tfer_1S_pb.m

% TFER_1S_PB    Evaluates the transfer function for a PMA in Case A (w/ parabolic flow).
% Author:       Timothy Sipkens, 2018-12-27
% 
% Inputs:
%   sp          Structure defining various setpoint parameters 
%               (e.g. m_star, V). Use 'get_setpoint' method to generate 
%               this structure.
%   m           Particle mass
%   d           Particle mobility diameter
%   z           Integer charge state
%   prop        Device properties (e.g. classifier length)
%
% Outputs:
%   Lambda      Transfer function
%   G0          Function mapping final to initial radial position
%=========================================================================%

function [Lambda,G0] = tfer_1S_pb(sp,m,d,z,prop)

[tau,~,~,rs] = parse_inputs(sp, m, d, z, prop);
        % parse inputs for common parameters

%-- Estimate device parameter --------------------------------------------%
lam = 2 .* tau .* ([sp.alpha]' .^ 2 - [sp.beta]' .^ 2 ./ (rs.^4)) .* prop.L ./ prop.v_bar;

A1 = -3 * prop.L ./ (2 .* lam .* prop.del^2);
A2 = rs.^2 + prop.rc^2 - 2*prop.rc.*rs - prop.del^2;

% Loop over setpoints.
Lambda = zeros(size(A1));
for jj=1:size(Lambda,1)
    A3 = @(r,ii) (r.^2) ./2 + (rs(jj,ii) - 2 * prop.rc) .* r;
    
    %-- Set up F function for minimization -------------------------------%
    F = @(r,ii) A1(jj,ii) .* (A2(jj,ii) .* log(r - rs(jj,ii)) + A3(r,ii));
    min_fun = @(rL,r0,ii) F(rL,ii) - F(r0,ii) - prop.L;

    %-- Evaluate G0 and transfer function --------------------------------%
    G0 = @(r) G_fun(min_fun, r, rs(jj,:), ...
        prop.r1, prop.r2, sp(jj).alpha, sp(jj).beta);

    ra = min(prop.r2, max(prop.r1, G0(prop.r1)));
    rb = min(prop.r2, max(prop.r1, G0(prop.r2)));

    Lambda(jj,:) = 3/4 .* (rb - ra) ./ prop.del - 1/4 .* ((rb - prop.rc) ./ prop.del).^3+...
        1/4 .* ((ra - prop.rc) ./ prop.del).^3;
end

end