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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]

Purpose: The present paper presents developments and advanced practical applications of Rasch's theory and statistical analysis to construct questionnaires for measuring a person's traits. The flaws of questionnaires providing raw scores are well known. Scores only approximate objective, linear measures. The Rasch Analysis allows you to turn raw scores into measures with an error estimate, satisfying fundamental measurement axioms (e.g., unidimensionality, linearity, generalizability). A previous companion article illustrated the most frequent graphic and numeric representations of results obtained through Rasch Analysis. A more advanced description of the method is presented here. Conclusions: Measures obtained through Rasch Analysis may foster the advancement of the scientific assessment of behaviours, perceptions, skills, attitudes, and knowledge so frequently faced in Physical and Rehabilitation Medicine, not less than in social and educational sciences. Furthermore, suggestions are given on interpreting and managing the inevitable discrepancies between observed scores and ideal measures (data-model "misfit"). Finally, twelve practical take-home messages for appraising published results are provided. The current work is the second of two papers addressed to rehabilitation clinicians looking for an in-depth introduction to the Rasch analysis. The first paper illustrates the most common results reported in published papers presenting the Rasch analysis of questionnaires. The present article illustrates more advanced applications of the Rasch analysis, also frequently found in publications. Twelve take-home messages are given for a critical appraisal of the results. [ABSTRACT FROM AUTHOR]

A mathematical model has been proposed to consider two distinct forms of psychological pressure that arise due to the COVID-19 situation and their impact on individuals' lives, including their mental well-being and happiness. For a more realistic situation, the effect of stochasticity should be taken into account. Hence, our paper mainly investigates the effect of stochastically environmental variability on the transmission dynamics of psychological stress. We obtain two thresholds ℛ s 1 and ℛ s 2 . If ℛ s 1 > 1 , the psychological stress will persist and there will be a unique stationary distribution; whereas if ℛ s 2 < 1 , the extinction of psychological stress is obtained. Moreover, we display the mean first passage time from the initial value to the state of disappearance in order to examine the impact of environmental disturbances; meanwhile, we conduct numerical simulations to illustrate the theoretical findings. [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]

In this paper, we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational inequality for the displacement field. We prove the unique weak solvability of the problem, then we state and prove some convergence results, for which we provide the corresponding mechanical interpretation. Next, we turn to the numerical approximation of the problem based on a finite element scheme. We use a relaxation method to solve the discrete problems that we implement on the computer. Using this method, we provide numerical simulations which validate our convergence results. [ABSTRACT FROM AUTHOR]

We present an intriguing topic in a mathematical modelling course where Lanchester models are taught to our students. Lanchester models are some of the earliest and most important models used for combat modelling. We describe modelling activities and the use of technology that can be implemented in teaching this topic in this paper. [ABSTRACT FROM AUTHOR]

Compartmental systems like the well‐famed SIR, SEIR, SQIR, SVIR, and their variants are efficient tools for the mathematical modeling of infectious illnesses, and they permit us to get a clear picture of how they proliferate. In actuality, the aleatory fluctuations factors present in the natural environment like storm surges, weather changes, and seismic tremors make the dissemination of epidemics susceptible to some randomness. This calls for a stronger mathematical formulation that takes into consideration this stochasticity effect. From this perspective, and in order to highlight in the same time the effect of the vaccination strategy, we survey in this paper an SVIR model with general incidence rates that is disturbed by both Brownian motions and Lévy jumps. Initially, we establish its well‐posedness in the sense that it has a unique positive and global‐in‐time solution. Then, we rely on some assumptions and nonstandard analytic techniques, to derive sufficient and almost necessary conditions for extinction, persistence in the mean, and also weak persistence. More explicitly, we identify firstly under some hypotheses a threshold λ$$ \lambda $$ between extinction and persistence in the mean. In other phrases, if λ<0$$ \lambda &lt;0 $$, the infected population dies out while it persists in the mean when λ>0$$ \lambda &gt;0 $$. Then, and by modifying the hypothetical framework in order to cover more incidence rates, we prove that λ$$ \lambda $$ can act also as a threshold between extinction and weak persistence. At last, we provide some numerical simulations to corroborate our findings and cover some particular cases of response functions. [ABSTRACT FROM AUTHOR]

The paper proposes a methodology for mathematical modeling of the phased development of nodes and transport routes in a hierarchical network with multicommodity discrete flows of correspondences based on solving the problems of optimizing its structure and distribution of flows. As a rule, such networks consist of a decentralized mainline network and networks in the internal service areas of mainline nodes. In a multicommodity network, each node can exchange correspondence (products, goods, cargo, messages) with the other nodes. Correspondence is characterized by a source node, a sink node, and a quantity, which for data transmission networks is given by the number of bytes, kilobytes, etc., and for transport networks by the number of cargo units in a package of uniform size. In the mainline network, all correspondences are transmitted via communication channels or transported by vehicles in transport units of a given size (capacity, volume). The authors considered the main postulates of generating a mathematical model of the perspective development of mainline network. They presented a method of mathematical modeling of the phased development of nodes and transport routes, which includes, for each stage of development, the forecasting of data and network parameters, solving the problem of packing correspondence and choosing the structure of the network, and solving the problem of distribution and routing of transport unit flows. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a mathematical model of atherosclerosis in one-dimensional geometry with a free boundary. The motion of the boundary is attributable to the concentration of cells in the intima and their interaction in the subendothelial space in addition to their influx through the boundary. A mathematical model that describes the main inflammatory processes in atherosclerosis is proposed, then, by considering some simplifications, a reduced model is obtained. Using a change of variables, the reduced model is converted to a fixed boundary model with space- and time-dependent coefficients and nonlinear terms. We study the existence of solution for the fixed boundary model starting with a model with linear terms then by applying the fixed point theorem. The wave solution is as well investigated along with numerical simulations. Then, we return to the reduced model, prove the existence of solution and present numerical results. Finally, we generalize the results to the complete model initially proposed. [ABSTRACT FROM AUTHOR]

This article presents a discussion on a study by Bradley Jones and Rachel T. Johnson on the use of Gaussian Process model in computer simulation research. The authors believe that the uncertainty intervals on unsampled points generated by using a plug-in approach from maximum likelihood estimates may be too short. Their own experiences confirm that computer models are widely used in many areas of science and engineering, and the need to understand the performance of such models is critical.

This paper proposes a modification of a Sliding Mode Classical Observer (SMCO) to adapt it to the fractional approach. This adaptation involves using a set of definitions based on fractional calculus theory, particularly the approach developed by Riemann–Liouville, resulting in a Sliding Mode Fractional Observer (SMFO). Both observers are used to perform disturbance reconstruction considered additive in a Quadrotor Unmanned Aerial Vehicle (UAV) model. Then, this work presents the fractional-order sliding mode observer's mathematical formulation and integration into the Quadrotor UAV model. To validate the quality of the disturbance reconstruction process of the proposed SMFO observer scheme, numerical simulations are carried out, where a reconstruction quality indicator (BQR) is proposed based on the analysis of performance indices such as the Mean Square Error (MSE), the First Probability Moment (FPM), and Second Probability Moment (SPM), which were obtained for both the SMCO and the SMFO. The simulation results demonstrate the efficacy of the proposed observer in accurately reconstructing disturbances under various environmental conditions. Comparative analyses with SMCO highlight the advantages of the fractional-order approach in terms of reconstruction accuracy and improvement of its transitory performance. Finally, the presented SMFO offers a promising avenue for enhancing the reliability and precision of disturbance estimation, ultimately contributing to the advancement of robust control strategies for Quadrotor UAV systems. [ABSTRACT FROM AUTHOR]

Micro-Electro-Mechanical System (MEMS)-based pressure sensors operating on the principle of piezoresistivity have found profound application in various fields like automobile, aerospace, aviation, biomedical and consumer electronics. Various research studies have been conducted to optimize the design of MEMS-based pressure sensors to meet specific requirements of different fields. Modification in the structure of the piezoresistors placed on these sensors has shown great effect in this regard. However, most of these improvements have been validated through fabrication and measurement, but there has been a lack of significant studies developing analytical models to explain these improvements. This paper studies the performance of a single-turn piezoresistor design on a square silicon diaphragm. The analytical model relates the dimensions of the single-turn piezoresistor on a square diaphragm to the output voltage, and hence, sensor sensitivity is laid out. The correctness of the relation is also validated through Finite Element Analysis (FEA) performed using COMSOL Multiphysics software. Hence, an optimized single-turn design is presented which achieves a sensitivity of 203.57 mV/V/MPa over a pressure range of 0–1 MPa. These results are then compared to work from existing literature. The comparison shows an improved performance which was achieved by optimizing the design through its derived analytical model. The proposed sensor can be utilized in disposable blood pressure measurement system where high sensor sensitivity is required. [ABSTRACT FROM AUTHOR]

The use of linear transformer drivers (LTDs) is widely considered the most promising technological approach for the development of future pulsed-power accelerators. In large-scale pulsed-power accelerators, abnormal conditions like switch prefire can occur frequently during tests and normal operations due to the presence of a large number of switches. The diagnosis of such faults based on signature waveforms requires further investigation. According to previous research, the characteristics of the magnetic cores greatly influence the fault waveforms. In this paper, a full-cycle mathematical model of the magnetic core is established utilizing a classical Preisach model based on experimental results. This model is coupled with the LTD circuit model in simulations, and simulation results are obtained under the condition of switch prefire. The simulation results are in good agreement with the experimental results from a four-stage LTD module with a sharing shell and de-ionized water insulated transmission line. The magnetization process of the cores is also determined under prefire conditions. Analyses of the magnetization process indicate that the completely demagnetized core shows high permeability under positive excitation and that the permeability abruptly decreases as the excitation is reversed. The hysteresis characteristics result in a phenomenon in which the output voltage in the prefired stage is almost unipolar. Finally, the features of the fault voltages captured in the experiments are also explained. [ABSTRACT FROM AUTHOR]

Rectangular concrete-filled steel tubular (RCFST) columns can be designed to have unequal wall thickness to maximize their resistance to combined axial and uniaxial bending loads. However, there is very little published research on their local–global interaction buckling behavior. This paper presents an efficient fiber-based simulation model for analyzing the inelastic interaction buckling of eccentrically loaded RCFST slender columns with unequal wall thickness. The model considers the progressive local–global interaction buckling, distributed plasticity, concrete cracking and crushing, second-order effects, and geometric imperfections. The mathematical model is programmed to compute not only the axial load–displacement responses but also the interaction curves of axial load and moment of slender RCFST columns. The simulation modeling is validated by experimentally measured data. The validated computer model is used to parametrically study the interaction local–global buckling responses of RCFST columns while the range analysis is conducted to identify the relative significance of key parameters. It is demonstrated that the proposed computer model accurately simulates experimentally measured responses. Hence, it can be used with confidence in practice to analyze and design RCFST slender columns fabricated with steel plates of unequal thickness. The existing design standard AS/NZS 2327:2017 provides acceptable strength predictions of RCFST slender columns and beam-columns while the procedure specified in Eurocode 4 overestimates their capacities. [ABSTRACT FROM AUTHOR]

This paper proposes a new method to improve re performance of intra-field interpolation which is the mos~ important element of deinterlacing method. Traditional edge- based methods were poor at determining accurate edge iirection which decides interpolation performance. The 7roposed method decides the direction and slope of edge based on locally adaptive-thresholded binary image to mprove efficiency and accuracy, and it also increased the ~orizontal size of search window to 15 for better direction ietermination at gentle slope. Compared to traditional edge- based methods, interpolation based on binary image, which is ,`enerated using the proposed method, leads to great erformance improvement. With computer simulations for a ~`ariety of images, this paper shows the new approach is much ~etter than traditional methods.. [ABSTRACT FROM AUTHOR]

This paper presents an implementation of an ~daptive beamformer in a hands-free unit. The proposec~ ~daptive beamformer suppresses stationary noise an~ nterference sound. The adaptive beamformer and acoustic `cho canceller were implemented in a compact hands-free mit with a low-cost DSP. Experimental results demonstrate he noise reduction performance of the hands-free unit'. [ABSTRACT FROM AUTHOR]

To have a more realistic model, in this paper, This manuscript is devoted to investigating a fractional-order mathematical model of Kouidere et al. That describes the dynamics of spread of African swine fever virus (ASFV). The aim of this work is to protect susceptible pigs from the virus, In our model, by including three controls which represent: the iron fencing and spraying pesticides and get rid. The aims of this paper is to reduce the number of infected pigs and ticks by using optimal control strategy and fractinal order derivation. Pontryagin's maximal principle is used to describe optimal controls with Caputo time-fractional derivative and the optimal system is resolved in an iterative manner. Numerical simulations are presented based on the presented method. We finished tis article with a conclusion. [ABSTRACT FROM AUTHOR]

In this paper, the mathematical modeling of the novel corona virus (COVID-19) is considered. A brief relationship between the unknown hosts and bats is described. Then the interaction among the seafood market and peoples is studied. After that, the proposed model is reduced by assuming that the seafood market has an adequate source of infection that is capable of spreading infection among the people. The reproductive number is calculated and it is proved that the proposed model is locally asymptotically stable when the reproductive number is less than unity. Then, the stability results of the endemic equilibria are also discussed. To understand the complex dynamical behavior, fractal-fractional derivative is used. Therefore, the proposed model is then converted to fractal-fractional order model in Atangana-Baleanu (AB) derivative and solved numerically by using two different techniques. For numerical simulation Adam-Bash Forth method based on piece-wise Lagrangian interpolation is used. The infection cases for Jan-21, 2020, till Jan-28, 2020 are considered. Then graphical consequences are compared with real reported data of Wuhan city to demonstrate the efficiency of the method proposed by us. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of chaos control in an economic mathematical dynamical model. By regarding the control variables as the bifurcation parameters, the stability of equilibria and the existence of Hopf bifurcations of the relevance feedback system are investigated, and the criterion of controllability for the chaotic system is obtained based on a time-delayed feedback control technique. Furthermore, numerical simulations are provided to demonstrate the feasibility of our methods and results. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the stability of hydro-turbine governing system (HTGS) with sloping ceiling tailrace tunnel (SCTT) and upstream surge tank (UST) considering nonlinear hydro-turbine characteristics (NHTCs). Firstly, the mathematical model of HTGS is presented based on nonlinear seventh-order state equation, which is verified by example analysis so as to study the stability of HTGS. Subsequently, the effect of HTGS parameters on the stability of the system is investigated with numerical simulation. Finally, the coupling effect mechanism of SCTT and UST on stability under the effect of NHTCs is revealed by using contrastive analysis. The results are summarized as follows: (1) T a , K d and T wt perform larger effect on the stability of HTGS, while the influence of F and T wy is mild; (2) the NHTCs are beneficial under negative load disturbance and unfavorable under positive load disturbance for the stability and dynamic performance of HTGS; (3) the coupling effect of SCTT and UST outperforms the results of SCTT or UST alone under all load disturbances; (4) the incorporation of UST to the established model plays a certain role in stability compensation, while the introduction of SCTT not only improves the stability but also achieves smaller amplitude and lower frequency. [ABSTRACT FROM AUTHOR]

This article presents a discussion on a study by Bradley Jones and Rachel T. Johnson on the use of Gaussian Process model in computer simulation research. The author believes that the researchers offer a clear and helpful introduction to ideas and methods used in the design and analysis of computer experiments. He provides some additional points of importance regarding analysis, design and computing.

This article presents a discussion on a study by Bradley Jones and Rachel T. Johnson on the use of Gaussian Process model in computer simulation research. The author believes that the Gaussian process model often performs adequately apparent nonstationarity. He explores the topic of model calibration, the relationship between the design and the model used to fit the data, and design augmentation.

This paper deals with the modeling and numerical simulations of multilane vehicular traffic according to the kinetic theory of active particles methods. The main idea of this theory is to consider each driver–vehicle system as a micro-system, where the microscopic state of particles is described by position, velocity, and activity which is an appropriate variable for modeling the quality of the driver-vehicle. The interactions between micro-systems are modeled by stochastic game theory. This leads to the derivation of a mathematical model within the framework of the approach of kinetic theory. The well-posedness of the related Cauchy problem for the spatially homogeneous case is established. Numerical simulations are carried out to show the ability of the proposed model to reproduce the empirical data such as the asymptotic property in time and the emerging behavior of clusters with a particular focus on the road environment conditions. [ABSTRACT FROM AUTHOR]

Modal-free optimization algorithms do not require specific mathematical models, and they, along with their other benefits, have great application potential in adaptive optics. In this study, two different algorithms, the single-dimensional perturbation descent algorithm (SDPD) and the second-order stochastic parallel gradient descent algorithm (2SPGD), are proposed for wavefront sensorless adaptive optics, and a theoretical analysis of the algorithms' convergence rates is presented. The results demonstrate that the single-dimensional perturbation descent algorithm outperforms the stochastic parallel gradient descent (SPGD) and 2SPGD algorithms in terms of convergence speed. Then, a 32-unit deformable mirror is constructed as the wavefront corrector, and the SPGD, single-dimensional perturbation descent, and 2SPSA algorithms are used in an adaptive optics numerical simulation model of the wavefront controller. Similarly, a 39-unit deformable mirror is constructed as the wavefront controller, and the SPGD and single-dimensional perturbation descent algorithms are used in an adaptive optics experimental verification device of the wavefront controller. The outcomes demonstrate that the convergence speed of the algorithm developed in this paper is more than twice as fast as that of the SPGD and 2SPGD algorithms, and the convergence accuracy of the algorithm is 4% better than that of the SPGD algorithm. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to propose new mathematical models for simulation of biosensors and to construct and investigate discrete methods for the efficient solution of the obtained systems of nonlinear PDEs. The classical linear diffusion operators are substituted with nonlocal fractional powers of elliptic operators. The splitting type finite volume scheme is used as a basic template for the introduction of new mathematical models. Therefore the accuracy of the splitting scheme is investigated and compared with the symmetric Crank-Nicolson scheme. The dependence of the approximation error on the regularity of the solution is investigated. Results of computational experiments for different values of fractional parameters are presented and analysed. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid variable-order mathematical model for multi-vaccination COVID-19 is analyzed. The hybrid variable-order derivative is defined as a linear combination of the variable-order integral of Riemann–Liouville and the variable-order Caputo derivative. A symmetry parameter σ is presented in order to be consistent with the physical model problem. The existence, uniqueness, boundedness and positivity of the proposed model are given. Moreover, the stability of the proposed model is discussed. The theta finite difference method with the discretization of the hybrid variable-order operator is developed for solving numerically the model problem. This method can be explicit or fully implicit with a large stability region depending on values of the factor Θ. The convergence and stability analysis of the proposed method are proved. Moreover, the fourth order generalized Runge–Kutta method is also used to study the proposed model. Comparative studies and numerical examples are presented. We found that the proposed model is also more general than the model in the previous study; the results obtained by the proposed method are more stable than previous research in this area. [ABSTRACT FROM AUTHOR]

Objective: Bioinformatics analyses have been becoming important research tools in the field of life science since 2000. New tools have been developed for the detection of allergens in food sources. This study investigated potential allergen proteins similar to the endochitinase class 1(Pers a 1) protein found in avocado using bioinformatics analysis tools. Materials and Methods: The potential allergens were examined with four different in silico tools: Clustal W for multiple sequence comparison, Swiss-MODEL for homology modeling, ProtParam for comparing protein parameters, and AlgPred for allergen prediction. Results: In silico analyses revealed high rates of similarities in protein sequences among the studied species. The highest percent identity was found in Cinnamomum micranthum f. kanehirae as 97.55 while the lowest percent identity was found in Diospyros kaki as 70.23. It is very important to note that 9 of the 10 potential allergen species investigated are plats consumed in daily life and these species were identified as allergens. According to the algorithm of BLAST search on allergen representative peptides (ARPs), ARPs were found in eight potential allergen proteins except for Prunus avium and Citrus unshiu. The ARP sequence related to Persea americana is LQLTWNYNYGAAGNSIGFNGLSNP. Conclusion: People who are allergic to avocado (Persea americana) may be advised to be careful while consuming foods such as Phoenix dactylifera, Allium sativum, Citrus unshiu, Diospyros kaki, and Spinacia oleracea. The present paper can be considered as a model study for understanding allergens in foods by using in silico tools. [ABSTRACT FROM AUTHOR]

This paper established a numerical simulation model to analyze the pressure transient and rate transient behaviors in reservoir with complex fracture network. Firstly, the fractures are introduced into the coordinate system through the position, angle, and length. Secondly, a mathematical model is established by using unstable seepage model. Thirdly, the central difference method was used to solve the model and local grid refinement method is introduced to describe the network fractures. Finally, we compared the results obtained from this paper's model with the production data. The results show acceptable and reasonable matches for typical well. Meanwhile, the sensitivity of two properties is discussed. The model solution is verified with an analytical method thoroughly. The novelty of this paper is to introduce each fracture in fracture network into the coordinate system. Then, the grid refinement is achieved according to the fracture information. The presented new model simplifies the analysis of the pressure transient and rate transient of the reservoir with complex fracture network, and it is more efficient than the conventional numerical method. Compared with the analytical methods, the new model describes the fractures system in more detail. However, the new model treats fractures as reservoirs with higher permeability in the central difference method, which is simpler and rougher than traditional numerical methods. [ABSTRACT FROM AUTHOR]

This paper concerns a hybrid vibration reduction system (HVRS) equipped with a linear electrodynamic motor (LM). The objective of the study was to implement the HVRS in a scaled vehicle suspension and reveal the benefits of its application in the system. First, a mathematical model of a quarter-vehicle suspension with the HVRS was formulated. Next, the dynamic similarity method was employed to conduct numerical simulations of the passive vibration reduction system (PVRS). Subsequently, an algorithm for HVRS controlling was developed. Then, the system was investigated experimentally under deterministic and random excitations. The results confirmed the effectiveness and applicability of the proposed HVRS. [ABSTRACT FROM AUTHOR]

This paper intends a Euler-Lagrange passivity-based controller (EL-PBC) for the three-level (TL) Ćuk PFC converter for EVs battery charging application. The TL Ćuk converter has features of reduced filter size and voltage stress of switches. First, the Euler-Lagrange formulation is used to develop the mathematical modelling. Then, the EL-PBC methodology is implemented by injecting a virtual resistor in series with the input inductor. Further, the stability analysis is also carried out. To improve the performances against input perturbations and reduce the steady state error, a PI controller is integrated with the aforesaid controller and its performances are investigated. Furthermore, the power quality of the charger is assessed and it satisfies IEC 61000-3-2 Class C standard. This controller is also compared with the benchmark PI controller. A prototype model of same specifications is tested in hardware in loop. Computer simulations and test results are presented to validate the theoretical aspects. [ABSTRACT FROM AUTHOR]

Through the use of a unique approach, we study the fractional Biswas–Milovic model with Kerr and parabolic law nonlinearities in this paper. The Caputo approach is used to take the fractional derivative. The method employed here is the homotopy perturbation transform method (HPTM), which combines the homotopy perturbation method (HPM) and Yang transform (YT). The HPTM combines the homotopy perturbation method, He's polynomials, and the Yang transform. He's polynomial is a wonderful tool for dealing with nonlinear terms. To confirm the validity of each result, the technique was substituted into the equation. The described techniques can be used to find the solutions to these kinds of equations as infinite series, and when these series are in closed form, they give a precise solution. Graphs are used to show the derived numerical results. The maple software package is used to carry out the numerical simulation work. The results of this research are highly positive and demonstrate how effective the suggested method is for mathematical modeling of natural occurrences. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is the numerical analysis of a class of mathematical models that describe the contact between a thermo-piezoelectric body and a conductive foundation. Under the assumption of a static process, the material's behavior is modeled with a linear thermo-electro-elastic constitutive law and the frictional contact with Signorini's and Tresca's laws. A variational problem is derived and the existence of a unique weak solution is proved by combining arguments from the theory of variational inequalities with linear strongly monotone Lipschitz continuous operators. A successive iteration technique to linearize the problem by transforming it into an incremental recursive form is proposed, and its convergence is established. An Augmented Lagrangian variant, known as the Alternating Direction Multiplier Method (ADMM), is employed to split the original problem into two subproblems, resolve them sequentially, as well as update the dual variables at each iteration. To illustrate the performance of the proposed approach, several numerical simulations on two-dimensional test problems are carried out. [ABSTRACT FROM AUTHOR]

In high-power laser systems, the large-aperture continuous phase plates (CPPs) are designed and fabricated with continuous varying structured topography to serve as the class of phase-modulating beam-conditioning optics. To achieve better optical performance, its fabrication highly depends on the reiterative figuring to eliminate the form error relative to the designed CPP surface. However, the characteristics of large aperture and complex structured topography make the quality inspection of CPPs still challenging. A typical inspection process includes measuring the CPPs with the sub-aperture stitching technique, followed by the characterization procedure with respect to the CPP design description. This paper proposes an innovative stitching-embedded characterization method for imprinting the large-aperture CPPs, which combines the sub-aperture stitching and characterization procedure together. First, the concept and mathematical model of the stitching-embedded characterization method is presented. Then, both numerical simulations and experiments were undertaken to verify the proposed method, and the results demonstrate its feasibility and reasonability to provide the more reliable form error evaluation while simplify the analysis procedure compared with the conventional inspection process. • The stitching-embedded characterization method is presented for imprinting the large-aperture CPPs. • The mathematical model is established to integrate the sub-aperture stitching into the characterization procedure. • Numerical simulations were undertaken to verify the proposed method, which can achieve sub-nanometer accuracy in simulation. • In application, the proposed method can achieve more reliable form error evaluation with lower time cost. [ABSTRACT FROM AUTHOR]

In this paper, a direct current (DC) motor speed control system with proportional-integral-derivative (PID) controller and Kalman filter is presented with consideration of disturbance, system variation, and feedback sensor noise and verified through computer simulations. Initially, a mathematical model for a DC motor system is introduced, after which the performance degradation due to disturbance and system variation in the basic open-loop control is revealed. To resolve this problem, a PID controller based feedback system is designed for the DC motor speed control system. Third, to improve the performance degradation due to feedback sensor noise that may occur during the feedback process, the Kalman filter is applied for the DC motor speed control system. Ultimately, it is verified that the designed DC motor speed control system with PID controller and Kalman filter not only satisfies all performance criteria but also has the ability to reject disturbance, cope with system variation and reduce feedback sensor noise. [ABSTRACT FROM AUTHOR]

Orthogonal/vector approximate message-passing (AMP) is a powerful message-passing (MP) algorithm for signal reconstruction in compressed sensing. This paper proves the convergence of Bayes-optimal orthogonal/vector AMP in the large system limit. The proof strategy is based on a novel long-memory (LM) MP approach: A first step is a construction of LM-MP that is guaranteed to converge systematically. A second step is a large-system analysis of LM-MP via an existing framework of state evolution. A third step is to prove the convergence of state evolution recursions for Bayes-optimal LM-MP via a new statistical interpretation of existing LM damping. The last is an exact reduction of the state evolution recursions for Bayes-optimal LM-MP to those for Bayes-optimal orthogonal/vector AMP. The convergence of the state evolution recursions for Bayes-optimal LM-MP implies that for Bayes-optimal orthogonal/vector AMP. Numerical simulations are presented to show the verification of state evolution results for damped orthogonal/vector AMP and a negative aspect of LM-MP in finite-sized systems. [ABSTRACT FROM AUTHOR]

Mechanics of multicomponent and multiphase media is a branch of fluid mechanics. Mathematical modeling of the dynamics of inhomogeneous media is of great importance because the experimental study of many of these processes is difficult. At the same time, many models are essentially nonlinear; for this reason, numerical methods are used to integrate such models. In a number of industrial energy technologies, to remove the dispersed component of an aerosol medium, gas–drop media are affected by acoustic fields. This is the reason for the interest in studying the dynamics of aerosols in acoustic fields, revealing the fundamental regularities of such flows, and also in developing mathematical models for the dynamics of aerosol media. Materials and methods. The paper presents a continuum mathematical model of aerosol dynamics. The model takes into account both intercomponent momentum exchange and intercomponent heat transfer. The system of equations of the mathematical model is solved by the finite difference method, and a nonlinear correction scheme is used to suppress numerical oscillations. Results. Oscillations of a gas suspension in a closed container at the resonance frequency are modeled. The distributions of physical parameters of the carrier medium and the dispersed component in the process of aerosol oscillations are obtained. Conclusions. Comparison of the results of numerical calculations with physical experiment data gives a satisfactory agreement. [ABSTRACT FROM AUTHOR]

In recent years, the mathematical model of memristor has attracted extensive attention from researchers, but the boundary effect of the memristor model is rarely considered. A memristor with the window function is proposed in this paper. First, the boundary effect of the device is ignored by the conventional memristive model, but the memristor model with the window function can effectively solve this problem. Then, based on the fractional difference theory, a discrete fractional mathematical model of memristor with the window function is studied. Meanwhile, the corresponding three memristor characteristics are verified for this model in the numerical simulations. Finally, the discrete fractional memristor model is applied to the Logistic map, and we construct a new chaotic map called the discrete fracmemristor Logistic map. The new chaotic sequence is observed. In addition, it provides important mathematical models for many fields, such as chaotic systems, chaotic circuits, and neural networks. [ABSTRACT FROM AUTHOR]

In this paper, role of chaotic systems with perpendicular line equilibrium, line equilibrium, and no-equilibrium is investigated by employing Mittage-Leffler kernel. The fractal-fractionalized mathematical and dynamical models have been observed for quasi-periodicity chaos and hyperchaos as well as simple periodicity chaos and hyperchaos. Each chaotic systems type is simulated on the basis on comparative analysis through Atangana-Baleanu fractal differential operator versus Atangana-Baleanu fractional differential operator. The numerical simulations have been performed by means of Adams-Bashforth-Moulton method for observing the controversial role of chaotic systems on the basis of phase portrait. The nonsingularity associate to the fractal fractional differentiation of Atangana-Baleanu has been introduced. Finally, 3D and 2D phase portraits of chaotic system with perpendicular line equilibrium, line equilibrium and no-equilibrium have been underlined to capture the similarities and differences among the depicted phase portraits parametrically. [ABSTRACT FROM AUTHOR]

The tip size of metal protrusions is an important factor affecting corona discharge, since it influences the electric filed, the ionization range and strength around the protrusion defect. Most existing studies on the influence of protrusion tip size on corona discharge are implemented by experimental methods. However, these studies are difficult to obtain the microphysical process of charged particles, which is related to the generation of current pulses and electromagnetic (EM) waves. In this paper, a hydrodynamic simulation model is proposed to study the effect of protrusion tip size on the microphysical process and current pulses of negative corona discharge. A mapping relationship between microscopic behaviors of charged particles and current pulses is established by this simulation method. Based on the comparison of microphysical quantities, the effect of defect tip size on the detailed parameters of current pulses is clearly explained. It shows that with the increase of tip size under a constant voltage, all the five parameters of current pluses increase. The rising time is related to the effective ionization coefficient, while the falling time is dependent on the velocities of positive and negative ions. The experiment and simulation results coincide in current waveforms and all five parameters. [ABSTRACT FROM AUTHOR]

Using both analytical and numerical methods, nonlinear dynamic behaviours including chaotic motions and subharmonic bifurcations of an inclined beam subjected to harmonic excitation in temperature field are investigated in this paper. Based on the Galerkin method, the mathematical model of motion is derived. Melnikov method is adopted to give an analytical expression of conditions for chaotic motions of the inclined beam. The chaotic feature on the inclined angle is studied in detail. It is presented that there exists a unique excitation frequency |$\omega ^*$|⁠ , such that the critical value of chaos is the monotone decreasing function of the inclination angle when the excitation frequency |$\omega <\omega ^*$|⁠ ; whereas |$\omega>\omega ^*$|⁠ , it is the monotone increasing function of the inclination angle. The subharmonic bifurcations are also studied. It is obtained that subharmonic bifurcations of even orders or odd orders may occur for this system. With the techniques of elliptic functions, it is proved rigorously that this system may undergo chaos through finite subharmonic bifurcations. Numerical simulations are given to verify the chaos threshold obtained by the analytical method. [ABSTRACT FROM AUTHOR]

Abstract: By analyzing COSMIC data, found more than 50% reduction in electron density during a solar eclipse at the F2-layer and above, with the peak of ∼70% at 370km. So great eclipse effect on topside ionosphere was very abnormal and much different from previous studies. However, by comparing the cosmic data with IRI results, we find that the abnormal reduction comes mainly from the significant local time variation at sunrise, not from the eclipse effect. Furthermore, we simulated the eclipse effect by using a theoretical model to confirm our analysis. [Copyright &y& Elsevier]

This paper addresses a first numerical simulation to the nonlinear dynamic system of equations that describes the prey-predator model at the predator mating period. Some male species accompany the females during the mating period. In this case, both male and female feed on the same prey. The presented work shows the numerical solution for this specific case of the prey-predator mathematical model via an exponential time differencing method. In addition, the paper provides the biological implication of the solution. [ABSTRACT FROM AUTHOR]

This article deals with the random sequential adsorption (RSA) of 2D disks of the same size on fractal surfaces with a Hausdorff dimension 1 < d < 2. According to the literature and confirmed by numerical simulations in the paper, the high coverage regime exhibits fractional dynamics, i.e., dynamics in t1/d where d is the fractal dimension of the surface. The main contribution this paper is that it proposes to capture this behavior with a particular class of nonlinear model: a driftless control affine model. [ABSTRACT FROM AUTHOR]