```
%% CNC自组装动力学仿真主程序（边界条件修正版）
clear; clc; close all;
%---------------------------
% 仿真参数设置
%---------------------------
Lx = 200; % x方向模拟区域尺寸(μm)
Ly = 200; % y方向尺寸
Nx = 16; % x方向网格数
Ny = 128; % y方向网格数
dx = Lx/Nx; % 空间步长
dy = Ly/Ny;
dt = 0.1; % 时间步长
total_time = 750; % 总模拟时间
steps = total_time/dt;
% Landau-de Gennes参数
a = -0.5; % 温度相关线性系数
B = 1.0; % 三阶项系数
C = 1.0; % 四阶项系数
L1 = 1.0; % 弹性常数L1
L2 = 0.5; % 手性扭曲耦合系数
p0 = 15; % 手性螺距(μm)
np = p0/(2*pi); % 螺距扭曲参数
%---------------------------
% 初始化场量
%---------------------------
Q = struct('xx', zeros(Ny,Nx), 'xy', zeros(Ny,Nx), 'yy', zeros(Ny,Nx));
% 初始条件：各向同性态添加随机扰动，并固定y边界
rng(2024);
Q.xx = 0.01*(rand(Ny,Nx)-0.5);
Q.xy = 0.01*(rand(Ny,Nx)-0.5);
Q.yy = -Q.xx;
% 固定y边界条件（取向沿x轴）
Q.xx(1,:) = 0.01; % y=0边界
Q.xx(end,:) = 0.01; % y=Ly边界
Q.xy(1,:) = 0;
Q.xy(end,:) = 0;
Q.yy = -Q.xx;
%---------------------------
% 预定义微分算子
%---------------------------
laplacian = @(M) (circshift(M,[0 1]) + circshift(M,[0 -1]) + ...
circshift(M,[1 0]) + circshift(M,[-1 0]) -4*M)/(dx^2);
gradientX = @(M) (circshift(M,[0 1]) - circshift(M,[0 -1]))/(2*dx);
gradientY = @(M) (circshift(M,[1 0]) - circshift(M,[-1 0]))/(2*dy);
%---------------------------
% 时间演化主循环
%---------------------------
for step = 1:steps
%=== 自由能导数计算 ===
Qnorm = Q.xx.^2 + 2*Q.xy.^2 + Q.yy.^2;
dF_dQ = a*(Q.xx+1i*Q.xy) - B*(Q.xx.^2-Q.xy.^2+1i*(Q.xx.*Q.xy+Q.xy.*Q.yy)) + C*Qnorm.*(Q.xx+1i*Q.xy);
%=== 弹性项计算 ===
elastic_term = L1*complex(laplacian(Q.xx), laplacian(Q.xy)) - 1i*L2*np*(gradientX(Q.xy)-gradientY(Q.xx));
%=== 时间推进 ===
Q.xx = Q.xx + dt*(real(dF_dQ) + real(elastic_term));
Q.xy = Q.xy + dt*(imag(dF_dQ) + imag(elastic_term));
Q.yy = -Q.xx;
%=== 边界条件处理 ===
Q = applyBoundaryConditions(Q, dx, dy); % 应用修正后的边界条件
%=== 可视化 ===
if mod(step,50)==0
plotCNCstructure(Q, dx, dy, step*dt);
end
end
%% 边界条件处理函数
function Q = applyBoundaryConditions(Q, dx, dy)
% x方向周期性边界
Q.xx = applyXPeriodic(Q.xx);
Q.xy = applyXPeriodic(Q.xy);
Q.yy = applyXPeriodic(Q.yy);
% y方向固定边界（取向沿x轴）
Q.xx(1,:) = 0.01; % y=0边界
Q.xx(end,:) = 0.01; % y=Ly边界
Q.xy(1,:) = 0;
Q.xy(end,:) = 0;
Q.yy = -Q.xx;
end
function M = applyXPeriodic(M)
% x方向周期性边界处理
M(:,1) = M(:,end-1);
M(:,end) = M(:,2);
end
%% 增强型可视化函数
function plotCNCstructure(Q, dx, dy, currentTime)
[X, Y] = meshgrid(0:dx:(size(Q.xx,2)-1)*dx, 0:dy:(size(Q.xx,1)-1)*dy);
% 计算序参数和取向角
S = sqrt(Q.xx.^2 + 2*Q.xy.^2 + Q.yy.^2);
theta = 0.5 * atan2(Q.xy, 0.5*(Q.xx - Q.yy)); % 角度范围[-π/2, π/2]
% 创建HSV颜色映射
hue = (theta + pi/2)/pi; % 映射到[0,1]
value = S/max(S(:));
hsvImg = cat(3, hue, ones(size(S)), value);
rgbImg = hsv2rgb(hsvImg);
% 矢量场参数
stride = 6;
[m,n] = size(S);
xq = 1:stride:n;
yq = 1:stride:m;
[Xq,Yq] = meshgrid(xq*dx, yq*dy);
U = cos(theta(yq,xq));
V = sin(theta(yq,xq));
% 绘制主图
figure(1);
clf;
imagesc([0, max(X(:))], [0, max(Y(:))], rgbImg);
hold on;
quiver(Xq, Yq, U, V, 0.5, 'k', 'LineWidth', 1.1);
axis equal tight;
% 坐标轴标注
xlabel('X (μm)');
ylabel('Y (μm)');
title(sprintf('CNC自组装过程 t = %.1f s', currentTime));
% 定制化颜色条
hcb = colorbar('Position',[0.92 0.1 0.02 0.8]);
colormap(hsv);
hcb.Ticks = 0:0.25:1;
hcb.TickLabels = {'-90°','-45°','0°','45°','90°'};
hcb.AxisLocation = 'in';
drawnow;
end```此代码平面内一直显黑色，请修改后重新输出
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