An Energetic Variational Approach for the Cahn--Hilliard Equation with Dynamic Boundary Condition: Model Derivation and Mathematical Analysis

The Cahn--Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In recent years, several types of dynamic boundary conditions have been proposed in order to account for possible short-range interactions of the material with the solid wall. Our first aim in this paper is to propose a new class of dynamic boundary conditions for the Cahn--Hilliard equation in a rather general setting. The derivation is based on an energetic variational approach that combines the least action principle and Onsager's principle of maximum energy dissipation. One feature of our model is that it naturally fulfills three important physical constraints such as conservation of mass, dissipation of energy and force balance relations. Next, we provide a comprehensive analysis of the resulting system of partial differential equations. Under suitable assumptions, we prove the existence and uniqueness of global weak/strong solutions to the initial boundary value problem with or without surface diffusion. Furthermore, we establish the uniqueness of asymptotic limit as $t\to+\infty$ and characterize the stability of local energy minimizers for the system.Comment: to appear in Arch. Rational Mech. Ana

Asymptotic behavior of a hydrodynamic system in the nematic liquid crystal flows

In this paper we study the long time behavior of the classical solutions to a hydrodynamical system modeling the flow of nematic liquid crystals. This system consists of a coupled system of Navier--Stokes equations and kinematic transport equations for the molecular orientations. By using a suitable Lojasiewicz--Simon type inequality, we prove the convergence of global solutions to single steady states as time tends to infinity. Moreover, we provide estimates for the convergence rate

Triazido­[tris­(2-pyridyl-κN)methyl­amine]cobalt(III)

The title compound, [Co(N3)3(C16H14N4)], was synthesized by hydro­thermal reaction of [Co(NH3)6](NO3)3, NaN3 and tris­(2-pyrid­yl)methyl­amine. The structure contains two independent complexes in the asymmetric unit, with closely comparable geometry. The CoIII atoms are hexa­coordinated by three N atoms from the tridentate tris­(2-pyrid­yl)methyl­amine ligands and three azide ions in a fac arrangement. N—H⋯N hydrogen bonds are formed between the amino group and the uncoordinated terminal N atoms of the azide ligands

Effects of aromatizable and nonaromatizable androgens on the sex inversion of red-spotted grouper (Epinephelus akaara)

The effects of aromatizable 17α-methyltestosterone (MT) and non-aromatizable 17α-methyldihydrotestosterone (MDHT) on sex inversion in red-spotted grouper, Epinephelus akaara, were investigated. Fish were implanted with MT, MDHT and MT+AI (aromatase inhibitor, AI) respectively for one month. The results showed that the three treated groups turned into transitional stage with intersex gonads, which contained atretic oocytes and spermatogenic germ cells at all stages of spermatogenesis. The controls did not change sex. The gonads of more than half MT-implanted fish were in early transitional stages of sex inversion, whereas those of more than half MDHT and MT+AI-implanted fish were in late transitional stages of sex inversion. No difference in serum estradiol-17β (E2) levels between the controls and the treated groups were observed, whereas 11-ketotestosterone (11-KT) and testosterone (T) levels increased in all treated groups. Significantly lower gonadosomatic index (GSI) and gonadal aromatase activity were observed in the treated groups, which were in accordance with the lower mRNA expression of P450aromA. However, P450aromB mRNA expression increased in the MT group, while it did not change in the MDHT group. These results suggest that the sex inversion of red-spotted grouper by MT and MDHT implantation might be due to the suppression of P450aromA gene expression, and resulting in both the decrease of the ovarian estrogen –secretion, as well as the increase in the 11-KT levels. Furthermore, the main reason for MT being less effective than MDHT might be due to partial aromatization of MT to estrogen

Single-photon transport and mechanical NOON state generation in microcavity optomechanics

We investigate the single-photon transport in a single-mode optical fiber coupled to an optomechanical system in the single-photon strong-coupling regime. The single-photon transmission amplitude is analytically obtained with a real-space approach and the effects of thermal noises are studied via master-equation simulations. The results provide an explicit understanding of optomechanical interaction and offer a useful guide for manipulating single photons in optomechanical systems. Based on the theoretical framework, we further propose a scheme to generate the mechanical NOON states with arbitrary phonon numbers by measuring the sideband photons. The probability for generating the NOON state with five phonons is over 0.15.Comment: 13 pages, 6 figure