scholarly journals Debonding waves in gel thin films

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200001
Author(s):  
Xianmin Xu ◽  
M. Carme Calderer ◽  
Masao Doi ◽  
Duvan Henao
Keyword(s):  
Thin Films ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Numerical Examples ◽  
Moving Substrate

We develop a mathematical model for the sliding of a gel sheet adhered to a moving substrate. The sliding takes place by the motion of detached region between the gel sheet and the substrates, i.e. the propagation of a Schallamach wave. Efficient numerical methods are developed to solve the problem. Numerical examples illustrate that the model can describe the Schallamach wave and are consistent with the existing experiments qualitatively.

Free and Forced Longitudinal Vibrations of Rods

2018 ◽  
Vol 931 ◽  
pp. 47-53 ◽  
Author(s):  
Khusen P. Kulterbaev ◽  
Lyalusya A. Baragunova ◽  
Maryana M. Shogenova
Keyword(s):  
Mathematical Model ◽  
Numerical Methods ◽  
Free Vibration ◽  
Cross Section ◽  
Forced Oscillations ◽  
Constant Cross Section ◽  
Longitudinal Vibrations ◽  
Numerical Examples ◽  
The Mathematical Model ◽  
Forced Longitudinal Oscillations

Free and forced longitudinal oscillations of homogeneous rods of constant cross section are considered. Analytical and numerical methods for solving problems are used. With free vibration, numerical examples are shown for a rod with a jammed and free end and for a rod with a concentrated non-deformable mass at the end, due to which the mathematical model accordingly changes. Forced oscillations are considered for distributed and concentrated loads. The eigenmodes of oscillations characteristic for continually discrete sisites are obtained.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

The Generation Principle and Mathematical Models of Double-Enveloping Internal Gear Pairs

2015 ◽  
Author(s):  
Xuan Li ◽  
Bingkui Chen ◽  
Yawen Wang ◽  
Guohua Sun ◽  
Teik C. Lim
Keyword(s):  
Mathematical Model ◽  
Load Capacity ◽  
Geometrical Shape ◽  
Gear Pair ◽  
Numerical Examples ◽  
Proposed Model ◽  
General Mathematical Model ◽  
Meshing Characteristics ◽  
Internal Gear ◽  
Tooth Pair

In this paper, the planar double-enveloping method is presented for the generation of tooth profiles of the internal gear pair for various applications, such as gerotors and gear reducers. The main characteristic of this method is the existence of double contact between one tooth pair such that the sealing property, the load capacity and the transmission precision can be significantly improved as compared to the conventional configuration by the single-enveloping theory. Firstly, the generation principle of the planar double-enveloping method is introduced. Based on the coordinate transformation and the envelope theory, the general mathematical model of the double-enveloping internal gear pair is presented. By using this model, users can directly design different geometrical shape profiles to obtain a double-enveloping internal gear pair with better meshing characteristics. Secondly, to validate the effectiveness of the proposed model, specific mathematical formulations of three double-enveloping internal gear pairs which apply circular, parabolic and elliptical curves as the generating curves are given. The equations of tooth profiles and meshing are derived and the composition of tooth profiles is analyzed. Finally, numerical examples are provided for an illustration.

scholarly journals Study on Optimal Placement and Reasonable Number of Viscoelastic Dampers by Improved Weight Coefficient Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Ji-ting Qu ◽  
Hong-nan Li
Keyword(s):  
Mathematical Model ◽  
Weight Coefficient ◽  
Optimal Placement ◽  
Optimal Method ◽  
Analogy Method ◽  
Numerical Examples ◽  
Viscoelastic Dampers ◽  
Reasonable Number ◽  
Coefficient Method

A new optimal method is presented by combining the weight coefficient with the theory of force analogy method. Firstly, a new mathematical model of location index is proposed, which deals with the determination of a reasonable number of dampers according to values of the location index. Secondly, the optimal locations of dampers are given. It can be specific from stories to spans. Numerical examples are illustrated to verify the effectiveness and feasibility of the proposed mathematical model and optimal method. At last, several significant conclusions are given based on numerical results.

Legendre Spectral Collocation Technique for Advection Dispersion Equations Included Riesz Fractional

2021 ◽  
Vol 6 (1) ◽  
pp. 9
Author(s):  
Mohamed M. Al-Shomrani ◽  
Mohamed A. Abdelkawy
Keyword(s):  
Numerical Methods ◽  
Numerical Algorithm ◽  
Spectral Collocation ◽  
Theoretical Formulation ◽  
Numerical Examples ◽  
Dispersion Equations ◽  
Advection Dispersion ◽  
Collocation Technique ◽  
Collocation Approach

The advection–dispersion equations have gotten a lot of theoretical attention. The difficulty in dealing with these problems stems from the fact that there is no perfect answer and that tackling them using local numerical methods is tough. The Riesz fractional advection–dispersion equations are quantitatively studied in this research. The numerical methodology is based on the collocation approach and a simple numerical algorithm. To show the technique’s performance and competency, a comprehensive theoretical formulation is provided, along with numerical examples.

scholarly journals A Mathematical Model and Numerical Solution of a Boundary Value Problem for a Multi-Structure Plate

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 244 ◽  
Author(s):  
Vildan Yazıcı ◽  
Zahir Muradoğlu
Keyword(s):  
Mathematical Model ◽  
Boundary Value Problem ◽  
Numerical Solution ◽  
Transmission Conditions ◽  
Numerical Examples ◽  
Deformation Problem ◽  
The Common ◽  
Plate System ◽  
Structure Plate ◽  
Numerical Approaches

This study examined the deformation problem of a plate system (formed side-by-side) composed of multi-structure plates. It obtained numerical approaches of the transmission conditions on the common border of plates that composed the system. Numerical examples were solved in different boundary and transmission conditions.

scholarly journals Modeling of the oxygen reduction reaction for dense LSM thin films

2017 ◽  
Vol 19 (45) ◽  
pp. 30464-30472 ◽  
Author(s):  
Tao Yang ◽  
Jian Liu ◽  
Yang Yu ◽  
Yueh-Lin Lee ◽  
Harry Finklea ◽  
...  
Keyword(s):  
Thin Films ◽  
Reaction Mechanism ◽  
Numerical Methods ◽  
Oxygen Reduction Reaction ◽  
Oxygen Reduction ◽  
Reduction Reaction

In the present study, the oxygen reduction reaction mechanism is investigated using numerical methods on a dense thin (La1−xSrx)yMnO3±δ film deposited on a YSZ substrate.

scholarly journals Mathematical model of Boltzmann’s sigmoidal equation applicable to the set-up of the RF-magnetron co-sputtering in thin films deposition of $$\hbox {Ba}_{{x}}\hbox {Sr}_{1-{x}} \hbox {TiO}_{3}$$ Ba x Sr 1 - x TiO 3

2017 ◽  
Vol 40 (5) ◽  
pp. 1043-1047 ◽  
Author(s):  
J Reséndiz-Muñoz ◽  
M A Corona-Rivera ◽  
J L Fernández-Muñoz ◽  
M Zapata-Torres ◽  
A Márquez-Herrera ◽  
...  
Keyword(s):  
Thin Films ◽  
Mathematical Model ◽  
Set Up

scholarly journals Creating better superconductors by periodic nanopatterning

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
Milan Allan ◽  
Mark H Fischer ◽  
Oliver Ostojic ◽  
Arjo Andringa
Keyword(s):  
Thin Films ◽  
Transition Temperature ◽  
Numerical Methods ◽  
Model Calculation ◽  
Lattice Mismatch ◽  
Specific Pattern ◽  
Design Parameters ◽  
Phonon Coupling ◽  
Electron Phonon Coupling ◽  
Correct Design

The quest to create superconductors with higher transition temperatures is as old as superconductivity itself. One strategy, popular after the realization that (conventional) superconductivity is mediated by phonons, is to chemically combine different elements within the crystalline unit cell to maximize the electron-phonon coupling. This led to the discovery of NbTi and Nb_33Sn, to name just the most technologically relevant examples. Here, we propose a radically different approach to transform a ‘pristine’ material into a better (meta-) superconductor by making use of modern fabrication techniques: designing and engineering the electronic properties of thin films via periodic patterning on the nanoscale. We present a model calculation to explore the key effects of different supercells that could be fabricated using nanofabrication or deliberate lattice mismatch, and demonstrate that specific pattern will enhance the coupling and the transition temperature. We also discuss how numerical methods could predict the correct design parameters to improve superconductivity in materials including Al, NbTi, and MgB_22.

Sign in / Sign up

Export Citation Format

Share Document