Angular structure factor of the hexatic-B liquid crystals: bridging theory and experiment

We found experimentally that angular profiles of the in-plane X-ray scattering in the hexatic-B phase are well approximated by a convolution of the Gaussian and Lorentzian functions. This result is supported by the known theoretical considerations.

Electrophilic cyclization of propargyl thioethers of 3-methyl(phenyl)-2-(prop-2-yn-1-ylthio)-7-(trifluoromethyl)quinazolin-4(3H)-ones by tellurium tetrahalides

The paper presents the results of the study of the process of electrophilic intramolecular cyclization of 3-methyl(phenyl)-2-(prop-2-yn-1-ylthio)-7-(trifluoromethyl)quinazolin-4(3H)-ones by tellurium tetrahalides. 3-Methyl(phenyl)-2-(prop-2-yn-1-ylthio)-7-(trifluoromethyl)quinazolin-4(3H)-ones were prepared by the alkylation of the corresponding thions with propargyl bromide in an alkaline alcohol medium. It is found that the interaction of propargyl thioethers of 3-substituted 2-thioxo-7-(trifluoromethyl)-2,3-dihydroquinazolin-4(1H)-ones with tellurium tetrahalides, which were obtained in situ from tellurium dioxide and six equivalents of corresponding concentrated hydrohalic acid, leads to the formation of halides of angular 4-methyl(phenyl)-5-oxo-1-((trihalotellanyl)methylidene)-8-(trifluoromethyl)-1,2,4,5-tetrahydrothiazolo[3,2-a]quinazolin-10-iums. The most optimal conditions for the tellurium-induced electrophilic heterocyclization of propargyl thioethers with tellurium terahalides are the use of glacial acetic acid as a solvent and stirring of the reaction mixture at room temperature for 24 hours. It is found that the electrophilic cyclization of 3-methyl(phenyl)-2-(prop-2-yn-1-ylthio)-7-(trifluoromethyl)quinazolin-4(3H)-ones by tellurium tetrahalides occurs stereoselectively with the formation of one configurational isomer. The influence of the nature of halogen in the electrophilic reagent and the substituent in position 3 of quinazoline is examined and it is found that these factors do not affect the regioselectivity of the electrophilic intramolecular cyclization process. As a result of the conducted study, potentially biologically active salts of tellurofunctionalized thiazolinoquinazolines of angular structure were received.

Analytical study of light ray trajectories in Kerr spacetime in the presence of an inhomogeneous anisotropic plasma

We calculate the exact solutions to the equations of motion that govern the light ray trajectories as they travel in a Kerr black hole’s exterior that is considered to be filled with an inhomogeneous and anisotropic plasmic medium. This is approached by characterizing the plasma through conceiving a radial and an angular structure function, which are let to be constant. The description of the motion is carried out by using the Hamilton–Jacobi method, that allows defining two effective potentials, characterizing the evolution of the polar coordinates. The elliptic integrals of motion are then solved analytically, and the evolution of coordinates is expressed in terms of the Mino time. This way, the three-dimensional demonstrations of the light ray trajectories are given respectively.

Learning to isolate muons

Distinguishing between prompt muons produced in heavy boson decay and muons produced in association with heavy-flavor jet production is an important task in analysis of collider physics data. We explore whether there is information available in calorimeter deposits that is not captured by the standard approach of isolation cones. We find that convolutional networks and particle-flow networks accessing the calorimeter cells surpass the performance of isolation cones, suggesting that the radial energy distribution and the angular structure of the calorimeter deposits surrounding the muon contain unused discrimination power. We assemble a small set of high-level observables which summarize the calorimeter information and close the performance gap with networks which analyze the calorimeter cells directly. These observables are theoretically well-defined and can be studied with collider data.

Mapping the gravitational-wave sky with LISA: A bayesian spherical harmonic approach

The millihertz gravitational-wave frequency band is expected to contain a rich symphony of signals with sources ranging from galactic white dwarf binaries to extreme mass ratio inspirals. Many of these gravitational-wave signals will not be individually resolvable. Instead, they will incoherently add to produce stochastic gravitational-wave confusion noise whose frequency content will be governed by the dynamics of the sources. The angular structure of the power of the confusion noise will be modulated by the distribution of the sources across the sky. Measurement of this structure can yield important information about the distribution of sources on galactic and extra-galactic scales, their astrophysics and their evolution over cosmic timescales. Moreover, since the confusion noise is part of the noise budget of LISA, mapping it will also be essential for studying resolvable signals. In this paper, we present a Bayesian algorithm to probe the angular distribution of the stochastic gravitational-wave confusion noise with LISA using a spherical harmonic basis. We develop a technique based on Clebsch-Gordan coefficients to mathematically constrain the spherical harmonics to yield a non-negative distribution, making them optimal for expanding the gravitational-wave power and amenable to Bayesian inference. We demonstrate these techniques using a series of simulations and analyses, including recovery of simulated distributed and localized sources of gravitational-wave power. We also apply this method to map the gravitational-wave foreground from galactic white-dwarfs using a simplified model of the galactic white dwarf distribution.

Genetic Optimization of a Manipulator: Comparison between Straight, Rounded, and Curved Mechanism Links

There are several ubiquitous kinematic structures that are used in industrial robots, with the most prominent being a six-axis angular structure. However, researchers are experimenting with task-based mechanism synthesis that could provide higher efficiency with custom optimized manipulators. Many studies have focused on finding the most efficient optimization algorithm for task-based robot manipulators. These manipulators, however, are usually optimized from simple modular joints and links, without exploring more elaborate modules. Here, we show that link modules defined by small numbers of parameters have better performance than more complicated ones. We compare four different manipulator link types, namely basic predefined links with fixed dimensions, straight links that can be optimized for different lengths, rounded links, and links with a curvature defined by a Hermite spline. Manipulators are then built from these modules using a genetic algorithm and are optimized for three different tasks. The results demonstrate that manipulators built from simple links not only converge faster, which is expected given the fewer optimized parameters, but also converge on lower cost values.

Long-term evolution of directional spectra of wind waves modelled by DNS and kinetic equations, and comparison with airborne measurements

<p>We consider the evolution of directional spectra of waves generated by constant and changing wind, modelling it by direct numerical simulation (DNS), based on the Zakharov equation. Results are compared with numerical simulations performed with the Hasselmann kinetic equation and the generalised kinetic equation, and with airborne measurements of waves generated by offshore wind, collected during the GOTEX experiment off the coast of Mexico. Modelling is performed with wind measured during the experiment, and the initial conditions are taken as the observed spectrum at the moment when wind waves prevail over swell after the initial part of the evolution.</p><p>Directional spreading is characterised by the second moment of the normalised angular distribution function, taken at selected wavenumbers relative to the spectral peak. We show that for scales longer than the spectral peak the angular spread predicted by the DNS is close to that predicted by both kinetic equations, but it underestimates the corresponding measured value, apparently due to the presence of swell. For the spectral peak and shorter waves, the DNS shows good agreement with the data. A notable feature is the steady growth of angular width at the spectral peak with time/fetch, in contrast to nearly constant width in the kinetic equations modelling. Dependence of angular width on wavenumber is shown to be much weaker than predicted by the kinetic equations. A more detailed consideration of the angular structure at the spectral peak at large fetches shows that the kinetic equations predict an angular distribution with a well-defined peak at the central angle, while the DNS reproduces the observed angular structure, with a flat peak over a range of angles.</p><p>In order to study in detail the differences between the predictions of the DNS and the kinetic equations modelling under idealised conditions, we also perform numerical simulations for the case of constant wind forcing. As in the previous case of forcing by real wind, the most striking difference between the kinetic equations and the DNS is the steady growth with time of angular width at the spectral peak, which is demonstrated by the DNS, but is not present in the modelling with the kinetic equations. We show that while the kinetic theory, both in the case of the Hasselmann equation and the generalised kinetic equation, predicts a relatively simple shape of the spectral peak, the DNS shows a more complicated structure, with a flat top and dependence of the peak position on angle. We discuss the approximations employed in the derivation of the kinetic theory and the possible causes of the found differences of directional structure.</p>

Overconstrained models of time delay lenses redux: how the angular tail wags the radial dog

The two properties of the radial mass distribution of a gravitational lens that are well constrained by Einstein rings are the Einstein radius RE and ξ2 = REα″(RE)/(1 − κE), where α″(RE) and κE are the second derivative of the deflection profile and the convergence at RE, respectively. However, if there is a tight mathematical relationship between the radial mass profile and the angular structure, as is true of ellipsoids, an Einstein ring can appear to strongly distinguish radial mass distributions with the same ξ2. This problem is beautifully illustrated by the ellipsoidal models in Millon et al. When using Einstein rings to constrain the radial mass distribution, the angular structure of the models must contain all the degrees of freedom expected in nature (e.g. external shear, different ellipticities for the stars and the dark matter, modest deviations from elliptical structure, modest twists of the axes, modest ellipticity gradients, etc.) that work to decouple the radial and angular structures of the gravity. Models of Einstein rings with too few angular degrees of freedom will lead to strongly biased likelihood distinctions between radial mass distributions and very precise but inaccurate estimates of H0 based on gravitational lens time delays.

Interferometric Processing of Acoustic Information by Using Extended Antennas in Dispersing Media

The theory of interferometric processing of acoustic information by using extended antennas in media with frequency dispersion is presented. The dependence between the two-dimensional spectral density of the two-fold Fourier transform of the interference pattern formed by a moving noise source and the aperture and angular structure of the received field is analyzed. The gain factor, directivity characteristic, and noise immunity of processing are estimated. Depending between the input signal/noise ratio on the antenna element and the maximal range of the noise source is obtained. This maximal range allows stable detection and estimation of direction, radial velocity, range and depth are close to real values. Numerical simulation results are presented and discussed.

Gamma-ray burst jet propagation, development of angular structure, and the luminosity function

The fate and observable properties of gamma-ray burst jets crucially depend on their interaction with the progenitor material that surrounds the central engine. We present a semi-analytical model of this interaction (which builds upon several previous analytical and numerical works) aimed at predicting the angular distribution of jet and cocoon energy and Lorentz factor after breakout given the properties of the ambient material and of the jet at launch. Using this model, we constructed synthetic populations of structured jets, assuming either a collapsar (for long gamma-ray bursts – LGRBs) or a binary neutron star merger (for short gamma-ray bursts – SGRBs) as progenitor. We assumed all progenitors to be identical, and we allowed little variability in the jet properties at launch: our populations therefore feature a quasi-universal structure. These populations are able to reproduce the main features of the observed LGRB and SGRB luminosity functions, although several uncertainties and caveats have yet to be addressed. We make our simulated populations publicly available.