Singular Regions Research Articles

Bouncing unitary cosmology II. Mini-superspace phenomenology

A companion paper provides a proposal for cosmic singularity resolution based upon general features of a bouncing unitary cosmological model in the mini-superspace approximation. This paper analyses novel phenomenology that can be identified within particular solutions of that model. First, we justify our choice of particular solutions based upon a clearly articulated and observationally-motivated principle. Second, we demonstrate that the chosen solutions follow a classical mini-superspace cosmology before smoothly bouncing off the classically singular region. Third, and most significantly, we identify a ‘Rayleigh-scattering’ limit for physically reasonable choices of parameters within which the solutions display effective behaviour that is insensitive to the details of rapidly oscillating Planck-scale physics. This effective physics is found to be compatible with an effective period of cosmic inflation well below the Planck scale. The detailed effective physics of this Rayleigh-scattering limit is provided via: (i) an exact analytical treatment of the model in the de Sitter limit; and (ii) numerical solutions of the full model.

On the Essential Self-Adjointness of Singular Sub-Laplacians

We prove a general essential self-adjointness criterion for sub-Laplacians on complete sub-Riemannian manifolds, defined with respect to singular measures. As a consequence, we show that the intrinsic sub-Laplacian (i.e. defined w.r.t. Popp's measure) is essentially self-adjoint on the equiregular connected components of a sub-Riemannian manifold. This result holds under mild regularity assumptions on the singular region, and when the latter does not contain characteristic points.

Geobotany in a fault in the world’s largest continuous wetland in central South America

The Pantanal is located in the center of South America in a tectonically active sedimentary basin of Quaternary age. Even though the relief is flat and the diversity of the sediments is low, its vegetation cover has high variability resulting from seasonal fluctuations in water levels and the presence of four surrounding biomes. Changes in elevation of less than 1 m influence the length and intensity of floods, powerfully affecting the vegetation. Faults with small vertical displacement can generate abrupt vegetation changes and, consequently, expressive vegetation lineaments. This study characterizes a lineament in the northern Pantanal, considering Land Surface Phenology, estimates of precipitation, and floristic survey. The phenological metrics, obtained from a 15-year time series from the Moderate Resolution Imaging Spectroradiometer processed by TIMESAT software, discriminate evergreen forests in the NW of this lineament from savanna-like physiognomies in the SE region. Plant taxonomic identification shows two distinct regional strata with a clear separation between species adapted to prolonged floods in the NW and typical species of the Cerrado biome, mostly xeromorphic, in the SE. Data from the Tropical Rainfall Measuring Mission complemented the analysis, showing different dependence on local rains on different sides of the lineament. The entire dataset defines this geological structure as a driver of the Pantanal’s plant communities, being a boundary for the extensive establishment of propagules of the Amazon biome. This research, in addition to advancing knowledge of this singular region, which is essential for management studies, can be a stimulus to biological and forest investigations.

Significance Of Slip Line Field Model In Accommodating All Machining Complex Behaviour

Abstract Slip line field theory of predicting failure mechanism by estimating a feasible region of stability of stresses between two curved lines separated by an angle, gives a more systematic way of modelling for the material flow nature at the points of singularity in the plastic-friction deformation zones. Recent trends in modelling of the slip line field also incorporates the presence of a stagnation region at the tool tip which ultimately give us a hint of the shape and size of the build up edge and Build up layer (BUE/BUL). This region can be modified by altering the slip field dimensions and positions making it a flexible system, at the same time which is satisfied by all governing dynamic equations and input parameters. Though the gradual increase in the size of the BUE during chip flow and then breaking up into fragments to form abrasives are yet to be simulated perfectly in compliance with experimental observations, still slip line field theory proves to be a potential contender in accommodating all other recent machining models which ultimately brings in robustness into it and a future possibility of adding a time varying nature to all field lines satisfied by these accommodated models. In the context of all the singular regions, the recent modelling works have been explained and how slip line field theory manages to fit into defining each region

Analysis of Mode Ⅲ Interface Fracture for Magneto-Electro-Elastic Materials

A novel finite element discretized symplectic method is developed for analyzing interface fracture of magneto-electro-elastic (MEE) materials under anti-plane loads. The overall cracked body is meshed by conventional finite elements and divided into a finite size singular region near the crack tip (near field) and a regular region far away from the crack tip (far field). In the near field, a based-Hamiltonian model is introduced to find the analytical series expressions, and the large number nodal unknowns are condensed into a small set of the undetermined coefficients of the symplectic series by a transformation. The nodal unknowns in the far field remain unchanged. The stress, electric and magnetic intensity factors, energy release rates (ERRs) and explicit expressions of singular field variables in the near field are simultaneously obtained without any processing.

An edge driven wavelet frame model for image restoration

Wavelet frame systems are known to be effective in capturing singularities from noisy and degraded images. In this paper, we introduce a new edge driven wavelet frame model for image restoration by approximating images as piecewise smooth functions. With an implicit representation of image singularities sets, the proposed model inflicts different strength of regularization on smooth and singular image regions and edges. The proposed edge driven model is robust to both image approximation and singularity estimation. The implicit formulation also enables an asymptotic analysis of the proposed models and a rigorous connection between the discrete model and a general continuous variational model. Finally, numerical results on image inpainting and deblurring show that the proposed model is compared favorably against several popular image restoration models.

Fragmentation and disk formation during high-mass star formation

Context. High-mass stars form in clusters, but neither the early fragmentation processes nor the detailed physical processes leading to the most massive stars are well understood. Aims. We aim to understand the fragmentation, as well as the disk formation, outflow generation, and chemical processes during high-mass star formation on spatial scales of individual cores. Methods. Using the IRAM Northern Extended Millimeter Array (NOEMA) in combination with the 30 m telescope, we have observed in the IRAM large program CORE the 1.37 mm continuum and spectral line emission at high angular resolution (~0.4″) for a sample of 20 well-known high-mass star-forming regions with distances below 5.5 kpc and luminosities larger than 104 L⊙. Results. We present the overall survey scope, the selected sample, the observational setup, and the main goals of CORE. Scientifically, we concentrated on the mm continuum emission on scales on the order of 1000 AU. We detect strong mm continuum emission from all regions, mostly due to the emission from cold dust. The fragmentation properties of the sample are diverse. We see extremes where some regions are dominated by a single high-mass core whereas others fragment into as many as 20 cores. A minimum-spanning-tree analysis finds fragmentation at scales on the order of the thermal Jeans length or smaller suggesting that turbulent fragmentation is less important than thermal gravitational fragmentation. The diversity of highly fragmented vs. singular regions can be explained by varying initial density structures and/or different initial magnetic field strengths. Conclusions. A large sample of high-mass star-forming regions at high spatial resolution allows us to study the fragmentation properties of young cluster-forming regions. The smallest observed separations between cores are found around the angular resolution limit which indicates that further fragmentation likely takes place on even smaller spatial scales. The CORE project with its numerous spectral line detections will address a diverse set of important physical and chemical questions in the field of high-mass star formation.

Enhanced real-time pose estimation for closed-loop robotic manipulation of magnetically actuated capsule endoscopes

Pose estimation methods for robotically guided magnetic actuation of capsule endoscopes have recently enabled trajectory following and automation of repetitive endoscopic maneuvers. However, these methods face significant challenges in their path to clinical adoption including the presence of regions of magnetic field singularity, where the accuracy of the system degrades, and the need for accurate initialization of the capsule’s pose. In particular, the singularity problem exists for any pose estimation method that utilizes a single source of magnetic field if the method does not rely on the motion of the magnet to obtain multiple measurements from different vantage points. We analyze the workspace of such pose estimation methods with the use of the point-dipole magnetic field model and show that singular regions exist in areas where the capsule is nominally located during magnetic actuation. As the dipole model can approximate most magnetic field sources, the problem discussed herein pertains to a wider set of pose estimation techniques. We then propose a novel hybrid approach employing static and time-varying magnetic field sources and show that this system has no regions of singularity. The proposed system was experimentally validated for accuracy, workspace size, update rate, and performance in regions of magnetic singularity. The system performed as well or better than prior pose estimation methods without requiring accurate initialization and was robust to magnetic singularity. Experimental demonstration of closed-loop control of a tethered magnetic device utilizing the developed pose estimation technique is provided to ascertain its suitability for robotically guided capsule endoscopy. Hence, advances in closed-loop control and intelligent automation of magnetically actuated capsule endoscopes can be further pursued toward clinical realization by employing this pose estimation system.

Three-Dimensional Peridynamic Model for Predicting Fracture Evolution during the Lithiation Process

Due to its large electric capacity, silicon has become one of the most promising electrode materials for lithium ion batteries. However, silicon undergoes large volumetric expansion and material stiffness reduction during the charging process. This can lead to fracture and failure of lithium-ion batteries. Damage formation and evolution inside the electrode are influenced by the lithium ion concentration and electrode material. High stress gradients induced by heterogeneous deformation can lead to massive migration of lithium ions towards high geometrical singularity regions, such as crack edge regions, which increases the lithium ion concentration. Fully coupled mechanical diffusion equations are important in describing the mechanics of this problem. In this study, the three-dimensional peridynamic theory is presented to solve the coupled field problem. In addition, the newly developed peridynamic differential operator concept is utilized to convert partial differential equations into peridynamic form for the diffusion equation. Spherical and cylindrical shaped energy storage structures with different pre-existing penny-shaped cracks are considered to demonstrate the capability of the developed framework. It is shown that peridynamic theory is a suitable tool for predicting crack evolution during the lithiation process.

Evaluation of notch stress intensity factors by the asymptotic expansion technique coupled with the finite element method

• The asymptotic expansion technique coupled with the FEM is proposed to evaluate notch stress intensity factors . • The singular order, stress angular function and amplitude coefficient in stress asymptotic field of a V-notch can be yielded. • There no special element is needed while the high computational accuracy is obtained. • The proposed method can be implanted into the commercial FE software to analyze V-notches in engineering structures. A characteristic analysis method coupled with the finite element method is proposed to calculate stress intensity factors for V-notches, in which the notched structure is divided into a singular stress sector and the remained part. The asymptotic expansions are introduced into the singular stress region to transform elastic governing equations into characteristic ordinary differential equations. The established equations are solved by the interpolating matrix method to provide stress singular orders and characteristic angular functions. The asymptotic solution in the singular stress region is then coupled with finite element equations built on the remained structure by interfacial continuous conditions to establish the system equations. Thus, the amplitude coefficients in the stress asymptotic expansions can be determined. The notch stress intensity factors can be evaluated after the stress angular functions and amplitude coefficients being obtained. A symmetric V-notch and an inclined V-notch are respectively investigated to verify the accuracy of calculated notch stress intensity factors by the proposed method through comparing with the reference ones. Due to only conventional finite element method is needed, the proposed method can be freely implanted into commercial finite element software to analyze the singular stress for the V-notched engineering structures. This method can be also easily generalized to analyze the singular physical field for V-notches in composite materials.

Energy emission from a high curvature region and its backreaction

A strong gravity naked singular region can give important clues towards understanding classical as well as spontaneous nature of General Relativity. We propose here a model for energy emission from a naked singular region in a self-similar dust spacetime by gluing two self-similar dust solutions at the Cauchy horizon. The energy is defined and evaluated as a surface energy of a null hypersurface, the null shell. Also included are scenarios of spontaneous creation or disappearance of a singularity, end of inflation, black hole formation and bubble nucleation. Our examples investigated here explicitly show that one can model unlimitedly luminous and energetic objects in the framework of General Relativity.

Hybridized Kibble-Zurek scaling in the driven critical dynamics across an overlapping critical region

The conventional Kibble-Zurek scaling describes the scaling behavior in the driven dynamics across a single critical region. In this paper, we study the driven dynamics across an overlapping critical region, in which a critical region (Region-A) is overlaid by another critical region (Region-B). We develop a hybridized Kibble-Zurek scaling (HKZS) to characterize the scaling behavior in the driven process. According to the HKZS, the driven dynamics in the overlapping region can be described by the critical theories for both Region-A and Region-B simultaneously. This results in a constraint on the scaling function in the overlapping critical region. We take the quantum Ising chain in an imaginary longitudinal-field as an example. In this model, the critical region of the Yang-Lee edge singularity and the critical region of the ferromagnetic-paramagnetic phase transition point overlap with each other. We numerically confirm the HKZS by simulating the driven dynamics in this overlapping region. The HKZSs in other models are also discussed.

Studies of modern Italian dog populations reveal multiple patterns for domestic breed evolution.

Through thousands of years of breeding and strong human selection, the dog (Canis lupus familiaris) exists today within hundreds of closed populations throughout the world, each with defined phenotypes. A singular geographic region with broad diversity in dog breeds presents an interesting opportunity to observe potential mechanisms of breed formation. Italy claims 14 internationally recognized dog breeds, with numerous additional local varieties. To determine the relationship among Italian dog populations, we integrated genetic data from 263 dogs representing 23 closed dog populations from Italy, seven Apennine gray wolves, and an established dataset of 161 globally recognized dog breeds, applying multiple genetic methods to characterize the modes by which breeds are formed within a single geographic region. Our consideration of each of five genetic analyses reveals a series of development events that mirror historical modes of breed formation, but with variations unique to the codevelopment of early dog and human populations. Using 142,840 genome‐wide SNPs and a dataset of 1,609 canines, representing 182 breeds and 16 wild canids, we identified breed development routes for the Italian breeds that included divergence from common populations for a specific purpose, admixture of regional stock with that from other regions, and isolated selection of local stock with specific attributes.

The rotational phase dependence of magnetar bursts

The trigger for the short bursts observed in $\gamma$-rays from many magnetar sources remains unknown. One particular open question in this context is the localization of burst emission to a singular active region or a larger area across the neutron star. While several observational studies have attempted to investigate this question by looking at the phase dependence of burst properties, results have been mixed. At the same time, it is not obvious a priori that bursts from a localized active region would actually give rise to a detectable phase-dependence, taking into account issues such as geometry, relativistic effects, and intrinsic burst properties such brightness and duration. In this paper, we build a simple theoretical model to investigate the circumstances under which the latter effects could affect detectability of a dependence of burst emission on rotational phase. We find that even for strongly phase-dependent emission, inferred burst properties may not show a rotational phase dependence depending on the geometry of the system and the observer. Furthermore, the observed properties of bursts with durations short as 10-20% of the spin period can vary strongly depending on the rotational phase at which the burst was emitted. We also show that detectability of a rotational phase dependence depends strongly on the minimum number of bursts observed, and find that existing burst samples may simply be too small to rule out a phase dependence.

Effects of phase singularity in the interference of two laser fields with a wide spectrum

The interference of laser beams with a wide spectrum is studied theoretically and numerically. It is shown that in the cross section of such intersecting beams in a small vicinity of zero of the complex mutual coherence function, the change in the argument of the slow amplitude of this function corresponds to the phase singularity. An approximate analytical representation of the mutual coherence function in the vicinity of the singularity point is given. It is found that an average ‘funnel’ diameter of the modulus of the mutual coherence function that arises in the singularity region does not depend on the intensity of the light beams and remains constant when the longitudinal coordinate changes. The emergence of phase dislocations in the interference pattern is established.

Prediction of the critical stress intensity factor of single-lap adhesive joints using a coupled ratio method and an analytical model

The ratio method coupled with the analytical Volkersen model is proposed for the prediction of critical stress intensity factor ( H c) in adhesively bonded single-lap joints. Based on the ratio method, it was shown that despite the singularity of the stress intensity factor ( H) near the bonding end, the ratio of H ( H c) for two single-lap joints with different substrate thicknesses is almost equal at singular and nonsingular regions. It was also found that for joints with different substrate thicknesses, the ratio of H based on the interface shear stress obtained by finite element method is almost equal to the ratio of H obtained using the Volkersen model based on the shear stress along the adhesive mid-plane. The proposed method was applied on single-lap joints with different substrate thicknesses and bonding lengths. According to the experimental results, it was shown that, despite the considerable errors which exist in the stress prediction using the Volkersen model, a combination of Volkersen model and the ratio method could predict the H c of the tested single-lap joints very well. Also using the obtained H c, failure loads of the tested joints were predicted. A good correlation was found between the experimental data and the theoretical predictions.

Resilience of hidden order to symmetry-preserving disorder

We study the robustness of non-local string order in two paradigmatic disordered spin-chain models, a spin-1/2 cluster-Ising and a spin-1 XXZ Heisenberg chain. In the clean case, they both display a transition from antiferromagnetic to string order. Applying a disorder which preserves the Hamiltonian symmetries, we find that the transition persists in both models. In the disordered cluster-Ising model we can study the transition analytically -- by applying the strongest coupling renormalization group -- and numerically -- by exploiting integrability to study the antiferromagnetic and string order parameters. We map the model into a quadratic fermion chain, where the transition appears as a change in the number of zero-energy edge modes. We also explore its zero-temperature-singularity behavior and find a transition from a non-singular to a singular region, at a point that is different from the one separating non-local and local ordering.} The disordered Heisenberg chain can be treated only numerically: by means of MPS-based simulations, we are able to locate the existence of a transition between antiferromagnetic and string-ordered phase, through the study of order parameters. Finally we discuss possible connections of our findings with many body localization.

Determination of Green's function for three-dimensional traction force reconstruction based on geometry and boundary conditions of cell culture matrices.

This study focused on the fundamental issue regarding extension of linear elasticity-based TFM to deal with physically realistic matrices (where cells are encapsulated), which concerns determination of the Green's function matching their geometry and boundary conditions. To increase fidelity in the estimate of traction forces for extreme conditions such as a sparse sampling of deformation field or targeting small focal adhesions, we numerically solved the singularity problem of the Green's function to avoid exclusion of singular point regions that could contain representative deformation indicators for such extreme conditions. The proposed approach to adapting the Green's function for the specific 3D cell culture situation was examined in a single case experimental study of endothelial cells in sprouting angiogenesis.

Are global hotspots of endemic richness shaped by plate tectonics?

Singular regions of the globe harbour a disproportionally large fraction of extant biodiversity. Spatial biodiversity gradients are frequently associated to extant ecological conditions using statistical models, but more rarely to paleo-environmental conditions, especially beyond the Quaternary. On one hand the role of plate tectonics in shaping the extant diversity of lineages is supported by numerous phylogenetic and fossil evidences, and on the other hand the spatial variation of biodiversity across the globe is rarely associated to geodynamic variables. In this study, we propose that plate tectonics explain the current location of hotspots of endemic richness across the globe. As an illustration, we used paleogeographies in a model, which quantifies through time and for each cell the potential dispersal across disconnected habitat patches. Rare events of dispersal across dynamic straits of unsuitable habitats allows species colonisation and that a subsequent absence of gene flow could lead to in-situ speciation. We evaluated whether this process could pinpoint the locations of hotspots of endemic richness computed from the ranges of 181,603 species across 14 taxonomic groups. The significant congruence between the regions highlighted by the model and the endemic richness provides evidences of the contribution of plate tectonics in shaping global biodiversity gradients. Places with high tectonic complexity, predominantly located at the confluence of major lithospheric plates such as the Mediterranean basin, Central America, Madagascar and South East Asia likely provided favourable circumstances for allopatric speciation and the emergence of new species across straits. While our illustration supports the role of plate tectonics, accounting for deep time geological events in spatial models of extant biodiversity is not straightforward. Future research should develop quantitative spatial models of biodiversity including the dynamic of ancient habitats.

Dynamics of Learning in MLP: Natural Gradient and Singularity Revisited.

The dynamics of supervised learning play a main role in deep learning, which takes place in the parameter space of a multilayer perceptron (MLP). We review the history of supervised stochastic gradient learning, focusing on its singular structure and natural gradient. The parameter space includes singular regions in which parameters are not identifiable. One of our results is a full exploration of the dynamical behaviors of stochastic gradient learning in an elementary singular network. The bad news is its pathological nature, in which part of the singular region becomes an attractor and another part a repulser at the same time, forming a Milnor attractor. A learning trajectory is attracted by the attractor region, staying in it for a long time, before it escapes the singular region through the repulser region. This is typical of plateau phenomena in learning. We demonstrate the strange topology of a singular region by introducing blow-down coordinates, which are useful for analyzing the natural gradient dynamics. We confirm that the natural gradient dynamics are free of critical slowdown. The second main result is the good news: the interactions of elementary singular networks eliminate the attractor part and the Milnor-type attractors disappear. This explains why large-scale networks do not suffer from serious critical slowdowns due to singularities. We finally show that the unit-wise natural gradient is effective for learning in spite of its low computational cost.