Space Variables Research Articles

$$\varvec{\Gamma }$$-Convergence and Stochastic Homogenization of Second-Order Singular Perturbation Models for Phase Transitions

AbstractWe study the effective behavior of random, heterogeneous, anisotropic, second-order phase transitions energies that arise in the study of pattern formations in physical–chemical systems. Specifically, we study the asymptotic behavior, as $$\varepsilon $$ ε goes to zero, of random heterogeneous anisotropic functionals in which the second-order perturbation competes not only with a double well potential but also with a possibly negative contribution given by the first-order term. We prove that, under suitable growth conditions and under a stationarity assumption, the functionals $$\Gamma $$ Γ -converge almost surely to a surface energy whose density is independent of the space variable. Furthermore, we show that the limit surface density can be described via a suitable cell formula and is deterministic when ergodicity is assumed.

Extended formulations for binary optimal control problems

AbstractExtended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by adding artificial variables, one can often find a small linear formulation, i.e., one containing a polynomial number of variables and constraints, such that the projection to the original space of variables yields a perfect linear formulation. Motivated by binary optimal control problems with switching constraints, we show that a similar approach can be useful also for optimization problems in function space, in order to model the closed convex hull of feasible controls in a compact way. More specifically, we present small extended formulations for switches with bounded variation and for dwell-time constraints. For general linear switching point constraints, we devise an extended model linearizing the problem, but show that a small extended formulation that is compatible with discretization cannot exist unless P = NP.

On the Non-Linearity of S-Type Variable Exponent Absolutely Summable New Difference Sequence Space

This article presents the domain of general quantum difference in Nakano sequence space. Some topological and geometric behavior, the multiplication mappings defined on it, and the spectrum of mapping ideals constructed by this space and s−numbers have been introduced. Existing results are constructed by controlling the general quantum difference and power of this new space, which is a major strength.

Quantitative analysis of wool and cashmere fiber mixtures using NIR spectroscopy

Abstract The quantitative determination of wool and cashmere mixed fiber is an indispensable quality control link in the textile industry, crucial for improving international trade status, ensuring product quality, and safeguarding consumer rights. Therefore, the goal of this study is to develop a reliable method for estimating fiber contents in wool–cashmere blends based on near-infrared (NIR) spectroscopy. A total of 210 mixed samples of 21 different proportions of cashmere and wool are prepared in the experiment, and data are collected in the NIR spectral band of 1,000–2,500 nm. Convolution Savitzky–Golay (S–G) combined with the second-order derivative is then used for spectral preprocessing. The variable iterative space shrinkage approach (VISSA) optimizes the characteristic wavelengths, and 339 wavelength points are selected. The prediction model of the least squares support vector machine (LSSVM) is established by particle swarm optimization (PSO), fast positioning, and analysis of key information related to the target in complex spectral data. Finally, the training set and the prediction set are divided according to the ratio of 8 : 2. Experiments show that in terms of modeling and prediction, the PSO-LSSVM model based on the wavelength selected by VISSA has a prediction determination coefficient R-squared of 0.9821, a prediction root mean square error of 1.1263, and an mean absolute error of 0.6527. The hybrid modeling method of VISSA, PSO, and LSSVM based on NIR spectroscopy (VISSA–PSO–LSSVM) can provide a more accurate and stable method for the non-destructive detection of cashmere and wool blended fiber content.

Expanded Functionality and Portability for the Colvars Library.

Colvars is an open-source C++ library that provides a modular toolkit for collective-variable-based molecular simulations. It allows practitioners to easily create and implement descriptors that best fit a process of interest and to apply a wide range of biasing algorithms in collective variable space. This paper reviews several features and improvements to Colvars that were added since its original introduction. Special attention is given to contributions that significantly expanded the capabilities of this software or its distribution with major MD simulation packages. Collective variables can now be optimized either manually or by machine-learning methods, and the space of descriptors can be explored interactively using the graphical interface included in VMD. Beyond the spatial coordinates of individual molecules, Colvars can now apply biasing forces to mesoscale structures and alchemical degrees of freedom and perform simulations guided by experimental data within ensemble averages or probability distributions. It also features advanced computational schemes to boost the accuracy, robustness, and general applicability of simulation methods, including extended-system and multiple-walker adaptive biasing force, boundary conditions for metadynamics, replica exchange with biasing potentials, and adiabatic bias molecular dynamics. The library is made available directly within the main distributions of the academic software GROMACS, LAMMPS, NAMD, Tinker-HP, and VMD. The robustness of the software and the reliability of the results are ensured through the use of continuous integration with a test suite within the source repository.

Higher-order fractional equations and related time-changed pseudo-processes

We study Cauchy problems of fractional differential equations in both space and time variables by expressing the solution in terms of “stochastic composition” of the solutions to two simpler problems. These Cauchy sub-problems respectively concern the space and the time differential operator involved in the main equation. We provide some probabilistic and pseudo-probabilistic applications, where the solution can be interpreted as the pseudo-transition density of a time-changed pseudo-process. To extend our results to higher order time-fractional problems, we introduce stable pseudo-subordinators as well as their pseudo-inverses. Finally, we present our results in the case of more general differential operators and we interpret the results by means of a linear combination of pseudo-subordinators and their inverse processes.

Rapid qualitative and quantitative detection for adulteration of Atractylodis Rhizoma using hyperspectral imaging combined with chemometric methods

In the field of traditional Chinese medicine, Atractylodis Rhizoma (AR) is commonly used for various diseases due to its excellent ability to dry dampness and strengthen the spleen, especially popular in East Asia. The aim of this study is to proposed Hyperspectral Imaging (HSI) in combination with chemometric methods for the rapid qualitative and quantitative detection of AR adulteration with other types of powder. Partial Least Squares Discriminant Analysis (PLS-DA) was used to construct the classification models the best, with the First-order Derivative (F-D) preprocessing method. The accuracy values of the test sets for classification models were above 99%. Furthermore, Partial Least Squares Regression (PLSR), Random Forest Regression (RFR), and BP Neural Network (BPNN) were used to quantitatively analyze the adulteration level. On the whole, the BPNN model has a relatively stable effect. The R-square (R2) values of different models were all greater than 0.97, the Root Mean Square Error (RMSE) values were all less than 0.0300, and the Relative Percentage Difference (RPD) values were over 6.00. After applying three characteristic wavelength selection algorithms, namely Iterative Retained Information Variable (IRIV), Successive Projections Algorithm (SPA), and Variable Iterative Space Shrinkage Approach (VISSA) algorithms, the classification accuracy values remained over 99.00% while the quantification models’ RPD values were over 4.00. These results demonstrate the reliability of using hyperspectral imaging combined with chemometrics methods for the adulteration problems in AR.

Dynamic Formulation of the Double Multiple Stream Tube Model of Offshore Vertical Axis Wind Turbines

Abstract The paper proposes a novel algorithm to simulate Vertical Axis Wind Turbines in floating motion based on a low-fidelity approach. The conventional Double Multiple Stream Tube Model is formulated as a steady state model to deal with the inherent unsteady aerodynamics of VAWTs. The Double Multiple Stream Tube Model makes use of an average contribution of the blade passages over a revolution to solve the Blade Element Momentum equation. The model reduces the dependence of the solution (the induction field) to a space variable. Floating Vertical Axis Wind Turbines undergoes a variation of aerodynamic quantities according to wave periods, also different from the rotor period. This paper provides a new formulation of the Double Multiple Stream Tube Model to solve the turbine rotation in time and space, introducing the variation of the platform velocity and a revised approach to the downstream actuator disc. The most impactful parameter is found to be the wave frequency: wave periods at full-scale are lower than the ones of the turbine rotor, featuring optimal operating points at low tip speed ratios. The increase of the wave frequency highlights the differences of the average torque prediction for a single blade up to 10% between the unsteady and the standard formulation. In this context, the development of fast low-fidelity computational tools play a key role in the assessment of the preliminary designs of Floating Offshore Vertical Axis Wind Turbines and it will be used to optimise the aerodynamic design of the laboratory scaled model under surge motion.

Toward aerodynamic surrogate modeling based on β-variational autoencoders

Surrogate models that combine dimensionality reduction and regression techniques are essential to reduce the need for costly high-fidelity computational fluid dynamics data. New approaches using β-variational autoencoder (β-VAE) architectures have shown promise in obtaining high-quality low-dimensional representations of high-dimensional flow data while enabling physical interpretation of their latent spaces. We propose a surrogate model based on latent space regression to predict pressure distributions on a transonic wing given the flight conditions: Mach number and angle of attack. The β-VAE model, enhanced with principal component analysis (PCA), maps high-dimensional data to a low-dimensional latent space, showing a direct correlation with flight conditions. Regularization through β requires careful tuning to improve overall performance, while PCA preprocessing helps to construct an effective latent space, improving autoencoder training and performance. Gaussian process regression is used to predict latent space variables from flight conditions, showing robust behavior independent of β, and the decoder reconstructs the high-dimensional pressure field data. This pipeline provides insight into unexplored flight conditions. Furthermore, a fine-tuning process of the decoder further refines the model, reducing the dependence on β and enhancing accuracy. Structured latent space, robust regression performance, and significant improvements in fine-tuning collectively create a highly accurate and efficient surrogate model. Our methodology demonstrates the effectiveness of β-VAEs for aerodynamic surrogate modeling, offering a rapid, cost-effective, and reliable alternative for aerodynamic data prediction.

Yet Another Discriminant Analysis (YADA): A Probabilistic Model for Machine Learning Applications

This paper presents a probabilistic model for various machine learning (ML) applications. While deep learning (DL) has produced state-of-the-art results in many domains, DL models are complex and over-parameterized, which leads to high uncertainty about what the model has learned, as well as its decision process. Further, DL models are not probabilistic, making reasoning about their output challenging. In contrast, the proposed model, referred to as Yet Another Discriminate Analysis(YADA), is less complex than other methods, is based on a mathematically rigorous foundation, and can be utilized for a wide variety of ML tasks including classification, explainability, and uncertainty quantification. YADA is thus competitive in most cases with many state-of-the-art DL models. Ideally, a probabilistic model would represent the full joint probability distribution of its features, but doing so is often computationally expensive and intractable. Hence, many probabilistic models assume that the features are either normally distributed, mutually independent, or both, which can severely limit their performance. YADA is an intermediate model that (1) captures the marginal distributions of each variable and the pairwise correlations between variables and (2) explicitly maps features to the space of multivariate Gaussian variables. Numerous mathematical properties of the YADA model can be derived, thereby improving the theoretic underpinnings of ML. Validation of the model can be statistically verified on new or held-out data using native properties of YADA. However, there are some engineering and practical challenges that we enumerate to make YADA more useful.

The Uniqueness and Iterative Properties of Positive Solution for a Coupled Singular Tempered Fractional System with Different Characteristics

In this paper, we focus on the uniqueness and iterative properties of positive solution for a coupled p-Laplacian system of singular tempered fractional equations with differential order and characteristics. Firstly, the system is converted to an integral equation, and then, a coupled iterative technique and some suitable growth conditions are proposed; furthermore, some elaborate results about the uniqueness and iterative properties of positive solutions of the system are established, which include the uniqueness, the convergence analysis, the asymptotic behavior, and error estimation, as well as the convergence rate of the positive solution. The interesting points of this paper are that the order of the system of equations is different and the nonlinear terms of the system possess the opposite monotonicity and allow for stronger singularities at space variables.

Second law and Liu relations: the no-reversible-direction axiom—revisited

AbstractA thermodynamic process is governed by balance equations in field-formulated thermodynamics. Especially the balance equation of entropy takes a prominent role: it introduces the Second Law in the form of a dissipation inequality via the non-negative entropy production. Balance equations and dissipation inequality are independent of the considered material which is described by additional constitutive equations which need the introduction of a state space which is spanned by the state space variables. Inserting these constitutive equations into the balance equations results in the balance equations on state space which include the first order time and position derivatives of the state space variables, called “higher derivatives” wich are directional derivatives in a mathematicle sense. Why do not appear the latter in the Liu Relations which pretend to describe material as well as the equations on state space do ? The answer is that the Liu Relations describe materials whose entropy production does not depend on the higher derivatives. Consequently, the Liu Relations are more specific than the balance equations on state space. A toy example concerning heat conduction in compressible fluids is in two different versions added for elucidation.

From ‘dankgevingsdag' to 'turkey party’: Historical sociolinguistic perspectives on loan strategies in Flemish-American heritage newspapers

Within the domain of historical sociolinguistics, attention for heritage languages has been on the rise in the last decade (see e.g., Brown 2019; Litty 2019). The goal of this paper is to contribute to that growing body of research studying the role of sociolinguistic factors in heritage language use in the past, by looking at the lexical output of Belgian emigrants in the United States using heritage newspapers. We will investigate the borrowing patterns in three Flemish-American newspapers that were published in the 19th and 20th centuries and circulated widely within the Flemish-American communities. We focus on (1) borrowing rate (how many English-origin lexemes are transferred?), and (2) borrowing type (which loan processes are involved?). The findings are interpreted in terms of the social variables time and space to chart diachronic as well as regional differences, besides looking at differences between the newspapers more generally.

Displacement-potential analysis of ply-stresses in a partially guided non-uniform short-column of hybrid laminated composites

Reliable and accurate analysis of local stresses in structural problems of fiber-reinforced laminated composites involving nonuniform geometry is of utmost practical importance, especially when they are subjected to local loads and supports. In this research, a new study of ply stresses in a partially guided, nonuniform, short composite column of hybrid laminates, subjected to an eccentrically distributed loading is conducted using an efficient computational scheme. The analytical modeling of the present mixed-boundary-value problem of laminated structure is realized in terms of a single scalar function of space variables (called as displacement-potential function), which is defined by the displacement components of plane elasticity, and is governed by a single fourth-order partial-differential equation of equilibrium. In this modeling approach, the original three-dimensional symmetric laminated column is reduced to a plane-stress scalar-field problem of an equivalent imaginary lamina in an attempt to obtain the corresponding strain field (global laminate strain), which is then used to determine the stress fields of individual plies through the respective transformed reduced stiffness matrices. A finite-difference based computational scheme is developed to solve the representative nonuniform equivalent lamina in terms of the displacement-potential function, which is however well capable of dealing with different ply materials as well as fiber orientations, together with the associated mixed and changeable physical conditions along the boundaries of the column. A 28-ply balanced hybrid laminate composed of boron-epoxy and glass-epoxy plies with various fiber orientation is considered as the structural material for the present column. The stress fields obtained for individual plies as well as the overall laminate are analyzed in the perspective of a number of practical issues of structural design, which include material hybridization, eccentricity of loading and attachment of partial guides to the column. The design stresses of the nonuniform laminated column are identified to be affected significantly by the material and orientation of fibers as well as the laminate hybridization. An attempt is also made to verify the soundness and accuracy of the present computational scheme through the comparison of the present potential-function solutions with those obtained by the conventional computational method.

Cauchy Type Nonlinear Inverse Problem in a Two-Layer Cylindrical Area

Various types of protective coatings, such as ceramics, are used to increase the efficiency of metal parts that are exposed to high heat loads. Maintaining mechanical properties and acceptable thermal stresses requires temperature control for components such as turbine blades, gun barrels or combustion chambers. This paper presents a new method for controlling thermal parameters by solving a non-stationary Cauchy problem for the heat conduction equation. The solution is presented in a cylindrical two-layer area considering the variation of the thermophysical parameters of the metal and ceramic. The non-linear equation was solved by successive approximation method using differential quotients for the space and time variable. In order to regularize the ill-conditioned inverse problem, a quasi-regularization method was applied by performing an energy balance for the ceramic. Numerical calculations were carried out for different thicknesses of the ceramic layer. The temperature, heat flux density and heat transfer coefficient for the protective layer were calculated. For the same values of the heat transfer coefficient for 0.1 and 0.3 mm thick protective layers, the difference in permissible gas temperature differs by 10.5 °C.

Kinematic-Muscular Synergies Describe Human Locomotion with a Set of Functional Synergies.

Kinematics, kinetics and biomechanics of human gait are widely investigated fields of research. The biomechanics of locomotion have been described as characterizing muscle activations and synergistic control, i.e., spatial and temporal patterns of coordinated muscle groups and joints. Both kinematic synergies and muscle synergies have been extracted from locomotion data, showing that in healthy people four-five synergies underlie human locomotion; such synergies are, in general, robust across subjects and might be altered by pathological gait, depending on the severity of the impairment. In this work, for the first time, we apply the mixed matrix factorization algorithm to the locomotion data of 15 healthy participants to extract hybrid kinematic-muscle synergies and show that they allow us to directly link task space variables (i.e., kinematics) to the neural structure of muscle synergies. We show that kinematic-muscle synergies can describe the biomechanics of motion to a better extent than muscle synergies or kinematic synergies alone. Moreover, this study shows that at a functional level, modular control of the lower limb during locomotion is based on an increased number of functional synergies with respect to standard muscle synergies and accounts for different biomechanical roles that each synergy may have within the movement. Kinematic-muscular synergies may have impact in future work for a deeper understanding of modular control and neuro-motor recovery in the medical and rehabilitation fields, as they associate neural and task space variables in the same factorization. Applications include the evaluation of post-stroke, Parkinson's disease and cerebral palsy patients, and for the design and development of robotic devices and exoskeletons during walking.

Flow dynamics over cylinder in two‐dimensional benchmark problem: A finite element approximation

This research investigates 2D benchmark flow around a circular cylinder, utilizing the incompressible Navier–Stokes equations alongside the continuity and energy equations. The numerical solution is achieved through finite element discretization for space variable, combined with a second‐order Crank–Nicolson scheme for time integration. The computational results are derived using the FEATFLOW finite element based library package. Our study focuses on the dimensionless form of the flow equations and examines three key dimensionless parameters: drag, lift, and pressure drop. Upon applying finite element method (FEM) discretization, the system is converted into a set of linear or nonlinear ordinary differential equations or algebraic equations for steady‐state scenarios. We then apply the Newton–Raphson method as the outer nonlinear solver, and the multigrid method for efficiently resolving the linear subproblems. To ensure numerical accuracy, we evaluated the and errors, confirming that the experimental order of convergence matches the theoretical predictions. Flow profiles were both graphically represented and tabulated, offering a detailed understanding of the simulation results.

Statistical Model of Ocular Wavefronts With Accommodation.

The purpose of this study was to determine the minimum number of orthonormal basis functions, applying Principal Component Analysis (PCA), to represent the most wavefront aberrations at different accommodation stages. The study also aims to generate synthetic wavefront data using these functions. Monocular wavefront data from 191 subjects (26.15 ± 5.56years old) were measured with a Hartmann-Shack aberrometer, simulating accommodation from 0 diopters (D) to 5 D in 1 D steps. The wavefronts for each accommodative demand were rescaled for different pupil sizes: 4.66, 4.76, 4.40, 4.09, 4.07, and 3.68mm. PCA was applied to 150 wavefront parameters (25 Zernike coefficients × 6 accommodation levels) to obtain eigenvectors for dimensional reduction. A total of 49 eigenvectors were modeled as a sum of 2 multivariate Gaussians, from which 1000 synthetic data sets were generated. The first 49 eigenvectors preserved 99.97% of the original data variability. No significant differences were observed between the mean values and standard deviation of the generated and original 49 eigenvectors (two one-sided test [TOST], P > 0.05/49) and (F-test, P > 0.05/49), both with Bonferroni correction. The mean values of the generated parameters (1000) were statistically equal to those of the original data (TOST, P > 0.05/150). The variability of the generated data was similar to the original data for the most important Zernike coefficients (F-test, P > 0.05/150). PCA significantly reduces the dimensionality of wavefront aberration data across 6 accommodative demands, reducing the variable space by over 66%. The synthetic data generated by the proposed wavefront model for accommodation closely resemble the original clinical data.

Effect of Different Injury Morphology of the Endplate on Intervertebral Disc Degeneration: Retrospective Cohort Study.

To describe a simplified classification scheme for endplate injury morphology based on 3D CT and to examine possible associations between endplate injury morphology and vertebral space and other variables such as type of fracture and disc degeneration in a group of patients with thoracolumbar fractures. This study was a retrospective cohort study. We collected patients with thoracolumbar fractures admitted from January 2015 to August 2020 and divided them into three groups based on the morphology of endplate injury (45 cases of mild endplate injury, 54 cases of moderate endplate injury, and 42 cases of severe endplate injury, SEI). Data of vertebral body and intervertebral space height and angle, the Pfirrmann grade, endplate healing morphology were collected during preoperative, postoperative, and long-term follow-up of patients in each group. One-way analysis of variance (ANOVA), chi-squared test, and repeated measurement ANOVA were used to compare and analyze the influence of endplate injury morphology on patient prognosis. Most moderate injuries to the endplate (fissure-type injury) and severe injuries (irregular depression-type injury, Schmorl's node-type injury) resulted in significant disc degeneration in the long-term transition. This study also showed significant differences in the height of the anterior margin of the injured spine and the intervertebral space height index during this process. The current study suggests that although the region of injury in endplate fissure-type injury is small preoperatively, it may be a major factor in leading to severe disc degeneration, loss of intervertebral height, and Cobb angle in the long term. The results of our study therefore may allow surgeons to predict the prognosis of patients with thoracolumbar fractures and guide their treatment.

Unsteady thermal efficiency and temperature isotherms of an inclined radiative porous concave parabolic tapered fin: An application of design of tapered fin featuring

The present article investigates the unsteady energy efficiency and isotherms for the inclined radiative concave parabolic fin. Fourier Law is employed by incorporating the radiation and convection phenomena. Darcy model has been employed to study the porous effects on a fin. The novelty of the present problem is transient thermal analysis of a radiative porous concave parabolic fin by consideration of fin tapper ratio and angle of inclination for several pertinent parameters. Calculation of fin efficiency is the added feature of present study. The governing partial differential is transformed into the dimensionless form by employing the non-dimensional variables. With the help of MATHEMATICA a partial differential equation is solved by applying the ND Solve. The isotherms are obtained for the variations in time and space variables. It is unveiled that temperature distribution diminishes for the upsurge in the convective radiative parameters. Temperature distribution elevates as the enhancement in heat generating parameter. It has been concluded that the fin taper ratio and angle of inclination palys a vital role in heat transfer performance. An elevated thermal dispersal is seen for increasng time.