log plot not plotting correctly

I am trying to get the following function, to plot with a log y axis. However, when I replace Plot with LogPlot, the plot is not computed correctly. Instead, a plot with incorrect x-axis is returned.

Constants  au = QuantityMagnitude[UnitConvert[Quantity[1, "AstronomicalUnit"], "Meters"]];  c = QuantityMagnitude[UnitConvert[Quantity[1, "SpeedOfLight"], "MetersPerSecond"]];  Qpr = 1;  Lsun = QuantityMagnitude[UnitConvert[Quantity[1, "SolarLuminosity"], "Watts"]];  Rsun = QuantityMagnitude[UnitConvert[Quantity[1, "SolarRadius"], "Meters"]];  Msun = QuantityMagnitude[UnitConvert[Quantity[1, "SolarMass"], "Kilograms"]];  G = QuantityMagnitude[UnitConvert[Quantity[1, "GravitationalConstant"], ("Meters"^2*"Newtons")/"Kilograms"^2]];  year = QuantityMagnitude[UnitConvert[Quantity[1, "Years"], "Seconds"]];  Myr = year*10^6;  Gyr = year*10^9;  Mwd = 0.6*Msun;  Cst = 1.27;  U = 1*10^17;   Functions  L[t_] := (3.26*Lsun*(Mwd/(0.6*Msun)))/(0.1 + t/Myr)^1.18;  Roche[dens_] := (0.65*Cst*Rsun*(Mwd/(0.6*Msun))^(1/3))/(dens/3000)^3^(-1);  Papsis[t_] := a[t]*(1 - e[t]);   Radiative Drag  RDdadtR\[Rho]a = -((3*L[t]*Qpr*(2 + 3*e[t]^2))/(c^2*(16*Pi*\[Rho]*Rast*a[t]*(1 - e[t]^2)^(3/2))));  RDdedtR\[Rho]a = -((15*L[t]*e[t])/(c^2*(32*Pi*Rast*\[Rho]*a[t]^2*Sqrt[1 - e[t]^2])));   RDsolR\[Rho]a = ParametricNDSolveValue[{Derivative[1][a][t] == RDdadtR\[Rho]a, Derivative[1][e][t] == RDdedtR\[Rho]a, a[0] == a0, e[0] == 0.3}, {a, e}, {t, 0, 9*Gyr},      {Rast, \[Rho], a0}];   fRDticks = {{Automatic, Automatic}, {Charting`FindTicks[{0, 1}, {0, 1/Myr}], Automatic}};   Manipulate[Column[{Style["Radiative Drag Working Plot", Bold], Plot[fun[func, t]/scale[func], {t, 0, 9*Gyr}, FrameTicks -> fRDticks,       Epilog -> {Red, Dashed, InfiniteLine[{{0, Roche[\[Rho]]}, {10, Roche[\[Rho]]}}]}, PlotStyle -> {Directive[Blue, Thickness[0.01]]}], Style["Compiled Plot", Bold],      If[comp === {}, Plot[fun[func, t]/scale[func], {t, 0, 9*Gyr}, FrameTicks -> fRDticks, Epilog -> {Red, Dashed, InfiniteLine[{{0, Roche[\[Rho]]}, {10, Roche[\[Rho]]}}]},        PlotStyle -> {Directive[Blue, Thickness[0.01]]}], Plot[comp/scale[func], {t, 0, 9*Gyr}, FrameTicks -> fRDticks,        Epilog -> {Red, Dashed, InfiniteLine[{{0, Roche[\[Rho]]}, {10, Roche[\[Rho]]}}]}, PlotStyle -> {Directive[Blue, Thickness[0.01]]}]]}],    {{func, 1}, {1 -> "a", 2 -> "e", 3 -> "q"}}, {{Rast, 0.005}, 0.0001, 0.1, 0.001, Appearance -> "Labeled"}, {{\[Rho], 3000}, 1000, 7000, 50, Appearance -> "Labeled"},    {{a0, 10, "a0 (au)"}, 1, 20, 0.2, Appearance -> "Labeled"}, Button["Append", AppendTo[comp, fun[func, t]]], Button["Reset", comp = {}],    TrackedSymbols -> {func, Rast, \[Rho], a0}, Initialization :> {comp = {}, fun[sel_, t_] := Switch[sel, 1, RDsolR\[Rho]a[Rast, \[Rho], a0*au][[1]][t], 2,        RDsolR\[Rho]a[Rast, \[Rho], a0*au][[2]][t], 3, RDsolR\[Rho]a[Rast, \[Rho], a0*au][[1]][t]*(1 - RDsolR\[Rho]a[Rast, \[Rho], a0*au][[2]][t])],      scale[sel_] := Switch[sel, 1 | 3, au, 2, 1]}] 

The question is- how do I get this plot to have a logarithmic y axis?

Thanks in advance.

Plotting horizontal line on Manipulate Plot

I have the following code, which outputs a Manipulate style plot. I want to draw a horizontal line on the plot related to q, with equation: y = Roche[\[rho]].

My code is as follows:

Constants  au = QuantityMagnitude[UnitConvert[Quantity[1, "AstronomicalUnit"], "Meters"]];  c = QuantityMagnitude[UnitConvert[Quantity[1, "SpeedOfLight"], "MetersPerSecond"]];  Qpr = 1;  Lsun = QuantityMagnitude[UnitConvert[Quantity[1, "SolarLuminosity"], "Watts"]];  Rsun = QuantityMagnitude[UnitConvert[Quantity[1, "SolarRadius"], "Meters"]];  Msun = QuantityMagnitude[UnitConvert[Quantity[1, "SolarMass"], "Kilograms"]];  G = QuantityMagnitude[UnitConvert[Quantity[1, "GravitationalConstant"], ("Meters"^2*"Newtons")/"Kilograms"^2]];  year = QuantityMagnitude[UnitConvert[Quantity[1, "Years"], "Seconds"]];  Myr = year*10^6;  Gyr = year*10^9;  Mwd = 0.6*Msun;  Cst = 1.27;  U = 1*10^17;   Functions  L[t_] := (3.26*Lsun*(Mwd/(0.6*Msun)))/(0.1 + t/Myr)^1.18;  Roche[dens_] := (0.65*Cst*Rsun*(Mwd/(0.6*Msun))^(1/3))/(dens/3000)^3^(-1);  Papsis[t_] := a[t]*(1 - e[t]);   Radiative Drag  RDdadtR\[Rho]a = -((3*L[t]*Qpr*(2 + 3*e[t]^2))/(c^2*(16*Pi*2000*Rast*a[t]*(1 - e[t]^2)^(3/2))));  RDdedtR\[Rho]a = -((15*L[t]*e[t])/(c^2*(32*Pi*Rast*2000*a[t]^2*Sqrt[1 - e[t]^2])));   Null  RDsolR\[Rho]a = ParametricNDSolveValue[{Derivative[1][a][t] == RDdadtR\[Rho]a, Derivative[1][e][t] == RDdedtR\[Rho]a, a[0] == a0, e[0] == 3/10}, {a, e}, {t, 0, 9*Gyr},      {Rast, \[Rho], a0}];   fRDticks = {{Automatic, Automatic}, {Charting`FindTicks[{0, 1}, {0, 1/Myr}], Automatic}};   Manipulate[Column[{Style["Working Plot", Bold], Plot[fun[func, t]/scale[func], {t, 0, 9*Gyr}, FrameTicks -> fRDticks,       PlotStyle -> {Directive[Blue, Thickness[0.01]]}], Style["Compiled Plot", Bold],      If[comp === {}, Plot[fun[func, t]/scale[func], {t, 0, 9*Gyr}, FrameTicks -> fRDticks, PlotStyle -> {Directive[Blue, Thickness[0.01]]}],       Plot[comp, {t, 0, 9*Gyr}, FrameTicks -> fRDticks, PlotStyle -> {Directive[Blue, Thickness[0.01]]}]]}], {{func, 1}, {1 -> "a", 2 -> "e", 3 -> "q"}},    {{Rast, 0.005}, 0.0001, 0.1, 0.001, Appearance -> "Labeled"}, {{\[Rho], 3000}, 1000, 7000, 50, Appearance -> "Labeled"},    {{a0, 10, "a0 (au)"}, 2, 20, 0.2, Appearance -> "Labeled"}, Button["Append", AppendTo[comp, fun[func, t]]], Button["Reset", comp = {}],    TrackedSymbols -> {func, Rast, \[Rho], a0}, Initialization :> {comp = {}, fun[sel_, t_] := Switch[sel, 1, RDsolR\[Rho]a[Rast, \[Rho], a0*au][[1]][t], 2,        RDsolR\[Rho]a[Rast, \[Rho], a0*au][[2]][t], 3, RDsolR\[Rho]a[Rast, \[Rho], a0*au][[1]][t]*(1 - RDsolR\[Rho]a[Rast, \[Rho], a0*au][[2]][t])],      scale[sel_] := Switch[sel, 1 | 3, au, 2, 1]}]  

I have tried to use Epilog but no line was displayed.

Any help would be appreciated.

Passing an expression to the Plot Function does not Work

Solving a differential equation I found that its solution was analytic, and I stored it as an expression from the default rule output of the DSolve[] function:

soleq2 = y[x] /. soleq2[[1, 1]]

Which has output:

Sqrt[x] BesselJ[Sqrt[13]/2, x] C[1] + Sqrt[x] BesselY[Sqrt[13]/2, x] C[2]

I then plotted this:

Manipulate[Plot[soleq2, {x, 0, 10}], {C[1], 0, 10}, {C[2], 0, 10}]

but the plot does not show anything, only the sliders for the modulation of C[1] and C[2]. I tried substituting these constants with other letters thinking their format might interfere with the kernel, but to no avail.

Why do the frame ticks disapear when a plot is exported as PNG?

I am using M12.0.0.0 on Ubuntu and I have these two plots:

plot1 = DensityPlot[Sin[x y], {x, -2, 2}, {y, 0, 4}, PlotPoints -> 80]; plot2 = Plot[Sin[x], {x, -10, 10}, Frame -> True]; 

when I export these plots as png the FramTicks disapear! here is plot1 as seen in the MMA notebook

enter image description here
and this how it looks when exported using Export["/.../plotq1.png", plot1,ImageResolution -> 500]
enter image description here

same thing also applies for plot2 in the notebook is like

enter image description here

and exported is like

enter image description here

Full line trajectories plot for the solution of Second Order nonlinear coupled differential equations

I wanted to plot a phase plane containing the trajectories of the solutions found by using ‘NDSolve’ using the initial conditions for x[0], y[0], x'[0] and y'[0]. The equations are: x”[t] – 2 y'[t] == -x[t] + y[t]^2; y”[t] + 2 x'[t] == x[t] + y[t] + x[t]*y[t]

The equilibrium point for the system is (0,0). I have plotted the stream plot for the system but unable to plot a phase portrait that would give me the full line trajectories of the system for different initial conditions. I am also looking for any periodic solution if present in it. The stream plot I got is given below and I would take initial conditions from it.

enter image description here

I get this by using the Parametric Plot of the NDSolve solution:

enter image description here

Kindly help in this capacity. Thanks in advance.

How to plot color range plot with data?

enter image description here

I have some data and want to plot it like in the figure mentioned but unable to do it. The code I tried is written below but it is not giving any plot. If anyone can resolve this is most welcome. The values in {} are {a1,b1,c1}.

Listlineplot{{0,-2,0},{0,-5,1},{0,-2,2},{0,-1,3},{0,0,4},{0,0,5}} {{1,-1,0},{1,-3,1},{1,-1,2},{1,0,3},{1,0,4}},{{2,-1,0},{2,-2,1},{2,-2,2},{2,-1,3},{2,0,4}},{{3,0,0},{3,-1,1},{3,-2,2},{3,-3,3},{3,-2,4}},{{4,0,0},{4,-1,1},{4,-2,2},{4,-3,3},{4,-1,4}},{{-1,-2,0},{-1,-1,1},{-1,-2,2},{-1,-2,3},{-1,-1,4}},{{-2,-2,0},{-2,-1,1},{-2,-2,2},{-2,-2,3},{-2,-1,4}},{{-3,-2,0},{-3,-1,1},{-3,-2,2},{-3,-2,3},{-3,-1,4}},{{-4,-2,0},{-4,-1,1},{-4,-2,2},{-4,-2,3},{-4,-1,4}},ColorFunction -> (Blend["VisibleSpectrum", #] &),   ColorFunctionScaling -> False, Filling -> Axis]      

Fitting model to intensity plot

I am trying to fit a model to the following dataset to extract numerical values for 4 parameters $ J_x$ , $ J_y$ , $ J_z$ , and $ g$ . I also know that $ g \approx 2$ in this case. The dataset is a list of quadruples: {x, energy, intensity, error} as shown below

dataset = {{0.01299648, 0.01203211, 0.1263361, 0.005950636}, {0.01299648, 0.04910681, 0.0336076, 0.002947696}, {0.01299648, 0.09977061, 0.001322289, 0.000413821}, {0.01299648, 0.1508783, 0.000499663, 0.000258259}, {0.01299648, 0.2008796, 0.000419055, 0.00024877}, {0.01299648, 0.2510364, 0.000421737, 0.000272571}, {0.01299648, 0.3009251, 0.000178943, 0.000156955}, {0.01299648, 0.3508747, 0.0000992, 0.0000883}, {0.01299648, 0.3999321, 0.000430162, 0.000468312}, {0.01299648, 0.4489179, 0.001252234, 0.000846992}, {0.01299648, 0.5002585, 0.000617269, 0.000553035}, {0.01299648, 0.5509165, 0.001468457, 0.000842178}, {0.01299648, 0.6011173, 0.003723728, 0.001349723}, {0.01299648, 0.6498302, 0.004062989, 0.001265983}, {0.01299648, 0.6988636, 0.001993023, 0.000906512}, {0.01299648, 0.7499531, 0.000721637, 0.000587884}, {0.01299648, 0.8010127, 0.000252952, 0.000316284}, {0.05334629, 0.01203211, 0.1305249, 0.004184997}, {0.05334629, 0.04910681, 0.03503799, 0.002187056}, {0.05334629, 0.09977061, 0.001494748, 0.000322744}, {0.05334629, 0.1508783, 0.000631434, 0.000216124}, {0.05334629, 0.2008796, 0.000516482, 0.000212526}, {0.05334629, 0.2510364, 0.000452927, 0.000203133}, {0.05334629, 0.3009251, 0.00038714, 0.000173926}, {0.05334629, 0.3508747, 0.000419254, 0.000179236}, {0.05334629, 0.3999321, 0.000425151, 0.000310161}, {0.05334629, 0.4489179, 0.000511058, 0.000412408}, {0.05334629, 0.5002585, 0.000683154, 0.000400352}, {0.05334629, 0.5509165, 0.001937698, 0.000617178}, {0.05334629, 0.6011173, 0.003902016, 0.000892543}, {0.05334629, 0.6498302, 0.00309874, 0.000839511}, {0.05334629, 0.6988636, 0.001156821, 0.000561058}, {0.05334629, 0.7499531, 0.000876003, 0.000445513}, {0.05334629, 0.8010127, 0.000494271, 0.000353135}, {0.05334629, 0.8507249, 0.000468474, 0.000405826}, {0.05334629, 0.9009042, 0.000227273, 0.000284132}, {0.09946869, 0.01203211, 0.1314684, 0.002607759}, {0.09946869, 0.04910681, 0.03540794, 0.001393436}, {0.09946869, 0.09977061, 0.001480958, 0.000215194}, {0.09946869, 0.1508783, 0.000518701, 0.000144396}, {0.09946869, 0.2008796, 0.00039427, 0.000139293}, {0.09946869, 0.2510364, 0.000395253, 0.000148412}, {0.09946869, 0.3009251, 0.000357242, 0.000144663}, {0.09946869, 0.3508747, 0.000435539, 0.000173756}, {0.09946869, 0.3999321, 0.000440639, 0.000186949}, {0.09946869, 0.4489179, 0.000453975, 0.000189049}, {0.09946869, 0.5002585, 0.000817151, 0.000265822}, {0.09946869, 0.5509165, 0.002821699, 0.000522746}, {0.09946869, 0.6011173, 0.005799377, 0.000790837}, {0.09946869, 0.6498302, 0.003142505, 0.000619193}, {0.09946869, 0.6988636, 0.00089875, 0.000377157}, {0.09946869, 0.7499531, 0.000935933, 0.000440654}, {0.09946869, 0.8010127, 0.000741281, 0.00040915}, {0.09946869, 0.8507249, 0.000379727, 0.000311241}, {0.09946869, 0.9009042, 0.000452129, 0.000372186}, {0.09946869, 0.9499643, 0.000321497, 0.000298012}, {0.09946869, 0.9987899, 0.000216047, 0.000265462}, {0.09946869, 1.049146, 0.000321083, 0.000405456}, {0.09946869, 1.100007, 0.00007, 0.000197968}, {0.09946869, 1.151003, 0.000371132, 0.000898138}, {0.09946869, 1.20088, 0.001603127, 0.001909191}, {0.1513923, 0.01203211, 0.1271927, 0.002382964}, {0.1513923, 0.04910681, 0.03466543, 0.001207942}, {0.1513923, 0.09977061, 0.001471831, 0.000180972}, {0.1513923, 0.1508783, 0.000458085, 0.000108564}, {0.1513923, 0.2008796, 0.000323088, 0.0000968}, {0.1513923, 0.2510364, 0.000262988, 0.0000927}, {0.1513923, 0.3009251, 0.000208331, 0.0000952}, {0.1513923, 0.3508747, 0.000261884, 0.000132211}, {0.1513923, 0.3999321, 0.000318829, 0.000154663}, {0.1513923, 0.4489179, 0.000390393, 0.000170512}, {0.1513923, 0.5002585, 0.000796483, 0.000230864}, {0.1513923, 0.5509165, 0.003169181, 0.00045884}, {0.1513923, 0.6011173, 0.006016299, 0.000634249}, {0.1513923, 0.6498302, 0.002961305, 0.000479318}, {0.1513923, 0.6988636, 0.00089255, 0.00030299}, {0.1513923, 0.7499531, 0.000601942, 0.000292041}, {0.1513923, 0.8010127, 0.000622036, 0.000308231}, {0.1513923, 0.8507249, 0.00059582, 0.000311122}, {0.1513923, 0.9009042, 0.000342461, 0.000258311}, {0.1513923, 0.9499643, 0.000365842, 0.000264302}, {0.1513923, 0.9987899, 0.000383168, 0.000282596}, {0.1513923, 1.049146, 0.000158197, 0.000218464}, {0.1513923, 1.100007, 0.0000797, 0.0001487}, {0.1513923, 1.151003, 0.000272186, 0.000602807}, {0.1513923, 1.20088, 0.000791483, 0.000943182}, {0.1513923, 1.24981, 0.000810134, 0.000846855}, {0.1513923, 1.298876, 0.001098106, 0.000878741}, {0.1513923, 1.35012, 0.001020097, 0.00091243}, {0.1513923, 1.400843, 0.00099628, 0.001472998}, {0.1513923, 1.45113, 0.001696679, 0.002615917}, {0.1513923, 1.487999, 0.00068497, 0.001417412}, {0.200413, 0.01203211, 0.1251366, 0.002421743}, {0.200413, 0.04910681, 0.03396657, 0.001239589}, {0.200413, 0.09977061, 0.001455514, 0.000186787}, {0.200413, 0.1508783, 0.000471295, 0.000107087}, {0.200413, 0.2008796, 0.000356116, 0.0000954}, {0.200413, 0.2510364, 0.000255785, 0.0000834}, {0.200413, 0.3009251, 0.000192659, 0.0000751}, {0.200413, 0.3508747, 0.000195415, 0.000086}, {0.200413, 0.3999321, 0.000212672, 0.0000972}, {0.200413, 0.4489179, 0.000201986, 0.0000998}, {0.200413, 0.5002585, 0.000452148, 0.00014457}, {0.200413, 0.5509165, 0.002283648, 0.000302595}, {0.200413, 0.6011173, 0.005130702, 0.000435712}, {0.200413, 0.6498302, 0.002947664, 0.000341739}, {0.200413, 0.6988636, 0.000885883, 0.00019889}, {0.200413, 0.7499531, 0.000353508, 0.000142375}, {0.200413, 0.8010127, 0.000337989, 0.000159135}, {0.200413, 0.8507249, 0.000294789, 0.00016511}, {0.200413, 0.9009042, 0.000287179, 0.00017037}, {0.200413, 0.9499643, 0.000311635, 0.000194681}, {0.200413, 0.9987899, 0.000207756, 0.000158586}, {0.200413, 1.049146, 0.000158257, 0.00013942}, {0.200413, 1.100007, 0.000190184, 0.000146221}, {0.200413, 1.151003, 0.000213257, 0.000208235}, {0.200413, 1.20088, 0.000336925, 0.000306631}, {0.200413, 1.24981, 0.000487695, 0.000424801}, {0.200413, 1.298876, 0.000638927, 0.000549385}, {0.200413, 1.35012, 0.001054225, 0.000776587}, 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0.000133103}, {0.7477285, 0.3999321, 0.000344739, 0.000279699}, {0.7477285, 0.4489179, 0.000390532, 0.000270478}, {0.7477285, 0.5002585, 0.000392541, 0.000259302}, {0.7477285, 0.5509165, 0.000149147, 0.000128412}, {0.7477285, 0.6011173, 0.000165453, 0.0000795}, {0.7477285, 0.6498302, 0.000452263, 0.000147439}, {0.7477285, 0.6988636, 0.000415388, 0.000125599}, {0.7477285, 0.7499531, 0.000297813, 0.000243738}, {0.7477285, 0.8010127, 0.000194161, 0.000304051}, {0.7477285, 0.8507249, 0.000154568, 0.00027359}, {0.7477285, 0.9009042, 0.000134434, 0.000251633}, {0.7477285, 0.9499643, 0.000110127, 0.00019129}, {0.7477285, 0.9987899, 0.000110382, 0.00010382}, {0.7477285, 1.049146, 0.000129385, 0.0000827}, {0.7477285, 1.100007, 0.000353017, 0.0000981}, {0.7477285, 1.151003, 0.000538544, 0.00013636}, {0.7477285, 1.20088, 0.00015782, 0.0000889}, {0.7477285, 1.24981, 0.0000696, 0.0000608}, {0.7477285, 1.298876, 0.000146578, 0.00013496}, {0.7477285, 1.35012, 0.000300833, 0.000205088}, {0.7477285, 1.400843, 0.000445233, 0.000245628}, {0.7477285, 1.45113, 0.000371585, 0.000403792}, {0.7477285, 1.487999, 0.00069879, 0.000703723}, {0.79343, 0.8010127, 0.000545414, 0.000697371}, {0.79343, 0.8507249, 0.000225278, 0.000428143}, {0.79343, 0.9009042, 0.000404924, 0.000554523}, {0.79343, 0.9499643, 0.000148193, 0.000297461}, {0.79343, 0.9987899, 0.000165649, 0.000213896}, {0.79343, 1.049146, 0.0000836, 0.000110634}, {0.79343, 1.100007, 0.000175279, 0.0000915}, {0.79343, 1.151003, 0.000331701, 0.000166089}, {0.79343, 1.20088, 0.000197516, 0.000136657}, {0.79343, 1.24981, 0.0000473, 0.0000663}, {0.79343, 1.298876, 0.000169997, 0.000187402}, {0.79343, 1.35012, 0.000461569, 0.000344723}, {0.79343, 1.400843, 0.000334411, 0.000273181}, {0.79343, 1.45113, 0.000547673, 0.000501559}, {0.79343, 1.487999, 0.000890756, 0.000845645}, {0.8292615, 1.35012, 0.000118945, 0.000182641}, {0.8292615, 1.400843, 0.000102903, 0.000170622}, {0.8292615, 1.45113, 0.000157944, 0.000294485}, {0.8292615, 1.487999, 0.000248875, 0.000441169}} 

My model yields the energy at a specific coordinate $ \boldsymbol{k} =\{k_x, k_y, k_z\}$ where $ \boldsymbol{k} = x(\boldsymbol{b}_1 + \boldsymbol{b}_2)$ . Here $ x$ is the first entry of each quadruple in the dataset, $ \boldsymbol{b}_1 = \{ 2 \pi, 2\pi/\sqrt{3}, 0 \}$ , and $ \boldsymbol{b}_2 = \{ 0, 4\pi/\sqrt{3}, 0 \}$

(* First obtain the measured energy values and store them in a list *) ω = DeleteDuplicates@*Flatten@dataset[[All, 2]]; b1 = {2π, (2π)/Sqrt[3], 0}; b2 = {0, (4π)/Sqrt[3], 0}; xKtoM = DeleteDuplicates@*Flatten@dataset[[All, 1]]; k = Table[xKtoM[[i]] (b1 + b2), {i, 1, Length[xKtoM]}]; 

I then go on to define my model

(* Bohr magneton μ in units of eV*T^-1 pulled from wikipedia*) μ = 5.7883818012*10^-5;  (* This is the model where we have taken the positive branch of the energy spectrum *) d[kx_, ky_, kz_, g_, Bz_, Jx_, Jy_, Jz_] := {1/2 (Jx + Jy) (Cos[k[[1]]] + Cos[k[[2]]] + Cos[k[[1]] + k[[2]]]) - 3 Jz + g \[Mu] Bz,  1/2 (Jx - Jy) (E^(-I 2 \[Pi]/3) Cos[k[[1]]] + E^(I 2 \[Pi]/3) Cos[k[[2]]] + Cos[k[[1]] + k[[2]]])};  spectrum[{kx_, ky_, kz_}] := Norm[d[kx, ky, kz, g, 4, Jx, Jy, Jz]]; (* Get the spectrum going from the high symmetry K \[Rule] M path using the k vector/list we defined above. This is the model we use for the dataset *) model = Map[spectrum, k]; 

From here I would have the energy values at 18 separate points if I had specified values for Jx, Jy, Jz, and g. I then thought to define a cost function that takes my model and subtracts the corresponding measured energy value and then try to find the minimum using the built-in FindMinimum function

(* Define a cost function between the model and the measured energy values Subscript[\[Omega], i] *) CostFunction[Jx_, Jy_, Jz_, g_] := Sum[Abs[model[[i]] - ω[[i]]]^2, {i, 1, Length[ω]}] (* Minimize this cost function to attempt to extract the parameters Jx, Jy, Jz, and g *) params = FindMinimum[model, {{Jx, 0.5}, {Jy, 0.5}, {Jz, 0.5}, {g, 2}}] 

My only issue with this is that

  1. My model is a list of functions while the measured energy values $ \omega$ is a list of real numbers
  2. Using FindMinimum yields quite a lot of errors

Is it possible to get around these issues using something like NonLinearModelFit or something similar? Let me know if I should clarify anything or add any additional info and thanks in advance!

Plot with Through[{f,g}[x]]… A bug or a misuse of Through[]?

I was expecting

Plot[{Sin[x], Cos[x]}, {x, -1, 1}, PlotLabels -> Automatic] 

and

Plot[Through[{Sin, Cos}[x]], {x, -1, 1}, PlotLabels -> Automatic] 

to give the same result, as

Through[{Sin, Cos}[x]] 

gives

{Sin[x], Cos[x]}

However I get this two different plots:

plot 1 plot 2

Is it a bug or do I misunderstand something? (maybe HoldAll Plot[] attribute does not mix well with Through[])

(I am running under Linux with MMA version 11.2.0 for Linux x86 (64-bit) (September 11, 2017))

Transforming a 3D into a 2D Plot

I have a ListPointPlot3D in which all points lie on a plane. I’d like to transform it into a simple 2D Plot by looking at the points from an orthogonal direction to that plane, but I don’t know how to do it. (The following is a MWE, not my actual data).

 points = Flatten[Permutations /@ IntegerPartitions[1, {3}, Range[0, 1, 1/5]], 1];  ListPointPlot3D[points]