https://community.wolfram.com RSS Feed for Wolfram Community showing questions tagged with Material Sciences sorted by active. https://community.wolfram.com/groups/-/m/t/171121 Many sub-fields of materials science are interested in understanding interfaces: if I deposit a layer of germanium on top of silicon, how is the germanium lattice distorted?  A challenge for any cellular automata-like model of this process is that the size of the lattice/grid changes: silicon atoms aren't the same size as germanium atoms.  Much searching of the Wolfram site has found a few CA models of deposition, but none that incorporates this somewhat critical aspect.  So...  Is it even possible to build a cellular automata with non-uniform cells, or does that put me into more traditional modeling domains?  More generally, any pointers to people using Mathematica to model crystal growth? At this point I'd be interested in any level of sophistication, from hard spheres all the way up, simply because there doesn't seem to be a whole lot out there.  Thanks!  Katherine  Katherine Derbyshire 2013-12-14T20:55:23Z https://community.wolfram.com/groups/-/m/t/3345812 I cannot find any package, tool, examples, or library in System Modeler related to electrochemistry or electrochemical processes, like electrochemical cell simulation, anodes, cathodes, electrochemical corrosion, or anything related to these topics. Can someone guide me on how to use the system modeler to simulate the corrosion process and cathodic protection? Regards, Rogelio Rogelio de las Casas 2024-12-27T16:03:01Z https://community.wolfram.com/groups/-/m/t/3254868 Hello colleagues, I have a problem that is interesting. I have the following equations: 1) diffusion equation D[cb[t, x], {x, 2}] == D[cb[t, x], t]/d d is the diffusion coefficient, 2) Adsorption on the boundary (x=0) D[s[t], t] == k1*cb[t, 0]*s[t, x] -sat) - k2*s[t] The BC and IC: D[s[t], t]==d*D[cb[t, x] at x=0 cb[t,a]== c0 (a and c0 constats) cb[0,x] ==c0 s[0]==0 I found very akward to solve it. Any way to solve it? Or referentes about coupling ODE and PDE in Wolfram? Mnele Wolfram 2024-08-23T21:04:28Z https://community.wolfram.com/groups/-/m/t/2714274 Dear community, I am having trouble in solving a non-linear, coupled system of equations to describe diffusion-controlled bubble growth in a viscoelastic medium. The problem is described in detail https://pubs.acs.org/doi/abs/10.1021/ie060295a . The equation I am trying to solve in time domain (t={0,0.01}) is: ![enter image description here][1] Where c'=c-c0, D is the diffusion coefficient and R is the bubble radius. The initial and boundary conditions are: ![enter image description here][2] ![enter image description here][3] Where Kh is a constant, Pg is a pressure computed from the momentum balance, Pg0 is the initial pressure in the bubble (constant) and S is the radius of the bubble shell. My way of solving it using NDsolve and implicit Runge Kutta method looks like the following: CR=Kh*P; CR0=Kh*P0 R=10^-6; Rshell=20*10^-6; concprof = NDSolve[{D[conc[y, t], t] == 9*Diff*D[(y + R^3)^(4/3)*D[conc[y, t], y], y], conc[y, 0] == 0, (conc[0, t] /. t ->0.01) == CR-C0, Derivative[1, 0][conc][(Rshell^3 - R^3), t] == 0}, conc, {y, 0, (Rshell^3 - R^3)}, {t,0, 0.01}, Method -> "ImplicitRungeKutta"] If doing so, I get "Boundary condition conc[0,0.01]==-0.0222257 is not specified on a single edge of the boundary of the computational domain." If I try in alternative: concprof = NDSolve[{D[conc[y, t], t] == 9*Diff*D[(y + R^3)^(4/3)*D[conc[y, t], y], y], conc[y, 0] == 0, conc[0, t]== CR-C0, Derivative[1, 0][conc][(Rshell^3 - R^3), t] == 0}, conc, {y, 0, (Rshell^3 - R^3)}, {t,0, 0.01}, Method -> "ImplicitRungeKutta"] I get NDSolve::ibcinc: Warning: boundary and initial conditions are inconsistent. Can someone help me understand what I am doing wrong? Thanks! [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Arafmanesh.PNG&userId=2714242 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=BC1.PNG&userId=2714242 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=IC.PNG&userId=2714242 Enrico Troisi 2022-12-02T10:26:44Z https://community.wolfram.com/groups/-/m/t/2613468 I am trying to translate an example code for graph convolution network from Deep Learning for Physical Scientists: Accelerating Research with Machine Learning. Edward O. Pyzer-Knapp et. al. They have an example (Chapter 6, Section 6.3, Page 104-106) where they build a graph convolution network using Keras. The model takes a 132*132 adjacency matrix built out of molecule connectivity, with a flag of 1 or 0 for active or inactive molecule. from tensorflow.keras import datasets, layers, models from sklearn.model_selection import train_test_split model = models.Sequential() model.add(layers.Conv2D(64, (3, 3), activation='relu', input_shape=(None, None, 1), padding='SAME')) model.add(layers.MaxPooling2D((2, 2))) model.add(layers.Conv2D(32, (3, 3), activation='relu')) model.add(layers.GlobalMaxPooling2D()) model.add(layers.Dense(2, activation='softmax')) model.compile(optimizer='adam', loss='sparse_categorical_crossentropy', metrics=['accuracy']) I would like to build this model in WL. My attempt thus far is net = NetChain[{ConvolutionLayer[64, {3, 3}], ElementwiseLayer["ReLU"], PoolingLayer[{2, 2}, "Function" -> Max], ConvolutionLayer[32, {2, 2}], PoolingLayer[{2, 2}, "Function" -> Max], LinearLayer[2], SoftmaxLayer[]}] I can't find the GlobalMaxPooling option, and I am uncertain if my convolution layers are set up correctly. I appreciate if anyone could show how this could be done. Thank you, Arun Sharma 2022-09-08T13:03:07Z https://community.wolfram.com/groups/-/m/t/908230 Hello! I'm trying to make a table of "Polymers" and get the following Data: "Name", "MolecularFormulaDisplay", "Resistivity" "DielectricConstant". I also plan to sort the table by DielectricConstant and filter Missing data. I just started as a Research Assistant at school, so I'm pretty new here. This is what I have so far, and I'm getting only Missing[NotAvailable]. I don't know whether the filter isn't working or DielectricConstant is inexistent for the class "Polymers". Short[DeleteCases[ Table[ChemicalData[#, prop], {prop, {"Name", "MolecularFormulaDisplay", "Resistivity", "DielectricConstant"}}] & /@ ChemicalData["Polymers"], {_, _, _, _Missing}], 4] vals = Table[ ChemicalData[#, prop], {prop, {"Name", "MolecularFormulaDisplay", "Resistivity", "DielectricConstant"}}] & /@ ChemicalData["Polymers"]; Text[Grid[ Prepend[vals[[1 ;; 10]], {"Name", "MolecularFormulaDisplay", "Resistivity", "DielectricConstant"}], Frame -> All, Background -> {None, {{{LightBlue, White}}, {1 -> LightYellow}}}, Alignment -> Left]] Henrique Padilha 2016-08-19T03:46:16Z https://community.wolfram.com/groups/-/m/t/2433168 Dear Wolfram team: I am just asking what to do if you take the divergence of a scalar. For example, thermal stresses are the result of changes in temperature, a scalar field. I am guessing that this "divergence" is actually a gradient, but I am not sure. Now I give the details of my example: EXAMPLE: Thermal elastic stresses. Note: before using the equations, the following quantities are defined: - coordinates: X={x1,x2,x3}; vars=Flatten[{t,X}]; - fields: stress S, displacement U, gravity G, temperature TK; S=Apply[s,vars];U=Apply[u,vars]; G=Apply[g,X]; TK=Apply[T,vars]; Then the equations: 1. Equation of motion: D[Div[S,X]+rho*D[U,{t,2}]==rho*G 2. constitutive equation: c and alpha are constants of elasticity and thermal expansion, respectively, and T0 is the (constant) reference temperature S=c*alpha*(TK-T0) After plugging definition (2) into equation (1) , I get into trouble as said before, because the temperature is a scalar! In many references I saw that a symbol called "KroneckerDelta" is used to turn scalars into tensors and vectors, among other things, but I have no idea how to use that symbol in the Wolfram Language... anyway, that symbol should be an array of constants (actually many "1"s and "0"s). Your help would be greatly appreciated. Merry Christhmas and keep the hope that 2022 would be better than 2020 and 2021! Alberto Silva Ariano 2021-12-28T01:12:36Z https://community.wolfram.com/groups/-/m/t/2391482 Hello, I am trying to display a contour plot and vary some values to see how the Fermi surface would chance but for some reason the plot wont show up, any ideas of what I am missing? ax = 2 ay; ty = 2 tx; co = 20; Manipulate[ ContourPlot[ co - 2 tx Cos[kx ax] - 2 ty Cos[ky ay], {kx, 0, 2 Pi}, {ky, 0, 2 Pi}], {ay, 0, 10}, {tx, 0, 10}] Macarena likethesong 2021-10-24T06:42:23Z https://community.wolfram.com/groups/-/m/t/1846513 I think it because it plots a function that find fit-parameter to not-small data. the only thing that help me get the plot in a reasonable time is to set PlotPoints->10, but when I go to PlotPoints->50 for more precise plot, it runs for hours. Is there other way to quicken the program? This is my code: t1Fitting[x_?NumericQ, y_?NumericQ, z_?NumericQ] := Module[{sol, data, fit, P1, P2, t, a}, sol = DSolve[{P1'[t] == -(2 y + x) P1[t] + (x - y) P2[t] + y P2'[t] == -(2 z + x) P2[t] + (x - z) P1[t] + z, P1[0] == 1, P2[0] == 0}, {P1, P2}, t]; data = Flatten[ Transpose[Table[N[P1[t] - P2[t] /. sol, 15], {t, 0, 25000, 10}]]]; fit = FindFit[data, Exp[-a t],a, t, WorkingPrecision -> 10]; a /. fit] t1Plot = DensityPlot3D[t1Fitting[x,y,z],{x, 10^-6, 10^-4}, {y, 10^-6, 10^-4}, {z, 10^-6, 10^-4}, PlotPoints -> 50] Sivan Harazi 2019-12-22T10:05:52Z https://community.wolfram.com/groups/-/m/t/1793845 Hi, I just wanted to share something interesting... If you want to get a list of a certain language's alphabet, use the code you see in the image below: (to see the list clearly, right click on the image and click on "open image in new tab") Eleazar Johannian 2019-09-22T17:44:04Z https://community.wolfram.com/groups/-/m/t/520537 I am a materials scientist studying the microstructures of alloys of tungsten, iron, and nickel processed using liquid-phase sintering. The alloys produce microstructures full of spheroid tungsten particles, some of them connected to other particles, within a matrix of iron-nickel alloy. In places where two particles connect, they form a "neck" between them, which appears as a solid-solid boundary extending in two directions to "triple-points" where the solid-liquid boundaries of the surfaces of the respective connected particles both intersect. The angles formed by the respective orientations of the three intersecting boudaries are known in literature as "dihedral angles" and are indicative of the respective energies of the boundaries that form them. The relative differences in boundary surface energies has dominating effects on the evolution of the microstructures of these alloys through the processing/sintering time, and so it is important to have tools that can take automated measurements of them as they appear in digital micrographs so that large samples of measurements may be accumulated to provide a large sample and more accurate estimates of the population statistics. I have developed Mathematica code that will binarize the grayscale images that I have, and refine these binary images so that they closely represent the shapes and contours of the surface boundaries of particles. Also, I have used the ImageCorners operation to identify the triple-points in the images with good success. This leaves me with the task of taking measurements of the angles at these triple points. Most of the discussion that I have seen so far involves measurements of angles at "branches" where vertexes are identified and numbered and then used to find the angles using the "VectorAngle" operation. This approach may work, but the closest that I have come to isolating branches in my images is by using the Perimeter function to make an image of just the pixels at the particle boundaries and their intersections. This leaves me with a bit of code left to do, and I am just starting out in Mathematica and not quite up to that task yet. Any help is appreciated. Phillip Green 2015-06-30T00:28:07Z https://community.wolfram.com/groups/-/m/t/1450254 Hi All, I'm trying to generate a mesh in order to do a heat transfer analysis and have come up with the code in the attached file based on the Wolfram documentation and other posts in the community. The mesh is broken up into 9 regions to which I would like to assign material properties. I've had a go at assigning point markers to nodes which I then intended to use to assign material properties. However, I've come unstuck because the number of incidents I've created doesn't match the number of nodes (i.e. entries in mesh["Coordinates"]) due to each region being meshed separately and there being two incident IDs per node at each interface between regions. I'm new to Mathematica so I'd be very grateful if anyone could shed some light on how best to go about this. Also, is there a way to show the IDs of all nodes (PointElements?) rather than just the ones on the boundary? I've written my own code to solve for heat transfer in a separate notebook. Many thanks, Archie Archie Watts-Farmer 2018-09-11T14:56:59Z https://community.wolfram.com/groups/-/m/t/1428840 In the process of publishing my _Mathematica_ package in a journal (_Journal of Applied Crystallography_), I need a couple of short reports from independent users – see the extract below. > If you are submitting an article to the Computer Programs category, > you should provide brief reports from two independent users (i.e. > users who are not colleagues or close collaborators of the authors) > that confirm the usefulness of the program and the adequacy of the > documentation. These reports will be used only during the review > process and will not be published. It is a package for doing basic crystallography-related operations in _Mathematica_. If anyone would like to try it out and play a little with the documentation to see that it works, and send a short report back to me, it would be much appreciated. You can get the package from [GitHub][1]. Edit: typo. [1]: https://github.com/Stianpr20/MaXrd/releases Stian Ramsnes 2018-08-29T12:57:26Z https://community.wolfram.com/groups/-/m/t/1126696 I am trying to solve the Heat Equation in 2D for a circular domain and I used the example attached, however, for some reason I do not get any answer from it, and in principle, it seems that I am following the same steps as in the original document from wolfram tutorials. Any help will be much appreciated. I am using version 11.1.1 David Quesada 2017-06-23T17:34:18Z https://community.wolfram.com/groups/-/m/t/1063422 I can look up a property of a material (e.g. density), I can use it in a calculation (e.g. multiply density by a volume) but I just cannot get wolfram alpha to use two propeties of the same material in a calculation (e.g. specific heat and density to get volumetric specific heat). What am I missing here? I can compare a property of different materials, but not use two properties of the same material. Oren Tirosh 2017-04-15T18:05:46Z https://community.wolfram.com/groups/-/m/t/1021169 I'm currently trying to solve a mass balance useful in metallurgical processing. There are 4 ingoing streams (streams "c", "f","h" and "o") and 3 outgoing streams ("m", "e" and "s") and 5 chemical elements: Cu, Fe, S, O, and Si. The components are written as moles/100g of the respective stream. The compositions of streams "m", "s", "o", "f" and "h" are known, but the Fe, Si and O content of stream "e" is unknown. The O content of it can be obtained by charge balance, given that the oxidation states are: Cu =+1, Fe= x (+2<x<+3), Si=+4, S= -2, O = -2. Note: The vector "A" is the vector of atomic weights, useful because the dot product of it and the composition vector of any stream must be 1 (i.e the sum of mass % of all components must be 100%). The factor "R" is the (known) iron/silicon ratio of stream "e" The equation I am trying to solve is the following lineal system: Fee = Sie*R Oe = (Cue*1 + Fee*x + Sie*4 - Se*2)/2 m = {Cum, Fem, Sm, Om, Sim } e = {Cue, Fee, Se, Oe, Sie } c = {Cuc, Fec, Sc, Oc, Sic } f = {Cuf, Fef, Sf, Of, Sif } h = {Cuh, Feh, Sh, Oh, Sih } s = {0, 0, Ss, 2 Ss, 0 } o = {0, 0, 0, Oo, 0 } A = {ACu, AFe, AS, AO, ASi } Solve[{Mm*m + Me*e + Ms*s == Mc*c +Mf*f +Mh*h +Mo*o, Mm + Me + Ms == Mc +Mf +Mh +Mo , e.A == 1}, {Mm, Me, Mf, Mh, Ms, Mo, Sie}, Reals] Unfortunately, the program does not run, even after a week of trying to symplify/rearrange the equations. I cannot find the mistake, it should run as a system of 7 equations with 7 unknowns. Perhaps there is some (implicit) unknown variable or equation redundant or missing in the system of equations. The unknown variables should be the following: Mm, Me, Ms, Mo, Mf, Mh = masses Mi of the streams "m", "s", "o", "f" , "h" and "e" Sie = silicon concentration in stream "e" Thank you in advance for your help, Alberto Alberto Silva Ariano 2017-02-25T23:21:42Z https://community.wolfram.com/groups/-/m/t/969705 Following some excellent advice on this forum, I have created an app where I plot columns to represent the strength and position of lines in difraction spectra for a number of materials The heart of the code is f1[l_, lower_, upper_] := (If[ Length[Select[b[[l]], #[[1]] > lower && #[[1]] < upper &]] > 0, Black, Red]) f[l_, u_] := ( colarr = f1[#, l, u] & /@ Range[num]; ListPointPlot3D[ res, Filling -> Bottom, ColorFunctionScaling -> False, ColorFunction -> Function[{x, y, z}, colarr[[x]] ] ] ) Manipulate[ f[ll, uu], {ll, 0, 19.9, Appearance -> "Labeled"}, {uu, .1, 20, Appearance -> "Labeled"}] b is a list of lists containing the pairs or points where b[[1]] [[1]] gives the position of the line res is another list derived from b like this res = {}; Do[ AppendTo[res, Map[Prepend[i], b[[i]]]], {i, num}]; It is a list of triplets giving the 3D points The idea is if the material has enough points within lower and upper bounds in the y axis it will be a different colour from the points for other materials This works great providing I want to plot a couple of hundred points but it just does not function when I want to plot 2000. SO MY QUESTION IS :- HOW DO I IMPROVE THE PERFORMANCE? One thing that I have thought of is that these are not really 2000 independent points. The are rows of points along each value of the x axis. Each row has typically 10 points, all of which will be the same colour. I wondered if I could create a single Line object ( with the 10 vertical lines in) , whose locartion and size would remain absolutely constant, but I would want to change the colour(of the whole Line) as the values of ll and uu were changed in the manipulate. I am going to experiment with this and maybe this will be even slower. Has anyone got any better ideas? Thanks Graham graham tranfield 2016-11-24T19:47:10Z https://community.wolfram.com/groups/-/m/t/837493 I am an M.Sc. student doing a project on mathematica. It is an extremely lengthy code but there are no mistakes in the maths part. Somewhere I have done wrong coding and I am not able to find it out. Most likely I have used wrong syntax due to which It is giving me a blank graph. If anyone could help me then it would be a very great help for me. pAA = 0.5*(1 - l) + l pBB = 0.5*(l - 1) + 1 pAB = 1 - pBB pBA = 1 - pAA bA = 0.99*x^2/(3*((1 + (3.92*x^2)/9)^0.5 - 1)) bB = 3.24*10^(-5)*x^2/(3*((1 + (4.2*10^(-9)*x^2)/9)^0.5 - 1)) D1 = (bA + bB)/2 D2 = (bA - bB)/2 alpha = 0.5*(bA + bB)/(bA*bB) beta = 0.5*(bA - bB)/(bA*bB) X = 0.25*beta*x l1 = 0.5*(pAA*Exp[-X] + pBB*Exp[X] + ((pAA*Exp[-X] + pBB*Exp[X])^2 - 4*l)^0.5) l2 = 0.5*(pAA*Exp[-X] + pBB*Exp[X] - ((pAA*Exp[-X] + pBB*Exp[X])^2 - 4*l)^0.5) C1 = 1 + (pAA*Exp[-X] - l1)^2/(pAB*pBA) C2 = 1 + (pAA*Exp[-X] - l2)^2/(pAB*pBA) phi1 = (pAA*Exp[-X] - l1)/(pAB*Exp[-X]) phi1$ = (pAA*Exp[-X] - l1)/(pBA*Exp[X]) phi2 = (pAA*Exp[-X] - l2)/(pAB*Exp[-X]) phi2$ = (pAA*Exp[-X] - l2)/(pBA*Exp[X]) shi1 = (pAA*Exp[-X] - l1)/(pAB*Exp[X]) shi1$ = (pAA*Exp[-X] - l1)/(pBA*Exp[-X]) shi2 = (pAA*Exp[-X] - l2)/(pAB*Exp[X]) shi2$ = (pAA*Exp[-X] - l2)/(pBA*Exp[-X]) EE = l1^49*(1/C1)*(0.5 - 0.5*phi1$)*(Exp[-X] - phi1*Exp[X]) + l2^49*(1/C2)*(0.5 - 0.5*phi2$)*(Exp[-X] - phi2*Exp[X]) k1 = (Exp[-X]*(1 - phi1)) + (Exp[X]*((-shi1*phi1) + (shi1*phi1*phi1$))) k2 = (-Exp[-X]* shi1$*(1 - phi1)) - (Exp[ X]*((-phi1*shi1*shi1$) + (phi1*phi1$*shi1*shi1$))) k3 = (Exp[-X]*(1 - phi1)) + (Exp[X]*((-shi2*phi1) + (shi2*phi1*phi1$))) k4 = (-Exp[-X]* shi2$*(1 - phi1)) - (Exp[ X]*((-phi1*shi2*shi2$) + (phi1*phi1$*shi2*shi2$))) k5 = (Exp[-X]*(1 - phi2)) + (Exp[X]*((-shi1*phi2) + (shi1*phi2*phi2$))) k6 = (-Exp[-X]* shi1$*(1 - phi2)) - (Exp[ X]*((-phi2*shi1*shi1$) + (phi2*phi2$*shi1*shi1$))) k7 = (Exp[-X]*(1 - phi2)) + (Exp[X]*((-shi2*phi2) + (shi2*phi2*phi2$))) k8 = (-Exp[-X]* shi2$*(1 - phi2)) - (Exp[ X]*((-phi2*shi2*shi2$) + (phi2*phi2$*shi2*shi2$))) T1 = 0.5*(((1/C1)^2)*50*(l1^(49))*(k1 + k2) + ((1/C1)*(1/C2)*((l1^50 - l2^50)/(l1 - l2))*(k3 + k4) + ((1/C1)*(1/C2)*((l2^50 - l1^50)/(l2 - l1))*(k5 + k6)) + ((1/C2)^2)*50*(l2^49)*(k7 + k8))) p1 = (((49*l1^49 - ((49*l1^49 - 49)*(l2/l1)^50))/(1 - (l2/l1))) - (l2/ l1)*((1 - (l2/l1)^49)/(1 - (l2/l1)^2))) p2 = (((49*l2^49 - ((49*l2^49 - 49)*(l2/l1)^50))/(1 - (l2/l1))) - (l1/ l2)*((1 - (l1/l2)^49)/(1 - (l2/l1)^2))) T2 = 0.5*((((1/C1)^2)*1225*(l1^(49))*(k1 + k2) + ((1/C1)*(1/C2)* p1*(k3 + k4) + ((1/C1)*(1/C2)* p2*(k5 + k6)) + ((1/C2)^2)*1225*(l2^(49))*(k7 + k8)))) p3 = (((49*l2^50 - ((49*l2^50 - 48)*(l1/l2)^49))/(1 - (l1/l2))) - (l1/ l2)*((1 - (l1/l2)^48)/(1 - (l1/l2)^2))) p4 = (((49*l1^50 - ((49*l1^50 - 48)*(l2/l1)^49))/(1 - (l2/l1))) - (l2/ l1)*((1 - (l2/l1)^48)/(1 - (l2/l1)^2))) T3 = 0.5*( (((1/C1)^2)*1225*(l1^(49))*(k1 + k2) + ((1/C1)*(1/C2)* p3*(k3 + k4) + ((1/C2)*(1/C1)* p4*(k5 + k6)) + ((1/C2)^2)*1225*(l2^49)*(k7 + k8)))) k9 = (k1*pAA*Exp[-X]) + (k2*pBA*Exp[-X]) k10 = (-k1*pAB*Exp[X]) - (k2*pBB*Exp[X]) k11 = (k3*pAA*Exp[-X]) + (k4*pBA*Exp[-X]) k12 = (-k3*pAB*Exp[X]) - (k4*pBB*Exp[X]) k13 = (k5*pAA*Exp[-X]) + (k6*pBA*Exp[-X]) k14 = (-k5*pAB*Exp[X]) - (k6*pBB*Exp[X]) k15 = (k7*pAA*Exp[-X]) + (k8*pBA*Exp[-X]) k16 = (-k7*pAB*Exp[X]) - (k8*pBB*Exp[X]) k17 = k9 - shi1*k10 - shi1$*k9 + shi1*shi1$*k10 k18 = k9 - shi2*k10 - shi2$*k9 + shi2*shi2$*k10 k19 = k11 - shi1*k12 - shi1$*k11 + shi1*shi1$*k12 k20 = k11 - shi2*k12 - shi2$*k11 + shi2*shi2$*k12 k21 = k13 - shi1*k14 - shi1$*k13 + shi1*shi1$*k14 k22 = k13 - shi2*k14 - shi2$*k13 + shi2*shi2$*k14 k23 = k15 - shi1*k16 - shi1$*k15 + shi1*shi1$*k16 k24 = k15 - shi2*k16 - shi2$*k15 + shi2*shi2$*k16 gec = 1225*l1^48 ged = (((49*l1^48) - (49*l1^48 - 48)*(l2/l1)^49)/(1 - (l2/ l1))) - ((l2/l1)*(1 - (l2/l1)^48)/(1 - (l2/l1))^2) gfc = (((49*l1^48) - (49*l1^48 - 48)*(l2/l1)^49)/(1 - (l2/ l1))) - ((l2/l1)*(1 - (l2/l1)^48)/(1 - (l2/l1))^2) hec = (((49*l1^48) - (49*l1^48 - 48)*(l2/l1)^49)/(1 - (l2/ l1))) - ((l2/l1)*(1 - (l2/l1)^48)/(1 - (l2/l1))^2) gfd = (((49*l2^48) - (49*l2^48 - 48)*(l1/l2)^49)/(1 - (l1/ l2))) - ((l1/l2)*(1 - (l1/l2)^48)/(1 - (l1/l2))^2) hed = (((49*l2^48) - (49*l2^48 - 48)*(l1/l2)^49)/(1 - (l1/ l2))) - ((l1/l2)*(1 - (l1/l2)^48)/(1 - (l1/l2))^2) hfc = (((49*l2^48) - (49*l2^48 - 48)*(l1/l2)^49)/(1 - (l1/ l2))) - ((l1/l2)*(1 - (l1/l2)^48)/(1 - (l1/l2))^2) hfd = 1225*l2^48 T4 = 0.5*(gec*k17 + ged*k18 + gfc*k19 + gfd*k20 + hec*k21 + hed*k22 + hfc*k23 + hfd*k24) f[x_, l_] := ((1.5*50*alpha + 0.25*50*x^2*(alpha^2 + beta^2) - 1.5*(1/EE)*beta*(1 + 0.33*alpha*x^2)*T1 + 0.25*50*49*alpha^2*x^2 - 0.5*(1/EE)*x^2*(alpha*beta*(T2 + T3)) + beta^2*T4)^0.5)/50 p = LogLinearPlot[f[x, 0.0], {x, 0.01, 10^8}, PlotRange -> All] [1]: http://community.wolfram.com//c/portal/getImageAttachment?filename=Capture1.PNG&userId=837473 Rahul Kumar 2016-04-11T10:47:07Z https://community.wolfram.com/groups/-/m/t/827541 The following use of NDSolve with time-dependent boundary conditions fails. There seems to be an uncompatibilty with the MethodOfLines Method since when I do not enforce it , no warning/errors are returned. Is there a way to fix this issue or shall I change of method ? NDSolve[{D[c[x, y, t], t] - Laplacian[c[x, y, t], {x, y}] == NeumannValue[0, x >= t], DirichletCondition[c[x, y, t] == 1, x <= t], c[x, y, 0] == 0}, c, {x, 0, 100}, {y , -.5, .5}, {t, 0, 100}, Method -> {"MethodOfLines", "SpatialDiscretization" -> "FiniteElement"}] Tristan Baumberger 2016-03-22T09:20:49Z https://community.wolfram.com/groups/-/m/t/748082 I am new to Wolfram but am looking for a way to model a ceramic printed circuit type board with thick copper foil on two sides under temperature cycling conditions to study ceramic cracking. Can someone suggest a consultant or the Wolfram modules needed to develop a mathematical model? Thank you Ron Ronald Visser 2015-12-01T13:28:35Z