Invariant Points Research Articles

Differentiation of the Multicomponent System Na,K,Sr∥Cl,NO3: Phase Diagram and Physicochemical Properties of Salt Mixtures in the System NaNO3—NaCl—KNO3—Sr(NO3)2

The differentiation of the quaternary reciprocal system Na,K,Sr∥Cl,NO3 was performed based on graph theory using special software. Stable and metastable complexes of the system were found using a matrix of reciprocal pairs of salts. For the first time, by physicochemical analysis methods (differential thermal, visual polythermal, and X-ray powder diffraction analyses using the method of thermal analysis of successive projections of the composition polytope), the quaternary system NaNO3-NaCl-KNO3-Sr(NO3)2, which is a stable complex of the quaternary reciprocal system Li,Ca,Ba∥F,WO4, was studied and the coordinates of invariant points were determined. The density and electrical conductivity were determined, volumetric changes were calculated, and the corrosion of 12Kh18N10T steel in eutectic and peritectic salt mixtures was investigated.

Solid-Liquid Equilibria in the Quaternary Systems KCl–MgCl2–SrCl2–H2O and NaCl–KCl–SrCl2–H2O at 348 K

Solid-liquid equilibria in the quaternary systems KCl–MgCl2–SrCl2–H2O and NaCl–KCl–SrCl2–H2O at 348 K were measured by the isothermal solution saturation method. The composition of the equilibrium solid phase, solubilities of salts, and densities of saturated solution in the two systems were determined. Phase diagrams, water content diagrams and solution density diagrams of quaternary systems were plotted according to experimental data. The phase diagram of the quaternary system NaCl–KCl–SrCl2–H2O has one invariant point, three univariant curves as the boundary of NaCl, KCl and SrCl2 · 2H2O. This phase diagrams were simple co-saturation type without complex salt and solid solution. For the quaternary system KCl–MgCl2–SrCl2–H2O, one complex salt KCl · MgCl2 · 6H2O (Car) had been found in this system, consisted of five univariant curves, two invariant points and four crystallization regions of MgCl2 · 6H2O (Bis), KCl, SrCl2 · 2H2O and KCl · MgCl2 · 6H2O. And the densities transformation rules were simply discussed. Simultaneously, the solubilities and densities data in invariant point of the quaternary system NaCl–KCl–SrCl2–H2O had been compared with the experimental data of previous researchers.

Phase Equilibria in the Aqueous Ternary Systems (NaCl + NaBO2 + H2O) and (Na2SO4 + NaBO2 + H2O) at 298.15 K and 0.1 MPa

With the isothermal dissolution equilibrium method and wet-residue method, the solubility data as well as physicochemical properties including density, refractive index, and pH value of the two ternary systems (NaCl + NaBO2 + H2O) and (Na2SO4 + NaBO2 + H2O) at 298.15 K and 0.1 MPa have been experimentally determined, and the relatively phase diagrams have been established for the first time. In the ternary system (NaCl + NaBO2 + H2O), two invariant points, three univariant curves, and three crystallization regions corresponding to sodium chloride (NaCl), sodium metaborate tetrahydrate (NaBO2·4H2O), and a congruent double salt teepleite (NaCl·NaBO2·2H2O) were detected. While in the ternary system (Na2SO4 + NaBO2 + H2O), there are one invariant point, two univariant curves, and two crystallization regions corresponding to NaBO2·4H2O and mirabilite (Na2SO4·10H2O). The physicochemical properties (density, refractive index, and pH value) in the two systems present a regular variation versus that with the chang...

Solid–Liquid Equilibria and Pitzer Model Simulation of the SrCl2–NH4Cl–MgCl2–H2O Quaternary System at T = 298 K

The solid–liquid equilibria data of the aqueous SrCl2–NH4Cl–MgCl2–H2O quaternary system at T = 298 K were measured. Results show that there are three three-salt cosaturation invariant points and fi...

Experimental Determination and Thermodynamic Modeling of Solid–Liquid Equilibria in the Quaternary System NaCl–KCl–SrCl2–H2O at 288.15 K

The solubilities in the quaternary system NaCl–KCl–SrCl2–H2O and its subsystem KCl–SrCl2–H2O at 288.15 K were investigated with the isothermal dissolution method. The phase diagram of the ternary system is composed of two single-salt crystallizations for KCl and SrCl2·6H2O, two solubility univariant curves, and one cosaturated point. The dry-salt diagram of the quaternary system consists of three single-salt crystallization fields for NaCl, KCl, and SrCl2·6H2O, three solubility univariant curves, and one invariant point. By combination of the determined solubilities and Pitzer binary parameters obtained in the literature, the lacking Pitzer mixing parameters θNa,Sr, θK,Sr, ΨNa,Sr,Cl, and ΨK,Sr,Cl and the solubility product constants of the solid salts for the systems were fitted on the basis of the Pitzer model. The model was then used to calculate the solubilties of the two systems. The theoretical results calculated using the model coincide with the experimental values.

Phase Equilibria of the Reciprocal Quaternary System (Na+, Ca2+//Cl–, Borate–H2O) at 288.15 K and 0.1 MPa

To exploit the valuable features of brine resources with high concentrations of borate ions, the solubility data and corresponding physicochemical properties (refractive index, density, viscosity, and pH) for the reciprocal quaternary system (Na+, Ca2+//Cl–, borate–H2O) at 288.15 K were determined experimentally using the method of isothermal dissolution equilibrium. The dry-salt and water-phase diagrams and the diagrams of physicochemical properties (refractive index, density, viscosity, and pH) against J(B4O72–) in the solution were established. In the dry-salt phase diagram of the quaternary system at 288.15 K, two invariant points, five univariant curves, and four crystallization regions corresponding to gowerite (CaB6O10·5H2O), borax (Na2B4O7·10H2O), antarcticite (CaCl2·6H2O), and sodium chloride (NaCl) were found. The area of crystallization region of CaB6O10·5H2O is larger than that of other coexisting salts, which indicates that the solubility of gowerite in this system is the lowest and that it i...

On a notion of toric special linear systems

In this note, we study linear systems on complete toric varieties X with an invariant point whose orbit under the action of Aut(X) contains the dense torus T of X. We give a characterization of such varieties in terms of its defining fan and introduce a new definition of expected dimension of linear systems which consider the contribution given by certain toric subvarieties. Finally, we study degenerations of linear systems on these toric varieties induced by toric degenerations.

Scene wireframes sketching for Unmanned Aerial Vehicles

This paper introduces novel insights to improve the state-of-the-art line-based unsupervised observation and abstraction models of man-made environments. The increasing use of autonomous UAVs inside buildings and around human-made structures demands new accurate and comprehensive representation of their operation environments. Most of the 3D scene abstraction methods use invariant feature point matching, nevertheless some sparse 3D point clouds do not concisely represent the structure of the environment. The presented approach is based on observation and representation models using the straight line segments. The goal of the work is a complete method based on the matching of lines, that provides a complementary approach to state-of-the-art methods when facing 3D scene representation of poor texture environments for future autonomous UAV. Oppositely to other recently published methods obtaining 3D line abstractions, the proposed method features 3D segment abstraction in the absence of a previously generated point based reconstruction. Another advantage is the ability to group the resulting 3D lines according to different planes, for exploiting coplanar line intersections. These intersections are used like feature points in the reconstruction process. It has been proved that this method exclusively based on lines can obtain spatial information in the adverse situations when a SIFT-like SfM pipeline fails to generate a dense point cloud.

Solid–Liquid Metastable Phase Equilibria in the Ternary System (MgCl2 + MgSO4 + H2O) at 323.15 K

The solubilities and the densities in the aqueous ternary system (MgCl2 + MgSO4 + H2O) at 323.15 K were determined by the isothermal evaporation method. The phase diagram was drawn for this system at 323.15 K. The phase diagram consists of two invariant points, three univariant curves, and three crystallization regions corresponding to bischofite (MgCl2 · 6H2O), tetrahydrate (MgSO4 · 4H2O) and hexahydrite (MgSO4 · 6H2O). Neither double salts nor solid solution was found. Based on the Pitzer and Harvie–Weare (HW) model, the solubility equilibrium constants for the salts were fitted with the solubilities in this research work, and the solubilities of the ternary system at 323.15 K were calculated. Comparisons between the calculated and measured solubilities show that the predicted data agree well with the experimental results.

Determination of the Invariant Point of the Korean VLBI Network Radio Telescopes: First Results at the Ulsan and Tamna Observatories

Determination of the Invariant Point of the Korean VLBI Network Radio Telescopes: First Results at the Ulsan and Tamna Observatories

Solid-liquid Equilibria in the Ternary Systems (NaCl+SrCl2+H2O) and (KCl+SrCl2+H2O) at 288.15 K and 0.1 MPa

Solid-liquid phase equilibria of the two ternary systems (NaCl+SrCl2+H2O) and (KCl+SrCl2+H2O) at T=288.15 K and p=0.1 MPa were studied using the isothermal dissolution equilibrium method. Solubilities of the equilibrium liquid phase were determined, and the solids were also investigated by the Schreinemaker method of wet residues. In the ternary system (NaCl+SrCl2+H2O) at 288.15 K, there is one invariant point corresponding to (NaCl+SrCl2·6H2O) and two crystallization regions corresponding to NaCl and SrCl2·6H2O. The crystallized area of SrCl2·6H2O decreased with the increasing temperature, while that of NaCl increased slightly. In the ternary system (KCl+SrCl2+H2O) at 288.15 K, there is one invariant point(KCl+SrCl2·6H2O) and two crystallization regions cor-responding to KCl and SrCl2·6H2O. Both systems belong to a simple eutectic type, and neither double salts nor solid solutions were formed. On the basis of Pitzer-Harvie-Weare model, the solubilities of the two systems at 288.15 K were demonstrated. A comparison showed that the calculated solubilities agreed well with the experimental data.

Metastable Phase Equilibrium of the Quaternary System Na+, Rb+, Mg2+//Cl–-H2O at 298.2 K

The component solubilities, densities and refractive indices of the quaternary system Na+, Rb+, Mg2+//Cl–-H2O at 298.2 K were measured using an isothermal evaporation method. Based on the gathered data, a metastable phase diagram, a water content diagram, and a density/refractive index vs. composition diagram were constructed. The results show that this system is of a complex type with a double salt rubidium carnallite (RbCl·MgCl2·6H2O) formed at 298.2 K. Double salt rubidium carnallite, whose component point locates in its own crystallization zone in the dry salt phase diagram, belongs to congruent double salt at 298.2 K. Accompanied by the double salt that was formed, there are two invariant points in the phase diagram that cosaturated with three salts and an equilibrated solution. The cosaturated salts for the two invariant points are MgCl2·6H2O+RbCl·MgCl2·6H2O+ NaCl and NaCl+RbCl+RbCl·MgCl2·6H2O, respectively. Both invariant points are commensurate invariant points in the evaporation process, and the two invariant points are evaporative dry points. The sizes of the crystalline regions of the salts are in the order of NaCl>RbCl>RbCl·MgCl2·6H2O>MgCl2·6H2O.

Metastable Phase Equilibrium in the Reciprocal Quaternary System LiCl+MgCl2+Li2SO4+MgSO4+H2O at 348.15 K and 0.1 MPa

The metastable solubilities and the physicochemical properties including density and pH of the reciprocal quaternary system(LiCl+MgCl2+Li2SO4+MgSO4+H2O) at 348.15 K and 0.1 MPa were determined using the isother-mal evaporation method. The dry-salt diagram and water-phase diagram were plotted based on the experimental data. There are five invariant points, eleven univariant curves, and seven crystallization zones corresponding to hexahy-drite, tetrahydrite, kieserite, bischofite, lithium sulfate monohydrate, lithium chloride monohydrate and lithium car-nallite. Comparison between the stable and metastable diagrams at 348.15 K indicates that the metastable phenome-non of magnesium sulfate is obvious, and the crystallization regions of hexahydrite and tetrahydrite disappear in the stable phase diagram. A comparison of the metastable dry-salt phase diagrams at 308.15, 323.15 and 348.15 K shows that with the increasing of temperature the epsomite crystallization zone disappears from the dry-salt phase diagram of 303.15 K, and a new kieserite crystallization zone is presented at 348.15 K. The density and pH in the metastable equilibrium solution present regular change with the increasing of Janecke index J(2Li+), and the calculated densities using the empirical equation agree well with the experimental values.

(Solid + Liquid) Phase Equilibria in the Quaternary System (NaBr + MgBr2 + CaBr2 + H2O) at 298.15 K

The solubilities of salts in the (NaBr + MgBr2 + CaBr2 + H2O) system and its two ternary subsystems (NaBr + MgBr2 + H2O) and (NaBr + CaBr2 + H2O) are investigated at 298.15 K by the isothermal dissolution equilibrium method. The equilibrium phase diagrams of the three systems were obtained using the experimental results. In the three systems, neither solid solution nor double salt was found. In the two ternary phase diagrams, there are two invariant points, three dissolution equilibrium curves and three crystallization fields. The equilibrium solid phases in the (NaBr + MgBr2 + H2O) system are NaBr, NaBr·2H2O and MgBr2·6H2O, and those in the (NaBr + CaBr2 + H2O) system are NaBr, NaBr·2H2O and CaBr2·6H2O. The phase diagram of the quaternary system at 298.15 K consists of one invariant point, four solubility curves and four regions (corresponding to NaBr, NaBr·2H2O, MgBr2·6H2O, and CaBr2·6H2O). The solubilities of salts in the quaternary system and its two subsystems were calculated at 298.15 K by Pizter eq...

Measurements and Calculations of Stable Phase Equilibria in Ternary Systems MgSO4(Rb2SO4) + Cs2SO4 + H2O at T = 298.2 K

The components (solubilities and densities) in aqueous stable equilibria systems Cs2SO4 + MgSO4 + H2O and Rb2SO4 + Cs2SO4 + H2O at T = 298.2 K have been studied by the isothermal dissolution equilibrium method. The wet residue method and the X-ray diffraction method were used to confirm the solid phase compositions. The ternary system Cs2SO4 + MgSO4 + H2O is a complex saturated type, with the commensurate double salt Cs2SO4·MgSO4·6H2O formed at the investigated temperature. There are two two-salt cosaturation invariant points, with the coexisting solid phases corresponding to commensurate type saturation points E1 (MgSO4·7H2O + Cs2SO4·MgSO4·6H2O) and E2 (Cs2SO4·MgSO4·6H2O + Cs2SO4), three monovariant curves, and three crystallization fields in the system of Cs2SO4 + MgSO4 + H2O. The ternary system Rb2SO4 + Cs2SO4 + H2O with solid solutions formed contains two cosaturated points, with the equilibrium solid phases of the saturation points F1 and F2 corresponding to [(Rb, Cs)2SO4] + Cs2SO4 and Rb2SO4 + [(Rb,...

Three-dimensional quantum anomalous Hall effect in ferromagnetic insulators

The quantum anomalous Hall effect (QAHE) hosts the dissipationless chiral edge states associated with the nonzero Chern number, providing potentially significant applications in future spintronics. The QAHE usually occurs in a two-dimensional (2D) system with time-reversal symmetry breaking. In this work, we propose that the QAHE can exist in three-dimensional (3D) ferromagnetic insulators. By imposing inversion symmetry, we develop the topological constraints dictating the appearance of 3D QAHE based on the parity analysis at the time-reversal invariant points in reciprocal space. Moreover, using first-principles calculations, we identify that 3D QAHE can be realized in a family of intrinsic ferromagnetic insulating oxides, including layered and non-layered compounds that share a centrosymmetric structure with space group $R\bar{3}m$ (No. 166). The Hall conductivity is quantized to be $-\frac{3e^2}{hc}$ with the lattice constant $c$ along $c$-axis. The chiral surface sheet states are clearly visible and uniquely distributed on the surfaces that are parallel to the magnetic moment. Our findings open a promising pathway to realize the QAHE in 3D ferromagnetic insulators.

Stable Phase Equilibria of the Quaternary System Na+//Cl–, NO3–, SO42––H2O at 353.15 K

The phase equilibria of the quaternary system Na+//Cl–, NO3–, SO42––H2O and the subsystems Na+//Cl–, SO42––H2O, Na+//Cl–, NO3––H2O, Na+//NO3–, SO42––H2O at 353.15 K were studied by the isothermal dissolution method. There are one invariant point, three univariant curves, three crystallization fields of single salt, three cocrystallization fields for two salts, and one cocrystallization field for three salts in the quaternary system. Neither double salt nor solid solution is found in the system at 353.15 K. At the invariant point of Na+//Cl–, NO3–, SO42––H2O system, the composition of the solution is NaCl 7.00 wt %, Na2SO4 1.59 wt %, NaNO3 47.79 wt %. The order of the solubility in the mixing solution of the single salts is Na2SO4 < NaCl < NaNO3. Moreover, the solubilities of the systems at 353.15 K were calculated theoretically by using the Pitzer ion interaction model. The high ionic strength was found to be a critical factor, which influenced the calculation accuracy significantly. All data and results ...

Solid–Liquid Equilibrium of the Quaternary System Lithium, Potassium, Rubidium, and Borate at T = 323 K

The solid–liquid equilibrium (SLE) of electrolyte mixtures Li+, K+, Rb+//borate–H2O at T = 323 K was studied by the isothermal dissolution method, and the X-ray diffraction method was used to confirm the solid-phase compositions. The analysis of phase diagram shows that the graph consists of one three-salt cosaturation invariant point and three regions of crystallization corresponding to single salts Li2B4O7·3H2O, K2B4O7·4H2O, and RbB5O8·4H2O, respectively. From the comparison of phase diagrams of system Li+, K+, Rb+//B4O72––H2O between 323 and 348 K, we can conclude that (1) the crystalline form of salts lithium borate, potassium borate, and rubidium borate did not change at 323 and 348 K and (2) the salt Li2B4O7·3H2O crystalline area decreases and the other two salt crystalline areas, K2B4O7·4H2O and RbB5O8·4H2O, increase at 323 K.

Solid-liquid phase equilibria in aqueous solutions of four common fertilizers at 303.2 K and atmospheric pressure

Application of liquid fertilizers can significantly improve the fertilizer utilization efficiency and labor efficiency. Phase equilibrium of various fertilizers in aqueous solution is the basis of manufacturing liquid fertilizers. The solid-liquid phase equilibria of ternary systems NH4H2PO4 + CO(NH2)2 + H2O, (NH4)2HPO4 + CO(NH2)2 + H2O, K2SO4 + CO(NH2)2 + H2O, K2SO4 + NH4H2PO4 + H2O and K2SO4 + (NH4)2HPO4 + H2O at 303.2 K were investigated by isothermal solution saturation method. The maximum nutrient content of (NH4)2HPO4 + CO(NH2)2 + H2O solution is 31.78 wt% at the saturated solution of (NH4)2HPO4, and the mass ratio of N: P2O5 is 1: 2.53. In the solutions of NH4H2PO4 + CO(NH2)2 + H2O, K2SO4 + CO(NH2)2 + H2O and K2SO4 + (NH4)2HPO4 + H2O, the corresponding maximum of nutrient contents all are obtained at the corresponding invariant points as 33.82 wt%, 27.32 wt% and 32.92 wt% respectively. And the mass ratios of nutrients are N: P2O5 of 2.69: 1, K2O: N of 1:15.66 and N: P2O5: K2O of 1.64: 4.15: 1, respectively. The maximal nutrient content in the K2SO4 + NH4H2PO4 + H2O saturation solution is 25.14 wt% and the corresponding mass ratio of N: P2O5: K2O is 1.26: 6.38: 1. Based on the phase equilibrium diagrams, the species and nutrient contents in liquid fertilizers all are adjustable by choosing different raw materials or modulating the prescription. The results provide fundamental data for the preparation of liquid fertilizers. It is also helpful to optimize the operation parameters in the manufacturing process, storage process or application process to avoid the precipitation of solid.

An Innovative Practical Automatic Segmentation of Ultrasound Computer Tomography Images Acquired from USCT System

A 3D ultrasound computer tomography (USCT) device with a nearly isotropic and spatially invariant 3D point spread function has been constructed at Institute for Data Processing and Electronic (IPE), Karlsruhe Institute of Technology (KIT). This device is currently applied in clinical studies for breast cancer screening. In this paper, a new method to develop an automated segmentation algorithm for USCT acquired images is proposed. The method employs distance regularized level set evolutionary (DRLSE) active contours along with surface fitting extrapolation and 3D binary mask generation for fully automatic segmentation outcome. In the first stage of the proposed algorithm, DRLSE is applied to those 3D USCT slice images which contain breast and are less affected by noise and ring artifacts named as Cat2. The DRLSE segmentation results are employed to extrapolate the rest of slice images known as Cat1. To overcome defectively segmented slice images, a 3D binary mask is generated out of USCT attenuation images. The 3D binary mask is multiplied by the DRLSE-based segmentation results to form finally segmented 3D USCT images. The method was tested on 12 clinical dataset images. According to F-measure criterion, the proposed method shows higher performance than the previously proposed semiautomatic segmentation one.