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Global center stable manifold for the defocusing energy critical wave equation with potential

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arXiv 2017年

作者： JIA, HAO LIU, BAOPING SCHLAG, WILHELM XU, GUIXIANG School of Mathematics Institute of Advanced study 1 Einstein Drive PrincetonNJ08540 United States Beijing International Center for Mathematical Research Peking University Beijing China University of Chicago Department of Mathematics 5734 South University Avenue ChicagoIL60636 United States Institute of Applied Physics and Computational Mathematics Beijing China

In this paper we consider the defocusing energy critical wave equation with a trapping potential in dimension 3. We prove that the set of initial data for which solutions scatter to an unstable excited state (Ø, 0) forms a finite co-dimensional path connected C1 manifold in the energy space. This manifold is a global and unique center-stable manifold associated with (Ø, 0). It is constructed in a first step locally around any solution scattering to Ø, which might be very far away from Ø in the H 1 × L2(R3) norm. In a second crucial step a no-return property is proved for any solution which starts near, but not on the local manifolds. This ensures that the local manifolds form a global one. Scattering to an unstable steady state is therefore a non-generic behavior, in a strong topological sense in the energy space. This extends our previous result [19] to the nonradial case. The new ingredients here are (i) application of the reversed Strichartz estimate from [3] to construct a local center stable manifold near any solution that scatters to (Ø, 0). This is needed since the endpoint of the standard Strichartz estimates fails nonradially. (ii) The nonradial channel of energy estimate introduced by Duyckaerts-Kenig-Merle [15], which is used to show that solutions that start off but near the local manifolds associated with Ø emit some amount of energy into the far field in excess of the amount of energy beyond that of the steady state Ø. Copyright © 2017, The Authors. All rights reserved.

关键词： Wave equations

A constructive approach to L0 penalized regression

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2018年第1期19卷

作者： Jian Huang Yuling Jiao Yanyan Liu Xiliang Lu Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong China School of Statistics and Mathematics Zhongnan University of Economics and Law Wuhan China and Institute of Big Data of Zhongnan University of Economics and Law School of Mathematics and Statistics Wuhan University Wuhan China School of Mathematics and Statistics Wuhan University Wuhan China and Hubei Key Laboratory of Computational Science

We propose a constructive approach to estimating sparse, high-dimensional linear regression models. The approach is a computational algorithm motivated from the KKT conditions for the l0-penalized least squares solutions. It generates a sequence of solutions iteratively, based on support detection using primal and dual information and root finding. We refer to the algorithm as SDAR for brevity. Under a sparse Riesz condition on the design matrix and certain other conditions, we show that with high probability, the l2 estimation error of the solution sequence decays exponentially to the minimax error bound in O(log(Rp√J)) iterations, where J is the number of important predictors and R is the relative magnitude of the nonzero target coefficients; and under a mutual coherence condition and certain other conditions, the l∞ estimation error decays to the optimal error bound in O(log(R)) iterations. Moreover the SDAR solution recovers the oracle least squares estimator within a finite number of iterations with high probability if the sparsity level is known. computational complexity analysis shows that the cost of SDAR is O(np) per iteration. We also consider an adaptive version of SDAR for use in practical applications where the true sparsity level is unknown. Simulation studies demonstrate that SDAR outperforms Lasso, MCP and two greedy methods in accuracy and efficiency.

关键词： KKT conditions geometrical convergence nonasymptotic error bounds oracle property root finding support detection

Sparsity-promoting and edge-preserving maximum a posteriori estimators in non-parametric bayesian inverse problems

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arXiv 2017年

作者： Agapiou, Sergios Burger, Martin Dashti, Masoumeh Helin, Tapio Department of Mathematics and Statistics University of Cyprus 1 University Avenue Nicosia2109 Cyprus Institute for Computational and Applied Mathematics Westfälische Wilhelms-Universität Münster and Cells in Motion Cluster of Excellence Münster Germany Department of Mathematics University of Sussex BrightonBN1 5DJ United Kingdom Department of Mathematics and Statistics University of Helsinki Gustaf Hallströmin katu 2b HelsinkiFI-00014 Finland

We consider the inverse problem of recovering an unknown functional parameter u in a separable Banach space, from a noisy observation y of its image through a known possibly non-linear ill-posed map G. The data y is finite-dimensional and the noise is Gaussian. We adopt a Bayesian approach to the problem and consider Besov space priors (see), which are well-known for their edge-preserving and sparsity-promoting properties and have recently attracted wide attention especially in the medical imaging community. Our key result is to show that in this non-parametric setup the maximum a posteriori (MAP) estimates are characterized by the minimizers of a generalized Onsager-Machlup functional of the posterior. This is done independently for the so-called weak and strong MAP estimates, which as we show coincide in our context. In addition, we prove a form of weak consistency for the MAP estimators in the infinitely informative data limit. Our results are remarkable for two reasons: first, the prior distribution is non-Gaussian and does not meet the smoothness conditions required in previous research on nonparametric MAP estimates. Second, the result analytically justifies existing uses of the MAP estimate in finite but high dimensional discretizations of Bayesian inverse problems with the considered Besov priors.49N45, 62C10, 62G05, 62G20 Copyright © 2017, The Authors. All rights reserved.

关键词： Banach spaces

Ion beam bunching via phase rotation in cascading laser-driven ion acceleration

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arXiv 2018年

作者： Wang, H.C. Weng, S.M. Liu, M. Chen, M. He, M.Q. Zhao, Q. Murakami, M. Sheng, Z.M. School of Physics and Astronomy Shanghai Jiao Tong University Shanghai200240 China Collaborative Innovation Center of IFSA Shanghai Jiao Tong University Shanghai200240 China Institute of Applied Physics and Computational Mathematics Beijing100094 China Institute of Laser Engineering Osaka University Osaka565-0871 Japan Tsung-Dao Lee Institute Shanghai200240 China SUPA Department of Physics University of Strathclyde GlasgowG4 0NG United Kingdom

The ion beam bunching in a cascaded target normal sheath acceleration is investigated by theoretical analysis and particle-in-cell simulations. It is found that a proton beam can be accelerated and bunched simultaneously by injecting it into the rising sheath field at the rear side of a laser-irradiated foil target. In the rising sheath field, the ion phase rotation may take place since the back-end protons of the beam feels a stronger field than the front-end protons. Consequently, the injected proton beam can be compressed in the longitudinal direction. At last, the vital role of the ion beam bunching is illustrated by the integrated simulations of two successive stages in a cascaded acceleration. Copyright © 2018, The Authors. All rights reserved.

关键词： Ion beams

The FRET-based structural dynamics challenge - community contributions to consistent and open science practices

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arXiv 2020年

作者： Lerner, Eitan Ambrose, Benjamin Barth, Anders Birkedal, Victoria Blanchard, Scott C. Börner, Richard Cordes, Thorben Craggs, Timothy D. Ha, Taekjip Haran, Gilad Hugel, Thorsten Ingargiola, Antonino Kapanidis, Achillefs Lamb, Don C. Laurence, Ted ki Lee, Nam Lemke, Edward A. Margeat, Emmanuel Michaelis, Jens Michalet, Xavier Nettels, Daniel Peulen, Thomas-Otavio Schuler, Benjamin Seidel, Claus A.M. Soleimaninejad, Hamid Weiss, Shimon Department of Biological Chemistry Alexander Silberman Institute of Life Sciences Faculty of Mathematics & Science Edmond J. Safra Campus Hebrew University of Jerusalem Jerusalem9190401 Israel Center for Nanoscience and Nanotechnology Hebrew University of Jerusalem Jerusalem9190401 Israel Department of Chemistry University of Sheffield Sheffield United Kingdom Lehrstuhl für Molekulare Physikalische Chemie Heinrich-Heine-Universität Düsseldorf Germany Department of Chemistry and iNANO center Aarhus University Aarhus8000 Denmark Department of Structural Biology St. Jude Children's Research Hospital MemphisTN United States Laserinstitut HS Mittweida University of Applied Science Mittweida Mittweida09648 Germany Physical and Synthetic Biology Faculty of Biology Ludwig-Maximilians-Universität München Planegg-Martinsried Germany Department of Biophysics and Biophysical Chemistry Johns Hopkins University School of Medicine BaltimoreMD21205 United States Department of Biophysics and Biophysical Chemistry Johns Hopkins University School of Medicine BaltimoreMD21205 United States Department of Biomedical Engineering Johns Hopkins University BaltimoreMD21205 United States Howard Hughes Medical Institute BaltimoreMD21205 United States Department of Chemical and Biological Physics Weizmann Institute of Science POB 26 Rehovot7610001 Israel Institute of Physical Chemistry and Signalling Research Centres BIOSS and CIBSS University of Freiburg Albertstraße 23a FreiburgD-79104 Germany Department of Chemistry and Biochemistry Department of Physiology University of California Los Angeles United States Biological Physics Research Group Clarendon Laboratory Department of Physics University of Oxford Oxford United Kingdom Ludwig-Maximilians-Universität München81377 Germany Physical and Life Sciences Directorate Lawrence Livermore National Laboratory LivermoreCA United States School of Chemistry Seoul National University Seoul Korea Republic of Departmen

Single-molecule Förster resonance energy transfer (smFRET) has become a mainstream technique for probing biomolecular structural dynamics. The rapid and wide adoption of the technique by an ever-increasing number of groups has generated many improvements and variations in the technique itself, in methods for sample preparation and characterization, in analysis of the data from such experiments, and in analysis codes and algorithms. Recently, several labs that employ smFRET have joined forces to try to bring the smFRET community together in adopting a consensus on how to perform experiments and analyze results for achieving quantitative structural information. These recent efforts include multi-lab blind-tests to assess the accuracy and precision of smFRET between different labs using different procedures, the formal assembly of the FRET community and development of smFRET procedures to be considered for entries in the wwPDB. Here we delve into the different approaches and viewpoints in the field. This position paper describes the current "state-of-the field", points to unresolved methodological issues for quantitative structural studies, provides a set of ‘soft recommendations’ about which an emerging consensus exists, and a list of resources that are openly available. To make further progress, we strongly encourage ‘open science’ practices. We hope that this position paper will provide a roadmap for newcomers to the field, as well as a reference for seasoned practitioners. Copyright © 2020, The Authors. All rights reserved.

关键词： Forster resonance energy transfer

Global acoustic daylight imaging in a stratified Earth-like model

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arXiv 2017年

作者： de Hoop, Maarten V. Garnier, Josselin Sølna, Knut Department of Computational and Applied Mathematics Department of Earth Science Rice University 6100 Main Street HoustonTX77005 United States Centre de Mathématiques Appliquées Ecole Polytechnique Palaiseau Cedex91128 France Department of Mathematics University at California at Irvine IrvineCA92697 United States

We present an analysis of acoustic daylight imaging in an Earth-like model assuming a random distribution of noise sources spatially supported in an annulus located away from the surface. We assume a situation with scalar wave propagation and that the measurements are of the wave field at the surface. Then, we obtain a relation between the autocorrelation function of the measurements and the trace of the scattered field generated by an impulsive source localized just below the surface. From this relation it is, for example, clear that the eigenfrequencies can be recovered from the autocorrelation. Moreover, the complete scattering operator can be extracted under the additional assumption that the annulus is close to the surface and has a thickness smaller than the typical wavelength.35R30, 35R60, 86A15 Copyright © 2017, The Authors. All rights reserved.

关键词： Autocorrelation

Measurements of Chemical Potentials in Pb-Pb Collisions at sNN=5.02 TeV

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Physical Review Letters 2024年第9期133卷 092301页

作者： S. Acharya D. Adamová G. Aglieri Rinella L. Aglietta M. Agnello N. Agrawal Z. Ahammed S. Ahmad S. U. Ahn I. Ahuja A. Akindinov M. Al-Turany D. Aleksandrov B. Alessandro H. M. Alfanda R. Alfaro Molina B. Ali A. Alici N. Alizadehvandchali A. Alkin J. Alme G. Alocco T. Alt A. R. Altamura I. Altsybeev J. R. Alvarado M. N. Anaam C. Andrei N. Andreou A. Andronic E. Andronov V. Anguelov F. Antinori P. Antonioli N. Apadula L. Aphecetche H. Appelshäuser C. Arata S. Arcelli M. Aresti R. Arnaldi J. G. M. C. A. Arneiro I. C. Arsene M. Arslandok A. Augustinus R. Averbeck M. D. Azmi H. Baba A. Badalà J. Bae Y. W. Baek X. Bai R. Bailhache Y. Bailung R. Bala A. Balbino A. Baldisseri B. Balis D. Banerjee Z. Banoo F. Barile L. Barioglio M. Barlou B. Barman G. G. Barnaföldi L. S. Barnby E. Barreau V. Barret L. Barreto C. Bartels K. Barth E. Bartsch N. Bastid S. Basu G. Batigne D. Battistini B. Batyunya D. Bauri J. L. Bazo Alba I. G. Bearden C. Beattie P. Becht D. Behera I. Belikov A. D. C. Bell Hechavarria F. Bellini R. Bellwied S. Belokurova L. G. E. Beltran Y. A. V. Beltran G. Bencedi S. Beole Y. Berdnikov A. Berdnikova L. Bergmann M. G. Besoiu L. Betev P. P. Bhaduri A. Bhasin M. A. Bhat B. Bhattacharjee L. Bianchi N. Bianchi J. Bielčík J. Bielčíková A. P. Bigot A. Bilandzic G. Biro S. Biswas N. Bize J. T. Blair D. Blau M. B. Blidaru N. Bluhme C. Blume G. Boca F. Bock T. Bodova S. Boi J. Bok L. Boldizsár M. Bombara P. M. Bond G. Bonomi H. Borel A. Borissov A. G. Borquez Carcamo H. Bossi E. Botta Y. E. M. Bouziani L. Bratrud P. Braun-Munzinger M. Bregant M. Broz G. E. Bruno M. D. Buckland D. Budnikov H. Buesching S. Bufalino P. Buhler N. Burmasov Z. Buthelezi A. Bylinkin S. A. Bysiak J. C. Cabanillas Noris M. Cai H. Caines A. Caliva E. Calvo Villar J. M. M. Camacho P. Camerini F. D. M. Canedo S. L. Cantway M. Carabas A. A. Carballo F. Carnesecchi R. Caron L. A. D. Carvalho J. Castillo Castellanos F. Catalano S. Cattaruzzi C. Ceballos Sanchez R. Cerri I. Chakaberia P. Chakraborty S. Chandra S. Chapeland M. Chartier S. Chattopadhyay Université Clermont Auvergne CNRS/IN2P3 LPC Clermont-Ferrand France Nuclear Physics Institute of the Czech Academy of Sciences Husinec-Řež Czech Republic European Organization for Nuclear Research (CERN) Geneva Switzerland Dipartimento di Fisica dell’Università and Sezione INFN Turin Italy Dipartimento DISAT del Politecnico and Sezione INFN Turin Italy Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN Bologna Italy Variable Energy Cyclotron Centre Homi Bhabha National Institute Kolkata India Department of Physics Aligarh Muslim University Aligarh India Korea Institute of Science and Technology Information Daejeon Republic of Korea Faculty of Science P.J. Šafárik University Košice Slovak Republic Affiliated with an institute covered by a cooperation agreement with CERN Research Division and ExtreMe Matter Institute EMMI GSI Helmholtzzentrum für Schwerionenforschung GmbH Darmstadt Germany INFN Sezione di Torino Turin Italy Central China Normal University Wuhan China Instituto de Física Universidad Nacional Autónoma de México Mexico City Mexico University of Houston Houston Texas USA Department of Physics and Technology University of Bergen Bergen Norway INFN Sezione di Cagliari Cagliari Italy Institut für Kernphysik Johann Wolfgang Goethe-Universität Frankfurt Frankfurt Germany INFN Sezione di Bari Bari Italy Physik Department Technische Universität München Munich Germany High Energy Physics Group Universidad Autónoma de Puebla Puebla Mexico Horia Hulubei National Institute of Physics and Nuclear Engineering Bucharest Romania University of Derby Derby United Kingdom Universität Münster Institut für Kernphysik Munster Germany Physikalisches Institut Ruprecht-Karls-Universität Heidelberg Heidelberg Germany INFN Sezione di Padova Padova Italy INFN Sezione di Bologna Bologna Italy Lawrence Berkeley National Laboratory Berkeley California USA SUBATECH IMT Atlantique Nantes Université CNRS-IN2P3 Nantes France Laboratoire d

This Letter presents the most precise measurement to date of the matter-antimatter imbalance at midrapidity in Pb-Pb collisions at a center-of-mass energy per nucleon pair sNN=5.02 TeV. Using the Statistical Hadronization framework, it is possible to obtain the value of the electric charge and baryon chemical potentials, μQ=−0.18±0.90 MeV and μB=0.71±0.45 MeV, with unprecedented precision. A centrality-differential study of the antiparticle-to-particle yield ratios of charged pions, protons, Ω baryons, and light (hyper)nuclei is performed. These results indicate that the system created in Pb-Pb collisions at the LHC is on average baryon-free and electrically neutral at midrapidity.

关键词： Particle & resonance production QCD phase transitions Quark-gluon plasma Relativistic heavy-ion collisions

Universality from disorder in the random-bond Blume-Capel model

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Physical Review E 2018年第4期97卷 040102(R)-040102(R)页

作者： N. G. Fytas J. Zierenberg P. E. Theodorakis M. Weigel W. Janke A. Malakis Applied Mathematics Research Centre Coventry University Coventry CV1 5FB United Kingdom Institut für Theoretische Physik Universität Leipzig Postfach 100 920 04009 Leipzig Germany Max Planck Institute for Dynamics and Self-Organization 37077 Göttingen Germany Bernstein Center for Computational Neuroscience 37077 Göttingen Germany Institute of Physics Polish Academy of Sciences Al. Lotników 32/46 02-668 Warsaw Poland Department of Physics Section of Solid State Physics University of Athens Panepistimiopolis GR 15784 Zografou Greece

Using high-precision Monte Carlo simulations and finite-size scaling we study the effect of quenched disorder in the exchange couplings on the Blume-Capel model on the square lattice. The first-order transition for large crystal-field coupling is softened to become continuous, with a divergent correlation length. An analysis of the scaling of the correlation length as well as the susceptibility and specific heat reveals that it belongs to the universality class of the Ising model with additional logarithmic corrections which is also observed for the Ising model itself if coupled to weak disorder. While the leading scaling behavior of the disordered system is therefore identical between the second-order and first-order segments of the phase diagram of the pure model, the finite-size scaling in the ex-first-order regime is affected by strong transient effects with a crossover length scale L*≈32 for the chosen parameters.

关键词： Critical phenomena Disordered systems Equilibrium lattice models Finite-size scaling Monte Carlo methods

Euclid: The Early Release Observations Lens Search Experiment

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arXiv 2024年

作者： Barroso, J.A. Acevedo O'Riordan, C.M. Clément, B. Tortora, C. Collett, T.E. Courbin, F. Gavazzi, R. Metcalf, R.B. Busillo, V. Andika, I.T. Cabanac, R. Courtois, H.M. Crook-Mansour, J. Delchambre, L. Despali, G. Ecker, L.R. Franco, A. Holloway, P. Jackson, N. Jahnke, K. Mahler, G. Marchetti, L. Matavulj, P. Melo, A. Meneghetti, M. Moustakas, L.A. Müller, O. Nucita, A.A. Paulino-Afonso, A. Pearson, J. Rojas, K. Scarlata, C. Schuldt, S. Serjeant, S. Sluse, D. Suyu, S.H. Vaccari, M. Verma, A. Vernardos, G. Walmsley, M. Bouy, H. Walth, G.L. Powell, D.M. Bolzonella, M. Cuillandre, J.-C. Kluge, M. Saifollahi, T. Schirmer, M. Stone, C. Acebron, A. Bazzanini, L. Díaz-Sánchez, A. Hogg, N.B. Koopmans, L.V.E. Kruk, S. Leuzzi, L. Manjón-García, A. Mannucci, F. Nagam, B.C. Pearce-Casey, R. Scharré, L. Wilde, J. Altieri, B. Amara, A. Andreon, S. Auricchio, N. Baccigalupi, C. Baldi, M. Balestra, A. Bardelli, S. Basset, A. Battaglia, P. Bender, R. Bonino, D. Branchini, E. Brescia, M. Brinchmann, J. Caillat, A. Camera, S. Candini, G.P. Capobianco, V. Carbone, C. Carretero, J. Casas, S. Castellano, M. Castignani, G. Cavuoti, S. Cimatti, A. Colodro-Conde, C. Congedo, G. Conselice, C.J. Conversi, L. Copin, Y. Corcione, L. Cropper, M. Da Silva, A. Degaudenzi, H. De Lucia, G. Dinis, J. Dubath, F. Dupac, X. Dusini, S. Farina, M. Farrens, S. Ferriol, S. Frailis, M. Franceschi, E. Galeotta, S. Garilli, B. George, K. Gillard, W. Gillis, B. Giocoli, C. Gómez-Alvarez, P. Grazian, A. Grupp, F. Guzzo, L. Haugan, S.V.H. Hoekstra, H. Holmes, W. Hook, I. Hormuth, F. Hornstrup, A. Jhabvala, M. Joachimi, B. Keihänen, E. Kermiche, S. Kiessling, A. Kubik, B. Kunz, M. Kurki-Suonio, H. Le Mignant, D. Ligori, S. Lilje, P.B. Lindholm, V. Lloro, I. Mainetti, G. Maiorano, E. Mansutti, O. Marcin, S. Marggraf, O. Martinelli, M. Martinet, N. Marulli, F. Massey, R. Medinaceli, E. Melchior, M. Mellier, Y. Merlin, E. Meylan, G. Observatoire de Sauverny Versoix1290 Switzerland Max-Planck-Institut für Astrophysik Karl-Schwarzschild-Str. 1 Garching85748 Germany Lausanne1015 Switzerland INAF-Osservatorio Astronomico di Capodimonte Via Moiariello 16 Napoli80131 Italy Institute of Cosmology and Gravitation University of Portsmouth PortsmouthPO1 3FX United Kingdom Martí i Franquès 1 Barcelona08028 Spain Passeig de Lluís Companys 23 Barcelona08010 Spain Aix-Marseille Université CNRS CNES LAM Marseille France Institut d'Astrophysique de Paris UMR 7095 CNRS Sorbonne Université 98 bis boulevard Arago Paris75014 France Dipartimento di Fisica e Astronomia "Augusto Righi" Alma Mater Studiorum Università di Bologna via Piero Gobetti 93/2 Bologna40129 Italy INAF-Osservatorio di Astrofisica e Scienza dello Spazio di Bologna Via Piero Gobetti 93/3 Bologna40129 Italy Department of Physics "E. Pancini" University Federico II Via Cinthia 6 Napoli80126 Italy INFN section of Naples Via Cinthia 6 Napoli80126 Italy Technical University of Munich TUM School of Natural Sciences Physics Department James-Franck-Str. 1 Garching85748 Germany Université de Toulouse CNRS UPS CNES 14 Av. Edouard Belin Toulouse31400 France UCB Lyon 1 CNRS IN2P3 IUF IP2I Lyon 4 rue Enrico Fermi Villeurbanne69622 France Department of Astronomy University of Cape Town Rondebosch Cape Town7700 South Africa STAR Institute Quartier Agora - Allée du six Août 19c LiègeB-4000 Belgium INFN-Sezione di Bologna Viale Berti Pichat 6/2 Bologna40127 Italy Universitäts-Sternwarte München Fakultät für Physik Ludwig-Maximilians-Universität München Scheinerstrasse 1 München81679 Germany Max Planck Institute for Extraterrestrial Physics Giessenbachstr. 1 Garching85748 Germany INFN Sezione di Lecce Via per Arnesano CP-193 Lecce73100 Italy Department of Mathematics and Physics E. De Giorgi University of Salento Via per Arnesano CP-I93 Lecce73100 Italy INAF-Sezione di Lecce c/o Dipartimento M

We investigate the ability of the Euclid telescope to detect galaxy-scale gravitational lenses. To do so, we perform a systematic visual inspection of the 0.7 deg2 Euclid ERO data towards the Perseus cluster using both the high-resolution VIS IE band, and the lower resolution NISP bands. We inspect every extended source brighter than magnitude 23 in IE with 41 expert human classifiers. This amounts to 12 086 stamps of 10′′ × 10′′. We find 3 grade A and 13 grade B candidates. We assess the validity of these 16 candidates by modelling them and checking that they are consistent with a single source lensed by a plausible mass distribution. Five of the candidates pass this check, five others are rejected by the modelling and six are inconclusive. Extrapolating from the five successfully modelled candidates, we infer that the full 14 000 deg2 of the Euclid Wide Survey should contain 100 000+70 000−30 000 galaxy-galaxy lenses that are both discoverable through visual inspection and have valid lens models. This is consistent with theoretical forecasts of 170 000 discoverable galaxy-galaxy lenses in Euclid. Our five modelled lenses have Einstein radii in the range 0′′ . 68 E ′′ . 24, but their Einstein radius distribution is on the higher side when compared to theoretical forecasts. This suggests that our methodology is likely missing small Einstein radius systems. Whilst it is implausible to visually inspect the full Euclid data set, our results corroborate the promise that Euclid will ultimately deliver a sample of around 105 galaxy-scale lenses. © 2024, CC BY.

关键词： Gravitational effects