LAUSR

On a higher integral invariant for closed magnetic lines, revisited

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0 Published in 2021 at "Journal of Geometry and Physics"

DOI: 10.1016/j.geomphys.2021.104379

Abstract: Abstract We recall a definition of an asymptotic invariant of classical link, which is called M-invariant. M-invariant is a special Massey integral, this integral has an ergodic form and is generalized for magnetic fields with… read more here.

Keywords: magnetic lines; integral invariant; closed magnetic; invariant ... See more keywords

Travelling waves for reaction–diffusion equations forced by translation invariant noise

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0 Published in 2020 at "Physica D: Nonlinear Phenomena"

DOI: 10.1016/j.physd.2019.132233

Abstract: Inspired by applications, we consider reaction-diffusion equations on $\mathbb{R}$ that are stochastically forced by a small multiplicative noise term that is white in time, coloured in space and invariant under translations. We show how these… read more here.

Keywords: travelling waves; diffusion equations; invariant; reaction diffusion ... See more keywords

Quench dynamics of Hopf insulators

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1 Published in 2020 at "Physical Review B"

DOI: 10.1103/physrevb.101.155131

Abstract: Hopf insulators are exotic topological states of matter outside the standard tenfold-way classification based on discrete symmetries. Its topology is captured by an integer invariant that describes the linking structures of the Hamiltonian in the… read more here.

Keywords: dynamics hopf; quench dynamics; topology; ensuremath ... See more keywords

Tree-Structured Polyhedral Invariant Set Calculations

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0 Published in 2020 at "IEEE Control Systems Letters"

DOI: 10.1109/lcsys.2019.2945721

Abstract: This letter provides a description of how hierarchical dependencies between inequalities can be exploited in order to efficiently calculate polyhedral approximations of maximal robust positive invariant sets using geometrically motivated methods. Due to the hierarchical… read more here.

Keywords: structured polyhedral; polyhedral invariant; invariant set; set calculations ... See more keywords

Topological Invariant Prediction via Deep Learning

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0 Published in 2020 at "Journal of the Korean Physical Society"

DOI: 10.3938/jkps.76.401

Abstract: Using a deep neural network model, we show that predicting an accurate topological invariant is possible from one-dimensional Hamiltonians, whose topological invariant is the winding number. Given a set of Hamiltonians in momentum space as… read more here.

Keywords: deep neural; topological invariant; invariant prediction; invariant ... See more keywords