Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic
Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1973-2102, August 2026.ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
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Physics-informed neural networks with hybrid Kolmogorov-Arnold network and augmented Lagrangian function for solving partial differential equations. [PDF]
Sci RepZhang Z +5 more
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NMR in Biomedicine, Volume 39, Issue 8, August 2026.Basal energetics and phosphocreatine (PCr) recovery kinetics of the lower leg anterior compartment (primarily tibialis anterior; TA) were evaluated at rest and after dorsiflexion muscle contractions in ambulatory boys with Duchenne muscular dystrophy (DMD) and unaffected controls using 31P‐MRS.
Pratiksha P. Awale +5 more
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Cavity expansion theory with state-dependent mohr-coulomb model and its application to cone penetration tests. [PDF]
PLoS OneLi B +5 more
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ChemSusChem, Volume 19, Issue 13, 14 July 2026.Silicon application as a support for Pd Nanoparticle catalysts in Heck–Cassar cross‐coupling under continuous flow. Electronic waste and end‐of‐life photovoltaic modules are positioning silicon as a high‐value material that will increasingly enter the waste stream in the coming years.
Tian Sang +6 more
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AI in chemical engineering: From promise to practice
AIChE Journal, Volume 72, Issue 7, July 2026.Abstract Artificial intelligence (AI) in chemical engineering has moved from promise to practice: physics‐aware (gray‐box) models are gaining traction, reinforcement learning complements model predictive control (MPC), and generative AI powers documentation, digitization, and safety workflows.
Jia Wei Chew +4 more
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Parabolic PDEs with Dynamic Data under a Bounded Slope Condition. [PDF]
Arch Ration Mech AnalBögelein V, Duzaar F, Treu G.
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Existence of Full Replica Symmetry Breaking for the Sherrington–Kirkpatrick Model at Low Temperature
Communications on Pure and Applied Mathematics, Volume 79, Issue 7, Page 1746-1770, July 2026.ABSTRACT We verify the existence of full replica symmetry breaking (FRSB) for the Sherrington–Kirkpatrick (SK) model and determine the structure of its Parisi measure slightly beyond the high temperature regime. More specifically, we prove that the support of the Parisi measure for the SK model consists of an interval starting at the origin slightly ...
Yuxin Zhou
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Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networks. [PDF]
Proc Natl Acad Sci U S AGao ML, Williams JP, Kutz JN.
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Local Polynomial Regression and Filtering for a Versatile Mesh‐Free PDE Solver
International Journal for Numerical Methods in Fluids, Volume 98, Issue 7, Page 804-839, July 2026.A high‐order, mesh‐free finite difference method for solving differential equations is presented. Both derivative approximation and scheme stabilisation is carried out by parametric or non‐parametric local polynomial regression, making the resulting numerical method accurate, simple and versatile. Numerous numerical benchmark tests are investigated for
Alberto M. Gambaruto
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