ssllys

How can I merge these four pictures into...

Asked: ssllys 35 Product: Maple

August 29 2018

2 0

>

restart:

>

(1)

>	e_oredr := 1:

>	ode := subs(D = sum('e^(i-1)*D[i]', 'i' = 1 .. e_oredr+1), ode);

(2)

>	u := sum('q[i]*e^i', 'i' = 0 .. e_oredr);

(3)

>	ode := collect(ode, e):

>

>	ode:=simplify(%,{e^3=0,e^2=0});

(4)

>

>	for i from 0 to e_oredr do eq[i] := coeff(lhs(ode), e, i) = 0 end do;

(5)

>

>	eq[1]:=convert(eq[1](t1, t2), diff);

alpha[2](t[1], t[2])*q[0](t[1], t[2])^3+alpha[1](t[1], t[2])*(diff(q[0](t[1], t[2]), t[1]))+2*(diff(diff(q[0](t[1], t[2]), t[1]), t[2]))+diff(diff(q[1](t[1], t[2]), t[1]), t[1])+q[1](t[1], t[2]) = 0

(6)

>

>	q[0] :=A(t2)exp(It1)+bexp(Iwt1)+conjugate(A)(t2)exp(-It1)+bexp(-Iwt1); convert(%, 'exp'); q[0] := unapply(%, (t1, t2)): # Chage the value

(7)

>

>	expand(lhs(eq[1])):

>	eq:=combine(%, exp):

>	eq:=simplify(%, power):

>	eq:=combine(subs(w=1/3+e*sigma,%),exp): ## substituting the detuning parameter

>	expand(%):

>	eq:=algsubs(t1*e=t2,%):

>

>	eq:=collect(%, exp(I*t1)):

>

>	coeff(%, exp(I*t1),1):

>	simplify(combine(%,exp));

exp((3*I)*sigma*t[2])*alpha[2](t[1], t[2])*b^3+3*alpha[2](t[1], t[2])*A(t[2])^2*(conjugate(A))(t[2])+6*alpha[2](t[1], t[2])*b^2*A(t[2])+I*A(t[2])*alpha[1](t[1], t[2])+(2*I)*(diff(A(t[2]), t[2]))

(8)

>	subs({A(t2)=a(t2)exp(Ibeta(t2))/2,conjugate(A)(t2)=a(t2)exp(-Ibeta(t2))/2},%);

exp((3*I)*sigma*t[2])*alpha[2](t[1], t[2])*b^3+(3/8)*alpha[2](t[1], t[2])*a(t[2])^3*(exp(I*beta(t[2])))^2*exp(-I*beta(t[2]))+3*alpha[2](t[1], t[2])*b^2*a(t[2])*exp(I*beta(t[2]))+((1/2)*I)*a(t[2])*exp(I*beta(t[2]))*alpha[1](t[1], t[2])+(2*I)*(diff((1/2)*a(t[2])*exp(I*beta(t[2])), t[2]))

(9)

>	combine(%,exp);

exp((3*I)*sigma*t[2])*alpha[2](t[1], t[2])*b^3+(3/8)*alpha[2](t[1], t[2])*a(t[2])^3*exp(I*beta(t[2]))+3*alpha[2](t[1], t[2])*b^2*a(t[2])*exp(I*beta(t[2]))+((1/2)*I)*a(t[2])*exp(I*beta(t[2]))*alpha[1](t[1], t[2])+(2*I)*((1/2)*(diff(a(t[2]), t[2]))*exp(I*beta(t[2]))+((1/2)*I)*a(t[2])*(diff(beta(t[2]), t[2]))*exp(I*beta(t[2])))

(10)

>	map(x->xexp(-Ibeta(t2)),%);

(11)

>	simplify(%,exp);

alpha[2](t[1], t[2])*b^3*exp(-I*(-3*sigma*t[2]+beta(t[2])))+(3/8)*alpha[2](t[1], t[2])*a(t[2])^3-a(t[2])*(diff(beta(t[2]), t[2]))+3*alpha[2](t[1], t[2])*b^2*a(t[2])+((1/2)*I)*a(t[2])*alpha[1](t[1], t[2])+I*(diff(a(t[2]), t[2]))

(12)

>	subs({3sigmat2-beta(t2)=C(t2),beta(t2)=3sigmat2-C(t2)},%);

alpha[2](t[1], t[2])*b^3*exp(I*C(t[2]))+(3/8)*alpha[2](t[1], t[2])*a(t[2])^3-a(t[2])*(diff(3*sigma*t[2]-C(t[2]), t[2]))+3*alpha[2](t[1], t[2])*b^2*a(t[2])+((1/2)*I)*a(t[2])*alpha[1](t[1], t[2])+I*(diff(a(t[2]), t[2]))

(13)

>	convert(%,trig);

alpha[2](t[1], t[2])*b^3*(cos(C(t[2]))+I*sin(C(t[2])))+(3/8)*alpha[2](t[1], t[2])*a(t[2])^3-a(t[2])*(3*sigma-(diff(C(t[2]), t[2])))+3*alpha[2](t[1], t[2])*b^2*a(t[2])+((1/2)*I)*a(t[2])*alpha[1](t[1], t[2])+I*(diff(a(t[2]), t[2]))

(14)

>

>	cond1 := collect(coeff(%, I, 0), [diff(C(t2), t2), cos(C(t2))]);

a(t[2])*(diff(C(t[2]), t[2]))+alpha[2](t[1], t[2])*b^3*cos(C(t[2]))+(3/8)*alpha[2](t[1], t[2])*a(t[2])^3-3*a(t[2])*sigma+3*alpha[2](t[1], t[2])*b^2*a(t[2])

(15)

>	cond2 := collect(coeff(%%, I, 1), [diff(A(t2), t2), sin(C(t2))]);

alpha[2](t[1], t[2])*b^3*sin(C(t[2]))+(1/2)*a(t[2])*alpha[1](t[1], t[2])+diff(a(t[2]), t[2])

(16)

>	a(t2):= a; C(t2):=C; cond1 = 0; cond2 =0;

alpha[2](t[1], t[2])*b^3*cos(C)+(3/8)*alpha[2](t[1], t[2])*a^3-3*a*sigma+3*alpha[2](t[1], t[2])*b^2*a = 0

alpha[2](t[1], t[2])*b^3*sin(C)+(1/2)*a*alpha[1](t[1], t[2]) = 0

(17)

>	alpha[1]:=unapply(alpha[1],[t1,t2]);alpha[2]:=unapply(alpha[2],[t1,t2]);

(18)

>	remove(has, cond1, cos)^2+remove(has, cond2, sin)^2 = select(has, cond1, cos)^2+select(has, cond2, sin)^2;

((3/8)*alpha[2]*a^3-3*a*sigma+3*alpha[2]*b^2*a)^2+(1/4)*a^2*alpha[1]^2 = alpha[2]^2*b^6*cos(C)^2+alpha[2]^2*b^6*sin(C)^2

(19)

>	simplify(%,'trig');

(9/64)*a^2*(a^2*alpha[2]+8*alpha[2]*b^2-8*sigma)^2+(1/4)*a^2*alpha[1]^2 = alpha[2]^2*b^6

(20)

>

af_eq:=%;

(9/64)*a^2*(a^2*alpha[2]+8*alpha[2]*b^2-8*sigma)^2+(1/4)*a^2*alpha[1]^2 = alpha[2]^2*b^6

(21)

>

##

>

##

>	b:=0.5*f0/(1-(1/3)^2);

(22)

>	with(plots, implicitplot):

>	f0 :=1; alpha[1]:=0.0087;alpha[2]:=2.5871; b:=0.5*f0/(1-(1/3)^2);#change the value

(23)

>	af_eq; curve1,curve2:=solve(af_eq, sigma): A0:=2:

(9/64)*a^2*(2.5871*a^2-8*sigma+6.548596875)^2+0.1892250000e-4*a^2 = .2120125612

(24)

>

pu1:=implicitplot([sigma=curve2,sigma=curve1],sigma =-5..20, a = 0 .. A0, numpoints = 200000, axes = box, axesfont=[SYMBOL, 14],labels = [sigma, a], labelfont = [SYMBOL, 16],color="red",tickmarks=[9,12],thickness=3,'view' = [-5 .. 20, 0 .. 6]):
pu2:=implicitplot([sigma=curve2,sigma=curve1],sigma =-5..20, a = A0 .. 10,linestyle=[1,3], numpoints = 20000, axes = box, axesfont=[SYMBOL, 14],labels = [sigma, a], labelfont = [SYMBOL, 16],color="red",tickmarks=[9,12],thickness=3,'view' = [-5 .. 20, 0 .. 6]):

>

A0:=-2:

>

pu3:=implicitplot([sigma=curve2,sigma=curve1],sigma =-5..20, a = -10 .. A0, linestyle=[3,1], numpoints = 200000, axes = box, axesfont=[SYMBOL, 14],labels = [sigma, a], labelfont = [SYMBOL, 16],color="red",tickmarks=[9,12],thickness=3,'view' = [-5 .. 20, -6 .. 0]):
pu4:=implicitplot([sigma=curve2,sigma=curve1],sigma =-5..20, a = A0 .. 0, numpoints = 20000, axes = box, axesfont=[SYMBOL, 14],labels = [sigma, a], labelfont = [SYMBOL, 16],color="red",tickmarks=[9,12],thickness=3,'view' = [-5 .. 20, -6 .. 0]):

>	pp1:=display([pu1,pu2,pu3,pu4]);

(25)

>	How can I merge these pictures into one

>

Like this one

Download merege_two_diagram.mw

Anxious!! How to express the part of the...

Asked: ssllys 35 Product: Maple

August 23 2018

1 2

How to express the part of unstable curve with a dashline. Hope someone can help me achieve this.

>

(3/8)*alpha[2](t[1], t[2])*A(t[2])^3*exp(I*B(t[2]))*exp(-I*B(t[2]))+((1/2)*I)*alpha[1](t[1], t[2])*A(t[2])*exp(I*B(t[2]))*exp(-I*B(t[2]))+I*(diff(A(t[2]), t[2]))*exp(I*B(t[2]))*exp(-I*B(t[2]))-A(t[2])*(diff(B(t[2]), t[2]))*exp(I*B(t[2]))*exp(-I*B(t[2]))-(1/2)*f0*exp(I*sigma*t[2])*exp(-I*B(t[2]))

(13)

>	combine(%, 'exp');

(3/8)*alpha[2](t[1], t[2])*A(t[2])^3+((1/2)*I)*alpha[1](t[1], t[2])*A(t[2])+I*(diff(A(t[2]), t[2]))-A(t[2])*(diff(B(t[2]), t[2]))-(1/2)*f0*exp(I*sigma*t[2]-I*B(t[2]))

(14)

>	subs(IB(t2)=Isigmat2-IC(t2),B(t2)=sigma*t2-C(t2), %);

(3/8)*alpha[2](t[1], t[2])*A(t[2])^3+((1/2)*I)*alpha[1](t[1], t[2])*A(t[2])+I*(diff(A(t[2]), t[2]))-A(t[2])*(diff(sigma*t[2]-C(t[2]), t[2]))-(1/2)*f0*exp(I*sigma*t[2]-I*(sigma*t[2]-C(t[2])))

(15)

>	conds := combine(%, 'exp');

(3/8)*alpha[2](t[1], t[2])*A(t[2])^3+((1/2)*I)*alpha[1](t[1], t[2])*A(t[2])+I*(diff(A(t[2]), t[2]))-A(t[2])*(sigma-(diff(C(t[2]), t[2])))-(1/2)*f0*exp(I*sigma*t[2]-I*(sigma*t[2]-C(t[2])))

(16)

>	convert(conds, 'trig');

(3/8)*alpha[2](t[1], t[2])*A(t[2])^3+((1/2)*I)*alpha[1](t[1], t[2])*A(t[2])+I*(diff(A(t[2]), t[2]))-A(t[2])*(sigma-(diff(C(t[2]), t[2])))-(1/2)*f0*(cos(C(t[2]))+I*sin(C(t[2])))

(17)

>	cond1 := collect(coeff(%, I, 0), [diff(A(t2), t2), cos(C(t2))]);

(3/8)*alpha[2](t[1], t[2])*A(t[2])^3-A(t[2])*(sigma-(diff(C(t[2]), t[2])))-(1/2)*f0*cos(C(t[2]))

(18)

>	cond2 := collect(coeff(`%%`, I, 1), [diff(A(t2), t2), sin(C(t2)), cos(C(t2))]);

(1/2)*alpha[1](t[1], t[2])*A(t[2])+diff(A(t[2]), t[2])-(1/2)*f0*sin(C(t[2]))

(19)

>	A(t2):= A; C(t2):=C; cond1 = 0; cond2 =0;

(3/8)*alpha[2](t[1], t[2])*A^3-A*sigma-(1/2)*f0*cos(C) = 0

(1/2)*alpha[1](t[1], t[2])*A-(1/2)*f0*sin(C) = 0

(20)

>	remove(has, cond1, cos)^2+remove(has, cond2, sin)^2 = simplify(select(has, cond1, cos)^2+select(has, cond2, sin)^2, 'trig');

((3/8)*alpha[2](t[1], t[2])*A^3-A*sigma)^2+(1/4)*alpha[1](t[1], t[2])^2*A^2 = (1/4)*f0^2

(21)

>

af_eq:=%;

((3/8)*alpha[2](t[1], t[2])*A^3-A*sigma)^2+(1/4)*alpha[1](t[1], t[2])^2*A^2 = (1/4)*f0^2

(22)

>	alpha[1]:=0.0087;alpha[2]:=2.5871;f0:=f[0]

(23)

>

##

>

>	e:='e': f0:='f0': alpha[1]:='alpha[1]': alpha[2]:='alpha[2]':

>

cond1;

(3/8)*alpha[2](t[1], t[2])*A^3-A*sigma-(1/2)*f0*cos(C)

(24)

>

cond2;

(1/2)*alpha[1](t[1], t[2])*A-(1/2)*f0*sin(C)

(25)

>	linalg[jacobian]([-cond2,-cond1/A],[A,C]);

$Matrix(2, 2, {(1, 1) = -(1/2)*alpha[1](t[1], t[2]), (1, 2) = (1/2)*f0*cos(C), (2, 1) = -((9/8)*alpha[2](t[1], t[2])*A^2-sigma)/A+((3/8)*alpha[2](t[1], t[2])*A^3-A*sigma-(1/2)*f0*cos(C))/A^2, (2, 2) = -(1/2)*f0*sin(C)/A})$

(26)

>

>	subs(cos(C)=solve(cond1,cos(C)),sin(C)=solve(cond2,sin(C)),%);

$Matrix(2, 2, {(1, 1) = -(1/2)*alpha[1](t[1], t[2]), (1, 2) = (1/8)*A*(3*alpha[2](t[1], t[2])*A^2-8*sigma), (2, 1) = -((9/8)*alpha[2](t[1], t[2])*A^2-sigma)/A+((3/8)*alpha[2](t[1], t[2])*A^3-A*sigma-(1/8)*A*(3*alpha[2](t[1], t[2])*A^2-8*sigma))/A^2, (2, 2) = -(1/2)*alpha[1](t[1], t[2])})$

(27)

>	map(simplify,%):

>	linalg[charpoly](%,lambda):

>	p:=collect(%,lambda);

(1/4)*alpha[1](t[1], t[2])^2+lambda*alpha[1](t[1], t[2])+lambda^2+(27/64)*A^4*alpha[2](t[1], t[2])^2-(3/2)*A^2*alpha[2](t[1], t[2])*sigma+sigma^2

(28)

>

>	coeff(p,lambda,0);

(1/4)*alpha[1](t[1], t[2])^2+(27/64)*A^4*alpha[2](t[1], t[2])^2-(3/2)*A^2*alpha[2](t[1], t[2])*sigma+sigma^2

(29)

>

>	stab_cond:=%;

(1/4)*alpha[1](t[1], t[2])^2+(27/64)*A^4*alpha[2](t[1], t[2])^2-(3/2)*A^2*alpha[2](t[1], t[2])*sigma+sigma^2

(30)

>

af_eq;

((3/8)*alpha[2](t[1], t[2])*A^3-A*sigma)^2+(1/4)*alpha[1](t[1], t[2])^2*A^2 = (1/4)*f0^2

(31)

>	with(plots, implicitplot,implicitplot3d):

>

>	f0 :=0.1; alpha[1]:=0.0087;alpha[2]:=2.5871;

(32)

>

>	p1:=implicitplot(stab_cond,sigma = -1.2 .. 2, A = 0 .. 2, numpoints = 20000, axes = box, axesfont=[SYMBOL, 14],labels = [sigma, A], labelfont = [SYMBOL, 16],color="Green",tickmarks=[9,12],thickness=2,linestyle=dash):

>	with(plots,textplot): with(plots,display):

>	ps1:=textplot([0.75, 0.65, "Unstable region"], 'align' = {'above', 'right'},rotation = 0.6, font=[Times,bold,12]):

>	pu1:=implicitplot(af_eq,sigma = -1.2 .. 2, A = 0 .. 2, numpoints = 20000, axes = box, axesfont=[SYMBOL, 14],labels = [sigma, A], labelfont = [SYMBOL, 16],color="red",tickmarks=[9,12],thickness=2):

>	pp1:=display({p1,ps1,pu1});

>	Like this picture.

Download how_to_draw_the_dashline_part.mw

Why does the "textplot" command not work...

Asked: ssllys 35 Product: Maple 2018

July 29 2018

1 1

Why does the "textplot" command not work? I just want to write

>

>	af_eq := (3alpha[2](t[1], t[2])A^3(1/8)-Asigma)^2+(1/4)alpha[1](t[1], t[2])^2A^2 = (1/4)*f0^2

(1)

>	alpha[1]:=0.0087;alpha[2]:=2.5871;f0:=f[0]

(2)

>

>	with(plots, implicitplot,implicitplot3d):

>	f0 :=0.1; alpha[1]:=0.0087;alpha[2]:=2.5871;

(3)

>	p1:=implicitplot(af_eq, sigma = -1.2 .. 2, A = 0 .. 2, numpoints = 20000, axes = box, axesfont=[SYMBOL, 14],labels = [sigma, A], labelfont = [SYMBOL, 16],color="Red",tickmarks=[9,12],thickness=2);

>

(4)

>

Download textplot_problem.mw

e some word inside the figure. Please help me

How could I substitute the (t1*e) into t...

Asked: ssllys 35 Product: Maple 2018

July 27 2018

1 0

How could I substitute the (t1*e) into t2 at the index of e? I am trying many ways to do that, but it doesn't work. please help me.

>

restart:

>

(1/8)*alpha[2](t[1], t[2])*b^3*exp((3*I)*omega*t[1])+(1/8)*alpha[2](t[1], t[2])*b^3*exp(-(3*I)*omega*t[1])+(1/8)*alpha[2](t[1], t[2])*A(t[2])^3*exp((3*I)*t[1])+(1/8)*alpha[2](t[1], t[2])*A(t[2])^3*exp(-(3*I)*t[1])+3*alpha[2](t[1], t[2])*b^3*exp(-I*omega*t[1])*(1/8)+3*alpha[2](t[1], t[2])*b^3*exp(I*omega*t[1])*(1/8)-I*alpha[1](t[1], t[2])*A(t[2])*exp(-I*t[1])*(1/2)+3*alpha[2](t[1], t[2])*A(t[2])^2*b*exp(-I*omega*t[1])*(1/4)-I*(diff(A(t[2]), t[2]))*exp(-I*t[1])+3*alpha[2](t[1], t[2])*A(t[2])*exp(-I*t[1])*b^2*(1/4)-I*alpha[1](t[1], t[2])*b*omega*exp(-I*omega*t[1])*(1/2)+I*alpha[1](t[1], t[2])*b*omega*exp(I*omega*t[1])*(1/2)+3*alpha[2](t[1], t[2])*A(t[2])^3*exp(-I*t[1])*(1/8)+I*(diff(A(t[2]), t[2]))*exp(I*t[1])+3*alpha[2](t[1], t[2])*A(t[2])*b^2*exp(-I*t[1]-(2*I)*omega*t[1])*(1/8)+3*alpha[2](t[1], t[2])*A(t[2])*b^2*exp(-I*t[1]+(2*I)*omega*t[1])*(1/8)+q[1](t[1], t[2])+3*alpha[2](t[1], t[2])*A(t[2])^2*b*exp(-(2*I)*t[1]-I*omega*t[1])*(1/8)+3*alpha[2](t[1], t[2])*A(t[2])^3*exp(I*t[1])*(1/8)+3*alpha[2](t[1], t[2])*A(t[2])^2*b*exp(-(2*I)*t[1]+I*omega*t[1])*(1/8)+3*alpha[2](t[1], t[2])*A(t[2])*b^2*exp(I*t[1]-(2*I)*omega*t[1])*(1/8)+3*alpha[2](t[1], t[2])*A(t[2])*b^2*exp(I*t[1]+(2*I)*omega*t[1])*(1/8)+diff(q[1](t[1], t[2]), t[1], t[1])+3*alpha[2](t[1], t[2])*A(t[2])^2*b*exp((2*I)*t[1]-I*omega*t[1])*(1/8)+3*alpha[2](t[1], t[2])*A(t[2])^2*b*exp((2*I)*t[1]+I*omega*t[1])*(1/8)+I*alpha[1](t[1], t[2])*A(t[2])*exp(I*t[1])*(1/2)+3*alpha[2](t[1], t[2])*A(t[2])^2*b*exp(I*omega*t[1])*(1/4)+3*alpha[2](t[1], t[2])*A(t[2])*exp(I*t[1])*b^2*(1/4);

(1)

>

>	eq:=combine(subs(w=3+e*sigma,%),exp);

(2)

>	expand(%);

(3)

>	eq:=combine(subs({e^(t1*e)=e^t2},%),exp);

(4)

>	How could I substitute the (t1e) into t2 at the index of e? I am trying many ways to do that, but it doesn't work. please help me. (t1e)=t2

Download question.mw

Help me extracting the data from the Map...

Asked: ssllys 35 Product: Maple 2018

July 26 2018

1 3

Help me extracting the data from the Maple figure. I was used the 'implicitplod3D' command to draw the figure. I want to save the parameters of sigma, A and f0 in Exce

>	af_eq := (3alpha[2](t[1], t[2])A^3(1/8)-Asigma)^2+(1/4)alpha[1](t[1], t[2])^2A^2 = (1/4)*f0^2

(1)

>	with(plots, implicitplot,implicitplot3d):

>	alpha[1]:=0.1;alpha[2]:=0.1299;

(2)

>

##3D

>	implicitplot3d(af_eq, sigma = -1.5 .. 1.5,f0 =0..0.5, A = 0 .. 5,numpoints = 20000,style=surfacecontour,contours = 15);

>

Download extract_data_from_the_figure.mw

l format. then, I can use the data draw a picture in other software. Many thanks.

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