Mathematical Modelling and Analysis

Modelling for a new mechanical passive damper and its mathematical analysis

Dai Watanabe — 2024-10-11

To improve ride comfort, an oil damper should restrain its damping force in a high-velocity range. A lot of dampers with such properties were developed. For example, the one controlling the flux of oil by a leaf valve is widely adapted and reasonable. However, it is difficult to represent its dynamics with a simple mathematical model, and the cost of a computational fluid dynamics is too expensive. To overcome the disadvantages, the first author in [15] developed the other mechanical oil damper with sub-pistons instead of the leaf valve, which enabled us to propose a simple mathematical model with linear ordinary differential equations, thanks to the simple mechanism to control the oil flow. In this article, we give a more detailed mathematical model for the damper taking the dynamic pressure resistance into account, which is represented by nonlinear ordinary differential equations. In addition, a numerical scheme for the model is also proposed and its mathematical analysis such as the validity of the numerical solutions is shown.

A class of explicit second derivative general linear methods for non-stiff ODEs

Mohammad Sharifi — 2024-10-11

In this paper, we construct explicit second derivative general linear methods (SGLMs) with quadratic stability and a large region of absolute stability for the numerical solution of non-stiff ODEs. The methods are constructed in two different cases: SGLMs with p = q = r = s and SGLMs with p = q and r = s = 2 in which p, q, r and s are respectively the order, stage order, the number of external stages and the number of internal stages. Examples of the methods up to order five are given. The efficiency of the constructed methods is illustrated by applying them to some well-known non-stiff problems and comparing the obtained results with those of general linear methods of the same order and stage order.

Micropolar fluid-thin elastic structure interaction: variational analysis

Grigory Panasenko — 2024-10-11

We consider the non-stationary flow of a micropolar fluid in a thin channel with an impervious wall and an elastic stiff wall, motivated by applications to blood flows through arteries. We assume that the elastic wall is composed of several layers with different elastic characteristics and that the domains occupied by the two media are infinite in one direction and the problem is periodic in the same direction. We provide a complete variational analysis of the two dimensional interaction between the micropolar fluid and the stratified elastic layer. For a suitable data regularity, we prove the existence, the uniqueness and the regularity of the solution to the variational problem associated to the physical system. Increasing the data regularity, we prove that the fluid pressure is unique, we obtain additional regularity for all the unknown functions and we show that the solution to the variational problem is solution for the physical system, as well.

A new approach for Solving a nonlinear system of second-order BVPs

Taher Amoozad — 2024-10-11

In this paper, we introduce a new approach based on the Reproducing Kernel Method (RKM) for solving a nonlinear system of second-order Boundary Value Problems (BVPs) without the Gram-Schmidt orthogonalization process. What motivates us to use the RKM without the Gram-Schmidt orthogonalization process is its easy implementation, elimination of the Gram-Schmidt process, fewer calculations, and high accuracy. Finally, the compatibility of numerical results and theorems demonstrates that the Present method is effective.

The BKM criterion to the 3D double-diffusive magneto convection systems involving planar components

Chol-Jun O — 2024-10-11

In this paper, we investigate the BKM type blowup criterion applied to 3D double-diffusive magneto convection systems. Specifically, we demonstrate that a unique local strong solution does not experience blow-up at time T, given that ). To prove this, we employ the logarithmic Sobolev inequality in the Besov spaces with negative indices and a well-known commutator estimate established by Kato and Ponce. This result is the further improvement and extension of the previous works by O (2021) and Wu (2023).

Averaged reaction for nonlinear boundary conditions on a grill-type Winkler foundation

Delfina Gómez — 2024-11-22

We consider a homogenization problem for the elasticity operator posed in a bounded domain of the half-space, a part of its boundary being in contact with the plane. This surface is traction-free out of “small regions”, where we impose nonlinear Winkler-Robin boundary conditions containing “large reaction parameters”. Non-periodical distribution of these regions is allowed provided that they have the same area. We show the convergence of solutions towards those of the homogenized problems depending on the relations between the parameters distance, sizes, and reaction.

A two-derivative time integrator for the Cahn-Hilliard equation

Eleni Theodosiou — 2024-11-22

This paper presents a two-derivative energy-stable method for the Cahn-Hilliard equation. We use a fully implicit time discretization with the addition of two stabilization terms to maintain the energy stability. As far as we know, this is the first time an energy-stable multiderivative method has been developed for phase-field models. We present numerical results of the novel method to support our mathematical analysis. In addition, we perform numerical experiments of two multiderivative predictor-corrector methods of fourth and sixth-order accuracy, and we show numerically that all the methods are energy stable.

Mirroring and nonlinear perturbation of a circuit's system with multiple attractors

Emile Franc Doungmo Goufo — 2024-11-29

We infix the duality-symmetric and the mirror symmetry conversion processes into a dynamical system representing an electric circuit diagram with three input (or output) as shown in Figure 2. Hence, a new non-linear variable order initial value problem is obtained and solved using the Haar wavelet numerical method (HWNM). Error, stability and entropy analyzes show the reliability of the method. Numerical simulations are then implemented and show for the new system, existence of various attractors’ types (point attractors (PAs), limit cycles, strange attractors (SAs), double attractor (DA), coexisting attractors (CoAs)) with their mirror reflections. Both are in a symmetrical structure in which they face each other, separated by a changing symmetry line and exhibiting similar properties. The circuit implementation using a Field Programmable Gate Array (FPGA) is performed and concur with the expected results.

Regions of existence and uniqueness for singular two-point boundary value problems

Shih-Hsiang Chang — 2024-11-29

A monotone iterative technique with lower and upper solutions is presented to identify the regions of existence for the solutions of singular two-point boundary value problems

without requiring the monotonicity conditions on f(x,y). Under an additional condition on f(x,y), uniqueness of the solution is also established. These existence and uniqueness results are constructive and complement the existing results. Four examples including some engineering problems are given to illustrate the applicability of the proposed approach.

The inverse problem of determining profiles of electrophysical parameters in eddy-current structuroscopy using apriori information on multifrequency probing

Volodymyr Ya. Halchenko — 2024-11-29

Based on the proposed methodology, the essence of which is to identify the profiles of electrophysical parameters of planar objects of eddy-current testing by means of surrogate optimization in the active PCA-space of reduced dimensionality, the effectiveness of the approach is proved by modeling the process of measurement control using apriori accumulated information about an object, in particular, multifrequency probing. The particularity of these studies is the consideration of previously collected information not only on profile variations, but also on the effect of various object probing frequencies on the signal of the surface probe. The functions of the storage device and information carrier were performed by a neural network metamodel, characterized by a high computational efficiency. Numerical experiments have determined the accuracy indicators of the proposed improved method for determining the distributions of magnetic permeability and electrical conductivity along the subsurface layer of a metal object with changes in a microstructure. The analysis of the modeling results indicates a significant reduction in the level of computational resources required to solve the problem and an increase in the accuracy of profile identification.

An effective numerical algorithm for coupled systems of Emden-Fowler equations via shifted airfoil functions of the first kind

Mohammad Izadi — 2024-11-29

The present paper deals with the designation of a new efficient numerical scheme for numerical solution of a class of coupled systems of Emden-Fowler equations describing several processes in applied sciences and technology. This method combines the shifted version of airfoil functions of the first kind (AFFK) and quasilinearization technique. More specifically, the quasilinearization technique is first applied to the original problem and the shifted AFFK (SAFFK) collocation matrix technique is then constructed for obtaining the solution of resulting family of submodels. We derive the error bound and analyze the convergence properties of the SAFFK. Computational and experimental simulations are carried out to describe the applicability and accuracy of the new technique. To show the benefit of the new approach, the computed numerical outcomes are compared with those results obtained via the Bernoulli and Haar wavelets collocation methods. It is evident from the numerical illustrations that the new developed scheme is superior to the existing available ones. The elapsed CPU time of the proposed method is provided.