An Analytical Approach to Obtaining the Stress Field of a Cylindrical Shell with a Circular Hole under Tension

The problem of a cylindrical shell with a circular hole under uniaxial tension is considered. The main obstacle of solving this problem is the necessity to find such coefficients in the expansion of the solution into a sum of basis functions, for which this solution satisfies the boundary conditions. The study of the classical works led to understanding that none of the so far proposed approaches can be considered successfully, and the results of these approaches differ, so it is not clear, which results can be used as a basis. In the present paper, a new analytical approach to studying this issue is proposed. It allows expanding the range of applicability of the solution and gives the opportunity for the analytical study of the stress state. The idea consists in expanding each of the basis functions in a Fourier series by dividing the variables, which allows obtaining explicitly an infinite system of algebraic equations for finding coefficients. One of the important steps of this research is that the authors were able to prove which exact equation is a linear combination of the others and exclude, which made it possible to compose a reduced system for finding unknown coefficients. The proposed approach, in contrast to most classical works, does not impose mathematical restrictions on the values of the main parameter characterizing the cylindrical shell. The existing restrictions are of mechanical nature, as larger cutouts require another model. Moreover, the numerical results obtained by the new method are presented in a fairly complete manner and they are compared with the results of the classical works.

Periarticular lesions as actual problem of general practice: modern possibilities of diagnosis and boosting effectiveness of treatment

Background. Lesions of extra-articular soft tissues occupy a leading place in the structure of diseases of the musculoskeletal system in primary health care. At the same time, insuffcient attention is paid to this pathology, which leads to a decrease in the quality of care for patients with extra-articular pathology.Objective. Increasing the awareness of general practitioners about the clinical forms of extra-articular soft tissue diseases, current approaches to diagnosis and treatment.Basic provisions. The article presents the characteristics of the main forms of periarticular lesions: periarthritis, incl. painful shoulder, tendonitis, tenosynovitis, capsulitis, bursitis. The leading mechanisms of periarticular disorders are presented, the clinical picture and diagnostic signs of particular forms are described. The role of modern methods of visualization of periarticular lesions using ultrasound and MRI is noted. The main approaches to the drug therapy of periarticular disorders are presented, including use of slow-acting symptom-modifying drugs (SYSADOA). The authors present their own data demonstrating the connective tissue metabolism disturbance in periarticular disorders as well as the effectiveness of the drug Alflutop in the treatment of periarticular lesions of a ‘mechanical’ nature.Conclusions. Primary forms of periarticular disorders are a consequence of microtraumatization and can be attributed to ‘mechanical’ types of damage. The ultrasound is pivotal in the diagnosis and evaluation the severity of the lesion and its origin. Biomarkers of connective tissue damage can be detected in the blood of patients with periarticular disorders. The treatment results can be improved with drugs from the SYSADOA group.

The Jaynes–Cummings model of a two-level atom in a single-mode para-Bose cavity field

The coherent states in the parity deformed analog of standard boson Glauber coherent states are generated, which admit a resolution of unity with a positive measure. The quantum-mechanical nature of the light field of these para-Bose states is studied, and it is found that para-Bose order plays an important role in the nonclassical behaviors including photon antibunching, sub-Poissonian statistics, signal-to-quantum noise ratio, quadrature squeezing effect, and multi-peaked number distribution. Furthermore, we consider the Jaynes-Cummings model of a two-level atom in a para-Bose cavity field with the initial states of the excited and Glauber coherent ones when the atom makes one-photon transitions, and obtain exact energy spectrum and eigenstates of the deformed model. Nonclassical properties of the time-evolved para-Bose atom-field states are exhibited through evaluating the fidelity, evolution of atomic inversion, level damping, and von Neumann entropy. It is shown that the evolution time and the para-Bose order control these properties.

Black Holes as Possible Dark Matter

Black holes and Dark matter are two fascinating things that are known very little. They may have non gravitational interactions, but those are definitely extremely feeble in comparison to their gravitational interactions. Nowadays some people think that one may contain the other. In this chapter we will see that some black holes may contain the dark matter. These black holes decay under Hawking radiation, but do not vanish completely. They produce stable end states due to both quantum gravitational effects and thermodynamic reasons. These end states are the replicas of what we call dark matter. We will develop the complete theory for decay of such black holes, starting from some scheme independent assumptions for the quantum mechanical nature of the black holes. We will then consider explicit examples of some black holes to show that they indeed produce replicas of dark matter at their end states. Thus this chapter is going to be a manuscript for theoretical development of black hole decay from a quantum mechanical perspective and its consequences for producing replicas of dark matter.

Time "mechanization" and Thomas Carlyle

English historian,publicist and philosopher Thomas Carlylesle(1795-1881) created a lot of valuable works,but researchers mark out his critical Essays and among them “Signs of Time” is the best.In this work the writer tries to make the reader active.He describes Victorian period,uses intellectual heroes of the past and is against Mechanisation of the present.He gives many arguments for perfect description in order to maintain a contact with a reader and to make it clear for the reader the meaning of Mechanism.So,he wants to emphasise mechanical nature of the society of that time,as these mechanisms become the target for every human.The Essay was written in 1829 in a journal Edinburgh Review and there should have been three book reviews,but he went far more beyond his particular aim and presented increasing the admiration of technical and mechanical things and regarded it as a decay of society.

Study on Evolution Characteristics and Instability Model of Overburden Stress Shell with the Longwall Mining along Strike

Roof fracture is one of the main reasons for dynamic disaster in working face. During the process of long wall mining, due to the continuous fracture and collapse of roof, a stress shell composed of high stress is formed around the surrounding rock of the stope. The gravity of the overlying rock is transferred to the coal body around the stope through the stress shell. With the advancing of the working face, the stress shell has undergone the dynamic evolution process of the initial shell, extension shell, and flat shell. Based on the theory of shell and plate, the mechanical model of elliptical thin rock plate is constructed. The stress and bending moment distribution expressions of elliptic structure are obtained under two boundary conditions: the surrounding fixed-supported edges and simply supported edges. The results show that cracks begin to appear at the middle point of the semimajor axis and propagate along both ends of the semimajor axis. Then the fracture begins at the end of the semiminor axis, and the crack extends along the arc direction, forming an “X-O” type fracture. Finally, the mechanical nature of the stress shell instability is the result of the tensile fracture of the bedrock at the top of the shell.

Optical current generation in graphene: CEP control vs. ω + 2ω control

The injection of directional currents in solids with strong optical fields has attracted tremendous attention as a route to realize ultrafast electronics based on the quantum-mechanical nature of electrons at femto- to attosecond timescales. Such currents are usually the result of an asymmetric population distribution imprinted by the temporal symmetry of the driving field. Here we compare two experimental schemes that allow control over the amplitude and direction of light-field-driven currents excited in graphene. Both schemes rely on shaping the incident laser field with one parameter only: either the carrier-envelope phase (CEP) of a single laser pulse or the relative phase between pulses oscillating at angular frequencies ω and 2ω, both for comparable laser parameters. We observe that the efficiency in generating a current via two-color-control exceeds that of CEP control by more than two orders of magnitude (7 nA vs. 18 pA), as the ω + 2ω field exhibits significantly more asymmetry in its temporal shape. We support this finding with numerical simulations that clearly show that two-color current control in graphene is superior, even down to single-cycle pulse durations. We expect our results to be relevant to experimentally access fundamental properties of any solid at ultrafast timescales, as well as for the emerging field of petahertz electronics.

The problem of the partial delamination of the elastic interface thin inclusion in the conditions of longitudinal shear of the bimaterial

The problem of longitudinal displacement of a bi -material with a thin inclusion of arbitrary physical and mechanical nature at the interface of the matrix materials is considered. The bulk is loaded by normal compression and various force factors in the longitudinal direction. The possibility of partial delamination of a part of the boundary between the inclusion and the matrix, where dry friction slip occurs, is assumed. A complete system of equations for the formulated problem is constructed. It is proposed to construct the solution using the structural modular method of jump functions, a description of which is given. A condition for the appearance of a slip zone on the inclusion-matrix boundary is founded. A convergent iterative algorithm for numerically analytical determination of the size of this zone is developed.