https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions tagged with Modeling sorted by active. https://community.wolfram.com/groups/-/m/t/3673962 ![View of the Moon from Artemis II][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=ArtemisIIFlyBy_final.gif&userId=20103 [2]: https://www.wolframcloud.com/obj/54c0ec26-f350-4965-a1bc-bd7b5e34dbf5 Jeffrey Bryant 2026-04-03T19:51:12Z https://community.wolfram.com/groups/-/m/t/3682521 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/ecb910fc-6c9c-4b3e-b082-4c29b8155e5a Housam Binous 2026-04-11T08:39:24Z https://community.wolfram.com/groups/-/m/t/3682155 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/c71dc2ab-aaae-483f-8ad8-c1df5123fa14 Housam Binous 2026-04-10T17:43:39Z https://community.wolfram.com/groups/-/m/t/3681925 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/64303660-b4e4-4803-a2d0-5adaa34c994e Housam Binous 2026-04-10T12:15:35Z https://community.wolfram.com/groups/-/m/t/3675919 **Intro** A fundamental question keeps coming up for me: If biological evolution operates in astronomically large spaces, why is search computationally tractable at all? Even a modest protein corresponds to a combinatorial space that is effectively impossible to exhaustively explore. Yet evolution does not behave like an unconstrained random search. So what makes the space navigable? **Essay** In 1859, two different perspectives on complexity emerged. Bernhard Riemann revealed deep structural order underlying the distribution of prime numbers. Charles Darwin introduced a dynamical process of variation and selection. Modern biology has successfully developed Darwin’s framework. However, something is often left implicit: the assumption that the search space is already structured in a way that makes local exploration effective. From a purely combinatorial perspective, this is problematic. Under simple assumptions (independent variation, no bias), expected search time grows exponentially with the amount of required information. In that regime, evolution would be computationally intractable. But real systems do not operate in that regime. Instead, they appear to evolve within a highly structured, constrained subspace, where: functional states are not isolated viable configurations form connected regions local mutations can traverse meaningful paths This suggests that evolution can be framed as a constrained search problem, rather than a purely stochastic process. Evolution is not merely a process acting within a space — it is a process shaped by the structure of the space it can access. This shifts the central question: What determines that accessible space? **A Minimal Computational Model** To make this concrete, consider a simple toy model. We define: a sequence space a mutation operator a constraint that restricts transitions **Basic setup** L = 20; randomSeq[] := RandomInteger[{0, 1}, L]; mutate[s_] := ReplacePart[s, RandomInteger[{1, L}] -> 1 - #] & @ s; **Fitness function** fitness[s_] := Boole[Total[s] > 12]; **Constraint energy** energy[s_] := Total[ Map[If[# === {1, 1}, 0, 1] &, Partition[s, 2, 1]] ]; **Dynamics: constrained vs unconstrained** stepConstrained[s_] := Module[{s2 = mutate[s]}, If[constraint[s, s2], s2, s] ]; stepRandom[s_] := mutate[s]; **Search experiment** findFunctional[step_, max_] := Module[ {s = randomSeq[], t = 0}, While[t < max && !TrueQ[fitness[s] == 1], s = step[s]; t++; ]; t ]; trialsConstrained = Table[ findFunctional[stepConstrained, 1000], {50} ]; trialsRandom = Table[ findFunctional[stepRandom, 1000], {50} ]; **Visualization** Histogram[ {trialsRandom, trialsConstrained}, ChartLegends -> {"Random", "Constrained"}, PlotTheme -> "Scientific", Frame -> True ] **Interpretation** In many runs, the constrained dynamics reaches functional states faster — not because the system is explicitly guided toward a target, but because the structure of the space itself has changed. Even in this minimal model, a key effect emerges: Pure random mutation behaves like unstructured search Even a simple constraint dramatically reshapes accessibility The constraint does not “guide” the system toward solutions. Instead, it reshapes the space such that functional paths become possible in the first place. **Open Questions** This raises several structural questions: - How can we formally define a constraint operator in general systems? - Can constraint-induced subspaces be measured or classified? - How does connectivity emerge in high-dimensional spaces under constraints? - Do constrained systems exhibit characteristic spectral signatures (e.g., non-random eigenvalue statistics)? **Closing Thought** The difference between intractable search and effective evolution may not lie in time or randomness — but in the geometry of the accessible space itself. Maurice Crutzen 2026-04-07T09:31:01Z https://community.wolfram.com/groups/-/m/t/3672762 ![Artemis II trajectory: crewed lunar flyby to launch on April 1, 2026][1] &[Wolfram Notebook][2] [ORIGINAL GIF]: https://community.wolfram.com//c/portal/getImageAttachment?filename=10956ArtemisIItrajectorycrewedlunarflybytolaunchonApril1,2026.gif&userId=20103 [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4398testing2-optimize.gif&userId=20103 [2]: https://www.wolframcloud.com/obj/1f4c613a-e72e-487b-9b5a-c75613d8a099 Jeffrey Bryant 2026-03-31T21:27:57Z https://community.wolfram.com/groups/-/m/t/3671469 Please suggest the needful. \[Tau] = 9.2; \[Mu] = 3.5; \[Alpha] = 0.5; \[Gamma] = 0.5; m = 5; \[Omega] = 1; \[Tau]c = 3; \[Epsilon] = 0.1; \[Eta] = 0.4; \[CapitalOmega] = 0.1; a = 4/(9 \[Gamma] \[Mu] ) (\[Mu] Cos[\[Tau] + \[Omega] \[Epsilon] \[Tau]] + \[Mu] \[Alpha] - \[Eta]); Tmax = 300; ClearAll[f, ψ, t] f[ψ_, τc_] := 2 Ω + (m/ 2)*(-(m/a)*Sin[τc + ω ϵ τc]* Sin[ψ]* Sin[(τc + ω ϵ τc) - ψ] - (m/a)* Sin[τc + ω ϵ τc]*Sin[ψ]* Sin[(τc + ω ϵ τc) + ψ]); tauList = Range[0, 10, 0.05]; psiInit = 1; forwardData = Reap[Do[sol = NDSolve[{ψ'[t] == f[ψ[t], τ], ψ[0] == psiInit}, ψ, {t, 0, Tmax}, MaxSteps -> Infinity]; (*remove transient*) psiFinal = Mean[Table[ψ[t] /. sol[[1]], {t, Tmax - 50, Tmax, 1}]]; Sow[{τ, psiFinal}]; psiInit = psiFinal; (*continuation*), {τ, tauList}]][[2, 1]]; tauListBack = Reverse[tauList]; psiInit = 7; backwardData = Reap[Do[sol = NDSolve[{ψ'[t] == f[ψ[t], τ], ψ[0] == psiInit}, ψ, {t, 0, Tmax}, MaxSteps -> Infinity]; psiFinal = Mean[Table[ψ[t] /. sol[[1]], {t, Tmax - 50, Tmax, 1}]]; Sow[{τ, psiFinal}]; psiInit = psiFinal; (*continuation*), {τ, tauListBack}]][[ 2, 1]]; Show[ListLinePlot[forwardData, PlotStyle -> Red], ListLinePlot[backwardData, PlotStyle -> Black], AxesLabel -> {"τc", "ψ"}, PlotRange -> All] Dia Ghosh 2026-03-29T06:23:06Z https://community.wolfram.com/groups/-/m/t/3671124 ![Fireflies or nature's cellular automaton][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4420FirefliesorNature%27sCellularAutomaton.gif&userId=20103 [2]: https://www.wolframcloud.com/obj/abfab849-1504-446c-90d3-4a5b862ab440 Kirill Vasin 2026-03-27T18:14:17Z https://community.wolfram.com/groups/-/m/t/3669198 I have measured an exponential decay which is distorted by detection system. I measured the transfer function of the detection system in frequency domain. I performed convolution between real true exponential and transfer function and fit it with experimental data. I get good agreement for lower time constant but for high time constant, it is not working. What would be the possible regions? (I only measure the amplitude as a function of frequency for the transfer function. I write a complex function with some parameters and fit it's absolute value with experimental transfer function to get the complex transfer function back.) &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/dba7629b-be33-4b95-a3d4-6e9e3f34ac3d Rajesh Chell 2026-03-25T18:07:32Z https://community.wolfram.com/groups/-/m/t/3669378 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/4305abfa-92dd-4101-a33c-7261820c91d5 Housam Binous 2026-03-25T17:40:15Z https://community.wolfram.com/groups/-/m/t/3668292 Greeting. I am trying to replicate the results in the Table. 4 in this paper [https://scispace.com/pdf/a-semi-analytical-state-space-approach-for-3d-transient-4l4ftso81u.pdf][1], "A semi-analytical state-space approach for 3D transient analysis of functionally graded material cylindrical shells". ![enter image description here][2] However, my code still gives wrong results and is far from the exact ones. I'm not sure whether the problems are in the code itself or elsewhere. ClearAll["Global`*"] (*1. INPUT PARAMETERS (Table 1)*) l = 0.3048; (*Length in m*) Rm = 0.0762; (*Radius in m*) h = 0.000254; (*Total thickness in m*) a = Rm + h; (*Outer radius in m*) b = Rm; (*Inner radius in m*) (*Depth-to-length ratio*)(*Material Properties*) \[Mu] = 0.3; \[Rho] = 7860; (*Density in kg/m^3*) Emod = 200*10^9; (*E in N/m^2*) Gmod = Emod/(2*(1 + \[Mu])); \[Lambda] = (Emod*\[Mu])/((1 + \[Mu])*(1 - 2*\[Mu])); (*Stiffness coefficients for isotropic material*) C11 = \[Lambda] + 2*Gmod; C12 = \[Lambda]; C13 = \[Lambda]; C22 = C11; C23 = \[Lambda]; C33 = C11; C44 = Gmod; C55 = Gmod; C66 = Gmod; (*Normalization parameters*) c = Sqrt[C33/\[Rho]]; lr = 4; (*2. DQM WEIGHTING MATRICES (Chebyshev-Gauss-Lobatto)*) GetDQM[Npts_?NumericQ] := Module[{xi, A, B, P}, xi = Table[N[(1 - Cos[(i - 1) Pi/(Npts - 1)])/2], {i, 1, Npts}]; A = Table[0, {Npts}, {Npts}]; Do[P[i_] := Product[If[i == j, 1, xi[[i]] - xi[[j]]], {j, 1, Npts}]; Do[If[i != j, A[[i, j]] = P[i]/((xi[[i]] - xi[[j]])*P[j])], {j, 1, Npts}]; A[[i, i]] = -Sum[A[[i, j]], {j, 1, Npts}], {i, 1, Npts}]; B = A.A; {N[A], N[B]}]; division[ri_, ro_, W_?NumericQ] := Table[N[(ri/ro + ((2*m - 1)*(ro - ri))/(2*W*ro))], {m, 1, W}]; C11bar = C11/C33; C12bar = C12/C33; C13bar = C13/C33; C22bar = C22/C33; C23bar = C23/C33; C44bar = C44/C33; C55bar = C55/C33; C66bar = C66/C33; C33bar = 1; (*Eta parameters from Eq.(19)*) eta1 = C12bar/C11bar - 1; eta2 = C22bar - C12bar^2/C11bar; eta3 = C23bar - (C12bar*C13bar)/C11bar; eta4 = C13bar^2/C11bar - C33bar; eta5 = (C12bar*C13bar)/C11bar - (C23bar + C44bar); (*3. REDUCED STATE SPACE MATRIX (Appendix A.1)*) (*State vector:{u_1...u_N,sigma_2...sigma_N-1,v_2...v_N-1,tau_1...tau_\ N}*) GetM[Omega_, j_, q_, N_?NumericQ, W1_, W2_] := Module[{\[Rho]bar, R, dim, i2m, M}, dim = 6*(N); R = division[b, a, lr][[q]]; \[Rho]bar = 1; M = ConstantArray[0, {dim, dim}]; i2m = 1; (*Sub-indices for state vector segments*) sIdx = 0; urIdx = N; utIdx = 2*(N); uzIdx = 3*(N); trzIdx = 4*(N); trtIdx = 5*(N); (*Subscript[d\[Sigma], r]/dr*) Do[Do[M[[sIdx + k, sIdx + k]] = eta1/R*i2m, {k, 2, N - 1}]; Do[M[[sIdx + i, urIdx + k]] = -((a^2*C55bar)/l^2)*W1[[i, 1]]*W1[[1, k]] - ( a^2*C55bar)/l^2*W1[[i, N]]*W1[[N, k]], {k, 2, N - 1}]; M[[sIdx + i, urIdx + i]] += (\[Rho]bar*Omega^2 + eta2/R^2)*i2m; Do[M[[sIdx + k, utIdx + k]] = j*eta2/R^2*i2m, {k, 2, N - 1}]; Do[M[[sIdx + i, uzIdx + k]] = a*eta3/(l*R)*W1[[i, k]], {k, 2, N - 1}]; Do[M[[sIdx + i, trzIdx + k]] = -(a/l)*W1[[i, k]], {k, 2, N - 1}]; Do[M[[sIdx + i, trtIdx + i]] = -(j/R)*i2m, {k, 2, N - 1}];, {i, 2, N - 1}]; (*Subscript[du, r]/dr*) Do[Do[M[[urIdx + k, sIdx + k]] = 1/C11bar*i2m, {k, 2, N - 1}]; Do[M[[urIdx + i, urIdx + i]] = -(C12bar/(R*C11bar))*i2m, {k, 2, N - 1}]; Do[M[[urIdx + i, utIdx + i]] = -(j*C12bar/(R*C11bar))*i2m, {k, 2, N - 1}]; Do[M[[urIdx + i, uzIdx + k]] = -(a*C13bar/(l*C11bar))* W1[[i, k]], {k, 2, N - 1}];, {i, 2, N - 1}]; (*Subscript[du, \[Theta]]/dr*) Do[Do[M[[utIdx + i, urIdx + i]] = (j/R)*i2m, {k, 2, N - 1}]; Do[M[[utIdx + i, utIdx + i]] = (1/R)*i2m, {k, 2, N - 1}]; Do[M[[utIdx + i, trtIdx + i]] = (1/C66bar)*i2m, {k, 2, N - 1}];, {i, 2, N - 1}]; (*Subscript[du, z]/dr*) Do[Do[M[[uzIdx + i, urIdx + k]] = -(a/l)*W1[[i, k]], {k, 2, N - 1}]; Do[M[[uzIdx + i, trzIdx + i]] = (1/C55bar)*i2m, {k, 2, N - 1}];, {i, 2, N - 1}]; (*Subscript[d\[Tau], rz]/dr*) Do[Do[M[[trzIdx + i, sIdx + k]] = -(a*C13bar/(l*C11bar))* W1[[i, k]], {k, 2, N - 1}]; Do[M[[trzIdx + i, urIdx + k]] = -(a*eta3/(l*R))*W1[[i, k]], {k, 2, N - 1}]; Do[M[[trzIdx + i, utIdx + k]] = -(j*a/(l*R))*(eta3 + C44bar)* W1[[i, k]], {k, 2, N - 1}]; Do[M[[trzIdx + i, uzIdx + k]] = (a^2*eta4/(l^2))* W2[[i, k]] - (a^2*C13bar^2/(l^2*C11bar))*W1[[i, 1]]* W1[[1, k]] - (a^2*C13bar^2/(l^2*C11bar))*W1[[i, N]]* W1[[N, k]], {k, 2, N - 1}]; M[[trzIdx + i, urIdx + i]] += (\[Rho]bar*Omega^2 + j^2*C44bar/R^2)*i2m; Do[M[[trzIdx + i, trzIdx + i]] = -(1/R)*i2m, {k, 2, N - 1}];, {i, 2, N - 1}]; (*Subscript[d\[Tau], r\[Theta]]/dr*) Do[Do[M[[trtIdx + i, sIdx + i]] = (j*C12bar/(R*C11bar))*i2m, {k, 2, N - 1}]; Do[M[[trtIdx + i, urIdx + i]] = (j*eta2/R^2)*i2m, {k, 2, N - 1}]; Do[M[[trtIdx + i, utIdx + k]] = -(a^2*C44bar/l^2)*W2[[i, k]], {k, 2, N - 1}]; M[[trtIdx + i, utIdx + i]] += (\[Rho]bar*Omega^2 + j^2*eta2/R^2)* i2m; Do[M[[trtIdx + i, uzIdx + k]] = (a*j/(l*R))*(eta3 + C44bar)* W1[[i, k]], {k, 2, N - 1}]; Do[M[[trtIdx + i, trtIdx + i]] = -(2/R)*i2m, {k, 2, N - 1}];, {i, 2, N - 1}]; M]; (*4. FREQUENCY SOLVER*) GetFreq[Omega_?NumericQ, Npts_?NumericQ] := Module[{W1, W2, S, Mi, subt, ss}, {W1, W2} = GetDQM[Npts]; S = IdentityMatrix[6*Npts]; Do[Mi = GetM[Omega, 5, k, Npts, W1, W2]; S = MatrixExp[Mi*(h)/(lr*a)].S;, {k, 1, lr}]; (*Partition for traction-free surface:Subscript[\[Sigma], r]= Subscript[\[Tau], rz]=Subscript[\[Tau], r\[Theta]]=0*) rowIdx = Join[Range[2, Npts - 1], Range[4 (Npts) + 2, 5 Npts - 1], Range[5 Npts + 2, 6 Npts - 1]]; colIdx = Join[Range[Npts + 2, 2 Npts - 1], Range[2 Npts + 2, 3 Npts - 1], Range[3 Npts + 2, 4 Npts - 1]]; subt = S[[rowIdx, colIdx]]; ss = Det[subt]; ss]; (*5. OUTPUT RESULTS (N=15)*) GetFreq[0.045, 15,5] Nval = 15; fscale = (1/(2 Pi*a))*Sqrt[C33/\[Rho]] Do[guess = Range[500, 800, 10][[j]]/fscale; sol = w /. Last@FindMinimum[Log[Abs[GetFreq[w, Nval, j]]], {w, guess}]; Print["Frequency for j = ", j] Print["Mode ", j, ": ", (sol)*fscale, " Hz"];, {j, 1, 6}]; Results: 12183.46984 0.04103921187 During evaluation of In[48]:= Frequency for j = 1 During evaluation of In[48]:= Mode 1: -0.0002906076168 Hz During evaluation of In[48]:= FindMinimum::lstol: The line search decreased the step size to within the tolerance specified by AccuracyGoal and PrecisionGoal but was unable to find a sufficient decrease in the function. You may need more than MachinePrecision digits of working precision to meet these tolerances. During evaluation of In[48]:= Frequency for j = 2 During evaluation of In[48]:= Mode 2: 0.0002546168015 Hz During evaluation of In[48]:= Frequency for j = 3 During evaluation of In[48]:= Mode 3: -0.00004378307522 Hz During evaluation of In[48]:= Frequency for j = 4 During evaluation of In[48]:= Mode 4: 0.0001423820262 Hz During evaluation of In[48]:= Frequency for j = 5 During evaluation of In[48]:= Mode 5: 0.0002601605751 Hz During evaluation of In[48]:= Frequency for j = 6 During evaluation of In[48]:= Mode 6: 0.0000456248529 Hz During evaluation of In[79]:= FindRoot::lstol: The line search decreased the step size to within tolerance specified by AccuracyGoal and PrecisionGoal but was unable to find a sufficient decrease in the merit function. You may need more than MachinePrecision digits of working precision to meet these tolerances. During evaluation of In[79]:= Frequency for j = 5 During evaluation of In[79]:= Mode 1: 0.00007144391358 Hz During evaluation of In[79]:= FindRoot::lstol: The line search decreased the step size to within tolerance specified by AccuracyGoal and PrecisionGoal but was unable to find a sufficient decrease in the merit function. You may need more than MachinePrecision digits of working precision to meet these tolerances. During evaluation of In[79]:= Frequency for j = 5 During evaluation of In[79]:= Mode 2: -0.0001566304623 Hz How can this code generate more robust results that converge to the values in Table 4 of the paper in the link? Here are the relevant equations used in the code. ![enter image description here][3] **Eq. 20 is used besides Eqs.(22,23) for formulating the matrix H in Eq.33** ![enter image description here][4] **Matrix H is used in Eq.38 to obtain the transfer matrix T. Then, as we have a stress-free case as boundary conditions in the radial direction, Eq. 40 will be reduced into a 3X3 matrix, from which we obtain the roots after taking its determinant = 0.** ![enter image description here][5] ![enter image description here][6] **The elements of H matrix** [1]: https://scispace.com/pdf/a-semi-analytical-state-space-approach-for-3d-transient-4l4ftso81u.pdf [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1.JPG&userId=3668257 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2.png&userId=3668257 [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=3.png&userId=3668257 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4.png&userId=3668257 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=5.png&userId=3668257 Ahmad AlMamo 2026-03-23T16:34:11Z https://community.wolfram.com/groups/-/m/t/3666873 &[N1 Wolfram Notebook][1] ![I1 Video of Phase variation collisions and of paired electrons][2] &[N2 Wolfram Notebook][3] ![I2 Static and Moving Electron][4] &[N3 Wolfram Notebook][5] ![I3 Electron in Electric and Magnetic field][6] &[N4 Wolfram Notebook][7] ![I4 Electron repulsion and attraction][8] &[N5 Wolfram Notebook][9] ![I5 Static Electron][10] &[N6 Wolfram Notebook][11] ![I6 V and Spin configuration parameters][12] &[N7 Wolfram Notebook][13] ![I7 Center of mass position][14] &[N8 Wolfram Notebook][15] ![I80 Electron collisions][16] ![I81 Paired Electrons][17] ![I83 Paired electrons in fields][18] ![I84 High speed electron interaction][19] ![I85 deep electron interaction][20] &[N9 Wolfram Notebook][21] ![I9 Paired electron Forces][22] &[N10 Wolfram Notebook][23] ![I100 Video of Paired electrons in circle][24] ![I101 Paired electrons][25] &[N11 Wolfram Notebook][26] ![I110 Video of Phase variations collisions][27] ![I111 Phase variations collisions][28] ![I112 Phase variations collisions2][29] &[N12 Wolfram Notebook][30] [1]: https://www.wolframcloud.com/obj/c9e64b30-730c-4ac6-a39b-1c70a81e2468 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1_TwoGIFs.gif&userId=3338874 [3]: https://www.wolframcloud.com/obj/2755250f-1a0b-4a2f-a763-95742c6336aa [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2_Static_Moving_Electron.png&userId=3338874 [5]: https://www.wolframcloud.com/obj/28e72ecd-d1ae-4f83-8165-4e43438ae220 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=3_OscillatingElectricField_LarmorinUniformMagneticField.png&userId=3338874 [7]: https://www.wolframcloud.com/obj/616d38cc-8ade-474c-a5de-1326507d26d0 [8]: https://community.wolfram.com//c/portal/getImageAttachment?filename=4_ElectronRepulsion_PairedElectrons.png&userId=3338874 [9]: https://www.wolframcloud.com/obj/dee3c521-fd12-489a-9a5e-cd73950cfd39 [10]: https://community.wolfram.com//c/portal/getImageAttachment?filename=5_StaticElectron.png&userId=3338874 [11]: https://www.wolframcloud.com/obj/8fa5a7a4-d2dd-4534-967b-1491e624f312 [12]: https://community.wolfram.com//c/portal/getImageAttachment?filename=6_V_Spin_ConfigurationParameters.png&userId=3338874 [13]: https://www.wolframcloud.com/obj/61b5e877-b120-426f-b1b0-68a0fc8b2362 [14]: https://community.wolfram.com//c/portal/getImageAttachment?filename=7_CenterofMassPosition.png&userId=3338874 [15]: https://www.wolframcloud.com/obj/5ab8c4b3-d899-469a-9843-243590564f38 [16]: https://community.wolfram.com//c/portal/getImageAttachment?filename=80_ElectronCollisionDifferentAngles.png&userId=3338874 [17]: https://community.wolfram.com//c/portal/getImageAttachment?filename=81_PairedElectrons.png&userId=3338874 [18]: https://community.wolfram.com//c/portal/getImageAttachment?filename=83_PairedElectronsVariations2.png&userId=3338874 [19]: https://community.wolfram.com//c/portal/getImageAttachment?filename=84_HighSpeedInteraction.png&userId=3338874 [20]: https://community.wolfram.com//c/portal/getImageAttachment?filename=85_DeepInteraction.png&userId=3338874 [21]: https://www.wolframcloud.com/obj/e5a50e75-b212-43e1-b169-060edbcbf1de [22]: https://community.wolfram.com//c/portal/getImageAttachment?filename=9_PairedForces.png&userId=3338874 [23]: https://www.wolframcloud.com/obj/e7875851-802f-485e-8179-66b49c6c4b0f [24]: https://community.wolfram.com//c/portal/getImageAttachment?filename=100_Pairedelectronsincircle2.gif&userId=3338874 [25]: https://community.wolfram.com//c/portal/getImageAttachment?filename=101_PairedElectrons.png&userId=3338874 [26]: https://www.wolframcloud.com/obj/fb6548b6-237a-472a-a65c-1ae38825674f [27]: https://community.wolfram.com//c/portal/getImageAttachment?filename=110_PhaseVariations64.gif&userId=3338874 [28]: https://community.wolfram.com//c/portal/getImageAttachment?filename=111_PhaseSensitivity1.png&userId=3338874 [29]: https://community.wolfram.com//c/portal/getImageAttachment?filename=112_PhaseSensitivity2.png&userId=3338874 [30]: https://www.wolframcloud.com/obj/e6b64e77-cd82-412b-a2a5-8809195bf951 Juan Barandiaran 2026-03-20T11:33:42Z https://community.wolfram.com/groups/-/m/t/3660101 ![Gibbs Ensemble Monte Carlo simulations for fluid phase equilibria: experimental data and estimations][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=GibbsEnsembleMonteCarlosimulationsforfluidphaseequilibriaexperimentaldataandestimations.jpg&userId=20103 [2]: https://www.wolframcloud.com/obj/a1f60ec0-d9c9-487a-bdc9-9b3f487bc534 Michael Haring 2026-03-13T14:16:05Z https://community.wolfram.com/groups/-/m/t/3646989 ![Salvo Combat Modeling: Battle of Coronel][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=SalvocombatmodelingBattleofCoronel.png&userId=20103 [2]: https://www.wolframcloud.com/obj/3a7678cb-0540-4a1d-85d8-793ac90dbe65 Anton Antonov 2026-03-01T18:18:51Z https://community.wolfram.com/groups/-/m/t/3647724 ![SO(3) Gauge Theory for Classical Mechanics in UD][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=5904SO%283%29gaugetheoryforclassicalmechanicsinUD.gif&userId=20103 [2]: https://www.wolframcloud.com/obj/d2ea36cc-f66d-4bd4-ac0d-f75831617d79 Brian Beckman 2026-03-02T03:13:38Z https://community.wolfram.com/groups/-/m/t/3644908 **TL;DR** I'm looking for someone to refactor a Mathematica notebook I've got from a fellow researcher so I can use it as a reliable reference implementation. I expect it's a few hours of work for the right person. I can offer financial compensation and/or my own technical expertise. Hello Wolfram community! I hope this is the right place for this kind of request. If not, my apologies! I'm a PhD student in the final stage of my project, an attempt at closed-loop control of water jets from firefighting robots using UAV imagery as feedback. The controller design is based on the Smith predictor architecture, which requires a predictive model to compensate for the long dead time of the system. Accurately predicting the trajectory of water jets is far from trivial. One of the most promising models I could find is described in https://link.springer.com/article/10.1007/s10694-021-01175-1. The model is formulated as a system of ordinary differential equations. I tried implementing it in Python so I can integrate it with my other components. It's almost complete, but despite several months of debugging I haven't been able to resolve the remaining issues. So I contacted the corresponding author. They confirmed some errors I found in the printed versions of the equations, and kindly provided their original Mathematica implementation. This helped, but my own implementation is still incomplete. The issues could stem from additional errors in the printed equations I/we haven't found yet, mistakes in my implementation, or differences in solver behavior (Mathematica's vs. SciPy's solve_ivp() function). Unfortunately, the notebook is hard for me to follow and differs quite a bit from the published paper (structure, variable naming, angle conventions, etc.). I've never worked with Mathematica and don't have the time nor patience to properly learn it before my deadline. The author is currently unable to provide further support, but since I'm getting more and more desperate to finish this subproject, I'm now seeking third-party help. I'm looking for someone to refactor the notebook into a clean, well-structured reference implementation. Specifically, I'd like them to - remove unused and redundant code (many expressions are duplicated) - improve structure - improve documentation - add small quality-of-life improvements if appropriate - flag any noticeable discrepancies The refactored version must reproduce the original results, in particular the figures shown in the paper. Ideally, it should make it easy to experiment with the equations and parameters. One specific goal is to verify whether the rearranged equation forms I use in Python (to match SciPy's solver interface) produce the same results as the original formulation. If you're interested, I'll obtain the author's permission and share the notebook privately so you can assess the scope before we discuss compensation. Bonus points if you have experience with physics-based simulations and are open to occasional follow-up questions :) Many thanks and regards! Merlin Stampa 2026-02-24T20:34:23Z https://community.wolfram.com/groups/-/m/t/3642631 We've just added a new YouTube playlist featuring presentations from the [System Modeler User Conference][1]! This collection brings together all talks from industry experts as they dive into the intersection of Wolfram System Modeler, Modelica, and FMI-based workflows. Start watching now on the [Wolfram R&D YouTube channel][2]! [![enter image description here][3]][4] [1]: https://www.bigmarker.com/wolfram-u/wsm-user-conference-2026 [2]: https://www.youtube.com/playlist?list=PLdIcYTEZ4S8S8zS3xq7I063ClFJTelVMq [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=SystemModelerUserConference1.png&userId=1660606 [4]: https://www.youtube.com/playlist?list=PLdIcYTEZ4S8S8zS3xq7I063ClFJTelVMq Keren Garcia 2026-02-20T22:34:35Z https://community.wolfram.com/groups/-/m/t/3645288 ![The solvation entropy of different simulation models of the hydrated electron][1] ![enter image description here][2] &[Wolfram Notebook][3] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=HydratedElectron3.gif&userId=20103 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2493_1772117967979.jpg&userId=11733 [3]: https://www.wolframcloud.com/obj/e9c01359-55d2-4bcd-87f5-c12cd1c938ae Will Borrelli 2026-02-25T21:54:29Z https://community.wolfram.com/groups/-/m/t/3645383 How do you tackle complex systems without getting lost in the code? Join us for a live Q&A with Ankit Naik, author of Thinking in Systems, Not Code, a book born from years of practical experience with Modelica, system-level modeling, and systems thinking. Ankit will dive into the ideas behind the book, including how to understand complex, multi-domain systems through structure, feedback, and interactions – not just code. Bring your questions! Don't miss out! Whether you're interested in system modeling, Modelica or Wolfram System Modeler, or ways to apply systems thinking in real-world projects, this is your opportunity to engage directly with the author. Watch the livestream tomorrow, February 26th at 9 AM CST on the [Wolfram R&D YouTube channel][1]! ![enter image description here][2] > Order the book here: https://a.co/d/07FFxRUd [1]: https://youtube.com/live/vnDNQ4YzyeE [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=MasteringComplexsystems.jpg&userId=20103 Keren Garcia 2026-02-25T15:19:30Z https://community.wolfram.com/groups/-/m/t/3642086 ![Using Mathematica for finite elements for engineers][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=UsingFiniteElementstoAnalyseStructuresinMathematica.png&userId=20103 [2]: https://www.wolframcloud.com/obj/62b222bc-f5df-49eb-a619-782ee5ac2cd5 Malcolm Woodruff 2026-02-20T09:39:17Z