195 research outputs found
Double-distribution-function discrete Boltzmann model for combustion
A 2-dimensional discrete Boltzmann model for combustion is presented.
Mathematically, the model is composed of two coupled discrete Boltzmann
equations for two species and a phenomenological equation for chemical reaction
process. Physically, the model is equivalent to a reactive Navier-Stokes model
supplemented by a coarse-grained model for the thermodynamic nonequilibrium
behaviours. This model adopts 16 discrete velocities. It works for both
subsonic and supersonic combustion phenomena with flexible specific heat ratio.
To discuss the physical accuracy of the coarse-grained model for nonequilibrium
behaviours, three other discrete velocity models are used for comparisons.
Numerical results are compared with analytical solutions based on both the
first-order and second-order truncations of the distribution function. It is
confirmed that the physical accuracy increases with the increasing moment
relations needed by nonequlibrium manifestations. Furthermore, compared with
the single distribution function model, this model can simulate more details of
combustion.Comment: Accepted for publication in Combustion and Flam
Modeling incompressible thermal flows using a central-moment-based lattice Boltzmann method
In this paper, a central-moment-based lattice Boltzmann (CLB) method for
incompressible thermal flows is proposed. In the method, the incompressible
Navier-Stokes equations and the convection-diffusion equation for the
temperature field are sloved separately by two different CLB equations. Through
the Chapman-Enskog analysis, the macroscopic governing equations for
incompressible thermal flows can be reproduced. For the flow field, the tedious
implementation for CLB method is simplified by using the shift matrix with a
simplified central-moment set, and the consistent forcing scheme is adopted to
incorporate forcing effects. Compared with several D2Q5
multiple-relaxation-time (MRT) lattice Boltzmann methods for the temperature
equation, the proposed method is shown to be better Galilean invariant through
measuring the thermal diffusivities on a moving reference frame. Thus a higher
Mach number can be used for convection flows, which decreases the computational
load significantly. Numerical simulations for several typical problems confirm
the accuracy, efficiency, and stability of the present method. The grid
convergence tests indicate that the proposed CLB method for incompressible
thermal flows is of second-order accuracy in space
Time-delayed impulsive control for discrete-time nonlinear systems with actuator saturation
This paper focuses on the problem of time-delayed impulsive control with actuator saturation for discrete-time dynamical systems. By establishing a delayed impulsive difference inequality, combining with convex analysis and inequality techniques, some sufficient conditions are obtained to ensure exponential stability for discrete-time dynamical systems via time-delayed impulsive controller with actuator saturation. The designed controller admits the existence of some transmission delays in impulsive feedback law, and the control input variables are required to stay within an availability zone. Several numerical simulations are also given to demonstrate the effectiveness of the proposed results. 
A semi-free weighting matrices approach for neutral-type delayed neural networks
AbstractIn this paper, a new approach is proposed for stability issues of neutral-type neural networks (DNNs) with constant delay. First, the semi-free weighting matrices are proposed and used instead of the known free weighting matrices to express the relationship between the terms in the LeibnizβNewton formula to simplify the system synthesis and to obtain less computation demand. Second, global exponential stability conditions which are less conservative and restrictive than the known results are derived. At the same time, based on the above approach, fewer variable matrices are introduced in the construction of the Lyapunov functional and augmented Lyapunov functional. Two examples are given to show their effectiveness and advantages over others
Multiple-relaxation-time lattice Boltzmann kinetic model for combustion
To probe both the Hydrodynamic Non-Equilibrium (HNE) and Thermodynamic
Non-Equilibrium (TNE) in the combustion process, a two-dimensional
Multiple-Relaxation-Time (MRT) version of Lattice Boltzmann Kinetic Model(LBKM)
for combustion phenomena is presented. The chemical energy released in the
progress of combustion is dynamically coupled into the system by adding a
chemical term to the LB kinetic equation. Beside describing the evolutions of
the conserved quantities, the density, momentum and energy, which are what the
Navier-Stokes model describes, the MRT-LBKM presents also a coarse-grained
description on the evolutions of some non-conserved quantities. The current
model works for both subsonic and supersonic flows with or without chemical
reaction. In this model both the specific-heat ratio and the Prandtl number are
flexible, the TNE effects are naturally presented in each simulation step. The
model is verified and validated via well-known benchmark tests. As an initial
application, various non-equilibrium behaviours, including the complex
interplays between various HNEs, between various TNEs and between the HNE and
TNE, around the detonation wave in the unsteady and steady one-dimensional
detonation processes are preliminarily probed. It is found that the system
viscosity (or heat conductivity) decreases the local TNE, but increase the
global TNE around the detonation wave, that even locally, the system viscosity
(or heat conductivity) results in two kinds of competing trends, to increase
and to decrease the TNE effects. The physical reason is that the viscosity (or
heat conductivity) takes part in both the thermodynamic and hydrodynamic
responses.Comment: 32 pages, 11 figure
Cooperative coloring of some graph families
Given a family of graphs on the vertex set , a
cooperative coloring of it is a choice of independent sets in
such that . For a graph class
, let be the minimum such that every
graph family with and for , has a cooperative coloring. For the class of
trees and the class of wheels, we get that
and . Also, we show that and , where
is the class of graphs whose components are balanced
complete bipartite graphs, and is the class of bipartite graphs
with one part size at most
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