A micromechanical model based on hypersingular integro-differential equations for analyzing micro-crazed interfaces between dissimilar elastic materials

2019 ◽  
Vol 41 (2) ◽  
pp. 193-206
Author(s):  
X. Wang ◽  
W. T. Ang ◽  
H. Fan
Keyword(s):  
Differential Equations ◽  
Micromechanical Model ◽  
Elastic Materials ◽  
Model Based

An example of H1-unboundedness of solutions to strongly elliptic systems of partial differential equations in a laminated geometry

1987 ◽  
Vol 105 (1) ◽  
pp. 77-82 ◽  
Author(s):  
Hervé Le Dret
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Elliptic Systems ◽  
Boundedness Of Solutions ◽  
Elastic Materials ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Hadamard Condition

SynopsisIn this paper, a counterexample is given to the H1-boundedness of solutions to a sequence of systems of linear partial differential equations uniformly satisfying a strict Legendre–Hadamard condition and whose coefficients depend on one direction only. This counterexample is relevant for the theory of homogenisation of laminated elastic materials.

An age-structured model of the human papillomavirus dynamics and optimal vaccine control

2017 ◽  
Vol 10 (06) ◽  
pp. 1750083 ◽  
Author(s):  
Mo’tassem Al-Arydah ◽  
Tufail Malik
Keyword(s):  
Human Papillomavirus ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Structured Model ◽  
Vaccination Programs ◽  
Model Based ◽  
Hpv Types ◽  
Catch Up ◽  
Age Structured ◽  
Age Structured Model

We formulate an age-structured model based on a system of nonlinear partial differential equations to assist the early and catch up female vaccination programs for human papillomavirus (HPV) types 6 and 11. Since these HPV types do not induce permanent immunity, the model, which stratifies the population based on age and gender, has a susceptible-infectious-susceptible (SIS) structure. We calculate the effective reproduction number [Formula: see text] for the model and describe the local-asymptotic stability of the disease-free equilibrium using [Formula: see text]. We prove the existence of an endemic equilibrium for [Formula: see text] for the no vaccine case. However, analysis of the model for the vaccine case reveals that it undergoes the phenomenon of backward bifurcation. To support our theoretical results, we estimate the age and time solution with the given data for Toronto population, when an early and catch up female vaccine program is adopted, and when there is no vaccine. We show that early and catch up female vaccine program eliminates the infection in both male and female populations over a period of 30 years. Finally, we introduce the optimal control to an age-dependent model based on ordinary differential equations and solve it numerically to obtain the most cost-effective method for introducing the catch up vaccine into the population.

Model Based Temperature Control in RTP Yielding ±0.1 °C accuracy on A 1000 °C, 2 second, 100 °C/s Spike Anneal

1998 ◽  
Vol 525 ◽  
Author(s):  
Peter Vandenabeele ◽  
Wayne Renken
Keyword(s):  
Differential Equations ◽  
Temperature Control ◽  
Control Method ◽  
Nonlinear Differential Equations ◽  
System Response ◽  
Model Based Control ◽  
First Order ◽  
Model Based ◽  
Measured System ◽  
Spike Anneal

ABSTRACTA Model Based Control method is presented for accurate control of RTP systems. The model uses 4 states: lamp filament temperature, wafer temperature, quartz temperature and TC temperature. A set of 4 first order, nonlinear differential equations describes the model. Feedback is achieved by updating the model, based on a comparison between actual (measured) system response and modeled system response.

scholarly journals Investigating market efficiency through a forecasting model based on differential equations

2017 ◽  
Vol 474 ◽  
pp. 199-212 ◽  
Author(s):  
Charlene C. de Resende ◽  
Adriano C.M. Pereira ◽  
Rodrigo T.N. Cardoso ◽  
A.R. Bosco de Magalhães
Keyword(s):  
Differential Equations ◽  
Market Efficiency ◽  
Forecasting Model ◽  
Model Based

scholarly journals Global Dynamics of the Hořava–Lifshitz Cosmological Model in a Non-Flat Universe with Non-Zero Cosmological Constant

Universe ◽  
2021 ◽  
Vol 7 (11) ◽  
pp. 445
Author(s):  
Fabao Gao ◽  
Jaume Llibre
Keyword(s):  
Differential Equations ◽  
Cosmological Model ◽  
Cosmological Constant ◽  
Qualitative Theory ◽  
Global Dynamics ◽  
Model Based ◽  
Flat Universe

When the cosmological constant is non-zero, the dynamics of the cosmological model based on Hořava–Lifshitz gravity in a non-flat universe are characterized by using the qualitative theory of differential equations.

scholarly journals The Morbidity of Multivariable Grey Model MGM(1,m)

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
Author(s):  
Haixia Wang ◽  
Lingdi Zhao ◽  
Mingzhao Hu
Keyword(s):  
Differential Equations ◽  
Grey Model ◽  
Grey Prediction ◽  
Model Based

This paper proposes the morbidity of the multivariable grey prediction MGM(1,m) model. Based on the morbidity of the differential equations, properties of matrix, and Gerschgorin Panel Theorem, we analyze the factors that affect the morbidity of the multivariable grey model and give a criterion to justify the morbidity of MGM(1,m). Finally, an example is presented to illustrate the practicality of our results.

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