Phase Entropy Research Articles

Currents Analysis of a Brushless Motor with Inverter Faults—Part I: Parameters of Entropy Functions and Open-Circuit Faults Detection

In the field of signal processing, it is interesting to explore signal irregularities. Indeed, entropy approaches are efficient to quantify the complexity of a time series; their ability to analyze and provide information related to signal complexity justifies their growing interest. Unfortunately, many entropies exist, each requiring setting parameter values, such as the data length N, the embedding dimension m, the time lag τ, the tolerance r and the scale s for the entropy calculation. Our aim is to determine a methodology to choose the suitable entropy and the suitable parameter values. Therefore, this paper focuses on the effects of their variation. For illustration purposes, a brushless motor with a three-phase inverter is investigated to discover unique faults, and then multiple permanent open-circuit faults. Starting from the brushless inverter under healthy and faulty conditions, the various possible switching faults are discussed. The occurrence of faults in an inverter leads to atypical characteristics of phase currents, which can increase the complexity in the brushless response. Thus, the performance of many entropies and multiscale entropies is discussed to evaluate the complexity of the phase currents. Herein, we introduce a mathematical model to help select the appropriate entropy functions with proper parameter values, for detecting open-circuit faults. Moreover, this mathematical model enables to pick up many usual entropies and multiscale entropies (bubble, phase, slope and conditional entropy) that can best detect faults, for up to four switches. Simulations are then carried out to select the best entropy functions able to differentiate healthy from open-circuit faulty conditions of the inverter.

Analysis of trends in phase change enthalpy, entropy and temperature for alkanes, alcohols and fatty acids

In this work, relationships for enthalpy changes and entropy changes associated with phase transitions, specifically for alkanes, alcohols, and fatty acids, were investigated. For each homologous series, linear correlations were observed between: enthalpy and entropy change, enthalpy change and number of carbon atoms, and entropy change and number of carbon atoms. The observed correlations are explained in terms of the molecular structure, especially the functional group. For a given number of carbon atoms, common behavior regarding enthalpy change (and entropy change) was also observed if the functional group changed, for alcohols, even for multiple functional groups, and for alkanes, even if branched. The investigations thus show general, common phase change behavior, and significantly improve the empirical description and theoretical understanding.

The highest melting point material: Searched by Bayesian global optimization with deep potential molecular dynamics

The interest in refractory materials is increasing rapidly in recent decades due to the development of hypersonic vehicles. However, the substance that has the highest melting point (<i>T</i>_m) keeps a secret, since precise measurements in extreme conditions are overwhelmingly difficult. In the present work, an accurate deep potential (DP) model of a Hf–Ta–C–N system was first trained, and then applied to search for the highest melting point material by molecular dynamics (MD) simulation and Bayesian global optimization (BGO). The predicted melting points agree well with the experiments and confirm that carbon site vacancies can enhance the melting point of rock-salt-structure carbides. The solid solution with N is verified as another new and more effective melting point enhancing approach for HfC, while a conventional routing of the solid solution with Ta (e.g., HfTa₄C₅) is not suggested to result in a maximum melting point. The highest melting point (~4236 K) is achieved with the composition of HfC_0.638N_0.271, which is ~80 K higher than the highest value in a Hf–C binary system. Dominating mechanism of the N addition is believed to be unstable C–N and N–N bonds in liquid phase, which reduces liquid phase entropy and renders the liquid phase less stable. The improved melting point and less gas generation during oxidation by the addition of N provide a new routing to modify thermal protection materials for the hypersonic vehicles.

Interfacial tension of carbon dioxide - water under conditions of CO2 geological storage and enhanced geothermal systems: A molecular dynamics study on the effect of temperature

In recent years, CO2 injection into geological formations under a wide range of temperature conditions, including super-hot geothermal reservoirs, has attracted much attention (i.e., higher than 500 K). Despite the importance, however, no study has been reported on the interfacial tension (IFT) of CO2 - water systems at temperatures higher than 478 K. In this study, we performed molecular dynamics (MD) simulations to estimate the CO2 - water IFT from 278 to 573 K at 8 to 50 MPa. Our results show the IFT at 10 MPa and 573 K is approximately 80% lower than that at a typical reservoir condition for CO2 geological storage. This indicates that the effect of the capillary pressure on the flow of CO2 and water in the geological formation is expected to be significantly reduced in such a super-hot geothermal reservoir.We discuss a possible mechanism for the IFT variation against temperature, including the maxima around 373 K at 8 to 12 MPa, which is reproduced and tackled by MD simulations for the first time. On the basis of the Gibbs-Duhem relation, the temperature dependence is directly related to the interfacial excess molar entropy. Our analyses show (1) the IFT increase is attributed to the substantial variation of the entropy and density of the bulk CO2 phase near the critical point, and (2) this variation is characterized by the distinct behavior of the molecular ordering and the mobility of CO2 at the interface, consistent with the close relationship between the disorder in molecular arrangement and configurational entropy.

Distinction of non-specific low back pain patients with proprioceptive disorders from healthy individuals by linear discriminant analysis.

The central nervous system (CNS) dynamically employs a sophisticated weighting strategy of sensory input, including vision, vestibular and proprioception signals, towards attaining optimal postural control during different conditions. Non-specific low back pain (NSLBP) patients frequently demonstrate postural control deficiencies which are generally attributed to challenges in proprioceptive reweighting, where they often rely on an ankle strategy regardless of postural conditions. Such impairment could lead to potential loss of balance, increased risk of falling, and Low back pain recurrence. In this study, linear and non-linear indicators were extracted from center-of-pressure (COP) and trunk sagittal angle data based on 4 conditions of vibration positioning (vibration on the back, ankle, none or both), 2 surface conditions (foam or rigid), and 2 different groups (healthy and non-specific low back pain patients). Linear discriminant analysis (LDA) was performed on linear and non-linear indicators to identify the best sensory condition towards accurate distinction of non-specific low back pain patients from healthy controls. Two indicators: Phase Plane Portrait ML and Entropy ML with foam surface condition and both ankle and back vibration on, were able to completely differentiate the non-specific low back pain groups. The proposed methodology can help clinicians quantitatively assess the sensory status of non-specific low back pain patients at the initial phase of diagnosis and throughout treatment. Although the results demonstrated the potential effectiveness of our approach in Low back pain patient distinction, a larger and more diverse population is required for comprehensive validation.

A Novel Reconfigurable Intelligent Surface for Wide-Angle Passive Beamforming

A design for a highly reconfigurable intelligent surface (RIS) that can provide 3-D passive reflective beamforming suitable for sub-6-GHz frequency bands is proposed. The RIS is based on a novel double-layer structure consisting of independently controllable and highly reconfigurable elements on top of a ground plane. The novelty of the structure is the use of reconfigurable RIS elements, whose size is of the order of a wavelength, which are optimized to function over wide incident and reflected angles. In addition, the individual elements each have four RF switches, in a 5 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 5 subelement structure, providing 16 different reflective phases, from 0° to 360° relative to the incident waves. To quantify the performance of RIS, the performance metric of phase entropy is defined and it is also used as an objective function for optimizing the design. An efficient analytical method for predicting the reflected waves from the RIS elements, as well as phase entropy, is also provided. For verification, a prototype of a 4 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 4-element RIS, with a total size of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.32\,\,\textrm {m}\,\,\times \,\,0.34\,\,\textrm {m}$ </tex-math></inline-formula> , is fabricated and an experimental setup for measuring the scattered pattern is described. It is shown that waves incident from various angles can be passively beam steered to any angle within 0°–360° azimuth and ±50° elevation angles. The high reconfigurability to manipulate incident waves makes the proposed RIS a promising surface for use in future high-capacity communication systems.

Reservoir Dynamic Interpretability for Time Series Prediction: A Permutation Entropy View.

An echo state network (ESN) is an efficient recurrent neural network (RNN) that is widely used in time series prediction tasks due to its simplicity and low training cost. However, the "black-box" nature of reservoirs hinders the development of ESN. Although a large number of studies have concentrated on reservoir interpretability, the perspective of reservoir modeling is relatively single, and the relationship between reservoir richness and reservoir projection capacity has not been effectively established. To tackle this problem, a novel reservoir interpretability framework based on permutation entropy (PE) theory is proposed in this paper. In structure, this framework consists of reservoir state extraction, PE modeling, and PE analysis. Based on these, the instantaneous reservoir states and neuronal time-varying states are extracted, which are followed by phase space reconstruction, sorting, and entropy calculation. Firstly, the obtained instantaneous state entropy (ISE) and global state entropy (GSE) can measure reservoir richness for interpreting good reservoir projection capacity. On the other hand, the multiscale complexity-entropy analysis of global and neuron-level reservoir states is performed to reveal more detailed dynamics. Finally, the relationships between ESN performance and reservoir dynamic are investigated via Pearson correlation, considering different prediction steps and time scales. Experimental evaluations on several benchmarks and real-world datasets demonstrate the effectiveness and superiority of the proposed reservoir interpretability framework.

Relationship between phase transition temperature and accessible volume for substituent in Cu(hfac)2 chain-polymer complexes with pyridine-based nitroxides

Reaction of Cu(hfac)2 with pyridyl-substituted nitronyl nitroxides yielded chain-polymer complexes {[Cu(hfac)2LR]2[Cu(hfac)2]}∞, where LR – 2-(4-R-pyridin-3-yl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl, R = Me, MeO, Et, n-Pr, i-Pr, n-Bu, and CP (cyclopentyl). X-ray crystallography experiments proved that the solid state of the investigated compounds has centrosymmetric dimers [Cu(hfac)2LR]2 bonded by the Cu(hfac)2 fragments into chain polymers. The environment of the Cu atoms in the dimeric fragments undergoes structural rearrangement upon temperature variation. Such transformations cause anomalous temperature dependences of µeff. We established the relationship between the phase transition temperature and the amount of space accessible for pyridine substituent R. In the complexes containing LMe, LMeO, Ln-Bu, and LCP substituents R occupy relatively small amount of space, which results in ordering of R and high transition temperatures of these complexes, whereas the presence of the accessible volume for the substituent disordering leads to increased entropy of the high temperature phase, and, therefore, decreased transition temperature of the complexes with LEt, Li-Pr, and Ln-Pr.

Correction: Ocádiz Flores et al. Thermodynamic Description of the ACl-ThCl4 (A = Li, Na, K) Systems. Thermo 2021, 1, 122–133

Corrected excess Gibbs energies of the liquid solutions in the ACl-ThCl4 (A = Li, Na, K), as well as revised standard enthalpies of formation and standard entropies of the intermediate phases occurring in the binary systems, are presented [...]

Residual entropy of the dilute Ising chain in a magnetic field.

The properties of the ground state of the simplest frustrated system, the dilute Ising chain in a magnetic field, are rigorously investigated over the entire range of concentrations of charged nonmagnetic impurities. Analytical methods are proposed for calculating the residual entropy of frustrated states, including states at phase boundaries, which are based on the Markov property of the system and involve solving a linear optimization problem for energy and a nonlinear optimization problem for entropy. These methods allow obvious generalizations for one-dimensional pseudospin models with anisotropic interactions. We calculate the composition, entropy, and magnetization for the ground state phases. We prove the absence of pseudotransitions in the dilute Ising chain, since the residual entropy of states at phase boundaries is always higher than the entropy of adjacent phases. The concentration dependencies of magnetization at the phase boundaries are obtained, and unlike linear dependencies for adjacent phases, they have nonlinear behavior. Field-induced transitions between ground states and entropy jumps associated with them are also considered, and in particular, it is shown that the field-induced transition from an antiferromagnetic state to a frustrated one is accompanied by charge ordering.

Universal Lifespan Trajectories of Source-Space Information Flow Extracted from Resting-State MEG Data.

Source activity was extracted from resting-state magnetoencephalography data of 103 subjects aged 18–60 years. The directionality of information flow was computed from the regional time courses using delay symbolic transfer entropy and phase entropy. The analysis yielded a dynamic source connectivity profile, disentangling the direction, strength, and time delay of the underlying causal interactions, producing independent time delays for cross-frequency amplitude-to-amplitude and phase-to-phase coupling. The computation of the dominant intrinsic coupling mode (DoCM) allowed me to estimate the probability distribution of the DoCM independently of phase and amplitude. The results support earlier observations of a posterior-to-anterior information flow for phase dynamics in {α1, α2, β, γ} and an opposite flow (anterior to posterior) in θ. Amplitude dynamics reveal posterior-to-anterior information flow in {α1, α2, γ}, a sensory-motor β-oriented pattern, and an anterior-to-posterior pattern in {δ, θ}. The DoCM between intra- and cross-frequency couplings (CFC) are reported here for the first time and independently for amplitude and phase; in both domains {δ, θ, α1}, frequencies are the main contributors to DoCM. Finally, a novel brain age index (BAI) is introduced, defined as the ratio of the probability distribution of inter- over intra-frequency couplings. This ratio shows a universal age trajectory: a rapid rise from the end of adolescence, reaching a peak in adulthood, and declining slowly thereafter. The universal pattern is seen in the BAI of each frequency studied and for both amplitude and phase domains. No such universal age dependence was previously reported.

Effects of CO2 injection volume and formation of in-situ new phase on oil phase behavior during CO2 injection for enhanced oil recovery (EOR) in tight oil reservoirs

CO2 injection in tight oil reservoirs is a proved method for enhanced oil recovery. The mass transfer between CO2 and oil makes the reservoir fluid phase behaviors very complex, and directly affects the recovery process. In this paper, a comprehensive study of interactions between CO2 and live oil and their phase behaviors were conducted by CO2 visual injecting experiment. Based on the calculation of phase equilibrium and entropy, the mass transfer of CO2 and live oil was divided into four stages, and the mechanism of CO2-live oil interactions elucidated. The results indicate that after CO2 injection, the oil will expand immediately, and the expansion of the oil volume is proportional to the pressure increase. In the early stage of CO2 injection, the mass transfer between CO2 and live oil will form an in-situ gas phase. The reduction in light oil components is mainly due to the CO2 dissolution and replacement, supplemented by the CO2 extraction, which resulted in a rapid decrease in oil volume. With the increase in CO2 injection, its ability to dissolve in the oil and replace the oil components weaken, and CO2 extraction becomes the main controlling factor for the reduction of light components of oil. Increasing pressure promotes the extraction capacity of CO2 for light oil components. Entropy change can accurately reflect the mass transfer process between CO2 and oil, during CO2 injection. These results can furnish an in-depth understanding of the complicated mechanisms and phases behavior in CO2 EOR in tight reservoirs.

On the weak solution to the spatially homogeneous Boltzmann equation with moderate soft potentials

Departing from the weak solution, we prove the uniqueness and long-time behavior of the weak solution to the non-cutoff spatially homogeneous Boltzmann equation with moderate soft potentials. The ingredients of the proof lie in the development of the localized techniques in phase and frequency spaces and entropy methods.

Thermodynamic assessment of lithium halide reciprocal salt systems for energy applications

Lithium halides are of interest because of their unique applications as fuel or coolants in molten salt reactors (MSRs) and electrolytes in thermally activated batteries. Because iodine is an important fission product for MSRs, the Molten Salt Thermal Properties Database-Thermochemical (MSTDB-TC) is being expanded to include relevant iodide reciprocal salt systems. In this work, we assess the thermochemical properties of lithium halide pseudobinary systems based on reported experimental phase diagrams, eutectic temperatures, and enthalpies of mixing. Within the framework of the modified quasi-chemical model in the quadruplet approximation (MQMQA), extrapolations to the related pseudoternary and pseudoquaternary systems have been performed. The pseudoquaternary representations of phase equilibria, enthalpy, entropy, and heat capacity are represented in the resultant models. Of interest for generating source terms for accident analysis is the ability to compute the vapor pressures of the dominant iodide species for the systems at any composition. An example of such calculations is provided for the LiF-LiI system at xLiI = 0.01 and xLiI = 0.70, in this case indicating that the LiI vapor species are predominant.

Early Detection of Alzheimer’s Disease With Nonlinear Features of EEG Signal and MRI Images by Convolutional Neural Network

Background: The main purpose of this study is to provide a method for early diagnosis of Alzheimer’s disease. This disease reduces memory function by destroying neurons in the nervous system and reducing connections and neural interactions. Alzheimer’s disease is on the rise and there is no cure for it. With the help of medical image processing, Alzheimer’s disease is determined and the similarity of the characteristics of brain signals with medical images is determined. Methods: Then, by presenting the characteristics of effective brain signals, the mild Alzheimer’s group is determined. The level of this disease should be diagnosed according to the relationship between this disease and different features in the brain signal and medical images. Results: For 40 participants brain signals and MRI images were recorded during 4 phase protocol and after appropriate preprocessing, nonlinear properties such as phase diagram, correlation dimension, entropy, and Lyapunov exponential are extracted and classification is done using a convolutional neural network (CNN). The use of this deep learning method can have more appropriate and accurate results among other classification methods. Conclusions: The accuracy of the results in the reminding phase is 97.5% for the brain signal and 99% for the MRI images, which is an acceptable result.

Understanding of glass-forming ability of Zr–Cu alloys from the perspective of vibrational entropy of crystalline phases

Glass formation is of fundamental importance for understanding the origin of glass transition and the design of new bulk metallic glasses. However, its nature has been extremely elusive and intangible over the past few decades. By combining experimental techniques and molecular dynamics simulations, we explored the mystery of glass-forming ability from the perspective of vibrational entropy in the prototypic Zr–Cu alloys. Our results suggest that the excess vibrational entropy of crystalline states and the low-frequency vibration modes can disclose the underlying physics behind good glass formers. The former works as an excellent indicator of glass formability to guide the more efficient composition design of novel glasses.

On the Structure of the Boolean Satisfiability Problem: A Survey

The Booleansatisfiability problem (SAT)is a fundamental NP-complete decision problem in automated reasoning and mathematical logic. As evidenced by the results of SAT competitions, the performance of SAT solvers varies substantially between different SAT categories (random, crafted, and industrial). A suggested explanation is that SAT solvers may exploit the underlying structure inherent to SAT instances. There have been attempts to define the structure of SAT in terms of structural measures such as phase transition, backbones, backdoors, small-world, scale-free, treewidth, centrality, community, self-similarity, and entropy. Still, the empirical evidence of structural measures for SAT has been provided for only some SAT categories. Furthermore, the evidence has not been theoretically proven. Also, the impact of structural measures on the behavior of SAT solvers has not been extensively examined. This work provides a comprehensive study on structural measures for SAT that have been presented in the literature. We provide an overview of the works on structural measures for SAT and their relatedness to the performance of SAT solvers. Accordingly, a taxonomy of structural measures for SAT is presented. We also review in detail important applications of structural measures for SAT, focusing mainly on enhancing SAT solvers, generating SAT instances, and classifying SAT instances.

Radiofrequency ablation of hepatocellular carcinoma: CT texture analysis of the ablated area to predict local recurrence

PurposeTo investigate the role of CT-texture analysis of liver ablation area to predict local recurrence after HCC ablation. MethodsPatients treated with liver ablation were retrospectively enrolled. CT-texture analysis was performed on the core and borders of ablation area 1–2 months after procedure. Tumors were grouped according to the onset of local recurrence at follow-up (persistence, recurrence-free, short- or long-term recurrence). Differences in texture parameters and which parameters were predictive of recurrence risk were assessed using a Cox regression model. Results151 HCCs were treated in 98 patients (72 ± 9 years, 83 men). 68 HCCs reported no disease recurrence, 32 persistent disease, 19 short-term and 32 long-term recurrence. Median follow-up was 280 [IQR: 156–569] days. Venous phase (Ven)Skewness (HR 6.07, 1.29–28.6, p =.02) and VenKurtosis (HR 2.27, 1.23–4.21, p =.01) of the ablation core were predictive of short-term recurrence. VenHUmean (HR 0.30, 0.11–0.81, p =.02) and VenGLRLM_HGRE (HR 1.06, 1.01–1.11, p =.02) of the core were independent predictors of tumor recurrence (C-index 0.64, CI 0.52–0.76, p =.03). Arterial phase (Art)Entropy of ablation border predicted the recurrence risk (HR 3.15, 1.05–9.42, p =.04) and values higher than 3.71 reported an increased recurrence incidence (p =.05). ArtHUstd (HR 1.14, 1.04–1.24, p =.01), LateHUmean (HR 8.69, 1.11–68.23, p =.04), LateGLRLM_HGRE (HR 0.9, 0.82–0.99, p =.03), LateGLZLM_HGZE (HR 1.01, 1.00–1.02, p <.01) and LateGLZLM_SZHGE (HR 0.99, 0.99–1.00, p =.02) of ablation border were independent predictors of local recurrence risk (C-index 0.73, CI 0.61–0.86, p <.01). ConclusionsCT texture analysis of ablation area performed at 1–2 months follow-up could estimate the risk of local recurrence of hepatocellular carcinoma treated by radiofrequency ablation.

Transition of a binary solution into an inhomogeneous phase

ABSTRACT The thermodynamics of phase transitions of binary solutions into spatially inhomogeneous one-dimensional states is studied theoretically by taking into account nonlinear effects. It is shown that below the spinodal decomposition temperature there first occurs a phase stratification, and at a lower temperature, after reaching the maximum possible stratification, there occurs a second-order transition into the phase with concentration waves. The contribution of inhomogeneity to the entropy and heat capacity of phases is calculated and the phase diagram in the coordinates temperature – average concentration is constructed.

Low-dose dobutamine stress gated blood pool SPECT assessment of left ventricular contractile reserve in ischemic cardiomyopathy: a feasibility study.

The purpose of the present study was to evaluate the feasibility of gated blood pool single-photon emission computed tomography (GBPS) with low-dose dobutamine (LDD) stress test, performed on a single-photon emission computed tomography (SPECT) camera equipped with cadmium-zinc-telluride (CZT) solid-state detectors, in assessing of left ventricle (LV) contractile reserve in patients with ischemic cardiomyopathy (ICM). A total of 52 patients (age 59 ± 7.2years, 47 men and 5 women) with ICM and a control group of 10 patients without obstructive coronary artery lesion underwent GBPS and transthoracic echocardiography (TTE) at rest and during LDD stress test (5, 10, 15µg/kg/min). The duration of each GBPS step was 5min. Stress-induced changes in LV ejection fraction (ΔLVEF), peak ejection rate, LV volumes, and mechanical dyssynchrony (phase histogram standard deviation, phase histogram bandwidth and entropy) obtained with GBPS were estimated. All GBPS indices except end-diastolic volume showed significant dynamics during stress test in both groups. The majority of parameters in ICM patients showed significant changes at a dobutamine dose of 10µg/kg/min as compared to the rest study. Seventeen percent of ICM patients, but none from the control group, showed a decrease in LVEF during stress, accompanied by a significant increase in entropy. The intra- and inter-observer reproducibility was excellent for both rest and stress studies. There was a moderate correlation (r = 0.5, p = 0.01) between GBPS and TTE, with a mean difference value of - 1.7 (95% confidence interval - 9.8; 6.4; p = 0.06) in ΔLVEF. Low-dose dobutamine stress GBPS performed with high-efficiency CZT-SPECT cameras can be performed for evaluating stress-induced changes in LV contractility and dyssynchrony with lower acquisition time. A dobutamine dose of 10µg/kg/min can potentially suffice to detect stress-induced changes in patients with ICM during GBPS. ClinicalTrials.gov identifier: NCT04508608 (August 7, 2020).