More Like this

1. Towards a Schinzel–Wójcik theorem for number fields

   https://doi.org/10.1007/s40879-025-00819-8  

   Pollack, Paul (June 2025, European Journal of Mathematics)

   Abstract Schinzel and Wójcik have shown that for every$$\alpha ,\beta \in \mathbb {Q}^{\times }\hspace{0.55542pt}{\setminus }\hspace{1.111pt}\{\pm 1\}$$ $\alpha ,\beta \in Q^{\times }\backslash \{\pm 1\}$, there are infinitely many primespwhere$$v_p(\alpha )=v_p(\beta )=0$$ $v_p\left(\alpha \right)=v_p\left(\beta \right)=0$and where$$\alpha $$ $\alpha$and$$\beta $$ $\beta$generate the same multiplicative group modp. We prove a weaker result in the same direction for algebraic numbers$$\alpha , \beta $$ $\alpha ,\beta$. Let$$\alpha , \beta \in \overline{\mathbb {Q}} ^{\times }$$ $\alpha ,\beta \in {\overline{Q}}^{\times }$, and suppose$$|N_{\mathbb {Q}(\alpha ,\beta )/\mathbb {Q}}(\alpha )|\ne 1$$ $|N_{Q(\alpha ,\beta )/Q}\left(\alpha \right)|\ne 1$and$$|N_{\mathbb {Q}(\alpha ,\beta )/\mathbb {Q}}(\beta )|\ne 1$$ $|N_{Q(\alpha ,\beta )/Q}\left(\beta \right)|\ne 1$. Then for some positive integer$$C = C(\alpha ,\beta )$$ $C=C(\alpha ,\beta )$, there are infinitely many prime idealsPof Equation missing<#comment/>where$$v_P(\alpha )=v_P(\beta )=0$$ $v_P\left(\alpha \right)=v_P\left(\beta \right)=0$and where the group$$\langle \beta \bmod {P}\rangle $$ $⟨\beta modP⟩$is a subgroup of$$\langle \alpha \bmod {P}\rangle $$ $⟨\alpha modP⟩$with$$[\langle \alpha \bmod {P}\rangle \,{:}\, \langle \beta \bmod {P}\rangle ]$$ $[⟨\alpha modP⟩:⟨\beta modP⟩]$dividingC. A key component of the proof is a theorem of Corvaja and Zannier bounding the greatest common divisor of shiftedS-units. 

   more » « less
2. Time-Global Regularity of the Navier–Stokes System with Hyper-Dissipation: Turbulent Scenario

   https://doi.org/10.1007/s40818-025-00199-y  

   Grujić, Zoran; Xu, Liaosha (March 2025, Annals of PDE)

   Abstract The question of whether the hyper-dissipative (HD) Navier-Stokes (NS) system can exhibit spontaneous formation of singularities in the super-critical regime–the hyperviscous effects being represented by a fractional power of the Laplacian, say$$\beta $$ $\beta$, confined to interval$$\bigl (1, \frac{5}{4}\bigr )$$ $(1,\frac{5}{4})$–has been a major open problem in the mathematical fluid dynamics since the foundational work of J.L. Lions in 1960s. In this work, an evidence of criticality of the Laplacian is presented, more precisely, a class of plausible blow-up scenarios is ruled out as soon as$$\beta $$ $\beta$is greater than one. While the framework is based on the ‘scale of sparseness’ of the super-level sets of the positive and negative parts of the components of the higher-order derivatives of the velocity previously introduced by the authors, a major novelty in the current work is classification of the HD flows near a potential spatiotemporal singularity in two main categories, ‘homogeneous’ (the case consistent with a near-steady behavior) and ‘non-homogenous’ (the case consistent with the formation and decay of turbulence). The main theorem states that in the non-homogeneous case any$$\beta $$ $\beta$greater than one prevents a singularity. In order to illustrate the impact of this result in a methodology-free setting, a two-parameter family of dynamically rescaled blow-up profiles is considered, and it is shown that as soon as$$\beta $$ $\beta$is greater than one, a new region in the parameter space is ruled out. More importantly, the region is a neighborhood (in the parameter space) of the self-similar profile, i.e., the approximately self-similar blow-up, a prime suspect in possible singularity formation, is ruled out for all HD NS models. 

   more » « less
3. CUPID, the Cuore upgrade with particle identification

   https://doi.org/10.1140/epjc/s10052-025-14352-1  

   Alfonso, K; Armatol, A; Augier, C; Avignone_III, F T; Azzolini, O; Barabash, A S; Bari, G; Barresi, A; Baudin, D; Bellini, F; et al (July 2025, The European Physical Journal C)

   Abstract CUPID, the CUORE Upgrade with Particle Identification, is a next-generation experiment to search for neutrinoless double beta decay ($$0\mathrm {\nu \beta \beta }$$ $0\nu \beta \beta$) and other rare events using enriched Li$$_{2}$$ $_2^{}$$$^{100}$$ $_{}^{100}$MoO$$_{4}$$ $_4^{}$scintillating bolometers. It will be hosted by the CUORE cryostat located at the Laboratori Nazionali del Gran Sasso in Italy. The main physics goal of CUPID is to search for$$0\mathrm {\nu \beta \beta }$$ $0\nu \beta \beta$of$$^{100}$$ $_{}^{100}$Mo with a discovery sensitivity covering the full neutrino mass regime in the inverted ordering scenario, as well as the portion of the normal ordering regime with lightest neutrino mass larger than 10 meV. With a conservative background index of 10$$^{-4}$$ $_{}^{-4}$ cts$$/($$ $/($keV$$\cdot $$ $·$kg$$\cdot $$ $·$yr$$)$$ $)$, 240 kg isotope mass, 5 keV FWHM energy resolution at 3 MeV and 10 live-years of data taking, CUPID will have a 90% C.L. half-life exclusion sensitivity of$$1.8\cdot 10^{27}$$ $1.8·{10}^{27}$ yr, corresponding to an effective Majorana neutrino mass ($$m_{\beta \beta }$$ $m_{\beta \beta }$) sensitivity of 9–15 meV, and a$$3\sigma $$ $3\sigma$discovery sensitivity of$$1\cdot 10^{27}$$ $1·{10}^{27}$ yr, corresponding to an$$m_{\beta \beta }$$ $m_{\beta \beta }$range of 12–21 meV. 

   more » « less
4. Generative models for simulation of KamLAND-Zen

   https://doi.org/10.1140/epjc/s10052-024-12980-7  

   Fu, Zhenghao; Grant, Christopher; Krawiec, Dominika M; Li, Aobo; Winslow, Lindley A (June 2024, The European Physical Journal C)

   Abstract The next generation of searches for neutrinoless double beta decay ($$0 \nu \beta \beta $$ $0\nu \beta \beta$) are poised to answer deep questions on the nature of neutrinos and the source of the Universe’s matter–antimatter asymmetry. They will be looking for event rates of less than one event per ton of instrumented isotope per year. To claim discovery, accurate and efficient simulations of detector events that mimic$$0 \nu \beta \beta $$ $0\nu \beta \beta$is critical. Traditional Monte Carlo (MC) simulations can be supplemented by machine-learning-based generative models. This work describes the performance of generative models that we designed for monolithic liquid scintillator detectors like KamLAND to produce accurate simulation data without a predefined physics model. We present their current ability to recover low-level features and perform interpolation. In the future, the results of these generative models can be used to improve event classification and background rejection by providing high-quality abundant generated data. 

   more » « less
5. The Transition from Darcy to Nonlinear Flow in Heterogeneous Porous Media: I—Single-Phase Flow

   https://doi.org/10.1007/s11242-024-02070-3  

   Arbabi, Sepehr; Sahimi, Muhammad (March 2024, Transport in Porous Media)

   Martin Blunt (Ed.)

   Abstract Using extensive numerical simulation of the Navier–Stokes equations, we study the transition from the Darcy’s law for slow flow of fluids through a disordered porous medium to the nonlinear flow regime in which the effect of inertia cannot be neglected. The porous medium is represented by two-dimensional slices of a three-dimensional image of a sandstone. We study the problem over wide ranges of porosity and the Reynolds number, as well as two types of boundary conditions, and compute essential features of fluid flow, namely, the strength of the vorticity, the effective permeability of the pore space, the frictional drag, and the relationship between the macroscopic pressure gradient$${\varvec{\nabla }}P$$ $\nabla P$and the fluid velocityv. The results indicate that when the Reynolds number Re is low enough that the Darcy’s law holds, the magnitude$$\omega _z$$ ${\omega }_z$of the vorticity is nearly zero. As Re increases, however, so also does$$\omega _z$$ ${\omega }_z$, and its rise from nearly zero begins at the same Re at which the Darcy’s law breaks down. We also show that a nonlinear relation between the macroscopic pressure gradient and the fluid velocityv, given by,$$-{\varvec{\nabla }}P=(\mu /K_e)\textbf{v}+\beta _n\rho |\textbf{v}|^2\textbf{v}$$ $-\nabla P=(\mu /K_e)v+{\beta }_n\rho {\left|v\right|}^{2}v$, provides accurate representation of the numerical data, where$$\mu$$ $\mu$and$$\rho$$ $\rho$are the fluid’s viscosity and density,$$K_e$$ $K_e$is the effective Darcy permeability in the linear regime, and$$\beta _n$$ ${\beta }_n$is a generalized nonlinear resistance. Theoretical justification for the relation is presented, and its predictions are also compared with those of the Forchheimer’s equation. 

   more » « less