Harnack inequality and regularity for degenerate quasilinear elliptic equations

We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions. The degeneracy is given by a suitable power of a strong $A_\infty$ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove $C^{1,\alpha}$ local estimates for solutions of a degenerate equation in non divergence form

Detection of Tiny Mechanical Motion by Means of the Ratchet Effect

We propose a position detection scheme for a nanoelectromechanical resonator based on the ratchet effect. This scheme has an advantage of being a dc measurement. We consider a three-junction SQUID where a part of the superconducting loop can perform mechanical motion. The response of the ratchet to a dc current is sensitive to the position of the resonator and the effect can be further enhanced by biasing the SQUID with an ac current. We discuss the feasibility of the proposed scheme in existing experimental setups.Comment: 8 pages, 9 figure

Role of the target orientation angle and orbital angular momentum in the evaporation residue production

The influence of the orientation angles of the target nucleus symmetry axis relative to the beam direction on the production of the evaporation residues is investigated for the $^{48}$Ca+$^{154}$Sm reaction as a function of the beam energy. At low energies ($E_{\rm c.m.}<$137 MeV), the yield of evaporation residues is observed only for collisions with small orientation angles ($\alpha_T<45^0$). At large energies (about $E_{\rm c.m.}=$140--180 MeV) all the orientation angles $\alpha_T$ can contribute to the evaporation residue cross section $\sigma_{ER}$ in the 10--100 mb range, and at $E_{c.m.}>$180 MeV $\sigma_{ER}$ ranges around 0.1--10 mb because the fission barrier for a compound nucleus decreases by increasing its excitation energy and angular momentum.Comment: 20 pages, 10 figures, submitted to JPS

Atomic gallium laser spectroscopy with violet/blue diode lasers

We describe the operation of two GaN-based diode lasers for the laser spectroscopy of gallium at 403 nm and 417 nm. Their use in an external cavity configuration enabled the investigation of absorption spectroscopy in a gallium hollow cathode. We have analyzed the Doppler broadened profiles accounting for hyperfine and isotope structure and extracting both the temperature and densities of the neutral atomic sample produced in the glow discharge. We have also built a setup to produce a thermal atomic beam of gallium. Using the GaN-based diode lasers we have studied the laser induced fluorescence and hyperfine resolved spectra of gallium.Comment: 10 pages, 7 figure

Sensitive methods for estimating the anchoring strength of nematic liquid crystals on Langmuir-Blodgett monolayers of fatty acids

The anchoring of the nematic liquid crystal N-(p-methoxybenzylidene)-p-butylaniline (MBBA) on Langmuir-Blodgett monolayers of fatty acids (COOHC$_{n}$H$_{2n+1}$) was studied as a function of the length of the fatty acid alkyl chains, $n$ ($n = 15, 17, 19, 21$). The monolayers were deposited onto ITO-coated glass plates which were used to assemble sandwich cells of various thickness that were filled with MBBA in the nematic phase. The mechanism of relaxation from the flow-induced quasi-planar to the surface-induced homeotropic alignment was studied for the four decreases linearly with increasing the length of the alkyl chains $n$ which suggests that the Langmuir-Blodgett film plays a role in the phenomenon. This fact was confirmed by a sensitive estimation of the anchoring strength of MBBA on the fatty acid monolayers after anchoring breaking which takes place at the transition between two electric-field--induced turbulent states, denoted as DSM1 and DSM2. It was found that the threshold electric field for the anchoring breaking, which can be considered as a measure of the anchoring strength, also decreases linearly as $n$ increases. Both methods thus possess a high sensitivity in resolving small differences in anchoring strength. In cells coated with mixed Langmuir-Blodgett monolayers of two fatty acids ($n=15$ and $n=17$) a maximum of the relaxation speed was observed when the two acids were present in equal amount. This observation homeotropic cells by changing the ratio between the components of the surfactant film.Comment: LaTeX article, 20 pages, 15 figures, 17 EPS files. 1 figure added, references moved. Submitted to Phys. Rev.

K-means Clustering to Study How Student Reasoning Lines Can Be Modified by a Learning Activity Based on Feynman\u2019s Unifying Approach

Research in Science Education has shown that often students need to learn how to identify differences and similarities between descriptive and explicative models. The development and use of explicative skills in the field of thermal science has always been a difficult objective to reach. A way to develop analogical reasoning is to use in Science Education unifying conceptual frameworks. In this paper we describe a 20-hour workshop focused on Feynman\u2019s Unifying Approach and the two-level system. We measure its efficacy in helping undergraduate chemical engineering students explain phenomena by applying an explanatory model. Contexts involve systems for which a process is activated by thermally overcoming a well-defined potential barrier. A questionnaire containing six open-ended questions was administered to the students before instruction. A second one, similar but focused on different physical content was administered after instruction. Responses were analysed using k-means Cluster Analysis and students\u2019 inferred lines of reasoning about the analysed phenomena were studied. We conclude that students reasoning lines seem to have clearly evolved to explicative ones and it is reasonable to think that the Feynman Unifying Approach has favoured this change

Massless Three Dimensional Quantum Electrodynamics and Thirring Model Constrained by Large Flavor Number

We explicitly prove that in three dimensional massless quantum electrodynamics at finite temperature, zero density and large number of flavors the number of infrared degrees of freedom is never larger than the corresponding number of ultraviolet. Such a result, strongly dependent on the asymptotic freedom of the theory, is reversed in three dimensional Thirring model due to the positive derivative of its running coupling constant