Invariant Points Research Articles

Adiabatic ground state preparation in an expanding lattice

We implement and characterize a numerical algorithm inspired by the $s$-source framework [Phys. Rev.~B 93, 045127 (2016)] for building a quantum many-body ground state wavefunction on a lattice of size $2L$ by applying adiabatic evolution to the corresponding ground state at size $L$, along with $L$ interleaved ancillae. The procedure can in principle be iterated to repeatedly double the size of the system. We implement the algorithm for several one dimensional spin model Hamiltonians, and find that the construction works particularly well when the gap is large and, interestingly, at scale invariant critical points. We explain this feature as a natural consequence of the lattice expansion procedure. This behavior holds for both the integrable transverse-field Ising model and non-integrable variations. We also develop an analytic perturbative understanding of the errors deep in either phase of the transverse field Ising model, and suggest how the circuit could be modified to parametrically reduce errors. In addition to sharpening our perspective on entanglement renormalization in 1D, the algorithm could also potentially be used to build states experimentally, enabling the realization of certain long-range correlated states with low depth quantum circuits.

Phase Equilibrium of the Ternary System K2SO4–KOH–H2O at 313.15, 333.15, 343.15, and 353.15 K

The phase equilibrium of the ternary system K2SO4–KOH–H2O at 313.15, 333.15, 343.15, and 353.15 K was researched by the isothermal dissolution method. There are one invariant point, two univariant ...

Solubility and phase diagram investigation of the ternary system LiCl–SrCl2–H2O at 323.15 K and 348.15 K

The solubility of the LiCl–SrCl2–H2O system along with its sub-binary systems LiCl–H2O and SrCl2–H2O at 323.15 K and 348.15 K has been measured via the Isothermal Dissolve Equilibrium (IDE) method. The gauged solubility for the LiCl–H2O and SrCl2–H2O binary systems is consistent with the result reported in literature. In view of the measured solubility and corresponding liquid-solid line results for the LiCl–SrCl2–H2O system at 323.15 K, exist four equilibrium solid phases, i.e. LiCl·H2O, SrCl2·H2O, SrCl2·2H2O and SrCl2·6H2O, and four corresponding independent crystallization regions for these solid phases, three invariant points E1, E2, E3 for LiCl·H2O and SrCl2·H2O, SrCl2·H2O and SrCl2·2H2O, SrCl2·2H2O and SrCl2·6H2O, respectively. For the solubility of this ternary system at 348.15 K, there are only three equilibrium solid phases, i.e. LiCl·H2O, SrCl2·H2O and SrCl2·2H2O, accordingly two invariant points, E1 for LiCl·H2O and SrCl2·H2O and E2 for SrCl2·H2O and SrCl2·2H2O. No existence of SrCl2·6H2O solid phase in this ternary system at 348.15 K. The comparison of the phase diagram at 323.15 K and 348.15 K indicates that, with the increase of temperature, the crystallization region of SrCl2·6H2O disappeared, however crystallization region of SrCl2·H2O became larger obviously.

Spatially Enhanced Spectral Unmixing Through Data Fusion of Spectral and Visible Images from Different Sensors

We propose an unmixing framework for enhancing endmember fraction maps using a combination of spectral and visible images. The new method, data fusion through spatial information-aided learning (DFuSIAL), is based on a learning process for the fusion of a multispectral image of low spatial resolution and a visible RGB image of high spatial resolution. Unlike commonly used methods, DFuSIAL allows for fusing data from different sensors. To achieve this objective, we apply a learning process using automatically extracted invariant points, which are assumed to have the same land cover type in both images. First, we estimate the fraction maps of a set of endmembers for the spectral image. Then, we train a spatial-features aided neural network (SFFAN) to learn the relationship between the fractions, the visible bands, and rotation-invariant spatial features for learning (RISFLs) that we extract from the RGB image. Our experiments show that the proposed DFuSIAL method obtains fraction maps with significantly enhanced spatial resolution and an average mean absolute error between 2% and 4% compared to the reference ground truth. Furthermore, it is shown that the proposed method is preferable to other examined state-of-the-art methods, especially when data is obtained from different instruments and in cases with missing-data pixels.

Novel and Robust Image Watermarking for Copyright Protection and Integrity Control

This paper presents a copyright protection and integrity verification watermarking scheme for color images. It uses the extracted features of the host image to generate a watermark, which is then embedded in the host image to produce a watermarked image. We have inserted the watermark in the frequency domain using discrete cosine transform. The choice of the positions of the watermark bits depends on a preprocessing study on the original and compressed–decompressed image. Then, we have implemented a blind detection algorithm. In order to counter rotation and cropping attacks, our scheme adopts Speeded-Up Robust Feature to locate invariant key points. The latter are extracted from the original image and used as part of the keys of our scheme to resynchronize only watermarked image altered by rotation and cropping. The robustness and integrity of our method are tested by executing Stirmark 3.1 attacks to the watermarked images. The experimental results show that our method affords a high level of imperceptibility and robustness against JPEG compression, unique and double Stirmark attacks.

Investigation of Phase Equilibria in the Ternary Systems RbCl–RbI–Rb2CrO4 and CsCl–CsI–Cs2CrO4

By differential thermal analysis, the ternary systems MCl–MI–M2CrO4 (M = Rb, Cs) were studied, and the characteristics (melting points, concentrations of components) of alloys at invariant equilibrium points of the systems were determined. The studied systems are systems of the same type that form by varying the alkali metal cation with increasing atomic number of the cation. In all the binary systems constituting the ternary systems, eutectics form. Based on analyzing the faceting elements, it was assumed that eutectics form in the ternary systems. Low-melting eutectic mixtures of alkali-metal halides and chromates are chemically stable even in the molten state and have low viscosity and low volatility, which makes them suitable for using as heat-storage materials or electrolytes for chemical current sources. Consideration of the systems MCl–MI–M2CrO4 (M = Li, Na, K, Rb, Cs) showed that the varying alkali metal cation in them does not affect the morphology of the liquidus.

GL2ℝ–invariant measures in marked strata : generic marked points, Earle–Kra for strata and illumination

We classify GL(2,R) invariant point markings over components of strata of Abelian differentials. Such point markings exist only when the component is hyperelliptic and arise from marking Weierstrass points or two points exchanged by the hyperelliptic involution. We show that these point markings can be used to determine the holomorphic sections of the universal curve restricted to orbifold covers of subvarieties of the moduli space of Riemann surfaces that contain a Teichmuller disk. The finite blocking problem is also solved for translation surfaces with dense GL(2,R) orbit.

Solid−liquid phase equilibria of the quinary system containing lithium, sodium, calcium, strontium and chloride ions at 273.15 K and 101.325 kPa

The solid–liquid phase equilibria of systems LiCl–NaCl–CaCl2–SrCl2–H2O and CaCl2–SrCl2–H2O at 273.15 K and 0.1 MPa were investigated with the isothermal equilibrium method. The solid–liquid equilibrium phase diagrams were constructed with the experimental solubilities. The phase diagram in the ternary system consists of one univariant solubility curve saturated with solid solution (Ca,Sr)Cl2·6H2O, and one crystallization field of the solid solution. There are three invariant points, seven isothermal univariant curves, and five crystallization regions saturated with NaCl corresponding to (Ca,Sr)Cl2·6H2O, SrCl2·2H2O, LiCl·2H2O, CaCl2·4H2O and LiCl·CaCl2·5H2O in the dry-salt diagram of the quinary system. The areas of crystallization zones decrease according to the above order. The J(NaCl), J(H2O), refractive index and density of the solution gradually change regularly with the increasing of J(CaCl2) in the solution. These results on phase diagrams of the quinary system can supply theoretical reference for lithium salts and strontium salts separation from calcium chloride type brine.

Stable phase equilibrium of the quaternary system NaCl-MgCl2-NH4Cl-H2O at 348.15 K and its application in industry

Based on the requirement of the new technology to achieve comprehensive utilization of sodium and magnesium resources by using the mother solution from the preparation of potassium salt as raw material, the phase equilibrium data of the quaternary system NH4Cl-MgCl2-NaCl-H2O as well as its ternary subsystems MgCl2-NH4Cl-H2O and NaCl-NH4Cl-H2O were investigated by an isothermal equilibrium method under atmospheric pressure at 348.15 K, and the dry-salt phase diagram and water-phase diagram were drawn. Two invariant points and four crystallization fields including two single salts NH4Cl and NaCl, one hydrate salt MgCl2·6H2O, and one double salt MgCl2·NH4Cl·6H2O were determined in this quaternary system. Combining our results with available experimental data in the literature, an optimized process to produce ammonium carnallite and NaCl was proposed. Using the Pitzer electrolyte solution model, the experimental results were regressed and calculated. The calculated values agree well with the experimental values.

Solid–Liquid Phase Equilibria in the Ternary Systems (LiBO2 + NaBO2 + H2O) and (LiBO2 + KBO2 + H2O) at 288.15 K and 0.1 MPa

Solid–liquid phase equilibria for the two aqueous systems (LiBO2 + NaBO2 + H2O) and (LiBO2 + KBO2 + H2O) at T = 288.15 K and p = 0.1 MPa were determined using the isothermal dissolution equilibrium method. The experimental results show that the phase diagrams consist of one two-salt co-saturated invariant point, two univariant solubility isotherms, and three crystallization fields. The two systems belong to simple co-saturated type, and neither double salt nor solid solution were found. The densities change regularly as the sodium metaborate (potassium metaborate) concentration increases in solution, and reach their maximum values at the invariant point. Based on the Pitzer and its extended Harvie–Moller–Weare (HMW) model, the solubilities for the ternary systems at 288.15 K were represented, and the calculated results agree well with the experimental values.

High Throughput Determination of Creep Parameters Using Cantilever Bending: Part II - Primary and Steady-State through Uniaxial Equivalency

Abstract

Solubilities, Densities and Refractive Indices for the Two Ternary Systems (Li2SO4 + LiB5O8 + H2O) and (LiCl + LiB5O8 + H2O) at 298.15 K and 101.325 kPa

In this paper, in order to guide the lithium salt production from solar ponds in salt lakes, the two ternary systems (Li2SO4 + LiB5O8 + H2O) and (LiCl + LiB5O8 + H2O) at 298.15 K and 101.325 kPa were studied using the isothermal dissolution experimental method. The solubilities, densities and refractive indices were measured experimentally. From the experimental data, the phase diagrams and the diagrams of physicochemical properties, including density and refractive index, against composition Li2SO4 and LiCl in each ternary system were established. The phase diagrams for the two ternary systems at 298.15 K all have one invariant point, two univariate solubility curves and two crystalline regions corresponding to lithium pentaborate pentahydrate (LiB5O8·5H2O), lithium sulfate monohydrate (Li2SO4·H2O, in the former system) and lithium chloride monohydrate (LiCl·H2O, in the later system). In addition, both ternary systems are of the hydrate type I, neither double salt nor solid solution were found. The variations of density and refractive index against the concentrations of lithium sulfate in the former system and lithium chloride in the later system are similar. On the basis of empirical formulae for density and refractive index, the calculated data agree well with the experimental values, which indicate that all data obtained are reliable.

Determination of NaCl and Na2SO4 Equilibrium Solubility in Cyclohexanol and Cyclohexanone Aqueous Solutions at 323.15 K

The equilibrium solubility and physical properties (nD, η, and ρ) of NaCl and Na2SO4 in cyclohexanol and cyclohexanone aqueous solutions at 323.15 K were determined by an isothermal solution saturation method. According to the experimental data, the phase diagrams and diagrams of physical properties vs composition were plotted. The system of NaCl and Na2SO4 in cyclohexanol aqueous solution at 323.15 K can be divided into one invariant point, two univariant curves, and three crystallization regions. The physical properties of this system changed regularly with the change of the solubility of Na2SO4. The solubility of Na2SO4 and NaCl significantly reduced due to the presence of cyclohexanol in water. With the increase of the cyclohexanol content in aqueous solution in the system, the crystallization region of Na2SO4 increased obviously. The system of NaCl and Na2SO4 in cyclohexanone aqueous solution consisted of one invariant point, two univariant curves, and two crystallization regions corresponding to NaC...

Phase equilibria in 4-pentyloxybenzoic acid - long-chain <i>n</i>-alkane systems

Objective. The work’s objective is to develop methods for the thermodynamic modeling of systems of liquid crystal - organic solvent. Methods. Four binary systems of nematic 4-pentyloxybenzoic acid (5OBA) with n-alkanes (hexadecane, octadecane, icosane, and docosane) were investigated via thermal analysis methods (differential thermal analysis, polarization microscopy, visual polythermal analysis, and the polytherm solubility method). The accuracy in determining phase transitions temperatures is within 0.3 K. To describe the phase equilibria, models based on the Hildebrand and Hansen solubility parameters were used. Hansen solubility parameters were estimated using the Stefanis scheme. Hildebrand solubility parameters, molar volumes, and vaporization enthalpies were calculated using a group contribution scheme. Results. Phase equilibria in the systems of 5OBA with n-alkanes were studied. Four T-x diagrams were obtained by thermal analysis methods, coordinates of invariant points (eutectics and metatectics) were determined in the systems. A linear dependence of the metatectic coordinate ( х 1 is a fraction of 5OBA, mol. %) on the number of C atoms in the alkane (N) was established: x 1 = -0.3131 x N + 85.467. Solubility polytherms of 5OBA with solvents of different polarity were obtained: n-alkanes (hexane, octane), cyclohexane, aromatic compounds (benzene, toluene, and o-xylene), chlorobenzene, ethyl acetate, acetone, 1,4-dioxane, alcohols (propan-2-ol, propan-1-ol, butan-1-ol), and acetonitrile. The dependence of 5OBA’s solubility on the difference in the solubility parameters of the components and the distance Ra was established. Conclusions. The model for regular solutions based on solubility parameters allows us to calculate the solubility polytherms of mesogens and to select solvents for the purification of mesogens by the mass crystallization method. The best solubility of 4-pentyloxybenzoic acid at 298 K appears in chlorobenzene.

Experimental study and theoretical simulation of fluid phase equilibrium in the subsystems of quinary system NaBr–KBr–MgBr2–SrBr2–H2O at 298 K

Abstract Underground brine known as one of special fluids existing in nature has been regarded as a kind of comprehensive mineral resource. After multi-step separation mining, it can realize the effective extraction and recovery of various mineral resources. Conducting a series of further studies on this kind of natural fluid, especially on the study of fluid phase equilibrium, will be of great significance to explore the rules of its geochemical evolution and formation, and to guide the follow-up fluid mineralization simulation. Based on the above considerations, stable phase equilibria and solubility data of unreported subsystems for quinary system NaBr–KBr–MgBr2–SrBr2–H2O at 298 K were determined by the method of isothermal dissolution equilibrium aiming at the compositions of the underground brine in western Sichuan Basin. The research contents in this work include two ternary systems (NaBr–SrBr2–H2O, KBr–SrBr2–H2O) and three quaternary systems (NaBr–KBr–SrBr2–H2O, NaBr–MgBr2–SrBr2–H2O, and KBr–MgBr2–SrBr2–H2O). The phase diagrams of listed above systems were all drawn by experimental data. The experimental results show that there are no solid solutions as well as any complex salts in the three ternary systems. These phase diagrams all contain two solid phase regions of crystallization, two isothermal dissolution curves and only one isothermal-isobaric invariant point. At 298 K, quaternary systems NaBr–KBr–SrBr2–H2O belongs to a simple type, and the phase diagram consists of only one isothermal-isobaric invariant point, three isothermal dissolution curves and three crystallization regions. In the phase diagram of quaternary system NaBr–MgBr2–SrBr2–H2O at 298 K, there are two isothermal-isobaric invariant points, five isothermal dissolution curves, and four crystallization regions. In the quaternary systems KBr–MgBr2–SrBr2–H2O at 298 K, it was found that one complex salt (KBr·MgBr2·6H2O) formed and the phase diagram has two isothermal-isobaric invariant points, five isothermal dissolution curves, and four crystallization regions. The solubilities of the above subsystems at 298 K were predicted accurately by referring to Pitzer's electrolyte solution theory. It was found that the predicted results were coincided basically with the experimental data.

Backward-link computational imaging using batch learning networks

Optical images are inevitably stained by the multiple aberrations from an optical imaging link itself (OILI, e.g., the camera itself involving an optical system, an electronic system, and a sensor). The development of techniques that enable optical full-link imaging without the OILI aberrations is desirable. In this paper, we demonstrate an aberration-free backward-link imaging method for optical full-link imaging. This method utilizes a batch learning network to reconstruct the invariable point spread function (IPSF) of the imaging processing, which is constant and produced by the design, fabrication, and assembly. The inverted IPSF in conjunction with a digital filter can correct the distorted wavefront aberrations caused by the OILI. This is confirmed experimentally. This method opens the door to aberration-free full-link optical imaging for the involved imaging system applications, such as Coarse Holography Displays.

Separation of K2CO3 from Li+ Brine with Aid of CO2 and Trace of Metastable Quaternary System Li+–K+–CO3 2−–HCO3 −–H2O

Abstract It is of importance to reclaim single-salt of potash from Li+-type brines of low concentration. In this work the potassium salts KHCO3 was efficiently separated from the lithium carbonate-type brines with the aid of CO2 carbonation. The phase field was provided in which the precipitation of KHCO3 occurs and single-salt of potassium can be obtained. The low concentration of [Li+] was also successfully concentrated to a high level (8.1 g/L), and this concentration can be used as sources for Li+-salts production using pre-developed strategies, which looks forward wider applications of the lithium resources of natural brine. This state-of-art was traced via isotherm evaporation on the quaternary system of Li+–K+–CO3 2−–H2O at 298.15 K in which the carbonation steps were performed by CO2. Metastable phase diagram was found to consist of three invariant points, seven univariant curves, and four crystallization fields corresponding to Li2CO3, KHCO3, potassium carbonate sesquihydrate (K2CO3 ⋅ 3/2H2O), and a potassium carbonate and potassium bicarbonate double salt (K2CO3 ⋅ 2 KHCO3 ⋅ 1.5H2O). There was no crystallization field corresponding to LiHCO3. The pH-composition diagram and density-composition diagram were also plotted. This work was carried out in aim of extracting/separating single salts of alkali metals from carbonate-type brines of west China.

Optimization of ultrasonic guided wave inspection in structural health monitoring based on thermal sensitivity evaluation

Damage detection in a mechanical structure using ultrasonic guided waves becomes even more problematic when the effect of variation in environmental and operating conditions, such as mechanical noise, temperature, flow rate, inner pressure, etc. is taken into account. The variation in these environmental and operating conditions can degrade the accuracy of the damage inspection process. The basic purpose of current research work is to propose a finite element model–based simulation model to identify and estimate the influence of environmental temperature on the measured signal and meanwhile perceive the temperature invariant points to provide an optimal baseline for thermal attenuation in real-time ultrasonic guided wave inspections. This model signifies the variation in material elastic properties, thermal sensitivities, and the abrupt changes in group and phase velocities of S0 wave mode with temperature. A low bandpass filter is used to keep the excitation frequency in a certain range and remove the noise from it. The numerical investigation is achieved in [Formula: see text] on the basis of six parameters, including variation in strain rate and stress, the amplitude of displacement, symmetric and anti-symmetric dispersion curves, time of flight, group velocity, and natural frequency of the beam. A wave velocity function has been generated in the Matlab® environment to calculate the group velocity of guided waves considering the effect of both temperature and excitation frequency. A linear fit curve (first-degree polynomial) is utilized in this function to analyze the effect of temperature on group velocity. An analytical estimation has also been applied to evaluate the impact of temperature on the material properties and damage detection. The simulation model is validated against the analytical group velocity results and experimental wave amplitude results. The comparison with minute percentage error is achieved in a convincing manner. The proposed thermal sensitivity simulation model is more efficient and reliable as compared to optimal baseline selection and baseline signal stretch. It detects not only the occurrence of damage but also examines the influence of environmental temperature on ultrasonic guided wave propagation and perceives the temperature invariant points to provide an optimal baseline for thermal attenuation in real-time ultrasonic guided wave inspections. This model can also be implemented practically in transportation and industrial applications to ensure structural reliability.

Measurements and calculations of solid-liquid equilibria in two quaternary systems: LiCl–NaCl–SrCl2–H2O and LiCl–KCl–SrCl2–H2O at 298 K

Using the method of isothermal dissolution equilibrium, stable phase equilibria of unreported strontium-containing systems LiCl–NaCl–SrCl2–H2O and LiCl–KCl–SrCl2–H2O at 298 K have been studied in accordance with the compositions of the underground brine in western Sichuan Basin. The experimental results show that there are no solid solution and complex salt in two quaternary systems. The phase diagram of quaternary system LiCl–NaCl–SrCl2–H2O consists of two invariant points, five isothermal dissolution curves and four crystallization regions. The quaternary system LiCl–KCl–SrCl2–H2O belongs to a simple type and the phase diagram consists of two invariant points, five isothermal dissolution curves and four crystallization regions. The solubilities of salts in the above systems were accurately calculated with Pitzer electrolyte solution theory. It was found that the calculated phase diagrams coincided basically with the experimental phase diagrams by evaluated the accuracy through the experimental results. Meanwhile, the applicability of Pitzer parameters selected in this paper was validated.

Rapid Defect Detection for Spacecraft in Infrared Reconstructed Images Using Image Mosaic Technique

In order to satisfy the real-time and large scale requirement of spacecraft nondestructive testing using optical pulsed thermography, in this research, we propose a novel approach based on image mosaic technique which can create large scale or panoramic image mosaics from a set of ordered infrared reconstruction images with overlapping areas for defect detection. First, infrared reconstruction images are extracted from the original thermal video stream by the ICA method based on the idea of blind source signal processing. Then for this research’s special mosaic object, a fast and accurate registration scheme is proposed. Abundant scale rotation invariant feature points are quickly obtained by using the hybrid feature detector and descriptor. Moreover, the feature matching process is realized by applying two-way FLANN and MSAC, parameters of the geometric transformation matrix are estimated by MSAC, and image mosaic is realized according to the geometric transformation model. The experimental results convinced the validity and efficiency of the proposed method.