scholarly journals An asymptotic preserving scheme for a tumor growth model of porous medium type

2021 ◽  
Author(s):  
Xinran Ruan ◽  
Noemi David
Keyword(s):  
Porous Medium ◽  
Tumor Growth ◽  
Pressure Gradients ◽  
Asymptotic Preserving ◽  
Tumor Growth Model ◽  
Mechanical Models ◽  
The Stability ◽  
Limiting Case ◽  
Medium Type ◽  
Stability Results

Mechanical models of tumor growth based on a porous medium approach have been attracting a lot of interest both analytically and numerically. In this paper, we study the stability properties of a finite difference scheme for a model where the density evolves down pressure gradients and the growth rate depends on the pressure and possibly nutrients. Based on the stability results, we prove the scheme to be asymptotic preserving (AP) in the incompressible limit. Numerical simulations are performed in order to investigate the regularity of the pressure. We study the sharpness of the $L^4$-uniform bound of the gradient, the limiting case being a solution whose support contains a bubble which closes-up in finite time generating a singularity, the so-called focusing solution.

Epitaxial Growth in Dislocation-Free Strained Alloy Films

2002 ◽  
Vol 715 ◽  
Author(s):  
Zhi-Feng Huang ◽  
Rashmi C. Desai
Keyword(s):  
Deposition Rate ◽  
Elastic Moduli ◽  
Composition Dependence ◽  
Critical Thickness ◽  
Lattice Misfit ◽  
Misfit Strain ◽  
Joint Stability ◽  
Alloy Films ◽  
The Stability ◽  
Stability Results

AbstractThe morphological and compositional instabilities in the heteroepitaxial strained alloy films have attracted intense interest from both experimentalists and theorists. To understand the mechanisms and properties for the generation of instabilities, we have developed a nonequilibrium, continuum model for the dislocation-free and coherent film systems. The early evolution processes of surface pro.les for both growing and postdeposition (non-growing) thin alloy films are studied through a linear stability analysis. We consider the coupling between top surface of the film and the underlying bulk, as well as the combination and interplay of different elastic effects. These e.ects are caused by filmsubstrate lattice misfit, composition dependence of film lattice constant (compositional stress), and composition dependence of both Young's and shear elastic moduli. The interplay of these factors as well as the growth temperature and deposition rate leads to rich and complicated stability results. For both the growing.lm and non-growing alloy free surface, we determine the stability conditions and diagrams for the system. These show the joint stability or instability for film morphology and compositional pro.les, as well as the asymmetry between tensile and compressive layers. The kinetic critical thickness for the onset of instability during.lm growth is also calculated, and its scaling behavior with respect to misfit strain and deposition rate determined. Our results have implications for real alloy growth systems such as SiGe and InGaAs, which agree with qualitative trends seen in recent experimental observations.

scholarly journals A stable scheme for a nonlinear, multiphase tumor growth model with an elastic membrane

2014 ◽  
Vol 30 (7) ◽  
pp. 726-754 ◽  
Author(s):  
Ying Chen ◽  
Steven M. Wise ◽  
Vivek B. Shenoy ◽  
John S. Lowengrub
Keyword(s):  
Tumor Growth ◽  
Growth Model ◽  
Elastic Membrane ◽  
Tumor Growth Model ◽  
Stable Scheme

scholarly journals Robust domain of attraction estimation for a tumor growth model

2021 ◽  
Vol 410 ◽  
pp. 126482
Author(s):  
Kaouther Moussa ◽  
Mirko Fiacchini ◽  
Mazen Alamir
Keyword(s):  
Tumor Growth ◽  
Growth Model ◽  
Domain Of Attraction ◽  
Tumor Growth Model

scholarly journals Personalized Radiotherapy Planning Based on a Computational Tumor Growth Model

2017 ◽  
Vol 36 (3) ◽  
pp. 815-825 ◽  
Author(s):  
Matthieu Le ◽  
Herve Delingette ◽  
Jayashree Kalpathy-Cramer ◽  
Elizabeth R. Gerstner ◽  
Tracy Batchelor ◽  
...  
Keyword(s):  
Tumor Growth ◽  
Growth Model ◽  
Radiotherapy Planning ◽  
Tumor Growth Model

SYSTEM IDENTIFICATION IN TUMOR GROWTH MODELING USING SEMI-EMPIRICAL EIGENFUNCTIONS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250003 ◽  
Author(s):  
THIERRY COLIN ◽  
ANGELO IOLLO ◽  
DAMIANO LOMBARDI ◽  
OLIVIER SAUT
Keyword(s):  
System Identification ◽  
Tumor Growth ◽  
Solution Space ◽  
Cellular Division ◽  
Volume Increase ◽  
Tumor Growth Model ◽  
Species Population ◽  
Tumor Growth Modeling ◽  
Low Dimensional ◽  
Semi Empirical

A tumor growth model based on a parametric system of partial differential equations is considered. The system corresponds to a phenomenological description of a multi-species population evolution. A velocity field taking into account the volume increase due to cellular division is introduced and the mechanical closure is provided by a Darcy-type law. The complexity of the biological phenomenon is taken into account through a set of parameters included in the model that need to be calibrated. To this end, a system identification method based on a low-dimensional representation of the solution space is introduced. We solve several idealized identification cases corresponding to typical situations where the information is scarce in time and in terms of observable fields. Finally, applications to actual clinical data are presented.

scholarly journals On Minimum-B Stabilization of Electrostatic Drift Instabilities

1966 ◽  
Vol 21 (11) ◽  
pp. 1953-1959 ◽  
Author(s):  
R. Saison ◽  
H. K. Wimmel
Keyword(s):  
Dispersion Relation ◽  
Particle Distribution ◽  
Inhomogeneous Plasma ◽  
Distribution Functions ◽  
Loss Cone ◽  
First Order ◽  
Stabilization Theorem ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Limiting Case

A check is made of a stabilization theorem of ROSENBLUTH and KRALL (Phys. Fluids 8, 1004 [1965]) according to which an inhomogeneous plasma in a minimum-B field (β ≪ 1) should be stable with respect to electrostatic drift instabilities when the particle distribution functions satisfy a condition given by TAYLOR, i. e. when f0 = f(W, μ) and ∂f/∂W < 0 Although the dispersion relation of ROSENBLUTH and KRALL is confirmed to first order in the gyroradii and in ε ≡ d ln B/dx z the stabilization theorem is refuted, as also is the validity of the stability criterion used by ROSEN-BLUTH and KRALL, ⟨j·E⟩ ≧ 0 for all real ω. In the case ωpi ≫ | Ωi | equilibria are given which satisfy the condition of TAYLOR and are nevertheless unstable. For instability it is necessary to have a non-monotonic ν ⊥ distribution; the instabilities involved are thus loss-cone unstable drift waves. In the spatially homogeneous limiting case the instability persists as a pure loss cone instability with Re[ω] =0. A necessary and sufficient condition for stability is D (ω =∞, k,…) ≦ k2 for all k, the dispersion relation being written in the form D (ω, k, K,...) = k2+K2. In the case ωpi ≪ | Ωi | adherence to the condition given by TAYLOR guarantees stability.

scholarly journals Bayesian Personalization of Brain Tumor Growth Model

2015 ◽  
pp. 424-432 ◽  
Author(s):  
Matthieu Lê ◽  
Hervé Delingette ◽  
Jayashree Kalpathy-Cramer ◽  
Elizabeth R. Gerstner ◽  
Tracy Batchelor ◽  
...  
Keyword(s):  
Brain Tumor ◽  
Tumor Growth ◽  
Growth Model ◽  
Tumor Growth Model

scholarly journals Analysis of dengue model with fractal-fractional Caputo–Fabrizio operator

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Fatmawati ◽  
Muhammad Altaf Khan ◽  
Cicik Alfiniyah ◽  
Ebraheem Alzahrani
Keyword(s):  
Statistical Data ◽  
Dengue Infection ◽  
Fractional Operator ◽  
Novel Approach ◽  
Reduction Number ◽  
Best Fitting ◽  
The Stability ◽  
Parameter Values ◽  
Graphical Illustration ◽  
Stability Results

AbstractIn this work, we study the dengue dynamics with fractal-factional Caputo–Fabrizio operator. We employ real statistical data of dengue infection cases of East Java, Indonesia, from 2018 and parameterize the dengue model. The estimated basic reduction number for this dataset is $\mathcal{R}_{0}\approx2.2020$ R 0 ≈ 2.2020 . We briefly show the stability results of the model for the case when the basic reproduction number is $\mathcal{R}_{0} <1$ R 0 < 1 . We apply the fractal-fractional operator in the framework of Caputo–Fabrizio to the model and present its numerical solution by using a novel approach. The parameter values estimated for the model are used to compare with fractal-fractional operator, and we suggest that the fractal-fractional operator provides the best fitting for real cases of dengue infection when varying the values of both operators’ orders. We suggest some more graphical illustration for the model variables with various orders of fractal and fractional.

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