NACO

In this paper, the nonlinear enzyme-catalytic kinetic system of
batch and continuous fermentation in the process of glycerol
bio-dissimilation is investigated. On the basis of both glycerol and
1,3-PD pass the cell membrane by active and passive diffusion under
substrate-sufficient conditions, we consider the delay of
concentration changes on both extracellular substances and
intracellular substances. We establish a nonlinear delay dynamical
system according to the batch and continuous fermentation of
bio-dissimilation of glycerol to 1,3-propanediol(1,3-PD) and we
propose an identification problem, in which the biological
robustness is taken as a performance index, constrained with
nonlinear delay dynamical system. An algorithm is constructed to
solve the identification problem and the numerical result shows the
values of time delays of glycerol, 3-HPA, 1,3-PD intracellular and
extracellular substances. This work will be helpful for deeply
understanding the metabolic mechanism of glycerol in batch and
continuous fermentation.

JIMO

In this study simplified mathematical models
of the nonlinear dynamic systems of dissimilation of glycerol to
1,3-propanediol by {\it Klebsiella pneumoniae} in continuous,
batch and fed-batch cultures are investigated. Considering big
errors between the experimental results and computational values
in the existing models, the parameter identification
models for these systems are established. The properties of the
solutions for the nonlinear dynamic systems are discussed and the
identifiability of the parameters is proved. In view of the
sudden increase of the glycerol
and alkali in fed-batch culture, this paper proposes a nonlinear
impulsive system of fed-batch culture. The existence, uniqueness
and regularity properties of piecewise solution for the system are
proved. Based on the nonlinear impulsive system, the paper
constructs an optimal control model in view of the controllability
of volumes of glycerol added to the reactor instantaneously, and
the existence of the optimal control is obtained.

JIMO

For the Arctic ice layer with high
temperature in summer, the concepts of enthalpy degree, specific
enthalpy and enthalpy conduction coefficient etc. are introduced
in terms of the concept of enthalpy in calorifics. Heat conduction
equation of enthalpy is constructed in the process of phase
transformation of the Arctic ice. The condition of determinant
solution and the identification model of diffusion coefficient of
enthalpy are presented. Half implicit difference scheme and
Schwartz alternating direction iteration are applied to solve the
enthalpy conduction equation and sensitivity equation. Furthermore
the Newton-Raphson algorithm is used for identification. The
numerical results illustrate that the mathematic model and
optimization algorithm are precise and feasible by the
data(2003.8)of the Second Chinese Arctic Research Expedition in
situ.

JIMO

This paper presents a mathematical model for Layout optimization
of structure with discrete variables. The optimization procedure
is composed of two kinds of sub-procedures of optimization: the
topological optimization and the shape optimization. In each one,
a comprehensive algorithm is used to treat the problem. The two
kinds of optimization procedures are used in turn until
convergence appears. After the dimension of the structure is
reduced, the delimiting combinatorial algorithm is used to search
for the better objective value. A couple of classical examples are
presented to show the efficiency of the method. Numerical results
indicate that the method is efficient and the optimal results are
satisfactory.

JIMO

In this paper, we propose a new
controlled multistage system to formulate the fed-batch culture
process of glycerol bio-dissimilation to 1,3-propanediol (1,3-PD) by
regarding the feeding rate of glycerol as a control function.
Compared with the previous systems, this system doesn't take the
feeding process as an impulsive form, but a time-continuous process,
which is much closer to the actual culture process. Some properties
of the above dynamical system are then proved. To maximize the
concentration of 1,3-PD at the terminal time, we develop an optimal
control model subject to our proposed controlled multistage system
and continuous state inequality constraints. The existence of
optimal control is proved by bounded variation theory. Through the
discretization of the control space, the control function is
approximated by piecewise constant functions. In this way, the
optimal control model is approximated by a sequence of parameter
optimization problems. The convergence analysis of this
approximation is also investigated. Furthermore, a global
optimization algorithm is constructed on the basis of the above
descretization concept and an improved Particle Swarm Optimization
(PSO) algorithm. Numerical results show that, by employing the
optimal control policy, the concentration of 1,3-PD at the terminal
time can be
increased considerably.

JIMO

Dissolved oxygen (DO) is one of the main parameters to assess the quality of lake water. This study is intended to construct a parabolic distributed parameter system to describe the variation of DO under the ice, and identify the vertical exchange coefficient *K* of DO with the field data. Based on the existence and uniqueness of the weak solution of this system, the fixed solution problem of the parabolic equation is transformed into a parameter identification model, which takes *K* as the identification parameter, and the deviation of the simulated and measured DO as the performance index. We prove the existence of the optimal parameter of the identification model, and derive the first order optimality conditions. Finally, we construct the optimization algorithm, and have carried out numerical simulation. According to the measured DO data in Lake Valkea-Kotinen (Finland), it can be found that the orders of magnitude of the coefficient *K* varying from 10^{-6} to 10^{-1} m^{2} s^{-1}, the calculated and measured DO values are in good agreement. Within this range of *K* values, the overall trends are very similar. In order to get better fitting, the formula needs to be adjusted based on microbial and chemical consumption rates of DO.