166 citations · 316 across the 24 of their papers we have counts for
24 papers
Pattern formation of a pathway-based diffusion model: linear stability analysis and an asymptotic preserving method
Yaming Zhang, Ning Jiang, Jiangyan Liang +2
We investigate the linear stability analysis of a pathway-based diffusion model (PBDM), which characterizes the dynamics of the engineered Escherichia coli populations [X. Xue and…
A fully asymptotic preserving decomposed multi-group method for the frequency-dependent radiative transfer equations
Xiaojiang Zhang, Peng Song, Yi Shi +1
The opacity of FRTE depends on not only the material temperature but also the frequency, whose values may vary several orders of magnitude for different frequencies. The gray radia…
Tumor boundary instability induced by nutrient consumption and supply
Yu Feng, Min Tang, Xiaoqian Xu +1
We investigate the tumor boundary instability induced by nutrient consumption and supply based on a Hele-Shaw model derived from taking the incompressible limit of a cell density m…
Kinetic chemotaxis tumbling kernel determined from macroscopic quantities
Kathrin Hellmuth, Christian Klingenberg, Qin Li +1
Chemotaxis is the physical phenomenon that bacteria adjust their motions according to chemical stimulus. A classical model for this phenomenon is a kinetic equation that describes…
Multiscale convergence of the inverse problem for chemotaxis in the Bayesian setting
Kathrin Hellmuth, Christian Klingenberg, Qin Li +1
Chemotaxis describes the movement of an organism, such as single or multi-cellular organisms and bacteria, in response to a chemical stimulus. Two widely used models to describe th…
On kinetic and macroscopic models for the stripe formation in engineered bacterial populations
Ning Jiang, Jiangyan Liang, Yi-Long Luo +2
We study the well-posedness of the biological models with AHL-dependent cell mobility on engineered Escherichia coli populations. For the kinetic model proposed by Xue-Xue-Tang rec…
A Spatial-Temporal asymptotic preserving scheme for radiation magnetohydrodynamics in the equilibrium and non-equilibrium diffusion limit
Shi Jin, Min Tang, Xiaojiang Zhang
The radiation magnetohydrodynamics (RMHD) system couples the ideal magnetohydrodynamics equations with a gray radiation transfer equation. The main challenge is that the radiation…
Mathematical Modelling and Analysis of Fractional Diffusion Induced by Intracellular Noise
Weiran Sun, Min Tang, Xiaoru Xue
In this paper we use an individual-based model and its associated kinetic equation to study the generation of long jumps in the motion of E. coli. These models relate the run-and-t…
Towards understanding the boundary propagation speeds in tumor growth models
Jian-Guo Liu, Min Tang, Li Wang +1
At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific…
Multiple asymptotics of Kinetic Equations with Internal States
Benoit Perthame, Weiran Sun, Min Tang +1
The run and tumble process is well established in order to describe the movement of bacteria in response to a chemical stimulus. However the relation between the tumbling rate and…
Analysis and computation of some tumor growth models with nutrient: from cell density models to free boundary dynamics
Jian-Guo Liu, Min Tang, Li Wang +1
In this paper, we study the tumor growth equation along with various models for the nutrient component, including the \emph{in vitro} model and the \emph{in vivo} model. At the cel…
The fractional diffusion limit of a kinetic model with biochemical pathway
Benoît Perthame, Weiran Sun, Min Tang
Kinetic-transport equations that take into account the intra-cellular pathways are now considered as the correct description of bacterial chemotaxis by run and tumble. Recent mathe…
An accurate front capturing scheme for tumor growth models with a free boundary limit
Jian-Guo Liu, Min Tang, Li Wang +1
We consider a class of tumor growth models under the combined effects of density-dependent pressure and cell multiplication, with a free boundary model as its singular limit when t…
Uniform convergent scheme for strongly anisotropic diffusion equations with closed field lines
Yihong Wang, Wenjun Ying, Min Tang
In magnetized plasma, the magnetic field confines particles around field lines. The ratio between the intensity of the parallel and perpendicular viscosity or heat conduction may r…
An Asymptotic Preserving method for strongly anisotropic diffusion equations based on field line integration
Min Tang, Yihong Wang
In magnetized plasma, the magnetic field confines the particles around the field lines. The anisotropy intensity in the viscosity and heat conduction may reach the order of $10^{12…
Macroscopic limits of pathway-based kinetic models for E.coli chemotaxis in large gradient environments
Weiran Sun, Min Tang
It is of great biological interest to understand the molecular origins of chemotactic behavior of E. coli by developing population-level models based on the underlying signaling pa…
Well-balanced and asymptotic preserving schemes for kinetic models
Casimir Emako, Min Tang
In this paper, we propose a general framework for designing numerical schemes that have both well-balanced (WB) and asymptotic preserving (AP) properties, for various kinds of kine…
Derivation of the bacterial run-and-tumble kinetic equation from a model with biochemical pathway
Benoît Perthame, Min Tang, Nicolas Vauchelet
Kinetic-transport equations are, by now, standard models to describe the dynamics of populations of bacteria moving by run-and-tumble. Experimental observations show that bacteria…
Traveling wave solution of the Hele-Shaw model of tumor growth with nutrient
Benoît Perthame, Min Tang, Nicolas Vauchelet
Several mathematical models of tumor growth are now commonly used to explain medical observations and predict cancer evolution based on images. These models incorporate mechanical…
Derivation of a Hele-Shaw type system from a cell model with active motion
Benoît Perthame, Fernando Quirós, Min Tang +1
We formulate a Hele-Shaw type free boundary problem for a tumor growing under the combined effects of pressure forces, cell multiplication and active motion, the latter being the n…
A pathway-based mean-field model for E. coli chemotaxis: Mathematical derivation and Keller-Segel limit
Guangwei Si, Min Tang, Xu Yang
A pathway-based mean-field theory (PBMFT) was recently proposed for E. coli chemotaxis in [G. Si, T. Wu, Q. Quyang and Y. Tu, Phys. Rev. Lett., 109 (2012), 048101]. In this paper,…
Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation
Gregoire Nadin, Benoit Perthame, Min Tang
This note investigates the properties of the traveling waves solutions of the nonlocal Fisher equation. The existence of such solutions has been proved recently in \cite{BNPR} but…
Traveling plateaus for a hyperbolic Keller-Segel system with attraction and repulsion: existence and branching instabilities
Benoit Perthame, Christian Schmeiser, Min Tang +1
How can repulsive and attractive forces, acting on a conservative system, create stable traveling patterns or branching instabilities? We have proposed to study this question in th…
All speed scheme for the low mach number limit of the Isentropic Euler equation
Pierre Degond, Min Tang
An all speed scheme for the Isentropic Euler equation is presented in this paper. When the Mach number tends to zero, the compressible Euler equation converges to its incompressibl…