Invariant Points Research Articles

Phase Equilibrium in the Aqueous Ternary System KH2PO4–NaH2PO4–H2O at 288.15 and 318.15 K

Phase equilibrium in the system KH2PO4–NaH2PO4–H2O at 288.15 and 318.15 K was determined using methods of isothermal solution saturation and moist residues. The equilibrium phase solid was also verified by X-ray diffraction (XRD). Furthermore, the crystallization areas in the phase diagram were analyzed and discussed. In the phase diagram of the two temperatures, there is one invariant point, two single saturated liquid curves, and two crystallization fields corresponding to the single salts NaH2PO4·2H2O, KH2PO4 at 288.15K and NaH2PO4·H2O, KH2PO4 at 318.15K. The density of saturated solutions for the systems studied at 288.15 and 318.15 K was measured and calculated to test the precision of the chosen model. This research filled the blank of phase diagram in this ternary system and can be applied to the production of potassium dihydrogen phosphate process to optimize the crystallization and separation process of potassium dihydrogen phosphate.

Phase Equilibria in the Quaternary Systems KCl–PbCl2–ZnCl2–H2O and MgCl2–PbCl2–ZnCl2–H2O at 373 K

In this work, the method of isothermal dissolution equilibrium was applied to investigating the phase equilibria of quaternary systems KCl–PbCl2–ZnCl2–H2O and MgCl2–PbCl2–ZnCl2–H2O at 373 K throughout the entire concentration range. Isothermal solubility and water content diagrams were constructed based on the measured solubility of components and the coexisting solid phase, respectively. The experimental results indicate that the phase diagram of the quaternary system KCl–PbCl2–ZnCl2–H2O at 373 K consists of three invariant points, seven univariant isothermal solubility curves, and five single solid-phase crystalline regions corresponding to KCl, PbCl2, KCl·2PbCl2, 2KCl·ZnCl2, and ZnCl2. It is shown that the phase diagram of the quaternary system MgCl2–PbCl2–ZnCl2–H2O at 373 K is made up of two invariant points, five univariant isothermal solubility curves, and four single solid-phase crystalline regions corresponding to MgCl2·6H2O, PbCl2, MgCl2·ZnCl2·5H2O, and ZnCl2.

Three-dimensional object tracking based on perspective scale invariant feature transform correspondences

Reconstructing three-dimensional (3-D) poses from matched feature correspondences is widely used in 3-D object tracking. The precision of correspondence matching plays a major role in the pose reconstruction. Without prior knowledge of the perspective camera model, state-of-the-art methods only deal with two-dimensional (2-D) planar affine transforms. An interest point’s detector and descriptor [perspective scale invariant feature transform (SIFT)] is proposed to overcome the side effects of viewpoint changing, i.e., our detector is invariant to viewpoint changing. Perspective SIFT is detected by the SIFT approach, where the sample region is determined by projecting the original sample region to the image plane based on the established camera model. An iterative algorithm then modifies the pose of the tracked object and it generally converges to a 3-D perspective invariant point. The pose of the tracked object is finally estimated by the combination of template warping and perspective SIFT correspondences. Thorough evaluations are performed on two public databases, the Biwi Head Pose dataset and the Boston University dataset. Comparisons illustrate that the proposed keypoint’s detector largely improves the tracking performance.

Interconnections between equilibrium topology and dynamical quantum phase transitions in a linearly ramped Haldane model

We study the behavior of Fisher Zeros (FZs) and dynamical quantum phase transitions (DQPTs) for a linearly ramped Haldane model occurring in the subsequent temporal evolution of the same and probe the intimate connection with the equilibrium topology of the model}. Here, we investigate the temporal evolution of the final state of the Haldane Hamiltonian (evolving with time-independent final Hamiltonian) reached following a linear ramping of the staggered (Semenoff) mass term from an initial to a final value, {first selecting a specific protocol}, so chosen that the system is ramped from one non-topological phase to the other through a topological phase. {We establish the existence of three possible behaviour of areas of FZs corresponding to a given sector: (i) no-DQPT, (ii) one-DQPT (intermediate) and (iii)two-DQPTs (re-entrant), depending on the inverse quenching rate $\tau$. Our study also reveals that the appearance of the areas of FZs is an artefact of the non-zero (quasi-momentum dependent) Haldane mass ($M_H$), whose absence leads to an emergent one-dimensional behaviour indicated by the shrinking of the areas FZs to lines and the non-analyticity in the dynamical "free energy" itself. Moreover, the characteristic rates of crossover between the three behaviour of FZs are determined by the time-reversal invariant quasi-momentum points of the Brillouin zone where $M_H$ vanishes. Thus, we observe that through the presence or absence of $M_H$, there exists an intimate relation to the topological properties of the equilibrium model even when the ramp drives the system far away from equilibrium.

Boundary points based scale invariant 3D point feature

In this paper, we propose a method for encoding scale invariant 3D point features. We extract a set of boundary points from a point cloud. Next, we apply the scale-space concept on the boundary points to detect the scale invariant point border. We confirm three orthometric axes as the local reference frames. Three distribution matrices are generated by implementing the strategy of SPIN image method, and one-row-vector of descriptors are finally calculated. Experimental results on simulated and real scene point clouds demonstrate that the scale-invariant features of 3D point clouds can be effectively encoded by our method.

RETRACTED ARTICLE: Scale invariant point feature (SIPF) for 3D point clouds and 3D multi-scale object detection

3D point clouds are important for the reconstruction of environment. However, comparing to the artificial VR scene representation methods, 3D point clouds are more difficult to correspond to real scenes. In this paper, a method for detecting keypoints and describing scale invariant point feature of 3D point clouds is proposed. To detect, we first select keypoints as the saliency points with fast changing speed along with all principal directions of the searching area of the point cloud. The searching area is a searching keyscale which represents the unique scale size of the point cloud. Then, the descriptor is encoded based on the shape of a border or silhouette of an object to be detected or recognized. We also introduce a vote-casting-based 3D multi-scale object detection method. Experimental results based on synthetic data, real data and vote-casting scheme show that we can easily deal with the different tasks without additional information.

Pressure dependence of the solubility of light fullerenes in n-nonane

Solubility of light fullerenes (C60 and C70) in n-nonane was investigated in the ranges of pressure form 0.1MPa up to 100MPa and temperature from 298.3K to 353.3K. Under isothermal conditions, the solubility, expressed as weight fraction of the fullerene in the solution, increases monotonously with increasing pressure. At ambient pressure, we have found that the temperature dependence of the solubility of C60 in n-nonane is non-monotonic: the solubility diagram consists of two branches corresponding to crystallization of different solid phases and one invariant point corresponding to simultaneous saturation of both phases. At 0.1MPa, the solubility diagram of the binary system C70 – n-nonane in the analysed temperature range consists of only one branch corresponding to crystallization of non-solvated C70.

Measurements and calculations of solid-liquid equilibria in quaternary system Li2SO4-Na2SO4-K2SO4-H2O at 288 K

The isothermal dissolution equilibrium method has been used to investigate the solid and liquid equilibria of quaternary system Li2SO4-Na2SO4-K2SO4-H2O at 288 K. The phase diagram and water diagram were plotted according to the experiment results. It was found that Li2SO4-Na2SO4-K2SO4-H2O quaternary system contains four double salts at 288 K. There are six invariant points, twelve univariant curves and seven areas of crystallization: Li2SO4 H2O, Na2SO4 10H2O, K2SO4, Li2SO4 3Na2SO4 12H2O, Li2SO4 K2SO4, Na2SO4 3K2SO4, 2Li2SO4 Na2SO4 K2SO4. Using the equilibrium solubility data of the quaternary system at 288 K, the solubility product(lnKsp) of solid phase 2Li2SO4 Na2SO4 K2SO4, which is not reported was acquired. Based on the chemical model of Pitzer’s electrolyte solution theory, the solubilities for the quaternary system Li2SO4-Na2SO4-K2SO4-H2O at 288 K were calculated with corresponding parameters. Compared the results of experimental measurement with those of calculation, it was showed that the calculated values had a good agreement with the experimental ones.

Phase equilibria in the system Na+, K+//SO42−-(CH2OH)2-H2O and Na+, K+//Cl−, SO42−-(CH2OH)2-H2O at 328.15 K

An experimental study on phase equilibria at 328.15K in the system (Na+, K+//Cl−, SO42−-(CH2OH)2-H2O) and its subsystem (Na+, K+//SO42−-(CH2OH)2-H2O) was carried out by the method of isothermal solution saturation. In these systems, the initial mass fraction of ethylene glycol is 30% in the salt-free binary solvent (water+ethylene glycol). The solubilities, densities, viscosities, and refractive indices of saturated solutions have been measured for the two systems. According to the experimental results, solubility curves and physical properties (ρ, η, nD) curves are plotted. In the subsystem (Na+, K+//SO42−-(CH2OH)2-H2O), there are two invariant points, three invariant curves, and three fields of crystallization corresponding to K2SO4, Na2SO4.3K2SO4, Na2SO4. In the system (Na+, K+//Cl−, SO42−-(CH2OH)2-H2O), there are five crystallization fields, seven univariant curves, and three eutonic points corresponding to three salts, that is (K2SO4+Na2SO4.3K2SO4+KCl), (Na2SO4+Na2SO4.3K2SO4+KCl) and (Na2SO4+NaCl+KCl), respectively. No solvate phases with ethylene glycol are observed and no solid solutions are found. All the physical properties (ρ, η, nD) of both systems change regularly with concentration change of the liquid phase. In comparison with the phase diagram of the system (Na+, K+//Cl−, SO42−-(CH2OH)2-H2O) at 328.15K and this quaternary system (Na+, K+//Cl−, SO42−-H2O) at 323.15K, the size of the salt crystallization fields changes significantly. The experimental results reveal that the presence of ethylene glycol significantly reduces the solubility of the salts in the aqueous solution. These changes between phase diagrams at different solvents and temperatures will be very useful for extracting the salts. According to this work, the measured values and phase equilibrium diagrams can be used for a new technology to design and optimize the production of K2SO4 by the conversion process with industrial KCl and mirabilite aqueous mixtures, and provide fundamental data support for chemical industry development.

A fully pipelined and parallel hardware architecture for real-time BRISK salient point extraction

Scale and rotation invariant salient point detection and matching algorithms are variously used in computer vision applications such as image matching, 3D localization and pose estimation. Recently, hardware implementation of image and video processing algorithms has emerged as a viable solution to handle the high computational complexity of applications like 3D pose estimation with several processing stages. The hardware implementation of various stages of theses algorithms can be executed in a pipelined manner to ensure the reality of time. In this paper, a new and fully pipelined hardware architecture is proposed for salient point detection using Binary Robust Invariant Scalable Keypoints (BRISK) algorithm. BRISK algorithm is a binary keypoint extractor that detects salient points by constructing a scale-space pyramid; therefore, its fixed-point hardware implementation in a pipelined manner is challenging because of the required synchronization for various layers in scale domain. The proposed hardware architecture was implemented using Verilog Hardware Description Language, and the functionality of the design was validated through several experiments. The proposed design was synthesized by using an ASIC digital design flow utilizing 180 nm CMOS technology as well as a Virtex-4 FPGA. The design is clocked at 90.91 MHz in ASIC implementation and achieves processing rate of 169.29 frames/s while running on input images with 800 × 600 resolution. The throughput of FPGA implementation is 180.44 frames/s with 96.89 MHz clock frequency for the same input image resolution. Experimental results confirm the efficiency of the proposed hardware architecture in comparison with software implementation.

On the structure of the melting diagrams of quaternary systems

Topological and geometric images of invariant and monovariant reactions with the participation of melt in quaternary systems were presented. A network of invariant points and monovariant lines characterizes the structure of the liquidus hypersurface. Each invariant reaction produces an association of four solid phases, which is an element of the solidus hypersurface. Its topology is conveniently described by a graph of adjacency of tetrahedra that partition the composition tetrahedron of a system with a given set of binary, ternary, and quaternary compounds. It was demonstrated that it is possible to construct a spatial network of invariant points and monovariant lines on the liquidus hypersurface using the tetrahedron incidence graph with consideration for the phase reactions occurring in the system.

Solid-liquid equilibrium of Na+//Cl−, NO3−, SO42− -H2O quaternary system at 373.15 K

Solid-liquid equilibrium (SLE) of Na+//Cl−, NO3−, SO42− -H2O quaternary system at 373.15 K was determined via isothermal solubility equilibrium method. The dry-salt phase diagram and the tri-prism stereogram of this system were obtained found on the solubility data. Without any solid solutions or double salts, the phase diagram is the simplest one of the quaternary system, consisting of one invariant point, three univariant curves, three crystallization fields of single salts, three cocrystallization fields for two salts and one cocrystallization field for three salts. At the same time, the physicochemical properties (density and conductivity) of this system were measured in the experiment. Moreover, comparing with the equilibrium phase diagrams in the temperature range from 258.15 K to 373.15 K, it could be found that the crystallization field of the double salt D (NaNO3.Na2SO4.10H2O) reduces with the temperature increases, and disappears at 373.15 K. With the growing temperature, the crystallization field of Na2SO4 enlarges while the crystallization fields of NaNO3 and NaCl both reduce. All above the experimental results obtained can be applied to solve the salt separation of the relative brine system mainly containing the four aforementioned ions as well as conduct further theoretical studies.

Solid-liquid phase equilibria of quaternary system NH4+//C1−, SO42−, H2PO4−–H2O and its subsystems NH4+//C1−, SO42−–H2O, NH4+//C1−, H2PO4−–H2O at 313.15 K

Solid–liquid phase equilibrium and physical properties of ternary systems NH4Cl-NH4H2PO4-H2O, NH4Cl-(NH4)2SO4-H2O and quaternary system NH4Cl-(NH4)2SO4-NH4H2PO4-H2O at 313.15K and atmospheric pressure were obtained by means of an isothermal solution method. The solid phases formed in the systems studied were determined by the Schreinemaker wet residue method. Based on the measured data, corresponding phase diagrams and the diagrams of physical properties versus composition were plotted. Neither complex salt nor solid solution is found in these systems at 313.15K. The ternary phase diagram of NH4+//C1−, H2PO4−–H2O contains one invariant point, and three crystallization regions (NH4H2PO4, NH4Cl, and (NH4Cl+NH4H2PO4)). The ternary phase diagram of NH4+//C1−, SO42−–H2O is similar to the previous one, also contains one invariant point, three crystallization regions ((NH4)2SO4, NH4Cl, and (NH4Cl+(NH4)2SO4)). The quaternary phase diagram of NH4+//C1−, SO42−, H2PO4−–H2O contains one quaternary invariant point, three crystallization regions ((NH4)2SO4, NH4Cl, and NH4H2PO4), and crystallization field of NH4H2PO4 is the largest one of them. All results obtained in this work can be used for the stripping process of solvent extraction in the production of potassium dihydrogen phosphate.

Nickel–Silver Monotectic in Alumina Crucible for Use with Contact Thermometry

Previously, the authors have published work describing a pure Ni fixed point within alumina crucibles. The success of this study stimulated working with the Ni–Ag monotectic point in alumina crucibles. Similar to eutectic points, the Ni–Ag monotectic temperature is an invariant point but it differs from a eutectic reaction in such a way that the monotectic phase change takes place from Ni–Ag liquid solution to Ni–Ag solid solution and Ag rich Ni–Ag liquid solution. In the phase diagram references, the Ni–Ag monotectic phase transition temperature is assigned to be about 20 $$^{\circ }$$ C below the pure Ni melting/freezing point. As is the case for pure Ni, mechanical stability is one of the concerns. Therefore, proper cell design is necessary to avoid breakage of the alumina crucible. The techniques used for the fabrication and measurement of the pure Ni cell were applied to the Ni–Ag cell as well. The cells have been successfully fabricated and the temperature measurement at the fixed point was carried out for more than 20 thermal cycles in total. A Pt/Pd thermocouple was used to measure the temperature and was calibrated from the tin point to the gold point to measure the ITS-90. Freezing plateaus are realized with the technique of “recurrent offset freezing method with reserved solid”. The duration of each freezing plateau is a minimum of 30 min. The monotectic transformation temperature for the best performed cell is determined as 1428.27 $$^{\circ }$$ C with a combined uncertainty of ±0.06 $$^{\circ }$$ C ( $${k}=1$$ ).

New results on affine invariant points

We prove a conjecture of B. Gr\"unbaum stating that the set of affine invariant points of a convex body equals to the set of points invariant under all affine linear symmetries of the convex body. As a consequence we give a short proof on the fact that the affine space of affine linear points is infinite dimensional. In particular, we show that the set of affine invariant points with no dual is of second category. We investigate extremal cases for a class of symmetry measures. We show that the center of the John and L\"owner ellipsoid can be far apart and we give the optimal order for the extremal distance of the two centers.

Salt–Water Phase Equilibria in Ternary Systems K+(Mg2+), NH4+//Cl––H2O at T = 273 K

Phase equilibria for two ternary systems K+, NH4+//Cl––H2O, and Mg2+, NH4+//Cl––H2O at T = 273 K were investigated by means of the isothermal saturation dissolution method. The density of each equilibrium liquid phase was determined by using the weighting bottle method. The compositions of the solid phases were confirmed using Scherinemakers’ wet residue method. The phase diagrams and the figures of density versus composition were plotted in accordance with the experimental data. The ternary system Mg2+, NH4+//Cl––H2O is a type of complex with an incongruent type complex salt ammonium carnallite (NH4Cl·MgCl2·6H2O) formed at 273 K, which consists of two invariant points, three monovariant curves, and three solid phase crystallization fields. The ternary system of K+, NH4+//Cl––H2O consists of three invariant points, four monovariant curves, and five solid phase crystallization fields and is also a type of complex with two solid solutions [(K, NH4)Cl] and [(NH4, K)Cl] found at 273 K. The comparison of obtained phase diagrams at 273 K in this work and 298 K has been deliberated.

A semi-active suspension control algorithm for vehicle comprehensive vertical dynamics performance

ABSTRACTComprehensive performance of the vehicle, including ride qualities and road-holding, is essentially of great value in practice. Many up-to-date semi-active control algorithms improve vehicle dynamics performance effectively. However, it is hard to improve comprehensive performance for the conflict between ride qualities and road-holding around the second-order resonance. Hence, a new control algorithm is proposed to achieve a good trade-off between ride qualities and road-holding. In this paper, the properties of the invariant points are analysed, which gives an insight into the performance conflicting around the second-order resonance. Based on it, a new control algorithm is proposed. The algorithm employs a novel frequency selector to balance suspension ride and handling performance by adopting a medium damping around the second-order resonance. The results of this study show that the proposed control algorithm could improve the performance of ride qualities and suspension working space up to 18.3% and 8.2%, respectively, with little loss of road-holding compared to the passive suspension. Consequently, the comprehensive performance can be improved by 6.6%. Hence, the proposed algorithm is of great potential to be implemented in practice.

Phase Equilibria in the Quaternary Systems KCl–K2B4O7–K2SO4–H2O and MgCl2–MgB4O7–MgSO4–H2O at 273 K

The method of isothermal dissolution equilibrium was used to study the solubilities of salts and the densities of saturated solutions in the two quaternary systems KCl–K2B4O7–K2SO4–H2O and MgCl2–MgB4O7–MgSO4–H2O at 273 K. The equilibrium solid phases were also determined by the method of X-ray diffraction. On the basis of experimental results, the phase diagrams and density versus composition diagrams of those quaternary systems at 273 K were plotted. The results indicate that both the phase diagrams of the two systems consist of one invariant point, three stable solubility isothermal curves, and three crystalline regions. The crystallization fields for the system KCl–K2B4O7–K2SO4–H2O correspond to K2B4O7·4H2O, KCl, and K2SO4. Those for the system MgCl2–MgB4O7–MgSO4–H2O correspond to MgB4O7·9H2O, MgCl2·6H2O and MgSO4·7H2O.

Solid–Liquid Equilibria in the Quaternary Systems NaBr–SrBr2–MgBr2–H2O and KBr–SrBr2–MgBr2–H2O at 323 K

The two quaternary systems NaBr–SrBr2–MgBr2–H2O and KBr–SrBr2–MgBr2–H2O at 323 K were constructed by the isothermal dissolution equilibrium method. The mass fraction of every component of the equilibrium liquid phase in the two systems at 323 K was calculated. The phase diagrams and water content diagrams were plotted in accordance with the Janecke indices of salts and water. The system NaBr–SrBr2–MgBr2–H2O at 323 K has two invariant points, five univariant curves, and four solid phase crystallization areas, which correspond to strontium bromide hexahydrate (SrBr2·6H2O), magnesium bromide hexahydrate (MgBr2·6H2O), sodium bromide (NaBr), and sodium bromide dihydrate (NaBr·2H2O). The system KBr–SrBr2–MgBr2–H2O at 323 K has double salt (KBr·MgBr2·6H2O) without solid solution formation. It has two invariant points, five univariant curves, and four solid phase crystallization areas corresponding to strontium bromide hexahydrate (SrBr2·6H2O), magnesium bromide hexahydrate (MgBr2·6H2O), double salt (KBr·MgBr2·6...

IMAGE FUSION FOR MULTIFOCUS IMAGES USING SPEEDUP ROBUST FEATURES

The multi-focus image fusion technique has emerged as major topic in image processing in order to generate all focus images with increased depth of field from multi focus photographs. Image fusion is the process of combining relevant information from two or more images into a single image. The image registration technique includes the entropy theory. Speed up Robust Features (SURF), feature detector and Binary Robust Invariant Scalable Key points (BRISK) feature descriptor is used in feature matching process. An improved RANDOM Sample Consensus (RANSAC) algorithm is adopted to reject incorrect matches. The registered images are fused using stationary wavelet transform (SWT).The experimental results prove that the proposed algorithm achieves better performance for unregistered multiple multi-focus images and it especially robust to scale and rotation translation compared with traditional direct fusion method.