Structure constants of $ \newcommand{\n}{\mathcal{N}} \newcommand{\shsl} \boldsymbol {\mathfrak{shs}[\boldsymbol \lambda]} \shsl\, $ : the deformed-oscillator point of view

We derive and spell out the structure constants of the $\mathbb{Z}_2$-graded algebra $\mathfrak{shs}[\lambda]\,$ by using deformed-oscillators techniques in $Aq(2;\nu)\,$, the universal enveloping algebra of the Wigner-deformed Heisenberg algebra in 2 dimensions. The use of Weyl ordering of the deformed oscillators is made throughout the paper, via the symbols of the operators and the corresponding associative, non-commutative star product. The deformed oscillator construction was used by Vasiliev in order to construct the higher spin algebras in three spacetime dimensions. We derive an expression for the structure constants of $\mathfrak{shs}[\lambda]\,$ and show that they must obey a recurrence relation as a consequence of the associativity of the star product. We solve this condition and show that the $\mathfrak{hs}[\lambda]\,$ structure constants are given by those postulated by Pope, Romans and Shen for the Lone Star product.

Higher spin gauge theory on fuzzy $S^4_N$

We examine in detail the higher spin fields which arise on the basic fuzzysphere $S^4_N$ in the semi-classical limit. The space of functions can beidentified with functions on classical $S^4$ taking values in a higher spinalgebra associated to $\mathfrak{so}(5)$. We derive an explicit and completeclassification of the scalars and one-forms on the semi-classical limit of$S_N^4$. The resulting kinematics is reminiscent of Vasiliev theory. Yang-Millsmatrix models naturally provide an action formulation for higher spin gaugetheory on $S^4$, with 4 irreducible modes for each spin $s\geq 1$. Wediagonalize the quadratic part of the effective action and exactly evaluate thequadratic part in the spin 2 sector. By identifying the linear perturbation ofthe effective metric, we obtain the exact kinetic term for all gravitoncandidates. At the classical level, matter $T_{\mu\nu}$ leads to threedifferent contributions to the linearized metric: one consistent withlinearized GR, one more rapidly decreasing contribution, and onenon-propagating contribution localized at $T_{\mu\nu}$. The latter is too largeto be physically acceptable, unless there is a significant induced quantumaction. This issue should be resolved on generalized fuzzy spaces.

Model of Environmental Development of the Urbanized Areas: Accounting of Ecological and other Factors

Research of frequency converters energy characteristics of drilling rigs

Savings of reinforcement in concrete continuous beam in calculation with redistribution of moments

Numerical simulation of helical flow in a cylindrical channel

One-pot synthesis of polythiol ligand for highly bright and stable hydrophilic quantum dots toward bioconjugate formation

A Kennicutt-Schmidt relation at molecular cloud scales and beyond

Using N-body/gasdynamic simulations of a Milky Way-like galaxy we analyse aKennicutt-Schmidt relation, $\Sigma_{SFR} \propto \Sigma_{gas}^N$, at differentspatial scales. We simulate synthetic observations in CO lines and UV band. Weadopt the star formation rate defined in two ways: based on free fall collapseof a molecular cloud - $\Sigma_{SFR, cl}$, and calculated by using a UV fluxcalibration - $\Sigma_{SFR, UV}$. We study a KS relation for spatially smoothedmaps with effective spatial resolution from molecular cloud scales to severalhundred parsecs. We find that for spatially and kinematically resolvedmolecular clouds the $\Sigma_{SFR, cl} \propto \Sigma_{\rm gas}^N$ relationfollows the power-law with index $N \approx 1.4$. Using UV flux as SFRcalibrator we confirm a systematic offset between the $\Sigma_{\rm UV}$ and$\Sigma_{\rm gas}$ distributions on scales compared to molecular cloud sizes.Degrading resolution of our simulated maps for surface densities of gas andstar formation rates we establish that there is no relation $\Sigma_{\rm SFR,UV} - \Sigma_{\rm gas}$ below the resolution $\sim 50$ pc. We find a transitionrange around scales $\sim 50-120$ pc, where the power-law index $N$ increasesfrom 0 to 1-1.8 and saturates for scales larger $\sim 120$ pc. A value of theindex saturated depends on a surface gas density threshold and it becomessteeper for higher $\Sigma_{gas}$ threshold. Averaging over scales with size of$>150$ pc the power-law index $N$ equals 1.3-1.4 for surface gas densitythreshold $\sim 5 M_\odot$pc$^{-2}$. At scales $>120$ pc surface SFR densitiesdetermined by using CO data and UV flux, $\Sigma_{\rm SFR, UV}/\Sigma_{\rm SFR,cl}$, demonstrate a discrepancy about a factor of 3. We argue that this may beoriginated from overestimating (constant) values of conversion factor, starformation efficiency or UV calibration used in our analysis.

Evolution of clustered supernovae

We study the merging and evolution of isolated supernovae (SNe) remnants in astellar cluster into a collective superbubble, with the help of 3-Dhydrodynamic simulations. We particularly focus on the transition stage whenthe isolated SNe remnants gradually combine to form a superbubble. We find thatwhen the SN rate is high ($\nu_{\rm sn}\sim 10^{-9}$ pc$^{-3}$ yr$^{-1}$), themerging phase lasts for $\sim 10^4$ yr, for $n=1\hbox{--}10$ cm$^{-3}$, and themerging phase lasts for a longer time ($\sim 0.1$ Myr or more) for lower SNrates ($\nu_{\rm sn}\le 10^{-10}$ pc$^{-3}$ yr$^{-1}$). During this transitionphase, the growing superbubble is filled with dense and cool fragments ofshells and most of the energy is radiated away during this merging process.After passing through the intermediate phase, the superbubble eventuallysettles on to a new power-law wind asymptote that is smaller than estimated ina continuous wind model. This results in a significant (more than {\it severaltimes}) underestimation of the mechanical luminosity needed to feed the bubble.We determine the X-ray and H$\alpha$ surface brightnesses as functions of timefor such merging SNe in a stellar cluster and find that clusters with high SNrate shine predominantly in soft X-rays and H$\alpha$. In particular, a lowvalue of the volume averaged H$\alpha$ to H$\beta$ ratio and its large spreadcan be a good indicator of the transition phase of merging SNe.

Primordial Black Holes as Dark Matter: Constraints From Compact Ultra-Faint Dwarfs

The ground-breaking detections of gravitational waves from black hole mergersby LIGO have rekindled interest in primordial black holes (PBHs) and thepossibility of dark matter being composed of PBHs. It has been suggested thatPBHs of tens of solar masses could serve as dark matter candidates. Recentanalytical studies demonstrated that compact ultra-faint dwarf galaxies canserve as a sensitive test for the PBH dark matter hypothesis, since stars insuch a halo-dominated system would be heated by the more massive PBHs, theirpresent-day distribution can provide strong constraints on PBH mass. In thisstudy, we further explore this scenario with more detailed calculations, usinga combination of dynamical simulations and Bayesian inference methods. Thejoint evolution of stars and PBH dark matter is followed with a Fokker-Planckcode PhaseFlow. We run a large suite of such simulations for different darkmatter parameters, then use a Markov Chain Monte Carlo approach to constrainthe PBH properties with observations of ultra-faint galaxies. We find thattwo-body relaxation between the stars and PBH drives up the stellar core size,and increases the central stellar velocity dispersion. Using the observedhalf-light radius and velocity dispersion of stars in the compact ultra-faintdwarf galaxies as joint constraints, we infer that these dwarfs may have acored dark matter halo with the central density in the range of 1-2$\rm{M_{\odot}/pc^3}$, and that the PBHs may have a mass range of 2-14$\rm{M_{\odot}}$ if they constitute all or a substantial fraction of the darkmatter.