Search Results (50)

In total, geodesic surfaces and their generalizations, namely totally umbilical and parallel surfaces, are well-known topics in Submanifold Theory and have been intensively studied in three-dimensional ambient spaces, both Riemannian and Lorentzian. In this paper, we prove the non-existence of parallel and totally umbilical (in particular, totally geodesic) surfaces for three-dimensional Lorentzian Lie groups, which admit a four-dimensional isometry group, but are neither of Bianchi–Cartan–Vranceanu-type nor homogeneous plane waves. Consequently, the results of the present paper complete the investigation of these fundamental types of surfaces in all homogeneous Lorentzian manifolds, whose isometry group is four-dimensional. As a byproduct, we describe a large class of flat surfaces of constant mean curvature in these ambient spaces and exhibit a family of examples. Full article

This paper investigates totally real submanifolds in a locally conformal Kaehler space form. Using the moving-frame method and constant mean curvature, we obtain the upper and lower bounds of the first eigenvalue for totally real submanifolds in a locally conformal Kaehler space form. We discussed the integral inequalities and their properties. Some previous results are generalized from our results. Full article

In this paper, we examine torse-forming vector fields to characterize extrinsic spheres (that is, totally umbilical hypersurfaces with nonzero constant mean curvatures) in Riemannian and Lorentzian manifolds. First, we analyze the properties of these vector fields on Riemannian manifolds. Next, we focus on Ricci solitons on Riemannian hypersurfaces induced by torse-forming vector fields of Riemannian or Lorentzian manifolds. Specifically, we show that such a hypersurface in the manifold with constant sectional curvature is either totally geodesic or an extrinsic sphere. Full article

We propose an unconditionally stable computational algorithm that preserves the maximum principle for the three-dimensional (3D) high-order Allen–Cahn (AC) equation. The presented algorithm applies an operator-splitting technique that decomposes the original equation into nonlinear and linear diffusion equations. To guarantee the unconditional stability of the numerical solution, we solve the nonlinear equation using the frozen coefficient technique, which simplifies computations by approximating variable coefficients by constants within small regions. For the linear equation, we use an implicit finite difference scheme under the operator-splitting method. To validate the efficiency of the proposed algorithm, we conducted several computational tests. The numerical results confirm that the scheme achieves unconditional stability even for large time step sizes and high-order polynomial potential. In addition, we analyze motion by mean curvature in three-dimensional space and show that the numerical solutions closely match the analytical solutions. Finally, the robustness of the method is evaluated under noisy data conditions, and its ability to accurately classify complex data structures is demonstrated. These results confirm the efficiency and reliability of the proposed computational algorithm for simulating phase-field models with a high-order polynomial potential. Full article

This study aimed to analyze the effect of 1% sodium hypochlorite (NaOCl) solution at different temperatures on endodontic file resistance to cyclic fatigue. A total of 90 files, Reciproc NiTi M-Wire^® (REC) (n = 30), WaveOne Gold^® (WOG) (n = 30), and Reciproc Blue^® (RB) (n = 30) were activated under constant irrigation with 1% NaOCl at 5, 37, and 60 °C in a stainless-steel artificial canal (curvature angle = 60°; radius = 5 mm). The time to the fracture and the maximum and minimum load were recorded for each instrument, and data were subjected to statistical analysis. A higher number of cycles to fracture at 5 °C was observed between WOG and RB compared to the REC system (p < 0.05). The RB files were more resistant to cyclic fatigue fracture at 60 °C than WOG and REC (p < 0.05). No statistically significant differences were found between the mean values of the three file types used at 37 °C. The high temperature of NaOCl significantly affects the lifespan of endodontic files, making them more prone to fractures due to cyclic fatigue. The files manufactured with heat treatment showed a longer life than M-wire reciproc files. Full article

A closed conformal vector field in de Sitter space $S_1^{n+1}\left(\overline{c}\right)$ induces a vector field on a spacelike hypersurface M of $S_1^{n+1}\left(\overline{c}\right)$, referred to as the induced vector field on M. This article investigates the characterization of compact spacelike hypersurfaces in de Sitter space without assuming the constancy of the mean curvature. Specifically, we establish that under certain conditions, a compact spacelike hypersurface in $S_1^{n+1}\left(\overline{c}\right)$ is a sphere, that is, a totally umbilical hypersurface with constant mean curvature. We also present a different characterization of compact spacelike hypersurfaces in de Sitter space as spheres by using a lower bound on the integral of the Ricci curvature of the compact hypersurface in the direction of the induced vector field. We also consider de Sitter space as a Robertson–Walker space and provide several characterizations of spheres within its spacelike hypersurfaces. Full article

The ability of computer simulations to model airflows in a tunnel can significantly contribute to the effectiveness of fire safety precautions. This study examines two ways of modelling the Polana tunnel (Slovakia) and its influence on the airflow created via longitudinal ventilation using a fire dynamics simulator. The first class of studied models is based on the assumption that the airflow in the tunnel is influenced to a large extent by the supporting structures and other installations under the tunnel ceiling. Due to the resolution of the computational grid, the constructions are modelled using a system of cuboids distributed along the tunnel at regular distances. The second class of models combines this approach with the previous one, in which tunnel drag is modelled by increased roughness of the tunnel walls. Unlike the previous model, the roughness values are not constant but reflect the curvature of the tunnel walls. The simulations results are compared against on-site measurements during a full-scale ventilation test conducted in 2017 by a grid of five anemometers, as well as with the results of the previous model. The results agree well with the experimental data with relative errors below 2% for bulk velocities and with mean absolute percentage deviations of 3, 6, and 10% for velocities measured using individual grid anemometers for three ventilation modes. The new models achieve several improvements in accuracy compared to the previous one. Full article

This study is focused on pioneering new upper bounds on mean curvature and constant sectional curvature relative to the first positive eigenvalue of the generalized Laplacian operator in the differentiable manifolds with a semi-symmetric metric connection. Multiple approaches are being explored to determine the principal eigenvalue for the generalized-Laplacian operator in closed oriented-slant submanifolds within a Sasakian space form (ssf) with a semi-symmetric metric (ssm) connection. By utilizing our findings on the Laplacian, we extend several Reilly-type inequalities to the generalized Laplacian on slant submanifolds within a unit sphere with a semi-symmetric metric (ssm) connection. The research is concluded with a detailed examination of specific scenarios. Full article

In this article, we consider the 4 + n dimensional spacetimes among which one is the four dimensional physical Universe and the other is an n-dimensional sphere with constant radius in the framework of Lanczos-Lovelock gravity. We find that the curvature of extra dimensional sphere contributes a huge but negative energy density provided that its radius is sufficiently small, such as the scale of Planck length. Therefore, the huge positive vacuum energy, i.e., the large positive cosmological constant is exactly cancelled out by the curvature of extra sphere. In the mean time the higher order of Lanczos-Lovelock term contributes an observations-allowed small cosmological constant if the number of extra dimensions is sufficiently large, such as n ≈ 69. Full article

In this paper, we conduct a thorough investigation of the surface and curvature tensions, $\sigma$ and $\gamma$, of three-flavor cold quark matter using the Nambu–Jona–Lasinio (NJL) model with vector interactions. Our approach ensures both local and global electric charge neutrality, as well as chemical equilibrium under weak interactions. By employing the multiple reflection expansion formalism to account for finite size effects, we explore the impact of specific input parameters, particularly the vector coupling constant ratio ${\eta }_V$, the radius R of quark matter droplets, as well as the charge-per-baryon ratio $\xi$ of the finite size configurations. We focus on the role of the contributions of each term of the NJL Lagrangian to the surface and curvature tensions in the mean field approximation. We find that the total surface tension exhibits two different density regimes: it remains roughly constant at around $100\mathrm{MeV}{\mathrm{fm}}^{-2}$ up to approximately 2–4 times the nuclear saturation density, and beyond this point, it becomes a steeply increasing function of $n_B$. The total surface and curvature tensions are relatively insensitive to variations in R but are affected by changes in $\xi$ and ${\eta }_V$. We observe that the largest contribution to $\sigma$ and $\gamma$ comes from the regularized divergent term, making these quantities significantly higher than those obtained within the MIT bag model. Full article

Granular soil is a porous medium composed of particles with different sizes and self-similar structures, exhibiting fractal characteristics. It is well established that variations in these fractal properties, such as particle size distribution (PSD), significantly influence the mechanical behavior of the soil. In this paper, a three-dimensional (3D) Discrete Element Method (DEM) is applied to study the mechanical and critical-state behavior of the idealized granular assemblages, in which various PSD shape parameters are considered, including the coefficient of uniformity (C_u), the coefficient of curvature (C_c), and the coefficient of size span (C_s). In addition, the same PSDs but with different mean particle sizes (D₅₀) are also employed in the numerical simulations to examine the particle size effect on the mechanical behavior of the granular media. Numerical triaxial tests are carried out by imposing axial compression under constant mean effective pressure conditions. A unique critical-state stress ratio in p′-q space is observed, indicating that the critical friction angle is independent of the shape of the PSD. However, in the e-p′ plane, the critical state line (CSL) shifts downward and rotates counterclockwise, as the grading becomes more widely distributed, i.e., the increasing coefficient of span (C_s). Additionally, a decrease in the coefficient of curvature (C_c) would also move the CSL downward but with negligible rotation. However, it is found that the variations in the mean particle size (D₅₀) and coefficient of uniformity (C_u) do not affect the position of the CSL in the e-p′ plane. The numerical findings may shed some light on the development of constitutive models of sand that undergo variations in the grading due to crushing and erosion, and address fractal problems related to micro-mechanics in soils. Full article

The Wintgen inequality is a significant result in the field of differential geometry, specifically related to the study of submanifolds in Riemannian manifolds. It was discovered by Pierre Wintgen. In the present work, we deal with the Riemannian maps between Riemannian manifolds that serve as a superb method for comparing the geometric structures of the source and target manifolds. This article is the first to explore a well-known conjecture, called DDVV inequality (a conjecture for Wintgen inequality on Riemannian submanifolds in real space forms proven by P.J. De Smet, F. Dillen, L. Verstraelen and L. Vrancken), for Riemannian maps, where we consider different space forms as target manifolds. There are numerous research problems related to such inequality in various ambient manifolds. These problems can all be explored within the general framework of Riemannian maps between various Riemannian manifolds equipped with notable geometric structures. Full article

Background: Pisa syndrome, also known as pleurothotonus, is a neurological condition characterized by more than ten degrees of constant lateral curvature of the spine when upright. In this way, the present manuscript aims to systematically review Pisa syndrome secondary to drugs. Methods: Two reviewers identified and assessed relevant reports in six databases without language restriction between January 1990 and June 2024. Results: The prevalence of Pisa syndrome varied from 0.037 to 9.3%. We found 109 articles containing 191 cases of drug-induced Pisa syndrome reported in the literature. The mean and median ages were 59.70 (SD = 19.02) and 67 (range = 12–98 years). The most prevalent sex was female, 56.91% (107/188). The most frequent medications associated with Pisa syndrome were acetylcholinesterase inhibitors in 87 individuals. Of 112 individuals in which the onset time from the medication to the movement disorder occurrence was reported, 59 took place within a month. In this way, a return to baseline was observed in 45.50% of the cases, and partial recovery was observed in 14.28%. Conclusion: We proposed new diagnostic criteria for Pisa syndrome based on previous findings in the literature. Moreover, multiple mechanisms are probably involved in balance control and the development of lateral trunk flexions. Full article

Helicoidal surfaces of constant mean curvature were fully described by do Carmo and Dajczer. However, the obtained parameterizations are given in terms of somewhat complicated integrals, and as a consequence, not many examples of such surfaces are visualized. In this paper, by using these methods in some particular cases, we provide several interesting visualizations involving these surfaces, mostly as an isometric deformation of a rotational surface. We also give interpretations of some older results involving helicoidal surfaces, motivated by the work carried out by Malkowsky and Veličković. All of the graphics in this paper were created in Wolfram Mathematica. Full article

In this note, we investigate the pinching problem for oriented compact submanifolds of dimension n with parallel normalized mean curvature vector in a space form $F^{n+p}\left(c\right)$. We first prove a codimension reduction theorem for submanifolds under lower Ricci curvature bounds. Moreover, if the submanifolds have constant normalized scalar curvature $R\ge c$, we obtain a classification theorem for submanifolds under lower Ricci curvature bounds. It should be emphasized that our Ricci pinching conditions are sharp for even n and $p=2$. Full article