A complementary covariant approach to gravito-electromagnetism

From a previous paper where we proposed a description of general relativity within the gravito-electromagnetic limit, we propose an alternative modified gravitational theory. As in the former version, we analyze the vector and tensor equations of motion, the gravitational continuity equation, the conservation of the energy, the energy-momentum tensor, the field tensor, and the constraints concerning these fields. The Lagrangian formulation is also exhibited as an unified and simple formulation that will be useful for future investigation.

Simulation study towards quantitative X-ray and neutron tensor tomography regarding the validity of linear approximations of dark-field anisotropy

Tensor tomography is fundamentally based on the assumption of a both anisotropic and linear contrast mechanism. While the X-ray or neutron dark-field contrast obtained with Talbot(-Lau) interferometers features the required anisotropy, a preceding detailed study of dark-field signal origination however found its specific orientation dependence to be a non-linear function of the underlying anisotropic mass distribution and its orientation, especially challenging the common assumption that dark-field signals are describable by a function over the unit sphere. Here, two approximative linear tensor models with reduced orientation dependence are investigated in a simulation study with regard to their applicability to grating based X-ray or neutron dark-field tensor tomography. By systematically simulating and reconstructing a large sample of isolated volume elements covering the full range of feasible anisotropies and orientations, direct correspondences are drawn between the respective tensors characterizing the physically based dark-field model used for signal synthesization and the mathematically motivated simplified models used for reconstruction. The anisotropy of freely rotating volume elements is thereby confirmed to be, for practical reconstruction purposes, approximable both as a function of the optical axis’ orientation or as a function of the interferometer’s grating orientation. The eigenvalues of the surrogate models’ tensors are found to exhibit fuzzy, yet almost linear relations to those of the synthesization model. Dominant orientations are found to be recoverable with a margin of error on the order of magnitude of 1$$^{\circ }$$ ∘ . Although the input data must adequately address the full orientation dependence of dark-field anisotropy, the present results clearly support the general feasibility of quantitative X-ray dark-field tensor tomography within an inherent yet acceptable statistical margin of uncertainty.

An Analysis of Gravitational waves

The September 14, 2015 gravitational wave observations showed the inspiral of two black holes observed from Hanford and Livingston LIGO observatories. This detection was significant for two reasons: firstly, it coupled the result and avoided the possibility of a false alarm by 5σ , meaning that the detected “noise” was indeed from an astronomical source of gravitational waves. We will discuss the primary landscape of gravitational waves, their mathematical structure and how they can be used to predict the masses of the merger system. We will also discuss gravitational wave detector optimisations, and then we will consider the results from the detected merger GW150914. We will consider a straight-forward mathematical approach, and we will primarily be interested in the mathematical modelling of gravitational waves from General Relativity (Section 1). We will first consider a “perturbed” Minkowski metric, and then we will discuss the properties of the perturbation addition tensor. We will then discuss on the gravitational field tensor, and how it arises from the perturbation tensor. We will then talk about the gauge condition, essentially the gauge “freedom” , and then we will talk about the curvature tensor, leading eventually to the effect of gravitational waves on a ring of particles. We will consider the polarisation tensor, which maps the amplitude and polarisation details. The polarisation splits into plus polarised and cross polarised waves, which is technically the effect of a propagating gravitational wave through a ring of particles. We will then talk about the linearized Einstein Field Equations, and how the physical system of merger is encoded into the mathematical structural unity of the metric. We will then talk about the detection of these gravitational waves and how the detector can be optimised, or how the detector can be set so that any “noise” detected can fall in the error margins, and how the detector can prevent the interferometric “photon-noise” from being detected (Section 2.2). Then, we will discuss data results from the source GW150914 detection by LIGO (Section 3).

Toward Nonlocal Electrodynamics of Accelerated Systems

We revisit acceleration-induced nonlocal electrodynamics and the phenomenon of photon spin-rotation coupling. The kernel of the theory for the electromagnetic field tensor involves parity violation under the assumption of linearity of the field kernel in the acceleration tensor. However, we show that parity conservation can be maintained by extending the field kernel to include quadratic terms in the acceleration tensor. The field kernel must vanish in the absence of acceleration; otherwise, a general dependence of the kernel on the acceleration tensor cannot be theoretically excluded. The physical implications of the quadratic kernel are briefly discussed.

Application of the normalized largest eigenvalue of structure tensor in the interpretation of potential field tensor data

Obtaining horizontal edges and the buried depths of geological bodies, using potential field tensor data directly is an outstanding question. The largest eigenvalue of the structure tensor is one of the commonly used edge detectors for delineating the horizontal edges without depth information of the potential field tensor data. In this study, we presented a normalized largest eigenvalue of structure tensor method based on the normalized downward continuation (NDC) to invert the source location parameters without any priori information. To improve the stability and accuracy of the NDC calculation, the Chebyshev–Pade´ approximation downward continuation method was introduced to obtain the potential field data on different depth levels. The new approach was tested on various models data with and without noise, which validated that it can simultaneously obtain the horizontal edges and the buried depths of the geological bodies. The satisfactory results demonstrated that the normalized largest eigenvalue of structure tensor can describe the locations of geological sources and decrease the noise interference magnified by the downward continuation. Finally, the method was applied to the gravity data over the Humble salt dome in USA, and the near-bottom magnetic data over the Southwest Indian Ridge. The results show a good correspondence to the results of previous work.

Numerical Modeling of Stress Disturbance Characteristics during Tunnel Excavation

The stress state and principal stress axis changes of the stress-field tensor are analyzed during the advancement of a tunnel face on the basis of a given case study of the Jinping II Hydropower Station in China. First, the prevailing pole diagram in geology is used to illustrate the rotation of the stress axes as the tunnel face advances. The results show that the orientation adjustments of principal stresses in different positions near the tunnel boundary share common characteristics. The major and minor principal stress axes ahead of the tunnel face will rotate to intersect with the excavation surface at an angle, with the intermediate principal stress axis being almost parallel to the excavation surface. Furthermore, the stress triaxiality that is commonly used to indicate the deformation and damage of metal materials is introduced to describe the stress state change of the excavation-induced stress. The stress triaxiality is found to represent the stress state change due to the variation in both the magnitude and orientation of the stress-field tensor. According to the physical meaning and the change law of the stress triaxiality, stress disturbance during tunnel excavation can be divided into four stages, and the stress disturbance zone is divided into a strong disturbance zone and a weak disturbance zone. The disturbance characteristics of different stages and the distribution patterns of various zones are analyzed, which may be useful for practical application in the design and construction of rock tunnels.

A Four-Node Tetrahedral Finite Element Based on Space Fiber Rotation Concept

The paper presents a four-node tetrahedral solid finite element SFR4 with rotational degrees of freedom (DOFs) based on the Space Fiber Rotation (SFR) concept for modeling three-dimensional solid structures. This SFR concept is based on the idea that a 3D virtual fiber, after a spatial rotation, introduces an enhancement of the strain field tensor approximation. Full numerical integration is used to evaluate the element stiffness matrix. To demonstrate the efficiency and accuracy of the developed four-node tetrahedron solid element and to compare its performance with the classical four-node tetrahedral element, extensive numerical studies are presented.