scholarly journals Development and steady states of transverse dunes: A numerical analysis of dune pattern coarsening and giant dunes

2015 ◽  
Vol 120 (10) ◽  
pp. 2200-2219 ◽  
Author(s):  
Xin Gao ◽  
Clément Narteau ◽  
Olivier Rozier
Keyword(s):  
Numerical Analysis ◽  
Steady States ◽  
Transverse Dunes

scholarly journals Piecewise synergetic systems and applications in biochemical systems theory

2017 ◽  
Vol 24 (1) ◽  
pp. 135-148
Author(s):  
Arcady Ponosov ◽  
Anna Machina ◽  
Valeria Tafintseva
Keyword(s):  
Numerical Analysis ◽  
Systems Theory ◽  
Optimization Problem ◽  
Compartment Model ◽  
Steady States ◽  
Estimation Of Parameters ◽  
Convergence Of Solutions ◽  
Biochemical Systems Theory ◽  
Biochemical Systems ◽  
Theoretical And Numerical Analysis

AbstractWe study piecewise synergetic systems originating from Biochemical Systems Theory. In the first part of the paper, the emphasis is put on practical calculations with such systems. We consider four examples: calculation of trajectories and steady states, solution of an optimization problem and a method of estimation of parameters (kinetic orders), all examples being biologically motivated. In the second part of the paper, we study convergence of solutions, in particularly, steady states, of a sequence of piecewise synergetic systems approximating an arbitrary compartment model. This convergence analysis is then applied to the optimization problem and the method of estimating sensitivities (kinetic orders) in a generic compartment model. In this paper we put forward arguments for the importance of the theoretical and numerical analysis of piecewise synergetic systems.

scholarly journals Bifurcation Analysis of a Model of Cancer

2016 ◽  
Vol 12 (3) ◽  
pp. 67 ◽  
Author(s):  
Abdo M. Al-Mahdi ◽  
Mustafa Q. Khirallah
Keyword(s):  
Numerical Analysis ◽  
Bifurcation Analysis ◽  
System Parameter ◽  
Steady States ◽  
Cancer Model ◽  
Unknown Parameters ◽  
Numerical Examples ◽  
System Parameters ◽  
Parameter Values

In this paper, we study the bifurcation of a cancer model with completely unknown parameters. The bifurcation analysis of the biologically feasible steady-states of this model will be discussed. It is proved that the system appears to exhibit many cases of bifurcation for some ranges of system parameters. Numerical analysis and extensive numerical examples of the bifurcation for some ranges were carried out for various system parameter values and different initial densities.

scholarly journals Spontaneous Formations of Dynamical Steady States in Polariton Condensates

2021 ◽  
Vol 9 ◽  
Author(s):  
Zhen-Xia Niu ◽  
Wei Zhang
Keyword(s):  
Numerical Analysis ◽  
Topological Defects ◽  
Steady States ◽  
Decay Rates ◽  
Winding Number ◽  
Fast Decay ◽  
Optical Pump ◽  
Long Time ◽  
Exciton Interactions ◽  
Bose Einstein

We present a numerical analysis on dynamical steady states of polariton Bose–Einstein condensates (BECs) in an incoherent exciton reservoir driven by a ring-shaped optical pump. The balance between the loss and gain of polariton BEC induces a variety of steady states with different configurations, including approximate Gaussian distribution and topological defects, such as vortex–antivortex pairs, vortices with a winding number, and solitons. Besides, the system becomes unstable under fast decay rates and small pumping ring, where BECs can no longer exist in the long-time limit. We also confirm the soliton is dynamically stable in this system, with a steady polariton current induced by the repulsive polariton–polariton and polariton–exciton interactions.

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