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Hochschild Cohomology of Isotropic Grassmannians
Anton Fonarev
https://arxiv.org/abs/2506.09727 https://arxiv.org/pdf/2506.09727

Hochschild Cohomology of Isotropic Grassmannians
We prove that nonspecial isotropic Grassmannians (that is, all isotropic Grassmannians which are neither (co)adjoint nor (co)minuscule, except $\mathsf{OGr}(n-1, 2n+1)$ for $n\geq 4$), are not Hochschild global, thus establishing a conjecture by P. Belmans and M. Smirnov. As a corollary, we conclude that Bott vanishing fails for all these varieties.

Thermodynamically consistent modelling and simulation of the moving contact line problem in non-isothermal compressible two-phase flows
Junkai Wang, Qiaolin He
https://arxiv.org/abs/2508.05711

Thermodynamically consistent modelling and simulation of the moving contact line problem in non-isothermal compressible two-phase flows
According to the dynamic van der Waals theory, we propose a thermodynamically consistent model for non-isothermal compressible two-phase flows with contact line motion. In this model, fluid temperature is treated as a primary variable, characterized by the proposed temperature equation instead of being obtained from intermediate variables such as total energy density, internal energy density and entropy density. The hydrodynamic boundary conditions, which represent a generalization of the gener…

Pseudoperiodic Spherical Boundary Conditions: Efficient And Isotropic 3D Particle Simulations Without Lattice Artifacts
Manuel Dedola, Ludovico Cademartiri
https://arxiv.org/abs/2507.07888

Pseudoperiodic Spherical Boundary Conditions: Efficient And Isotropic 3D Particle Simulations Without Lattice Artifacts
Periodic Boundary Conditions (PBC) introduce well-known lattice artifacts. We present a novel Pseudoperiodic Spherical Boundary Condition (SBC) that is perfectly isotropic. Through detailed comparative simulations, we demonstrate that SBC eliminates the structural and dynamic anisotropy inherent to PBC. For the crowded systems where these artifacts are most prominent, our method is also computationally more efficient than standard Minimum Image Convention implementations. This establishes SBC a…

Decorrelation phenomena in mixed moments for orthogonal families of $L$-Functions and their applications: automorphic periods, Fourier coefficients of half-integral weight forms, and isotropy subgroups of Tate--Shafarevich groups
Shenghao Hua
https://arxiv.org/abs/2508.07734

Decorrelation phenomena in mixed moments for orthogonal families of $L$-Functions and their applications: automorphic periods, Fourier coefficients of half-integral weight forms, and isotropy subgroups of Tate--Shafarevich groups
The Keating--Snaith conjecture for orthogonal families may be viewed as analogous to a Gaussian distribution with a negative mean, and the possibility that mixed moments resemble a composition of independent moments, these two insights were combined and applied in Lester and Radziwiłł's proof of quantum unique ergodicity for half-integral weight automorphic forms, via Soundararajan's method under the Generalized Riemann Hypothesis (GRH). This observation also yields a crucial and nontrivial s…

Three-Dimensional Isotropic STED Nanoscopy using a Single Objective
Renlong Zhang, Xiaoyu Weng, Haoxian Zhou, Luwei Wang, Fangrui Lin, Wei Yan, Xiumin Gao, Bin Yu, Danying Lin, Liwei Liu, Chenshuang Zhang, Kayla K. Green, Ewoud R. E. Schmidt, Songlin Zhuang, Junle Qu
https://arxiv.org/abs/2507.06718

Three-Dimensional Isotropic STED Nanoscopy using a Single Objective
Accurate three-dimensional (3D) imaging requires an isotropic point spread function (PSF). However, the inherent missing aperture of a single objective lens results in an elongated, cigar-like PSF, which has rendered isotropic resolution in fluorescence microscopy seemingly insurmountable without a 4π configuration for decades. To address this long-standing challenge, we introduce ISO-STED (Isotropic Single-Objective STED) Nanoscopy, a novel approach that employs a single objective lens and a …

Cherenkov radiation in isotropic chiral matter: the space-frequency domain
R. Mart\'inez von Dossow, Eduardo Barredo-Alamilla, Maxim A. Gorlach, Luis F. Urrutia
https://arxiv.org/abs/2507.06369

Cherenkov radiation in isotropic chiral matter: the space-frequency domain
The electromagnetic response of isotropic chiral matter, as described by Carroll-Field-Jackiw electrodynamics, arises in distinct physical contexts ranging from condensed matter systems to Lorentz-violating extensions of high-energy physics. Here, we derive exact expressions for the circularly polarized electromagnetic fields that contribute independently to Cherenkov radiation in isotropic chiral matter. Each spectral energy distribution is gauge-invariant and positive, yielding radiation that…

Reconciling Inflation with Hubble Anisotropies
Brett McInnes
https://arxiv.org/abs/2508.06796 https://arxiv.org/pdf/2508.06796

Reconciling Inflation with Hubble Anisotropies
There have been persistent suggestions, based on several diverse data sets, that the cosmic expansion is not exactly isotropic. It is not easy to develop a coherent theoretical account of such a ``Hubble anisotropy'', for, in standard General Relativity, intuition suggests that it contradicts the predictions of the very successful Inflationary hypothesis. We put this intuition on a firm basis, by proving that if we [a] make use of an Inflationary theory in which Inflation isotropises spatial ge…

CMB line-of-sight integrators for nearly-isotropic cosmological models
Jo\~ao G. Vicente, Thiago S. Pereira, Cyril Pitrou
https://arxiv.org/abs/2506.07786 …

CMB line-of-sight integrators for nearly-isotropic cosmological models
Homogeneous and nearly-isotropic cosmological models are natural extensions of standard Friedmann cosmologies. Constraining their features is crucial, as any detection of their properties would impact our understanding of inflation and the cosmological principle. Since these models evolve as a set of non-interacting scalar, vector, and tensor modes on top of homogeneous and isotropic spacetimes, their imprints on cosmological observables, particularly the CMB, can be obtained using standard lin…

Deformation of ellipsoidal droplets in homogeneous and isotropic turbulence
Fabio Guglietta, Diego Taglienti, Mauro Sbragaglia
https://arxiv.org/abs/2506.09692

Deformation of ellipsoidal droplets in homogeneous and isotropic turbulence
We study the statistics of deformation of neutrally buoyant droplets in homogeneous isotropic turbulence (HIT), wherein the characteristic droplet size $R$ is smaller than the characteristic Kolmogorov scale $η$ of the turbulent flow. We systematically focus on the characterization of droplet statistics obtained with various phenomenological ellipsoidal models (EMs) -- assuming that the droplet preserves the ellipsoidal shape at all times - with the droplet moving as a passive tracer in the tu…