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INVARIANT MEASURES FOR REDUCIBLE GENERALIZED BRATTELI DIAGRAMS

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arXiv 2024年

作者： Bezuglyi, Sergey Karpel, Olena Kwiatkowski, Jan Department of Mathematics University of Iowa Iowa CityIA52242-1419 United States AGH University of Krakow Faculty of Applied Mathematics al. Adama Mickiewicza 30 Kraków30-059 Poland B. Verkin Institute for Low Temperature Physics and Engineering 47 Nauky Ave. Kharkiv61103 Ukraine Faculty of Mathematics and Computer Science Nicolaus Copernicus University ul. Chopina 12/18 Toruń 87-100 Poland

In 2010, Bezuglyi, Kwiatkowski, Medynets and Solomyak [Ergodic Theory Dynam. Systems 30 (2010), no.4, 973-1007] found a complete description of the set of probability ergodic tail invariant measures on the path space of a standard (classical) stationary reducible Bratteli diagram. It was shown that every distinguished eigenvalue for the incidence matrix determines a probability ergodic invariant measure. In this paper, we show that this result does not hold for stationary reducible generalized Bratteli diagrams. We consider classes of stationary and non-stationary reducible generalized Bratteli diagrams with infinitely many simple standard subdiagrams, in particular, with infinitely many odometers as subdiagrams. We characterize the sets of all probability ergodic invariant measures for such diagrams and study partial orders under which the diagrams can support a Vershik *** Codes 37A05, 37B05, 37A40, 54H05, 05C60 © 2024, CC BY.

关键词： Dynamical systems

HORIZONTALLY STATIONARY GENERALIZED BRATTELI DIAGRAMS

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arXiv 2024年

作者： Bezuglyi, Sergey Jorgensen, Palle E.T. Karpel, Olena Kwiatkowski, Jan Department of Mathematics University of Iowa Iowa CityIA52242-1419 United States AGH University of Krakow Faculty of Applied Mathematics al. Adama Mick-iewicza 30 Kraków30-059 Poland B. Verkin Institute for Low Temperature Physics and Engineering 47 Nauky Ave. Kharkiv61103 Ukraine Faculty of Mathematics and Computer Science Nicolaus Copernicus University ul. Chopina 12/18 Toruń87-100 Poland

Bratteli diagrams with countably infinite levels exhibit a new phenomenon: they can be horizontally stationary. The incidence matrices of these horizontally stationary Bratteli diagrams are infinite banded Toeplitz matrices. In this paper, we study the fundamental properties of horizontally stationary Bratteli diagrams. In these diagrams, we provide an explicit description of ergodic tail invariant probability measures. For a certain class of horizontally stationary Bratteli diagrams, we prove that all ergodic tail invariant probability measures are extensions of measures from odometers. Additionally, we establish conditions for the existence of a continuous Vershik map on the path space of a horizontally stationary Bratteli *** Codes 37A05, 37B05, 37A40, 54H05, 05C60 © 2024, CC BY.

关键词： Graphic methods

Kepler problem and chiral effective dynamics

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arXiv 2022年

作者： Bolonek-Lasoń, Katarzyna Gonera, Joanna Kosiński, Piotr Department of Statistical Methods Faculty of Economics and Sociology University of Lodz 41/43 Rewolucji 1905 St. Lodz90-214 Poland Department of Computer Science Faculty of Physics and Applied Informatics University of Lodz 149/153 Pomorska St. Lodz90-236 Poland

It is shown that by an appropriate canonical transformation Kepler dynamics can be put in the form which allows to exhibit the structure of the symmetry transformations related to the superintegrability. They appear to fit nicely into general scheme of nonlinear realizations. In new coordinates the Kepler dynamics results from dimensional reduction of that describing low energy mesons with spontaneously broken chiral symmetry. Copyright © 2022, The Authors. All rights reserved.

关键词： Dynamics

Improving Group Lasso for high-dimensional categorical data

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arXiv 2022年

作者： Nowakowski, Szymon Pokarowski, Piotr Rejchel, Wojciech Soltys, Agnieszka Faculty of Physics University of Warsaw Pasteura 5 Warsaw02-093 Poland Institute of Applied Mathematics and Mechanics University of Warsaw Banacha 2 Warsaw02-097 Poland Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 Toruń87-100 Poland

Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm for selection continuous or categorical variables, but all estimates related to a selected factor usually differ. Therefore, a fitted model may not be sparse, which makes the model interpretation difficult. To obtain a sparse solution of the Group Lasso we propose the following two-step procedure: first, we reduce data dimensionality using the Group Lasso;then to choose the final model we use an information criterion on a small family of models prepared by clustering levels of individual factors. We investigate selection correctness of the algorithm in a sparse high-dimensional scenario. We also test our method on synthetic as well as real datasets and show that it performs better than the state of the art algorithms with respect to the prediction accuracy or model dimension. © 2022, CC BY.

关键词： Clustering algorithms

Interfacial spintronic THz emission

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arXiv 2023年

作者： Agarwal, Piyush Medwal, Rohit Dongol, Keynesh Mohan, John Rex Yang, Yingshu Asada, Hironori Fukuma, Yasuhiro Singh, Ranjan Division of Physics and Applied Physics School of Physical and Mathematical Sciences Nanyang Technological University 21 Nanyang Link Singapore637371 Singapore Center for Disruptive Photonic Technologies The Photonics Institute Nanyang Technological University Singapore639798 Singapore Department of Physics Indian Institute of Technology Uttar Pradesh Kanpur208016 India Department of Electronic Devices and Engineering Graduate School of Science and Engineering Yamaguchi University Ube755-8611 Japan Department of Physics and Information Technology Faculty of Computer Science and System Engineering Kyushu Institute of Technology Iizuka820-8502 Japan

The broken inversion symmetry at the ferromagnet (FM)/heavy-metal (HM) interface leads to spin-dependent degeneracy of the energy band, forming spin-polarized surface states. As a result, the interface serves as an effective medium for converting spin accumulation into two-dimensional charge current through the inverse Rashba-Edelstein effect. Exploring and assessing this spin-to-charge conversion (SCC) phenomenon at the FM/HM interface could offer a promising avenue to surpass the presumed limits of SCC in bulk HM layers. We utilize spintronic heterostructures as a platform to measure the spin-to-charge conversion (SCC) experienced by photoexcited spin currents. These heterostructures emit terahertz electric field when illuminated by femtosecond laser pulses, enabling us to quantitatively assess the ultrafast SCC process. Our results demonstrate a robust interfacial spin-to-charge conversion (iSCC) within a synthetic antiferromagnetic heterostructure, specifically for the NiFe/Ru/NiFe configuration, by isolating the SCC contribution originating from the interface itself, separate from the bulk heavy-metal (HM) region. Moreover, the iSCC at the NiFe/Ru interface is discovered to be approximately 27% of the strength observed in the highest spin-Hall conducting heavy-metal, Pt. Our results thus highlight the significance of interfacial engineering as a promising pathway for achieving efficient ultrafast spintronic devices. Copyright © 2023, The Authors. All rights reserved.

关键词： Electric fields

Microstructure of Rapidly Solidified Al45cr7 and Al45v7 Intermetallic Alloys for Catalytic Applications

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SSRN

SSRN 2022年

作者： Zięba, Amelia Stan-Glowińska, Katarzyna Rogal, Lukasz Czaja, Pawel Przewoźnik, Janusz Chulist, Robert Duraczyńska, Dorota Lityńska-Dobrzyńska, Lidia Reymonta 25 Krakow30-059 Poland AGH University of Science and Technology Faculty of Physics and Applied Computer Science Department of Solid State Physics Al. Mickiewicza 30 Krakow30-059 Poland The Jerzy Haber Institute of Catalysis and Surface Chemistry Polish Academy of Sciences Niezapominajek 8 Krakow30-239 Poland

Alloys with the nominal compositions of Al-13.5 at.% Cr and Al-13.5 at.% V, corresponding to the Al45Cr7 and Al45V7 intermetallic compounds were produced by the melt spinning technique. The obtained ribbons in the form of fragmented brittle flakes were 20-70 µm in thickness and about 5 mm in width. The microstructure and phase composition of the as-spun and heat-treated (100 hours at 600 °C) ribbons were examined by X-ray diffraction, scanning and transmission electron microscopy. In the as-spun state, both ribbons showed a multiphase microstructure. In addition to the Al45Cr7 phase in the Al-Cr alloy and the Al3 V phase in the Al-V alloy, they contained α(Al) solid solution and an icosahedral quasicrystal. The heat-treated alloys were almost single-phase and contained a stable monoclinic phases: Al45Cr7 or Al45V7. The as-spun and heat-treated alloys were used as catalysts for the phenylacetylene hydrogenation reaction. Prior to the catalytic tests, the ribbons were pulverized and sieved to select the powder fraction below 32 µm. All tested materials ensured high activity, above 80% and a high activity rate. The homogenized powders showed slightly better performance than those in the as-spun state. The obtained results open a new area of intermetallic catalysts previously not considered in the case of hydrogenation reactions. © 2022, The Authors. All rights reserved.

关键词： Aluminum alloys

Tailoring the energy landscape of a Bloch point singularity with curvature

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arXiv 2024年

作者： Ruiz-Gomez, Sandra Abert, Claas Morales-Fernández, Pamela Fernandez-Gonzalez, Claudia Koraltan, Sabri Danesi, Lukas Suess, Dieter Foerster, Michael Nino, Miguel Ángel Mandziak, Anna Wilgocka-Ślęzak, Dorota Nita, Pawel Koenig, Markus Seifert, Sebastian Rodríguez, Aurelio Hierro Fernández-Pacheco, Amalio Donnelly, Claire Max Planck Institute for Chemical Physics of Solids Dresden01187 Germany Faculty of Physics University of Vienna Vienna1010 Austria Research Platform MMM Mathematics-Magnetism-Materials University of Vienna Vienna1010 Austria ALBA Synchrotron Light Source CELLS Cerdanyola del Valles Barcelona08290 Spain Vienna Doctoral School in Physics University of Vienna Vienna Austria SOLARIS Synchrotron light Sources Crakow30-392 Poland Jerzy Haber Institute of Catalysis and Surface Chemistry PAC Krakow30-239 Poland Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University Crakow30-348 Poland Depto. Física Universidad de Oviedo Oviedo33007 Spain Institute of Applied Physics TU Wien Wiedner Hauptstr. 8-10/134 Vienna1040 Austria Hiroshima University Hiroshima739-8526 Japan

Topological defects, or singularities, play a key role in the statics and dynamics of complex systems. In magnetism, Bloch point singularities represent point defects that mediate the nucleation of textures such as skyrmions and hopfions. However, while the textures are typically stabilised in chiral magnets, the influence of chirality on the Bloch point singularities remains relatively unexplored. Here we harness advanced three-dimensional nanofabrication to explore the influence of chirality on Bloch point singularities by introducing curvature-induced symmetry breaking in a ferromagnetic nanowire. Combining X-ray magnetic microscopy with the application of in situ magnetic fields, we demonstrate that Bloch point singularity-containing domain walls are stabilised in straight regions of the sample, and determine that curvature can be used to tune the energy landscape of the Bloch points. Not only are we able to pattern pinning points but, by controlling the gradient of curvature, we define asymmetric potential wells to realise a robust Bloch point shift-register with non-reciprocal behaviour. These insights into the influence of symmetry and chirality on singularities offers a route to the controlled nucleation and propagation of topological textures, providing opportunities for logic and computing devices. Copyright © 2024, The Authors. All rights reserved.

关键词： Nucleation

Results on resonance production in heavy-ion collisions from the ATLAS experiment at the LhC

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Acta Physica Polonica B, Proceedings Supplement

Acta Physica Polonica B, Proceedings Supplement 2019年第2期12卷 295-300页

作者： Kremer, Jakub AGH University of Science and Technology Faculty of Physics and Applied Computer Science Al. Mickiewicza 30 Kraków30-059 Poland

Recent ATLAS measurements of quarkonia and open charm production are presented for proton–lead and lead–lead collisions. The studies of charmonia production in ultrarelativistic nucleus–nucleus collisions offer a handle on the properties of the hot and dense quark–gluon plasma created in these collisions. In particular, a strong suppression relative to proton–proton collisions is expected. On the other hand, measurements of quarkonia and charmed meson production in proton–nucleus collisions allow to study cold nuclear matter effects such as initial-state energy loss or nuclear modifications of parton distribution functions. © 2019 Jagellonian University. All rights reserved.

关键词： Energy dissipation

On the linearity and stability of electrostatic structures based on the Schamel equation

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arXiv 2024年

作者： Schamel, Hans Pelinovsky, Efim Flamarion, Marcelo V. Physikalisches Institut Universität Bayreuth Bayreuth95440 Germany Faculty of Informatics Mathematics and Computer Science HSE University Nizhny Novgorod603155 Russia Gaponov-Grekhov Institute of Applied Physics Nizhny Novgorod603122 Russia Departamento Ciencias—Sección Matemáticas Pontificia Universidad Católica del Perú Av. Universitaria 1801 Lima San Miguel15088 Peru

This paper contributes in the first part to the correct understanding of the linear limit in the Schamel equation (S-equation) from the perspective of structure formation in collisionless plasmas. The corresponding modes near equilibrium turn out to be nonlinear modes of the underlying microscopic Vlasov-Poisson (VP) system, for which particle trapping is essential and which propagate with one of the slow acoustic velocities. A simple shift of the electrostatic potential to a new pedestal leads to non-negativity and thus mitigates the positivity problem of the S-equation. The stability of a solitary electron hole (bright soliton), based on both the S-equation and an earlier transverse but limited VP instability analysis, exhibits marginal longitudinal stability and linear perturbations in the form of the asymmetric shift eigenmode of a solvable Schrödinger problem. This finding on the predominance of shift-mode perturbation thus provides a new clue for the general kinetic proof of the marginal stability and transversal instability of electrostatic structures including undisclosed potentials. Copyright © 2024, The Authors. All rights reserved.

关键词： Collisionless plasmas