为什么当我增加点数时我的附着力会增加

Question

function adh = adhesionScheme(o,H, delta, m, n,walls,wallsInt,wallsExt)

% flag whether we have walls or not
confined = 0;
if ~isempty(walls) || ~isempty(wallsInt)
  confined = 1;
end
% flag for whether there are two sets of walls with different
% discretization
diffDiscWalls = 0;
if ~isempty(wallsInt)
  diffDiscWalls = 1;
end

oc = curve;

% Compute x,y coordinates of net repulsive force on each point of each
% vesicle due to all other vesicles and walls
adh = zeros(2*o.N,o.nv);

[ox,oy] = oc.getXY(o.X);

if confined
  if ~diffDiscWalls 
    [xwalls,ywalls] = oc.getXY(walls.X);
    Nbd = walls.N;
    
  else
    [xwallsInt,ywallsInt] = oc.getXY(wallsInt.X);
    NbdInt = wallsInt.N;
    
    [xwallsExt,ywallsExt] = oc.getXY(wallsExt.X);
    NbdExt = wallsExt.N;
  end
end

for k = 1:o.nv  
  adhx = zeros(o.N,1); adhy = zeros(o.N,1);  
  
  [~,arcLen] = oc.arcLengthParameter(ox(:,k),oy(:,k));
  hmax = max(diff(arcLen));
  
  notk = [(1:k-1) (k+1:o.nv)];
  notk_ox = ox(:,notk);
  notk_oy = oy(:,notk);

  
  for j = 1 : o.N
    if o.nv ~= 1  
        % Find the distances to each point on a vesicle 
        dist = ((ox(j,k) - notk_ox).^2 + ...
            (oy(j,k) - notk_oy).^2).^0.5;

        dF = (delta^(m-n) - dist.^(m-n))./(dist.^(m+2));

        adhx(j) = sum(sum((ox(j,k) - notk_ox).*dF));
        adhy(j) = sum(sum((oy(j,k) - notk_oy).*dF));
    end
    if confined
      etaWalls = hmax*minDistt;  
      if ~diffDiscWalls  
        dist = ((ox(j,k) - xwalls).^2 + (oy(j,k) - ywalls).^2).^0.5;
        
        % Stiffness l^2
        dF = (delta.^(m-n) - dist.^(m-n))./dist.^(m+2);
        

        wallAdhx = sum(sum((ox(j,k)-xwalls).*dF)); % why there is multiplication by 2?????
        wallAdhy = sum(sum((oy(j,k)-ywalls).*dF)); % Because We calculate adh differently 
      
        % Repulsion due to wall has to beat repulsion due to vesicles if a
        % vesicle is a sandwich between a vesicle and a wall
        adhx(j) = adhx(j) + wallAdhx;
        adhy(j) = adhy(j) + wallAdhy;
      else
        % Interior walls    
        dist = ((ox(j,k) - xwallsInt).^2 + (oy(j,k) - ywallsInt).^2).^0.5;
        L = floor(etaWalls./dist);
      
        % Stiffness l^2
        dF = (delta.^(m-n) - dist.^(m-n))./dist.^(m+2);
      
        wallIntAdhx = sum(sum((ox(j,k)-xwallsInt).*dF));
        wallIntAdhy = sum(sum((oy(j,k)-ywallsInt).*dF));
        
        % Exterior wall
        dist = ((ox(j,k) - xwallsExt).^2 + (oy(j,k) - ywallsExt).^2).^0.5;
        L = floor(etaWalls./dist);
      
        % Stiffness l^2
        dF = (delta.^(m-n) - dist.^(m-n))./dist.^(m+2);
      
        wallExtAdhx = sum(sum((ox(j,k)-xwallsExt).*dF));
        wallExtAdhy = sum(sum((oy(j,k)-ywallsExt).*dF));
      
        % Repulsion due to wall has to beat repulsion due to vesicles if a
        % vesicle is a sandwich between a vesicle and a wall
        adhx(j) = repx(j) + wallIntAdhx + wallExtAdhx;
        adhy(j) = repy(j) + wallIntAdhy + wallExtAdhy; 
          
      end % diffDiscWalls
    end % confined
  end % o.N
  % Adhesion on the kth vesicle multiplied with Adhesion Constants
  adh(:,k) = -(H * m * delta^n)*[adhx; adhy];
end % o.nv
end % AdhesionScheme

这是以下方程的实现粘附力方程

我们和我的顾问讨论过，看来我的实施没有任何问题。 主要问题是，当我增加点数时，附着力会急剧增加。第二个问题是常数 H 应该是正值，但这会使力变弱并且囊泡不会粘附。当我使用负 H 时，它的效果与文献中的结果几乎完美。

我尝试使用 32 点作为基础来调整值，如下所示：

  adj_factor = (o.N / 32);
  adh(:,k) = -(H * m * delta^n)*[adhx; adhy]/ adj_factor;

下面只是调试线路，以查看每次运行代码时力如何变化。

disp('Total adhesion force on the  first vesicle:');
disp(norm(adh(:,1)));
disp('\n');
total_points = o.N * o.nv;
normalized_adh = adh / total_points;
disp('Normalized adhesion force per point:');
disp(norm(normalized_adh));

Answer 1

当你用黎曼和来近似 γk 上的积分时，你没有忘记 dSy 吗？

然后，增加点数将减小与每个点相关的 dSy 的大小，这应该抵消粘附力的增加。