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).