The general approach for the consideration of the magnetoelectric effects in ferroic nanorods is proposed in the framework of the phenomenological theory. The intrinsic surface stress, magneto- and electrostriction as well as piezoelectric and piezomagnetic effects are included into the free energy. The intrinsic surface stress under the curved nanoparticle surface is shown to play an important role in the shift of ferroelectric and ferromagnetic transition temperatures and built-in magnetic and electric fields appearance, which are inversely proportional to the nanorod radius. We consider the case of quadratic and linear magnetoelectric coupling coefficients. The linear coupling coefficient is radius independent, whereas the quadratic ones include terms inversely proportional to the nanorod radius and thus strongly increase with decrease of the radius. The predicted giant relative dielectric tunability in the vicinity of ferromagnetic and ferroelectric phase transition points induced by quadratic magnetoelectric coupling increases by 2-50 times. The quadratic magnetoelectric coupling dramatically changes the phase diagrams of ferroic nanorods when the radius decreases. In particular the second order phase transition may become a first one, the triple point state characterized by continuous set of order parameters appears at zero external electric and magnetic fields and the tricritical points appear under external fields.

The maximum energy of electrons in supernova remnant (SNR) shocks is typically limited by radiative losses, where the synchrotron cooling time equals the acceleration time. The low speed of shocks in a dense medium increases the acceleration time, leading to lower maximum electron energies and fainter X-ray emissions. However, in Kepler's SNR, an enhanced electron acceleration, which proceeds close to the Bohm limit, occurs in the north of its shell, where the shock is slowed by a dense circumstellar medium (CSM). To investigate whether this scenario still holds at smaller scales, we analyzed the temporal evolution of the X-ray synchrotron flux in filamentary structures, using the two deepest Chandra/ACIS X-ray observations, performed in 2006 and 2014. We examined spectra from different filaments, we measured their proper motion and calculated the acceleration to synchrotron time-scale ratios. The interaction with the turbulent and dense northern CSM induces competing effects on electron acceleration: on one hand, turbulence reduces the electron mean free path enhancing the acceleration efficiency, on the other hand, lower shock velocities increase the acceleration time-scale. In most filaments, these effects compensate each other, but in one region the acceleration time-scale exceeds the synchrotron time-scale, resulting in a significant decrease in nonthermal X-ray emission from 2006 to 2014, indicating fading synchrotron emission. Our findings provide a coherent understanding of the different regimes of electron acceleration observed in Kepler's SNR through various diagnostics.

Mg2+ effect on the thermal stability of the double-stranded polynucleotide polyIpolyC (IC) under conditions close to physiological ones (0.1M Na+, pH7) was studied by the differential UV spectroscopy. The initial increase of the ion concentration ([Mg2+]) leads to the increase of the melting temperature (Tm) and to the decrease of the absorption hyperchromicity value that is caused by the helix-coil transition (hmax). Mg2+ interacts to p-electrons of hypoxanthine or cytosine rings (cation-p-interaction). When [Mg2+] reaches a critical value of about 10-4 M, Tm decreases and hmax increase to values close to one observed in the absence of magnesium. It is supposed that at [Mg2+]=[Mg2+]cr IC transits into a new structural state. With [Mg2+>[Mg2+]cr Tm increases again and hmax slowly decreases. Key words: polynucleotides, thermal stability, metal ions.

We recently described a specific type of attractors of two-dimensional discontinuous piecewise linear maps, characterized by two discontinuity lines dividing the phase plane into three partitions, related to economic applications. To our knowledge, this type of attractor, which we call a weird quasiperiodic attractor, has not yet been studied in detail. They have a rather complex geometric structure and other interesting properties that are worth understanding better. To this end, we consider a simpler map that can also possess weird quasiperiodic attractors, namely, a 2D discontinuous piecewise linear map $F$ with a single discontinuity line dividing the phase plane into two partitions, where two different homogeneous linear maps are defined. Map $F$ depends on four parameters -- the traces and determinants of the two Jacobian matrices. In the parameter space of map $F$, we obtain specific regions associated with the existence of weird quasiperiodic attractors; describe some characteristic properties of these attractors; and explain one of the possible mechanisms of their appearance.

$D$-optimal designs originate in statistics literature as an approach for optimal experimental designs. In numerical analysis points and weights resulting from maximal determinants turned out to be useful for quadrature and interpolation. Also recently, two of the present authors and coauthors investigated a connection to the discretization problem for the uniform norm. Here we use this approach of maximizing the determinant of a certain Gramian matrix with respect to points and weights for the construction of tight frames and exact Marcinkiewicz-Zygmund inequalities in $L_2$. We present a direct and constructive approach resulting in a discrete measure with at most $N \leq n^2+1$ atoms, which discretely and accurately subsamples the $L_2$-norm of complex-valued functions contained in a given $n$-dimensional subspace. This approach can as well be used for the reconstruction of functions from general RKHS in $L_2$ where one only has access to the most important eigenfunctions. We verifiably and deterministically construct points and weights for a weighted least squares recovery procedure and pay in the rate of convergence compared to earlier optimal, however probabilistic approaches. The general results apply to the $d$-sphere or multivariate trigonometric polynomials on $\mathbb{T}^d$ spectrally supported on arbitrary finite index sets~$I \subset \mathbb{Z}^d$. They can be discretized using at most $|I|^2-|I|+1$ points and weights. Numerical experiments indicate the sharpness of this result. As a negative result we prove that, in general, it is not possible to control the number of points in a reconstructing lattice rule only in the cardinality $|I|$ without additional condition on the structure of $I$. We support our findings with numerical experiments.

General approach for consideration of primary ferroic (ferroelectric, ferromagnetic, ferroelastic) nanoparticles phase transitions was proposed in phenomenological theory framework. The surface stress, order parameter gradient, striction as well as depolarization and demagnetization effects were included into the free energy. The strong intrinsic surface stress under the curved nanoparticle surface was shown to play the important role in the shift of transition temperature (if any) up to the appearance of new ordered phase absent in the bulk ferroic. The approximate analytical expression for the size-induced ferroelectric transition temperature dependence on cylindrical or spherical nanoparticle sizes, polarization gradient coefficient, correlation radius, intrinsic surface stress and electrostriction coefficient was derived. It was shown that the transition temperature of nanoparticle could be higher than the one of the bulk material. The best conditions of ferroelectric properties conservation and enhancement in nanowires correspond to the radius 5-50nm and compressive surface stress. Under the favorable conditions size effects (spatial confinement) induces ferroelectric phase in incipient ferroelectrics nanowires and nanospheres. The prediction of size-induced ferroelectricity in KTaO3 nanorods with radius less then 5-20 nm at room temperatures could be important for the next step of device miniaturization based on 3D nanostructures.

A system of two cubic reaction-diffusion equations for two independent gene frequencies arising in population dynamics is studied. Depending on values of coefficients, all possible Lie and $Q$-conditional (nonclassical) symmetries are identified. A wide range of new exact solutions is constructed, including those expressible in terms of a Lambert function and not obtainable by Lie symmetries. An example of a new real-world application of the system is discussed. A general algorithm for finding Q-conditional symmetries of nonlinear evolution systems of the most general form is presented in a useful form for other researchers.

Two-dimensional van der Waals magnets show strong interconnection between their electrical, magnetic, and structural properties. Here we reveal the emergence of a luminescent transition upon crossing the N\'eel transition temperature of CrPS$_4$, a layered antiferromagnetic semiconductor. This luminescent transition occurs above the lowest absorption level. We attribute the optical transitions to excited states of the t$_{\rm 2g}$ orbitals of the Cr$^{3+}$ ions, which are influenced by the distortion of the octahedral crystal field. Specifically, we find at the crossing of the N\'eel temperature changes the distortion from an anti-polar to polar arrangement, thereby not only activating an additional luminescent pathway but also inducing a significant in-plane static dipole moment detected by a marked enhancement in the intensity of the second harmonic generation. Our findings suggest the presence of a multiferroic state in CrPS$_4$ below the N\'eel temperature.

Piecewise smooth systems are intensively studied today in many application areas, such as economics, finance, engineering, biology, and ecology. In this work, we consider a class of one-dimensional piecewise linear discontinuous maps with a finite number of partitions and functions sharing the same real fixed point. We show that the dynamics of this class of maps can be analyzed using the well-known piecewise linear circle map and prove that their bounded behavior, unrelated to the fixed point, may consist of either nonhyperbolic cycles or quasiperiodic orbits densely filling certain segments, with possible coexistence. A corresponding model describing the price dynamics of a financial market serves as an illustrative example. While simulated model dynamics may be mistaken for chaotic behavior, our results demonstrate that they are quasiperiodic.

In this work, we consider a class of $n$-dimensional, $n\geq2$, piecewise linear discontinuous maps that can exhibit a new type of attractor, called a weird quasiperiodic attractor. While the dynamics associated with these attractors may appear chaotic, we prove that chaos cannot occur. The considered class of $n$-dimensional maps allows for any finite number of partitions, separated by various types of discontinuity sets. The key characteristic, beyond discontinuity, is that all functions defining the map have the same real fixed point. These maps cannot have hyperbolic cycles other than the fixed point itself. We consider the two-dimensional case in detail. We prove that in nongeneric cases, the restriction, or the first return, of the map to a segment of straight line is reducible to a piecewise linear circle map. The generic attractor, different from the fixed point, is a weird quasiperiodic attractor, which may coexist with other attractors or attracting sets. We illustrate the existence of these attractors through numerous examples, using functions with different types of Jacobian matrices, as well as with different types of discontinuity sets. In some cases, we describe possible mechanisms leading to the appearance of these attractors. We also give examples in the three-dimensional space. Several properties of this new type of attractor remain open for further investigation.

Supernova (SN) 1987A provides a unique window into the aftermath of a massive stellar explosion, offering key insights into the ejecta's morphology, composition, explosion mechanism, progenitor system, and circumstellar medium (CSM) interaction. We investigate large-scale ejecta asymmetries in SN 1987A. By comparing the simulations with JWST observations and making predictions for XRISM, we aim to refine our understanding of the explosion mechanism and the remnant's evolution. We performed 3D MHD simulations that trace the evolution of SN 1987A from the SN to the SNR, extending our predictions up to 5000 years into the future and considering the Ni-bubble effects. The simulation results are compared with JWST observations and used to predict XRISM spectra, to evaluate the accuracy of the modeled ejecta structure. Our simulations reproduce the large-scale Fe-rich ejecta morphology seen by JWST, revealing two clumps suggestive of a bipolar explosion. Ni-bubble effects in the first year boost Fe-rich ejecta expansion and their interaction with the reverse shock. However, discrepancies with JWST observations in clump velocities and spatial distribution suggest stronger explosion asymmetries than modeled. Since 2021, our models predict that shocked ejecta have contributed increasingly to X-ray emission, now rivaling shocked CSM and soon dominating as the latter fades. Future XRISM observations will trace the evolution of these ejecta structures, refining constraints on explosion geometry. Early remnant asymmetries from CSM interaction may persist for at least 100 years. Our results underscore the role of asymmetric core-collapse mechanisms in shaping SN 1987A's ejecta and constraining its explosion geometry. Future studies should explore more extreme asymmetries, in neutrino-driven core collapse or magneto-rotational SN models, to identify the origin of its bipolar Fe-rich structure.

We investigate the thermodynamic properties of an interacting Bose gas with a condensate within the energy-functional formulation of the Hartree-Fock-Bogoliubov approach. For a contact interaction, we derive a self-consistent solution to the HFB equations that intrinsically eliminates divergence. This solution characterizes the equilibrium state featuring a condensate of correlated pairs of particles. We analyze the temperature dependence of key thermodynamic quantities such as condensate density, chemical potential, entropy, pressure, specific heat capacity at constant volume, and isothermal compressibility and compare them with predictions from the Popov approximation. Our results reveal a first-order phase transition between the normal state and the degenerate state, accompanied by an increased transition temperature relative to the ideal Bose gas. Analysis of the compressibility indicates that a pure pair condensate is unstable, and the stable equilibrium corresponds to a mixture of single-particle and pair condensates.

Context. Deriving the mass and large-scale asymmetries of radioactive isotopes offers valuable insights into the complex phases of a supernova explosion. Important examples are $^{56}$Ni, with its decay products $^{56}$Co and $^{56}$Fe, and $^{44}$Ti, which are studied through their X-rays emission lines and provide a powerful diagnostic tool to probe the explosive nucleosynthesis processes in the inner layers of the exploding star. Aims. In this framework, SN 1987A provides a privileged laboratory being the youngest supernova remnant from which the mass of Ti has been estimated. However, some tension exists in determining the initial mass of $^{44}$Ti. Previous analysis, relying on \textit{NuSTAR} and \textit{INTEGRAL} data, report $M_{44} = (1.5 \pm 0.3) \times 10^{-4}$ $M_\odot$ and $M_{44}=(3.1 \pm 0.8) \times 10^{-4} M_\odot$, respectively. In this paper we estimate the initial mass of $^{44}$Ti via its decay product, the $^{44}$Sc emission line at 4.09 keV, using \textit{Chandra} observations. Methods. We perform multi-epoch spectral analysis focusing on the inner part of the remnant, to minimize the contamination from the X-ray emission stemming from the shocked plasma. As a result, we provide the detection of $^{44}$Sc emission line in the central part of SN 1987A with a $\sim$99.7\% (3 $\sigma$) significance. Results. The simultaneous fit of the spectra extracted from observations between 2016 and 2021 provides a line flux of $6.8^{+2.2}_{-2.3}\times 10^{-7}$ photons s$^{-1}$ cm$^{-2}$ corresponding to a $^{44}$Ti mass $M_{44}=(1.6\pm0.5) \times 10^{-4} M_\odot$ (errors at the $90\%$ confidence level). The results obtained with our spectral analysis seem to align with those derived with NuSTAR.

T Coronae Borealis (T CrB) is a symbiotic recurrent nova with eruptions in 1866 and 1946. Mounting evidence suggests an imminent outburst, offering a rare opportunity to observe a nearby nova in detail. We constrain the circumbinary medium (CBM) by modeling inter-eruption radio observations and simulate the hydrodynamic evolution of the upcoming outburst to predict its X-ray signatures, focusing on the roles of the red giant companion, accretion disk, and equatorial density enhancement (EDE). We model thermal radio emission from a CBM composed of a spherical wind and a torus-like EDE to estimate its density. We then perform 3D hydrodynamic simulations of the nova outburst, varying explosion energy, ejecta mass, and CBM configuration. From these, we synthesize X-ray light curves and spectra as they would appear to XMM-Newton and XRISM. The CBM in T CrB is significantly less dense than in other symbiotic novae, with a mass-loss rate of $\dot{M} \approx 4 \times 10^{-9}$ M$_{\odot}$ yr$^{-1}$ for a 10 km s$^{-1}$ wind. Despite the low-density EDE, the blast is collimated along the poles by the accretion disk and EDE, producing a bipolar shock. The red giant partially shields the ejecta, forming a bow shock and hot wake. X-ray evolution proceeds through three phases: an early phase (first few hours) dominated by shocked disk material; an intermediate phase ($\sim 1$ week-1 month) driven by reverse-shocked ejecta; and a late phase dominated by shocked EDE. Soft X-rays trace shocked ejecta, hard X-rays arise from shocked ambient gas, and synthetic spectra show asymmetric, blueshifted lines due to absorption by expanding ejecta. The X-ray evolution resembles that of RS Oph and V745 Sco, with a peak luminosity of $L_\mathrm{X} \approx 10^{36}$ erg s$^{-1}$, but features a more prolonged soft X-ray phase, reflecting the lower CBM density and distinct ejecta-environment interaction.

By using surface brightness maps of Tycho's supernova remnant (SNR) in radio and X-rays, along with the properties of thermal and synchrotron emission, we have derived the post-shock density and magnetic field strength distributions over the projection of this remnant. Our analysis reveals a density gradient oriented towards the north-west, while the magnetic field strength gradient aligns with the Galactic plane, pointing eastward. Additionally, utilizing this magnetic field map, we have derived the spatial distributions of the cut-off frequency and maximum energy of electrons in Tycho's SNR. We further comment on the implications of these findings for interpreting the gamma-ray emission from Tycho's SNR.