scholarly journals Mathematical Model and Numerical Simulation for Tissue Growth on Bioscaffolds

2019 ◽  
Vol 9 (19) ◽  
pp. 4058 ◽  
Author(s):  
Hyun Geun Lee ◽  
Jintae Park ◽  
Sungha Yoon ◽  
Chaeyoung Lee ◽  
Junseok Kim
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Numerical Simulations ◽  
Mean Curvature ◽  
Simulation Method ◽  
Euler Method ◽  
Tissue Growth ◽  
Local Curvature ◽  
Motion By Mean Curvature ◽  
The Mathematical Model

Tissue growth on bioscaffolds can be controlled using substrate geometry such as substrate curvature. In this study, we present a mathematical model and numerical simulation method for tissue growth on a bioscaffold to investigate the effect of local curvature on tissue growth. The mathematical model is based on the Allen–Cahn (AC) equation, which has been extensively used to model many problems involving motion by mean curvature. By solving the AC equation using the explicit Euler method, the proposed method is simple and fast. Numerical simulations on various geometries are presented to demonstrate the applicability of the proposed framework on tissue growth on a bioscaffold.

Systems Actuated by Shape Memory Alloys: Identification and Modeling

2021 ◽  
Vol 1 (2) ◽  
pp. 12-20
Author(s):  
Najmeh Keshtkar ◽  
Johannes Mersch ◽  
Konrad Katzer ◽  
Felix Lohse ◽  
Lars Natkowski ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Numerical Simulations ◽  
Shape Memory ◽  
Transfer Equation ◽  
Mechanical Parameters ◽  
Heat Transfer Equation ◽  
The Mathematical Model

This paper presents the identification of thermal and mechanical parameters of shape memory alloys by using the heat transfer equation and a constitutive model. The identified parameters are then used to describe the mathematical model of a fiber-elastomer composite embedded with shape memory alloys. To verify the validity of the obtained equations, numerical simulations of the SMA temperature and composite bending are carried out and compared with the experimental results.

MATHEMATICAL ANALYSIS OF THE ENDEMIC EQUILIBRIUM OF MALARIAHYGIENE MODEL

2021 ◽  
Vol 5 (10) ◽  
Author(s):  
Oluwafemi Temidayo J. ◽  
Azuaba E. ◽  
Lasisi N. O.
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
The Mathematical Model ◽  
Globally Stable ◽  
Well Posed ◽  
The Basic Reproduction Number ◽  
Invariant Principle

In this study, we analyzed the endemic equilibrium point of a malaria-hygiene mathematical model. We prove that the mathematical model is biological and meaningfully well-posed. We also compute the basic reproduction number using the next generation method. Stability analysis of the endemic equilibrium point show that the point is locally stable if reproduction number is greater that unity and globally stable by the Lasalle’s invariant principle. Numerical simulation to show the dynamics of the compartment at various hygiene rate was carried out.

Numerical Simulation of Subsea Cluster Manifold Installation by the Sheave Method

2018 ◽  
Author(s):  
Yu Zhao ◽  
Yingying Wang ◽  
Liwei Li ◽  
Chao Yang ◽  
Yang Du ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
South China Sea ◽  
Deep Sea ◽  
High Reliability ◽  
Two Dimensional ◽  
Complex Environment ◽  
Lumped Mass ◽  
Lumped Mass Method ◽  
The Mathematical Model

The sheave installation method (SIM) is an effective and non-conventional method to solve the installation of subsea equipment in deep water (>1000m), which has been developed to deploy the 175t Roncador Manifold I into 1,885 meters water depth in 2002. With the weight increment of subsea cluster manifold, how to solve its installation with the high reliability in the deep sea is still a great challenge. In this paper, the installation of the 300t subsea cluster manifold using the SIM is studied in the two-dimensional coordinate system. The mathematical model is established and the lumped mass method is used to calculate the hydrodynamic forces of the wireropes. Taking into account the complex environment loads, the numerical simulation of the lowering process is carried out by OrcaFlex. The displacement and vibration of the subsea cluster manifold in the z-axis direction and the effective tension at the top of the wireropes can be gotten, which can provide guidance for the installation of the cluster manifold in the South China Sea.

scholarly journals Population Behavior in the Mathematical Model of the Spread of COVID19 Type SEIRS

2021 ◽  
Vol 6 (2) ◽  
pp. 83-88
Author(s):  
Asmaidi As Med ◽  
Resky Rusnanda
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Everyday Life ◽  
Applied Mathematics ◽  
Living Things ◽  
Simulation Results ◽  
Parameter Values ◽  
The Mathematical Model ◽  
Disease Free

Mathematical modeling utilized to simplify real phenomena that occur in everyday life. Mathematical modeling is popular to modeling the case of the spread of disease in an area, the growth of living things, and social behavior in everyday life and so on. This type of research is included in the study of theoretical and applied mathematics. The research steps carried out include 1) constructing a mathematical model type SEIRS, 2) analysis on the SEIRS type mathematical model by using parameter values for conditions 1and , 3) Numerical simulation to see the behavior of the population in the model, and 4) to conclude the results of the numerical simulation of the SEIRS type mathematical model. The simulation results show that the model stabilized in disease free quilibrium for the condition  and stabilized in endemic equilibrium for the condition .

scholarly journals Numerical simulation of changes in the electric properties of biological tissues under local heating by laser radiation

2021 ◽  
Vol 2090 (1) ◽  
pp. 012049
Author(s):  
N V Kovalenko ◽  
A V Smirnov ◽  
O A Ryabushkin
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Laser Radiation ◽  
Optical Radiation ◽  
Local Heating ◽  
Biological Tissues ◽  
Electric Properties ◽  
Reliable Tool ◽  
The Mathematical Model

Abstract The mathematical model that describes the local heating of biological tissues by optical radiation is introduced. Changes of the electric properties of biological tissues in such process can be used as a reliable tool for analyzing heating and damage degrees of tissues.

scholarly journals On Numerical Simulation Approach for Multiple Resonance Modes in Servo Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Qixin Zhu ◽  
Hongli Liu ◽  
Yiyi Yin ◽  
Lei Xiong ◽  
Yonghong Zhu
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Closed Loop ◽  
Resonance Mode ◽  
Servo Control ◽  
Simulation Approach ◽  
Servo Systems ◽  
Resonance Modes ◽  
Resonant Part ◽  
The Mathematical Model

Mechanical resonance is one of the most pervasive problems in servo control. Closed-loop simulations are requisite when the servo control system with high accuracy is designed. The mathematical model of resonance mode must be considered when the closed-loop simulations of servo systems are done. There will be a big difference between the simulation results and the real actualities of servo systems when the resonance mode is not considered in simulations. Firstly, the mathematical model of resonance mode is introduced in this paper. This model can be perceived as a product of a differentiation element and an oscillating element. Secondly, the second-order differentiation element is proposed to simulate the resonant part and the oscillating element is proposed to simulate the antiresonant part. Thirdly, the simulation approach for two resonance modes in servo systems is proposed. Similarly, this approach can be extended to the simulation of three or even more resonances in servo systems. Finally, two numerical simulation examples are given.

Dynamics of Shock Waves in the Cylindrical Channel With Confusers

2009 ◽  
Vol 4 (2) ◽  
pp. 13-18
Author(s):  
Igor Anufriev ◽  
Aleksandr Golovanov ◽  
Aleksandr Tsimbalyuk ◽  
Oleg Sharypov
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Shock Wave ◽  
Shock Wave Front ◽  
Gas Flow ◽  
Cylindrical Channel ◽  
Maximal Pressure ◽  
The Mathematical Model ◽  
Forest Combustible ◽  
Gunpowder Charge

Current work covers experimental and theoretical investigation of conic confusers impact on the intensity shock wave, generated in the shock tube by explosion of gunpowder charge. For given conditions optimal geometric characteristics of the confuser, providing maximal pressure in the shock wave front, were found experimentally. The mathematical model was developed and numerical simulation of the axisymmetric shock-wave gas flow in the channel was carried out. Experimentally was shown, that the application of the optimal confuser provides significant increase of the efficiency gasdynamic effect on the combustion of forest combustible materials.

scholarly journals Study on Fluorine Pollution in a Slag Yard

2019 ◽  
Vol 9 (5) ◽  
pp. 847
Author(s):  
Lide Wei ◽  
Changfu Wei ◽  
Sugang Sui
Keyword(s):  
Numerical Simulation ◽  
Experimental Investigation ◽  
Numerical Simulations ◽  
Solute Transport ◽  
Large Scale ◽  
Three Dimensional ◽  
Simulation Method ◽  
Laboratory Studies ◽  
Survey Results ◽  
Simulation Results

This paper suggests a large-scale three-dimensional numerical simulation method to investigate the fluorine pollution near a slag yard. The large-scale three-dimensional numerical simulation method included an experimental investigation, laboratory studies of solute transport during absorption of water by soil, and large-scale three-dimensional numerical simulations of solute transport. The experimental results showed that the concentrations of fluorine from smelting slag and construction waste soil were well over the discharge limit of 0.1 kg/m3 recommended by Chinese guidelines. The key parameters of the materials used for large-scale three-dimensional numerical simulations were determined based on an experimental investigation, laboratory studies, and soil saturation of survey results and back analyses. A large-scale three-dimensional numerical simulation of solute transport was performed, and its results were compared to the experiment results. The simulation results showed that the clay near the slag had a high saturation of approximately 0.9, consistent with the survey results. Comparison of the results showed that the results of the numerical simulation of solute transport and the test results were nearly identical, and that the numerical simulation results could be used as the basis for groundwater environmental evaluation.

scholarly journals Automated continuous verification for numerical simulation

2011 ◽  
Vol 4 (2) ◽  
pp. 435-449 ◽  
Author(s):  
P. E. Farrell ◽  
M. D. Piggott ◽  
G. J. Gorman ◽  
D. A. Ham ◽  
C. R. Wilson ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Computational Model ◽  
Discrete Event ◽  
Software Implementation ◽  
Test Cases ◽  
Continuous Development ◽  
Wide Applicability ◽  
Model Code ◽  
The Mathematical Model

Abstract. Verification is a process crucially important for the final users of a computational model: code is useless if its results cannot be relied upon. Typically, verification is seen as a discrete event, performed once and for all after development is complete. However, this does not reflect the reality that many geoscientific codes undergo continuous development of the mathematical model, discretisation and software implementation. Therefore, we advocate that in such cases verification must be continuous and happen in parallel with development: the desirability of their automation follows immediately. This paper discusses a framework for automated continuous verification of wide applicability to any kind of numerical simulation. It also documents a range of test cases to show the possibilities of the framework.

Research on the Blank Design Method of Closed Rolling the High-Neck Flange

2011 ◽  
Vol 314-316 ◽  
pp. 594-598
Author(s):  
Min Xiao ◽  
Xue Dao Shu
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Design Method ◽  
Scientific Basis ◽  
Shape Design ◽  
Blank Design ◽  
Rolling Method ◽  
Blank Shape ◽  
Blank Size ◽  
The Mathematical Model

Blank shape design is the prerequisite and foundation of optimization for the closed forming the high-neck flange. This paper obtained the design formulas of blank size with analyzing the mathematical model of flank blank based on the principle of volume invariably during the rolling process.The blank of a special flange was designed by this method which was validated by the numerical simulation under the DEFORM software. The results indicate that the product is qualified with the blank shape based on this method. These research conclusions can provide scientific basis for forming the high-neck flange with rolling method.

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