The evolution of a crystal surface: Analysis of a one-dimensional step train connecting two facets in the ADL regime

We study the evolution of a monotone step train separating two facets of a crystal surface. The model is one-dimensional and we consider only the attachment-detachment-limited regime. Starting with the well-known ODEs for the velocities of the steps, we consider the system of ODEs giving the evolution of the “discrete slopes.” It is the l²-steepest-descent of a certain functional. Using this structure, we prove that the solution exists for all time and is asymptotically self-similar. We also discuss the continuum limit of the discrete self-similar solution, characterizing it variationally, identifying its regularity, and discussing its qualitative behavior. Our approach suggests a PDE for the slope as a function of height and time in the continuum setting. However, existence, uniqueness, and asymptotic self-similarity remain open for the continuum version of the problem.     

饱和的多孔介质中含夹杂时的磁流体动力学自然对流

在一个多孔介质中含倾斜矩形夹杂物时,数值地研究磁流体动力学自然对流热交换问题,矩形夹杂的边界条件为两个绝热壁和两个等温壁,使用适当的变量集,将控制方程:连续性条件、推广的Darcy定理--Forchheimer律、能量方程变换为无量纲形式,然后使用有限差分格式求解,磁效应数、Darcy-Rayleigh数、矩形夹杂物的倾斜角以及纵横比作为控制参数,得到多孔介质中含矩形夹杂物时,磁效应数和倾斜角参数影响流体流动和热交换的规律.     

A conductance study of the binding of benzo-15-crown-5 with alkali cations in acetonitrile

The decrease in the molar electrolytic conductance of Na⁺, K⁺, Rb⁺, and Cs⁺ tetraphenylborates, caused by the addition of benzo-15-crown-5 in acetonitrile at constant ionic strength, is analyzed according to a model involving 1:1 stoichiometry. The stability constant,K, and the limiting molar conductivity, _c , for each 1:1 complex are determined from the conductance measurements by using a nonlinear least squares curve fitting procedure. The stability sequence of the 1:1 complexes, as deduced from data at 288, 293, 298, 303, and 308 K, has the order Na⁺>K⁺>Rb⁺>Cs⁺. Values of H ⁰, S ⁰, and _c at 298 K are reported and their significance is discussed.     

On the homogeneous nucleation and propagation of dislocations under shock compression

The dynamic response of crystalline materials subjected to extreme shock compression is not well understood. The interaction between the propagating shock wave and the material’s defect occurs at the sub-nanosecond timescale which makes in situ experimental measurements very challenging. Therefore, computer simulation coupled with theoretical modelling and available experimental data is useful to determine the underlying physics behind shock-induced plasticity. In this work, multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper reported at ultra-high strain rates shock loading. We compare the value of threshold stress for homogeneous nucleation obtained from elastodynamic solution and standard nucleation theory with MDDP predictions for copper single crystals oriented in the [0 0 1]. MDDP homogeneous nucleation simulations are then carried out to investigate several aspects of shock-induced deformation such as; stress profile characteristics, plastic relaxation, dislocation microstructure evolution and temperature rise behind the wave front. The computation results show that the stresses exhibit an elastic overshoot followed by rapid relaxation such that the 1D state of strain is transformed into a 3D state of strain due to plastic flow. We demonstrate that MDDP computations of the dislocation density, peak pressure, dynamics yielding and flow stress are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models. MDDP-based models for dislocation density evolution, saturation dislocation density, temperature rise due to plastic work and strain rate hardening are proposed. Additionally, we demonstrated using MDDP computations along with recent experimental reports the breakdown of the fourth power law of Swegle and Grady in the homogeneous nucleation regime.     

The kinetics and molecular modeling of the complexation of tenoxicam with cyclodextrins in solution

The effect of cyclodextrins on photodegradation of tenoxicam (TEN) was studied at pH 4, 7 and 10. After 60 min of irradiation with UV light, the photodegradation was extensive. All cyclodextrins (alpha, beta, or gamma) stabilize TEN and reduce the rate of photodegradation. The largest effect of cyclodextrins is at pH 7. Molecular modeling results help to explain and manipulate the results. The results are discussed and compared with other results from previous studies.     

Dislocation transmission across the Cu/Ni interface: a hybrid atomistic–continuum study

The strengthening mechanisms in bimetallic Cu/Ni thin layers are investigated using a hybrid approach that links the parametric dislocation dynamics method with ab initio calculations. The hybrid approach is an extension of the Peierls–Nabarro (PN) model to bimaterials, where the dislocation spreading over the interface is explicitly accounted for. The model takes into account all three components of atomic displacements of the dislocation and utilizes the entire generalized stacking fault energy surface (GSFS) to capture the essential features of dislocation core structure. Both coherent and incoherent interfaces are considered and the lattice resistance of dislocation motion is estimated through the ab initio-determined GSFS. The effects of the mismatch in the elastic properties, GSFS and lattice parameters on the spreading of the dislocation onto the interface and the transmission across the interface are studied in detail. The hybrid model shows that the dislocation dissociates into partials in both Cu and Ni, and the dislocation core is squeezed near the interface facilitating the spreading process, and leaving an interfacial ledge. The competition of dislocation spreading and transmission depends on the characteristics of the GSFS of the interface. The strength of the bimaterial can be greatly enhanced by the spreading of the glide dislocation, and also increased by the pre-existence of misfit dislocations. In contrast to other available PN models, dislocation core spreading in the two dissimilar materials and on their common interface must be simultaneously considered because of the significant effects on the transmission stress.     

Complexation and thermodynamic studies of oxathiadibenzocrown ethers with Cu2+, Pb2+, Zn2+ and Cd2+ ions

A thermodynamic study of the complexation of Cu²⁺, Pb²⁺, Zn²⁺ and Cd²⁺ ions with 1 and 2 in acetonitrile has been carried out. The study was conducted in the temperature range 283–308 K using a conductometric technique. The observed molar conductivity, Λ, was found to decrease significantly for mole ratios [L]_t/[M]_t less than unity in all cases. A model involving 1:1 stoichiometry has been used to analyze the conductivity data. The stability constant, K, for each 1:1 complex was determined from the conductivity data by using a nonlinear least-squares curve fitting procedure. The results show that compound 1 has no peak selectivity for any of the metal cations, while compound 2 selectively associates with Cu²⁺ and Pb²⁺. Complexes of 1 have the following stability order Pb²⁺ > Cu²⁺ > Zn²⁺ > Cd²⁺  and Pb²⁺ > Cu²⁺ for the complexes of 2. The ?H° and ?S° values for the complexation process were obtained from the slope and intercept of the Van’t Hoff plots respectively. All ?G° values were negative and were determined from the Gibbs–Helmholtz equation and the significance of these values is discussed.     

A thermodynamic study of the association of alkali metal cations with dicyclohexano-18-crown-6

A thermodynamic study of the association of Na⁺, K⁺, Rb⁺, and Cs⁺ with dicyclohexano-18-crown-6 in acetonitrile has been carried out at 308, 303, 298, 293, and 288 K using a conductometric technique. The observed molar conductivities, A, were found to decrease significantly for mole ratios less than unity. A model involving 11 stoichiometry has been used to analyze the conductivity data. The stability constant,K, and the limiting molar conductivity, A _c , for each 11 complex were determined from the conductivity data by using a nonlinear least squares curve fitting procedure. The binding sequence, based on the value of logK at 298 K, as derived from this study is K⁺>Na⁺>Rb⁺>Cs⁺. Values of H ^o and S ^o are reported and their significance is discussed.     

Concave polyarenes with sulfide-linked flaps and tentacles: new electron-rich hosts for fullerenes

Pentakis(1,4-benzodithiino)corannulene (6) in CS2 formed the strongest 1:1 complexes with C60 and C70 of any corannulene derivative yet reported. The 1,3,5,7,9-pentakis(propylthio)corannulene (4b) formed weaker 1:1 complexes with C60 and C70 in CS2, whereas the decakis(propylthio)corannulene (5b) and unsubstituted corannulene (1) showed no evidence for complexation with either C60 or C70 in CS2.     

Synthesis of hexahomotrioxacalix[3]naphtalenes and a study of their alkali-metal cation binding properties

The first syntheses of the C3-symmetrical and unsymmetrical hexahomotrioxacalix[3]naphthalenes 3 and 4, respectively, and the corresponding tert-butyl hexahomotrioxacalix[3]naphthalene 3a are reported. A convergent synthesis of the linear hexahomotrimer precursors 19 and 19a is described, but the direct synthesis of 3 and 3a can also be achieved from the monomers 20 and 20a, respectively. A limited study of the binding properties of alkali-metal cations by 3 or 3a using a picrate-CHCl3 extraction showed only weak abilities to bind with the cations examined.