Phase Equilibria in the System CaO-SiO2-La2O3-Nb2O5 at 1400 °C

CaO-SiO2-La2O3-Nb2O5 system is of great significance for the pyrometallurgical utilization of Bayan Obo tailing resources. In the present work, the phase equilibrium of this quaternary system at 1400 °C was determined by a thermodynamic equilibrium experiment. On the basis of the recently determined CaO-La2O3-Nb2O5 phase diagram, some boundary surfaces of primary phase fields of CaO-SiO2-La2O3-Nb2O5 phase diagram were modified; then, the 1400 °C isothermal surface in the primary phase fields of SiO2, CaNb2O6, Ca2Nb2O7, and LaNbO4 was constructed, respectively. On this basis, CaO-SiO2-Nb2O5 pseudo-ternary phase diagrams with w(La2O3) = 5%, 10%, 15%, and 20% were determined, respectively. Considering the importance of equilibrium crystallization reaction type, we proposed a new rule named Tangent Line Rule to judge the univariant reaction type in the quaternary phase diagram. By applying Tangent Line Rule and Tangent Plane Rule previously proposed, some univariant and bivariant crystallization reaction types in the CaO-SiO2-La2O3- Nb2O5 phase diagram were determined, respectively. The current work can provide original data for the establishment of a thermodynamic database of Nb-bearing and REE-bearing slag system; the proposed Tangent Line Rule will promote the application of a spatial quaternary phase diagram.

An analysis of the unified formulation for the equilibrium problem of compositional multiphase mixtures

In this paper , we conduct a thorough mathematical analysis of the unified formulation advocated by Lauser et al . [ Adv . Water Res . 34 (2011), 957-966] for compositional multiphase flows in porous media . The interest of this formulation lies in its potential to automatically handle the appearance and disappearance of phases. However , its practical implementation turned out to be not always robust for realistic fugacity laws associated with cubic equations of state , as shown by Ben Gharbia and Flauraud [ Oil & Gas Sci . Technol . 74 (2019), 43]. By focusing on the subproblem of phase equilibrium , we derive sufficient conditions for the existence of the corresponding system of equations. We trace back the difficulty of cubic laws to a deficiency of the Gibbs functions that comes into play due to the `` unifying '' feature of the new formulation. We propose a partial remedy for this problem by extending the domain of definition of these functions in a natural way . Besides , we highlight the crucial but seemingly unknown fact that the unified formulation encapsulates all the properties known to physicists on phase equilibrium , such as the tangent plane criterion and the minimization of the Gibbs energy of the mixture.

Membrane remodeling due to mixture of multiple curvature proteins: Insights from mesoscopic continuum modeling

We present an extension of the Monte Carlo based mesoscopic membrane model where the membrane is represented as a dynamically triangulated surface and the proteins are modeled as anisotropic inclusions formulated as in-plane nematic field variables adhering to the deformable elastic sheet. The local orientation of the nematic field lies in the local tangent plane of the membrane and is free to rotate in this plane. Protein-membrane interactions are modeled as anisotropic spontaneous curvatures of the membrane and protein-protein interactions are modeled by the splay and bend terms of Frank's free energy for nematic liquid crystals. In the extended model, we have augmented the Hamiltonian to study membrane deformation due to a mixture of multiple types of curvature generating proteins. This feature opens the door for understanding how multiple different kinds of curvature-generating proteins may be working in a coordinated manner to induce desired membrane morphologies. For example, among other things, we study membrane deformations and tubulation due to a mixture of positive and negative curvature proteins as mimics of various proteins from BAR domain family working together for curvature formation and stabilization. We also study the effect of membrane anisotropy, which manifests as membrane localization and differential binding affinity of a given curvature protein, leading to insights into the tightly regulated cargo sorting and transport processes. Our simulation results show different morphologies of deformed vesicles that depend on the curvatures and densities of the participating proteins as well as on the protein-protein and membrane-proteins interactions.

Generalized model of Kapitza conductance across rough interfaces

This paper is devoted to the theoretical prediction of the interfacial heat transfer in nanostructured materials. The main task of this work is the analysis of interaction of elastic waves with the rough interface between two different solids. The presence of toughness leads to a significant increase in the resistance to heat transfer in nanostructures. This fundamental problem is discussed in relation to the commonly used method of wave scattering at rough surface: the Kirchhoff tangent plane method. The method assumes that at the point of the rough surface profile, the surface is regarded as locally smooth, and the reflection and transmission of the incident wave can be described by the scattering at the tangent plane of this point. Based on the elastic wave theory, we use the frequency-dependent continuity conditions to calculate the energy transmission coefficient at the interface. And then its effective value at the rough interface is estimated by using the Kirchhoff method. By substituting this effective value into the formula of Kapitza conductance, we can calculate the Kapitza conductance at the rough interface and analyze the effect of roughness on the interfacial heat transfer.

Wavefronts and modal structure of long surface and internal ring waves on a parallel shear current

We study long surface and internal ring waves propagating in a stratified fluid over a parallel shear current. The far-field modal and amplitude equations for the ring waves are presented in dimensional form. We re-derive the modal equations from the formulation for plane waves tangent to the ring wave, which opens a way to obtaining important characteristics of the ring waves (group speed, wave action conservation law) and to constructing more general ‘hybrid solutions’ consisting of a part of a ring wave and two tangent plane waves. The modal equations constitute a new spectral problem, and are analysed for a number of examples of surface ring waves in a homogeneous fluid and internal ring waves in a stratified fluid. Detailed analysis is developed for the case of a two-layered fluid with a linear shear current where we study their wavefronts and two-dimensional modal structure. Comparisons are made between the modal functions (i.e. eigenfunctions of the relevant spectral problems) for the surface waves in homogeneous and two-layered fluids, as well as the interfacial waves described exactly and in the rigid-lid approximation. We also analyse the wavefronts of surface and interfacial waves for a large family of power-law upper-layer currents, which can be used to model wind generated currents, river inflows and exchange flows in straits. Global and local measures of the deformation of wavefronts are introduced and evaluated.

Color Point Cloud Registration Algorithm Based on Hue

ICP is a well-known method for point cloud registration but it only uses geometric information to do this, which will result in bad results in some similar structures. Adding color information when registering will improve the performance. However, color information of point cloud, such as gray, varies differently under different lighting conditions. Using gray as the color information to register can cause large errors and even wrong results. To solve this problem, we propose a color point cloud registration algorithm based on hue, which has good robustness at different lighting conditions. We extract the hue component according to the color information of point clouds and make the hue distribution of the tangent plane continuous. The error function consists of color and geometric error of two point clouds under the current transformation. We optimize the error function using the Gauss–Newton method. If the value of the error function is less than the preset threshold or the maximum number of iterations is reached, the current transformation relationship is required. We use RGB-D Scenes V2 dataset to evaluate our algorithm and the results show that the average recall of our algorithms is 8.63% higher than that of some excellent algorithms, and its RMSE of 14.3% is lower than that of the other compared algorithms.

Pansu–Wulff shapes in ℍ1

We consider an asymmetric left-invariant norm ∥ ⋅ ∥ K {\|\cdot\|_{K}} in the first Heisenberg group ℍ 1 {\mathbb{H}^{1}} induced by a convex body K ⊂ ℝ 2 {K\subset\mathbb{R}^{2}} containing the origin in its interior. Associated to ∥ ⋅ ∥ K {\|\cdot\|_{K}} there is a perimeter functional, that coincides with the classical sub-Riemannian perimeter in case K is the closed unit disk centered at the origin of ℝ 2 {{\mathbb{R}}^{2}} . Under the assumption that K has C 2 {C^{2}} boundary with strictly positive geodesic curvature we compute the first variation formula of perimeter for sets with C 2 {C^{2}} boundary. The localization of the variational formula in the non-singular part of the boundary, composed of the points where the tangent plane is not horizontal, allows us to define a mean curvature function H K {H_{K}} out of the singular set. In the case of non-vanishing mean curvature, the condition that H K {H_{K}} be constant implies that the non-singular portion of the boundary is foliated by horizontal liftings of translations of ∂ ⁡ K {\partial K} dilated by a factor of 1 H K {\frac{1}{H_{K}}} . Based on this we can define a sphere 𝕊 K {\mathbb{S}_{K}} with constant mean curvature 1 by considering the union of all horizontal liftings of ∂ ⁡ K {\partial K} starting from ( 0 , 0 , 0 ) {(0,0,0)} until they meet again in a point of the vertical axis. We give some geometric properties of this sphere and, moreover, we prove that, up to non-homogeneous dilations and left-translations, they are the only solutions of the sub-Finsler isoperimetric problem in a restricted class of sets.

A Local Approach for Computing Smooth B-spline Surfaces for Arbitrary Quadrilateral Base Meshes

We present a method for approximating surface data of arbitrary topology by a model of smoothly connected B-spline surfaces. Most of the existing solutions for this problem use constructions with limited degrees of freedom or they address smoothness between surfaces in a post-processing step, often leading to undesirable surface behavior in proximity of the boundaries. Our contribution is the design of a local method for the approximation process. We compute a smooth B-spline surface approximation without imposing restrictions on the topology of a quadrilateral base mesh defining the individual B-spline surfaces, the used B-spline knot vectors, or the number of B-spline control points. Exact tangent plane continuity can generally not be achieved for a set of B-spline surfaces for an arbitrary underlying quadrilateral base mesh. Our method generates a set of B-spline surfaces that lead to a nearly tangent plane continuous surface approximation and is watertight, i.e., continuous. The presented examples demonstrate that we can generate B-spline approximations with differences of normal vectors along shared boundary curves of less than one degree. Our approach can also be adapted to locally utilize other approximation methods leading to higher orders of continuity.