Some classes of Kenmotsu manifolds with respect to semi-symmetric metric connection

In this paper, we study conharmonic curvature tensor in Kenmotsu manifolds with respect to semi-symmetric metric connection and also characterize conharmonically flat, conharmonically semi-symmetric and φ-conharmonically flat Kenmotsu manifolds with respect to semi-symmetric metric connection.     

Reflective mode of deformed-helix ferroelectric liquid crystal cells for sensing applications

We present a detailed theoretical and experimental study of the reflectance response of a deformed-helix ferroelectric (DHF) liquid crystal (LC) cell to an applied voltage under cross-polarisers. Using a model based on the effective dielectric tensor approximation, we derive simple analytical formulas to design a LC cell with maximum modulation depth and optimal linearity of the electro-optical response intensity versus the electric field. Our experimental results show that the cell works at frequencies up to 10 kHz and exhibits excellent linearity, with a total harmonic distortion as low as ?70 dB. These findings suggest that DHF-LCs can be exploited to develop simple and accurate optical sensors.     

First stability eigenvalue characterization of CMC Hopf tori into Riemannian Killing submersions

We find out upper bounds for the first eigenvalue of the stability operator for compact constant mean curvature orientable surfaces immersed in a Riemannian Killing submersion. As a consequence, the strong stability of such surfaces is studied. We also characterize constant mean curvature Hopf tori as the only ones attaining the bound in certain cases.     

The effect of noise on the dirac phase of electron in the presence of screw dislocation

The effect of noise on the Dirac phase of electron in the presence of screw dislocation is studied. An uncorrelated noise, which coincides with the nature of thermal fluctuations, is adopted. Results indicate that the Dirac phase is robust against the existing noise in the system.     

薄板弯曲分析的节点积分高阶无网格法

采用高阶无网格法求解薄板弯曲问题，在已发展的线性曲率光顺方案的基础上，通过引入泰勒展开技术，建立了能够精确再现纯弯曲和线性弯曲模式的节点积分方法。与之相比，目前无网格薄板分析主要采用的节点积分方法仅能精确再现纯弯曲模式。数值结果表明，本文方法可精确通过纯弯曲和线性弯曲试验，且能得到光滑、无振荡的弯矩场。与标准的高斯积分方法和目前已存在的节点积分方法相比，本文方法在计算精度、效率以及弯矩分布等方面均展现出显著优势。     

The prescribed Ricci curvature problem on three‐dimensional unimodular Lie groups

Let G be a three‐dimensional unimodular Lie group, and let T be a left‐invariant symmetric (0,2)‐tensor field on G. We provide the necessary and sufficient conditions on T for the existence of a pair consisting of a left‐invariant Riemannian metric g and a positive constant c such that , where is the Ricci curvature of g. We also discuss the uniqueness of such pairs and show that, in most cases, there exists at most one positive constant c such that is solvable for some left‐invariant Riemannian metric g.     

Mean curvature flow with free boundary – Type 2 singularities

In this paper we give sufficient conditions that guarantee the mean curvature flow with free boundary on a pinched cylinder develops a Type 2 curvature singularity. We additionally prove that Type 0 singularities may only occur at infinity.     

A cost‐effective curvature calculation approach for interfacial flows on unstructured meshes

We present a simple and cost‐effective curvature calculation approach for simulations of interfacial flows on structured and unstructured grids. The interface is defined using volume fractions, and the interface curvature is obtained as a function of the gradients of volume fractions. The gradient computation is based on a recently proposed gradient recovery method that mimicks the least squares approach without the need to solve a system of equations and is quite easy to implement on arbitrary polygonal meshes. The resulting interface curvature is used in a continuum surface force formulation within the framework of a well‐balanced finite‐volume algorithm to simulate multiphase flows dominated by surface tension. We show that the proposed curvature calculation is at least as accurate as some of the existing approaches on unstructured meshes while being straightforward to implement on any mesh topology. Numerical investigations also show that spurious currents in stationary problems that are dependent on the curvature calculation methodology are also acceptably low using the proposed approach. Studies on capillary waves and rising bubbles in viscous flows lend credence to the ability of the proposed method as an inexpensive, robust, and reasonably accurate approach for curvature calculation and numerical simulation of multiphase flows.     

Geometric derivation of the microscopic stress: A covariant central force decomposition

We revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation is the Doyle–Ericksen formula, which states that the Cauchy stress tensor is the derivative of the free-energy with respect to the ambient metric tensor and which follows from a covariance argument. Thus, our approach to define the microscopic stress tensor does not rely on the statement of balance of linear momentum as in the classical Irving–Kirkwood–Noll approach. Nevertheless, the resulting stress tensor satisfies balance of linear and angular momentum. Furthermore, our approach removes the ambiguity in the definition of the microscopic stress in the presence of multibody interactions by naturally suggesting a canonical and physically motivated force decomposition into pairwise terms, a key ingredient in this theory. As a result, our approach provides objective expressions to compute a microscopic stress for a system in equilibrium and for force-fields expanded into multibody interactions of arbitrarily high order. We illustrate the proposed methodology with molecular dynamics simulations of a fibrous protein using a force-field involving up to 5-body interactions.