Criterion of Quantum Entanglement and the Covariance Correlation Tensor in the Theory of Quantum Network

This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum network of three nodes, thus gives the criterion of entanglement for this case, i.e. the conditions of complete separability and partial separability for a given quantum state of three bodies. Finally it discusses the general case for the quantum network of nodes.

Correspondence Between Bell Bases and Oriented Links in Knot Theory

From the comparison of correlation tensor in the theory of quantum network, the Alexander relation matrix in the theory of knot crystals and the identical inversion relations under the action of Pauli matrices, we show that there is a one to one correspondence between four Bell bases and four oriented links of the linkage in knot theory.

Numerical modelling of spatially and temporally distributed on‑fault induced seismicity:implication for seismic hazards

Induced seismicity is strongly related to various engineering projects that cause anthropogenic in-situ stress change at a great depth.Hence,there is a need to estimate and mitigate the associated risks.In the past,various simulation methods have been developed and applied to induced seismicity analysis,but there is still a fundamental diference between simulation results and feld observations in terms of the spatial distribution of seismic events and its frequency.The present study aims to develop a method to simulate spatially distributed on-fault seismicity whilst reproducing a complex stress state in the fault zone.Hence,an equivalent continuum model is constructed,based on a discrete fracture network within a fault damage zone,by employing the crack tensor theory.A fault core is simulated at the center of the model as a discontinuous plane.Using the model,a heterogeneous stress state with stress anomalies in the fault zone is frst simulated by applying tractions on the model outer boundaries.Subsequently,the efective normal stress on the fault plane is decreased in a stepwise manner to induce slip.The simulation result is validated in terms of the b-value and other seismic source parameters,hence demonstrating that the model can reproduce spatially and temporally distributed on-fault seismicity.Further analysis on the parameters shows the variation of frequency-magnitude distribution before the occurrence of large seismic events.This variation is found to be consistent with feld observations,thus suggesting the potential use of this simulation method in evaluating the risk for seismic hazards in various engineering projects.

Linear polarization holography

Polarization holography is a newly researched field,that has gained traction with the development of tensor theory.It primarily focuses on the interaction between polarization waves and photosensitive materials.The extraordinary capabil-ities in modulating the amplitude,phase,and polarization of light have resulted in several new applications,such as holo-graphic storage technology,multichannel polarization multiplexing,vector beams,and optical functional devices.In this paper,fundamental research on polarization holography with linear polarized wave,a component of the theory of polariz-ation holography,has been reviewed.Primarily,the effect of various polarization changes on the linear and nonlinear po-larization characteristics of reconstructed wave under continuous exposure and during holographic recording and recon-struction have been focused upon.The polarization modulation realized using these polarization characteristics exhibits unusual functionalities,rendering polarization holography as an attractive research topic in many fields of applications.This paper aims to provide readers with new insights and broaden the application of polarization holography in more sci-entific and technological research fields.

Separability of Pure States and Mixed States of the Quantum Network of Two Nodes

This article discusses the separability of the pure states and mixed states of the quantum network of two nodes by means of the criterion of no entanglement in terms of the covariance correlation tensor in quantum network theory, i.e. for a composite system consisting of two nodes. The covariance correlation tensor is equal to zero for all possible and .

SIMULATION OF FABRIC DRAPE USING A THIN PLATE ELEMENT WITH FINITE ROTATION

The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representation of finite rotation is introduced. The strain energy function accounting for the material symmetry is obtained by the tensor representation theory. To avoid shear locking, the assumed strain technique for transverse shear is adopted. The conjugate gradient method with a proposed line search algorithm is employed to minimize energy and reach the final shape of fabric. The draping behavior of a rectangular piece of fabric over a rectangular table is simulated. (Author abstract) 9 Refs.

Reconstruction of constant slow-roll inflation

Using the relations between the slow-roll parameters and the power spectra for the single field slow-roll inflation, we derive the scalar spectral tilt n, and the tensor to scalar ratio r for the constant slow-roll inflation, and obtain the constraint on the slow-roll parameter ηfrom the Planck 2015 results. The inflationary potential for the constant slow-roll inflation is then reconstructed in the framework of both general relativity and the scalar-tensor theory of gravity, and compared with the recently reconstructed E model potential. In the strong coupling limit, we show that the η attractor is reached.