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Several well-established approaches to physical modeling synthesis for musical instruments exist. Finite-difference time-domain methods are known for their generality and flexibility in terms of the systems one can model but are less flexible with regard to smooth parameter variations due to their reliance on a static grid. This paper presents the dynamic grid, a method to smoothly change grid configurations of finite-difference time-domain schemes based on sub-audio–rate time variation of parameters. This allows for extensions of the behavior of physical models beyond the physically possible, broadening the range of expressive possibilities for the musician. The method is applied to the 1D wave equation, the stiff string, and 2D systems, including the 2D wave equation and thin plate. Results show that the method does not introduce noticeable artefacts when changing between grid configurations for systems, including loss. Several well-established approaches to physical modeling synthesis for musical instruments exist. Finite-difference time-domain methods are known for their generality and flexibility in terms of the systems one can model but are less flexible with regard to smooth parameter variations due to their reliance on a static grid. This paper presents the dynamic grid, a method to smoothly change grid configurations of finite-difference time-domain schemes based on sub- audio–rate time variation of parameters. This allows for extensions of the behavior of physical models beyond the physically possible, broadening the range of expressive possibilities for the musician. The method is applied to the 1D wave equation, the stiff string, and 2D systems, including the 2D wave equation and thin plate. Results show that the method does not introduce noticeable artefacts when changing between grid configurations for systems, including loss.

In this article, the issue of exponential stability (ES) is investigated for a class of switched stochastic neural networks (SSNNs) with proportional delay (PD). The key feature of PD is an unbounded time-varying delay. By considering the comparison principle and combining the extended formula for the variation of parameters, we conquer the difficulty in consideration of PD effects for such networks for the first time, where the subsystems addressed may be stable or unstable. New delay-dependent conditions with respect to the mean-square ES of systems are established by employing the average dwell-time (ADT) technique, stochastic analysis theory, and Lyapunov approach. It is shown that the acquired minimum average dwell time (MADT) is not only relevant to the stable subsystems (SSs) and unstable subsystems (USs) but also dependent on the decay ratio (DR), increasing ratio (IR), as well as PD. Finally, the availability of the derived results under an average dwell-time-switched regulation (ADTSR) is illustrated through two numerical simulation examples.

In this research paper, we discuss systems of conformable linear differential equations. The conformable fundamental exponential matrix has been used to express the solution of the homogeneous and nonhomogeneous systems. The method of variation of parameters has been investigated to find the particular solution of the conformable system of nonhomogeneous linear differential equations. Several illustrative examples have been provided at the end of our study to validate all obtained results.

A new 3D chaotic system with only one nonlinear term is constructed in this paper, which has conservative and dissipative features respectively by choosing different parameters. The complex dynamic behaviors of the system are analyzed theoretically and numerically by using nonlinear analytical tools, such as Lyapunov exponents, phase portraits, and bifurcation diagrams. In a certain range of parameters, the new system is a non-Hamiltonian conservative chaotic system, which can produce infinitely many coexisting conservative flows. With the variation of parameters, the divergence of the system is less than zero, and the system can also generate hidden and self-excited attractors with multi-scroll. To verify the feasibility of the new system, it has been implemented by field-programmable gate array; phase diagrams obtained in the experiment are consistent with the simulation of the data.

A new method is presented for optimum cross-sectional design of planar frame structures combining reinforcement learning (RL) and metaheuristics. The method starts from RL jointly using artificial neural network so that the action taker, or the agent, can choose a proper action on which members to be increased, reduced or kept their size. The size of the neural network is compressed into small numbers of inputs and outputs utilizing story-wise decomposition of the frame. The trained agent is used in the process of generating a neighborhood solution during optimization with simulated annealing (SA) and particle swarm optimization (PSO). Because the proposed method is able to explore the solution space efficiently, better optimal solutions can be found with less computational cost compared with those obtained solely by metaheuristics. Utilization of RL agent also leads to high-quality optimal solutions regardless of variation of parameters of SA and PSO or initial solution. Furthermore, once the agent is trained, it can be applied to optimization of other frames with different numbers of stories and spans.

This study proposed an efficient numerical technique for coupled differential equations (CDEs) using the clique polynomials of the Complete graph. Recently, Graph theory has dragged the attention of many mathematicians due to its wide applications. Here, some problems have been considered to examine the proposed scheme proficiency. Some theorems on convergence are discussed. Here, the CDEs are rehabilitated into an algebraic equation system using the clique polynomials and collocation technique. The proposed scheme results are compared with the undetermined coefficients (UDCM) and variation of parameters method (VPM) solutions through tables and graphs. Obtained results reveal that the current approach is more accurate.

The steady-state error and torque ripple caused by the mismatch or variation of parameters in the deadbeat predictive current control of permanent magnet synchronous motor are presented in this paper. An improved adaptive deadbeat current predictive model only related to inductance parameters is proposed. The influence of inductance variation on the system stability margin is quantitatively analyzed. When the variation is less than 50%, the system performance can be improved obviously. When the variation reaches 50%, the system will oscillate and cannot operate stably. The feed forward control strategy is introduced to improve the stability margin of the system, and the inductance disturbance of the system oscillation is expanded to 67%. Simulations and experiments are carried out for traditional deadbeat current predictive model, adaptive deadbeat predictive model, and adaptive model with feed forward control. Results show that under various working conditions, the effectiveness of the proposed method in eliminating the steady-state error caused by parameter disturbances is verified. The current distortion and torque ripple are also restrained. Both robustness and steady-state performance of the system are improved.

The article examines the social factors influence on prosodic manifestation of syntactic and macrosyntactic units. The data collected during suprasegmental analysis of spontaneous speech are used, which are directly related to the syntactic level, namely: the average length of a phrase in words and in syntagmas and the average length of a syntagma in phonetic words, as well as parameters associated with the design of the whole text: the number of composition blocks in the text, their length in phrases, the length of the whole text in phrases and words. The results of statistical modeling of the influence of the factors "age", "type of education", "level of education" and "gender" clearly indicate that the factors "type of education" and "gender" significantly influence the variation of syntactic and macrosyntactic parameters of an oral text. The factor "type of education" significantly affects the number of phrases in the text and the length of the text block in phrases – both parameters are significantly higher for the speakers who specialize in Humanities compared to those who specialize in Sciences. The length of the syntagma depends on the speaker’ gender – syntagmas produced by male speakers are longer.

In this study, we propose a numerical scheme for stochastic oscillators with additive noise obtained by the method of variation of constants formula using generalized numerical integrators. For both of the displacement and the velocity components, we show that the scheme has an order of 3/2 in one step convergence and a first order in overall convergence. Theoretical statements are supported by numerical experiments.

The article is devoted to the problem of obtaining computationally efficient mathematical models of dynamic objects with viscoelastic properties on the basis of equivalent transformations of primary mathematical descriptions in the form of integro-differential equations to Volterra integral equations. This takes into account the significantly growing in recent years, the possibilities of computer engineering and software engineering, as well as the positive properties of integral models in their numerical implementation: computational stability, good convergence, resistance to high-frequency spectra of noise, a computational efficiency. Methods of transformation of dynamic models are given, which allow to reduce integro-differential equations to integral equations with Volterra operator, which simplifies the problem of creating modelling algorithms. In particular, the application of integral models in computer modelling problems, which are obtained from primary integro-differential models using the following methods of equivalent transformations: the method of variation of constants, the method of senior derivative, the modified method of substituting variables, which in numerical implementation using quadrature formulas allows to obtain recurrent formulas. An example of application of this method is given. The possibility of solving the direct and inverse problem of determining the impact on a multimass system using the integral form of the Cauchy problem is demonstrated. It is shown that the problem of developing more complete and thorough mathematical models of dynamical systems, namely in the form of integro-differential equations, is important and relevant, and their numerical implementation is necessary for a wide range of applied modelling problems.

In this paper, we study a fourth order linear differential equation. We found an upper bound for the solutions of this differential equation and also, we prove that all the solutions are in L4(0, ∞). By comparing these results we obtain that all the eigenfunction of the boundary value problem generated by this differential equation are bounded and in L4(0, ∞).

In this work, we study time discretization of subdiffusion equations, that is, fractional differential equations of order α ∈ ( 0 , 1 ) . Assuming that A is the generator of a fractional resolvent family { S α , α ( t ) } t ≥ 0 , which allows to write the solution to the subdiffusion equation ∂ t α u ( t ) = A u ( t ) + f ( t ) as a variation of constants formula, we find an interesting connection between { S α , α ( t ) } t ≥ 0 and a discrete resolvent family { S α , α n } n ∈ N and then, by using the properties of { S α , α ( t ) } t ≥ 0 , we study the existence of solutions to the discrete subdiffusion equation C ∇ α u n = A u n + f n , n ∈ N , where, based on the backward Euler method for a τ > 0 given, C ∇ α u n is an approximation of ∂ t α u ( t ) at time t n ≔ τ n . We study simultaneously the fractional derivative in the Caputo and Riemann–Liouville sense. We also provide error estimates and some experiments to illustrate the results.

This paper proposes an analytical solution of removing end-of-life GEO satellites to the GEO graveyard region using solar radiation pressure (SRP) and impulsive thrusts. The dynamic model of a GEO satellite equipped with a solar sail is first built upon the magnitude comparisons of different accelerations exerted on the satellite. Then the dynamic system is constructed based on the Gauss’s Variation of Parameter (VOP) equations, and linearized along a nominal trajectory. Control angles of the sail and impulsive thrust vectors are generated using the proposed optimal hybrid disturbance-accommodation tracking maneuvers. Simulations indicate that, to remove a satellite in 360 days using only SRP with the proposed method, a minimal area-to-mass (A/M) ratio of 0.13 m 2 / kg is required. When the A/M ratio of spacecraft is smaller than the minimal value, impulsive thrusts are applied to assist the removal process. For a satellite with an A/M ratio of 0.1 m 2 / kg , a total impulse of 10.5 m / s is required.

In this paper, we extend to the non-Hille–Yosida case a variation of constants formula for a nonautonomous and nonhomogeneous Cauchy problems first obtained by Gühring and Räbiger. By using this variation of constants formula, we derive a necessary and sufficient condition for the existence of an exponential dichotomy for the evolution family generated by the associated nonautonomous homogeneous problem. We also prove a persistence result of the exponential dichotomy for small perturbations. Finally, we illustrate our results by considering two examples. The first example is a parabolic equation with nonlocal and nonautonomous boundary conditions, and the second example is an age-structured model that is a hyperbolic equation.

Made available in DSpace on 2020-12-12T01:23:01Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-01-01 In this paper, an abstract degenerate hyperbolic equation is considered that includes the semilinear Blackstock–Crighton–Westervelt equation. By proposing a new approach based on strongly continuous semigroups and resolvent families of operators, we prove an explicit representation of the strong and mild solutions for the linearized model by means of a kind of variation of parameters formula. Moreover, we show that under nonlocal initial conditions, the existence of a mild solution of the semilinear equation can be established. Institute of Biosciences Humanities and Exact Sciences (Ibilce) São Paulo State University (Unesp), Campus São José do Rio Preto Departamento de Matemática y Ciencia de la Computación Universidad de Santiago de Chile, las Sophoras 173, Estación central Institute of Biosciences Humanities and Exact Sciences (Ibilce) São Paulo State University (Unesp), Campus São José do Rio Preto

In this paper, the impulsive effects on projective synchronization between the parameter mismatched neural networks with mixed time-varying delays have been analyzed. Since complete synchronization is not possible due to the existence of parameter mismatch and projective factor, a drive has been taken to achieve the weak projective synchronization of different neural networks under impulsive control strategies. Through the use of matrix measure technique and the extended comparison principle based on the formula of variation of parameters for mixed time-varying delayed impulsive systems, sufficient criteria have been derived for exponential convergence of the networks under the effects of extensive range of impulse. Instead of upper or lower bound of the impulsive interval, the concept of the average impulsive interval is applied to estimate the number of impulsive points in an interval. The concept of calculus is applied for optimizing the synchronization error bounds which are obtained because of different ranges of impulse. Finally, the numerical simulations for various impulsive ranges for different cases are presented graphically to validate the efficiency of the theoretical results.

The design optimization of thermal-driven actuators is a challenging task because the performance depends on multiple materials parameters, structural parameters, and working conditions. In this work, we adopted large scale finite element simulation together with machine learning algorithm to fulfill the on-demand design of thermal actuators. Finite element analysis was used to simulate the performance of thermal actuator with two-layer structure, which generated large amount of dataset by considering the variation of parameters including the moduli, thermal expansion coefficient, sample thickness and length, and temperature. Support vector regression (SVR) was adopted to establish the relationship between multiple input parameters and the resulting contact pressure. Thereafter, a simple interior point algorithm was used to achieve the on-demand design based on the SVR model. The contact pressures of thermal actuator constructed from the optimized parameters deviated less than 15% of the target values.

A simple, yet accurate modified multi-scale method (MMSM) for an approximately analytical solution in nonlinear oscillators with two time scales under forced harmonic excitation is proposed. This method depends on the classical multi-scale method (MSM) and the method of variation of parameters. Assuming that the forced excitation is a constant, one could easily obtain the approximate analytical solution of the simplified system based on the traditional MSM. Then, this solution for the oscillator under forced harmonic excitation could be established after replacing the harmonic excitation by the constant excitation. To certify the correctness and precision of the proposed analytical method, the van der Pol system with two scales subject to slowly periodic excitation is investigated; this system presents rich dynamical phenomena such as spiking (SP), spiking-quiescence (SP-QS), and quiescence (QS) responses. The approximate analytical expressions of the three types of responses are given by the MMSM, and it can be found that the precision of the new analytical method is higher than that of the classical MSM and better than that of the harmonic balance method (HBM). The results obtained by the present method are considerably better than those obtained by traditional methods, quantitatively and qualitatively, particularly when the excitation frequency is far less than the natural frequency of the system.

In order to study the dissemination mechanism of knowledge, a SIRI dynamics model with the learning rate, the forgetting rate and the recalling rate is constructed in this paper. Stability of equilibria and global dynamics of the SIRI model are analyzed. Two thresholds that determine whether knowledge is disseminated are given. We describe the stability of the equilibria for the SIRI model in which there are an equilibrium and a line of equilibria. In particular, we find the dividing curve function which is used to partition invariant set in order to discuss the local stability, and obtain the equation of the wave peak value or wave trough value in the process of knowledge dissemination. Numerical simulations are provided to support the theoretical results. The complicated dynamics properties exhibit that the model is very sensitive to variation of parameters, which play an important role on controlling and administering the knowledge dissemination.

A detailed study of the evolution of local and integral parameters of momentum, heat, and mass transfer processes in hydrocarbon gas mixtures under separation conditions at given temperature and pressure values in working media is carried out within the framework of the principles of equilibrium thermodynamics using the Aspen HYSYS software package, namely, the Peng-Robinson equation of state for real gas mixtures, the principles of statistical mechanics, the approaches of corresponding states, the Chapman-Enskog and the Golubev methods, and the theory of similarity and dimensional analysis. The limits of similarity method applicability in quantitative estimates and qualitative forecasts of the mechanisms and configurations of convective heat and mass transfer in oil treatment units are established. The paper also discusses results of the analog method application in separation process modeling for momentum, heat and mass transfer processes in the problems of oil and gas industry. The conclusions about the aspects of property changes in complex mixtures and about heat and mass transfer intensity during separation, which violate a triple analogy in non-isothermal homogeneous and heterogeneous media, are recommended to take into account when designing real equipment.

The Aim of the paper is to develop an algorithm of prompt detection of the moment of dependability characteristics variation in a system that consists of a set of homogeneous elements, assuming that failures of such elements occur at random moments in time, are a Poisson flow of events and, consequently, the time intervals between them are an exponential probability distribution. In order to solve the problem, it is suggested using one of the classical algorithms of detection of “imbalance” of a discrete random process, i.e. spontaneous change of one of its probabilistic characteristics. As such a characteristic, the exponential distribution parameter θ was chosen, that is uniquely associated with the mean time between failures Тmn: θ = 1/Тmn. It is believed that the imbalance consists in the discontinuous variation of parameter θ from the initial steady state θ = θ0 to the level of minimal (expected, maximum allowable, critical) imbalance, when θ = θ1 > θ0. In this paper, the imbalance is detected using the cumulative sum algorithm (CUSUM) as it has certain optimal properties and is widely used in practice. For this algorithm, the required design ratios, descriptions of its properties and features are provided. The paper proposes a procedure for synthesizing the control algorithm with desired properties, in the course of which, based on the user-selected values of desired mean time between false alarms , initial basic level θ0 and nominal imbalance θ1 > θ0, the value of decision boundary Н is identified, the speed of algorithm action is estimated trough the calculation of the average lag in the detection of nominal imbalance , along with its efficiency for various values of d, that quantitatively characterize the value of imbalance: d=θ1/ θ0. For the purpose of practical implementation of the synthesis procedure, the paper cites reference data, that was obtained by means of simulation and that ensures the development of the control algorithm with required characteristics. It is noted that the presented synthesis procedure can, in principle, also be used for cases of gradual (continuous) change of parameter θ. However, the statistical properties of the control procedure will remain unclear as they require sufficiently intense additional research.

This paper presents a novel power regulation controller for grid-connected voltage source converter (VSC). The proposed controller is usually applied to achieve smooth active and reactive power dynamics against the variation of parameters. The dynamic performance of grid-connected VSC is sensitive to parameter variation, threatening the safe operation especially when the relative stability is low. Moreover, there is no possibility to modify the dynamic response without the loss of power regulation precision or output voltage and frequency accuracy. In this paper, an improvement in the dynamic response is achieved by introducing feedforward branches into the VSC power regulation controller. Owing to the model reduction mechanism, the VSC provides smooth dynamic response and robustness against the variation of parameters. Simulation and experiment results are presented to prove the effectiveness of this approach, which shows excellent performance as opposed to the conventional controller paradigm.

The windings of a traction transformer are always be threatened by the fluctuation of the load. Frequency response analysis (FRA) is regarded as the most effective method to diagnose the winding deformation. Appropriate FRA modelling method may help to predict typical winding faults for large transformers. The existing model usually simplify dozens of winding disks into several disks, it is applicable when analysing small displacement. However, when the disks between windings are seriously misplaced, the conventional model may not be suitable. This study presents an improved lumped parameter circuit model considering intersection capacitances and mutual inductance between windings. The feasibility of the proposed model is verified based on a 10 kV test transformer. Finally, the model is applied for a 220 kV traction transformer, the variation of parameters and features are analysed for axial displacement of different windings. The results show that the axial displacement may lead to increase of resonance frequency and decrease of amplitude. The low-frequency band (1–30 kHz) may be regarded as visible features for diagnosing axial displacement of H winding and the middle frequency band (50–200 kHz) may be a characteristic band for diagnosing axial displacement of T winding.

The use of partition function zeros in the study of phase transition is growing in the last decade mainly due to improved numerical methods as well as novel formulations and analysis. In this paper the impact of different parameters choice for the energy probability distribution (EPD) zeros recently introduced by Costa et al is explored in search for optimal values. Our results indicate that the EPD method is very robust against parameter variations and only small deviations on estimated critical temperatures are found even for large variation of parameters, allowing to obtain accurate results with low computational cost. A proposal to circumvent potential convergence issues of the original algorithm is presented and validated for the case where it occurs.

Supercapacitor (SC) is one of the most trending energy storage solutions. The SCs equivalent circuit models have been extensively applied to energy management because of their accuracy and simplicity. However, there is a difficulty in solving the conventional differential equation-based model used to characterize the electrical behavior of SCs operating in constant power applications. Hence, numerical or metaheuristic techniques have been used in the literature to derive SC's internal voltage at any time. In this work, a thorough mathematical analysis that enables a precise calculation of the electrical variables implied in the charge/discharge processes of SCs operated at constant power as a function of time is presented. First, the transcendental discharge voltage expression of SCs operating at constant power is formulated, and then it was solved using the Special Trans Function theory (STFT). The precision of calculation of the method used for solving the transcendental expression is presented and discussed. Second, the transcendental voltage of charging expression of SCs operating at constant power as a function of time is also formulated, and then it was solved using Lambert W equation. Third, a comparison of different methods for solving mentioned equations is presented. Fourth, the electrical variables involved in the charge/discharge processes of SCs – voltage, current, power, energy, state of charge, and power loss are investigated. Furthermore, the results obtained for the variation of parameters and their operating conditions demonstrate the proposed equations’ applicability and accuracy. Finally, the results obtained validate that the closed-form expressions suggested in this paper are accurate and straightforward, which can contribute to proper modeling, investigation, sizing, regulation, and control of constant power SCs in modern energy systems.

We consider possibility to increase field-effect transistor's density in a switched-capacitor step-down DC-DC converter. Based on this approach we analyzed manufacturing of the converter in a heterostructure with special structure. Some specific sections of the heterostructure must be doped by ion implantation or by diffusion. After this procedure optimized annealing has been done. We also obtained conditions for decreasing of mismatch-induced stress value in this heterostructure. An analytical approach for analysis of heat and mass transport in multilayer structures has been introduced. The approach gives a possibility without crosslinking of solutionson interfaces between layers, take into account (i) spatial variation of parameters of considered processes; (ii) temporal variation of parameters of considered processes; (iii) nonlinearity of considered processes; (iv) mismatch-induced stress.

The mathematical modelling in relation to the Six-degree freedom system of train suspension is developed and simulated for their dynamic characteristics. The important challenge in the suspension system is vertical displacement obtained from the vehicle body. To reduce vertical displacement, an analysis of the model is done by variation of parameters such as stiffness of spring and damping coefficient. The model has been created by deriving the equations of a system using Newton’s law. The developed model has the potential to analyse the dynamic characteristics of the suspension system for both displacement of the vehicle body and displacement of the wheel. The outcome of this research revealed that Secondary spring stiffness is the most dominant factor to influence the displacement of the vehicle body; Primary damping coefficient is the most dominant factor to influence displacement of the wheel.

We apply the "systematic" $1^{st}$ order cosmological perturbation theory method to re-derive the formulation of an inflationary model generated by variation of constants, then to study the case where it is non-minimally coupled to gravity within both the "Metric" and "Palatini" formulations. Accommodating Planck 2018 data with a length scale $\ell$ larger than Planck Length $L_{pl}$ requires amending the model. First, we assume $f(R)$ gravity where we show that an $R^2$-term within Palatini formulation is able to make the model viable. All along the discussions, we elucidate the origin of the difference between the "Metric" and "Palatini" formalisms, and also highlight the terms dropped when applying the shortcut "potential formulae method", unlike the "systematic' method", for the observable parameters. Second, another variant of the model, represented by a two-exponentials potential, fits also the data with $\ell> L_{pl}$., 16 pages, 3 figures. Major revision. Version to appear in IJMPA

The dynamics of the systems with non-smoothness and the coupling of multiple scales have become the key subject because of their wide applications in science and engineering problems. The main purpose of the manuscript is to investigate the complicated dynamics in non-smooth systems caused by the coupling of two scales in frequency domain. Based on a common model of the boost converter controlled by a SMC-Washout as an example, By introducing a periodically changed electric power source and taking suitable parameter values, a piecewise non-smooth Filippov system with two scales in frequency domain is established. For the case when the exciting frequency is far less than the natural frequency, the whole exciting term can be regarded as a slow-varying parameter. Upon the analysis of the two subsystems located in two regions divided by the non-smooth boundary, the evolution of the equilibrium branches as well as the bifurcations with the variation of the slow-varying parameter are derived. Two typical cases corresponding to different distribution of the equilibrium branches as well as the bifurcations with the variation of the slow-varying parameter are taken into consideration, in which different types of bursting oscillations can be observed. By introducing the concept of the transformed phase portrait, the associated bifurcation mechanism of the bursting oscillations is presented. It is found that, the equilibrium branches and the related bifurcations may change with the variation of parameters, which may not only affect the quiescent states and the spiking states, but also influence the bifurcations between the two states, leading to different forms of bursting oscillations. It is pointed out that, when the trajectory of system jumps between different stable equilibrium branches of the two subsystems located in two associated regions, the types of point/point bursting oscillations may be obtained, while with the variation of the parameters, when the stable limit cycles involves the attractors, the types of point/cycle bursting oscillations may appear.

Solutions to nonlinear boundary value problems modelling physical phenomena in engineering applications have traditionally been approximated using numerical methods. More recently, several semi-analytical methods have been developed and used extensively in diverse engineering applications. This work compares the method of variation of parameters to semi-analytical methods for solving nonlinear boundary value problems arising in engineering. The accuracy and efficiency of the method of variation of parameters are compared to those of two widely used semi-analytical methods, the Adomian decomposition method and the differential transformation method, for three practical engineering boundary value problems: (1) the deflection of a cantilevered beam with a concentrated load, (2) an adiabatic tubular chemical reactor which processes an irreversible exothermal reaction, and (3) the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylinder conduit. The accuracy and convergence of each method is investigated using the error remainder function. The method of variation of parameters is significantly more efficient than both the semi-analytical methods and traditional numerical methods while maintaining comparable accuracy. Unlike the semi-analytical methods, the efficiency of variation of parameters is independent of the nonlinearity. Variation of parameters is shown to be an attractive alternative to semi-analytical methods and traditional numerical methods for solving boundary value problems encountered in engineering applications in which solution efficiency is important.

We introduce the fractional delayed matrix cosine and sine functions and use the variation of constants method to obtain an explicit formula for a solution to the initial value problem for a Riemann–Liouville sequential fractional linear time-delay system of order 1 2 α ≤ 2 . Our results extend those for fractional linear time-delay systems and novel for the classical case α = 1 .

This paper discusses Green’s matrix of nonlinear boundary value problem of first-order differential system with rectangular coeffisients, especially about its properties. In this case, the differential equation of the form with boundary conditions of the form and which is a real matrix with whose entries are continuous on and . , are nonsingular matrices such that and are constant vectors. To get the Green’s matrix and the assosiated generalized Green’s matrix, we change the boundary condition problem into an equivalent differential equation by using the properties of the Moore-Penrose generalized inverse, then its solution is found by using method of variation of parameters. The last we prove that the defined matrices satisfy the properties of green’s function. The result is the corresponding the Green’s matrix and the assosiated generalized Green’s matrix have the property of Green’s functions with the jump-discontinuity.

This paper presents a mathematical model of pitting corrosion formed by eight non-linear coupled differential equations and their boundary equations. In this model we studied the effect of the variation of parameter values (temperature, crevice depth, oxygen and sodium chloride concentration outside the cavity, and pH) on all the concentrations of the species, and on their differences with their concentrations outside the crevice and along the cavity using the network method. Moreover, a sensitivity study of the system parameters has been carried out. No simplifications have been considered, although the model is firmly coupled and susceptible to any variation of the aforementioned parameters. The development of the model is clearly explained. The results are compared with data published in the scientific literature for domains that establish the most complex and complete scenarios to verify the reliability of the model. One of the practical applications of this work, among others, is focused on the possible effects of this type of corrosion on the reinforced concrete, in buried pipes and on ship hulls. Keywords: Pitting corrosion, Prediction, Numerical methods, Reinforced concrete, Steel, Network method

Aim: The present study was conducted to evaluate the capacity of Listeria monocytogenes (L.m), Listeria innocua (L.i), and Escherichia coli to form biofilms on polystyrene support under different parameters by performing crystal violet (CV) staining technique. Materials and Methods: Different suspensions were prepared with single strains and with multiple combinations of strains including two serogroups of L.m (IIa and IIb), L.i, and E. coli strains at different microbial load. Selected strains and combinations were grown in biofilms for 6 days attached to polystyrene microplates under aerobic and microaerophilic conditions. The evaluation of the power of adhesion and biofilm formation was determined by CV staining followed by the measurement of optical density at 24 h, 72 h, and 6 days incubation time with and without renewal of the culture medium. Results: All the strains tested, presented more or less adhesion power depending on the variation of the studied parameters as well as the ability to form multispecies biofilms. Their development is more important by renewing the culture medium and increasing the initial load of bacteria. The ability to adhere and form biofilms differs from one serogroup to another within the same species. In bacterial combination, strains and species of bacteria adopt different behaviors. Conclusion: The ability to form biofilms is a key factor in the persistence of tested strains in the environment. Our study showed that L.m, L.i, and E. coli could adhere to polystyrene and form biofilms under different conditions. More researches are necessary to understand the mechanisms of biofilm formation and the influence of different parameters in their development.