We prove a theorem on the existence of a nonzero periodic solution to a system of differential equations using the fixed-point method for a nonlinear operator defined on the product of two compact ...sets.
The transformation of a subnanosecond ultrawideband electromagnetic pulse (UWB EMP) in a large-volume transparent plasma has been demonstrated experimentally using a large-scale KROT plasma device. ...The column of the plasma generated in the device chamber has a length of more than 4 m and a diameter of more than 1 m. This allows one to implement the regime of quasiuniform ionization, which is necessary to simulate UWB EMP propagation through the ionosphere. It is shown that the length of the wave propagation path in the plasma is sufficient for dispersion transformation of the pulse retaining the envelope of its frequency spectrum.
Abstract
The meteorological conditions in which organogenesis stages take place and hydrothermal regime can determine the phenotypic manifestation of quantitative signs, such as, for example, the ...activity of alpha-amylase. The purpose of our work was to determine what factors (temperature, precipitation, heterothermal coefficient) affect the enzyme activity, at what time of the vegetation, and in what way this influence is evident. The analysis of weather conditions and falling number (FN) for the period from 2011 to 2020 was carried out. Analysis of the FN value over 10 years showed that it can vary from 90 s to 429 s, and at that, the nature of its change is the same, regardless of whether we are considering one variety or the average value for a group of varieties. The correlation coefficient between the FN of a group of varieties and individual FN is 0.94-0.98. Generally, during the vegetation season, the alpha-amylase activity was influenced to a greater extent by the amount of precipitation than by temperature. This dependence is negative - an increase in precipitation leads to a decrease in the FN, and, consequently, to an increase in the enzyme activity. However, it was found that in different phases of ontogeny the influence of temperature and precipitation can be diametrically opposite.
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•A TTM + P continuum model has been derived, accounting for plasmons within a Two-Temperature description.•Plasmon fields are deduced from the linearized hydrodynamic model for free ...electrons.•The strength of excitation of the plasmon fields is highly dependent on the angle of incidence of the laser pulse.•Interference between laser and plasmon fields leads to a spatially modulated lattice temperature distribution.•Such temperature modulation may contribute to LIPSS formation.•The model can be adjusted to account for interband transitions at short wavelengths as well.
We propose a model accounting for plasmons within a two temperature description, to investigate the role of surface plasmon polaritons (SPP) in the energy redistribution between laser excited electrons and the lattice, leading to surface restructuring of the material. This energy transfer can lead to the creation of laser induced surface structures in metals illuminated by an ultrashort laser pulse. The Two Temperature Model+Plasmon (TTM + P) equations are constructed by applying perturbation theory on the energy-, momentum- and density conservation equations of free electrons in metals. We consider three subsystems: the lattice, the thermalized electrons and the SPP, subject to an external laser field irradiation. The interference between the laser and SPP fields leads to spatially modulated energy absorption by the electronic system, and, through electron–phonon collisions, periodically shapes the lattice temperature. A numerical analysis is performed on a 1D model for gold. We show the emergence of a periodic modulation of the lattice temperature, which may contribute to laser-induced periodic surface structures (LIPSS).
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•Analytical energy density rate for laser energy absorption is derived.•Interference of the excited SPP with the laser light is considered.•The interference pattern coexists along ...long distances.•The modulation of the laser deposited energy is close to the laser wavelength.•The results are applicable for the description of LIPSS as well as plasmonics.
The accurate calculation of laser energy absorption during femto- or picosecond laser pulse experiments is very important for the description of the formation of periodic surface structures. On a rough material surface, a crack or a step edge, ultrashort laser pulses can excite surface plasmon polaritons (SPP), i.e. surface plasmons coupled to a laser-electromagnetic wave. The interference of such plasmon wave and the incoming pulse leads to a periodic modulation of the deposited laser energy on the surface of the sample. In the present work, within the frames of a Two Temperature Model we propose the analytical form of the source term, which takes into account SPP excited at a step edge of a dielectric-metal interface upon irradiation of an ultrashort laser pulse at normal incidence. The influence of the laser pulse parameters on energy absorption is quantified for the example of gold. This result can be used for nanophotonic applications and for the theoretical investigation of the evolution of electronic and lattice temperatures and, therefore, of the formation of surfaces with predestined properties under controlled conditions.
We consider a nonlinear system of differential equations in a general case with a singular matrix at the derivatives, with a vector deviation which depends on a parameter. We seek for a periodic ...solution to the system in the set of trigonometric series such that the sequences of their coefficients belong to the space
l
1
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We use the method, representing a space as a direct sum of subspaces, and the method of a fixed point of a nonlinear operator as the main investigation techniques.
We reduce the question on the existence of a periodic solution to that of the solvability of an operator equation, whose principal part is defined in a finite-dimensional space.
We prove a theorem on the unique existence of a solution to a nonlinear equation with maxima and demonstrate its continuous dependence on the initial function and the parameter of the problem. We ...also establish conditions for the existence of a nonzero solution to a two-point boundary-value periodic problem in dependence of both linear and nonlinear terms of the equation.
Tanks for storing oil and oil products during operation are exposed to a combination of external, static, low-cycle, temperature, snow and wind loads, bottom sediments, etc., which leads to a ...decrease in operational reliability and a decrease in the durability of tank structures. Numerical modeling methods, in contrast to standard methods for calculating strength and stability, allow us to create an adequate finite element model at the stage of development of a geometric model. This article describes the analysis of the stress-strain state of the tank taking into account bottom sediments of oil products and the influence of the temperature of the oil product and the environment using the Ansys software package. Based on the analysis of the stress-strain state using finite element modeling on the example of a vertical steel tank, it was shown that the stresses in the zone of the miter weld, as well as in the places of installation of the receiving-distributing branch pipe and the manhole, are maximum. It is in these zones that the influence of bottom sediment and temperature is significant, since they form local elevated stress zones, which increase significantly when the walls are thinned.
Based on testing angle-ply composite specimens with different lay-ups, the lamina elastic properties are defined by minimization of the error function determining the differences between the ...predicted and measured strains. The problem that a number of the measured values obtained as a result of testing exceeds that of the lamina elastic constants is resolved by using the linear algebra methods with assessment of stability of the solutions against random perturbations of the matrix and/or column of free terms. Based on the lamina elastic constants defined, an analysis of the lamina nonlinear and time-depended properties is carried out and the lamina in-plane shear creep is described, the weak singular Abel's operator and matrix algorithms being used. To obtain the explicit forms of stiffness and compliance matrices of laminated composites on the basis of classical lamination theory relations, the assumption that their physical nonlinearity and rheological characteristics are substantially determined by the corresponding lamina in-plane shear properties is used, and the corresponding constitutive equations are derived to describe the anisotropy of their nonlinear and time-dependent properties. Testing a number of angle-ply polymer composite specimens under time variable loading shows the applicability of the approach elaborated. The satisfactory agreement between experimental and predicted data is observed.
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