Singular Behavior Research Articles

Symmetries and singular behaviors with Bohmian trajectories

Symmetries and singular behaviors with Bohmian trajectories

Patterns of overeating in middle-aged Chinese from Hong Kong

Abstract Background Obesity is one of the most important risk factors for non-communicable diseases worldwide. Overweightness may be attributable to a wide spectrum of overeating behaviours. However, the various types of overeating behaviors are under-studied in Asia, particularly in non-adolescent age groups. This study aims to estimate the prevalence and factors associated with various overeating patterns among middle-aged Chinese adults. Methods A random telephone survey was conducted in 2023 on Hong Kong Chinese adults between 35 and 59 years or age (n = 785). An instrument composed of modified Positive-Negative Emotional Eating (EE) Scale, Night Eating Questionnaire-Chinese (NEQ), Binge Eating Disorder Screener (BED-7), Depression Anxiety and Stress Scales (DASS-21), demographic factors, BMI and number of reported gastrointestinal (GI) conditions was used. Multiple regression analyses were conducted to test the association of demographic factors, BMI, GI conditions as well as dysphoric mood with overeating behaviors. Results Hong Kong Chinese middle-aged adults reported the following past-month prevalence of overeating behaviors: positive EE (26.1%), general overeating (12.4%), negative EE (9.2%), binge eating (6.0%) and night eating behavior (1.8%). Nightshift work, mental stress, being single and younger age were common risk factors for the various overeating patterns among middle-aged men. Anxiety, high/low educational levels and younger age were common risk factors among middle-aged women. Obesity was associated with binge eating and positive EE in men (OR: 1.7-4.0) and associated with negative EE and general overeating (OR:2.3-2.7) in women. Conclusions This study noted that binge eating, night eating, positive/negative EE, and GOB were distinct eating patterns requiring different clinical approaches. The significant association between various overeating behaviors with BMI, indicates that these individuals should be prioritized to receive healthy eating interventions. Key messages • Adult overeating is not a singular behavior but represents an array of different eating patterns with different risk factors. • Like their Western counterparts, overeating behaviors in Chinese adults are often linked to dysphoric mood, therefore treatment of obesity may require psychological counseling.

On the non-flatness nature of noncommutative Minkowski spacetime and the singular behavior of probes

It is more than a century-old concept that the Minkowski spacetime is flat. From the pure geometric point of view, we explicitly address the issue of whether a noncommutative Minkowski spacetime is flat or not. In the framework of the twisted-diffeomorphism approach to noncommutative gravity with canonical type noncommutative (NC) coordinate structure, one important result that we get is that the NC Minkowski spacetime parametrized either with spherical polar coordinates or with parabolic coordinates has nontrivial NC corrections to Riemann curvature tensor, Ricci tensor and curvature scalars. Another crucial result is that the curvature scalars have singular behavior at certain points, and these singularities are not coordinate singularities. The nature of these singularities clearly points towards the idea of high-energetic probes turning into black holes. The absence of any such noncommutative corrections, and thus any such singularities, in the cases of Cartesian coordinates and cylindrical coordinates leads to the conclusion that high-energetic probes do not turn into black holes when the canonical NC structure is considered for these coordinates.

Electrically charged black holes in [formula omitted]-Euler–Heisenberg theory

Drawing on the concept of the non-linear dynamics of electromagnetic fields in vacuum in terms of the Euler–Heisenberg system, a static and spherically symmetric black hole solution is derived by coupling the Euler–Heisenberg term and F(R) gravity. In applying the curvature singularity tools, the black hole solution induces a singular behaviour at the centre r=0 while exhibiting a regular shape at high distances. Using the heat capacity (CQ) and the Helmholtz free energy (F), we analyse the thermodynamic stability locally and globally. Furthermore, an investigation is conducted using class tools of Geometrothermodynamics (GTs) features such as Weinhold, Ruppeiner, Hendi–Panahiyan–Eslam–Momennia (HPEM), and Quevedo to identify phase transition points associated with heat capacity, including both physical boundary points (root of the heat capacity) and second critical phase transition points (divergent points of the heat capacity). We have even examined the relevant sparsity of Hawking radiation, showing how the black hole solution behaves as a black body at specific limits. Overall, this study enhances our knowledge of the mergers of a class of non-linear dynamics of electromagnetic fields in a vacuum within F(R) gravity by modelling black hole solutions.

Exponential mixing for singular skew-products

Abstract We study skew-products of the form ( x , u ) ↦ ( f x , u + φ ( x ) ) where f is a non-uniformly expanding map on a manifold X and φ : X → S 1 is piecewise C 1 . If the systems satisfies mild assumptions (in particular singular behaviour of ϕ is permitted) then we prove that the map mixes exponentially with respect to the unique SRB measure. This extends previous results by allowing singular behaviour in the fibre map.

Crack tip stress intensification in strain-induced crystallized elastomer

Natural rubber (NR) exhibits strain-induced crystallization (SIC), enhancing tearing strength and crack resistance. However, the reinforcement mechanism along with nonuniform strain around a crack tip remains unclear. We reveal the nonuniform stress field around a crack tip using the DIC-based deformation field data and a hyperelasticity approach. A hyperelastic strain energy density function (W) is derived to be able to replicate stress-strain data across various deformations, encompassing equal and unequal biaxial, uniaxial, and pure shear stretching. These data cover the full range and magnitude of deformations around the crack tip. SIC significantly impacts the singular behaviors of strain and stress near the crack tip, causing a pronounced stress increase and strain decrease within the SIC zone that extends up to approximately 100 μm away from the crack tip. This results in a distinct crossover in singularity power-law index between the SIC zone and the fully amorphous zone. With increasing crack opening, the stress upturn intensifies, and the crossover shifts away from the crack tip due to SIC zone enlargement and local crystallinity increase. These findings deepen our understanding of the physics of SIC near crack tips and its reinforcement mechanism in strain-induced crystallizable soft solid materials.

Adhesion of a nematic elastomer cylinder.

Reversible dry adhesion is exploited by lizards and insects in nature, and is of interest to robotics and bio-medicine. In this paper, we use numerical simulation to study how the soft elasticity of liquid crystal elastomers can affect its adhesion and provide a technological opportunity. Liquid crystal elastomers are cross-linked elastomer networks with liquid crystal mesogens incorporated into the main or side chain. Polydomain liquid crystalline (nematic) elastomers exhibit unusual mechanical properties like soft elasticity, where the material deforms at nearly constant stress, due to the reorientation of mesogens. Our study reveals that the soft elasticity of nematic elastomers dramatically affects the interfacial stress distribution at the interface of a nematic elastomer cylinder adhered to a rigid substrate. The stress near the edge of the nematic cylinder under tensile load deviates from the singular behavior predicted for linear elastic materials, and the maximum normal stress reduces dramatically. This suggests that nematic elastomers should display extremely high, but controllable adhesion, consistent with the available experimental observations.

An advanced fast multipole dual boundary element method for analyzing multiple cracks propagation

A new fast multipole dual boundary element method (FMDBEM) is developed to analyze multiple crack propagations. To evaluate accurately the stress fields around the crack tip, a variable-order asymptotic element (VAE) is first proposed to express the singular behavior. This VAE is also suitable for the V-notches with different opening angles, requiring only minor adjustments of stress exponents. Then the VAE is introduced into the FMDBEM framework, where several singularity problems of integrals are solved. Finally, the FMDBEM with VAEs, combined with an adaptive scheme, is used to determine the crack propagation paths. Numerical examples show that the present method is accurate and easy to implement making it an appealing tool for analyzing large complex structures that include randomly distributed cracks and notches.

Impact of Barrow’s entropy on topological classification of higher-dimensional black holes

In this paper, we explore the impact of Barrow’s entropy on the topological classification of d-dimensional black holes (BHs). Specifically, we examine the Gauss–Bonnet (GB) and singly rotating Kerr black holes (KBHs) as well as their AdS counterparts. We notice that Barrow’s entropy significantly influences the topological numbers of these BHs. To understand these effects, we use the thermodynamic domain — the space defined by thermodynamic variables like temperature and pressure — to study topologically inspired defects in the BHs. These defects are points in the thermodynamic domain where singular or discontinuous behavior occurs. By computing the winding numbers of these defects, which are integers that count how many times a loop around the defect encircles the origin, we can understand the local and global topology of the BHs. Our analysis suggest that the topological number [Formula: see text] derived from Barrow’s statistics differs from the one obtained using Gibbs–Boltzmann statistics. Furthermore, we observe that BHs can undergo topological phase transitions that characterize them in different thermodynamic topological classes. Overall, these findings demonstrate the importance of Barrow’s entropy in understanding the topological classification of BHs, and highlight the potential for further research in this area.

Error analysis of an L2-type method on graded meshes for semilinear subdiffusion equations

A semilinear initial–boundary value problem with a Caputo time derivative of fractional order α∈(0,1) is considered, solutions of which typically exhibit a singular behaviour at an initial time. For an L2-type discretization of order 3−α, we give sharp pointwise-in-time error bounds on graded temporal meshes with arbitrary degree of grading.

Unconditional error analysis of the linearized transformed [formula omitted] virtual element method for nonlinear coupled time-fractional Schrödinger equations

This paper constructs a linearized transformed L1 virtual element method for the generalized nonlinear coupled time-fractional Schrödinger equations. The solutions to such problems typically exhibit singular behavior at the beginning. To avoid this pitfall, we introduce an identical s-fractional differential system derived from a smoothing transformation of variables t=s1/α, 0<α<1. By utilizing the discrete complementary convolution kernels, we prove the boundedness and error estimates of the solution of time-discrete system. Moreover, the unconditionally optimal error bounds of the proposed fully discrete scheme are derived in L2-norm without restriction on the grid ratio. Finally, numerical tests on a set of polygonal meshes are presented to verify the theoretical results.

Finite Element Method on locally refined composite meshes for Dirichlet fractional Laplacian

It is known that the solution of the Dirichlet fractional Laplacian in a bounded domain exhibits singular behavior near the boundary. Consequently, numerical discretizations on quasi-uniform meshes lead to low accuracy and nonphysical solutions. We adopt a finite element discretization on locally refined composite meshes, which consist in a combination of graded meshes near the singularity and uniform meshes where the solution is smooth. We also provide a reference strategy on parameter selection of locally refined composite meshes. Numerical tests confirm that finite element method on locally refined composite meshes has higher accuracy than uniform meshes, but the computational cost is less than that of graded meshes. Our method is applied to discrete the fractional-in-space Allen–Cahn equation and the fractional Burgers equation with Dirichlet fractional Laplacian, some new observations are discovered from our numerical results.

Singularities of the hyperbolic elastic flow: convergence, quantization and blow-ups

We study the elastic flow of closed curves and of open curves with clamped boundary conditions in the hyperbolic plane. While global existence and convergence toward critical points for initial data with sufficiently small energy is already known, this study pioneers an investigation into the flow’s singular behavior. We prove a convergence theorem without assuming smallness of the initial energy, coupled with a quantification of potential singularities: Each singularity carries an energy cost of at least 8. Moreover, the blow-ups of the singularities are explicitly classified. A further contribution is an explicit understanding of the singular limit of the elastic flow of λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document}-figure-eights, a class of curves that previously served in showing sharpness of the energy threshold 16 for the smooth convergence of the elastic flow of closed curves.

L1-FEM discretizations for two-dimensional multiterm fractional delay diffusion equations

A two-dimensional multiterm fractional delay diffusion equation is considered. The representation of the exact solution of the equation is derived and it is shown that the solution exhibits singular behaviors at multiple nodes due to the initial singularity and time delay. This results in the numerical schemes for solving the equation typically have a lower order of convergence in time. The problem is approximated in time by the L1 and Alikhanov schemes on symmetrical graded meshes, while in space the standard finite element method is applied. Numerical stability and convergence are presented for the schemes. Numerical experiments are performed to show the effectiveness of the schemes.

Co-occurrence of problematic facebook and video game use: prevalence and association with mental health disorders among adolescents

IntroductionThe rapid proliferation of technology and its impact on adolescents’ lives have raised concerns about addictive behaviors and its potential consequences, including behavioral and mental health problems. This study investigates the prevalence and risk factors associated with the co-occurrence of Problematic Facebook Use and Problematic Video game Use among Tunisian adolescents.MethodologyWe conducted a cross-sectional study in the urban area of Sousse governorate in Tunisia during the 2018/2019 school year. We selected a representative sample of high school students enrolled in public educational institutions in Sousse. Data collection was performed through a self-administered structured questionnaire, which gathered information on sociodemographic characteristics, lifestyle behaviors, and mental health disorders. Problematic Facebook Use was assessed using the validated Arabic version of the Bergen Scale, while Problematic Video Game Use was measured using the 21-point Lemmens Scale, which was translated into Arabic. Statistical analysis was carried out using the SPSS program (version 20).ResultsWe enrolled a total of 1342 high school students in our study, of whom, 63.2% were female with a mean age of 17.5 ± 1.44 years. The prevalence of Problematic Facebook Use and Problematic Video Game Use was 28.3% and 13% respectively. Regarding the co-occurrence of the two problematic behaviors, 31.3% of participants faced a singular addictive behavior, either related to problematic Facebook or video game use, while 5% had both addictive behaviors simultaneously. In a multivariate analysis, risk factors for the co-occurrence of Problematic Facebook and Video Game Use, in decreasing order of significance, included severe depression (AOR = 4.527; p = 0.003), anxiety (AOR = 4.216; p = 0.001), male gender (AOR = 4.130; p < 0.001), problematic internet use (AOR = 3.477; p = 0.006), as well as moderate depression (AOR = 3.048; p = 0.007).ConclusionOur study found that Problematic Facebook and Video Game Use were prevalent among Tunisian adolescents. The co-occurrence of these disorders is strongly linked to male gender, problematic internet use, depression, and anxiety disorders. These findings underscore the urgency of implementing tailored and effective awareness and prevention programs to address these emerging challenges.

Combining Laplace transform and Variational iteration method for solving singular IVPs and BVPs of Lane–Emden type equation

This study uses the combined Laplace transform and variational iteration method to analytically solve initial value problems (IVPs) and boundary value problems (BVPs) of Lane- Emden- equation with singular behaviour at . Initially, this method requires calculating the lagrange multiplayer, and after its value was calculated, it was found to be equal , this method is applying on several problems and the results were improved using Padé approximations, the results were compared with the exact solution by calculating the absolute error value between them.

Topological behavior of spectral singularities in topological Weyl semimetals.

In this study, we examine the topological character of spectral singularities by using transverse magnetic (TM) mode configuration in a Topological Weyl Semimetal (TWSM). TM mode configuration restrains the effect of Kerr/Faraday rotations and therefore does not allow an extra degree of freedom to occur. We find out that surface currents arise due to topological terms on the surface of TWSM slab where no Fermi arcs are localized. We also investigate the contribution of the Θ-term, which is the origin of axions in topological materials, and especially theb-term, to the topological properties. As a result of our study, we clearly reveal the topological character ofb-term for the first time and we demonstrate the Weyl degeneracy situation in an obvious manner. Our system produces circular currents in the plane of propagation, maintaining a cyclotron shape motion. The presence ofb-term causes the induced current to be topologically protected. Our findings verify that topological properties of TWSM containing two opposite chirality Weyl fermions are robust against external influences. With the findings of our study, the appropriate conditions for the construction of a topological laser and the values that the system parameters can take have been demonstrated.

Singular and Nonsingular Transitions in the Infrared Plasmons of Nearly Touching Nanocube Dimers.

Narrow gaps between plasmon-supporting materials can confine infrared electromagnetic energy at the nanoscale, thus enabling applications in areas such as optical sensing. However, in nanoparticle dimers, the nature of the transition between touching (zero gap) and nearly nontouching (nonzero gap ≲15 nm) regimes is still a subject of debate. Here, we observe both singular and nonsingular transitions in infrared plasmons confined to dimers of fluorine-doped indium oxide nanocubes when moving from touching to nontouching configurations depending on the dimensionality of the contact region. Through spatially resolved electron energy-loss spectroscopy, we find a continuous spectral evolution of the lowest-order plasmon mode across the transition for finite touching areas, in excellent agreement with the simulations. This behavior challenges the widely accepted idea that a singular transition always emerges in the near-touching regime of plasmonic particle dimers. The apparent contradiction is resolved by theoretically examining different types of gap morphologies, revealing that the presence of a finite touching area renders the transition nonsingular, while one-dimensional and point-like contacts produce a singular behavior in which the lowest-order dipolar mode in the touching configuration, characterized by a net induced charge in each of the particles, becomes unphysical as soon as they are separated. Our results provide valuable insights into the nature of dimer plasmons in highly doped semiconductors.

AN EFFICIENT SPECTRAL METHOD FOR NONLINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH WEAKLY SINGULAR KERNELS

For Volterra integro-differential equations (VIDEs) with weakly singular kernels, their solutions are singular at the initial time. This property brings a great challenge to traditional numerical methods. Here, we investigate the numerical approximation for the solution of the nonlinear model with weakly singular kernels. Due to its characteristic, we split the interval and focus on the first one to save operation. We employ the corresponding singular functions as basis functions in the first interval to simulate its singular behavior, and take the Legendre polynomials as basis functions in the other one. Then the corresponding hp-version spectral method is proposed, the existence and uniqueness of solution to the numerical scheme are proved, the hp-version optimal convergence is derived. Numerical experiments verify the effectiveness of the proposed method.

Semi-analytic PINN methods for boundary layer problems in a rectangular domain

Singularly perturbed boundary value problems pose a significant challenge for their numerical approximations because of the presence of sharp boundary layers. These sharp boundary layers are responsible for the stiffness of solutions, which leads to large computational errors, if not properly handled. It is well-known that the classical numerical methods as well as the Physics-Informed Neural Networks (PINNs) require some special treatments near the boundary, e.g., using extensive mesh refinements or finer collocation points, in order to obtain an accurate approximate solution especially inside of the stiff boundary layer. In this article, we modify the PINNs and construct our new semi-analytic SL-PINNs suitable for singularly perturbed boundary value problems. Performing the boundary layer analysis, we first find the corrector functions describing the singular behavior of the stiff solutions inside boundary layers. Then we obtain the SL-PINN approximations of the singularly perturbed problems by embedding the explicit correctors in the structure of PINNs or by training the correctors together with the PINN approximations. Our numerical experiments confirm that our new SL-PINN methods produce stable and accurate approximations for stiff solutions.