We investigate the kinetic behavior of a two-species catalysis-driven aggregation model, in which coagulation of species A occurs only with the help of species B. We suppose the monomers of species B are stable and ca...We investigate the kinetic behavior of a two-species catalysis-driven aggregation model, in which coagulation of species A occurs only with the help of species B. We suppose the monomers of species B are stable and cannot selfcoagulate in reaction processes. Meanwhile, the monomers are continuously injected into the system. The model with a constant rate kernel is investigated by means of the mean-field rate equation. We show that the Mneties of the system depends crucially on the details of the input term. The injection rate of species B is assumed to take the given time- dependent form K（t） -t^λ, and the sealing solution of the duster size distribution is then investigated analytically. It is found that the cluster size distribution can satisfy the conventional or modified scaling form in most cases.展开更多
The arguments in this paper lead to a new definition of thermodynamic equilibrium that remedies the deficiencies of the current forms. This definition relates thermodynamic equilibrium to its physical causes and accou...The arguments in this paper lead to a new definition of thermodynamic equilibrium that remedies the deficiencies of the current forms. This definition relates thermodynamic equilibrium to its physical causes and accounts for all factors that determine it for all types of equilibrium. Standard definitions of thermodynamic equilibrium are incomplete. They do not take account of all factors that determine such equilibriums, discuss the impediments which may prevent them being reached or relate the properties that define equilibriums to the physical reasons that determine them when impediments are present. The laws of thermodynamics determine the requirements for equilibrium. These laws arise from the physical behaviour of the molecules in molecular systems and are consequences of the conservation of energy, the energies of molecules, statistics, Newton＇s laws of motion, and the equi-partition of energy. The standard definition of thermodynamic equilibrium correctly defines equilibrium whenever impediments are not factors. The discussion demonstrates how impediments arise, accounts for their role in defining equilibrium and how they relate to the energies of molecules at the conditions of the system. The new definition applies to all types of equilibrium.展开更多
This paper deals with a scalar conservation law in 1-D space dimension, and in particular, the focus is on the stability analysis for such an equation. The problem of feedback stabilization under proportional-integral...This paper deals with a scalar conservation law in 1-D space dimension, and in particular, the focus is on the stability analysis for such an equation. The problem of feedback stabilization under proportional-integral-derivative(PID for short) boundary control is addressed. In the proportional-integral(PI for short) controller case, by spectral analysis, the authors provide a complete characterization of the set of stabilizing feedback parameters, and determine the corresponding time delay stability interval. Moreover, the stability of the equilibrium is discussed by Lyapunov function techniques, and by this approach the exponential stability when a damping term is added to the classical PI controller scheme is proved. Also, based on Pontryagin results on stability for quasipolynomials, it is shown that the closed-loop system sub ject to PID control is always unstable.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No.10305009the Natural Science Foundation of Zhejiang Province of China under Grant No.102067
文摘We investigate the kinetic behavior of a two-species catalysis-driven aggregation model, in which coagulation of species A occurs only with the help of species B. We suppose the monomers of species B are stable and cannot selfcoagulate in reaction processes. Meanwhile, the monomers are continuously injected into the system. The model with a constant rate kernel is investigated by means of the mean-field rate equation. We show that the Mneties of the system depends crucially on the details of the input term. The injection rate of species B is assumed to take the given time- dependent form K（t） -t^λ, and the sealing solution of the duster size distribution is then investigated analytically. It is found that the cluster size distribution can satisfy the conventional or modified scaling form in most cases.
文摘The arguments in this paper lead to a new definition of thermodynamic equilibrium that remedies the deficiencies of the current forms. This definition relates thermodynamic equilibrium to its physical causes and accounts for all factors that determine it for all types of equilibrium. Standard definitions of thermodynamic equilibrium are incomplete. They do not take account of all factors that determine such equilibriums, discuss the impediments which may prevent them being reached or relate the properties that define equilibriums to the physical reasons that determine them when impediments are present. The laws of thermodynamics determine the requirements for equilibrium. These laws arise from the physical behaviour of the molecules in molecular systems and are consequences of the conservation of energy, the energies of molecules, statistics, Newton＇s laws of motion, and the equi-partition of energy. The standard definition of thermodynamic equilibrium correctly defines equilibrium whenever impediments are not factors. The discussion demonstrates how impediments arise, accounts for their role in defining equilibrium and how they relate to the energies of molecules at the conditions of the system. The new definition applies to all types of equilibrium.
基金supported by the ERC Advanced Grant 266907(CPDENL)of the 7th Research Framework Programme(FP7)FIRST,Initial Training Network of the European Commission(No.238702)PITNGA-2009-238702
文摘This paper deals with a scalar conservation law in 1-D space dimension, and in particular, the focus is on the stability analysis for such an equation. The problem of feedback stabilization under proportional-integral-derivative(PID for short) boundary control is addressed. In the proportional-integral(PI for short) controller case, by spectral analysis, the authors provide a complete characterization of the set of stabilizing feedback parameters, and determine the corresponding time delay stability interval. Moreover, the stability of the equilibrium is discussed by Lyapunov function techniques, and by this approach the exponential stability when a damping term is added to the classical PI controller scheme is proved. Also, based on Pontryagin results on stability for quasipolynomials, it is shown that the closed-loop system sub ject to PID control is always unstable.
