https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions tagged with Physics sorted by new. https://community.wolfram.com/groups/-/m/t/3685762 ![NISQ-compatible quantum cryptography based on Parrondo dynamics in discrete-time quantum walks][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=NISQ-compatiblequantumcryptographybasedonParrondodynamicsindiscrete-timequan.jpg&userId=20103 [2]: https://www.wolframcloud.com/obj/9df2f82a-8c8d-42cd-a106-dfa8e0004fe2 Colin Benjamin 2026-04-13T15:56:42Z https://community.wolfram.com/groups/-/m/t/3682254 ![enter image description here][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=8239hero.png&userId=20103 [2]: https://www.wolframcloud.com/obj/27b9cbf2-47f5-4888-81b8-aa014c78b0c6 Myrto Terpsiadou 2026-04-11T13:27:03Z https://community.wolfram.com/groups/-/m/t/3681468 ![Atomic-scale stick-slip through a point defect][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Atomic-scalestick-slipthroughapointdefect.png&userId=20103 [2]: https://www.wolframcloud.com/obj/34d3352e-a7a1-41b4-be41-b4ebe4ca62dd Enrico Gnecco 2026-04-10T17:00:36Z https://community.wolfram.com/groups/-/m/t/3674654 ![Neural excitability, sparsity & the bridge to AI][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=5237hero.png&userId=20103 [2]: https://www.wolframcloud.com/obj/9dd8b8b7-ab62-4227-90c8-7b74b24ce525 Guhan Thiagarajan 2026-04-06T04:54:16Z https://community.wolfram.com/groups/-/m/t/3674011 The Genetic Code as Geometry on Q_6: Hidden Mathematical Structure in the Codon Hypercube S.H. Bachani, Merlin Digital, Dubai, UAE April 2026 **Abstract** This computational exploration demonstrates how the 64 genetic codons, naturally embedded on a 6-dimensional hypercube (Q_6), reveal unexpected physical structure when annotated with ab initio quantum chemistry data. By analyzing the graph Laplacian of formation and solvation energies, we show that clinical pathogenicity in genetic mutations can be predicted from first principles without machine learning. 1. The Codon Hypercube Every codon consists of three nucleotide positions drawn from \{U, C, A, G\}. By encoding these as 2-bit values (U=00, C=01, A=10, G=11), each codon becomes a 6-bit binary string. Consequently, the 64 codons naturally occupy the vertices of Q_6, the 6-dimensional hypercube. (* Nucleotide encoding *) [span_7](start_span)nucBits = <|"U" -> 0, "C" -> 1, "A" -> 2, "G" -> 3|>;[span_7](end_span) [span_8](start_span)nucFromBits = <|0 -> "U", 1 -> "C", 2 -> "A", 3 -> "G"|>;[span_8](end_span) (* Codon to Q6 vertex *) codonToVertex[codon_String] := nucBits[StringTake[codon, {1}]] * 16 + nucBits[StringTake[codon, {2}]] * 4 + [span_9](start_span)nucBits[StringTake[codon, {3}]];[span_9](end_span) (* Q6 vertex to codon *) vertexToCodon[s_Integer] := nucFromBits[BitAnd[BitShiftRight[s, 4], 3]] <> nucFromBits[BitAnd[BitShiftRight[s, 2], 3]] <> [span_10](start_span)nucFromBits[BitAnd[s, 3]];[span_10](end_span) (* Construct Q6 *) [span_11](start_span)Q6 = HypercubeGraph[6];[span_11](end_span) Q_6 has 64 vertices and 192 edges. Each edge connects codons that differ by a single-bit mutation—representing the minimal change at one nucleotide position. 2. Formation Energies and Curvature Using standard HF/6-31G* values, we place formation energies (V_{ef}) at each vertex. The 64 codons partition into exactly 21 energy classes (20 amino acids + 1 stop signal). To measure how a codon's energy differs from its mutational neighborhood, we use the discrete Laplacian: High magnitude |\nabla^2 V| indicates a codon sits at a "peak" or "valley" where mutations cause large physicochemical shifts. Low |\nabla^2 V| indicates an energy "plateau" where mutations are tolerated. 3. Predicting Mutation Pathogenicity Analysis of 203,156 ClinVar variants reveals that the geometry of Q_6 predicts clinical outcomes: * Mean |\nabla^2 V| for Pathogenic variants: 90.7 * Mean |\nabla^2 V| for Benign variants: 40.1 Pathogenic mutations originate preferentially from high-curvature positions on the hypercube. This physical metric is orthogonal to existing tools like AlphaMissense, capturing a different physical dimension of vulnerability. 4. Solvation and Multi-Landscape Analysis A second landscape—solvation free energy (\Delta G_{solv})—reproduces experimental hydrophobicity (\rho = 0.810) without empirical fitting. The Laplacians of these two fields (\nabla^2 V_{ef} and \nabla^2 V_{solv}) are nearly independent (\rho = 0.167), representing distinct axes of "product disruption" and "folding disruption". 5. Questions for the Community * Is the genetic code a ground state? Does the standard code minimize the "frustration" (sum of energy differences across edges) compared to random reassignments on Q_6? * Why Q_6? Is there a geometric constraint that makes 6-dimensional space optimal for encoding 21 energy classes? * Quantum Hardware: This structure maps to a 6-qubit register, currently used in topologically-constrained quantum lattice architectures (US Patent 64/027,290). References * [1] Bachani, S.H. (2026). Computational framework for genomic analysis using hexagramic principles. Int. J. Phys. * [2] US Patent Application 64/027,290 (April 3, 2026). * [3] Wolfram, S. (2025). What's Special about Life? Suhail Bachani 2026-04-03T22:12:16Z 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/3673723 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/c4a1ef8d-8d48-4bf8-abe0-0eac4501058d Tigran Nersissian 2026-04-03T02:25:29Z https://community.wolfram.com/groups/-/m/t/3673820 I’m having some startup difficulty with the first example in Guide to Modern Physics (James W. Rohlf). The book has all the right topics but I cannot enter the examples successfully. I am running Mathematica 14.3 on a Mac Book Pro with M5 Pro, OS Tahoe and 24 GB of memory. The file myFile.nb shows what I typed. Notice that the N[UnitConvert[e, C],4] does not give the expected answer. I am not sure what to type for e. If I use the Basic Math Paclet, e is that transcendental number, not the ElementaryCharge definition. I can get the correct answer with a copy/paste from the original Quantity definition. But notice that I copied 1 C, not just C. Quantity["ElementaryCharge"] returns e Quantity["Coulambs"] returns 1 C N[UnitConvert[e,C] returns UnitConvert[e,1 C],4] N[UnitConvert[e,1 C],4] returns 1.602 x 10-19 Then I went on Rohlf’s site and bought the files that contain the example Mathmatica code. They were not what I expected. It was just the code without any further explanation. I want to be able to type the code in, not use copy/paste.But if I copy/paste the code from this file, it works fine. And yes, the e is in italic, indicating it is the definition of ElementaryCharge. I don’t know how to input that number. Because I bought the file from Rohlf, I don't think it is appropriate to include it. I may be breaking some copyright rule by posting a file that I bought in a forum. When I copy/paste I get N[UnitConvert[e,C],4] returns 1.602 x 10-19 I can also get the example to work by explicitly using Quantity to define ElementaryCharge and Coulambs, but that’s not what th example does. N[UnitConvert[Quantity["ElementaryCharge"],Quantity["Coulombs"]],4 returns 1.602 x 10-19 So I don't know how to run this example the way that the book does. This is just the first example and I fear I may experience the same problem with the others. What am I doing wrong? Theodore Kubaska 2026-04-03T02:09:35Z https://community.wolfram.com/groups/-/m/t/3672541 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/7c20d0a3-0451-4f2c-95b5-d4014f395ab4 Rudnei Ramos 2026-03-31T17:01:30Z https://community.wolfram.com/groups/-/m/t/3672532 ![Adiabatic quantum computing: spectral analysis and simulation of a one-qubit system][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Adiabaticquantumcomputingspectralanalysisandsimulationofaone-qubitsystem.png&userId=20103 [2]: https://www.wolframcloud.com/obj/57c27ccc-c9d9-456a-8535-b7e58d5abb07 Sebastian Rodriguez 2026-03-31T17:00:25Z https://community.wolfram.com/groups/-/m/t/3671922 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/53dcf037-fe9d-4e60-a6b9-aaf92a854da6 Brian Beckman 2026-03-30T15:51:29Z https://community.wolfram.com/groups/-/m/t/3672004 ![Continuous recovery of phase from single interferogram][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Continuousrecoveryofphasefromsingleinterferogram.png&userId=20103 [2]: https://www.wolframcloud.com/obj/0a308f66-8cbd-46e9-9aeb-61b1ddd4f2fa Slava Berejnov 2026-03-30T13:21:39Z 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/3670916 I am an accountant who saw the zero-sum of gravity and mass as an apparent ledger, and applied a double-entry architecture to the Bekenstein Bound. If mass and gravity cancel each other out, then mass cannot be a primary property, it must be a debit. This framework proposes that Mass is equal to: Informational Capacity (a distinct category) * Load (a separate distinct category, hence, do not algebraically cancel the ln3 operators) * The Dilution Factor. This notebook demonstrates a scaling identity that perfectly derives the Earth's compactness ratio while mathematically resolving the I=0 singularity. You will also see another macro and 2 micro proofs. It believe it also offers solutions to: The Vacuum Catastrophe Matter-Antimatter Asymmetry Micro/Macro Unification The Neutron Star Mass Gap I am seeking feedback on the Trinary stabilizer and its implications for the Cosmological Constant Problem. &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/b12b05f1-52a2-49e9-a8d4-2cf130ab5030 Keithen Hamilton 2026-03-26T23:26:15Z 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/3666521 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/f11d23b7-da4b-4d24-b10f-dc65abfedc9c Bruno Tenorio 2026-03-20T01:11:50Z https://community.wolfram.com/groups/-/m/t/3666356 ![Transmon cQED: Wolfram x Qolab collaboration][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=TransmoncQEDWolframxQolabcollaboration.png&userId=20103 [2]: https://www.wolframcloud.com/obj/b9ec38cb-ced0-4358-9444-86fda1bf6c37 Mohammad Bahrami 2026-03-19T17:52:37Z https://community.wolfram.com/groups/-/m/t/3665192 ![Efficient Trotter-Suzuki schemes for long-time quantum dynamics][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=EfficientTrotter-Suzukischemesforlong-timequantumdynamics.jpg&userId=20103 [2]: https://www.wolframcloud.com/obj/212ddd07-dfd3-4721-be9f-c529773c40fe Marko Maležič 2026-03-17T17:10:08Z https://community.wolfram.com/groups/-/m/t/3663446 ![The Ruliad concept: some ideas and observations][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=TheRuliadconceptsomeideasandexamples.png&userId=20103 [2]: https://www.wolframcloud.com/obj/db1cd65f-d494-49cb-8414-bcaed8b4ffef Denis Ivanov 2026-03-17T04:57:25Z https://community.wolfram.com/groups/-/m/t/3663240 ![Neural network prediction of the Hubble space telescope semimajor axis][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=NeuralnetworkpredictionoftheHubblespacetelescopesemimajoraxis.png&userId=20103 [2]: https://www.wolframcloud.com/obj/3123cb4a-98ab-4f56-87e9-c3cc99f58051 Akram Masoud 2026-03-16T17:55:03Z