Behavior of solution of the elasticity problem for a radial inhomogeneous cylinder with small thickness

A non-axisymmetric problem of the theory of elasticity for a radial inhomogeneous cylinder of small thickness is studied. It is assumed that the elastic moduli are arbitrary positive piecewise continuous functions of a variable along the radius. Using the method of asymptotic integration of the equations of the theory of elasticity, based on three iterative processes, a qualitative analysis of the stress-strain state of a radial inhomogeneous cylinder is carried out. On the basis of the first iterative process of the method of asymptotic integration of the equations of the theory of elasticity, particular solutions of the equilibrium equations are constructed in the case when a smooth load is specified on the lateral surface of the cylinder. An algorithm for constructing partial solutions of the equilibrium equations for special types of loads, the lateral surface of which is loaded by forces polynomially dependent on the axial coordinate, is carried out. Homogeneous solutions are constructed, i.e., any solutions of the equilibrium equations that satisfy the condition of the absence of stresses on the lateral surfaces. It is shown that homogeneous solutions are composed of three types: penetrating solutions, solutions of the simple edge effect type, and boundary layer solutions. The nature of the stress-strain state is established. It is found that the penetrating solution and solutions having the character of the edge effect determine the internal stress-strain state of a radial inhomogeneous cylinder. Solutions that have the character of a boundary layer are localized at the ends of the cylinder and exponentially decrease with distance from the ends. These solutions are absent in applied shell theories. Based on the obtained asymptotic expansions of homogeneous solutions, it is possible to carry out estimates to determine the range of applicability of existing applied theories for cylindrical shells. Based on the constructed solutions, it is possible to propose a new refined applied theory.

Dark soliton solutions of the cubic-quintic complex Ginzburg–Landau equation with high-order terms and potential barriers in normal-dispersion fiber lasers

In this paper, we numerically study dark solitons in normal-dispersion optical fibers described by the cubic-quintic complex Ginzburg–Landau equation. The effects of the third-order dispersion, self-steepening, stimulated Raman dispersion, and external potentials are also considered. The existence, chaotic content and interactions of these objects are analyzed, as well as the tunneling through a potential barrier and the formation of dark breathers aside from dark solitons in two dimensions and their mutual interactions as well as with periodic potentials. Furthermore, the homogeneous solutions of the model and the conditions for their stability are also analytically obtained.

Spatiotemporal patterns induced by four mechanisms in a tussock sedge model with discrete time and space variables

In this paper, we investigate the spatiotemporal patterns of a freshwater tussock sedge model with discrete time and space variables. We first analyze the kinetic system and show the parametric conditions for flip and Neimark–Sacker bifurcations respectively. With spatial diffusion, we then show that the obtained stable homogeneous solutions can experience Turing instability under certain conditions. Through numerical simulations, we find periodic doubling cascade, periodic window, invariant cycles, chaotic behaviors, and some interesting spatial patterns, which are induced by four mechanisms: pure-Turing instability, flip-Turing instability, Neimark–Sacker–Turing instability, and chaos.

Surface contact behavior of functionally graded thermoelectric materials indented by a conducting punch

The contact problem for thermoelectric materials with functionally graded properties is considered. The material properties, such as the electric conductivity, the thermal conductivity, the shear modulus, and the thermal expansion coefficient, vary in an exponential function. Using the Fourier transform technique, the electro-thermo-elastic problems are transformed into three sets of singular integral equations which are solved numerically in terms of the unknown normal electric current density, the normal energy flux, and the contact pressure. Meanwhile, the complex homogeneous solutions of the displacement fields caused by the gradient parameters are simplified with the help of Euler’s formula. After addressing the non-linearity excited by thermoelectric effects, the particular solutions of the displacement fields can be assessed. The effects of various combinations of material gradient parameters and thermoelectric loads on the contact behaviors of thermoelectric materials are presented. The results give a deep insight into the contact damage mechanism of functionally graded thermoelectric materials (FGTEMs).

Ultrasensitive homogeneous detection of microRNAs in a single cell with specifically designed exponential amplification

We firstly developed an ultrasensitive method based on specifically designed exponential amplification for miRNA detection with simple operation in homogeneous solutions. The proposed assay can detect as low as 1...

Existence of axisymmetric and homogeneous solutions of Navier-Stokes equations in cone regions

<p style='text-indent:20px;'>In this paper, we study axisymmetric homogeneous solutions of the Navier-Stokes equations in cone regions. In [James Serrin. The swirling vortex. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 271(1214):325-360, 1972.], Serrin studied the boundary value problem in half-space minus <inline-formula><tex-math id="M1">\begin{document}$ x_3 $\end{document}</tex-math></inline-formula>-axis, and used it to model the dynamics of tornado. We extend Serrin's work to general cone regions minus <inline-formula><tex-math id="M2">\begin{document}$ x_3 $\end{document}</tex-math></inline-formula>-axis. All axisymmetric homogeneous solutions of the boundary value problem have three possible patterns, which can be classified by two parameters. Some existence results are obtained as well.</p>

Mineral composition and formation conditions of the Inkur tungsten deposit ores (Dzhidinsky ore field, South-Western Transbaikalia)

The aim of the study is to clarify the mineral composition and determine the conditions of the formation of the quartz-hubnerite veins of the Inkur stockwork tungsten deposit (the Dzhidinsky ore field, South-Western Transbaikalia). The research methods include a mineralogical and petrographic description of the ore quartz-hubnerite veins; an electron microprobe analysis of the mineral associations; thermometry, cryometry, and Raman spectroscopy of the individual fluid inclusions in quartz, fluorite, hubnerite, and muscovite. The mineralogical and petrographic studies has made it possible to clarify the mineral composition of the Inkur deposit ores and determine the mineral paragenesis formation sequence. The fluid inclusion studies have established that the ore deposition was occurring in the relatively low-salinity (~5.7–14.6 wt. % eq. NaCl) homogeneous solutions due to a decrease of the temperature. The study of the salt composition of the solutions has identified Ca chloride as a prevailing component, with NaCl, KCl, and MgCl as admixtures. CO2 and N2 have been identified in the gas phase of inclusions. Two stages of mineral formation have been defined: high-temperature (≥300 °С) and low-temperature (≥2.00–300 °С). The conducted studies allow qualitative estimation of the chemical composition of the ore-forming solutions. It has been established that one of the main factors of the hubnerite deposition is a temperature factor.