Tootfinder

Phase-field and lip-field approaches for fracture with extreme mesh deformation (X-Mesh): a one-dimensional study
Nicolas Mo\"es, Beno\^it L\'e, Nicolas Chevaugeon, Jean-Fran\c{c}ois Remacle
https://arxiv.org/abs/2509.04971

Phase-field and lip-field approaches for fracture with extreme mesh deformation (X-Mesh): a one-dimensional study
We consider a one-dimensional fracture problem modelled using either the phase-field or lip-field approach. In both cases, we optimise the incremental potential with respect to the displacement and damage fields and the nodal coordinates of the mesh. This is thus a variational mesh study. We observe that, as the damage reaches its maximum value, the optimisation drives the most damaged element to zero size as the damage reaches its maximum value. This peculiar element provides a precise displac…

QCD condensates and $\alpha_s$ from $e^ e^-$ and $\tau$-decays
Stephan Narison (LUPM-CNRS Montpellier-FR,iHEPMAD-Univ. Antananarivo-MG)
https://arxiv.org/abs/2508.05434 https://…

QCD condensates and $α_s$ from $e^+e^-$ and $τ$-decays
In this talk, I review the determinations of the QCD condensates and $α_s$ within the SVZ expansion using the ratio of Laplace sum rule (LSR) and $τ$-like moments in $e^+e^-\to I=1$ Hadrons and in $τ\to ν_τ+$Hadrons Axial-vector (A) and V-A channels. Some misprints in the original papers [1-3] have been corrected. We found that the value of the gluon condensate agrees with the one $\langle α_s G^2\rangle=(6.35\pm 0.35)\times 10^{-2}$ GeV$^4$ from quarkonia and some other sum rules but les…

Cosmic ray energy spectra derived from KASCADE-Grande data using post-LHC hadronic interaction models
D. Kang, J. C. Arteaga-Vel\'azquez, M. Bertaina, A. Chiavassa, A. L. Colmenero-C\'esar, K. Daumiller, V. de Souza, R. Engel, A. Gherghel-Lascu, C. Grupen, A. Haungs, J. R. H\"orandel, T. Huege, K. -H. Kampert, K. Link, H. J. Mathes, S. Ostapchenko, T. Pierog, D. Rivera-Rangel, M. Roth, H. Schieler, F. G. Schr\"oder, O. Sima, A. Weindl, J. Wochele, J. Zabierowski
…

Cosmic ray energy spectra derived from KASCADE-Grande data using post-LHC hadronic interaction models
KASCADE-Grande was dedicated to measuring the energy spectrum and mass composition of cosmic rays in the energy range of 10 PeV to 1 EeV. We observed a knee-like structure in the heavy mass component at around 100 PeV and an ankle-like structure in the light component. In this contribution, we present updated energy spectra based on shower size measurements, using the post-LHC hadronic models QGSJet-II-04, EPOS-LHC, and SIBYLL 2.3d, including accounting for shower-to-shower fluctuations. In add…

Study on the certain type of nonlinear algebraic partial differential equation in $\mathbb{C}^m$
Sujoy Majumder, Debabrata Pramanik, Nabadwip Sarkar
https://arxiv.org/abs/2508.15857

Study on the certain type of nonlinear algebraic partial differential equation in $\mathbb{C}^m$
In the paper, using Nevanlinna's value distribution theory of meromorphic functions in $\mathbb{C}^m$, we study for the existence of entire solutions $f$ in $\mathbb{C}^m$ of the following algebraic partial differential equation \[f^n(z)+P_d(f(z))=p(z)e^{\langle α,\ol z\rangle},\] where $P_d(f)$ is an algebraic differential polynomial in $f$ of degree $d \leq n-2$, $n \geq 3$ is an integer, $p$ is a non-zero polynomial, $α=(α_{1},\ldots,α_{m})\neq (0,\ldots,0)$ and $\langle α,\ol z\rangle=…