Several Pulsar Timing Array (PTA) collaborations have recently reported the evidence for a stochastic gravitational-wave background (SGWB), which can unveil the formation of primordial seeds of inhomogeneities in the early universe. With the SGWB parameters inferred from PTAs data, we can make a prediction of the seeds for early galaxy formation from the domain walls in the axion-like particles (ALPs) field distribution. This also naturally provides a solution to the observation of high redshifts by the James Webb Space Telescope. The predicted photon coupling of the ALP is within the reach of future experimental searches.

Turbulence is indispensable to redistribute nutrients for all life forms larger than microbial, on land and in the ocean. Yet, the development of deep-sea turbulence has not been studied in three dimensions (3D). As a disproportionate laboratory, an array of nearly 3000 high-resolution temperature sensors had been installed for three years on the flat 2500-m deep bottom of the Mediterranean Sea. The time series from the half-cubic hectometer 3D mooring-array allows for the creation of unique movies of deep-sea water motions. Although temperature differences are typically 0.001degrC, variable convection-turbulence is observed as expected from geothermal heating through the flat seafloor. During about 40% of the time, an additional turbulence, 3 times stronger in magnitude, is observed from slantwise advected warmer waters to pass in turbulent clouds. Besides turbulent clouds and seafloor heating, movies also reveal weakly turbulent interfacial-wave breakdown that commonly occurs in the open ocean far away from boundaries.

Primordial Black Holes (PBH) could dominate in the early universe and, evaporating before Big bang Nucleosynthesis, can provide new freeze in mechanism of dark matter (DM) production. The proposed scenario is considered for two possible mechanisms of PBH formation and the corresponding continuous PBH mass spectra so that the effect of non-single PBH mass spectrum is taken into account in the results of PBH evaporation, by which PBH dominance in the early universe ends. We specify the conditions under which the proposed scenario can explain production of dark matter in very early Universe.

The phase diagram and the order parameters of the exactly solvable quantum 1D model are analysed. The model in its spin representation is the dimerized XY spin chain in the presence of uniform and staggered transverse fields. In the fermionic representation this model is the dimerized non-interacting Kitaev chain with a modulated chemical potential. The model has a rich phase diagram which contains phases with local and non-local (string) orders. We have calculated within the same systematic framework the local order parameters (spontaneous magnetization) and the non-local string order parameters, along with the topological winding numbers for all domains of the phase diagram. The topologically nontrivial phase is shown to have a peculiar oscillating string order with the wavenumber $q=\pi/2$, awaiting for its experimental confirmation.

We explore how inflationary features shape the early stages of cosmic structure formation. Using the transfer function formalism, we trace the evolution of primordial perturbations, showing how causal physics and oscillatory signatures from inflation influence the matter power spectrum. The variance of smoothed density fields is then applied to model the collapse of overdense regions and predict dark matter halo abundances through the Press-Schechter framework. Extending to the baryonic sector, we analyze primordial gas collapse in minihalos, emphasizing molecular hydrogen cooling and the thermochemical pathways leading to Population III star formation. Finally, we examine primordial black holes as potential seeds for early galaxies, connecting their accretion-driven growth to the stellar masses and disk properties of high-redshift systems. Our results indicate that oscillatory features from inflation can leave measurable imprints on halo abundances and early galaxy properties, providing a testable link between high-energy physics and astrophysical observations with JWST

In this paper, the physical approach to model external (air-induced) passive intermodulation (PIM) is presented in a frequency-division duplexing (FDD) multiple-input multiple-output (MIMO) system with an arbitrary number of transceiver chains. The external PIM is a special case of intermodulation distortion (IMD), mainly generated by metallic objects possessing nonlinear properties ("rusty bolt" effect). Typically, such sources are located in the near-field or transition region of the antenna array. PIM products may fall into the receiver band of the FDD system, negatively affecting the uplink signal. In contrast to other works, this one directly simulates the physical external PIM. The system includes models of a point-source external PIM, a finite-length dipole antenna, a MIMO antenna array, and a baseband multicarrier 5G NR OFDM signal. The Channel coefficients method for multi-PIM-source compensation is replicated to verify the proposed external PIM modelling approach. Simulation results of artificially generated PIM cancellation show similar performance as real-life experiments. Therefore, the proposed approach allows testing PIM compensation algorithms on large systems with many antennas and arbitrary array structures. This eliminates the need for experiments with real hardware at the development stage of the PIM cancellation algorithm.

Classical Landau theory considers structural phase transitions and crystallization as a condensation of several critical density waves whose wave vectors are symmetrically equivalent. Analyzing the simplest nonequilibrium Landau potentials obtained for decagonal and dodecagonal cases, we derive constraints on the phases of the critical waves and deduce two pairs of flat tilings that are the simplest from the viewpoint of our theory. Each pair corresponds to the same irreducible interference pattern: the vertices of the first and second tilings are located at its minima and maxima, respectively. The first decagonal pair consists of the Penrose P1 tiling and the Tie and Navette one. The second pair is represented by dodecagonal tiling of squares, triangles, and shields, and previously unidentified one formed by regular dodecagons and identical deformed pentagons. Surprisingly, the proposed method for finding extrema of interference patterns provides a straightforward way to generate the Penrose tiling P3 and its more complicated analogues with 2n-fold symmetries. Within Landau theory, we discuss the assembly of the square-triangular tiling and its relationship with the dodecagonal tiling that includes shields. Then we develop a nonequilibrium assembly approach that is based on Landau theory and allows us to produce tilings with random phason strain characteristic of quasicrystals. Interestingly, the approach can generate tilings without or with a minimum number of defective tiles. Examples of real systems rationalized within Landau theory are considered as well. Finally, the derivation of other tilings arising from the reducible interference patterns is discussed, and the relative complexity of non-phenomenological interactions required for the assembly of decagonal and dodecagonal structures is analyzed.

Stars form from the gravitational collapse of dense molecular cloud cores. In the protostellar phase, mass accretes from the core onto a protostar, likely through an accretion disk, and it is during this phase that the initial masses of stars and the initial conditions for planet formation are set. Over the past decade, new observational capabilities provided by the Spitzer Space Telescope and Herschel Space Observatory have enabled wide-field surveys of entire star-forming clouds with unprecedented sensitivity, resolution, and infrared wavelength coverage. We review resulting advances in the field, focusing both on the observations themselves and the constraints they place on theoretical models of star formation and protostellar evolution. We also emphasize open questions and outline new directions needed to further advance the field.

We study the problem of selling an asset near its ultimate maximum in the minimax setting. The regret-based notion of a perfect stopping time is introduced. A perfect stopping time is uniquely characterized by its optimality properties and has the following form: one should sell the asset if its price deviates from the running maximum by a certain time-dependent quantity. The related selling rule improves any earlier one and cannot be improved by further delay. The results, which are applicable to a quite general price model, are illustrated by several examples.

Classical Landau theory considers structural phase transitions and crystallization as a condensation of several critical density waves whose wave vectors are symmetrically equivalent. Analyzing the simplest nonequilibrium Landau potentials obtained for decagonal and dodecagonal cases, we derive constraints on the phases of the critical waves and deduce two pairs of flat tilings that are the simplest from the viewpoint of our theory. Each pair corresponds to the same irreducible interference pattern: the vertices of the first and second tilings are located at its minima and maxima, respectively. The first decagonal pair consists of the Penrose P1 tiling and the Tie and Navette one. The second pair is represented by dodecagonal tiling of squares, triangles, and shields, and previously unidentified one formed by regular dodecagons and identical deformed pentagons. Surprisingly, the proposed method for finding extrema of interference patterns provides a straightforward way to generate the Penrose tiling P3 and its more complicated analogues with 2n-fold symmetries. Within Landau theory, we discuss the assembly of the square-triangular tiling and its relationship with the dodecagonal tiling that includes shields. Then we develop a nonequilibrium assembly approach that is based on Landau theory and allows us to produce tilings with random phason strain characteristic of quasicrystals. Interestingly, the approach can generate tilings without or with a minimum number of defective tiles. Examples of real systems rationalized within Landau theory are considered as well. Finally, the derivation of other tilings arising from the reducible interference patterns is discussed, and the relative complexity of non-phenomenological interactions required for the assembly of decagonal and dodecagonal structures is analyzed.

We introduce the first open-source model for translation between the vulnerable Chechen language and Russian, and the dataset collected to train and evaluate it. We explore fine-tuning capabilities for including a new language into a large language model system for multilingual translation NLLB-200. The BLEU / ChrF++ scores for our model are 8.34 / 34.69 and 20.89 / 44.55 for translation from Russian to Chechen and reverse direction, respectively. The release of the translation models is accompanied by the distribution of parallel words, phrases and sentences corpora and multilingual sentence encoder adapted to the Chechen language.

The article presents the results of analysis of the spatial arrangement of the wells on the unique slab from Srubna burial of kurgan field Tavriya-1 (Rostov region, Russia) by astronomical methods. At the slab revealed two interrelated groups of wells, one of which - in the form of a circle, is proposed to interpret how analemmatic sundial, and second group, consisting of disparate wells, as auxiliary astronomical markers of rising luminaries directions, to correct the position of the gnomon. Simultaneous location of both groups of wells on the same slab is a possible indication of one of the stages of development of the design features analemmatic sundial - setting movable gnomon and technology of measuring time with it. It may point to local origin, as the very idea of analemmatic sundial as well technology measurement of time with them. The article also describes the model analemmatic sundial, hour marks which in many cases coincide with the wells arranged in a circle, particularly in a working range from 6 to 18 hours. In the study proposed a method which can identify moments of solstices and equinoxes in ancient times with the help of the gnomon of analemmatic sundial and mobile gnomons, installed in wells belonging to the second group. The opportunity of use analemmatic sundial as moondial in a full moon night. Slab with two groups of wells is proposed to consider, as the oldest astronomical instrument discovered in the Northern Black Sea coast, which allowed to observe the apparent motion of the Sun and the Moon and allowed measure the time during the day, using analemmatic sundial and at night during the full Moon - with the help of moondial. Keywords: analemmatic sundial, moondial, srubna burial, slab, wells, cupped depressions, gnomon, model, technology, astronomical methods, archaeoastronomy.

The traditional paradigm of viscosity-dominated evolution of protoplanetary discs has been recently challenged by magnetized disc winds. However, distinguishing wind-driven and turbulence-driven accretion through observations has been difficult. In this study, we present a novel approach to identifying their separate contribution to angular momentum transport by studying the gap and ring morphology of planet-forming discs in the ALMA continuum. We model the gap-opening process of planets in discs with both viscous evolution and wind-driven accretion by 2D multi-fluid hydrodynamical simulations. Our results show that gap-opening planets in wind-driven accreting discs generate characteristic substructures that differ from those in purely viscous discs. Specifically, we demonstrate that discs, where wind-driven accretion dominates the production of substructures, exhibit significant asymmetries. Based on the diverse outputs of mock images in the ALMA continuum, we roughly divide the planet-induced features into four regimes (moderate-viscosity dominated, moderate-wind dominated, strong-wind dominated, inviscid). The classification of these regimes sets up a potential method to constrain the strength of magnetized disc wind and viscosity based on the observed gap and ring morphology. We discuss the asymmetry feature in our mock images and its potential manifestation in ALMA observations.

Hole-doped cuprates demonstrate partially coexisting pseudogap, charge density wave (CDW) and superconducting phases. Recently their common nature was supposed due to similar doping dependence of their critical temperatures. In the CDW phase, a large frozen deformation of strongly ionic lattice is observed. Like for a single carrier in a highly polarizable lattice, for multiple carriers in it the choice between delocalized states of all the carriers and autolocalized states of some part of them is determined by minimum of free energy of interacting carrier and phonon fields. Applying variational approach, we calculate free energy of a two-liquid system of carriers with cuprates-like dispersion comprising liquid of autolocalized carriers (large polarons and bipolarons) and Fermi liquid of delocalized carriers. Comparing it with the free energy of pure Fermi liquid and calculating (with standard methods of Bose-liquid theory) a temperature of superfluid transition in the large-bipolaron liquid we identify areas with presence of pseudogap (caused by impact of (bi)polaron potential on delocalized quasiparticles), CDW and superconductivity in a phase diagram. They are in the same places as in hole-doped cuprates, and similarly to cuprates the shape of the calculated phase diagram is stable with respect to wide-range change of the system characteristics. Like in cuprates, the calculated temperature of the superconducting transition increases with the number of conducting planes in the unit cell, the calculated superfluid density decreases with doping at overdoping, and the bipolaron density (together with bipolaronic plasmon energy) saturates at optimal doping. The results obtained allow us to discuss ways of increasing the temperature of the superfluid transition in large-bipolaron liquid and open a possibility of studying the current-carrying state and properties of bipolaron condensate.

We prove a variant of the central limit theorem (CLT) for a sequence of i.i.d. random variables $\xi_j$, perturbed by a stochastic sequence of linear transformations $A_j$, representing the model uncertainty. The limit, corresponding to a "worst" sequence $A_j$, is expressed in terms of the viscosity solution of the $G$-heat equation. In the context of the CLT under sublinear expectations this nonlinear parabolic equation appeared previously in the papers of S.Peng. Our proof is based on the technique of half-relaxed limits from the theory of approximation schemes for fully nonlinear partial differential equations.

We present the latest development of the disk gravitational instability and fragmentation model, originally introduced by us to explain episodic accretion bursts in the early stages of star formation. Using our numerical hydrodynamics model with improved disk thermal balance and star-disk interaction, we computed the evolution of protostellar disks formed from the gravitational collapse of prestellar cores. In agreement with our previous studies, we find that cores of higher initial mass and angular momentum produce disks that are more favorable to gravitational instability and fragmentation, while a higher background irradiation and magnetic fields moderate the disk tendency to fragment. The protostellar accretion in our models is time-variable, thanks to the nonlinear interaction between different spiral modes in the gravitationally unstable disk, and can undergo episodic bursts when fragments migrate onto the star owing to the gravitational interaction with other fragments or spiral arms. Most bursts occur in the partly embedded Class I phase, with a smaller fraction taking place in the deeply embedded Class 0 phase and a few possible bursts in the optically visible Class II phase. The average burst duration and mean luminosity are found to be in good agreement with those inferred from observations of FU-Orionis-type eruptions. The model predicts the existence of two types of bursts: the isolated ones, showing well-defined luminosity peaks separated with prolonged periods (~ 10^4 yr) of quiescent accretion, and clustered ones, demonstrating several bursts occurring one after another during just a few hundred years. Finally, we estimate that 40\%--70\% of the star-forming cores can display bursts after forming a star-disk system.