Smooth decay of a function

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Saurav
Saurav 2020-7-26
评论： Saurav 2020-7-27
I have a function which dies of quickely. I need this function to smoothly decay off to 0 . Is there any way in Matlab to make that happen?
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Image Analyst
Image Analyst 2020-7-26
Please give values for everything in that alphabet soup. And include a screenshot of what you got, and what you'd like to achieve, but only after you read this link.
T = linspace(-5, 5, 500);
Tc = 3;
y = 2;
a = 7;
b = 6;
m = ((-b + (((b*b)-(4*y*a*(T-Tc))).^0.5))/(2*y)).^0.5;
subplot(2, 1, 1);
plot(T, real(m), 'b-', 'LineWidth', 2);
title('Real(m) vs. T', 'FontSize', 20);
grid on;
xlabel('T', 'FontSize', 20);
ylabel('real(m)', 'FontSize', 20);
% For T>Tc, m(T) becomes complex so m(T>Tc)=0
% Hence I want m(T) to smoothly decay to 0 for T>Tc
subplot(2, 1, 2);
plot(T, imag(m), 'b-', 'LineWidth', 2);
title('Imag(m) vs. T', 'FontSize', 20);
grid on;
xlabel('T', 'FontSize', 20);
ylabel('imag(m)', 'FontSize', 20);
For the random values I chose, it does look like the curve approaches the Tc point smoothly. What does it look like for you, with your values???
Saurav
Saurav 2020-7-27
Sir, curve is smooth till Tc then as per the function it must go to 0 for T>Tc but I want to modify the function in such way that for T>Tc curve smoothly decays to 0 with finite first derrivative for entire range of values

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回答（1 个）

Alan Stevens
Alan Stevens 2020-7-26
编辑：Alan Stevens 2020-7-26
How about writing a function like:
function mfn = mvalue(T,Tc,a,b,y)
disc = b^2 - 4*y*a*(T - Tc);
quad = -b + disc^0.5/(2*y);
if disc>0 && quad>0
mfn = quad^0.5;
else
mfn = 0;
end
end
and then calling
m(i) = mvalue(T(i), Tc, a, b, y);
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Alan Stevens
Alan Stevens 2020-7-26
编辑：Alan Stevens 2020-7-26
Impossible to tell without knowing about the system you are modelling. Mathematically you could probably multiply m by some sort of exponential decay term. However, would that make sense in the context of your model?
Saurav
Saurav 2020-7-27
Sir, I want the function to decay to 0 over small range with small change to curve for lets say
( Tc-delta,Tc+delta) range for delta-->0 with ensuring first derrivative remaining finite for entire range.Directly multiplying the function with exponential decay will highly modify the function.I tried adding small expo. decay to this function at the end for T>Tc but it creates knife edge point in the function at T=Tc. All i am asking is there any way to smooth the function in matlab because in verilog it automatically creates smooth function for such discontinuities. Thanks in advance.

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