Spin-symmetric solution of an interacting quantum dot attached to superconducting leads: Andreev states and the 0−π0-\pi transition

Behavior of Andreev gap states in a quantum dot with Coulomb repulsion symmetrically attached to superconducting leads is studied via the perturbation expansion in the interaction strength. We find the exact asymptotic form of the spin-symmetric solution for the Andreev states continuously approaching the Fermi level. We thereby derive a critical interaction at which the Andreev states at zero temperature merge at the Fermi energy, being the upper bound for the $0-\pi$ transition. We show that the spin-symmetric solution becomes degenerate beyond this interaction, in the $\pi$ phase, and the Andreev states do not split unless the degeneracy is lifted. We further demonstrate that the degeneracy of the spin-symmetric state extends also into the $0$ phase in which the solutions with zero and non-zero frequencies of the Andreev states may coexist.Comment: 12 pages, 4 figure

Heat-Conducting, Compressible Mixtures with Multicomponent Diffusion: Construction of a Weak Solution

We investigate a coupling between the compressible Navier'stokes-Fourier system and the full Maxwell'stefan equations. This model describes the motion of a chemically reacting heat-conducting gaseous mixture. The viscosity coefficients are density-dependent functions vanishing in a vacuum and the internal pressure depends on species concentrations. By several levels of approximation we prove the global-in-time existence of weak solutions on the three-dimensional torus

Approximate solutions to a model of two-component reactive flow

We consider a model of motion of binary mixture, based on the compressible Navier-Stokes system. The mass balances of chemically reacting species are described by the reaction-diffusion equations with generalized form of multicomponent difiusion ux. Under a special relation between the two density dependent viscosity coefficients and for singular cold pressure we construct the weak solutions passing through several levels of approximation

Chemically reacting mixtures in terms of degenerated parabolic setting

The paper analyzes basic mathematical questions for a model of chemically reacting mixtures. We derive a model of several (finite) component compressible gas taking rigorously into account the thermodynamical regime. Mathematical description of the model leads to a degenerate parabolic equation with hyperbolic deviation. The thermodynamics implies that the diffusion terms are non-symmetric, not positively defined, and cross-diffusion effects must be strongly marked. The mathematical goal is to establish the existence of weak solutions globally in time for arbitrary number of reacting species. A key point is an entropy-like estimate showing possible renormalization of the system. © 2013 AIP Publishing LLC

Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor

In this paper we provide a sufficient condition, in terms of only one of the nine entries of the gradient tensor, i.e., the Jacobian matrix of the velocity vector field, for the global regularity of strong solutions to the three-dimensional Navier-Stokes equations in the whole space, as well as for the case of periodic boundary conditions

Enrichment of the HR 8799 planets by minor bodies and dust

Context. In the Solar System, minor bodies and dust deliver various materials to planetary surfaces. Several exoplanetary systems are known to host inner and outer belts, analogues of the main asteroid belt and the Kuiper belt, respectively. Aims: We study the possibility that exominor bodies and exodust deliver volatiles and refractories to the exoplanets in the well-characterised system HR 8799. Methods: We performed N-body simulations to study the impact rates of minor bodies in the system HR 8799. The model consists of the host star, four giant planets (HR 8799 e, d, c, and b), 650 000 test particles representing the inner belt, and 1 450 000 test particles representing the outer belt. Moreover we modelled dust populations that originate from both belts. Results: Within a million years, the two belts evolve towards the expected dynamical structure (also derived in other works), where mean-motion resonances with the planets carve the analogues of Kirkwood gaps. We find that, after this point, the planets suffer impacts by objects from the inner and outer belt at rates that are essentially constant with time, while dust populations do not contribute significantly to the delivery process. We convert the impact rates to volatile and refractory delivery rates using our best estimates of the total mass contained in the belts and their volatile and refractory content. Over their lifetime, the four giant planets receive between 10-4 and 10-3 M⊕ of material from both belts. Conclusions: The total amount of delivered volatiles and refractories, 5 × 10-3 M⊕, is small compared to the total mass of the planets, 11 × 103 M⊕. However, if the planets were formed to be volatile-rich, their exogenous enrichment in refractory material may well be significant and observable, for example with JWST-MIRI. If terrestrial planets exist within the snow line of the system, volatile delivery would be an important astrobiological mechanism and may be observable as atmospheric trace gases

LiBC by polarized Raman spectroscopy: Evidence for lower crystal symmetry ?

The paper presents polarized Raman scattering study on a few-micron-size crystallite of LiBC with natural faces. The experiment on as grown sample has revealed a four lattice modes with frequencies at 1276 cm^-1, 830 cm^-1, 546 cm^-1 and 170 cm^-1, respectively. The number of observed Raman lines and their selection rules are incompatible with the assumed D6h symmetry. The modes at 1276 cm^-1 and 170 cm^-1 correspond to the expected Raman active modes. In contrast with the superconducting compound MgB2, the B-C bond stretching mode (at 1276 cm^-1) has rather small damping. The two "forbidden" modes (at 830 cm^-1 and 546 cm^-1) disappeared after subsequent thermal treatment.Comment: 4 pages, LaTeX, complementary experimental resul

Vapor pressure and thermophysical properties of eugenol and (+)-carvone

In this work, vapor pressures, liquid-phase heat capacities, and phase behavior of two monoterpenoids, (þ)-carvone and eugenol were studied. The vapor pressure experiments were performed using a static method over an environmentally relevant range of temperatures, from 258 K to 308 K. Liquid-phase heat capacities were measured by Tian-Calvet calorimetry between 265 K and 355 K. The phase behavior was investigated by heat-flux differential scanning calorimetry from 183 K. Experimental data were supplemented by ideal-gas thermodynamic properties obtained by combining quantum chemical and statistical thermodynamic calculations. Vapor pressures and heat capacities obtained in this work along with selected literature values were treated simultaneously by multi-property correlation in order to obtain a consistent description of thermodynamically linked properties. To our knowledge, liquid-phase heat capacities and phase behavior of eugenol are reported for the first time in this work.The authors M.F., K.R., V. S., and V.P. acknowledge financial support from the Czech Science Foundation (GACR no. 17-03875S) and specific university research (MSMT No. 20-SVV/2018). The authors S.M.V., O.F., and S.P.P. acknowledge financial support from the project POCI-01-0145-FEDER-006984 e Associate Laboratory LSRE-LCM (UID/EQU/50020/2019) funded by national funds through FCT/MCTES (PIDDAC). S.M.V. also acknowledges FCT for his PhD grant (SFRH/BD/138149/2018).info:eu-repo/semantics/publishedVersio

Enrichment of the HR 8799 planets by minor bodies and dust

In the Solar System, minor bodies and dust deliver various materials to planetary surfaces. Several exoplanetary systems are known to host inner and outer belts, analogues of the main asteroid belt and the Kuiper belt. We study the possibility that exominor bodies and exodust deliver volatiles and refractories to the exoplanets in the system HR8799 by performing N-body simulations. The model consists of the host star, four giant planets (HR8799 e, d, c, and b), 650000 test particles representing the inner belt, and 1450000 test particles representing the outer belt. Moreover we modelled dust populations that originate from both belts. Within a million years, the two belts evolve towards the expected dynamical structure (also derived in other works), where mean-motion resonances with the planets carve the analogues of Kirkwood gaps. We find that, after this point, the planets suffer impacts by objects from the inner and outer belt at rates that are essentially constant with time, while dust populations do not contribute significantly to the delivery process. We convert the impact rates to volatile and refractory delivery rates using our best estimates of the total mass contained in the belts and their volatile and refractory content. Over their lifetime, the four giant planets receive between $10^{-4}$ and 10^{-3}M_\bigoplus of material from both belts. The total amount of delivered volatiles and refractories, {5\times10^{-3}\textrm{M}_\bigoplus}, is small compared to the total mass of the planets, 11\times10^{3}\textrm{M}_\bigoplus. However, if the planets were formed to be volatile-rich, their exogenous enrichment in refractory material may well be significant and observable, for example with JWST-MIRI. If terrestrial planets exist within the snow line of the system, volatile delivery would be an important astrobiological mechanism and may be observable as atmospheric trace gases.Comment: 11 pages, 8 figures, accepted for publication in Astronomy&Astrophysic