单机无穷大系统
此处 以一单机无穷大系统(SMIB)作为例子，以便更好地 理解上述概念。虽然图1 的相轨迹簇依赖于系统的 参数，但图1 能代表典型的自治SMIB 相图的特性。
基于21个网页-
其基本思路是将一多机系统根据运行工况和故障条件等值成一单机无穷大系统（OMIB），然后在等值系统上，结合不同的积分方法，应用等面积定则进行暂态稳定分析。
基于11个网页-
one machine - infinity bus
英文电子专业词汇（新手必备）（转载）之一-女性世界 ...
动态 dynamic (state)
单机无穷大系统one machine - infinity bus
机端电压控制AVR ...
基于4个网页-
The one-machine infinite system
求翻译：one fell off and bumped his head 是什么意思? ...
爱是远远城市里有所依托的幸福 >> Love is far relying on in the city of happiness
小高姐 >> Small high-sister
单机无穷大系统 >> The one-machine infinite system ...
基于3个网页-
one generator and one infinite bus system
single machine to infinite system
single-machine infinite-bus system
one-machine infinite-bus power system
Initial value balance
a single machine to infinite system
one machine infinite bus power system
one machine infinite bus power systems
更多收起网络短语
one machine - infinity bus
&2,447,543篇论文数据，部分数据来源于
建立了带有TCR的单机无穷大系统的非线性状态方程，用以简化和模拟实际电力系统。
Nonlinear state equation of single machine infinite bus system with TCR is established to simplify and simulate real power system.
提出了一种利用协同控制理论设计可控串联补偿电容器（TCSC）控制器的方案，并以单机无穷大系统为例进行了仿真试验。
A method based on synergetic control theory for the design of TCSC controller is presented and the simulation in a single machine infinite bus power system is made.
采用MATLAB分析工具对单机无穷大系统暂态过程进行仿真，介绍了PSS的基本功能，并分析了PSS对于系统暂态稳定性的影响。
This paper simulates the transient process of a single machine infinite bus system in MATLAB and introduces the basic function of PSS as well as its influence on power system.
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3秒自动关闭窗口Kundur单机无穷大系统小干扰稳定性matlab程序
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Title: Example 12.3 (page 752) 注：中文版12.2 P489
% By: Sonny
Lloyd&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
% Copyright:
2009&&&&&&&&&
% Text Reference: Power System Stability and Control by Prabha
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
clear,clc, % clear memory and workspace
s = tf('s'); % specifies the transfer function H(s) = s (Laplace
digits(4);& % define precision, useful for
symbolic math operations
pi/180;&&&&&
% conversion factor from degs to radians
rad2deg = 1/deg2&& %
conversion factor from radians to deg
%% Objectives:
% The objective of this example is to analyze the small-signal
% characterics of the system about the steady-state opeating
% following the loss of circuit 2.
%% Assumptions:
% The effects of amortisseurs may be neglected
% Neglect saliency of rotor
%% Operating Conditions:
0.9;&&&&&&
%[w] active power supplied by generator
0.3;&&&&&&
%[var] reactive power supplied by generator, overexcited)
%[Vll] magnitude, line-to-line terminal voltage
Et_angle = 36;& %[deg]&
Et=Et_mag*exp(j*deg2rad*(Et_angle));&&&&&
% polar notation
% NOTE to get Et in rectangular form: abs(Et),
rad2deg*(angle(Et))
0.995;&&&&
%{Vll] magnitudeline-to-line bus voltage
EB_angle = 0;&&
EB=EB_mag*exp(j*deg2rad*(EB_angle));&&&&&
% polar notation
%% A 555MVA, 60Hz turbine generator has the following
parameters:
% GIVEN SPECIFICAITON:
555e6;&&&&&
%[VA] total power base
60;&&&&&&&&
%[Hz] frequency
Xd=1.81;&&& %
note that in PU system, Ld = Xd
Xp_d=0.3;&& %X'd
Ra = 0.003;
Tp_d0 = 8;& %[s]
% The above parameters are unsaturated values
% The effect of saturation is to be represented by assuming that d
% axes have similar saturation characteristics with:
Asat =0.031; Bsat = 6.93; YTI = 0.8;& % based on
definitions of section 3.8.2
% NOTE: giving the saturation characteristics in this manor means
% to CALCULATE saturation coefficients Ksd, Ksq.
%% Network Connection
% Generator is connected to an infinite bus through a step-up
transformer
% (Xtrans = j0.15) and two parallel transmission lines (Xl1 = j0.5,
Xl2 = 0.093)
% assuming lossless conditions.
0.15;&&& %[ohm]
impedance of step-up transformer
0.5;&&&&&&&
%[ohm] impedance of line 1&
0.93;&&&&&&
%[ohm] impedance of line 2&
% Compute the equivalent network (single line)
Xe = Xtrans + Xl1;& %[ohm] equivalent network
impedance, recall line 2 is out of service
0;&&&&&&&&&&&&
%[ohm] assume no losses
%% The per unit fundamental parameters
% elements of d- and q-axis equivalent circuits of the equivalent
% First compute the unsaturated mutual inductances (pg. 154)
Ladu = Xd -
% mutual inductance, unsaturated value
Laqu = Xq -
% mutual inductance, unsaturated value
% Compute the rotor leakage inductances from the expressions for
% and subtransient inductances (pg.
% Based on equation 4.29, the expression for L'd based on the
% definition is:& L'd = Ll +
Ladu*Lfd/(Ladu+Lfd);&
% note L'd =X'dm & Ll = Xl& -- L'd is a GIVEN
VALUE (and is the unsaturated value)
% we need to solve for Lfd (unsaturated rotor field
inductance)
% therefore:& L'd(Ladu+Lfd) = Ll*(Ladu +
Lfd)+Ladu*Lfd
%&&&&&&&&&&&&
Lfd(L'd-Ll-Ladu) = -L'd*Ladu + Ll*Ladu
Lfd = (-Xp_d*Ladu + Xl*Ladu)/(Xp_d-Xl-Ladu);& %
unsaturated value, rotor field inductance
Lp_adu = 1/((1/Ladu)+1/(Lfd)); % L'ad = X'ad mutual unsaturated
%%%%%%%%& is this even used anywhere?
% Next we compute the rotor resistances from the expressions for
% open-circuit time constants: Equ. 4.15 and 4.23
% T'd0 = (Ladu+Lfd)/Rfd& [pu]
% NOTE: The time constant in per unit is equal to 377 times the
% constant in seconds (pg 155)
Rfd = (Ladu + Lfd)/(377*Tp_d0);& %[pu]
%% Initial Steady-State Values:
%[VA] total power at generator output in rect. notation
abs(St);&&&
%[VA] magnitude of total power&
St_angle = rad2deg*(angle(St));& %[deg]
conj(St)/conj(Et);&&&&&&&
% [A] phase current.& Take conjugate to recognize
that current is positive out of generator
It_mag = abs(It);
It_angle = rad2deg*(angle(It));& % [deg] phase
current angle&&
% SOLVE for saturated coefficients of Ksq,
Yat0 = abs(Et + It*(Ra+j*Xl));
YIO = Asat*exp(Bsat*(Yat0-YTI));
Ksd = Yat0/(Yat0+YIO);& % saturation coefficient,
same as value given on pg. 753
K&&&&&&&&&&&&&
% saturation coefficient, same as value given on pg. 753
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Find the saturated values for parameters
Lads = Ksd * L& % Ld mutual inductance,
saturated value
Laqs = Ksq * L& % Lq mutual inductance,
saturated value
Lp_ads = 1/((1/Lads)+(1/Lfd));& % saturated value
inductance of L'd& (see eq. 12.91)
Lds = Lads+Xl;& % the SATURATED euiv. of Ld or Xd
(previously defined)
Lqs = Laqs+Xl;& % the SATURATED euiv. of Lq or Xq
(previously defined)
%%%Lp_ds = 1/((1/Lds)+(1/Lfd));&&
???????????
Xads = L&&&
% equivalenet when in per unit
% equivalenet when in per unit
% equivalenet when in per unit
%Xp_ds = Lp_&&
???????????
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The network constraint equation&
% As a check, we know Ebus (EB) as it was given, 0.9950
% Since, Et = EB + (RE + jXE)*It
EB_check = Et - (Re + j*Xe)*It;
EB_mag_check = abs(EB_check);
EB_angle_check = rad2deg*(angle(EB_check));
% Calculate the internal rotor angle (Si).& See
Figure 3.23, pg 101.
%Check calculation of Si_angle using test data from text page
%Xqs = 1.494; It_mag = 1; Et_mag = 1; St_angle = 26 % test #'s page
rad2deg*(atan((Xqs*It_mag*cos(deg2rad*(St_angle))-Ra*It_mag*sin(deg2rad*(St_angle)))/(Et_mag+Ra*It_mag*cos(deg2rad*(St_angle))+Xqs*It_mag*sin(deg2rad*(St_angle)))));
% Another way of calculating the internal rotor angle:
% Decompose into d-q components, see figure 12.6
Etq = Et + (Ra + j*Xqs)*It;
Etq_mag = abs(Etq);
Etq_angle = rad2deg*(angle(Etq));
Si_angle_verify = Etq_angle - Et_& % [deg]
internal angle (see Section 3.6.3), between Et and
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Calculate Initial Conditions, as outlined on page 746, solutions
given on pg. 753
ed0 = real(Et_mag*sin(deg2rad*(Si))); % real part of
|Et|*sin(Si)
eq0 = real(Et_mag*cos(deg2rad*(Si))); % real part of
|Et|*cos(Si)
id0 = real(It_mag*sin(deg2rad*(Si+St_angle))); % real part of
|It|*sin(Si+phi)
iq0 = real(It_mag*cos(deg2rad*(Si+St_angle))); % real part of
|It|*cos(Si+phi)
% Solve for S0, equations on page 746, solutions given on pg.
EBd0 = ed0 - Re*id0+Xe*iq0;
EBq0 = eq0 - Re*iq0-Xe*id0;
rad2deg*(atan(EBd0/EBq0));&&
% Solve for Efd0, equations on page 746, solutions given on pg.
�2 = sqrt((EBd0^2+EBq0^2));& % NOTE: this is same
value as given for EB
(eq0+Ra*iq0+Lds*id0)/L&& % as
per pg 746
Ladu*ifd0;&&&&&&&&&&&&&&&&&&
% as per pg 746
Lads*(-id0+ifd0);&&&&&&&&&&&&
% as per pg 746
-Laqs*iq0;&&&&&&&&&&&&&&&&&&
% as per pg 746
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Small Signal Analysis
% "Since we are expressing small-signal performance in terms of
% values of flux linkages and currents, a distinction has to be
made etween
% TOTAL saturation "s" and INCREMENTAL saturation
"i".& Incremental
% saturation is associated with perturbed values of flux linkages
% currents."
% Solve for Incremental values, Ksd(incr) & Ksq(incr)
Ksdi = 1/(1+Bsat*Asat*exp(Bsat*(Yat0 - YTI))); % incremental
saturation, verify on page 753
Ladi = Ksdi*L&& % Incremental
mutual inductances
Laqi = Ksdi*L&& % Incremental
mutual inductances
Ldi = Ladi +
Incremental inductance
Lqi = Laqi +
Incremental inductance
Lp_adi = 1/((1/Ladi)+(1/Lfd));& % Incremental
mutual inductance of
% Equivalent in per unit system
% Equivalent in per unit system
L&&&&&&&&&
% Equivalent in per unit system
L&&&&&&&&&
% Equivalent in per unit system
% Equivalent in per unit system
% Preparing to linearize.. see page 742
% NOTE:& use of "incremental" values, as per
RT = Ra+Re;
Xe+X&&&&&&
% Text shows Xqs .. but here we use "i", the incremental
XTd = Xe+Xp_di+Xl;& % Text shows Xqs .. but here
we use "i", the incremental value
D = RT^2+XTq*XTd;
% Linearized system equations (pg. 742)
m1 = (EB_mag*(XTq*sin(deg2rad*(S0)) -
RT*cos(deg2rad*(S0))))/D;
n1 = (EB_mag*(RT*sin(deg2rad*(S0)) +
XTd*cos(deg2rad*(S0))))/D;
m2 = XTq/D * Ladi/(Ladi +
n2 = RT/D *
Ladi/(Ladi+Lfd);&&&&&&
% %%%% SUMMARY: Initial Steady-state Values of the System
% disp('SUMMARY: Initial Steady-state Values of the System
Varaibles:')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The Constants associated with the block diagram (fig. 12.9)
K1 = n1*(Yad0+Laqi*id0)-m1*(Yaq0+Lp_adi*iq0); % eq.
12.113& NOTE: incremental values used
K2 = n2*(Yad0 + Laqi*id0)-m2*(Yaq0+Lp_adi*iq0)+Lp_adi/Lfd*iq0; %
eq. 12.114 NOTE: incremental values used
%% Construct State-Space Matrix
a11 = -KD/(2*H);
a12 = -K1/(2*H);
a13 = -K2/(2*H);
a21 = 2*pi*f0;
a32 = -((2*pi*f0)*Rfd/Lfd)*m1*Lp_& % NOTE: use
of incremental value
a33 = -((2*pi*f0)*Rfd/Lfd)*(1-Lp_adi/Lfd +
m2*Lp_adi);& % NOTE: use of incremental
% Construct the A-matrix
A = [a11 a12 a13; a21 a22 a22; a31 a32 a33]; % A-matrix of
%disp('The A-matrix:'); disp(A); %Displays the A-matrix to
b11 = 1/(2*H);
b32 = (2*pi*f0)*Rfd/L&&
%%%%%& Why is this unsaturated mutual inductance
% The Constants associated with the block diagram (fig. 12.9)
K3 = -b32/a33;
K4 = -a32/b32;
T3 = -1/a33;
%% Eigenvalues&
% %%%%%%%%%%%%%%%%%%%%%%%%%& TEST from pg
%%%%%%%%%%%%%%%%%%%%%%%%&
A = [(-1.43) -0.108; 377 0]; % with KD& =
10& %%%%%%%%%%%%%%%%%%%%%%%%%%%
[eigen_Vec, eigen_Val] =
eig(A);&&&&
% eigen vectors and eigenvalues, where the eigen values are in a
diagonal matrix
disp('The Eignvalues:'); disp(diag(eigen_Val));& %
Displays eigenvalues to workspace
%disp('Characteristic Equation:');
disp(poly(A));&&&
% Displays characteristic equation
% define a symbol for lamda% At = [(-1.43) -0.108; 377
Dh = diag(h)*eye(size(A));& % form a diagonal
matrix of lambda, same size as A-matrix
dec= vpa((A-Dh));&& % convert to
decimal values
sort(det(dec));&&&&
% characteristic equation is the determinant of (A-D),
disp('Characteristic Equation:')
pretty(eq1)&& % displays result
in a "pretty" way
% Define 2nd order characteristic equation variables
% char_eq = h^2+2*phi*wn*h+wn^2;
% disp('of the form:')
% pretty(char_eq)
% Look at the characteristic equation enter in wn
% wn = sqrt(8.318);&& % [rad]
undamped natural frequency&
wn/(2*pi);&&&&
% [Hz] undamped natural frequency&
% sigma = 1.430/(2*wn);&& %
Damping ratio
wn*sqrt(1-sigma^2);&&&
%[rad] damped frequency
wd/(2*pi);&&&&
% [Hz] damped frequency
% Find Right Eigenvector and eigenvalue, check with page 735
syms phi_11 phi_21 phi_31 phi_12 phi_22 phi_32 phi_31 phi_32
phi_33;& % manually determined
&[right,ev]=eig(A);
&disp('The Right Eigenvector Matrix:')
&disp(right)
% Method 2
% For the first eigenvalue
eig1= diag(eigen_Val(1))*eye(size(A));& % (lamda *
eig1a= vpa((A-eig1));&& %
(A-lamda*I) answer convert to decimal values
phi_m1 = [phi_11; phi_21;];& % first matrix of phi
eig1b = eig1a * phi_m1;
% one of the eigenvecotors corresesponding to an eigenvalue has to
% arbitrarily, therefore let phi_21 = 1, and solve for
%phi_21 = 1;
[phi_11]=solve(subs(eig1b(1), phi_21, 1))
% Similarily, for the second eigenvalue
eig2= diag(eigen_Val(2))*eye(size(A));& % (lamda *
eig2a= vpa((A-eig2));&& %
(A-lamda*I) answer convert to decimal values
phi_m2 = [phi_12; phi_22;];& % first matrix of phi
eig2b = eig2a * phi_m2;
% one of the eigenvecotors corresesponding to an eigenvalue has to
% arbitrarily, therefore let phi_22 = 1, and solve for
%phi_22 = 1;
[phi_12]=solve(subs(eig1b(2), phi_22, 1))
% Find left eigenvector, check with page 736
&left=inv(right);
&disp('The Left Eigenvector Matrix:')
&disp(left)
%% Plotting
% Plot Eigenvalues:
% figure(1)
% real_eigen=real(eig(A));
% imag_eigen=imag(eig(A));
% plot(real_eigen,imag_eigen,'*')
% xlabel ('Real')
% ylabel ('Imaginary')
% title ('System Eigen Values')
Identity = eye(size(A)); % returns an identity matrix the same size
Use [W,D] = eig(A.'); W = conj(W) to compute the left
eigenvectors.
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-> 单机无穷大系统
1)&&single-machine infinite-bus system
单机无穷大系统
A method to design the excitation controller of single-machine infinite-bus system is proposed based on iterative learning control theory,which removes the restriction of perfect tracking in limited time span.
基于迭代学习控制理论提出了一种设计单机无穷大系统励磁控制器的新方法,克服了迭代学习控制在有限时间区间上实现完全跟踪的限制。
The simulation results on a single-machine infinite-bus system including ASVG show that the proposed SMVSC can effectively improve stability and dynamic characteristics of power system.
针对含ASVG的单机无穷大系统进行的电力系统仿真,结果表明,所设计的滑模变结构控制器能有效地提高电力系统的稳定性,改善动态响应品质。
2)&&single machine infinite bus system
单机无穷大系统
Nonlinear state equation of single machine infinite bus system with TCR is established to simplify and simulate real power system.
建立了带有TCR的单机无穷大系统的非线性状态方程,用以简化和模拟实际电力系统。
3)&&single-machine infinite-bus system
单机-无穷大系统
The ideal simulation result is obtained by the simulation analysis of short-circuit fault of the single-machine infinite-bus system.
介绍了电力系统模型和Matlab/Simulink中的SPS模块的主要功能,通过对单机-无穷大系统的短路故障的仿真分析,得到了理想的仿真效果。
4)&&one-machine infinite-bus power system
单机-无穷大系统
5)&&a single machine to infinite system
单机–无穷大系统
6)&&one machine infinite bus power systems
单机无穷大电力系统
补充资料：无穷粒子随机系统
&&&&　　描述无穷粒子系统的随机场及随机过程。　　　　相变问题是平衡态统计物理中一个很重要的问题。经典的处理方法是研究有限粒子系统的吉布斯态（平衡态）的某些函数（如序参数、比能等）当系统扩张成无穷粒子系统时的性质，从而得到有关相变的结论。由于相变问题本质上是无穷粒子系统的一种集体现象，20世纪60年代后期一些学者用现代概率理论直接定义无穷粒子系统的吉布斯态(吉布斯随机场)。70年代初以来，又陆续提出了一些类型的马尔可夫过程作为吉布斯态的动态模型，这就是无穷质点马尔可夫过程。　　　　吉布斯态 　它是描述无穷粒子系统的一种概率分布，为易于理解，以伊辛模型为例来说明。　　　　全体n维整点集记作Zn,设S是Zn的有限子集（参数集），它表示粒子所在的位置，每一u∈S处的粒子的状态ηu=+1或－1，对任何u，v∈S,u≠v，有一数J(u，v)≥0(J (u,v)=J(v,u))与之对应，它表示u、v两处的粒子相互作用的强度，这就是 S上的一个伊辛模型。称集（ηu取定 +1或-1）是整个系统的一个组态(样本点),系统的全体组态集(样本空间)用x表示，令　　　　表组态η∈x的能量，决定x上的一个概率测度,其中β>0为常数。概率μ 称为由J(u,v)决定的(有限)S上的伊辛模型的平衡态，或称吉布斯态。如果令，,xu为取值±1的随机变量,μ为随机向量{xu:u∈S}的一个概率分布。类似地，对S的任何非空子集Λ, 集（ξu取定+1或－1）表示Λ上的子系统的组态,Λ上的子系统的全体组态集用x(Λ)表示。经过计算可得：　　　　命题 　在S \Λ上的组态为ξ(∈x (S\Λ))的条件下，Λ上的组态ξ(∈x(Λ))的条件概率等于式中，ξ∪ξ为S上的组态。　　　　这一命题启示了直接定义S=Zn上的伊辛模型的吉布斯态的途径。直观地说,它就是x上具有命题所述性质的概率测度μ，即对Zn的任何有限子集Λ,在Zn\Λ上组态为ξ（∈x(Zn\Λ)）的条件下,Λ上的组态ξ(∈x(Λ))关于μ的条件概率为由(1)定义的μΛ({ξ};ξ)。它的严格数学定义如下:设S=Zn,x，x(Λ)的定义仍如上,其中Λ不一定有限,J (u,v)还满足条件。于是对S的任何有限子集Λ及ξ ∈x(Λ),ξ∈x (S \Λ)，可按(1)定义μΛ({ξ};ξ)，对给定的ξ ∈x (S \Λ)，它是x (Λ)上的概率测度。再令 F为包含一切形如 {ξ∪ξ:ξ∈x(S\Λ)}(ξ ∈x (Λ),Λ为S的有限子集)的组态集的最小σ域,它表示组态的事件σ域；对给定的Λ嶅S，F(Λ)为包含一切形如{ξ∪ξ∪ω：ξ∈x (Λ1)，ω ∈x(S\Λ)}(其中为有限集，ξ∈x(Λ\Λ1))的组态集的最小σ域,它是F中那些在Λ上就能观察到的组态事件组成的σ域。设μ 为F上的概率测度,如果对S的任何有限子集Λ，任何ξ∈x (Λ),条件概率（见条件期望）
(2)对μ几乎必然成立，则称μ为S上伊辛模型的吉布斯态。　　　　如果令则xu是(x,F)上取值±1的随机变量，F(Λ)是随机变量族{xu: u∈Λ}所产生的σ域,吉布斯态μ是随机过程{xu:u∈S}的分布，对S的任何有限子集Λ，任何ξ∈x(Λ)，
(2┡)对μ几乎必然成立。称具有吉布斯态的随机过程{xu:u∈S}为S上伊辛模型的吉布斯随机场。　　　　伊辛模型的吉布斯态总是存在的m它与函数J(u,v)及参数β有关，但是对给定的J及β,它未必惟一。如果对给定的J,存在βc∈(0,∞)，使当β<βc时,吉布斯态惟一，当β>βc时,吉布斯态不惟一,则称此伊辛模型有相变,βc称为它的临界点。　　　　从这样定义的吉布斯态出发，可以证明用经典方法得到的一些物理结果：①设J(u，v)=J(0,u-v)对一切u,v∈S,u≠v成立,若存在r>0使对一切u∈S且│u│=1有J(0,|u|)≥r,则当n≥2时，伊辛模型有相变。②若当|u-v│=1时J (u,v)=1，当│u-v│≠1时J(u,v)=0，则称相应的伊辛模型为紧邻的。紧邻伊辛模型当 n=1时无相变,当n≥2时有相变；当n=2时,βc已算出（这是L.昂萨格1944年得到的一个著名结果），而对n≥3的情形，βc的值还不知道。求出 n=3时的βc值是一个重要而未解决的问题。关于伊辛模型还有很多没有解决的、在数学上值得研究、在物理上有意义的问题。　　　　不限于伊辛模型,按照(2)的方式还可以定义十分广泛的吉布斯态与正则吉布斯态以及相变的概念，大部分平衡态统计物理的模型都可以纳入这个框架，而且已经得到它们的存在性与惟一性的一些条件。相变问题的研究尚有待深入。　　　　无穷质点马尔可夫过程 　从统计物理来看，作为无穷粒子系统的平衡态的吉布斯态应该是系统的某一可逆物理过程的定态。因此在概率论中提出了如下形式的问题：是否存在以(x,F)为状态空间的马尔可夫过程{ηt:t≥0},它的分布满足下列要求：①对任何u,v∈S,u≠v，η∈x，当t→0时，有　　
(3)式中；②F上的概率测度 μ是伊辛模型的吉布斯态，当且仅当以 μ为初始分布的该过程是一个时间可逆的马尔可夫过程。所谓时间可逆就是当时间"倒转"时，过程的分布不变，即对任何任何Bk∈F，k＝0，1，...，l，都有。 这个问题已经解决。对更一般的с(u,x),由(3)决定的马尔可夫过程称为自旋变相（或称生灭型）过程，它与排他（或称粒子运动型）过程是最早提出的两类无穷质点马尔可夫过程。对自旋变相过程与排他过程的上述问题（可逆性问?猓??丫?玫浇咏?暾?慕峁?唤?昀矗?泄?д咴谡夥矫娼?辛斯ぷ鳌?　　　　无穷质点马尔可夫过程虽然是由平衡统计物理引起的，但近年来不断提出了新的模型。这些模型涉及非平衡统计物理、化学、生物、医学以及社会科学。它的研究已进入非平衡系统的范围，遍历性理论是它的主要研究方向。这是概率论中一个值得注意的正在发展的新分支。　　　　参考书目　　　陈木法著：《跳过程与无穷粒子系统》，北京师范大学出版社，北京，1986。　　　普雷斯顿著，严士健等译：《随机场》，北京师范大学出版社，北京，1983。(C.Preston,Rαndom Field,Lecture Notes in Mαthemαtics534,Springer-Verlag,Berlin, 1956.)　　　D.Ruelle,Stαtisticαl Mechαnics:Rigorous Results,W.A.Benjamin, Reading Mass.,1969.　　　Ya.G.Sinai,Theory of Phαse Trαnsitions:Rigorous Results, Pergamon Press, London,1982.　　　T.Liggett,Interαcting Pαrticle
Systems,Springer-Verlag, New York,1985.　　
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