Singular Locus Research Articles

Generalized, Three-Dimensional Wind Tunnel Wall Correction Using Nonlinear Least-Squares Optimization

A novel three-dimensional technique for correcting wind tunnel measurements for wall interference has been developed. The flow around the test body and its wake is approximated as a series of inviscid singularities, while the wind tunnel walls and model support are approximated using a panel method. A nonlinear least-squares approach with trust-region reflective optimization is then used to obtain the strength and locations of singularities together with the domain boundary panel strengths by fitting to measured wall pressures. The technique is demonstrated using computational fluid dynamics for the test case of a well-documented slender delta wing body with high blockage and validated against both experiments and legacy data. The nonlinear least-squares wall correction method is shown to demonstrate a significant improvement in wall corrections compared to the classical two-variable technique.

New mapping algorithm SHIM (SVD, Hilbert Identifying Method) for the extraction of phase singularities and spiral waves in cardiac arrhythmias

Background and ObjectiveAtrial fibrillation (AF) is the most prevalent cardiac arrhythmia worldwide. The effectiveness of AF ablation is restricted primarily by inaccuracies in the voltage-map videos (VMVs) acquired through multielectrode catheters. We introduce an innovative algorithm improving map quality and pinpointing the precise locations of action potential singularities. MethodsThe methodology relies on three key operations: singular value decomposition (SVD), Hilbert transform, and identifying the ridge of singularities SHIM (SVD, Hilbert, Identifying Method). To check its feasibility, this approach was used to analyze record sources from two distinct origins: a) cultures of cardiac cells, and b) real-world atrial fibrillation (AF) measurements. Efficacy is exemplified through four illustrative cases, two involving cultures of cardiac cells exposing action potential spirals, and two clinical cases involving basket catheter voltage-map videos. Resolution goodness is measured by a new method of the ratio of the peak’s height divided by the average width at half maximum or the width of the ridge-of-peaks cross-section. ResultsIn the first sample, the driving rotor became evident only following the SVD procedure stage, and its stable center became more pronounced after the H and I stages. In the case of spiral splitting, SHIM extracted all the individual tiny spiral centers. In the VMVs obtained from the basket catheters, even when the image sharpness was suboptimal, distinct singularity ridges were easily discernible with peak intensities larger than 1. ConclusionThe cumulative impact of the three stages of our analysis suggests that our novel method may excel in identifying problematic sources more effectively than previously utilized systems.

Types of connected components of the singular locus of the moduli space of compact Riemann surfaces

AbstractIn 2012 G. Bartolini and M. Izquierdo showed that all equisymmetric strata of Broughton’s stratification, corresponding to the actions of groups of order 2 and 3 on Riemann surfaces of genus g are contained in the same connected component $$\mathcal {C}_g^{2,3}$$ C g 2 , 3 of the singular locus $$\mathcal {S}_g$$ S g . The other components that were known to the literature were those composed of points of certain single strata. This motivated the question of whether the singular locus can contain connected components different from $$\mathcal {C}_g^{2,3}$$ C g 2 , 3 and being the union of at least two strata. The existence of such components was proved for infinitely many genera by G. Gromadzki and the author. In this paper, we will describe and classify all types of connected components of the singular locus. In particular, we prove that every connected component different than $$\mathcal {C}_g^{2,3}$$ C g 2 , 3 coincides with some Cornalba component, and we give necessary and sufficient conditions for a cyclic action to define such a component.

Singular loci of algebras over ramified discrete valuation rings

AbstractWhen is a field, the classical Jacobian criterion computes the singular locus of an equidimensional, finitely generated ‐algebra as the closed subset of an ideal generated by appropriate minors of the so‐called Jacobian matrix. Recently, Hochster‐Jeffries and Saito have extended this result for algebras over any unramified discrete valuation ring of mixed characteristic via the use of ‐derivations. Motivated by these results, in this paper, we state and prove an analogous Jacobian criterion for algebras over ramified discrete valuation rings of mixed characteristic.

Tumor suppressor miR-317 and lncRNA Peony are expressed from a polycistronic non-coding RNA locus that regulates germline differentiation and testis morphology.

This research focuses on investigating the impact of non-coding RNAs on stem cell biology and differentiation processes. We found that miR-317 plays a role in germline stem cell progeny differentiation. miR-317 and its neighbor, the lncRNA Peony, originate and are co-expressed from a singular polycistronic non-coding RNA locus. Alternative polyadenylation is implicated in regulation of their differential expression. While the increased expression of the lncRNA Peony results in the disruption of the muscle sheath covering the testis, the absence of miR-317 leads to the emergence of germline tumors in young flies. The deficiency of miR-317 increases Notch signaling activity in the somatic cyst cells, which drives germline tumorigenesis. Germline tumors also arise from upregulation of several predicted targets of miR-317, among which are regulators of the Notch pathway. This implicates miR-317 as a novel tumor suppressor that modulates Notch signaling strength.

Lines on $$K3$$–Quartics Via Triangular Sets

AbstractWe prove the sharp upper bound of at most 52 lines on a complex $$K3$$ K 3 –surface of degree 4 with a non-empty singular locus. We also classify the configurations of more than 48 lines on smooth complex quartics.

On mediation: ethnographic and statistical analysis of an Indian helpline for reporting "Sound Abuse in Public Spaces"

This paper focuses on the Indian program "National Initiative for Safe Sound", a non-profit group based in Kerala. One of NISS's main actions is running a telephone helpline for residents "to report sound abuse in public spaces." It provides the population with its first opportunity to speak out about the disturbing noises they endure, and is an invitation to nurture sonic citizenship via intermediation with noise-makers. Unlike governmental services that gather data in pre-established categories, the helpline foregrounds the fundamentally sociological aspects of sound annoyance. As part of its telephone exchange, the helpline maintains a register recording some personal information, details on the context of the noise, and the indicated sound sources. Ethnographic and statistical analyses are combined to precisely identify the social and geographical origin of callers, categories of sound sources, and the nature of the conflicts that emerge from the experience of unwanted sound. This paper describes local singularities and remarkable differences with comparable, earlier studies based on "official" noise complaints in other countries. We favored an anthropological approach, offering an initial analysis of the profile of people calling in with complaints, and their highly conflictual relationship with the sounds entering the public space from places of worship.

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We analyse the backreacted geometry corresponding to a stack of M5-branes wrapped on a spindle, with a view towards precision tests of the dual N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 superconformal field theory. We carefully study the singular loci of the uplifted geometry and show that these correspond to C3/Zn conical singularities. Therefore, these solutions present one of the first explicit realisations of honest locally N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 preserving punctures in class S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{S} $$\\end{document}. Additionally we study the symmetries and anomalies of the dual field theory through anomaly inflow and compute a variety of holographic observables including dimensions of BPS operators. This work paves the way for advancements in the study and identification of the precise dual field theories.

Analytic continuations and numerical evaluation of the Appell F1, F3, Lauricella [formula omitted] and Lauricella-Saran [formula omitted] and their application to Feynman integrals

We present our investigation of the study of two variable hypergeometric series, namely Appell F1 and F3 series, and obtain a comprehensive list of its analytic continuations enough to cover the whole real (x,y) plane, except on their singular loci. We also derive analytic continuations of their 3-variable generalisation, the Lauricella FD(3) series and the Lauricella-Saran FS(3) series, leveraging the analytic continuations of F1 and F3, which ensures that the whole real (x,y,z) space is covered, except on the singular loci of these functions. While these studies are motivated by the frequent occurrence of these multivariable hypergeometric functions in Feynman integral evaluation, they can also be used whenever they appear in other branches of mathematical physics. To facilitate their practical use, for analytical and numerical purposes, we provide four packages: AppellF1.wl, AppellF3.wl, LauricellaFD.wl, and LauricellaSaranFS.wl in Mathematica. These packages are applicable for generic as well as non-generic values of parameters, keeping in mind their utilities in the evaluation of the Feynman integrals. We explicitly present various physical applications of these packages in the context of Feynman integral evaluation and compare the results using other packages such as FIESTA. Upon applying the appropriate conventions for numerical evaluation, we find that the results obtained from our packages are consistent. Various Mathematica notebooks demonstrating different numerical results are also provided along with this paper.Program summaryProgram title: AppellF1.wl, AppellF3.wl, LauricellaFD.wl, LauricellaSaranFS.wl.CPC Library link to program files:https://doi.org/10.17632/ycz85rgzxj.1Developer's repository link: https://github.com/souvik5151/Appell_Lauricella_Saran_functionsLicensing provisions: GNU General Public License v.3.0.Programming language: Wolfram MathematicaNature of problem: To find and develop a numerically consistent implementation of the analytic continuations of various two and three-variable hypergeometric functions, namely Appell F1, F3, Lauricella FD(3) and Lauricella-Saran FS(3) that typically appear in the evaluation of Feynman integrals.Solution method: Use the method of Olsson to find the analytic continuation of these functions and to implement these analytic continuations, following appropriate convention, in Mathematica for consistent numerical evaluation. For the values of the Pochhammer parameters corresponding to the non-generic cases, a proper limiting procedure is implemented internally.

Kinematic analysis and experimental validation of a tripod parallel continuum manipulator

A tripod is a classical lower mobility parallel manipulator with three degrees of freedom. The usual geometrical constraints enforce a type of motion with two rotations on a horizontal plane and a translational motion in a vertical direction. These devices are applicable where a task requires a precise orientational motion. Nevertheless, some parasitic motions occur on the constrained degrees of freedom. Parallel Continuum Manipulators are devices where some elements have been replaced by slender rods whose deformation is source of mobility, allowing the elimination of some of the kinematic joints. This type of closed-loop compliant mechanisms have some features that can be useful in certain applications, e.g., the deformed state introduces a certain preload that avoids backslash, they have an inherent compliance that can be useful in some delicate tasks, and a certain control on wrench applied can be obtained. In this article, the comprehensive kinetostatic analysis of a tripod-type parallel continuum manipulator, 3 P ¯ FS , is explained and compared with that of its rigid counterpart 3 P ¯ RS . Workspace and singularity locus is obtained, positioning accuracy and wrench generation are evaluated experimentally.

Early-time resonances in the three-dimensional wall-bounded axisymmetric Euler and related equations

We investigate the complex-time analytic structure of solutions of the three-dimensional (3D)-axisymmetric, wall-bounded, incompressible Euler equations, by starting with the initial data proposed in Luo and Hou [“Potentially singular solutions of the 3D axisymmetric Euler equations,” Proc. Natl. Acad. Sci. U. S. A. 111(36), 12968–12973 (2014)], to study a possible finite-time singularity. We use our pseudospectral Fourier–Chebyshev method [Kolluru et al., “Insights from a pseudospectral study of a potentially singular solution of the three-dimensional axisymmetric incompressible Euler equation,” Phys. Rev. E 105(6), 065107 (2022)], with quadruple-precision arithmetic, to compute the time-Taylor-series coefficients of the flow fields, up to a high order. We show that the resulting approximations display early-time resonances; the initial spatial location of these structures is different from that for the tygers, which we have obtained in Kolluru et al. [“Insights from a pseudospectral study of a potentially singular solution of the three-dimensional axisymmetric incompressible Euler equation,” Phys. Rev. E 105(6), 065107 (2022)]. We then perform asymptotic analysis of the Taylor-series coefficients, by using generalized ratio methods, to extract the location and nature of the convergence-limiting singularities and demonstrate that these singularities are distributed around the origin, in the complex-t2 plane, along two curves that resemble the shape of an eye. We obtain similar results for the one-dimensional (1D) wall-approximation (of the full 3D-axisymmetric Euler equation) called the 1D Hou–Luo model, for which we use Fourier-pseudospectral methods to compute the time-Taylor-series coefficients of the flow fields. Our work examines the link between tygers, in Galerkin-truncated pseudospectral studies, and early-time resonances, in truncated time-Taylor expansions of solutions of partial differential equations, such as those we consider.

Spatio-temporal analysis of Permian-Cretaceous magmatic activities in the Tengchong block: Implications for tectono-magmatic evolution

Understanding the tectono-magmatic evolution history of the Tengchong block is crucial for elucidating the formation of the Eastern Tethys tectonic domain. However, the correlation and evolution of the Tengchong block with the Sibumasu and Lhasa blocks is controversial during the Permian and Cretaceous. This study explores the information contained within magmatic rocks using big data and spatio-temporal analysis, providing quantitative constraints for the discussion of the tectono-magmatic evolution of the Tengchong block. To more accurately assess true magma activities and reduce errors caused by preservation and sampling processes, we utilized local singularity analysis to obtain the singularity index time-series. Correlation analysis of zircon ages and εHf(t) (correlation coefficient ≥ 0.5) values indicates that the Tengchong block is more similar to the Sibumasu block. Results from time-lagged cross-correlation analysis indicate that the Tengchong block and Sibumasu block exhibit a shorter lag in magmatic activities (3 Myr). Wavelet analysis reveals similar periods of collision-related magmatic activities (57 Myr and 43 Myr). Integrating evidence from paleontology and ophiolite belts, we propose that the Tengchong block co-evolved more closely with the Sibumasu block than with the Lhasa block, suggesting similar tectonic processes during the Early Permian to Early Cretaceous. Approximately 250–236 Ma, in the western Tengchong block, partial melting of the lower crust occurs due to crustal thickening. Around 219–213 Ma and 198–180 Ma, after the Tengchong block collided with the Eurasian continent, the subduction of the Meso-Tethys Ocean commenced. Around 130–111 Ma, the overall tectonic feature was a scissor-like closure of the Meso-Tethys Ocean from north to south.

Geochemical anomaly separation based on geology, geostatistics, compositional data and local singularity analyses: A case study from the kuh panj copper deposit, Iran

This study combines geochemical anomaly separation with geostatistical approaches and compositional data analysis. To have a reasonable model for abnormal areas, suggesting the optimal drilling coordinates, one needs to consider some effective geological controllers on the mineralization such as lithology, alteration, and tectonic processes. The lithogeochemical samples at 608 locations were processed from the copper porphyry mineralization area of Kuh Panj, Iran, to illustrate the proposed approach. The heterogeneity of rock type domains was detected using contact analysis. Based on this, plurigaussian simulation made it possible to model the uneconomic dykes of the area. Copper-molybdenum grades and filler as geochemical components were transformed into multivariate normal data using isometric logarithmic ratio-flow anamorphosis. Hierarchical rock type-grade simulation reproduced the grade behavior at hard rock type boundaries. Selection of a dense and regular simulation grid minimized the smoothing effect caused by interpolation of the singularity index values. Finally, unsupervised machine learning identified the anomaly zone by clustering the results of the singularity analysis. Validation using drilling data and the geological map shows that the anomaly separation, considering the geological conditions and the compositional nature of the geochemical data, can provide a reliable model of the geochemical anomalies in the Kuh Panj deposit.

Dissecting polytopes: Landau singularities and asymptotic expansions in 2 → 2 scattering

Parametric representations of Feynman integrals have a key property: many, frequently all, of the Landau singularities appear as endpoint divergences. This leads to a geometric interpretation of the singularities as faces of Newton polytopes, which facilitates algorithmic evaluation by sector decomposition and asymptotic expansion by the method of regions. Here we identify cases where some singularities appear instead as pinches in parametric space for general kinematics, and we then extend the applicability of sector decomposition and the method of regions algorithms to such integrals, by dissecting the Newton polytope on the singular locus. We focus on 2 → 2 massless scattering, where we show that pinches in parameter space occur starting from three loops in particular nonplanar graphs due to cancellation between terms of opposite sign in the second Symanzik polynomial. While the affected integrals cannot be evaluated by standard sector decomposition, we show how they can be computed by first linearising the graph polynomial and then splitting the integration domain at the singularity, so as to turn it into an endpoint divergence. Furthermore, we demonstrate that obtaining the correct asymptotic expansion of such integrals by the method of regions requires the introduction of new regions, which can be systematically identified as facets of the dissected polytope. In certain instances, these hidden regions exclusively govern the leading power behaviour of the integral. In momentum space, we find that in the on-shell expansion for wide-angle scattering the new regions are characterised by having two or more connected hard subgraphs, while in the Regge limit they are characterised by Glauber modes.

Topological Structures of Energy Flow: Poynting Vector Skyrmions.

Topological properties of energy flow of light are fundamentally interesting and may introduce novel physical phenomena associated with directional light scattering and optical trapping. In this Letter, skyrmionlike structures formed by Poynting vectors are unveiled in the focal region of two pairs of counterpropagating cylindrical vector vortex beams in free space. The appearance of local phase singularities, and the distinct traveling and standing wave modes of different field components passing through the focal spot lead to a Néel-Bloch-Néel transition of Poynting vector skyrmion textures along the light propagating direction. By shaping the wave front of the incident beams with patterned amplitudes, the topological invariant of the Poynting vector skyrmions can be further tuned in a prospective area. This work expands the family of optical skyrmions and holds great potential in energy flow associated applications.

Beam Dynamic Equations for Predictive Modeling of Semicircular Canal Pathologies

This short paper presents a general strategy devoted to an original analytical approach of looped 1.5D equations. It considers particular properties of rod/beam equations for wave and structural modal representation. Specific boundary conditions introduce local singularities representing discontinuities and inversions. The process presented in the paper links this kind of original analysis with possible models of the physiological and pathological dynamic behavior of solid-fluid interaction in inner-ear elements such as the anterior and superior semicircular canals. Thus, these models propose a robust representation of these elements, offering observation/control perspectives for diagnostics and cure.

Remarks on geometric engineering, symmetry TFTs and anomalies

Geometric engineering is a collection of tools developed to establish dictionaries between local singularities in string theory and (supersymmetric) quantum fields. Extended operators and defects, as well as their higher quantum numbers captured by topological symmetries, can be encoded within geometric engineering dictionaries. In this paper we revisit and clarify aspects of these techniques, with special emphasis on ’t Hooft anomalies, interpreted from the SymTFT perspective as obstructions to the existence of Neumann boundary conditions. These obstructions to gauging higher symmetries are captured via higher link correlators for the SymTFT on spheres. In this work, we give the geometric engineering counterpart of this construction in terms of higher links of topological membranes. We provide a consistency check in the context of 5D SCFTs with anomalous 1-form symmetries, where we give two independent derivations of the anomaly in terms of higher links, one purely field theoretical and the other purely geometrical. Along the way, we also recover the construction of non-invertible duality defects in 4D N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM from a geometric engineering perspective.

Necessary and sufficient conditions for Kolmogorov’s flux laws on T2 and T3

Necessary and sufficient conditions for the third order Kolmogorov universal scaling flux laws are derived for the stochastically forced incompressible Navier Stokes equations on the torus in 2D and 3D. This paper rigorously generalises the result of (Bedrossian 2019 Commun. Math. Phys. 367 1045–75) to functions which are heavy-tailed in Fourier space or have local finite time singularities in the inviscid limit. In other words, we have rigorously derived the existence of the well known physical relationships, the direct and inverse cascades. Furthermore we show that the rate of the direct cascade is proportional to the amount of energy ‘escaping to infinity’ in spectral space as well as a measure of the total singularities within the solution. Similarly, an inverse cascade is proportional to the amount of energy that moves towards the k = 0 Fourier mode in the invisicid limit.

Steady Boussinesq convection: Parametric analyticity and computation

AbstractSteady solutions to the Navier–Stokes equations with internal temperature forcing are considered. The equations are solved in two dimensions using the Boussinesq approximation to couple temperature and density fluctuations. A perturbative Stokes expansion is used to prove that that steady flow variables are parametrically analytic in the size of the forcing. The Stokes expansion is complemented with analytic continuation, via functional Padé approximation. The zeros of the denominator polynomials in the Padé approximants are observed to agree with a numerical prediction for the location of singularities of the steady flow solutions. The Padé representations not only prove to be good approximations to the true flow solutions for moderate intensity forcing, but are also used to initialize a Newton solver to compute large amplitude solutions. The composite procedure is used to compute steady flow solutions with forcing several orders of magnitude larger than the fixed‐point method developed in previous work.

Partition five-axis surface machining of CFRP laminate structures considering fiber orientation

ABSTRACT Carbon Fiber Reinforced Polymer (CFRP) is commonly employed in advanced industries, acclaimed for their outstanding mechanical properties. The inherent anisotropy of CFRP necessitates careful consideration of the Fiber Cutting Angle (FCA) to achieve optimal surface quality during machining, a challenge that intensifies with curved surface components due to the continuous variability of FCA. In the machining of CFRP curved surfaces, the presence of local singularity precipitates abrupt changes in tool orientation, adversely affecting surface integrity and machining efficiency. To solve this problem, this study proposed a toolpath partitioning method specifically designed for the machining of CFRP curved surfaces, aiming to mitigate the effects of local singularity. Additionally, a novel tool positioning strategy accounting for dual fiber orientations in the machining of bidirectional CFRP curved surfaces was developed. The practical applicability of these methodologies was assessed through the manufacturing of an internal fixation plate via 5-axis machining of bidirectional CFRP laminates. Comparative microscopic observations and surface profile assessments demonstrate a marked improvement in surface quality relative to traditional 3-axis machining, alongside a 25% reduction in machining time compared to 5-axis machining processes absent the partitioning method.