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On the evolution of the mass density profile of dense molecular clouds
S. Donkov, I. Zh. Stefanov, T. V. Veltchev, R. S. Klessen
https://arxiv.org/abs/2506.16854

On the evolution of the mass density profile of dense molecular clouds
We aim to obtain the equations which govern the evolution of the mass density profile of a dense irrotational molecular cloud (MC). Our study is based on the notion of "ensemble of MCs", introduced in our previous work. The MCs are modeled by use of the "ensemble abstract representative member": a spherically symmetric, isotropic and isothermal MC which accretes radially matter from its surroundings. Applying the equations of hydrodynamics to a self-gravitating isothermal spherical gas cloud, w…

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Generalized Eshelby's inclusion and inhomogeneity problems for transient heat transfer
Chunlin Wu, Zhenhua Wei, Huiming Yin
https://arxiv.org/abs/2506.16498

Generalized Eshelby's inclusion and inhomogeneity problems for transient heat transfer
Eshelby's problems have been generalized to arbitrary shape of polygonal, polyhedral, and ellipsoidal inclusions embedded in an infinite isotropic domain under transient heat transfer, and Eshelby's tensors have been analytically derived to evaluate disturbed thermal fields caused by inclusions with a polynomial-form eigen-fields. Transformed coordinates are applied to arbitrarily shaped inclusions for domain integrals of transient fundamental solutions. This formulation is for general transien…

10,000 Resolved Triples from Gaia: Empirical Constraints on Triple Star Populations
Cheyanne Shariat, Kareem El-Badry, Smadar Naoz
https://arxiv.org/abs/2506.16513

10,000 Resolved Triples from Gaia: Empirical Constraints on Triple Star Populations
We present a catalog of $\sim 10,000$ resolved triple star systems within 500 pc of the Sun, constructed using Gaia data. The triples include main-sequence, red giant, and white dwarf components spanning separations of 10 to 50,000 au. A well-characterized selection function allows us to constrain intrinsic demographics of the triple star population. We find that (a) all systems are compatible with being hierarchical and dynamically stable; (b) mutual orbital inclinations are isotropic for wide…

Thin active nematohydrodynamic layers: asymptotic theories and instabilities
Mehrana R. Nejad
https://arxiv.org/abs/2506.16523 https://

Thin active nematohydrodynamic layers: asymptotic theories and instabilities
Starting from a three-dimensional description of an active nematic layer, we employ an asymptotic theory to derive a series of low-dimensional continuum models that capture the coupled dynamics of flat and curved films, including variations in film thickness, shape deformations, internal velocity fields, and the dynamics of orientational order. Using this asymptotic theory, we investigate instabilities driven by activity in both the nematic and isotropic phases for cylindrical and flat films.…

Beyond Blur: A Fluid Perspective on Generative Diffusion Models
Grzegorz Gruszczynski, Michal Jan Wlodarczyk, Jakub J Meixner, Przemyslaw Musialski
https://arxiv.org/abs/2506.16827

Beyond Blur: A Fluid Perspective on Generative Diffusion Models
We propose a novel PDE-driven corruption process for generative image synthesis based on advection-diffusion processes which generalizes existing PDE-based approaches. Our forward pass formulates image corruption via a physically motivated PDE that couples directional advection with isotropic diffusion and Gaussian noise, controlled by dimensionless numbers (Peclet, Fourier). We implement this PDE numerically through a GPU-accelerated custom Lattice Boltzmann solver for fast evaluation. To indu…

Complete systems of solutions, transmutations and Darboux transform for Sturm-Liouville equations in impedance form
V\'ictor A. Vicente-Ben\'itez
https://arxiv.org/abs/2506.16604

Complete systems of solutions, transmutations and Darboux transform for Sturm-Liouville equations in impedance form
We present the construction of a complete system of functions associated with the Sturm-Liouville equation in impedance form on a finite interval $I$, given an impedance function $a\in L^2(I)$. The system, known as the formal powers, is generated through recursive integration of the impedance function $a$ and its reciprocal. We establish the completeness of this system in the space $L^p$ with the weight function $a^2$. Under additional conditions on $a$, we extend the completeness of this compl…

The isotropy of cosmic expansion in the early and late Universe
Alan Junzhe Zhou, Scott Dodelson, Daniel Scolnic
https://arxiv.org/abs/2506.14878 https://

The isotropy of cosmic expansion in the early and late Universe
We test the isotropy of cosmic expansion by combining several probes for the first time, constructing full-sky maps of expansion rate variation using Type Ia supernovae, fundamental plane galaxies, and CMB temperature fluctuations. We find no hint of anisotropy or correlation between early- and late-Universe expansion across all systematic models. The 99% confidence upper limits on expansion rate anisotropy are 0.39% for low-redshift supernovae, 0.95% for high-redshift CMB, and 0.37% when combi…

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A Kaleidoscope of Topological Structures in Dipolar Bose-Einstein Condensates with Weyl-Like Spin-Orbit Coupling in Anharmonic Trap
Yun Liu, Zu-Jian Ying
https://arxiv.org/abs/2506.16734

A Kaleidoscope of Topological Structures in Dipolar Bose-Einstein Condensates with Weyl-Like Spin-Orbit Coupling in Anharmonic Trap
Dipole-dipole interaction (DDI) possesses characteristics different from the conventional isotropic s-wave interaction in Bose-Einstein condensates (BECs), the interplay of DDI with spin-orbit coupling (SOC) and rotation may induce novel quantum properties. We systematically analyze the effects of the DDI, Weyl-like SOC, rotation and trap anharmonicity in the ground state of two-componen BECs. The interplay of these factors leads to a kaleidoscope of quantum states of quantum defects and quantu…