Invariant Points Research Articles

Invariance Properties of the Entropy Production, and the Entropic Pairing of Inertial Frames of Reference by Shear-Flow Systems.

This study examines the invariance properties of the thermodynamic entropy production in its global (integral), local (differential), bilinear, and macroscopic formulations, including dimensional scaling, invariance to fixed displacements, rotations or reflections of the coordinates, time antisymmetry, Galilean invariance, and Lie point symmetry. The Lie invariance is shown to be the most general, encompassing the other invariances. In a shear-flow system involving fluid flow relative to a solid boundary at steady state, the Galilean invariance property is then shown to preference a unique pair of inertial frames of reference—here termed an entropic pair—respectively moving with the solid or the mean fluid flow. This challenges the Newtonian viewpoint that all inertial frames of reference are equivalent. Furthermore, the existence of a shear flow subsystem with an entropic pair different to that of the surrounding system, or a subsystem with one or more changing entropic pair(s), requires a source of negentropy—a power source scaled by an absolute temperature—to drive the subsystem. Through the analysis of different shear flow subsystems, we present a series of governing principles to describe their entropic pairing properties and sources of negentropy. These are unaffected by Galilean transformations, and so can be understood to “lie above” the Galilean inertial framework of Newtonian mechanics. The analyses provide a new perspective into the field of entropic mechanics, the study of the relative motions of objects with friction.

Phase equilibria and phase diagrams for the aqueous ternary system containing potassium, chlorine and metaborate ions at 298.15 and 323.15 K and 101.325 kPa

Equilibria data and the physicochemical properties including density and refractive index for the ternary system (KCl + KBO2 + H2O) at 298.15 and 323.15 K were determined and proposed with the isothermal dissolution equilibrium and wet-reside solid phase (Schreinemarkers rule) methods. Also, the phase diagram and chart of physicochemical properties were constructed based on experimental data. For both temperatures, one invariant point, two univariant curves, two crystallization regions corresponding to KCl and KBO2·4/3H2O were found. Noticeably, with the rise of temperature, the solubilities of the single salts of KCl and KBO2·4/3H2O become large; meanwhile, the solubilities data at the invariant point also increase. What’s more, the physicochemical properties, including density and refractive index, change systematically in the wake of the concentration of potassium chloride, and due to the increase of solubilities along with the augment of temperature, the density and refractive index at 323.15 K have been increased compared at 298.15 K. The calculated values of the density and refractive index correlated using the empirical equations were consistent with the experimental data and the parameters obtained in our work are authentic.

Model Predictive Control of COVID-19 Pandemic with Social Isolation and Vaccination Policies in Thailand

This study concerns the COVID-19 pandemic in Thailand related to social isolation and vaccination policies. The behavior of disease spread is described by an epidemic model via a system of ordinary differential equations. The invariant region and equilibrium point of the model, as well as the basic reproduction number, are also examined. Moreover, the model is fitted to real data for the second wave and the third wave of the pandemic in Thailand by a sum square error method in order to forecast the future spread of infectious diseases at each time. Furthermore, the model predictive control technique with quadratic programming is used to investigate the schedule of preventive measures over a time horizon. As a result, firstly, the plan results are proposed to solve the limitation of ICU capacity and increase the survival rate of patients. Secondly, the plan to control the outbreak without vaccination shows a strict policy that is difficult to do practically. Finally, the vaccination plan significantly prevents disease transmission, since the populations who get the vaccination have immunity against the virus. Moreover, the outbreak is controlled in 28 weeks. The results of a measurement strategy for preventing the disease are examined and compared with a control and without a control. Thus, the schedule over a time horizon can be suitably used for controlling.

Dynamic response of multi-degree-of-freedom systems with a Coulomb friction contact under harmonic excitation

This paper investigates the steady-state response of a harmonically excited multi-degree-of-freedom (MDOF) system with a Coulomb contact between: (1) a mass and a fixed wall; (2) two different masses; (3) a mass and an oscillating base. Although discrete MDOF models are commonly used at early design stages to analyse the dynamic performances of engineering structures, the current understanding of the friction damping effects on MDOF behaviour is still limited due to the absence of analytical solutions. In this contribution, closed-form expressions of the continuous time response, the displacement transmissibility and the phase angle of each mass of the system are derived and validated numerically for 2DOF and 5DOF systems. Moreover, the features of the analytical response are investigated, obtaining the following results: (i) the determination of the minimum amounts of friction for which the resonant peaks become finite and (ii) for which stick-slip motion can be observed at high frequencies; (iii) an equation for the evaluation of invariant points for the displacement transmissibilities; (iv) a better understanding of phenomena such as the inversions of the transmissibility curves and the onset of additional resonant peaks due to the permanent sticking of the mass in contact. All these results show that MDOF systems exhibit significantly different dynamic behaviours depending on whether the friction contact and the harmonic excitation are applied to the same or different masses.

A Pulsed Eddy Current Testing Sensor Made of Low-Cost Off-the-Shelf Components: Overview and Application to Pseudo-Noise Excitation

A low-cost device for eddy current non-destructive testing made of off-the-shelf components is described. The system consists of a dual H-bridge stepper motor driver, a coil wound in-house on an additively manufactured support, a tunneling magnetoresistance sensor, and a data generation/acquisition module. The system is compact, and it can flexibly generate rectangular pulses, square wave bursts and arbitrary binary excitation waveforms. Among these, in this paper pseudo-noise binary signals were used within a pulse-compression measurement protocol to increase the SNR and the inspection sensitivity with respect to pulsed excitation. A benchmark sample was analyzed, and all the defects were correctly located, demonstrating a good detection capability of the overall hardware-software solution proposed. It was also found that pulse-compression output signals can be further processed as standard pulsed eddy current data. Features can be extracted from them for defect classification purposes and the lift-off invariant point can be used for imaging. These results were achieved by assembling a low-cost handy device, which can be further improved in portability and performances using different off-the-shelf components and by integrating it with a single-board PC, paving the way for future developments in this field.

Solid-liquid phase equilibria of the quaternary system Na+//Cl−, NO3−, SO42−-H2O at 358.15 K

The stable (solid + liquid) phase equilibrium and the solution density of the quaternary system Na+//Cl−, NO3−, SO42−-H2O and its subsystems at 358.15 K were determined by the isothermal solution saturation method and moist residues. All phase diagrams of ternary systems for Na+//Cl−, SO42−-H2O, Na+//Cl−, NO3−-H2O, Na+// NO3−, SO42−-H2O at 358.15 K contain one invariant point, two invariant curves, and three crystallization regions. Neither double salt nor solid solution is found in the three ternary systems at 358.15 K. When NaCl, NaNO3, and Na2SO4 are analyzed as (7.02, 48.62, 1.58) wt %, respectively, the quaternary system Na+//Cl−, NO3−, SO42−-H2O reach saturation at 358.15 K. The phase diagram of the quaternary system at 358.15 K includes one invariant point, three invariant curves, and three crystallization regions. The three crystallization regions correspond to NaCl, NaNO3, and Na2SO4 and the Na2SO4 crystallization region is much bigger than that of the other two salts. Moreover, using the “translation technology”, the phase diagram of Na+//Cl−, SO42−, NO3−-H2O system can be predicted and constructed. All experimental data, especially the crystalline regions, can provide the fundamental basis for the design and optimization of the crystallization process of NaCl, NaNO3, and Na2SO4 in coal chemical high salinity wastewater.

Solid-liquid phase equilibrium and phase diagram of the ternary system (NaNO3 + CsNO3 + H2O) and its application for cesium nitrate separation

In order to separate cesium nitrate from the eluant mixture sodium nitrate solution, the phase equilibrium of the ternary system (NaNO3 + CsNO3 + H2O) at 338.15 K and 0.1 MPa was investigated using the isothermal equilibrium solution method, and the solubilities and physicochemical properties (density and refractive index) of the system were determined, experimentally. According to the experimental data, the phase diagram and physicochemical properties versus the composition diagram of the ternary system at 338.15 K were established for the first time. There is one invariant point (NaNO3 + CsNO3), two univariant curves, and two crystallizing regions corresponding to NaNO3 and CsNO3. The phase diagram belongs to a simple-type ternary system, and neither double salt nor solid solution was formed. Based on the phase diagrams of this system at 298.15 and 338.15 K, the cycle separation process for CsNO3 recovery from the eluant of sodium nitrate mixture solution was evolved. It is worth noting that 90.29 % CsNO3 can be separated from the mixed solution after three cycles. It is significant for the green recovery of cesium nitrate from the eluent solution containing sodium nitrate effectively.

Implementation of Visual Sentiment Analysis on Flickr Images

Visual sentiment analysis is the way to automatically recognize positive and negative emotions from images, videos, graphics and stickers. To estimate the polarity of the sentiment evoked by images in terms of positive or negative sentiment, most of the state of the art works exploit the text associated with a social post provided by the user. However, such textual data is typically noisy due to the subjectivity of the user, which usually includes text useful to maximize the diffusion of the social post. This System will extract three views: visual view, subjective text view and objective text view of Flickr images and will give sentiment polarity positive, negative or neutral based on the hypothesis table. Subjective text view gives sentiment polarity using VADER (Valence Aware Dictionary and sEntiment Reasoner) and objective text view gives sentiment polarity with three convolution neural network models. This system implements VGG-16, Inception-V3 and ResNet-50 convolution neural networks with pre pre-trained ImageNet dataset. The text extracted through these three convolution networks is given to VADER as input to find sentiment polarity. This system implements visual view using a bag of visual word model with BRISK (Binary Robust Invariant Scalable Key points) descriptor. System has a training dataset of 30000 positive, negative and neutral images. All the three views’ sentiment polarity is compared. The final sentiment polarity is calculated as positive if two or more views gives positive sentiment polarity, as negative if two or more views gives negative sentiment polarity and as neutral if two or more views gives neutral sentiment polarity. If all three views give unique polarity then the polarity of the objective text view is given as output sentiment polarity.

Broadband microwave reflectometry plasma diagnostic based on invariant point of reflection data

Reentry plasma sheath diagnostic plays extremely important roles in the research of the blackout problem. In this paper, a broadband microwave reflectometer based on the invariant point of reflection data has been designed and developed for the reentry plasma sheath diagnostic. The invariant point Y(ωp, 1) is derivable from the broadband reflection data. The electron density and collision frequency are measured simultaneously. The diagnostic algorithm was verified by the simulation analysis and diagnostic experiment. The algorithm has low computational complexity and relatively high precision. This algorithm offers a certain reference value for the plasma sheath diagnostic of reentry vehicles or hypersonic vehicles in the future. Especially, the design of broadband VVD antenna with heat-resistant wave-transparent composites has certain practical values.

Bayesian automated weighting of aggregated DFT, MD, and experimental data for candidate thermodynamic models of aluminum with uncertainty quantification

Atomic-scale modeling methods such as density functional theory (DFT) and molecular dynamics (MD) can predict the thermodynamic properties of materials at a lower cost than experimental measurements. However, their regular usage in thermodynamic model construction is hampered by the lack of quantitative agreement with experimental measurements and the lack of uncertainty estimates on the data. To make regular usage of this atomistic simulation data, it is important to assess whether the atomistic simulation datasets, by themselves or in combination with experimental measurements, result in the same physics-informed models best supported by experimental measurements alone. In this work, models of aluminum thermodynamic properties are discussed using three data sources: atomistic calculations (DFT and MD), experiments, and a combination of atomistic calculations and experiments. The study shows that, after ensuring self-consistency in predicting key invariant points, both experimental measurements and atomistic calculations can significantly contribute to an optimal model.

Solid–Liquid Phase Equilibria of the Quaternary system Li2SO4–LiBO2–Li2B4O7–H2O and the Ternary Subsystem LiBO2–Li2B4O7–H2O at T = 288.15 K and p = 0.1 MPa

The solubilities, densities, refractive indices, and pH values in the systems LiBO2–Li2B4O7–H2O and Li2SO4–LiBO2–Li2B4O7–H2O at 288.15 K were studied by the classical dissolution method in this paper. The solid–liquid equilibrium phase diagrams and the physicochemical property diagrams were constructed with the experimental results. The phase diagram of the ternary system is composed of two single-salt crystallizations of LiBO2·8H2O and Li2B4O7·3H2O, two solubility univariant curves, and one invariant point saturated with the above salts. The comparison for the phase diagrams in the ternary system at different temperatures shows that the solubilities of lithium metaborate and lithium tetraborate in this system are in a positive correlation with the temperature. The dry-salt diagram of the quaternary system consists of three single-salt crystallization fields for Li2SO4·H2O, LiBO2·8H2O, and Li2B4O7·3H2O, three univariant solubility curves, and one invariant point. The physicochemical properties in the two systems change regularly as the concentration increases in solution. The calculated densities and refractive indices with empirical equations are in good agreement with the experimental results.

Scaling of the disorder operator at (2+1)d U(1) quantum criticality

We study disorder operator, defined as a symmetry transformation applied to a finite region, across a continuous quantum phase transition in $(2+1)d$. We show analytically that, at a conformally invariant critical point with U(1) symmetry, the disorder operator with a small U(1) rotation angle defined on a rectangle region exhibits power-law scaling with the perimeter of the rectangle. The exponent is proportional to the current central charge of the critical theory. Such a universal scaling behavior is due to the sharp corners of the region and we further obtain a general formula for the exponent when the corner is nearly smooth. To probe the full parameter regime, we carry out systematic computation of the U(1) disorder parameter in the square lattice Bose-Hubbard model across the superfluid-insulator transition with large-scale quantum Monte Carlo simulations, and confirm the presence of the universal corner correction. The exponent of the corner term determined from numerical simulations agrees well with the analytical predictions.

Phase Equilibria on the Reciprocal Quaternary System K+, Rb+ // Cl–, and Borate–H2O at T = 323.2 K and p = 94.77 kPa

The isothermal dissolution method was applied for the phase equilibrium experiment of the quaternary system K+, Rb+ // Cl–, and borate–H2O at T = 323.2 K and p = 94.77 kPa. The solubilities and refractive indices (nD) of the system were determined experimentally. The coexisting salts of the quaternary invariant points were identified using the X-ray diffraction (XRD) method. Based on the measured data, the stable phase diagram and the figures of water content and refractive index (nD) vs composition were plotted for this system at 323.2 K. The results show that the system belongs to a complex type with the formation of a solid solution [(K, Rb)Cl]. The stable phase diagram consists of three quaternary invariant points, seven isothermal dissolution curves, and five crystallization regions corresponding to KCl, RbCl, RbB5O6(OH)4·2H2O, K2B4O5(OH)4·2H2O, and [(K, Rb)Cl]. The size of the RbB5O6(OH)4·2H2O crystallization zone is the largest among the coexisting salts in the quaternary system, which means it is the most easily crystallized from the mixed solution containing potassium, rubidium, chloride, and borate.

Aperiodic order and spherical diffraction, II: translation bounded measures on homogeneous spaces

We study the auto-correlation measures of invariant random point processes in the hyperbolic plane which arise from various classes of aperiodic Delone sets. More generally, we study auto-correlation measures for large classes of Delone sets in (and even translation bounded measures on) arbitrary locally compact homogeneous metric spaces. We then specialize to the case of weighted model sets, in which we are able to derive more concrete formulas for the auto-correlation. In the case of Riemannian symmetric spaces we also explain how the auto-correlation of a weighted model set in a Riemannian symmetric space can be identified with a (typically non-tempered) positive-definite distribution on mathbb {R}^n. This paves the way for a diffraction theory for such model sets, which will be discussed in the sequel to the present article.

Phase diagrams and thermochemical modeling of salt lake brine systems. V. [formula omitted]-[formula omitted]-[formula omitted]-[formula omitted]-[formula omitted]-[formula omitted]-[formula omitted] system

This paper is part of a series of studies on the development of a multi-temperature thermodynamically consistent model for salt lake brine systems. The objective of this study is to extend the sulfate binary models published in our previous study to multi-component systems, i.e. Li+-Na+-K+-Mg2+-Ca2+-SO42−-H2O and its sub- ternary, quaternary and quinary systems. The model is based on our revised Pitzer–Simonson–Clegg equations and the CALPHAD-type thermodynamic framework. Ternary PSC mixing parameters of 10 systems and standard Gibbs energy of double salts occurred in these ternary systems are determined by fitting ternary solubility data at various temperatures. The standard Gibbs energy of triple salts 2Li2SO4·Na2SO4·K2SO4(cr) and polyhalite are determined by fitting their solubility data in corresponding quaternary systems (i.e. Li2SO4+Na2SO4+K2SO4+H2O and K2SO4+MgSO4+CaSO4+H2O). The ternary model reproduces these fitted data well for most systems. With the help of these ternary models, complete phase diagrams of these ternary systems are critically constructed from the lowest eutectic temperature to approximately 373.15 K. In addition, phase diagrams of 10 quaternary systems and invariant points in a quinary system are predicted using the PSC parameters determined from binary and ternary systems. These results are consistent with most available experimental data, indicting a very good predictive ability of the model for multi-component systems. In the following study of our series work, we will combine the multi-component sulfate part and our previously published multi-component chloride part to achieve a complete model for the core salt brine system Li+-Na+-K+-Mg2+-Ca2+-SO42−-Cl−-H2O.

Solid–liquid equilibria in the systems cesium bromide + holmium bromide + water and cesium bromide + holmium bromide + hydrobromic acid (~11.7 mass %) + water at T = 298.15 K

The (Solid–Liquid) phase equilibria for the systems of cesium bromide + holmium bromide + water and cesium bromide + holmium bromide + hydrobromic acid (~11.7 mass %) + water at T = 298.15 K were researched by the isothermal dissolution equilibrium method. According to the experimental data, the phase diagrams of the two systems were depicted. There were two invariant points, three invariant curves, and three crystallization fields (CsBr, Cs3Ho2Br9·16H2O, HoBr3·8H2O) in the two phase diagrams. Cs3Ho2Br9·16H2O was incongruently soluble in the two systems. The solubility of HoBr3 measured in water at T = 298.15 K is 65.41 mass %. The compound Cs3Ho2Br9·16H2O was investigated using chemical analysis, XRD and TG-DTG analysis. The standard molar enthalpy of solution of Cs3Ho2Br9·16H2O in water was measured to be −(5.54 ± 0.28) kJ/mol by a microcalorimetry, and its standard molar enthalpy of formation was determined as being –(7846.5 ± 1.2) kJ/mol.

Innovative negative-stiffness inerter-based mechanical networks

This paper presents the optimal design for novel negative-stiffness non-traditional inerter-based dynamic vibration absorbers called NS-NIDVAs. The underlying idea of negative-stiffness inerter-based mechanical networks (NS-IMNs) was inspired by the negative-stiffness technology concept. Firstly, the non-dimensional mathematical models for NS-NIDVAs are established considering the harmonic force excitation case, and then the dimensionless frequency response functions of the primary structure are computed for optimization purposes. Therefore, a dynamic stability analysis was conducted in order to determine the allowable boundary on negative stiffness variable. Moreover, the Extended Fixed Points Technique (EFPT) has been proposed as an optimal calibration procedure taking in account the undamped system case. In order to ensure a trade-off among the invariant points of the primary structure's FRFs, a constraint equation was added to the EFPT's optimality approach. It was proved that the allowable negative stiffness solution computed by the constraint equation is in accordance with that provided by the Routh- Hurwitz stability criterion. The short optimal explicit functions revealed that the NS-NIDVA-C4 has a similar optimal tuning magnitude as the NS-NIDVA-C6 and C3, with the devices providing the same dynamic performance. In view of this dynamic characteristic, the H∞ performance measure is computed for both NS-NIDVAs devices considering a practical application mass ratio range. When the NS-NIDVA-C4’s performance is compared to the other passive high-performance devices, an improvement of more than 50% in DMF reduction is obtained. Additionally, the NS-NIDVA-C4 can broaden the effective operating bandwidth from 46% to 82% when compared to the classic DVA. Therefore, it has been proved that NS-NIDVA-C4 has the versatility of yielding high-performance with a small physical mass of the DVA, which is the significant finding of this work.

Ternary solid–liquid phase equilibrium and phase diagram for DL-malic acid+fumaric acid+water system and molecular simulation

Solubility of DL-malic acid and fumaric acid in water for binary and ternary systems was determined through high-performance liquid chromatography (HPLC) at atmospheric pressure in this study. Six isothermal ternary phase diagrams were established at temperatures of 283.15, 293.15, 303.15, 313.15, 323.15, and 333.15 K. Every isothermal ternary phase diagram contains three crystalline regions (pure DL-malic acid, pure fumaric acid, and mixture of DL-malic acid and fumaric acid), two co-saturated boundary curves, and one invariant co-saturated point. All diagrams show that the crystalline region of fumaric acid (III) is significantly larger than that of DL-malic acid (II) at six temperatures. Wilson, NRTL, and Margules models were used to correlate and predict binary and ternary system data and the corresponding calculation precision was assessed using relative average deviation (RAD) and root-mean-square deviation (RMSD). The calculated results of Wilson and NRTL models were consistent with experimental data, and maximum values of RAD and RMSD were 2.93 × 10−2 and 3.67 × 10−3, respectively. Margules model can be used to fit solubility data of DL-malic acid unlike those of fumaric acid. Interaction energy and hydrogen bond length of DL-malic acid and fumaric acid with water were calculated via molecular simulation, and the results can be used to explain solubility behavior of DL-malic acid and fumaric acid in water.

Chiralities of nodal points along high-symmetry lines with screw rotation symmetry

Screw rotations in nonsymmorphic space group symmetries induce the presence of hourglass and accordion-shape band structures along screw invariant lines whenever spin-orbit coupling is non-negligible. These structures induce topological enforced Weyl points on the band intersections. In this work we show that the chirality of each Weyl point is related to the representations of the cyclic group on the bands that form the intersection. To achieve this, we calculate the Picard group of isomorphism classes of complex line bundles over the two-dimensional sphere with cyclic group action, and we show how the chirality (Chern number) relates to the eigenvalues of the rotation action on the rotation invariant points. Then we write an explicit Hamiltonian endowed with a cyclic action whose eigenfunctions restricted to a sphere realize the equivariant line bundles described before. As a consequence of this relation, we determine the chiralities of the nodal points appearing on the hourglass and accordion shape structures on screw invariant lines of the nonsymmorphic materials ${\mathrm{PI}}_{3}$ (SG: $\mathrm{P}{6}_{3}$), ${\mathrm{Pd}}_{3}\mathrm{N}$ (SG: $\mathrm{P}{6}_{3}22$), ${\mathrm{AgF}}_{3}$ (SG: $\mathrm{P}{6}_{1}22$), and ${\mathrm{AuF}}_{3}$ (SG: $\mathrm{P}{6}_{1}22$), and we corroborate these results with the Berry curvature and symmetry eigenvalues calculations for the electronic wave function.

Skewness-Based Projection Pursuit as an Eigenvector Problem in Scale Mixtures of Skew-Normal Distributions

This paper addresses the projection pursuit problem assuming that the distribution of the input vector belongs to the flexible and wide family of multivariate scale mixtures of skew normal distributions. Under this assumption, skewness-based projection pursuit is set out as an eigenvector problem, described in terms of the third order cumulant matrix, as well as an eigenvector problem that involves the simultaneous diagonalization of the scatter matrices of the model. Both approaches lead to dominant eigenvectors proportional to the shape parametric vector, which accounts for the multivariate asymmetry of the model; they also shed light on the parametric interpretability of the invariant coordinate selection method and point out some alternatives for estimating the projection pursuit direction. The theoretical findings are further investigated through a simulation study whose results provide insights about the usefulness of skewness model-based projection pursuit in the statistical practice.