variable theory
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Author(s):  
V.N. Zakharov ◽  
V.A. Trofimov ◽  
A.V. Shlyapin

Formation of the stress-and-strain state of the rock mass in the roof of mined coal seam depends on the development of the mined-out space. It is believed that the coal seam is located deep enough and it can be assumed that the effect of the daylight surface on its condition can be neglected. In this case, the solution is based on the analytical approach using methods of the complex variable theory and it is reduced to the construction of a single permission analytical function. The paper reviews the evolution of the deformation processes in development of the mined-out space in presence of a hard-to-collapse elastic roof, which is capable of sinking smoothly over time, without sudden caving on the landings on the floor. A particular attention is paid to the phase when the roof and the floor touch each other, i.e. the roof caving, starting from the first touching and up to its complete caving. In this case, two sections of the hanging roof are formed, that are gradually reducing in length as the dimensions of the mined-out space increase. The area of roof caving is progressively increasing, and the vertical compressive stresses at the boundary are gradually rising, tending to reach the initial vertical pressure at the depth of the formation before the start of its mining. Tension zones relative to the horizontal and vertical stresses are identified, that are attributed to the areas of roof hang-up, which may determine the location of zones with higher methane and formation water permeability, both in the rocks between the seams and in the coal seam.


Aerospace ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 17
Author(s):  
Chenchun Chiu ◽  
Shaochen Tseng ◽  
Chingkong Chao ◽  
Jheyuan Guo

The failure analysis of a non-circular hole with an inclusion layer embedded in an infinite cracked matrix under a remote in-plane uniform load is presented. In this study, a series solution of stress functions for both the matrix and inclusion layer is obtained using the complex variable theory in conjunction with the method of conformal mapping. The stress intensity factor (SIF) can then be determined numerically by solving the singular integral equation (SIE) for the interaction among different crack sites, material properties, and geometries of irregular holes with an inclusion layer. In particular, the failure behavior of composite structures associated with an approximately triangular hole and an approximately square hole with inclusion layers, such as those of oxides, nitrides, and sulfides, is examined in detail. The results demonstrate that a softer layer would enhance the SIF and a stiffer layer would restrain the SIF when a crack is near the inclusion layer. It can be concluded that crack propagation would be suppressed by a stiffer layer even when a micro-defect such as a hole resides in the inclusion layer.


2021 ◽  
pp. e20210023
Author(s):  
Stéphanie E. M. Gauvin ◽  
Kathleen E. Merwin ◽  
Jessica A. Maxwell ◽  
Chelsea D. Kilimnik ◽  
John Kitchener Sakaluk

Sexual scientists typically default to appraising the reliability of their self-report measures by calculating one or more α coefficients. Despite the prolific use of α, few researchers understand how to situate and make sense of α within the psychometric theories used to develop the measures used in their research (e.g., latent variable theory) and many unknowingly violate the assumptions of α. In this paper, we describe the disconnect between α and latent variable theory and the subsequent restrictive assumptions α makes. Simultaneously, we introduce an alternative metric of reliability—omega (ɷ)—that is compatible with latent variable theory. Subsequently, we provide a tutorial to walk readers through didactic examples on how to calculate ɷ metrics of reliability using the getOmega() function—a simple open-source function we created to automate the estimation of ɷ. We then introduce the Measurement of Sexuality and Intimacy Constructs (MoSaIC) project to provide insight into the state of reliability in sexuality science. We do this through contrasting α and ɷ estimates of reliability across seven sexuality measures, selected based on their emerging and pre-existing relevance and influence in the field of sexuality, in both a queer (LGBTQ+) sample ( n = 545) and a United States’ representative sample ( n = 548). We finish our paper with pragmatic suggestions for editors, reviewers, and authors. By more deeply understanding one’s options of reliability metrics, sexual scientists may carefully consider how they present and assess their measures’ reliability, and ultimately help improve our science’s replicability.


Author(s):  
Cem Civelek

Purpose The purpose of this paper is to analyze the dynamical state of a discrete time engineering/physical dynamic system. The analysis is performed based on observability, controllability and stability first using difference equations of generalized motion obtained through discrete time equations of dissipative generalized motion derived from discrete Lagrange-dissipative model [{L,D}-model] for short of a discrete time observed dynamic system. As a next step, the same system has also been analyzed related to observability, controllability and stability concepts but this time using discrete dissipative canonical equations derived from a discrete Hamiltonian system together with discrete generalized velocity proportional Rayleigh dissipation function. The methods have been applied to a coupled (electromechanical) example in different formulation types. Design/methodology/approach An observability, controllability and stability analysis of a discrete time observed dynamic system using discrete equations of generalized motion obtained through discrete {L,D}-model and discrete dissipative canonical equations obtained through discrete Hamiltonian together with discrete generalized velocity proportional Rayleigh dissipation function. Findings The related analysis can be carried out easily depending on the values of classical elements. Originality/value Discrete equations of generalized motion and discrete dissipative canonical equations obtained by discrete Lagrangian and discrete Hamiltonian, respectively, together with velocity proportional discrete dissipative function are used to analyze a discrete time observed engineering system by means of observability, controllability and stability using state variable theory and in the method proposed, the physical quantities do not need to be converted one to another.


2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhiqiang Wang ◽  
Chao Wu ◽  
Jianqiao Luo ◽  
Wenyu Lv ◽  
Lei Shi ◽  
...  

Aiming at the problem of the serious deformation of the mining roadways in the trapezoidal section of the coal mine, the method of combining theoretical analysis and field application is used to study the surrounding rock control method of the trapezoidal roadways. The conformal mapping function of the trapezoidal roadways is calculated by the theory of complex change, and then from the analytical solution of the tangential stress distributed in the surrounding rock of trapezoidal roadways which is under the influence of the bidirectional unequal pressure, homogeneous, isotropic, and elastic rock mass is obtained. Research studies show that the roof-stress distribution of the trapezoidal roadways is uniform and the confining pressure is small, while the two sidewalls and the floor are opposite. The stress distribution of the two sidewalls and the floor varies greatly, and the stress concentration factor is large. The top corner of the trapezoidal roadways is basically not affected by stress concentration, but the stress concentration coefficient at the bottom corner is relatively large, and reinforcement measures are required in the roadway support. Based on the aforementioned research results, the multisupport scheme of “bolting with wire mesh and anchor cable + W-type steel belt + joist steel shed support + anchor cable grouting” was proposed to the surrounding rock of trapezoidal roadways with large stress caused by mining influence, thus solving the actual mining problem.


Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 499
Author(s):  
Joseph Bowles ◽  
Flavien Hirsch ◽  
Daniel Cavalcanti

Activation of Bell nonlocality refers to the phenomenon that some entangled mixed states that admit a local hidden variable model in the standard Bell scenario nevertheless reveal their nonlocal nature in more exotic measurement scenarios. We present such a scenario that involves broadcasting the local subsystems of a single-copy of a bipartite quantum state to multiple parties, and use the scenario to study the nonlocal properties of the two-qubit isotropic state:ρα=α|Φ+⟩⟨Φ+|+(1−α)14.We present two main results, considering that Nature allows for (i) the most general no-signalling correlations, and (ii) the most general quantum correlations at the level of any hidden variable theory. We show that the state does not admit a local hidden variable description for α>0.559 and α>12, in cases (i) and (ii) respectively, which in both cases provides a device-independent certification of the entanglement of the state. These bounds are significantly lower than the previously best-known bound of 0.697 for both Bell nonlocality and device-independent entanglement certification using a single copy of the state. Our results show that strong examples of non-classicality are possible with a small number of resources.


2021 ◽  
Vol 53 (7) ◽  
Author(s):  
Ali Motazedifard ◽  
Seyed Ahmad Madani ◽  
N. S. Vayaghan

AbstractUsing the type-I SPDC process in BBO nonlinear crystal, we generate a polarization-entangled state near to the maximally-entangled Bell-state with high-visibility (high-brightness) 98.50 ± 1.33% (87.71 ± 4.45%) for HV (DA) basis. We calculate the CHSH version of the Bell inequality, as a nonlocal realism test, and find a strong violation from the classical physics or any hidden variable theory, S = 2.71 ± 0.10. Via measuring the coincidence count rate in the SPDC process, we obtain the quantum efficiency of single-photon detectors around (25.5 ± 3.4)%, which is in good agreement to their manufacturer company. As expected, we verify the linear dependency of the CC rate vs. pump power of input CW-laser, which may yield to find the effective second-order susceptibility crystal. Using the theory of the measurement of qubits, includes a tomographic reconstruction of quantum states due to the linear set of 16 polarization-measurement, together with a maximum-likelihood-technique, which is based on the numerical optimization, we calculate the physical non-negative definite density matrices, which implies on the non-separability and entanglement of prepared state. By having the maximum likelihood density operator, we calculate precisely the entanglement measures such as Concurrence, entanglement of formation, tangle, logarithmic negativity, and different entanglement entropies such as linear entropy, Von-Neumann entropy, and Renyi 2-entropy. Finally, this high-brightness and low-rate entangled photons source can be used for short-range quantum measurements in the Lab.


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