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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.

With the variation of parameters, the performance of the buck-boost converters may degrade due to the nonlinear phenomenon such as Neimark-Sacker bifurcation, period doubling bifurcation, even chaos. In this paper, a method to suppress the bifurcation and improve system stability through improving the control principle is indicated. By changing the control principle of the conventional OCC, the proposed one-cycle energy balance control method achieve the one-cycle control by keeping the energy balance of the circuit in each switching cycle. Then the poles of system transfer function are adjusted and the parameter stability range is extended, which achieve the objective of suppressing the bifurcation. Furthermore, such adjustments do not increase the order of the transfer function, thus there is no increase in the computational complexity. Compared with the conventional OCC method, the theoretical analysis based on the sampled-data model demonstrates the ability of the proposed method to suppress the bifurcation and extend the parameter range. Further simulation and experimental results also validate the theoretical analysis.

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.

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.

Summary This article is devoted to studying the problem of globally and exponentially adaptive cluster synchronization for a class of Lur'e dynamical networks with multiple time‐varying delays and ...

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.

One of actual problem of the solid state electronics, which is intensively solving, is increasing of integration rate of elements of integrated circuits. Increasing of the integration rate leads to necessity to decrease their dimensions. To decrease the above dimensions, one can use different approaches. In this paper, we introduce an approach to increase density of field-effect heterotransistors framework a comparator in the latch state. Based on the approach, one shall consider manufacturing of the comparator in a heterostructure with specific configuration. Several required areas of the heterostructure should be doped by diffusion or by ion implantation. After that dopant and radiation defects should by annealed framework an optimized scheme. We also consider an approach to decrease value of mismatch-induced stress in the considered heterostructure. We also introduce an analytical approach to analyze mass and heat transport in the heterostructures during manufacturing of integrated circuits with account mismatch-induced stress. The approach gives a possibility to analyze mass and heat transport in multilayer structures without crosslinking of solutions on interfaces between layers. The approach also gives a possibility to take into account spatial and temporal variation of parameters of considered processes. Based on the approach, we analyzed manufacturing of an integrated circuit to increase density of their elements.

In this paper, a novel four-dimensional chaotic system with three quadratic nonlinearities and only one unstable equilibrium is reported. The dynamical behaviors with respect to system parameters and initial conditions are analyzed. It shows that the novel system performs periodic, quasi-periodic and chaotic motions with the variation of parameters and generates a pair of symmetric coexisting attractors for different initial conditions. Moreover the circuit implementation and impulsive synchronization control of the system are well investigated with the achievement of some theoretical and numerical results.

In this paper we gave a general formula for particular solution of the non-homogenous linear ordinary differential equation in a method of variation of parameters of kth order. We solved the linear...

The solution to the problem of the shape of the lateral surface of a vertical 3D catenoidal liquid bridge of small volume between two arbitrary convex solid surfaces in the axisymmetric case taking into account the gravity force is presented. A variational formulation of the initial problem is given. The solution is found by the iteration method under the assumption of a small Bond number. An algorithm of the iterative process is proposed. We have detected domains of variation of parameters in which the uniqueness of the solution is not observed. It is found that the maximal number of different lateral surface profiles of the liquid bridge, which correspond to a single chosen set of parameters, is four. By way of example, the problem of the liquid bridge shape between two spheres is solved.

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.

This paper focuses an optimal policy of an inventory model for deteriorating items with trapezoidal type demand rate and the three-parameter Weibull distribution deterioration rate. The model allows shortages which are completely backlogged in order to achieve better preserving amenity. The authors present some optimal solutions which leads to determine the total inventory cost in which the collective behavior of customers hinges on the waiting time. An easy-to-use optimization technique is included to find the shortage time point and order quantity to minimize the total system cost. Taking into account the above-mentioned assumptions, different kinds of numerical examples are considered to illustrate the theoretical behavior of the framed optimization model. The sensitivity analysis is made for this problem with variation of parameters. The study shows that the optimal solution not only exists but also is unique and is less expensive to operate if the factors of three-phase variation, representing the growth, the steady, and the decline phases of demand with respect to time are considered.

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.

Evolution takes place in ecological system which involves interactions with other species. To describe such evolution, the modeling of predator-prey system is essential with simultaneous evolution of interacting species. In this paper, a predator-prey system with rapid predator evolution is proposed and studied. Rapid evolution is considered to affect the outcomes of simultaneous ecological change of dieting. The change of such diet is fast compared to the timescale of ecological system. We introduce a timescale difference parameter between the dynamics of a predator trait and the ecological system. The model is analyzed in terms of theoretical as well as numerical point of view. The comparisons are shown in between ecological and evolutionary dynamics. Simulated results illustrate that evolution causes chaotic dynamics and it will be controlled to periodic orbits, and stable steady state by increasing parameter values. On the other hand, the ecological system has only limit cycle and steady state dynamics with the variation of parameters. Therefore, the evolution makes the predator-prey dynamics to more complex. The proposed model is applicable in large population size, short generation times, and well-changed environment system. More preciously, the system has the suitable applicability in plankton system.

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.

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.

In this paper, we introduce a generating function of sums of two-parameter deformations of multiple polylogarithms, denoted by Φ2(a;p,q), and study a q-difference equation satisfied by it. We show that this q-difference equation can be solved by expanding Φ2(a;p,q) into power series of the parameter p and then using the method of variation of constants. By letting $p \rightarrow 0$ in the main theorem, we find that the generating function of sums of q-interpolated multiple zeta values can be written in terms of the q-hypergeometric function 3ϕ2, which is due to Li-Wakabayashi.

In this paper, the model of the rudder electromechanical actuation system is established, and the effect of the pole-zero on the resonance is analyzed. Furthermore, Linear extended state observer (LESO) was designed on the premise of retaining the zero of the linear displacement of the servo actuator. The state and disturbance of the system were observed and compensated, and the active disturbance rejection control (ADRC) law was designed according to the desired poles. Simulation results show that the proposed control strategy can suppress the resonance caused by the system structure and the fluctuation of system performance caused by load disturbance, and obtain the dynamic quality of line and angle feedback. Moreover, the system shows good adaptability and robustness to the variation of parameters and load torque in a large range.

Instead of a single model for one discipline, thermoelastic analysis involves at least a thermal model and a structural model. In many cases, these two analysis steps are followed by a RF or optical simulation to determine the impact on the performance of the instrument of the thermoelastic responses. Each analysis step is accompanied with uncertainties. Besides the thermal and structural analyses, the transfer of temperature data introduces additional uncertainties. A method based on factors of safety, as is used in structural analysis to cover uncertainties, is discussed. Although the method can be pragmatic, this approach is often lacking a physical basis, may not be compatible with the requirements for specific cases, and the values used for these factors are to a large extent ambiguous. Stochastic approaches are known to be powerful for estimating ranges in the responses due to variation of parameters. Although the Monte Carlo method is well known and robust, it is computationally expensive. Promising alternative methods to quantify uncertainties of the responses, among many others, are the Latin hypercube sampling (LHS) method and the Rosenblueth \(2k+1\) Point Estimates Moments (PEM) method. The significance of the random design variables on the random output is detected through a sensitivity analysis, i.e. by a regression analysis method or as an intermediate result of the Rosenblueth PEM method. The section concludes with several worked out examples.

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