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We present a mathematical model for the slow combustion (smoldering) of a two-dimensional sheet of paper. We describe the evolution of the char region, and we investigate the effects of an orthogonal air flow on the shape of the combustion front. The mathematical formulation consists in a set of two nonlinear PDEs for the temperature and the oxygen concentrations coupled with one ODE for the cellulose concentration. The (dimensionless) problem is solved numerically by means of a spectral collocation scheme based on Chebyshev polynomials. Our results show that the Péclet and the Lewis number strongly influence the shape of the ignition front and that the advancement of the combustion front does not occur if advection and diffusion are neglected (zero Péclet and Lewis numbers). In particular we observe that the burning region and the ignition front are strongly influenced by the velocity of the airflow and by the mass and heat transport phenomena due to diffusion and advection. We shall see that the increasing of the ratio between the convective and diffusive characteristic times (Péclet number) and the decreasing of the ratio between the mass and heat diffusive characteristic times (Lewis number) have a "flattening effect" on the combustion front. [ABSTRACT FROM AUTHOR]

In this article, we present a mathematical model and numerical simulation of the coffee-ring effect on porous papers. The numerical method is based on Monte Carlo simulation. The proposed model is simple but can capture the main mechanism of coffee stain formation on porous papers. Several numerical experiments are presented to demonstrate the performance of the proposed algorithm. We can obtain the coffee-ring effect on porous papers as the computer simulation results. [ABSTRACT FROM AUTHOR]

The Buck converter is a commonly used voltage regulator (VR) structure that supplies power to the load devices and responds to load transients. In most of the applications, the VR is controlled by voltage or current mode control, and some nonlinear approaches are used to improve the transient response which brings more complexities to the closed loop design. To achieve a fast transient response without over-regulation under a load step transient, this paper proposes a digital single-cycle regulation (SCCR) controller, which comprised a fast path, a slow path, and a neutralization path. Unlike the conventional PID control, the neutralization path of the SCCR controller is used to offset the excessive energy change in the first cycle after a load step occurs, which makes the inductor current reach its new static condition in a shorter period of time. The mathematical model of the SCCR control is established in this paper and a scanning algorithm is proposed for the design of the compensator parameters. Experimental results are presented to verify the improvement of the transient response when compared to the conventional and nonlinear PID control, the recovery time is decreased by 64.3% and 43% for load step-up and step-down when compared with nonlinear PID control. [ABSTRACT FROM AUTHOR]

In automata networks, it is well known that the way entities update their states over time has a major impact on their dynamics. In particular, depending on the chosen update schedule, the underlying dynamical systems may exhibit more or less asymptotic dynamical behaviours such as fixed points or limit cycles. Since such mathematical models have been used in the framework of biological networks modelling, the question of choosing appropriate update schedules has arised soon. In this note, focusing on Boolean networks, our aim is to emphasise that the adequate way of thinking regulations and genetic expression over time is certainly not to consider a wall segregating synchronicity from asynchronicity because they actually complement rather well. In particular, we highlight that specific update schedules, namely block-parallel update schedules, whose intrinsic features are still not known from a theoretical point of view, admit realistic and pertinent properties in the context of biological modelling and deserve certainly more attention from the community. [ABSTRACT FROM AUTHOR]

The methodology used for analyzing the survival process should keep in mind heterogeneity in empirical data. Cross-sectional data are more heterogeneous in comparison with birth-cohort data. [ABSTRACT FROM AUTHOR]

A series of shredded paper fire experiments were conducted by means of a calorimeter. The mass loss rate and heat release rate were measured. The flame spread process was recorded, which shows that the flame spread process can be divided into four typical stages, and the mean spread rates along different directions were obtained from the observed combustion process. Based on the mean flame spread rate, a mathematical model for predicting the burning surface as a function of time during the four stages is established. Combining this model with the effective heat of combustion calculated from measured mass loss rate and heat release rate, an improved model to predict the heat release rate as a function of time was developed. In this model, the linear relationship between heat release rate and burning surface is found, and the predicted result agrees well with the measured heat release rate. [ABSTRACT FROM AUTHOR]

The paper presents a brief analytical review of the current state of research in the field of recovery and its modeling in order to predict the structure and properties, as well as a review of experimental research methods and mathematical models of the processes of structure formation during annealing of cold-rolled steels. The paper also presents the results of an experimental study of the recovery process in cold-rolled automotive steels using various techniques and describes a mathematical model for calculating the kinetics of this process depending on the temperature and chemical composition of steels. [ABSTRACT FROM AUTHOR]

Photoacoustic (PA) medical imaging is a crossbred technique relying on light-induced ultrasonic waves due to the PA effect phenomenon recorded primarily in 1880 by A. G. Bell. Numerical simulation, also known as in-silico, studies assist scientists in minimizing incorrect PA experiments in both in-vitro and in-vivo. Numerical modeling techniques help to achieve a fast simulation process in contrast to pure mathematics alone. However, if a suitable facilitated mathematical model can be established prior to applying numerical modeling, it will be of great interest to the whole numeric model. Numerous mathematical equations, theorems, and propositions have been proposed to model the whole PA signal generation and propagation process in biological media. However, most of them are complicated and difficult to be understood by researchers, especially beginners. That's why this paper was introduced. Our paper aims to simplify the understanding of the generation and propagation process of biomedical PA waves. We have developed a facilitated mathematical model for the entire process. The introduced developed mathematical model is based on three steps: (1) pulsed laser stimulation, (2) light diffusion, and (3) PA stress wave generation and propagation. The developed mathematical model has been implemented utilizing COMSOL Multiphysics, which relies on the finite element method (FEM) numerical modeling principle. The in-silico time-dependent study's results confirmed that the proposed mathematical model is a simple, efficient, accurate, and quick starting point for researchers to simulate biomedical PA signals' generation and propagation process utilizing any suitable software such as COMSOL multiphysics. [ABSTRACT FROM AUTHOR]

To model advanced 3-D forming strategies for paper materials, the effects of environmental conditions on the mechanical behavior must be quantitatively and qualitatively understood. A tensile test method has been created, verified, and implemented to test paper at various moisture content and temperature levels. Testing results for one type of paper for moisture contents from 6.9 to 13.8 percent and temperatures from 23 to 168 degrees Celsius are presented and discussed. Coupled moisture and temperature effects have been discovered for maximum stress. Uncoupled effects have been discovered for elastic modulus, tangent modulus, hardening modulus, strain at break, tensile energy absorption (TEA), and approximate plastic strain. A hyperbolic tangent function is also utilized which captures the entire one-dimensional stress-strain response of paper. The effects of moisture and temperature on the three coefficients in the hyperbolic tangent function may be assumed to be uncoupled, which may simplify the development of moisture- and temperature-dependent constitutive models. All parameters were affected by both moisture and temperature with the exception of TEA, which was found to only be significantly dependent on temperature. [ABSTRACT FROM AUTHOR]

We summarize the papers published by Einstein in the Annalen der Physik in the years 1902-1904 on the derivation of the properties of thermal equilibrium on the basis of the mechanical equations of motion and of the calculus of probabilities. We point out the line of thought that led Einstein to an especially economical foundation of the discipline, and to focus on fluctuations of the energy as a possible tool for establishing the validity of this foundation. We also sketch a comparison of Einstein's approach with that of Gibbs, suggesting that although they obtained similar results, they had different motivations and interpreted them in very different ways. [ABSTRACT FROM AUTHOR]

A chemo-mechanical model is developed to investigate the effects on the stress development of the coating of polycrystalline Ni-rich LiNixMnyCozO2 (x ⩾ 0.8) (NMC) particles with poly(3,4-ethylenedioxythiophene) (PEDOT). The simulation results show that the coating of primary NMC particles significantly reduces the stress generation by efficiently accommodating the volume change associated with the lithium diffusion, and the coating layer plays roles both as a cushion against the volume change and a channel for the lithium transport, promoting the lithium distribution across the secondary particles more homogeneously. Besides, the lower stiffness, higher ionic conductivity, and larger thickness of the coating layer improve the stress mitigation. This paper provides a mathematical framework for calculating the chemo-mechanical responses of anisotropic electrode materials and fundamental insights into how the coating of NMC active particles mitigates stress levels. [ABSTRACT FROM AUTHOR]

In the present paper, an improved mathematical model is developed based on a new refined sinusoidal shear deformation theory with only four unknown variables for static bending and dynamic analysis of functionally graded (FG) doubly-curved shell structures. The proposed higher-order shell theory yields an adequate distribution of the transverse shear strains through the thickness by satisfying the tensile-free boundary conditions at the top and bottom surfaces of the shell. The mechanical properties are supposed to change gradually through the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents. The shell equilibrium equations for this study are derived from Hamilton's variational principle and subsequently solved for simply supported boundary conditions by using the Navier solution methodology. However, this improved model is substantiated by several numerical results for the mechanical behavior of FG shell structures having different geometrical configurations, namely, cylindrical, spherical, hyperbolic paraboloid, and elliptical paraboloid shapes, which were compared, and successfully converged with the corresponding results found by alternative higher-order shear deformation models to validate the accuracy of the proposed theory. [ABSTRACT FROM AUTHOR]

This paper proposes the Love Evolution Algorithm (LEA), a novel evolutionary algorithm inspired by the stimulus–value–role theory. The optimization process of the LEA includes three phases: stimulus, value, and role. Both partners evolve through these phases and benefit from them regardless of the outcome of the relationship. This inspiration is abstracted into mathematical models for global optimization. The efficiency of the LEA is validated through numerical experiments with CEC2017 benchmark functions, outperforming seven metaheuristic algorithms as evidenced by the Wilcoxon signed-rank test and the Friedman test. Further tests using the CEC2022 benchmark functions confirm the competitiveness of the LEA compared to seven state-of-the-art metaheuristics. Lastly, the study extends to real-world problems, demonstrating the performance of the LEA across eight diverse engineering problems. Source codes of the LEA are publicly available at https://ww2.mathworks.cn/matlabcentral/fileexchange/159101-love-evolution-algorithm. [ABSTRACT FROM AUTHOR]

This paper studies a mathematical model of the phase transition process as a moving boundary problem (MBP). An equation describing the temperature-dependent thermal conductivity and Robin-type boundary condition at the fixed boundary is used in the model. In order to solve the considered MBP, we propose an iterative-based Keller box method (KBM) for the numerical approximation and boundary immobilization method (BIM) to immobilize the moving boundary. In addition, KBM incorporates nonlinearities in thermal conductivity and boundary conditions. We study the stability and consistency and found out that the scheme is second-order accurate in both time and space. A specific case having a similarity solution has been considered to validate the numerical scheme. Our numerical results show that the KBM is in good agreement with the similarity solution. In addition, the rate of convergence of the KBM scheme is two. Different parameters and temperature-dependent thermal conductivity are studied to determine how these affect the position of the moving boundary. [ABSTRACT FROM AUTHOR]

In this study, we present an exact derivation of a meso-scale mathematical model for analyzing heat transfer in nanofluids through variational convergence, targeting the reduction of discrepancies between theoretical predictions and experimental data. The model derives distinct sets of partial differential equations for microscale, mesoscale, and macroscale simulations, taking into account several influencing factors across different scales. By employing the weak convergence of distributions and the theory of distributions, we establish variational convergence between the PDEs at different scales. Significantly, the mesoscale model leads to a derivation of the quadratic dependence of thermal conductivity on the particle volume fraction. Our numerical evaluations reveal a marked improvement in prediction accuracy, with the proposed model reducing prediction error in some cases by as much as 92% compared to some existing linear models. Additionally, when tested against available experimental data, the model shows a closer alignment reinforcing its potential for enhancing the prediction and understanding of nanofluid heat transfer. Hence, this paper represents a valuable contribution to nanofluid heat transfer research, providing a promising direction for future advancements in the field. [ABSTRACT FROM AUTHOR]

In this paper, a practical scenario of multicasting through heterogeneous cellular network has been considered. The macro base station of macro cell transmits confidential information to its intended multicast macro users and multiple eavesdroppers try to decode this information and pico base station of pico cell transmits confidential information to its intended multicast pico users. Authors are interested to develop a mathematical model consists of the closed-form analytical expression for the secrecy multicast capacity (SMC) to protect that confidential information from eavesdropping. The results show that the simultaneous effects of double scatterer and correlation significantly reduce the security in multicasting but these reduction in the security can be compensated by antenna diversity at the multicast users. The results also show the effect of double scatterer on different correlation scenario (Constant Correlation and Jakes Correlation) in terms of the correlation figures of transmit, receive and scatterer correlation matrices. [ABSTRACT FROM AUTHOR]

Time of day affects how well the immune system responds to viral or bacterial infections. While it is well known that the immune system is regulated by the circadian clock, the dynamic origin of time-of-day-dependent immunity remains unclear. In this paper, we studied the circadian control of immune response upon infection of influenza A virus through mathematical modeling. Dynamic simulation analyses revealed that the time-of-day-dependent immunity was rooted in the relative phase between the circadian clock and the pulse of viral infection. The relative phase, which depends on the time the infection occurs, plays a crucial role in the immune response. It can drive the immune system to one of two distinct bistable states, a high inflammatory state with a higher mortality rate or a safe state characterized by low inflammation. The mechanism we found here also explained why the same species infected by different viruses has different time-of-day-dependent immunities. Further, the time-of-day-dependent immunity was found to be abolished when the immune system was regulated by an impaired circadian clock with decreased oscillation amplitude or without oscillations. [ABSTRACT FROM AUTHOR]

Nowadays, supply chain (SC) decentralised decision making is the most usual situation in SC operations planning. In this context, different companies can collaboratively plan to achieve a certain level of individual and SC performance. However in many cases, there is reluctance to collaborate because it is not known a priori which benefits will be reported. This paper aims to develop a mathematical programming-based methodology for the evaluation of different supply chain collaborative planning scenarios (MPM-SC-CP). It is assumed that different SC decision centres (DCs) make decisions based on mixed and integer linear programming models. Two main inputs feed the proposed MPM-SC-CP, a framework and associated methodology that support the integrated conceptual and analytical modeling of the SC-CP process in which several DCs make decisions according to spatio-temporal integration. Finally, an application to a real ceramic SC was conducted. [ABSTRACT FROM AUTHOR]

In this paper, we consider a mathematical model "politics-economy" described by a nonlinear system of differential equations with a parameter and obtain conditions for the existence of a nonzero positive periodic solution. [ABSTRACT FROM AUTHOR]

In this paper, we consider model problems of chemical kinetics that lead to singularly perturbed parabolic equations in domains with nonsmooth boundaries. The solvability of such problems depends on the properties of the inhomogeneity at corner points of the boundary. [ABSTRACT FROM AUTHOR]

Robust reliability Generation Expansion Planning (GEP) turns out to be a crucial step for an efficient energy management system in a modern power grid, especially under renewable energy employment. The integration of all such components in a GEP model makes it a large-scale, nonlinear, and mixed-variable mathematical modeling problem. In this paper, the presence of wind energy uncertainty is analyzed. Both long and short-term uncertainties are incorporated into the proposed GEP model. The first step concerns the impact of long-term wind uncertainties through the annual variations of the capacity credit of two real sites in Egypt at Zafaranh and Shark El-ouinate. The second step deals with the short-term uncertainties of each wind site. The wind speed uncertainty of each wind site is modeled by probability distribution function. Then, wind power is estimated from the wind power curve for each wind site and Monte-Carlo Simulation is performed. Fast Gas Turbine and/or Pump Hydro Storage are incorporated to cope with short-term uncertainties. Sensitivity analysis is implemented for 3, 6, and 12 stages as short and long planning horizons to minimize the total costs with wind energy penetration and emission reduction over planning horizons. Also, a novel Honey Badger Algorithm (HBA) with model modifications such as Virtual Mapping Procedure, Penalty Factor Approach, and the Modified of Intelligent Initial Population Generation is utilized for solving the proposed GEP problem. The obtained results are compared with other algorithms to ensure the superior performance of the proposed HBA. According to the results of the applicable test systems, the proposed HBA performs better than the others, with percentage reductions over CSA, AO, BES, and PSO ranging up to 4.2, 2.72, 2.7, and 3.4%, respectively. [ABSTRACT FROM AUTHOR]

The paper is devoted to crop production adaptation to climate change. It considers the problem of finding the future optimal structure of the sowing area, considering the possible climate change scenario. It implies finding a distribution of the sowing area for different groups of crops that would maximize the average annual yield while limiting the risk of shortfall in crop production due to adverse weather conditions. The authors have developed a mathematical model to solve this problem and used it for computations. [ABSTRACT FROM AUTHOR]

This manuscript delves into the examination of the stochastic fractional derivative of Drinfel'd-Sokolov-Wilson equation, a mathematical model applicable in the fields of electromagnetism and fluid mechanics. In our study, the proposed equation is through examined through various viewpoints, encompassing soliton dynamics, bifurcation analysis, chaotic behaviors, and sensitivity analysis. A few dark and bright shaped soliton solutions, including the unperturbed term, are also examined, and the various 2D and 3D solitonic structures are computed using the Tanh-method. It is found that a saddle point bifurcation causes the transition from periodic behavior to quasi-periodic behavior in a sensitive area. Further analysis reveals favorable conditions for the multidimensional bifurcation of dynamic behavioral solutions. Different types of wave solutions are identified in certain solutions by entering numerous values for the parameters, demonstrating the effectiveness and precision of Tanh-methods. A planar dynamical system is then created using the Galilean transformation, with the actual model serving as a starting point. It is observed that a few physical criteria in the discussed equation exhibit more multi-stable properties, as many multi-stability structures are employed by some individuals. Moreover, sensitivity behavior is employed to examine perturbed dynamical systems across diverse initial conditions. The techniques and findings presented in this paper can be extended to investigate a broader spectrum of nonlinear wave phenomena. [ABSTRACT FROM AUTHOR]

Analyzing the viscoelastic characteristics of materials, especially polymers, is essential for understanding their mechanical properties and their capacity to function in different conditions. This paper presents a novel viscoelastic heat transfer model that integrates a memory-based derivative with the Moore–Gibson–Thomson (MGT) equation. The purpose is to examine the viscoelastic characteristics of materials and assess their response to external stresses and deformations over a certain period of time. In addition to incorporating the third-type thermoelastic model that Green and Naghdi provided, the derivation of this thermo-viscoelastic model included the integration of heat flow and its time derivative into Fourier's equation. To verify and understand the proposed model, it was applied to consider an unbounded viscoelastic semi-space immersed in a uniform magnetic field and exposed to non-Gaussian laser radiation as a heat source. An analysis of computational results was conducted to evaluate how the behavior of the field variables under consideration is affected by viscoelastic coefficients and memory-based derived factors. [ABSTRACT FROM AUTHOR]

The paper presents research on identifying a biomechanical parameter from a theoretical model of changes during osteoarthritis. In vitro experiments were carried out on quasi-3D chondrocyte cultures seeded on corn-starch hydrogel materials and subjected to mechanical stress on a designed and constructed stand. The results were adapted to a mathematical model and calculated on a simplified two-dimensional specimen. Numerical simulations have been performed to illustrate the growth of bone spurs. The observed changes of variables which determine osteophytes are qualitative and more correlated to the real-life observations. [ABSTRACT FROM AUTHOR]

The Electronic Personal Health Record (EPHR) provides an innovative service for citizens and professionals to manage health data, promoting patient-centred care. It enhances communication between patients and physicians and improves accessibility to documents for remote medical information management. The study aims to assess the prevalence of awareness and acceptance of the EPHR in northern Italy and define determinants and barriers to its implementation. In 2022, a region-wide cross-sectional study was carried out through a paper-based and online survey shared among adult citizens. Univariable and multivariable regression models analysed the association between the outcome variables (knowledge and attitudes toward the EPHR) and selected independent variables. Overall, 1634 people were surveyed, and two-thirds were aware of the EPHR. Among those unaware of the EPHR, a high prevalence of specific socio-demographic groups, such as foreign-born individuals and those with lower educational levels, was highlighted. Multivariable regression models showed a positive association between being aware of the EPHR and educational level, health literacy, and perceived poor health status, whereas age was negatively associated. A higher knowledge of the EPHR was associated with a higher attitude towards the EPHR. The current analysis confirms a lack of awareness regarding the existence of the EPHR, especially among certain disadvantaged demographic groups. This should serve as a driving force for a powerful campaign tailored to specific categories of citizens for enhancing knowledge and usage of the EPHR. Involving professionals in promoting this tool is crucial for helping patients and managing health data. [ABSTRACT FROM AUTHOR]

Shear-induced droplet formation is important in many industrial applications, primarily focusing on droplet sizes and pinch-off frequency. We propose a one-dimensional mathematical model that describes the effect of shear forces on the droplet interface evolution. The aim of this paper is to simulate paraffin wax droplets in a co-flowing fluid using the proposed model to estimate the droplet volume rate for different flow velocities. Thus, the study focuses only on the dripping regime. This one-dimensional model has a single parameter that arises from the force balance on the interface. This parameter is related to the shear layer thickness and hence influenced by the change in quantities like velocity, viscosity, and surface tension. The correlation describing the dependence of the parameter on these quantities using non-dimensional numbers is presented. The model is then cross-validated with the previous computational and experimental data. We use PETSc, an open-source solver toolkit, to implement our model using a mixed finite element discretization. We present the simulation results for liquid paraffin wax under fast-moving airflow with a range of velocities. [ABSTRACT FROM AUTHOR]

The authors comment on the article "Closed-form analytical solutions for assessing the consequences of sea-level rise on groundwater resources in sloping coastal aquifers" published in a previous issue of the journal. They state concerns over the impact of sea-level rise on seawater intrusion, and mention limitations to the article associated with the choice of mathematical model and inland boundary condition. They mention the possibility of employing the Strack single potential approach.

We revisit two old and apparently little known papers by Basuev (Teoret Mat Fiz 37(1):130-134, , Teoret Mat Fiz 39(1):94-105, ) and show that the results contained there yield strong improvements on current lower bounds of the convergence radius of the Mayer series for continuous particle systems interacting via a very large class of stable and tempered potentials, which includes the Lennard-Jones type potentials. In particular we analyze the case of the classical Lennard-Jones gas under the light of the Basuev scheme and, using also some new results (Yuhjtman in J Stat Phys 160(6): 1684-1695, ) on this model recently obtained by one of us, we provide a new lower bound for the Mayer series convergence radius of the classical Lennard-Jones gas, which improves by a factor of the order 10 on the current best lower bound recently obtained in de Lima and Procacci (J Stat Phys 157(3):422-435, ). [ABSTRACT FROM AUTHOR]

One century after the seminal work by Leonor Michaelis and Maud Menten devoted to the theoretical study of the enzymatic reactions, in this paper, we give an overview of the most recent trends concerning the mathematical modeling of several enzymatic mechanisms, focusing on its asymptotic analysis, which needs the use of advanced mathematical tools, such as center manifold theory, normal forms, and bifurcation theory. Moreover, we present some perspectives, linking the models here presented with similar models, arising from different research fields. [ABSTRACT FROM AUTHOR]

The electronic, magnetic, mechanical, and other properties of crystalline substances are determined by their structure, i.e., by the periodicity and symmetry of the lattice; therefore, the determination of the structure is an important stage in the study of the characteristics of such materials. This paper considers a number of metals having a crystal lattice of the hexagonal closely packed (HCP) structural type: beryllium, cerium, cobalt, dysprosium, erbium, gadolinium, hafnium, holmium, lanthanum, lutetium, magnesium, neodymium, osmium, praseodymium, rhenium, ruthenium, scandium, terbium, titanium, thallium, thulium, yttrium, and zirconium. The application of the annealing simulation algorithm to find the metric parameters of the materials under consideration is shown using the close packing model, which is widely used in crystallographic calculations. The in-house software implementation of the simulated annealing algorithm presented in this paper allows us to determine the coordinates of the atoms included in the unit cell of the crystal lattice, as well as calculate the lattice constants and the packing density of atoms in the crystal cell of the HCP structural type using the given chemical formula and spatial symmetry group. These structural characteristics can be used as the input parameters in modeling the electronic, magnetic, and other properties of the considered materials. This paper compares the values of the crystal lattice constants obtained as a result of the numerical simulation with the published data. [ABSTRACT FROM AUTHOR]

The optimal construction of long-span ziplines represents a complex engineering and construction task, especially from a safety point of view. In contemporary literature and engineering practice, there are no appropriate theoretical bases, standards and recommendations directly related to this issue. The aim of this work is to try to define the appropriate theoretical and professional basis for the design of these devices. The paper describes the procedure for creating a mathematical model of a zipline, followed by experimental verification of the formed mathematical model on a particular zipline, and afterwards by an analysis of the influencing parameters. The beginning of the paper defines the theoretical background that is necessary for the mathematical model forming of descending a rider down a heavy rope that takes into account mechanical and aerodynamical resistances that occur during the descent, after which a description of formation of the model itself is given. The next part of the paper gives a detailed description of the zipline on which the measurements were made, and a complete description of the used measuring equipment. Then succeeding part contains measurement results, followed by verification of the mathematical model by comparing the measured and calculated values. In the end, the influence of relevant parameters are analyzed by using the mathematical model and adequate conclusions are drawn. [ABSTRACT FROM AUTHOR]

In modern discrete functional semiconductor devices and structural elements of micro- and nanoelectronics, use is made of materials with anisotropy of electrical properties. In particular, such materials are crystalline thermoelectrics, layered graphite structures, and strained silicon. In the practical application of these semiconductors, it becomes necessary to measure their kinetic coefficients. However, the electrodynamics of these media differs from that of isotropic ones, which requires the correction of existing methods for measuring the conductivity and concentration of the majority charge carriers. The paper presents a technique for solving the Neumann problem with inhomogeneous boundary conditions for the electric field potential in a rectangular region in a relatively weak magnetic field in a linear approximation. The boundary value problem considered in the paper is encountered in the analysis of measurements of the Hall effect by probe methods. Using the perturbation theory and the Fourier method, an expression for the Hall field potential is obtained and presented in rectangular coordinates as a series of harmonic functions, which is convenient for further application. Practically important expressions for analyzing the results of Hall measurements by probe methods have been obtained for anisotropic samples with flat boundaries. Analysis of the obtained solution and computer simulation of the electric potential in anisotropic semiconductor wafers with flat boundaries are performed. An experimental verification of the obtained distributions of potentials and practical recommendations on the application of the obtained theoretical expressions are presented. [ABSTRACT FROM AUTHOR]

Objective: The purpose of this paper is to re-visit the design of three steps in the freeze-drying process, namely freezing, primary drying, and secondary drying steps. Specifically, up-to-date recommendations for selecting freeze-drying conditions are provided based on the physical–chemical properties of formulations and engineering considerations. Methods and Results: This paper discusses the fundamental factors to consider when selecting freezing, primary drying, and secondary drying conditions, and offers mathematical models for predicting the duration of each segment and product temperature during primary drying. Three simple heat/mass transfer primary drying (PD) models were tested, and their ability to predict product temperature and sublimation time showed good agreement. The PD models were validated based on the experimental data and utilized to tabulate the primary drying conditions for common pharmaceutical formulations, including amorphous and partially crystalline products. Examples of calculated drying cycles, including all steps, for typical amorphous and crystalline formulations are provided. Conclusions: The authors revisited advice from a seminal paper by Tang and Pikal (Pharm Res. 21(2):191-200, 2004) on selecting freeze-drying process conditions and found that the majority of recommendations are still applicable today. There have been a number of advancements, including methods to promote ice nucleation and computer modeling for all steps of freeze-drying process. The authors created a database for primary drying and provided examples of complete freeze-drying cycles design. The paper may supplement the knowledge of scientists and formulators and serve as a user-friendly tool for quickly estimating the design space. [ABSTRACT FROM AUTHOR]

With this note, we want to open a discussion on the duality theory for Interval Optimization. We begin by showing that some duality results Wu ( J Optim Theory Appl 144:615-628, ) are useless. [ABSTRACT FROM AUTHOR]

Since the discovery and the development of many technological instruments such as modern communication and communication technologies, digital media has served widely from the technology, and thus intersected quasi all life's domains, by providing news, information, and also discussions of quasi all subjects. In social sciences, for example, a major part of digital media sites discusses the well-being of both individuals, and societies, especially with the presence of many challenging phenomena like pandemics, wars, and financial crises. A major concern for QoL index for example resides in whether it is a uniform stable index or on the contrary a non-uniform index depending strongly and point-wisely on the time scale. This motivates the consideration of a non-uniform QoL index based on non-uniform wavelets to take into account the influence of many factors issued from political, social, environmental, economic effects according to the time scale. The model developed is tested on Saudi Arabia QoL index case. Recall that the Kingdom of Saudi Arabia has fixed many aims in its 2030-vision plan including the quality of life as a major goal. For example, the KSA worldwide NEOM project necessitates surely a supportive environment to be realized. The second purpose of our paper is also to study the impact of digital media such as social one on the QoL. Therefore, the data collected is basically issued from a set of conversations on social media platforms. To obtain a suitable time series, we developed a backward-forward non-uniform wavelet forecasting model to extend the data sample suitably. The whole time series is by the next applied for the QoL index dynamics and interpretations. The findings showed that effectively, the QoL index is never a stable single index on the whole year, but on the contrary, the dependence on the time scale is non-uniform. Moreover, to interpret suitably and for a correct policy, the non-uniform behavior should be considered adequately. [ABSTRACT FROM AUTHOR]

In the traditional tobacco drying process, there is often a problem of uneven drying, which is closely related to drying conditions such as air velocity and temperature. To better understand the drying characteristics of tobacco, its drying kinetic performance were experimentally studied and predicted in this paper. In the drying experiment, the range of air temperature and velocity is 20–60℃ and 0.95–4.93 m/s, respectively. The results show that the effective diffusion coefficient increases with the increase of air temperature and decreases with the increase of air velocity. The effective moisture diffusivity( D eff ) ranges from 2.077 × 10–7 to 9.136 × 10–7 m2/s. Additionally, the activation energy (Ea) is between 14.292 and 21.032 kJ/mol according to Arrhenius law. Among the six commonly used empirical correlations, the logarithmic model has higher prediction accuracy, but it has a prediction deviation of more than 20% in the later stage of drying. Based on the logarithmic model and the two models, a new prediction model of tobacco drying characteristics was proposed with a maximum relative deviation error of less than 1%. [ABSTRACT FROM AUTHOR]

In this paper, the structural vibration control of short-period systems by a sliding model of a tuned liquid column damper (herein referred to as STLCD) is investigated from both theoretical and experimental points of view. The proposed STLCD is essentially composed of a U-tube container with liquid inside, which can slide on a linear guide rail and is connected to the structure by a spring-dashpot system. Unlike traditional fixed TLCDs, this type of arrangement allows the proposed STLCD to be tuned to short-period structural systems since the spring can be used for tuning while the dashpot provides additional damping. Details on the selection of the optimal design parameters of the STLCD are provided, and the validity of the introduced mathematical model is verified both in time and frequency domains through experimental tests conducted at the Laboratory of Experimental Dynamics at the University of Palermo, Italy. For the experimental tests, a scale model of an STLCD-controlled structure is considered, focusing on the reduction of the roof accelerations. Finally, for comparison purposes, the control performance of the proposed control strategy for the vibration suppression of stiff structures is evaluated by analyzing its structural responses in contrast with the corresponding uncontrolled structure under harmonic excitations. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the difference between the deterministic and stochastic models of nonlocal diffusion. We use a nonlocal reaction-diffusion equation and a multi-dimensional jump Markov process to analyze these mathematical models. First, we demonstrate that the difference converges to 0 in probability with a supremum norm for a sizeable network. Next, we consider the rescaled difference and show that it converges to a stochastic process in distribution on the Skorokhod space. [ABSTRACT FROM AUTHOR]

Elite sports contexts are highly pressurised and frequently enforce a win-at-all-costs approach. This narrow focus on performance outcomes can potentially contribute in negative ways to the mental health of those within these environments. In this Current Opinion paper, we propose a model that outlines how key elements contributing to psychologically safe or unsafe environments may contribute to better or worse mental health outcomes, respectively. In an environment in which individuals feel safe to show their authentic selves rather than 'wear a mask', different experiences of mental health are likely to be normalised, help-seeking behaviour increased, and thus, mental health outcomes enhanced. We outline how sports teams and organisations can contribute to this through the creation of appropriate policies and procedures, in addition to leaders modelling and reinforcing positive cultural norms. It is intended that the theoretical model can inform stakeholders in elite sport as well as future research directions. [ABSTRACT FROM AUTHOR]

The penetration coefficient can represent the relationship between force and depth in the rock drilling process, but its understanding is limited. Therefore, based on the rock drilling theory with a hydraulic breaking hammer, a mathematical model of the penetration coefficient is established in this paper, and the main influencing factors of the penetration coefficient are determined. The discrete element method is used to establish a rock simulation model that can represent the real characteristics, and the variation law of the penetration coefficient under cyclic impact is studied. In addition, the drilling processes of drill bits with different impact velocities, shapes, and angles are simulated to evaluate the effects of operational parameters on the penetration coefficient. The results show that cyclic impact will change the rock cohesion and affect the change in the penetration coefficient. With an increase in impact times by the same drill bit, the penetration coefficient first increases and tends to be stable, and then decreases. Regarding operational parameters, the impact velocity has little effect on the penetration coefficient, while the shape and angle of the drill bit have a significant effect on the penetration coefficient, and a drill bit with a smaller angle is accompanied by more rock debris. Highlights: A theoretical model of the penetration coefficient is established. DEM simulation reveals the rock drilling mechanism under cyclic impact. The effect law and significance of operation parameters are obtained. [ABSTRACT FROM AUTHOR]

Clinical abbreviation disambiguation is a crucial task in the biomedical domain, as the accurate identification of the intended meanings or expansions of abbreviations in clinical texts is vital for medical information retrieval and analysis. Existing approaches have shown promising results, but challenges such as limited instances and ambiguous interpretations persist. In this paper, we propose an approach to address these challenges and enhance the performance of clinical abbreviation disambiguation. Our objective is to leverage the power of Large Language Models (LLMs) and employ a Generative Model (GM) to augment the dataset with contextually relevant instances, enabling more accurate disambiguation across diverse clinical contexts. We integrate the contextual understanding of LLMs, represented by BlueBERT and Transformers, with data augmentation using a Generative Model, called Biomedical Generative Pre-trained Transformer (BIOGPT), that is pretrained on an extensive corpus of biomedical literature to capture the intricacies of medical terminology and context. By providing the BIOGPT with relevant medical terms and sense information, we generate diverse instances of clinical text that accurately represent the intended meanings of abbreviations. We evaluate our approach on the widely recognized CASI dataset, carefully partitioned into training, validation, and test sets. The incorporation of data augmentation with the GM improves the model's performance, particularly for senses with limited instances, effectively addressing dataset imbalance and challenges posed by similar concepts. The results demonstrate the efficacy of our proposed method, showcasing the significance of LLMs and generative techniques in clinical abbreviation disambiguation. Our model achieves a good accuracy on the test set, outperforming previous methods. [ABSTRACT FROM AUTHOR]

Lighter-than-air (LTA) aerial vehicles such as airships and aerostats can be found in various strategic and commercial applications, primarily due to their capability to hover and stealth. The mathematical model of these vehicles helps in understanding their complex dynamics and designing and developing proper stabilisation systems for them. Stability derivatives have been used for developing mathematical models for heavier-than-air aerial vehicles since their introduction. This paper presents a methodology to develop a mathematical model of an aerostat based on stability derivatives. One of the major contributions of this study is the estimation of aerostat's added mass terms expressed as longitudinal stability derivatives due to acceleration of the longitudinal motion variables. A longitudinally decoupled linear mathematical model of a single-tethered aerostat using stability derivatives is investigated in this study. A computational fluid dynamics (CFD)-based analysis of the 3D model of the vehicle is used to obtain the stability derivatives. The methodology presented considers the aerostat and tether models separately before coupling them to create the full model. The stability derivative analysis is carried out using ANSYS Fluent, and the coupled tethered aerostat model is investigated using MATLAB 2020. The negative pitch angle of the aerostat is caused by the selection of the pitching centre as the aerostat centre of volume instead of the tether confluence point. The tension force on the tether, which is proportional to the wind velocity, and aerostat velocity components are found to be stabilised within 200–400 s. [ABSTRACT FROM AUTHOR]

Sustainability is an issue of worldwide concern. Twitter is one of the most popular social networks, which makes it particularly interesting for exploring opinions and characteristics related to issues of social preoccupation. This paper aims to gain a better understanding of the activity related to sustainability that takes place on twitter. In addition to building a mathematical model to identify account typologies (bot and human users), different behavioural patterns were detected using clustering analysis mainly in the mechanisms of posting tweets and retweets). The model took as explanatory variables, certain characteristics of the user's profile and her/his activity. A lexicon-based sentiment analysis in the period from 2006 to 2022 was also carried out in conjunction with a keyword study based on centrality metrics. We found that, in both bot and human users, messages showed mostly a positive sentiment. Bots had a higher percentage of neutral messages than human users. With respect to the used keywords certain commonalities but also slight differences between humans and bots were identified. [ABSTRACT FROM AUTHOR]

The paper considers the problem of controlling processes whose mathematical model is an initial–boundary value problem for a pseudohyperbolic linear differential equation of high order in the spatial variable and second order in the time variable. The pseudohyperbolic equation is a generalization of the ordinary hyperbolic equation typical in vibration theory. As examples, we consider models of vibrations of moving elastic materials. For the model problems, an energy identity is established and conditions for the uniqueness of a solution are formulated. As an optimization problem, we consider the problem of controlling the right-hand side so as to minimize a quadratic integral functional that evaluates the proximity of the solution to the objective function. From the original functional, a transition is made to a majorant functional, for which the corresponding upper bound is established. An explicit expression for the gradient of this functional is obtained, and adjoint initial–boundary value problems are derived. [ABSTRACT FROM AUTHOR]

Recovering three-dimensional structure from images is one of the important researches in computer vision. The quality of feature matching is one of the keys to obtaining more accurate results. However, as different objects or different surfaces of objects have similar images with the same elements and different typography, the camera pose estimation will be wrong and the task will fail. This paper proposes a new mismatch elimination algorithm based on global topology consistency. We first formulate the matching task as a mathematical model based on the global constraints, then convert the feature matching into grid matching, calculate the confidence of the grids according to the changes in the angle and displacement between correspondence grid vectors, and remove the mismatches with low confidence. The experiments have demonstrated that our proposed method performs better than the state-of-the-art feature matching methods to accomplish outlier match rejection in the task of similar image matching and could be helped to obtain the correct camera pose to reconstruct more complete and more accurate object models. [ABSTRACT FROM AUTHOR]

Mathematical models of cancer and bacterial evolution have generally stemmed from a gene-centric framework, assuming clonal evolution via acquisition of resistance-conferring mutations and selection of their corresponding subpopulations. More recently, the role of phenotypic plasticity has been recognized and models accounting for phenotypic switching between discrete cell states (e.g., epithelial and mesenchymal) have been developed. However, seldom do models incorporate both plasticity and mutationally driven resistance, particularly when the state space is continuous and resistance evolves in a continuous fashion. In this paper, we develop a framework to model plastic and mutational mechanisms of acquiring resistance in a continuous gradual fashion. We use this framework to examine ways in which cancer and bacterial populations can respond to stress and consider implications for therapeutic strategies. Although we primarily discuss our framework in the context of cancer and bacteria, it applies broadly to any system capable of evolving via plasticity and genetic evolution. [ABSTRACT FROM AUTHOR]

Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. While current methods can identify such equations, they often require extensive manual hyperparameter tuning, limiting their applicability. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques to smooth the signal, sparse regression to identify the relevant parameters, and bootstrap confidence intervals to quantify the uncertainty of the estimates. We evaluate our method on well-known ordinary differential equations with an ensemble of random initial conditions, time series of increasing length, and varying signal-to-noise ratios. Our algorithm consistently identifies three-dimensional systems, given moderately-sized time series and high levels of signal quality relative to background noise. By accurately discovering dynamical systems automatically, our methodology has the potential to impact the understanding of complex systems, especially in fields where data are abundant, but developing mathematical models demands considerable effort. Discovering nonlinear differential equations from empirical data is a significant challenge, often requiring manual parameter tuning. This paper introduces a machine learning method integrating denoising techniques, sparse regression, and bootstrap confidence intervals, which shows consistent accuracy in identifying 3D dynamical systems with moderate data size and high signal quality. [ABSTRACT FROM AUTHOR]

The paper introduces a mathematical model based on the discrete element method, presenting the results of its application to simulate the movement of briquetted mass within the working chamber of the extruder. This model accounts for the adhesive interaction among particles within the mixture. The simulation results provide a qualitative and quantitative description of the displacement and compaction of the briquetted mass. They allow the flow structure to be visualized and the distribution of velocities and the moment on the screw axis during the extrusion process to be determined. Furthermore, a digital twin of the pug sealer–extruder unit was created through finite element modeling. The results obtained from this digital twin can be used to optimize the operational parameters of extrusion briquette equipment. In addition, by using the developed model, the process of mixing binder materials with a briquetted mixture at various volumes of the added binder was studied. [ABSTRACT FROM AUTHOR]