https://community.wolfram.com RSS Feed for Wolfram Community showing ideas tagged with Material Sciences sorted by active. https://community.wolfram.com/groups/-/m/t/3638297 ![Simulating Plastic Polymer Degradation][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=7682image.png&userId=911151 [2]: https://www.wolframcloud.com/obj/cde0818d-a5d1-40b6-88d8-a26734298c8f Wolfram Education Programs 2026-02-11T16:24:46Z https://community.wolfram.com/groups/-/m/t/3528683 ![Hyperbolic spin liquids][1] ![Hyperbolic spin liquids][2] &[Wolfram Notebook][3] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=hyperbolic_spin_liquids-optimize.gif&userId=20103 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2653Main11082025.png&userId=20103 [3]: https://www.wolframcloud.com/obj/d5789705-fc5d-4d54-85b7-d4517cf44a61 Patrick M. Lenggenhager 2025-08-11T15:17:47Z https://community.wolfram.com/groups/-/m/t/3631500 ![Intrinsic and tunable superconducting diode effect in quantum spin hall systems][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=IntrinsicandTunableSuperconductingDiodeEffectinQuantumSpinHallSystems.png&userId=20103 [2]: https://www.wolframcloud.com/obj/d6918ac4-8260-4f85-aff7-814a79b808dd Samuele Fracassi 2026-01-30T17:06:12Z https://community.wolfram.com/groups/-/m/t/3586246 ![Site-Decorated Model for Unconventional Frustrated Magnets: Ultranarrow Phase Crossover and Spin Reversal Transition][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Image20251205201239.jpg&userId=20103 [2]: https://www.wolframcloud.com/obj/e5fceeef-338f-4e54-83e4-1d5ccfc44cac Weiguo Yin 2025-12-05T16:49:31Z https://community.wolfram.com/groups/-/m/t/3558674 ![Understanding the 2025 Nobel Prize in physics through the eyes of an engineer][1] This year, the Nobel Prize in Physics was awarded to John Clarke, Michel H. Devoret, and John M. Martinis > "for the discovery of macroscopic quantum mechanical tunnelling and energy quantisation in an electric circuit". [nobelprize.org/prizes/physics/2025/summary][2] When I first read the citation, the only words that resonated with me were "electric circuits." As an engineer, that was something familiar—but macroscopic quantum tunnelling? That sounded mysterious. So, I decided to explore what it really means—by modeling it, simulating it, and connecting it back to engineering intuition. ---------- Some background... ================== From Classical Mechanics to Quantum Tunnelling ---------------------------------------------- When you throw a ball at a wall, it bounces back. It never appears on the other side. But at the atomic scale, particles can tunnel through barriers they shouldn't be able to cross. This is what made quantum mechanics famous for being bizarre yet real. ![enter image description here][3] The Schrödinger equation (1926) predicts this behavior— the particle's wavefunction "leaks" into forbidden regions, giving a finite probability of finding it beyond the barrier. Early Applications: Radioactive Decay and Fusion ------------------------------------------------ Quantum tunnelling first explained alpha decay—how alpha particles escape the nucleus. It also revealed why decay is probabilistic: the rate depends on the barrier height and thickness. As summarized by the Nobel committee: > "Tunnelling is also necessary for fusion to occur in our Sun, where the temperature and pressure are too low to classically allow two protons to overcome Coulomb repulsion and form a helium nucleus." From Atoms to Superconductors ----------------------------- In the 1950s, Bardeen, Cooper, and Schrieffer formulated the BCS theory of superconductivity (Nobel 1972). They showed that electrons can pair up into Cooper pairs, forming a collective quantum state that moves without resistance—a superfluid of electrons. It's like fluid flow with zero viscosity: perfectly lossless. The Josephson Prediction (1962) ------------------------------- Brian Josephson, then a graduate student, predicted that Cooper pairs could tunnel across a thin insulating barrier between two superconductors—even with no voltage applied. This means a supercurrent can flow purely due to phase difference between superconductors despite being separated by an insulating barrier. ![enter image description here][4] The effect was confirmed experimentally in 1963 and led to SQUIDs (Superconducting Quantum Interference Devices), used for ultra-precise magnetic sensing. That theoretical leap—showing that quantum tunnelling can appear in an ordinary-looking circuit—laid the groundwork for this year's Nobel Prize. ---------- Modeling & Simulation ===================== The Current-Biased Josephson Junction ------------------------------------- A Josephson junction is a simple device: two superconductors separated by an insulating barrier. ![enter image description here][5] Equation (1) is called the first Josephson relation or weak-link current-phase relation, and equation (2) is called the second Josephson relation or superconducting phase evolution equation. In circuit terms, it behaves like a nonlinear inductor with some capacitance and damping resistance. ![enter image description here][6] On left you see the schematics of the Josephson junction and on the right is a model in Wolfram System Modeler (a Modelica language based tool). You can read more about the equations involved by reading the following paper (especially the section on "The current-biased Josephson junction") https://www.nobelprize.org/uploads/2025/10/advanced-physicsprize2025.pdf To understand the characteristics of the Josephson junction, we have connected it to a current source that produces the bias current. ![enter image description here][7] Understanding Key Characteristics --------------------------------- A Josephson junction is characterized by a parameter called critical current. Let's observe the behavior for three different bias currents. - Bias current < Critical current ![enter image description here][8] The phase "particle" sits in a well: The voltage drop across the junction settles to around 0 and the energy potential is constant. - Bias current > Critical current ![enter image description here][9] The particle rolls downhill: The junction is in a resistive state, represented by the non-zero voltage drop across the junction. The energy potential continuously decreases. - Bias current is around the Critical current ![enter image description here][10] Occasional escapes from wells (Quantum tunnelling regime): The junction is usually superconducting (voltage drop around 0), but occasionally becomes resistive, and the energy potential drops. The occasional escapes can be thermally activated. Understanding Energy Landscape—The Tilted Washboard --------------------------------------------------- One of the interesting characteristics to observe in this model the potential energy stored in the junction. ![enter image description here][11] - Bias current > Critical current ![enter image description here][12] - Bias current is around the Critical current ![enter image description here][13] Visually, the potential looks like a washboard potential. Let's compare it with the figure presented in the Nobel Committee report: ![enter image description here][14] At zero temperature, a classical particle would stay forever in one well, but a quantum system can tunnel out, leading to macroscopic quantum tunnelling (MQT)—the phenomenon recognized by this year's Nobel Prize. Advantages of Lumped Modeling ----------------------------- The modeling that I showed above is a lumped model. Lumped-element modeling enables engineers to represent quantum circuits—comprising Josephson junctions, capacitors, and inductors—as networks of nonlinear circuit elements that obey the same physical laws as classical RLC systems. By formulating these as differential equations (e.g., RCSJ model), one can simulate the voltage, current, and phase dynamics to predict energy levels and coupling between qubits. This approach enables intuitive circuit-level design and parameter tuning before moving to full quantum or electromagnetic simulations. ---------- From Models to Modern Technology -------------------------------- These equations underpin a vast range of modern technologies: - Quantum computers—Superconducting qubits (transmon, flux, phase qubits) use Josephson junctions as tunable nonlinear inductors. - SQUID magnetometers—Detect magnetic fields down to femtotesla levels. - Quantum amplifiers—Low-noise amplifiers for qubit readout and deep-space communications. - Voltage standards—Arrays of Josephson junctions define the volt via the Josephson constant. The same "washboard" dynamics that I simulated in System Modeler are what experimentalists fine-tune at milli-Kelvin temperatures to design qubits and sensors. ---------- Chronology of Key Discoveries ----------------------------- - 1933: Erwin Schrödinger: Quantum wave equation; tunnelling concept - 1957—1972: Bardeen, Cooper, Schrieffer: BCS theory: superconductivity & Cooper pairs - 1962—1973: Brian Josephson, Esaki, Giaever: Quantum tunnelling in superconductors - 1980s—1990s: John Clarke, Michel Devoret: Observation of macroscopic quantum tunnelling - 2000s—2020s: John Martinis & teams: Superconducting qubits and quantum circuits - 2025: Clarke, Devoret, Martinis: Quantised energy levels in circuits ---------- Further Reading --------------- Scientific background from the Nobel Committee: https://www.nobelprize.org/prizes/physics/2025/advanced-information/ [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=1759937945354.png&userId=1522613 [2]: https://www.nobelprize.org/prizes/physics/2025/summary/ [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-10-08170931.png&userId=1522613 [4]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-10-08171703.png&userId=1522613 [5]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-10-08180104.png&userId=1522613 [6]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-10-08161618.png&userId=1522613 [7]: https://community.wolfram.com//c/portal/getImageAttachment?filename=.png&userId=1522613 [8]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-10-08134345.png&userId=1522613 [9]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-10-08134419.png&userId=1522613 [10]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-10-08134442.png&userId=1522613 [11]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-10-08180309.png&userId=1522613 [12]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-10-08134757.png&userId=1522613 [13]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-10-08135150.png&userId=1522613 [14]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-10-08125827.png&userId=1522613 Ankit Naik 2025-10-09T07:56:51Z https://community.wolfram.com/groups/-/m/t/3523218 ![Getting started with hyperuniformity in condensed matter with Wolfram dynamic interactivity tools][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Main01082025.png&userId=20103 [2]: https://www.wolframcloud.com/obj/fbdd606b-a31f-4471-9ceb-0894ff6c44e6 Jessica Alfonsi 2025-08-01T18:48:46Z https://community.wolfram.com/groups/-/m/t/3530595 ![Phase switch driven by the hidden half-ice, half-fire state in a ferrimagnet][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=model_zero-T-phase-diagram.png&userId=20103 [2]: https://www.wolframcloud.com/obj/55563d71-159c-40a1-bc8f-229f4bde89f1 Weiguo Yin 2025-08-14T19:49:49Z https://community.wolfram.com/groups/-/m/t/3528022 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/a12cdc4d-8580-4da4-8608-0d8979ee07f2 Matthew Kafker 2025-08-10T21:32:41Z https://community.wolfram.com/groups/-/m/t/3501343 ![Interlocked: computational chainmail engineering][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2025-07-10at4.03.37%E2%80%AFPM.png&userId=3489769 [2]: https://www.wolframcloud.com/obj/05eb3d4b-bac8-468c-be6f-952fb37a1284 Rakhi Jain 2025-07-10T20:08:50Z https://community.wolfram.com/groups/-/m/t/3432114 ![Adsorption of ions from aqueous solutions by ferroelectric nanoparticles. Electric polarization.][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=8218Main25032025.png&userId=20103 [2]: https://www.wolframcloud.com/obj/fc7b6689-75c6-4cf4-bb10-606896072ed7 Anna Morozovska 2025-03-25T14:50:40Z https://community.wolfram.com/groups/-/m/t/3413942 ![Geometry and mechanics of non-Euclidean curved-crease origami. Nontrivial Gaussian curvature, Euler's buckling behavior.][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Main10032025.png&userId=20103 [2]: https://www.wolframcloud.com/obj/0a28694f-4a5f-4b8a-b1e9-37b9e74706de Fan Feng 2025-03-10T15:04:39Z https://community.wolfram.com/groups/-/m/t/3412145 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/920faadc-7575-4770-ad24-ca2e104b5cea Redad Mehdi 2025-03-07T19:50:54Z https://community.wolfram.com/groups/-/m/t/3398827 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/0aa03a8f-199e-4b82-ae83-21d5dbcb2212 Gay Wilson 2025-02-21T19:13:50Z https://community.wolfram.com/groups/-/m/t/3314703 ![FEM modeling for plasticity in solid mechanics][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Main04112024.png&userId=20103 [2]: https://www.wolframcloud.com/obj/7948203d-4074-4a57-96ae-f348d59d71c3 Alessandro Mastrofini 2024-11-04T21:03:36Z https://community.wolfram.com/groups/-/m/t/3330805 ![Mean-field elastic moduli of a three-dimensional, cell-based vertex model][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Main29112024.png&userId=20103 [2]: https://www.wolframcloud.com/obj/72ae5209-647a-4179-a9e6-f276e4e553f1 Kyung Eun Kim 2024-11-29T20:06:58Z https://community.wolfram.com/groups/-/m/t/3327833 ![Magnetochiral Charge Pumping due to Charge Trapping and Skin Effects in Chirality-Induced Spin Selectivity][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Figure2-S6.jpg&userId=2610276 [2]: https://www.wolframcloud.com/obj/cc809489-220b-4b2d-aa10-6f2d0d8de1cf Kai Zhang 2024-11-24T16:40:45Z https://community.wolfram.com/groups/-/m/t/3210091 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/158c2618-22ea-4c32-aada-f997d1d9cbdf Xuelian Liu 2024-07-10T02:19:19Z https://community.wolfram.com/groups/-/m/t/3288963 ![enter image description here][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Main01102024.png&userId=20103 [2]: https://www.wolframcloud.com/obj/7f959940-163f-40c4-a122-e86781741ed1 Kaijie Yang 2024-10-01T15:33:12Z https://community.wolfram.com/groups/-/m/t/3273116 ![Lagrangian approach to origami vertex analysis: kinematics][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2244MainImage.png&userId=20103 [2]: https://www.wolframcloud.com/obj/f9705140-8d5e-4a36-aa1f-3341e4664f66 Matthew Grasinger 2024-09-12T18:44:04Z https://community.wolfram.com/groups/-/m/t/3180725 ![The monoclinic map T of Eq. (57) together with two XISO-approximations B and K to T. The elastic map B is the XISO-approximation whose regular axis coincides with the 2-fold axis k of T.][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=9999Lead.png&userId=20103 [2]: https://www.wolframcloud.com/obj/d90e95c4-a979-461f-bce5-d4ce5dc6ad3b Carl Tape 2024-05-22T19:22:05Z