On certain regularities of the response of a medium upon generation of the triple frequency of a few-period laser pulse in the case of its passage through an optically thin nonlinear layer

The response of a medium at the triple frequency under the action of few-period laser pulses is considered within the framework of the thin-optical-layer approximation for the case where the triple frequency is close to the natural frequency of the linear oscillator. It is shown that a bistable dependence of the polarization amplitudes on the external action amplitude simultaneously appears at both the natural frequency and the frequency of the external action. This allows one, in particular, to reveal the presence of bistability of the regime of third harmonic generation in a physical experiment by using the transmitted radiation of the acting pulse. A decrease in the duration of the pulse incident on the medium leads to an increase in the hysteresis loops. The effect of the absolute phase of a short pulse on the spectral composition of the response of the medium is studied. For pulses of medium duration, in addition to the resonant response of the medium, the presence of the dynamic response of the medium at the triple frequency was revealed, despite a detuning of the latter from the resonance. The presence of this frequency in the spectrum of the response of the medium results in the dependence of the resonant response of the medium on the absolute phase even for a sufficiently long pulse containing tens oscillations of the electric field strength under the pulse envelope. To obtain the dynamics of the spectral lines from the results of computer simulation, the Fourier-Gabor method is used, the applicability of which is demonstrated by the comparison of the results obtained on its basis with the corresponding analytical dependences.     

Continuous-distribution puddle model for conduction in trilayer graphene

Influence of the weak electric field on the electronic structure of the Fibonacci superlattice is considered. The electric field produces a nonlinear dynamics of the energy spectrum of the aperiodic superlattice. Mechanism of the nonlinearity is explained in terms of energy levels anticrossings. The multifractal formalism is applied to investigate the effect of weak electric field on the statistical properties of electronic eigenfunctions. It is shown that the applied electric field does not remove the multifractal character of the electronic eigenfunctions, and that the singularity spectrum remains non-parabolic, however with a modified shape. Changes of the distances between energy levels of neighbouring eigenstates lead to the changes of the inverse participation ratio of the corresponding eigenfunctions in the weak electric field. It is demonstrated, that the local minima of the inverse participation ratio in the vicinity of the anticrossings correspond to discontinuity of the first derivative of the difference between marginal values of the singularity strength. Analysis of the generalized dimension as a function of the electric field shows that the electric field correlates spatial fluctuations of the neighbouring electronic eigenfunction amplitudes in the vicinity of anticrossings, and the nonlinear character of the scaling exponent confirms multifractality of the corresponding electronic eigenfunctions.     

Quantum coherence and entangled states in intracavity third subharmonic generation process

The dynamics of correlation of photon number fluctuations of interacting modes for the process of intracavity third subharmonic generation is investigated. It is shown that the entangled field states by the variables of photon number can be obtained in this system. The quantum dynamics of the photons number, the quantum entropy and the Wigner function of the stationary states of the fundamental mode and the third subharmonic mode have also been studied. It is found that the dynamics of these quantities depends highly on the value of the coupling coefficient of the interacting modes. It is shown that at long interaction times and for the large values of the coupling coefficient of the modes, the mode of the third subharmonic is localized in the three-component state with the same probability of detection of the mode in each component of the state. The quantum entropy of the state is less than the maximal entropy of the three-component state ln3, which points out the presence of quantum mechanical interference between the components of the state of third subharmonic mode.     

Polarized fluorescence in investigation of rotational diffusion of the fluorescein family markers in bovine serum albumin solutions

The analysis of polarized fluorescence of the fluorescein family markers was conducted and parameters of their rotational diffusion in bovine serum albumin solutions (BSA) were determined. The degree of fluorescence anisotropy of the markers increases in the BSA solutions, as well as the time of rotational relaxation of the markers, while the rotational-diffusion coefficient of the markers decreases. The differences in the rotational-diffusion parameters between the markers are determined by the values of the electronegativity of the atoms in their structural formulas: the increase of the electronegativity of the atoms in the structural formulas of the markers results in the increase of the degree of fluorescence anisotropy, a decrease of the rotational-diffusion coefficient, and in the increase of the rotational-relaxation time both in the solutions without the protein and with BSA.     

3D problem of heat and mass transfer at the ignition of a combustible liquid by a heated metal particle

A nonlinear nonstationary 3D problem of heat and mass transfer at gas phase ignition of a combustible liquid spread on the surface of a solid body by a metal particle heated to a high temperature is solved. This is done within the framework of a model taking into account the heat conduction and evaporation of the liquid, the diffusion and convection of the combustible vapors in the oxidizer medium, the crystallization of the ignition source, the kinetics of the processes of evaporation and ignition of liquids, the dependence of the thermophysical characteristics of the interacting substances on the temperature, and the moisture content of the oxidizer—air. The dependences of the ignition delay time of the liquid on the temperature and sizes of the heating source are established. Limiting values of the temperature and particle sizes at which the ignition conditions take place are determined. The influence of the air humidity on the inertia of the process being investigated is analyzed. A comparison of numerical values of typical parameters of the process under investigation for 2D and 3D models is performed.     

Scattering of centimeter radiowaves in a gas ionized by radioactive radiation: Cluster plasma formation

A theoretical explanation is proposed for an anomalously high reflectivity of air masses exposed to radioactive radiation relative to electromagnetic waves from the rf range. The mechanism of formation of the reflected signal is connected with a change in the electric parameters of the ionized gas. The concentration of free charges under the typical conditions of radioactive contamination is ten orders of magnitude lower than that required for the formation of an experimentally detectable reflected signal. The discrepancy between the values of reflectivity observed under the real conditions of radar probing and predicted theoretically on the basis of the elementary theory of a weakly ionized gas amounts to 20 orders of magnitude. It is shown that the inclusion of the variation of the mass and the critical capture radius of ions due to their hydration changes the difference between the theoretical predictions and the experimental observations insignificantly. The discrepancy becomes smaller (but only by 1.5 orders of magnitude) when the scattering of radiowaves from turbulent vortices is taken into account. The mechanism of the formation of the high reflectivity is associated with slowing down the recombination and with the accumulation of a profuse population of unrecombined ionic pairs stabilized in the clusters of water molecules. The steady-state concentration of such electrically neutral clusters is several orders of magnitude higher than the concentration of free hydrated ions. A variation of the intensity of ionizing radiation is accompanied by proportional variations of both components. The recombination barrier is formed as a result of drawing dipole molecules into the gap between ions at the final stage of motion of counterions towards one another before their recombination. The accumulation of ionic pairs ensures the multiple enhancement of the sensitivity of the electric properties of cold plasma to the effect of ionizing radiation. A quantitative kinetic theory of the effect is constructed. The numerical calculations of the parameters of the pre-recombination states of ions against the background of the molecular component are made using computer simulation at the microscopic level. The steady-state recombination rate is an exponential function of the pre-recombination barrier height and decreases rapidly even upon an insignificant change in the number of molecules involved in an ion recombination act. The obtained theoretical conclusions are confirmed by the independent results of observations of the strong absorption band in the atmosphere in the middle part of the IR spectrum, which is attributed to the anomalously high concentration of electrically neutral water clusters.     

Instanton-like self-dual solution to lattice Euclidean Gravity: Difference from Eguchi–Hanson solution to continuous gravity

An analytical solution has been obtained for the spherical isothermal expansion of the outer layer of a ball whose mass increases at a constant areal density of the heated layer, which is equal to the product of the initial values of the depth of heating and the density of the layer for the entire time of expansion into vacuum. This solution differs from the known solution for the isothermal spherical expansion of a given mass of a material in a slower decrease in the density and, as a result, in the pressure of the expanding material with the time. In particular, it describes the expansion of the boundary layer of the ball heated by a flow of fast electrons in application to the problem of the ignition of an inertial confinement fusion target by a shock wave induced because of the heating of the target by the flow of laser-accelerated fast electrons (shock ignition).     

Fluctuations in the number of photons above the bifurcation point in the process of third harmonic generation

The quantum fluctuation of the number of photons of the fundamental mode and of the third harmonic in the process of intracavity generation of the third harmonic in the region of unstable behavior of the system is studied. The distribution functions of the number of photons of interacting modes, as well as the function of the joint distribution of the number of photons of the fundamental mode and of the third harmonic, are calculated in the positive P-representation.     

Fresnel diffraction of truncated Gaussian beam

We study the Fresnel diffraction of Gaussian beam truncated by one circular aperture, and give the general analytic expression of the Fresnel diffraction of truncated Gaussian beam denoted by Bessel functions. Then the characteristic of the axial diffraction fluctuation and the influence of the caliber of the circular aperture and the wave waist of Gaussian beam on the diffraction distributions are discussed, respectively. Through the numerical calculations, the characteristics of the transverse diffraction are presented and the relationship of the fluctuation of the transverse diffraction profile and the position of the axial point is shown. The physical origin of the fluctuation of Fresnel diffraction intensities of truncated Gaussian beam is expressed in terms of Fresnel half-zone theory. These phenomena and the conclusions are important for the measurement of the parameters of the beam and its applications.