Results 21 to 30 of about 1,157 (82)

Efficient Dynamics: Reduced‐Order Modeling of the Time‐Dependent Schrödinger Equation

Advanced Physics Research, Volume 5, Issue 2, February 2026.
Reduced‐order modeling (ROM) approaches for the time‐dependent Schrödinger equation are investigated, highlighting their ability to simulate quantum dynamics efficiently. Proper Orthogonal Decomposition, Dynamic Mode Decomposition, and Reduced Basis Methods are compared across canonical systems and extended to higher dimensions.
Kolade M. Owolabi
wiley   +1 more source

Differential equations and conformal structures

, 2006
We provide five examples of conformal geometries which are naturally associated with ordinary differential equations (ODEs). The first example describes a one-to-one correspondence between the Wuenschmann class of 3rd order ODEs considered modulo contact
Cartan, Cartan, Cartan, Cartan, Chern, Dunajski, Fefferman, Fefferman, Fritelli, Fritelli, Fritelli, Hilbert, Kobayashi, Newman, Newman, Nurowski, Olver, Paweł Nurowski, Penrose, Penrose, Petrov, Tod, Wuenschmann   +22 more
core   +1 more source

Inverse Design in Nanophotonics via Representation Learning

Advanced Optical Materials, Volume 14, Issue 1, 9 January 2026.
This review frames machine learning (ML) in nanophotonics through a classification based on where ML is applied. We categorize methods as either output‐side, which create differentiable surrogates for solving Maxwell's partial differential equations (PDEs), or input‐side, which learn compact representations of device geometry.
Reza Marzban, Ali Adibi, Raphaël Pestourie   +2 more
wiley   +1 more source

Trisecting non-Lagrangian theories [PDF]

, 2017
We propose a way to define and compute invariants of general smooth 4-manifolds based on topological twists of non-Lagrangian 4d N=2 and N=3 theories in which the problem is reduced to a fairly standard computation in topological A-model, albeit with ...
Gukov, Sergei
core   +4 more sources

Incremental Model Order Reduction of Smoothed‐Particle Hydrodynamic Simulations

International Journal for Numerical Methods in Fluids, Volume 97, Issue 12, Page 1571-1594, December 2025.
The paper presents the development of an incremental singular value decomposition strategy for compressing time‐dependent particle simulation results, addressing gaps in the data matrices caused by temporally inactive particles. The approach reduces memory requirements by about 90%, increases the computational effort by about 10%, and preserves the ...
Eduardo Di Costanzo, Niklas Kühl, Jean‐Christophe Marongiu, Thomas Rung   +3 more
wiley   +1 more source

Higher‐Order, Mixed‐Hybrid Finite Elements for Kirchhoff–Love Shells

International Journal for Numerical Methods in Engineering, Volume 126, Issue 21, 15 November 2025.
ABSTRACT A novel mixed‐hybrid method for Kirchhoff–Love shells is proposed that enables the use of classical, possibly higher‐order Lagrange elements in numerical analyses. In contrast to purely displacement‐based formulations that require higher continuity of shape functions as in isogeometric analysis (IGA), the mixed formulation features ...
Jonas Neumeyer, Michael Wolfgang Kaiser, Thomas‐Peter Fries   +2 more
wiley   +1 more source

Integrable equations of the dispersionless Hirota type and hypersurfaces in the Lagrangian Grassmannian [PDF]

, 2007
We investigate integrable second order equations of the form F(u_{xx}, u_{xy}, u_{yy}, u_{xt}, u_{yt}, u_{tt})=0. Familiar examples include the Boyer-Finley equation, the potential form of the dispersionless Kadomtsev-Petviashvili equation, the ...
Ferapontov, E. V., Hadjikos, L., Khusnutdinova, K. R.   +2 more
core   +1 more source

Machine‐learning‐assisted photonic device development: a multiscale approach from theory to characterization

Nanophotonics, Volume 14, Issue 23, Page 3761-3793, 02 November 2025.
Abstract Photonic device development (PDD) has achieved remarkable success in designing and implementing new devices for controlling light across various wavelengths, scales, and applications, including telecommunications, imaging, sensing, and quantum information processing.
Yuheng Chen, Alexander Montes McNeil, Taehyuk Park, Blake A. Wilson, Vaishnavi Iyer, Michael Bezick, Jae‐Ik Choi, Rohan Ojha, Pravin Mahendran, Daksh Kumar Singh, Geetika Chitturi, Peigang Chen, Trang Do, Alexander V. Kildishev, Vladimir M. Shalaev, Michael Moebius, Wenshan Cai, Yongmin Liu, Alexandra Boltasseva   +18 more
wiley   +1 more source

Continuous symmetry reduction and return maps for high-dimensional flows

, 2010
We present two continuous symmetry reduction methods for reducing high-dimensional dissipative flows to local return maps. In the Hilbert polynomial basis approach, the equivariant dynamics is rewritten in terms of invariant coordinates. In the method of
Anosov, Arnol’d, Bakasov, Barkley, Beyn, Biktashev, Bredon, Broucke, Cartan, Chenciner, Chenciner, Chenciner, Chossat, Christiansen, Cushman, Cvitanović, Cvitanović, Cvitanović, Cvitanović, Evangelos Siminos, Faisst, Fels, Fels, Fiedler, Fiedler, Field, Fowler, Gatermann, Gibbon, Gibson, Gilmore, Gilmore, Golubitsky, Guillemin, Haller, Hof, Hoyle, Huygens, Kawahara, Kirwan, Krupa, Lan, Lan, Letellier, Lorenz, Malige, Marsden, Marsden, Mielke, Mostow, Ning, Ning, Ning, Ning, Olver, Palais, Poincaré, Predrag Cvitanović, Rand, Rowley, Rowley, Ruelle, Sadovski, Sandstede, Sandstede, Toronov, Toronov, Tucker, Viswanath, Vladimirov, Wedin, Yoder, Zeghlache   +72 more
core   +1 more source

On the central quadric ansatz: integrable models and Painleve reductions [PDF]

, 2012
It was observed by Tod and later by Dunajski and Tod that the Boyer-Finley (BF) and the dispersionless Kadomtsev-Petviashvili (dKP) equations possess solutions whose level surfaces are central quadrics in the space of independent variables (the so-called
A Zhang, B Huard, Calderbank D M J, Dryuma V, Dunajski M, E V Ferapontov, Ferapontov E V, Grundland A M, Huard B, Pavlov M V, Tod K P, Tsarev S P   +11 more
core   +2 more sources