Discrete state space method and modal extension method based impact sound synthesis model

Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite-state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into an expanded one where each discrete state is represented as a further distinct species. This translation exactly preserves the stochastic dynamics, but the DRE of the expanded network can be interpreted as a correction to the original one. The effectiveness of FSE is demonstrated in models that challenge state-of-the-art techniques due to intrinsic noise, multi-scale populations and multi-stability.

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Hybrid System Control Using Discrete State Space Analysis

IEEE Latin America Transactions ◽

10.1109/tla.2017.7932689 ◽

2017 ◽

Vol 15 (6) ◽

pp. 1027-1033

Author(s):

A. Favela ◽

D. Capriles

Keyword(s):

State Space ◽

Hybrid System ◽

System Control ◽

Discrete State ◽

Space Analysis ◽

State Space Analysis ◽

Discrete State Space

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Study on Small Fluctuation Stability in Air Cushion Surge Chamber Based on State Space Method

Volume 1A, Symposia: Keynotes; Advances in Numerical Modeling for Turbomachinery Flow Optimization; Fluid Machinery; Industrial and Environmental Applications of Fluid Mechanics; Pumping Machinery ◽

10.1115/fedsm2017-69229 ◽

2017 ◽

Author(s):

Jiachun Liu ◽

Jian Zhang ◽

Xiaodong Yu ◽

Hui Xie

Keyword(s):

State Space ◽

Great Influence ◽

State Space Method ◽

Actual System ◽

Small Fluctuation ◽

Chamber Height ◽

Air Chamber ◽

Water Conveyance ◽

Air Cushion ◽

Space Method

In this paper, on the basis of the state space method and actual system arrangement, the small fluctuation mathematical model of the water conveyance system with air cushion surge chamber (ACSC) was established. According to the basic equations of ACSC, the ideal gas state equation and the units constant output equation, the formula describing the stable cross-section area (SCSA) of ACSC was deduced, and the small fluctuation stability (SFS) of water conveyance system was analyzed. The corresponding results showed that the air chamber constant had a great influence on the SCSA of ACSC. When the air chamber constant became larger, the quality of the system small fluctuation went worse. The higher upstream water level and the lower initial air chamber height will lead to a smaller initial air chamber constant of ACSC, which is destructive for the stability of the system small fluctuation; As long as the equivalent air quality and air chamber volume are constant, good quality system small fluctuations could be obtained when the initial air chamber height is small and the area of ACSC is large.

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