Multiple steady state phenomenon in martensitic transformation

Based on the basic facts that the martensitic transformation is a physical phenomenon which occurs in non equilibrium conditions and there exists the feedback mechanism in the martensitic transformation, the dynamical processes of the isothermal and athermal martensitic transformations were analyzed by using nonlinear theory and a bifurcation theory model was established. It is shown that a multiple steady state phenomenon can take place as austenite is cooled, and the transitions of the steady state temperature between the branches of stable steady states can be considered the transformation from austenite to martensite. This model can estimate the starting temperature of the martensitic transformation and explain some experimental features of the martensitic transformation such as the effects of cooling rate, fluctuation and austenitic grain size on the martensitic transformation. [

A Mathematical Model of the Photosynthetic Carbon Metabolism Has Multiple Steady States Under the Same Parameter Conditions

This paper analyzes a mathematical model of the photosynthetic carbon metabolism, which incorporates not only the Calvin-Benson cycle, but also another two important metabolic pathways： starch synthesis and photorespiratory pathway. Theoretically, the paper shows the existence of steady states, stability and instability of the steady states, the effects of CO2 concentration on steady states. Especially, a critical point is found, the system has only one steady state with C02 concentration in the left neighborhood of the critical point, but has two with C02 concentration in the right neighborhood. In addition, the paper also explores the influence of C02 concentration on the efficiency of photosynthesis. These theoretical results not only provide insight to the kinetic behaviors of the photosynthetic carbon metabolism, but also can be used to help improving the efficiency of photosynthesis in plants.

The Bifurcation Behavior of CO Coupling Reactor

The bifurcation behavior of the CO coupling reactor was examined based on the one-dimensional pseudo homogeneous axial dispersion dynamic model. The method of finite difference was used for solving the boundary value problem; the continuation technique and the direct method were applied to determine the bifurcation diagram. The effects of dimensionless adiabatic temperature rise, Damkohler number, activation energy, heat transfer coefficient and feed ratio on the bifurcation behavior were investigated. It was shown that there existed static bifurcation and the oscillations did not occur in the reactor. The result also revealed that the reactor exhibited at most 1-3-1 multiplicity patterns within the range of practical possible parameters and the measures, such as weakening the axial dispersion of reactor, enhancing heat transfer, decreasing the concentration of ethyl nitrite, were efficient for avoiding the possible risk of multiple steady states.

Development of a bifurcation analysis approach based on gPROMS platform

A bifurcation analysis approach is developed based on the process simulator gPROMS platform, which can automatically trace a solution path, detect and pass the bifurcation points and check the stability of solutions. The arclength continuation algorithm is incorporated as a process entity in gPROMS to overcome the limit of turning points and get multiple solutions with respect to a user-defined parameter. The bifurcation points are detected through a bifurcation test function τ which is written in C ++ routine as a foreign object connected with gPROMS through Foreign Process Interface. The stability analysis is realized by evaluating eigenvalues of the Jacobian matrix of each steady state solution. Two reference cases of an adiabatic CSTR and a homogenous azeotropic distillation from literature are studied, which successfully validate the reliability of the proposed approach. Besides the multiple steady states and Hopf bifurcation points, a more complex homoclinic bifurcation behavior is found for the distillation case compared to literature.

An Improved Cass-Koopmans Model with Endogenous Fertility under the CES Production Technology

Under the CES production technology, an improved Cass Coopmans model with solvable endogenous fertility is given. We prove that there are multiple growth paths and multiple steady states when CES 0<σ<1 and the technology level is high enough; the growth path and the steady state is unique when σ>1 and the ratio of capital is smaller than a constant. So, the dynamic system which describes the model undergoes a bifurcation when σ=1 . We discuss the economic sense of the main results we give.

Simultaneous H_2/H_∞ Stabilization for Chemical Reaction Systems Based on Orthogonal Complement Space

This paper presents a simultaneous H2/H∞ stabilization problem for the chemical reaction systems which can be modeled as a finite collection of subsystems. A single dynamic output feedback controller which simultaneously stabilizes the multiple subsystems and captures the mixed H2/H∞ control performance is designed. To ensure that the stability condition, the H2 characterization and the H∞ characterization can be enforced within a unified matrix inequality framework, a novel technique based on orthogonal complement space is developed. Within such a framework, the controller gain is parameterized by the introduction of a common free positive definite matrix, which is independent of the multiple Lyapunov matrices. An iterative linear matrix inequality （ILMI） algorithm using Matlab Yalmip toolbox is established to deal with the proposed framework. Simulation results of a typical chemical reaction system are exploited to show the validity of the proposed methodology.

A Semi-Implicit Fractional Step Method Immersed Boundary Method for the Numerical Simulation of Natural Convection Non-Boussinesq Flows

The paper presents a novel pressure-corrected formulation of the immersed boundary method(IBM)for the simulation of fully compressible non-Boussinesq natural convection flows.The formulation incorporated into the pressure-based fractional step approach facilitates simulation of the flows in the presence of an immersed body characterized by a complex geometry.Here,we first present extensive grid independence and verification studies addressing incompressible pressure-driven flow in an extended channel and non-Boussinesq natural convection flow in a differentially heated cavity.Next,the steady-state non-Boussinesq natural convection flow developing in the presence of hot cylinders of various diameters placed within a cold square cavity is thoroughly investigated.The obtained results are presented and analyzed in terms of the spatial distribution of path lines and temperature fields and of heat flux values typical of the hot cylinder and the cold cavity surfaces.Flow characteristics of multiple steady-state solutions discovered for several configurations are presented and discussed in detail.