Research
Research
Research
Research
5,677+ open-access research outputs.
As an alternative to PINNs, a Deep Ritz framework is proposed to solve fully nonlinear PDEs. A least-squares algorithm is advocated to decouple the nonlinearities from the variational features of seve…
Quantum integrable spin chains are known to possess a large family of long-range deformations generated by the local, boost and bilocal operators. Although these deformations are well-understood on th…
We study a generalisation of the set-theoretic Yang-Baxter equation and investigate the connection between its solutions and matrix refactorisation problems. We refer to such solutions as scalene Yang…
Differential-difference matrix Lax representations (Lax pairs), gauge transformations, and discrete Miura-type transformations (MTs) belong to the main tools in the theory of (nonlinear) integrable di…
We will generalize the concept of aggregation function for mathematical structures as a certain function between quantales. In fact, these functions turn to be exactly the lax morphism of quantales. T…
The intrinsic anomalous Hall effect (IAHE) provides a powerful transport fingerprint of quantum magnets, with its linear and second-order responses distinguishing ferromagnets and $\mathcal{P}\mathcal…
We propose a general framework for integrable field theories in arbitrary spacetime dimension $d+1$ which is based on $d$-term $L_\infty$-algebras. Specifically, we introduce cyclic $L_\infty$-algebra…
The theory of 2-monads entails that, for a strict monoidal category C, there is a strict monoidal category L(C) such that strict monoidal functors from L(C) are precisely the lax monoidal functors fro…
We study the semi-discrete approximation of Aubry and Mather sets for Tonelli Lagrangians on the flat torus. Starting from the discrete Lax--Oleinik equation, we introduce natural discrete analogues o…
In this paper, we study nonlinear integrable equations with three independent variables of the following types: Toda-type lattices, semi-discrete lattices, and fully discrete Hirota-Miwa type models. …
We place several known indicators of Kochen--Specker contextuality -- the KCBS correlator $\chi$, the contextual fraction $\CF$, the Shannon-entropic $n$-cycle inequality of Chaves and Fritz, and the …
The radioisotope $^{125}\text{Xe}$ is a short-lived ($T_{1/2}\sim16.9 h$) activation product of the neutron calibrations performed in the LUX-ZEPLIN experiment. Subsequently, $^{125}$Xe decays primari…
Semi-discrete (differential-difference) matrix Lax representations (Lax pairs) play an essential role in the theory of integrable differential-difference equations. Fix a (1+1)-dimensional evolution…
The relativistic hydrodynamics (RHD) equations can give rise to solutions which have shocks, contact discontinuities, and other sharp structures, which interact and evolve over time. Capturing these s…
We introduce the use of a crossed pair of Multilayer Laue Lenses (MLLs) as an objective in Dark-Field X-ray Microscopy (DFXM). In a demonstration experiment at the ID03 beamline at ESRF, two flat Mo-S…
This paper investigates the geometric and cohomological properties of non-K\"ahler SYZ mirror symmetry for dual torus fibrations over solvmanifolds in the sense of Lau, Tseng and Yau. We are mainly co…
We construct Orlov-Schulman symmetries for the self-dual conformal structure (SDCS) hierarchy. We provide an explicit proof of compatibility of additional symmetries with the basic Lax-Sato flows of t…
The multi-scale and non-linear nature of phase-field models of solidification requires fine spatial and temporal discretization, leading to long computation times. This could be overcome with artifici…
We analyze optimal complexity of adaptive finite element methods (AFEMs) for general second-order linear elliptic partial differential equations (PDEs) in the Lax-Milgram setting. To this end, we form…
The Cahn--Hilliard equation is a fundamental model for describing phase separation phenomena in binary mixtures. Traditional numerical methods, such as finite difference and finite element methods, of…
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