Distribution Of Critical Points Research Articles

Forecasts for WEAVE-QSO: 3D clustering and connectivity of critical points with Lyman-α tomography

ABSTRACT The upcoming WEAVE-QSO survey will target a high density of quasars over a large area, enabling the reconstruction of the 3D density field through Lyman-α (Ly-α) tomography over unprecedented volumes smoothed on intermediate cosmological scales (≈ 16 Mpc h−1). We produce mocks of the Ly-α forest using Ly-α Mass Association Scheme, and reconstruct the 3D density field between sightlines through Wiener filtering in a configuration compatible with the future WEAVE-QSO observations. The fidelity of the reconstruction is assessed by measuring one- and two-point statistics from the distribution of critical points in the cosmic web. In addition, initial Lagrangian statistics are predicted from the first principles, and measurements of the connectivity of the cosmic web are performed. The reconstruction captures well the expected features in the auto- and cross-correlations of the critical points. This remains true after a realistic noise is added to the synthetic spectra, even though sparsity of sightlines introduces systematics, especially in the cross-correlations of points with mixed signature. Specifically, the most striking clustering features involving filaments and walls could be measured with up to 4σ of significance with a WEAVE-QSO-like survey. Moreover, the connectivity of each peak identified in the reconstructed field is globally consistent with its counterpart in the original field, indicating that the reconstruction preserves the geometry of the density field not only statistically, but also locally. Hence, the critical points’ relative positions within the tomographic reconstruction could be used as standard rulers for dark energy by WEAVE-QSO and similar surveys.

Synthesis, structural properties and potent bioactivities supported by molecular docking and DFT studies of new hydrazones derived from 5-chloroisatin and 2-thiophenecarboxaldehyde

New hydrazones were synthesized by employing a convergent synthetic methodology involving condensation of N-alkyl 5-chloroisatins with hydrazone derived from 2-thiophenecarboxaldehyde. The synthesized compounds were fully characterized using UV/Vis., Infrared, 1H and 13C NMR spectroscopies as well as single crystal X-rays diffraction analysis. Bader's theory of ‘atoms in molecules’ confirmed the existence of all nonbonding interactions. Connectivity between isomers of synthesized compounds was characterized by the distribution of critical points, isatin surfaces, and bond paths. The presence of electrostatic potential on oxygen and hydrogen atoms was evaluated by means of MEP calculations, which showed that the oxygen atom acts as nucleophilic center for electrophilic hydrogen atom. Compound 6 exhibited potent anti-oxidant potential (DPPH, ABTS, NBT) with IC50 values of 46 ± 0.72 μM/mL. These compounds were also screened for in vitro cholinesterases inhibition, where compound 6 presented effective inhibition against AChE and BChE in comparison to the standard drugs; allanzanthane and galanthamine in a dose reliant mode. The IC50 values of both compounds (6 and 7) against AChE were determined to be 20.21 ± 0.06 & 16.22 ± 0.18 μM and against BChE, as 28.01 ± 0.01 & 20.11 ± 0.12 μM, respectively. Molecular docking studies supported these results and helped to establish structure activity relationship. The results reported in this manuscript are anticipated to be beneficial for understanding the solid-state architecture of the X-ray structures of new hydrazone conjugates of 5-chloroisatin & 2-thiophenecarboxaldehyde. On the other hand their intriguing biological potentials can create quest among scientific community to further analyze such molecules for drug discovery purposes.

Fatigue residual life estimation of jib structure based on improved v‐SVR algorithm obtaining equivalent load spectrum

AbstractFatigue tests of truck crane jib structure have great difficulty, long testing cycle, and high cost. Therefore, with the portfolio strategy for “collection, prediction, measurement and simulation” being introduced, an improved support vector regression (v‐SVR) algorithm is proposed to predict the equivalent load spectrum based on the small measured load spectrum and the fatigue residual life evaluation model is built. First, the v‐SVR algorithm corrected in kernel function, decision function, and parameter optimization is utilized to acquire the equivalent load spectrum. Second, the distribution of critical points is determined by the case‐based reasoning technique. The simulation model of first main stress‐time histories for critical points is established, and the two‐dimensional stress spectrum is obtained by the rain‐flow counting method. Finally, the fatigue residual life of jib structure is estimated by the Forman formula. Taking ZLJ5551JQZ110V truck crane jib structure as an example, the effectiveness of the above method is validated.

VISUALIZATION OF FLOW THROUGH THE TURBINE BLADE CASCADE WITH OPTIMIZED STREAMWISE BOUNDARY LAYER FENCE

The present study focuses on the study of critical points formed on the surfaces of a turbine cascade with and without streamwise endwall fences with the help of flow visualization. A fence whose height varies linearly from the leading edge to the trailing edge and is located in the middle of the flow passage produces the least Coefficient of Secondary Kinetic Energy (CSKE) and is the optimum fence. The reduction in CSKE by the optimum fence is 27% compared to the baseline case. The geometry of the fence is new and is reported for the first time. The objective of the fence is to block the passage vortex from crossing the passage and impinging on the suction surface of the blade. A saddle point is formed near the leading edge on the endwall for baseline and optimum fence cases. There is nearly no change in saddle point location. Distribution of critical points on the endwall near the trailing edge of the blade is symmetrical for the baseline case, while no symmetry exists for the optimum fence case. Based on skin friction line patterns, it is clear that the pressure-side leg of the horseshoe vortex is diverted by the optimum fence, and hence, impinged on the suction surface of the blade with reduced intensity. Skin friction lines on the suction surface show that with application of the optimum fence, the spanwise penetration of the passage vortex is reduced by 33%.

Dynamical modeling of viral spread in spatially distributed populations: stochastic origins of oscillations and density dependence

In order to understand the spatio-temporal structure of epidemics beyond that permitted with classical SIR (susceptible-infective-recovered)-type models, a new mathematical model for the spread of a viral disease in a population of spatially distributed hosts is described. The positions of the hosts are randomly generated in a rectangular habitat. Encounters between any pair of individuals are according to a Poisson process with a mean rate that declines exponentially as the distance between them increases. The contact rate allows the mean rates to be set at a certain number of encounters per day on average. The relevant state variables for each individual at any time are given by the solution of a pair of coupled differential equations for the viral load and the quantity of general immune system effectors which reduce the viral load. The parameters describing within-host viral-immune system dynamics are generated randomly to reflect variability across a population. Transmission is assumed to depend on the viral loads in donors and occurs with a probability p trans . The initial conditions are such that one randomly chosen individual carries a randomly chosen amount of the virus, whereas the rest of the population is uninfected. Simulations reveal local or whole-population responses. Whole-population disease spread may be in the form of isolated or multiple occurrences, the latter often being approximately periodic. The mechanisms of this oscillatory behaviour are analyzed in terms of several parameters and the distribution of critical points in the host dynamical systems. Increased contact rate, increased probability of transmission and decreased threshold for viral transmission, decreased immune strength and increased viral growth rate all increase the probability of multiple outbreaks and the distribution of the critical points also plays a role.

The multiplicity of the Lyashko-Looijenga mapping on the discriminant strata of even and odd polynomials

Hurwitz reduced this to a combinatorial problem and conjectured the solution for rational functions with one degenerate critical level (proven combinatorially in 1996 by Goulden and Jackson [?] and Strehl [?], and from the singularity point of view in 1997 by Goryunov and Lando [?]). Lando and Zvonkine [?] solved the problem for non-Morse polynomials with fixed degenerate critical levels and we obtain a solution for even and odd polynomials. Our main tool, as it is in [?], is the Lyashko-Looijenga, LL, mapping which associates to a polynomial of degree n the unordered set of its n − 1 critical values. In particular we calculate the number of topological types of even and odd polynomials in a given discriminant stratum. The discriminant of a family of polynomials is the set of polynomials with multiple roots. Within this set lie various strata determined by the distribution of critical points on fixed critical levels. We call these strata discriminant strata and we define them using passports . The number of topological types that we are seeking is closely related to the degree of the LL mapping on the discriminant strata.

Critical Points Near the Focus of Systems of Different Fresnel Number

Abstract Lommel's theory of light focusing is here extended to an examination of the distribution of critical points near the focus of a uniform, converging, monochromatic spherical wave diffracted at a circular aperture with a range of different values of the Fresnel number. It is found that all the off-axis intensity maxima and minima lie on the straight lines that pass through the centres of the dark rings of the Airy pattern. Moreover, these intensity extrema are located near those geometrical wavefronts which have radii that are integral multiples of 2π, as measured in a dimensionless coordinate system. These results not only provide us with a comprehensive knowledge of the structure of a focused field, but also with a method of constructing a sketch map of the three-dimensional intensity distribution near the focus of systems of different Fresnel number.

Least-Squares Estimation, Linear Programming, and Momentum: A Geometric Parametrization of Local Minima

In contrast to estimation by ordinary least squares, estimation by total least squares has much less favourable properties as far as existence and uniqueness of local minima is concerned. Indeed, as elementary examples show, and contrary to intuition gleaned from the Gauss-Markov theorem for ordinary least squares, for certain data sets this problem can have nonisolated local minima and local maxima. Using Morse theory and the Lie theory of coadjoint orbits, we show that, despite this apparent degeneracy, the distribution of critical points of least-squares problems is remarkably well behaved. For arbitrary data, the least-squares function is perfect in the sense of the Morse-Bott theory. In particular, the set of local minima always forms a connected manifold while there exists a unique minimum value.

Experimental evidence for the residual stress interpretation of transition rounding in CoBr2.5H2O

High-resolution specific heat measurements have shown repeatedly that real magnetic crystals lose their divergent character in the immediate neighbourhood of TN. White et al (1974) and others have accounted for the observed rounding with a distribution of critical points, attributable to residual stresses that vary throughout the sample. Bartis has opposed this view with a model containing a distinct intermediate stage in the ordering process. New experimental evidence is presented in favour of the residual stress interpretation by means of a noise analysis of continuous heating measurements on CoBr2.6H2O. A large component of low-frequency noise is found near TN that is attributed to the sample studied and not the apparatus or method of analysis. It is argued that the graininess of the transition temperatures of a stress-induced ensemble of domains has been detected.