments.Comment: 5 pages, 4 figures + supplementary materials (17 pages), to be published in Phys. Rev. Let

Site specific radon regimes of a cave system

The spatial and temporal variation of air-borne 222Rn concentration was continuously measured during 1990-94 with monthly changed etched track detectors in the Pál-völgy and Mátyás-hegy caves, Budapest, Hungary in order to identify site-specific behaviour of radon variations. We found winter minimum and summer maximum levels at each measuring site. In the Pál-völgy cave these end values increased with the distance from the entrance. The maximum-to-minimum ratio, however, showed a broad peak between the entrance and deep cave region. This behaviour can be attributed to the seasonal and depth dependence pattern of the advective dilution effect caused by intrusion of outside radon free air. Far from the entrance radon concentration goes to a saturation value, which approaches the level found in a highly unventilated remote cavity of the cave. In the Mátyás-hegy cave the maximum-to-minimum ratios were small and nearly constant, indicating that the measuring sites belong to deeper parts of the system. The higher maximum values, on the other hand, are attributed to smaller passage sizes of this part. High similarity was found in the temporal variation of radon concentration in the neighbouring parts of the two caves, which reinforced the assumed but by man unpenetrable connection between them