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Showing papers on "Singularity published in 2022"


Journal ArticleDOI
TL;DR: In this paper , an efficient algorithm based on the Galerkin method using biorthogonal Hermite cubic spline multi-wavelets (BHCSMWs) was proposed.

34 citations


Journal ArticleDOI
19 Jan 2022-EPL
TL;DR: In this article , it has been shown that the H 0 tension may be eliminated if an abrupt physics transition changed the Cepheid parameters in the near past of the Universe, nearly 70-150 Myrs ago.
Abstract: In the recent literature it has been shown that the H 0 tension may be eliminated if an abrupt physics transition changed the Cepheid parameters in the near past of the Universe, nearly 70–150 Myrs ago. In this letter we stress the possibility that this abrupt transition was caused by the smooth passage of our Universe through a pressure finite-time cosmological singularity. Being a non-crushing type singularity the pressure singularity can leave its imprints in the Universe, since it occurs globally and literally everywhere. We discuss how this scenario could easily be realized by F(R) gravity, with the strong energy conditions being satisfied without the need for a scalar field or specific matter fluids. We also stress the fact that the pressure singularity can affect the effective gravitational constant of F(R) gravity. Moreover, we stress the fact that pressure singularities can disrupt the trajectories of bound objects in the Universe, which is also pointed out in the literature, even in the context of general relativity. We also show numerically in a general relativistic framework that elliptic trajectories are distorted and changed to different elliptic trajectories when the Universe passes through the pressure singularity. Such a disruption of the trajectories could have tidal effects on the surface of the Earth, for example on sea waters and oceans, regarding the distortion of Moon's elliptic trajectory. Accordingly, the distortion of Earth's trajectory around the Sun could have affected climatologically the Earth 70–150 Myrs ago.

25 citations


Journal ArticleDOI
TL;DR: In this article , a fuzzy adaptive design is proposed to solve the finite-time constrained tracking for hypersonic flight vehicles (HFVs) by considering actuator dynamics and asymmetric time-varying constraints.
Abstract: This article proposes a fuzzy adaptive design solving the finite-time constrained tracking for hypersonic flight vehicles (HFVs). Actuator dynamics and asymmetric time-varying constraints are considered when solving this problem. The main features of the proposed design lie in 1) introducing a novel piecewise but differentiable switching control law, with an appropriate design thought to avoid the singularity issues typical of finite-time control; 2) handling actuator magnitude, bandwidth, and rate constraints, thanks to the introduction of an auxiliary compensating system counteracting the adverse effects caused by actuator physical constraints, while guaranteeing the closed-loop stability; and 3) handling asymmetric time-varying state constraints, thanks to the introduction of tan-type barrier Lyapunov functions working for both constrained and unconstrained scenarios. Comparative simulation results illustrate the effectiveness of the proposed strategy over existing methods for HFVs in terms of convergence, smoothness, actuator performance, and constraints satisfaction.

24 citations


Journal ArticleDOI
TL;DR: In this paper , the authors argue that humans possess multiple internal languages of thought, akin to computer languages, which encode and compress structures in various domains (mathematics, music, shape, etc.).

21 citations


Journal ArticleDOI
TL;DR: In this paper , a radial basis function neural network (RBFNN) is used to estimate uncertainties in the robotic system dynamics to avoid the singularity of terminal sliding-mode control (TSMC), and a modified sliding variable is adopted.
Abstract: This article investigates the predefined time trajectory tracking control of uncertain nonlinear robotic systems. A radial basis function neural network (RBFNN) is used to estimate uncertainties in the robotic system dynamics. To avoid the singularity of terminal sliding-mode control (TSMC), a modified sliding variable is adopted. In order to realize that the tracking errors can converge to a small neighborhood of the origin in predefined time, within which the maximum convergence time can be adjusted by explicit parameters in advance, a nonsingular TSMC based on the RBFNN is proposed. Experiments on a ROKAE platform demonstrate the effectiveness and advantage of the proposed control method.

20 citations


Journal ArticleDOI
TL;DR: In this paper , the authors take advantage of envelope theory and singularity theory to study the evolutoids and pedaloids in Minkowski plane and illustrate an internal correlation from algebraic and geometric viewpoints.

19 citations


Journal ArticleDOI
23 Sep 2022-Symmetry
TL;DR: In this article , the parametric equation of the Bishop frame for a timelike sweeping surface with a unit speed Timelike curve in Minkowski 3-space is given.
Abstract: In this paper, we give the parametric equation of the Bishop frame for a timelike sweeping surface with a unit speed timelike curve in Minkowski 3-space. We introduce a new geometric invariant to explain the geometric properties and local singularities of this timelike surface. We derive the sufficient and necessary conditions for this timelike surface to be a timelike developable ruled surface. Afterwards, we take advantage of singularity theory to give the classification of singularities of this timelike developable surface. Furthermore, we give some representative examples to show the applications of the theoretical results.

16 citations


Journal ArticleDOI
TL;DR: In this article, the existence of a radial solution for the eigenvalue problem of a singular k-Hessian equation is established via Schauder's fixed point theorem under the case where the nonlinearity possesses a singularity with respect to the space variable.

16 citations


Journal ArticleDOI
TL;DR: In this article , mathematical analysis and numerical methods for Caputo-Hadamard fractional diffusion-wave equations with initial singularity are investigated by adopting the modified Laplace transform and the well-known finite Fourier sine transform, and the regularity and logarithmic decay of its solution are researched.

16 citations


Journal ArticleDOI
TL;DR: In this paper , a set of finite energy smooth initial data for which the corresponding solutions to the compressible three-dimensional Navier-Stokes and Euler equations implode (with infinite density) at a later time at a point, and the associated formation of singularity is described.
Abstract: In this paper and its sequel, we construct a set of finite energy smooth initial data for which the corresponding solutions to the compressible three-dimensional Navier-Stokes and Euler equations implode (with infinite density) at a later time at a point, and we completely describe the associated formation of singularity. This paper is concerned with existence of smooth self-similar profiles for the barotropic Euler equations in dimension $d\ge 2$ with decaying density at spatial infinity. The phase portrait of the nonlinear ODE governing the equation for spherically symmetric self-similar solutions has been introduced in the pioneering work of Guderley. It allows us to construct global profiles of the self-similar problem, which however turn out to be generically non-smooth across the associated acoustic cone. In a suitable range of barotropic laws and for a sequence of quantized speeds accumulating to a critical value, we prove the existence of non-generic $\mathcal{C}^\infty$ self-similar solutions with suitable decay at infinity. The $\mathcal{C}^\infty$ regularity is used in a fundamental way in our companion paper (part II) in the analysis of the associated linearized operator and leads, in turn, to the construction of finite energy blow up solutions of the compressible Euler and Navier-Stokes equations in dimensions $d=2,3$.

15 citations


Journal ArticleDOI
TL;DR: In this paper , the authors revisited the computation of bubble wall friction during a cosmological first-order phase transition, using an extended fluid Ansatz to solve the linearized Boltzmann equation.
Abstract: Abstract We revisit the computation of bubble wall friction during a cosmological first-order phase transition, using an extended fluid Ansatz to solve the linearized Boltzmann equation. A singularity is found in the fluctuations of background species as the wall approaches the speed of sound. Using hydrodynamics, we argue that a discontinuity across the speed of sound is expected on general grounds, which manifests itself as the singularity in the solution of the linearized system. We discuss this result in comparison with alternative approaches proposed recently, which find a regular behaviour of the friction for all velocities.

Journal ArticleDOI
25 Mar 2022-Universe
TL;DR: In this paper , the authors review the physical mechanism leading to the instability of the central core, arguing that non-perturbative backreation is non-negligible and must be taken into account to provide a meaningful description of physical black holes.
Abstract: Regular black holes represent a conservative model in which the classical singularity is replaced by a non-singular core without necessarily modifying the spacetime outside the trapping horizon. Given the possible lack of phenomenological signatures, it is crucial to study the consistency of the model. In this short work, we review the physical mechanism leading to the instability of the central core, arguing that that non-perturbative backreation is non-negligible and must be taken into account to provide a meaningful description of physical black holes.

Journal ArticleDOI
TL;DR: In this article, a pair of hybrid block techniques is constructed and successfully applied to integrate Emden-Fowler third-order singular boundary problems, and the numerical results are compared with other recent numerical approaches in the literature.

Journal ArticleDOI
19 May 2022-Universe
TL;DR: In this paper , the presence of a Type-IV singularity (a mild singularity) can influence the dynamics of a bouncing universe, and the authors examined the bounce cosmology that appears with a Type IV singularity in the context of a ghost-free Gauss-Bonnet theory of gravity.
Abstract: This work explains how the presence of a Type-IV singularity (a mild singularity) can influence the dynamics of a bouncing universe. In particular, we examine the bounce cosmology that appears with a Type-IV singularity in the context of a ghost-free Gauss–Bonnet theory of gravity. Depending on the time of occurrence of the Type-IV singularity, three different cases may arise—when the singularity occurs before the bounce, after the bounce, or at the instant of the bounce. However, in all of these cases, we find that in the case when the singularity “globally” affects the spacetime, the scalar power spectrum becomes red-tilted, and the tensor-to-scalar ratio is too large to be consistent with the observational data. Based on these findings, we investigate a different bouncing scenario which also appears with a Type-IV singularity, and wherein the singularity affects the spacetime “locally” around the time when it occurs. As a result, and unlike the previous scenario, the perturbation modes in the second bouncing scenario are likely to be generated far away from the bounce in the deep contracting phase. This finally results in the simultaneous compatibility of the observable quantities with the Planck data and ensures the viability of the bounce model where the Type-IV singularity has local effects on the spacetime around the time of the singularity.

Journal ArticleDOI
TL;DR: In this paper , the authors proposed seven criteria to single out physically reasonable non-singular black-hole models and adopt them to four different spherically symmetric models with a regular center and their rotating counterparts.
Abstract: We propose seven criteria to single out physically reasonable non-singular black-hole models and adopt them to four different spherically symmetric models with a regular center and their rotating counterparts. In general relativity, all such non-singular black holes are non-generic with a certain matter field including a class of nonlinear electromagnetic fields. According to a criterion that the effective energy-momentum tensor should satisfy all the standard energy conditions in asymptotically flat regions, the well-known Bardeen and Hayward black holes are discarded. In contrast, the Dymnikova and Fan-Wang black holes respect the dominant energy condition everywhere. Although the rotating Fan-Wang black hole contains a curvature singularity, the rotating Dymnikova black hole is free from scalar polynomial curvature singularities and closed timelike curves. In addition, the dominant energy condition is respected on and outside the event horizons in the latter case. The absence of parallelly propagated curvature singularities remains an open question.

Journal ArticleDOI
TL;DR: In this article , a pair of hybrid block techniques is constructed and successfully applied to integrate Emden-Fowler third-order singular boundary problems, and the numerical results are compared with other recent numerical approaches in the literature.

Journal ArticleDOI
TL;DR: In this article , an all-order resurgence analysis of a quantum field theory renormalon that contributes to an anomalous dimension in six-dimensional scalar theory and is governed by a third-order nonlinear differential equation is performed.

Journal ArticleDOI
TL;DR: In this article , the amplitudes of periodic responses of the nonlinear system are obtained by using the harmonic balance method, and a general method based on the singularity theory is proposed to reveal all kinds of responses under a given set of parameters.

Journal ArticleDOI
TL;DR: In this article , an attitude synchronization problem with velocity-free measurements is investigated for multiple rigid body systems under event-triggered mechanism, and the convergence of synchronization is analyzed based on a positively invariant set contained in SO(3), which inherently avoids the singularity problem or non-uniqueness issue for the attitude representation.

Journal ArticleDOI
TL;DR: In this paper , a new adaptive prescribed performance control (PPC) strategy is proposed for a family of underactuated surface vessels (USVs) under model uncertainties and disturbances, where the adaptive technique is devoted to tackling model imperfections as usual, whereas the constraint-handling technique is adopted in a novel way.
Abstract: This article is dealt with the problem of trajectory tracking with prescribed performance for a family of underactuated surface vessels (USVs) under model uncertainties and disturbances. The prescribed performance means that the USV tracks a given trajectory with the arbitrarily predefined speed of response and accuracy. The existing prescribed performance control (PPC) solutions and the traditional robust control approaches for USVs may have the singularity issue or cause a discontinuous control signal. Thereby, a new-type adaptive PPC strategy is put forward in this article. The adaptive technique is devoted to tackling model imperfections as usual, whereas the constraint-handling technique is adopted in a novel way. Herein, we first construct an auxiliary variable instead of using the approach angle or azimuth angle. Then, we impose constraints on the position error, not the tracking error, and the auxiliary variable, simultaneously. In this way, the predefined performance is achieved by moreover a singularity-free continuous control action. These theoretical findings are illustrated via a comparative simulation study.

Journal ArticleDOI
TL;DR: In this paper , the authors considered the Navier-Stokes and Euler equations and proved that the corresponding solutions to both equations implode at a later time at a point, and completely describe the associated formation of singularity.
Abstract: In this paper, which continues our investigation of strong singularity formation in compressible fluids, we consider the compressible three-dimensional Navier-Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations implode (with infinite density) at a later time at a point, and completely describe the associated formation of singularity. An essential step in the proof is the existence of $\mathcal{C}^\infty$ smooth self-similar solutions to the compressible Euler equations for quantized values of the speed constructed in our companion paper (part I). All blow up dynamics obtained for the Navier-Stokes problem are of type II (non self-similar).


Journal ArticleDOI
TL;DR: An overview of the recent surge in interest in multipole sources and their fields to achieve useful radiated and scattered fields with, for example, high directivities in preferred directions is given in this paper .
Abstract: Multipole expansions are an essential analysis tool in the foundations of the descriptions of the electromagnetic fields radiated by electric and magnetic sources. Nevertheless, practical antenna systems generally rely on them as an academic explanation, not as a fundamental building block. An overview of the recent surge in interest in multipole sources and their fields to achieve useful radiated and scattered fields with, for example, high directivities in preferred directions is given. Topics include Huygens sources, dielectric-based Mie-tronics, edge-singularity multipoles, and exotic metamaterial-inspired superdirective lenses and radiators. While there has been a never-ending stream of physics publications, little has happened in the engineering electromagnetics community. I will try to answer the title with examples that may stimulate interest in the field.

Journal ArticleDOI
TL;DR: In this paper , the 3d McKay correspondence was used to derive the Coulomb branch information of the 5d SCFT, which is applied to toric, non-toric hypersurface and complete intersection cases.
Abstract: We study the orbifold singularities $X=\mathbb{C}^3/\Gamma$ where $\Gamma$ is a finite subgroup of $SU(3)$. M-theory on this orbifold singularity gives rise to a 5d SCFT, which is investigated with two methods. The first approach is via 3d McKay correspondence which relates the group theoretic data of $\Gamma$ to the physical properties of the 5d SCFT. In particular, the 1-form symmetry of the 5d SCFT is read off from the McKay quiver of $\Gamma$ in an elegant way. The second method is to explicitly resolve the singularity $X$ and study the Coulomb branch information of the 5d SCFT, which is applied to toric, non-toric hypersurface and complete intersection cases. Many new theories are constructed, either with or without an IR quiver gauge theory description. We find that many resolved Calabi-Yau threefolds, $\widetilde{X}$, contain compact exceptional divisors that are singular by themselves. Moreover, for certain cases of $\Gamma$, the orbifold singularity $\mathbb{C}^3/\Gamma$ can be embedded in an elliptic model and gives rise to a 6d (1,0) SCFT in the F-theory construction. Such 6d theory is naturally related to the 5d SCFT defined on the same singularity. We find examples of rank-1 6d SCFTs without a gauge group, which are potentially different from the rank-1 E-string theory.

Journal ArticleDOI
TL;DR: In this article , the internal structure of anisotropic black holes with charged vector hairs is studied and a general proof of no inner horizon of these black holes is presented and the geometry ends at a spacelike singularity.
Abstract: A bstract We study the internal structure of anisotropic black holes with charged vector hairs. Taking advantage of the scaling symmetries of the system, some radially conserved charges are found via the extension of the Noether theorem. Then, a general proof of no inner horizon of these black holes is presented and the geometry ends at a spacelike singularity. Before reaching the singularity, we find several intermediate regimes both analytically and numerically. In addition to the Einstein-Rosen bridge contracting towards the singularity, the instability triggered by the vector hair results in the oscillations of vector condensate and the anisotropy of spatial geometry. Moreover, the latter oscillates at twice the frequency of the condensate. Then, the geometry enters into Kasner epochs with spatial anisotropy. Due to the effects from vector condensate and U(1) gauge potential, there is generically a never-ending alternation of Kasner epochs towards the singularity. The character of evolution on approaching the singularity is found to be described by the Kasner epoch alternation with flipping of powers of the Belinskii-Khalatnikov-Lifshitz type.

Journal ArticleDOI
TL;DR: In this article , the authors define the singularity conditions for continuum parallel robots and prove that some singularities appear when the robot potential energy has a local isovalue and that these singularities separate the stable configurations from the unstable ones in the workspace.
Abstract: Research on continuum parallel robots has been essentially devoted to the computation of their geometricostatic models and of their performance in terms of workspace size, accuracy, compliance, force transmission, and manipulability. Their singularity analysis has been limited to the identification of a limited number of singular configurations, without any deep investigation of the physical phenomena occurring in these singularities. In this article, we define the singularity conditions for continuum parallel robots. We provide a straightforward interpretation of the phenomena occurring in singularities. Especially, we prove that some singularities appear when the robot potential energy has a local isovalue. Because of this property, we show that these singularities separate the stable configurations from the unstable ones in the workspace. Moreover, on such singularities, the robot can freely move along a given direction without any constraint under the action of small perturbations. We illustrate the singularity phenomena and their effects by simulations performed with two different continuum parallel robots.

Journal ArticleDOI
TL;DR: In this paper , the authors study systems with energy bands in two dimensions, hosting higher order Van Hove singularities (HOVHS) in the presence of disorder, using standard diagrammatic techniques for impurity averaging.
Abstract: We study systems with energy bands in two dimensions, hosting higher order Van Hove singularities (HOVHS) in the presence of disorder, using standard diagrammatic techniques for impurity averaging. In the clean limit, such singularities cause power-law divergence in the density of states (DOS), and this is expected to strongly affect electronic correlation. In order to analyse the signatures of these singularities in disordered systems, we employ various Born approximations, culminating in the self-consistent (non) Born approximation. Although the divergence of the DOS is smeared, we find that the shape of the DOS, as characterized by the power law tail and the universal ratio of prefactors, is retained slightly away from the singularity. This could help us to understand current and future experiments on materials that can be tuned to host HOVHS. The impurity induced smearing is calculated and analysed for several test cases of singularities. We also study the effects of impurities on electrical conductivity and determine the regimes where the quantitative features of the power law DOS manifest in the conductivity.

Journal ArticleDOI
TL;DR: In this paper , the authors demonstrate the singularities splitting phenomenon and propose an analysis method, based on which one may rapidly estimate the modal components of impure vortex light, and compare the spiral and fork wire interference patterns in distinguishing splitting singularities.
Abstract: Abstract It is the basic characteristic of pure vortex light that there is a phase singularity at the origin. Such a singularity may be multiple degenerate, which determines the order of vortex light. Singularities splitting phenomenon means that singularities no longer concentrate at the origin but distribute around the space, usually occurring in impure vortex light. In this paper, we demonstrate the singularities splitting phenomenon and propose an analysis method, based on which one may rapidly estimate the modal components of impure vortex light. As two common singularity discrimination methods, the spiral and fork wire interference patterns are compared in distinguishing splitting singularities. The most widely used spiral interference pattern is revealed to be the worst form because of the low resolution. Instead, the fork wire interference pattern is with higher and easily adjusted resolution. 1‰ impurity is still able to be distinguished through fork wire interference patterns in the experiment.

Journal ArticleDOI
TL;DR: In this article , a quantum description of electrically charged spherically symmetric black holes given by coherent states of gravitons in which both the central singularity and the Cauchy horizon are not realised is presented.
Abstract: We present a quantum description of electrically charged spherically symmetric black holes given by coherent states of gravitons in which both the central singularity and the Cauchy horizon are not realised.

Journal ArticleDOI
TL;DR: In this paper , the authors show how IR loop effects impact positivity bounds in effective field theories with causal and unitary UV completions, and propose a new simple analytic approach to dispersive bounds, which are instead insensitive to the singularities, and explicitly compute the finite contributions from loops.
Abstract: We show how calculable IR loop effects impact positivity bounds in effective field theories with causal and unitary UV completions. We identify infrared singularities that appear in dispersion relations at $|t|\ensuremath{\lesssim}{m}^{2}$. In the massless limit, they weaken two-sided bounds based on crossing symmetry, such as the lower bound on the amplitude for Galileon scattering. For amplitudes that are analytic in $s$ even for large negative $t$, i.e., $|t|\ensuremath{\gg}{m}^{2}$, we propose a new simple analytic approach to dispersive bounds, which are instead insensitive to the singularities, and explicitly compute the finite contributions from loops. Finally, we show that the singularity do not affect the bounds based on smearing in the impact parameter.