## plotting – How to plot two time intervals of a graph simultaneoulsy?

the graphs of my provided code look approximately like the picture below. How can I plot such gpaph, help me please. Any suggestion appreciated. Thanks a lot.

Subscript(C, i)=2.5*10^6
Subscript(k, e)=315
σ=1*10^-9
Subscript(S, e)=1.58*10^-5
g=2.3*10^16
Subscript(C, e)=2.1*10^4
τ=1*10^-15
a=1/τ
Subscript(w, 1)=1
Subscript(s, 1)=y/(Subscript(w, 1)*σ)
Subscript(b, 1)=g/Subscript(C, e)*(1+(Subscript(k, e)*Subscript(s, 1)^2)/g)
Subscript(Δ, 1)=Sqrt(Subscript(b, 1)^2-4*Subscript(k, e)*Subscript(s, 1)^2*g/(Subscript(C, i)*Subscript(C, e)))
Subscript(p, 11)=(-Subscript(b, 1)+Subscript(Δ, 1))/2
Subscript(p, 12)=(-Subscript(b, 1)-Subscript(Δ, 1))/2
Subscript(T, i)=(Subscript(S, e)*g)/(2*π*τ*Subscript(C, i)*Subscript(C, e))*NIntegrate(BesselJ(0,y)*Exp(-((σ^2*Subscript(s, 1)^2)/4))*(Exp(-a*t)/((a+Subscript(p, 11))*(a+Subscript(p, 12)))+1/(Subscript(p, 11)-Subscript(p, 12))*(Exp(Subscript(p, 11)*t)/(Subscript(p, 11)+a)-Exp(Subscript(p, 12)*t)/(Subscript(p, 12)+a)))*y/(σ*Subscript(w, 1))^2,{y,0,100})
Subscript(T, e)=Subscript(T, i)+Subscript(S, e)/(2*π*τ*Subscript(C, e))*NIntegrate(BesselJ(0,y)*Exp(-((σ^2*Subscript(s, 1)^2)/4))*(-((a*Exp(-a*t))/((a+Subscript(p, 11))*(a+Subscript(p, 12))))+1/(Subscript(p, 11)-Subscript(p, 12))*((Subscript(p, 11)*Exp(Subscript(p, 11)*t))/(Subscript(p, 11)+a)-(Subscript(p, 12)*Exp(Subscript(p, 12)*t))/(Subscript(p, 12)+a)))*y/(σ*Subscript(w, 1))^2,{y,0,100})
Plot(Subscript(T, e),{t,0,1*10^-14})
Plot(Subscript(T, i),{t,0,1*10^-14})

## plotting – how to Plot Hermite-Gaussian Beams with a random phase (2)

Please help me figure out how to write a program in “mathematica”. I don’t have enough time to understand the syntax of the language.

I found a great option for a simple case for the Hermite-Gaussian Beams.

Imn(x_, y_, m_, n_) := (HermiteH(m, x) Exp(-x^2/2))^2 (HermiteH(n, y) Exp(-y^2/2))^2

opts = Sequence(PlotRange -> All, ColorFunction -> GrayLevel, Frame -> False, PlotRangePadding -> None);

TableForm(
Table(
DensityPlot(Imn(x, y, m, n), {x, -5, 5}, {y, -5, 5}, Evaluate@opts,
Epilog -> Text(Style(StringJoin(ToString /@ {m, n}), 24, White), Scaled({0.5, 0.1}))
),
{n, 0, 3}, {m, 0, 3}
),
TableSpacing -> {0, 0}
)

Here I found a similar option that I need, but I was unable to remake it for myself.

F1(u_, v_, x_, y_,z_)=(1/w0)*(1/Sqrt(Pi*2^(u + v + 1)*u!*v!))*(w(z))^-1*Exp(-(x^2 + y^2)*w^2(z)^-1)*HermiteH(v, Sqrt(2) y *w(z)^-1)* HermiteH(u, Sqrt(2) x*w(z)^-1)*Exp(I(k*z + (k (x^2 + y^2))/2*(R(z))^-1 - (u + v + 1) (Phi)))
w0 = 1*10^-6;
zR = 1/2 k*(w0)^2;
k = (2 (Pi))/(Lambda);
(Lambda) = 0.55*10^-6;
w(z_) = w0 Sqrt(1 + (z/zR)^2);
R(z_) = z + (zR)^2/z;
(Phi) = ArcTan(z/zR);
F1(m_, n_, x_, y_) =Sqrt(1/(2^(m + n - 1)*Pi*m!*n!))*HermiteH(m, Sqrt(2) x)*HermiteH(n, Sqrt(2) y)*Exp(-(x^2 + y^2));
t11 = DensityPlot((F1(0, 2, x, y)^2), {x, -3, 3}, {y, -3, 3}, PlotRange -> All, ColorFunction -> "SunsetColors",PlotLegends -> Automatic)

But I really need to make the phase random.

I also found an option for matlab, but I could not use it:
https://uk.mathworks.com/matlabcentral/fileexchange/29258-plot-hermite-gaussian-beams

The spatial distribution of the field amplitude of the Hermite-Gaussian mode propagating along the z-axis is determined by the product of the Hermite polynomials and the Gaussian function:

I need the initial phase to be random in the range from 0 to Pi

I have a problem to write formulas and output an image similar to the example. I really like debts and with interest to understand everything, but now I do not have enough time.

## How can I plot the Fourier transform of the signal in Matlab?

I have a signal to compute its Fourier transform. I computed the Fourier transform of it as below, but I need to plot its Fourier transform on Matlab. How can I do this?

The signal is:

$$x(t) = e^{-3|t|}sin(2𝑡)u(t)$$

Also, how can I plot the Fourier transform of this signal?

The Fourier transform that I computed is:

$$3j/(9(w+2)^{2})-3j/(9+(w-2)^{2})$$

## plotting – How to plot clusters with binary matrix and coordinates?

I have to lists, x and y that contain the coordinates of $$N$$ nodes. The nodes are divided into non overlapping clusters. The clustering information is provided in a binary matrix $$M$$ of size $$Ctimes N$$, where $$C$$ is the number of clusters. If $$M_{c,n}=1$$, then node $$n$$ belongs to cluster $$c$$.

How can I show the clusters graphically?

## How to plot a complex function?

We cannot plot graph of a complex function $$f:mathbb {Cto C}$$ as it requires $$4$$ dimensions.But we can show how the mapping transforms the domain plane into image plane.We can draw grid lines parallel and perpendicular to $$x$$-axis and see how the grid lines are modified.But often it becomes tedious task to plot these kind of diagrams.Is there any systematic procedure to draw such figures without help of any software?

For example , $$z^2,z^3,sin(z),log(z),exp(z)$$ etc.

I want a method to visualize any given function.Is there a way out?

## plotting – Manipulate formula and several value on the Plot

I want to show the numerical results of (universal) gravitation.

However, how to give the value in the control bar?

G = 6.67259*10^(-11);
Manipulate(
Show(Plot(G*(M*m)/R^2, {R, 0, 1},
PlotRange -> {{0, 1.2}, {0, 2*10^(-8)}}),
Graphics({Red, PointSize(Large), Point({r, G*(M*m)/r^2})})), {
{M, 5}, 1, 10, Appearance -> "Labeled"}, {{m, 1}, 1, 10,
Appearance -> "Labeled"}, {{r, 0.3}, 0.1, 1,
Appearance -> "Labeled"}, Text@Style("F=", Black),
TrackedSymbols :> {M, m, r})

## How can I plot a 2D matrix with this style?

It is possible to plot the matrix like in the image. I’m using

ListPointPlot3D[amn, PlotRange -> All, Filling -> Axis]

Where amn is the 2D matrix but the result is not near to the image

## plotting – How can I switch off PlotRangeClipping from one side of the plot?

I want to make PlotRangeClipping -> True on each side of the plot (see code below) except the top side must be PlotRangeClipping -> Flase, is that possible?

Plot({x, -x}, {x, -5, 5}, PlotRange -> {{-1, 0}, {-3, 3}},
Frame -> True,PlotLegends ->
Placed(LineLegend({"Y1", "Y2"}, LegendLayout -> {"Row", 1},
LegendMarkerSize -> 20), {{0.5, 0.5}, {0.5, -1.8}}),
PlotRangePadding -> None, PlotRangeClipping -> False,

## calculus and analysis – EllepticPi argumet is complex. so can not plot it. How to handle this problem?

inttau(r_)=-(1/Sqrt(0.0345106153943703 - ((37.3042 - r) (-25.578 + r) (62.8822 +
r))/(3000 r)))

This is my function of r, now I integrated it w r t r

tauanalytical(r_) = Integrate(inttau(r), r)

This is what I got after integration, I got this result.

-((2.3094 Sqrt(1. + 62.1447/r) (-31.0723 + r) EllipticPi(3.,ArcSin(0.57735 Sqrt(1. + 62.1447/r)), 1.))/Sqrt(-0.965489 + 20./r + 0.000333333 r^2))

later I tried to find the numerical value of;

tauanalytical(30) // N

I got this, no the exact number , which I was expecting

-126.491 EllipticPi(3., -1.5708 + 0.153761 I, 1.)

Here the second argument of Ellepticpi comes out to be imaginary , it should be real . Please provide necessary assistance.

## plotting – List of conditions Plot

I made a table of conditions, namely conditions that define spheres. But I can’t plot those in “RegionPlot3D”, I would really like to know what I can do to surpass this problem.

When I get the condition, the “squares” appear in mathematical notation $$(x-1)^2$$ like this instead of $$(x-1) wedge$$ 2, I don’t know if it generates some kind of problem