Cross Coefficients Research Articles

Symmetry-preserving modeling for lithographic imaging.

In computational imaging and lithography, it has been a challenge for a numerical model to faithfully preserve symmetries in the physical imaging system. In this Letter, we present a project-to-symmetry-subspace (PTSS) method to prevent symmetry loss during the iterative generation of optical kernels. Essentially, PTSS is to project iterative vectors onto a predefined symmetric subspace when decomposing the transmission cross coefficient (TCC). Simulation results demonstrate the PTSS-generation of a truncated set of optical kernels that are substantially free of symmetry error, regardless of the order of truncation.

Accelerating extreme ultraviolet lithography simulation with weakly guiding approximation and source position dependent transmission cross coefficient formula

Accelerating extreme ultraviolet lithography simulation with weakly guiding approximation and source position dependent transmission cross coefficient formula

An unsupervised deep learning framework for large-scale lung CT deformable image registration

Accurate lung CT deformable image registration is especially useful in many medical image analyzing domains. In this paper, we present a novel unsupervised deep learning framework to speed up registration processing with high accuracy. Our approach consists of a convolutional neural network (CNN) model with frequent connections between layers for extracting robust image features, and of well-designed pre-processing and post-processing techniques to handle with large images without losing the precision. Additionally, during training stage, the local cross coefficient (LCC) and L2-norm for gradients of dense displacement fields (DDF) are adopted to form loss function in the model. Experiments on a large-scale lung CT dataset with each image size of over 400 × 400 × 350 show that our method achieves the best performances on Dice score of 0.9245 and mean squared error (MSE) of 0.0046 compared with some traditional and learning-based methods. Besides, our model has been proved to be robust for various deformations. Above all, our method is several orders of magnitude faster than the state-of-the-art non-learning-based algorithms.

Counterion Transference Numbers in the Cell Model of a Charged Membrane

The paper suggests exact formulae for calculating the electromigration, diffusion and convective numbers of counterion transport in the cell model of a charged membrane depending on the physicochemical parameters and the equilibrium concentration of the electrolyte. The cell model was previously developed to calculate all the kinetic coefficients of the Onsager matrix and the asymmetry of the cross coefficients was established. The limiting case of an ideally selective membrane is studied in detail, for which approximate formulae for transference numbers are obtained. The obtained dependences are illustrated by graphs using the example of the MK-40 cation-exchange membrane after conditioning at room temperature. The proposed method for calculating the transference numbers is applicable to any single-layer membranes in binary electrolyte solutions.

Intraoperative Assessment of Breast Cancer Tissues after Breast-Conserving Surgery Based on Mapping the Attenuation Coefficients in 3D Cross-Polarization Optical Coherence Tomography.

Intraoperative differentiation of tumorous from non-tumorous tissue can help in the assessment of resection margins in breast cancer and its response to therapy and, potentially, reduce the incidence of tumor recurrence. In this study, the calculation of the attenuation coefficient and its color-coded 2D distribution was performed for different breast cancer subtypes using spectral-domain CP OCT. A total of 68 freshly excised human breast specimens containing tumorous and surrounding non-tumorous tissues after BCS was studied. Immediately after obtaining structural 3D CP OCT images, en face color-coded attenuation coefficient maps were built in co-(Att(co)) and cross-(Att(cross)) polarization channels using a depth-resolved approach to calculating the values in each A-scan. We determined spatially localized signal attenuation in both channels and reported ranges of attenuation coefficients to five selected breast tissue regions (adipose tissue, non-tumorous fibrous connective tissue, hyalinized tumor stroma, low-density tumor cells in the fibrotic tumor stroma and high-density clusters of tumor cells). The Att(cross) coefficient exhibited a stronger gain contrast of studied tissues compared to the Att(co) coefficient (i.e., conventional attenuation coefficient) and, therefore, allowed improved differentiation of all breast tissue types. It has been shown that color-coded attenuation coefficient maps may be used to detect inter- and intra-tumor heterogeneity of various breast cancer subtypes as well as to assess the effectiveness of therapy. For the first time, the optimal threshold values of the attenuation coefficients to differentiate tumorous from non-tumorous breast tissues were determined. Diagnostic testing values for Att(cross) coefficient were higher for differentiation of tumor cell areas and tumor stroma from non-tumorous fibrous connective tissue: diagnostic accuracy was 91-99%, sensitivity-96-98%, and specificity-87-99%. Att(co) coefficient is more suitable for the differentiation of tumor cell areas from adipose tissue: diagnostic accuracy was 83%, sensitivity-84%, and specificity-84%. Therefore, the present study provides a new diagnostic approach to the differentiation of breast cancer tissue types based on the assessment of the attenuation coefficient from real-time CP OCT data and has the potential to be used for further rapid and accurate intraoperative assessment of the resection margins during BCS.

High-Degree Collisional Moments of Inelastic Maxwell Mixtures—Application to the Homogeneous Cooling and Uniform Shear Flow States

The Boltzmann equation for d-dimensional inelastic Maxwell models is considered to determine the collisional moments of the second, third and fourth degree in a granular binary mixture. These collisional moments are exactly evaluated in terms of the velocity moments of the distribution function of each species when diffusion is absent (mass flux of each species vanishes). The corresponding associated eigenvalues as well as cross coefficients are obtained as functions of the coefficients of normal restitution and the parameters of the mixture (masses, diameters and composition). The results are applied to the analysis of the time evolution of the moments (scaled with a thermal speed) in two different nonequilibrium situations: the homogeneous cooling state (HCS) and the uniform (or simple) shear flow (USF) state. In the case of the HCS, in contrast to what happens for simple granular gases, it is demonstrated that the third and fourth degree moments could diverge in time for given values of the parameters of the system. An exhaustive study on the influence of the parameter space of the mixture on the time behavior of these moments is carried out. Then, the time evolution of the second- and third-degree velocity moments in the USF is studied in the tracer limit (namely, when the concentration of one of the species is negligible). As expected, while the second-degree moments are always convergent, the third-degree moments of the tracer species can be also divergent in the long time limit.

Effect of potassium dihydrogen citrate on the diffusion behaviour of citric acid

Ternary mutual diffusion coefficients (D11, D22, D12, and D21) in aqueous solutions of citric acid (H3Cit) (component 1) plus potassium dihydrogen citrate (KH2Cit) (component 2) at 298.15 K and concentrations up to 0.040 mol dm−3 were measured using a Taylor scattering method. The obtaining of the negative values for D12 and D21 cross coefficients, mainly in dilute solutions and for the first ones, indicates that there is a strongly coupled diffusion of these components. In fact, the concentration gradients of KH2Cit drive substantial counter current coupled flows of H3Cit citric acid, indicating that each mol of diffusing potassium dihydrogen citrate can counteract the transport of up to 0.74 mol of citric acid, approximately. A better interpretation of the electrostatic mechanism for the coupled diffusion of KH2Cit and H3Cit was achieved based on the values predicted by the Nernst-Planck equations, having been verified as a good agreement between them and experimental data.

Ternary Diffusion and Thermodynamic Interaction in the β Solid Solutions of Ti–Al–Zr Alloys at 1473 K

Interdiffusion in Ti-rich β solid solutions in Ti–Al–Zr alloys was investigated at 1473 K. In the β Ti–Al–Zr alloys, the main interdiffusion coefficients (i.e., and , respectively) and the cross interdiffusion coefficients, (i.e., and , respectively) have positive values, as well as a slight concentration dependence. The values of are larger than those of . In Ti–Al–X (= V, Cr, Fe, Co, Zr) alloys, the values of the main coefficients are at 1473 K. Repulsive interactions occur between Al and X (= V, Cr, Fe, Co, Zr) atoms in the Ti–Al–X alloys, because the ratio values of the cross coefficients to the main ones are positive in sign. On the other hand, the interactions between Ti (solvent) and X (= V, Cr, Fe, Co, Zr) (or Al) atoms are attractive in the present alloys because the ratio of the converted interdiffusion coefficients is negative values.

FINANCIAL STABILITY AND RESISTANCE OF BANK IN THE CURRENT CONDITIONS OF MARTIAL LAW

The article examines the theoretical foundations of financial stability and stability of a banking institution, examines the main interpretations of approaches to defining the concept of "financial stability". The relationship between the concepts of "financial stability" and "financial stability" was studied, and as a result, it was determined that ensuring the financial stability of banks is the basis of a stable banking system, a key to the success of economic transformations and macroeconomic development. Indicators of financial stability and financial stability of the bank, using JSC CB "Privatbank" were studied as the main object of the study. In order to analyze the financial stability of JSC CB "Privatbank", its financial statements were examined and the reliability coefficient was calculated; financial leverage ratio; the coefficient of participation of equity capital in the formation of assets; capital multiplier factor. The paper calculates the stability and stability indicators of the bank. For a generalized comprehensive assessment of the bank's activity, an integral indicator of the bank's financial stability was calculated using data from the financial statements for 2020-2022. As a result of the study, a methodology for assessing the financial stability and stability of the bank was determined, which takes into account the versatile aspects of the bank's activity by selecting parametric coefficients The article examines the stability of JSC KB "Privatbank" in modern conditions of risks and losses during the martial law in Ukraine. In order to study the influence of the current conditions of martial law on the stability of the bank, the calculation of the coefficients of financial stability was carried out for the period of January-September 2022. The calculation of financial stability was carried out based on the analysis of the general coefficient of stability, the coefficient of instant liquidity, the cross coefficient, the general coefficient of liquidity, the coefficient of capital protection, the coefficient of capitalization of profit. The study analyzed the stability of the bank based on the results of the calculations. In general, the indicator of the financial stability of the bank is not sufficient for stable functioning, the bank is recommended to pay attention to indicators that have an impact on the financial stability of the bank to increase stability, such as: equity, working and liquid assets, liabilities, both short-term and long-term , authorized and protected capital.

Hybrid fiber interferometer sensor for simultaneous measurement of strain and temperature with refractive index insensitivity

A hybrid fiber interferometer sensor is proposed and demonstrated for simultaneous measurement of strain and temperature with insensitivity to external refractive index. This sensor consists of a 5 cm few-mode fiber (FMF) cascaded with a 37μm hollow-core fiber (HCF). The other end of the FMF is offset spliced to the lead-out single-mode fiber (SMF) to excite high-order modes inside the core. A Fabry–Perot interferometer (FPI) micro-cavity is formed by the HCF and two splicing interfaces, the interference pattern of which can be observed in the reflection spectrum. The FMF-based core-mismatched structure forms a Mach–Zehnder interferometer (MZI) and the interference pattern can be collected in the transmission spectrum. The simulation result shows that the interference in MZI is mainly generated from the LP11 and LP21 mode in the FMF. A cross coefficient matrix for dual-parameter sensing can be achieved by the different responses of FPI and MZI to strain and temperature. Experimental results show that proposed sensor has the maximum strain sensitivity of 5.89 pm/με and the maximum temperature sensitivity of -38.8 pm/°C. We also tested the refractive index characteristics of this sensor and results show that it is insensitive to the variation of external refractive index. In addition, the cross coefficient matrix of this scheme has a good condition number of 6.72.

Fabrication and Characterization of Femtosecond Laser Inscribed Long-Period Fiber Grating in Few-Mode Fiber

We experimentally investigated the fabrication and characterization of long-period fiber grating in few-mode fiber (FMF-LPFGs) by using the femtosecond laser direct writing technique. Thanks to the high flexibility and repeatability of this technique, stable FMF-LPFGs fabrication technology has been developed. In addition, the properties of FMF-LPFGs have also been characterized. The coupling of LP <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</sub> - LP <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> and LP <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">01</sub> - cladding mode LP <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">13</sub> were investigated by both the transmission spectrum and the mode patterns. The temperature, strain and twist sensitivities of the resonance dips were calibrated by experiments, and the sensitivity difference between the dips was explained. By using their disparate responses to external temperature and strain, a cross coefficient matrix was established and dual-parameter discrimination determination is realized. This work provides a thoroughly theoretical and experimental investigation on the fabrication and characterization of FMF-LPFGs based on femtosecond laser direct writing technique. It is believed that the flexible and efficient LPFGs fabrication technique will benefit a lot in the future for developing various functional specialty optical fiber devices and sensors.

A Cell Model of an Ion-Exchange Membrane. Capillary-Osmosis and Reverse-Osmosis Coefficients

The capillary-osmosis and reverse-osmosis coefficients of an ion-exchange membrane have been calculated as the kinetic coefficients of the Onsager matrix within the thermodynamics of nonequilibrium processes and on the basis of the cell model proposed previously by the author for charged porous layers. The membrane is assumed to consist of an ordered set of spherical completely porous charged particles placed into spherical shells filled with a binary electrolyte solution. Boundary value problems have been analytically solved to determine the capillary-osmosis and reverse-osmosis coefficients of such a membrane under the Kuwabara boundary condition imposed on the cell surface. The consideration has been implemented within the framework of small deviations of system parameters from their equilibrium values under the action of external fields. Different particular cases of the obtained exact analytical equations have been studied including the case of a binary symmetric electrolyte and an ideally selective membrane. It has been shown that, for the considered cell model of an ion-exchange membrane, the Onsager reciprocity theorem is violated; i.e., the found kinetic cross coefficients are unequal to each other. The violation is explained by the fact that the reciprocity theorem is valid only for systems implying the linear thermodynamics of irreversible processes, for which generalized flows are equal to zero at nonzero thermodynamic forces.

Study on Angular Free Vibration Stability and Parameters Influence of Dry Gas Seal Based on the Characteristic Equation

Based on Laplace transform and Hurwitz stability criterion, the system characteristic equation and algebraic stability criterion of the two degree-of-freedom angular free vibration of dry gas seal are derived. The effects of rotational inertia, stiffness and damping parameters on the angular free vibration stability of dry gas seal are analyzed by using the root locus method and the concept of the closed-loop dominant pole. The results show that the constraint condition of rotational inertia is the most demanding of all stability conditions. Both the angular main damping and main stiffness are not simply the larger the better, but there are preferred values in the interval greater than the stability threshold. The approach of the absolute value of the cross coefficient to zero is beneficial to the suppression of angular free vibration. There is a threshold of rotational inertia, which makes the cross stiffness change from having only the lower limit value to both the upper and lower critical values at the same time.

Prediction of formaldehyde and residual methanol concentration in formalin using near infrared spectroscopy

Amino resins are produced by two main processes: the strong acid process and the alkaline-acid process. Both use formaldehyde and a base (e.g. sodium hydroxide) in their formulation. In this work, Forward Interval Partial Least Squares methodology was applied to create prediction models for the determination of the concentration of formaldehyde and residual methanol (that is present in the formaldehyde solution) used in the production of amino resins. Near infrared (NIR) spectra were acquired at two different temperatures: 18 and 35°C. A Partial Least Squares calibration models were established with the measured values from reference methods: namely, sodium sulfite (formaldehyde) and gas chromatography (methanol). The performances of the best models were compared using the root mean square error of cross validation (RMSECV) and coefficient of determination for prediction (r2). The best results obtained a r2 above 0.994. The RMSECV values obtained were 0.063% (m/m) and 0.031% (m/m) for the formaldehyde and methanol concentration, respectively. External validation was performed using different formaldehyde solution samples. The NIR methodology presented in this work proved to be effective and enables a significant time reduction, when compared to the reference methods, in the measurement of formaldehyde and methanol concentrations.

Nonequilibrium thermodynamic model of diffusion processes in the steel - carbon thin film tribological system

A nonequilibrium thermodynamic model of dissipative processes in the tribological system steel – carbon thin film was developed. Cross coefficients and driving forces in the Onsager equation for the diffusion of carbon onto the friction surface of hypereutectoid steel are calculated. The thermodynamic conditions for the implementation of the selective transfer process in the tribological system under consideration are determined. Simple differential equations are obtained for the tribological system of carbon steel - graphite, which describe the effect of stresses on the diffusion of carbon, production based on nonequilibrium thermodynamics. It is shown, that the implementation of selective transfer requires the development of diffusion processes without the formation of excess phases. Therefore, carbon steel should be alloyed mainly with elements of the first group that increase the thermodynamic activity of carbon in steel - silicon, nickel, copper, cobalt and phosphorus. Recommendations are formulated on metallic materials choosing for minimal contact wear in contacted pairs of machines parts.

Non-equilibrium thermodynamics of light-induced transport phenomena in a binary gas mixture

A kinetic theory of transfer processes in a binary gas mixture in a capillary under the action of resonant laser radiation in the presence of pressure, temperature, and concentration gradients is presented. Based on linearized modified Boltzmann equations for the resonant and buffer gases, expressions for kinetic coefficients describing the transfer processes of mass, heat and emitted electromagnetic energy by the excited particles of the gas mixture are obtained. For the cross coefficients, the Onsager reciprocal principle is proved, which is valid for any Knudsen numbers and any law of interaction of gas mixture particles with each other and the boundary surface. Light-induced phenomena associated with the system's possible non-equilibrium stationary states are analyzed.

An overview of thermotransport in fluorite-related ionic oxides

Abstract In this overview, we summarize the phenomenon of thermotransport (the close coupling of mass transport and heat transport) in two fast ion conductors: yttria-doped zirconia and gadolinia-doped ceria. We focus on two recent molecular dynamics calculations using the Green-Kubo formalism. We show that the Onsager thermotransport cross coefficient (mass-heat coupling) is negative, meaning that oxygen ions would drift, in principle, to the hot side in a temperature gradient. Simulation results presented in this overview show reasonable agreement with available experimental data for thermal conductivity. Results of this study suggest that the coupling between mass and heat transport in oxygen ion electrolytes could have significant effect for practical applications.

Simulation of the ionic conductivity, thermal conductivity and thermotransport of doped zirconia using molecular dynamics

This study focuses on a number of transport phenomena in yttria-stabilized zirconia (YSZ). A molecular dynamics simulation based on the Green-Kubo formalism is applied to calculate the lattice thermal conductivity, oxygen diffusion coefficient, ionic conductivity and thermotransport at different concentrations (i.e., 4, 8, 10, 12, 16 and 20 mol% of Y2O3) over a temperature range from 700 K to 1500 K. The results show that the YSZ has a low thermal conductivity in comparison with pure zirconia. The oxygen tracer diffusion coefficient, as calculated from the mean square displacements, and also the ionic conductivity show an activation energy of 0.85eV. The Onsager cross coefficient associated with thermotransport is negative, meaning that the drift of anions in a temperature gradient would be from a cold region to a hot region. All of the simulation results presented show reasonable agreement with available experimental data.

Non-equilibrium thermodynamics model for calculating diffusion fluxes under phase transformations in alloy steels

The phase transformations in alloyed iron-carbon alloys is largely related to diffusion of components, foremost to the carbon. For the analysis of diffusive processes in alloy steels, it is possible to use the mathematical methods of non-equilibrium thermodynamics. The equation for the diffusive fluxes of the system contains unknown in general case of coefficients activity of elements and vacancies, and their derivatives for to the concentrations, that extraordinarily makes it difficult being of values of cross coefficients. In the article a non-equilibrium thermodynamics methodology of calculation of diffusive fluxes at presence of two phases in alloy steels is described. It allows one to calculate both direct- and cross coefficients in the Onsager equations. Formulas for calculation of thermodynamics forces in the alloy steel – for iron, alloying element of substitution – chrome, of element of introduction – carbon and vacancies, are presented. Common expressions are suggested for calculation of cross-factors, motive forces and fluxes in the Onsager’s equations for a multicomponent thermodynamic system. The example of using the developed model to find changes in concentrations and diffusion fluxes over time is given. For the model system used, it was established that at the stage of predominant diffusion of carbon in the alloy steel, cementite inclusions with a size of about 18 nm are formed rather quickly (within ~ 200 s). The technique developed in the article allows one to perform diffusion kinetics calculations in multicomponent thermodynamic systems, which are also iron-carbon alloys and to control the size of the phases formed, for example, of carbide nanoparticles.

Simulation of the Ionic Conductivity, Thermal Conductivity and Thermotransport of Doped Zirconia Using Molecular Dynamics

This study focuses on a number of transport phenomena in yttria-stabilised zirconia (YSZ). A molecular dynamics simulation based on the Green-Kubo formalism is applied to calculate the lattice thermal conductivity, oxygen diffusion coefficient, ionic conductivity and thermotransport at different concentrations (i.e., 4, 8, 10, 12, 16 and 20 mol% of Y 2 O 3 ) over a temperature range from 700 K to 1500 K. The results show that the YSZ has a low thermal conductivity in comparison with pure zirconia. The oxygen tracer diffusion coefficient, as calculated from the mean square displacements, and also the ionic conductivity show an activation energy of 0.85eV. The Onsager cross coefficient associated with thermotransport is negative, meaning that the drift of anions in a temperature gradient would be from a cold region to a hot region. All of the simulation results presented show reasonable agreement with available experimental data.