St Petersburg Polytechnic University Journal-Physics and Mathematics最新文献

The probe light scattering on the cold optically dense atomic ensemble is studied theoretically in the paper. In order to describe multiple scattering of light in the context of quantum electrodynamics, the Konstantinov–Perel–Keldysh diagram technique has been used. This technique allows to rewrite the considered case of light scattering in terms of diagram series where each term describes incoherent scattering of certain order. Decoding these terms allowed us to obtain the explicit analytical expression for the cross-section of multiple incoherent scattering for the case of stationary two-level atoms (transition J_g = 0 → J_e = 1). The numerical analysis of this expression carried out by applying the Monte-Carlo simulation made it possible to find an influence of different orders of scattering on forming the angular dependence of scattered light intensity.

A mathematical model for membrane's vibration process is used in this paper. The model is based on seeking a solution of the second-order hyperbolic differential equation. A new inverse problem is set and investigated in two versions. In the first version the known data are as follows: the coefficient defining the phase velocity, the starting data of the Cauchy problem, the Cauchy problem solution on two given planes, derivatives of the solution along the vector being normal to these planes. The challenge has been in localizing the support of the right-hand side of the equation for vibrations. The algorithm permitting to find the bounded domain containing the unknown support was designed. In the second version the algorithm refers to the case where the coefficient defining the phase velocity is unknown but an interval of its possible values is known. A series of runs was performed to illustrate the proposed model.

The paper presents the results of development and practical implementation of wireless networks of controlled spectrally tunable light emitting diode (LED) light sources using RF transceivers operating in the unlicensed frequency bands of 868 and 2400 MHz. Such sources allow synthesizing either a white light with various color temperatures or a colored light with different tints; they are of significant interest in connection with general lighting and with some special applications. The problems of practical realization of light sources and their optimization with respect to luminous efficiency, dynamic range and the distance of wireless control have been investigated.

In this paper, we have considered the problem of effectively forming the representative sample for training a neural network of the multilayer perceptron (MLP) type. An approach based on the use of clustering that allowed to increase the entropy of the training set was put forward. Various clustering algorithms were examined in order to form the representative sample. The algorithm-based clustering of factor spaces of various dimensions was carried out, and a representative sample was formed. To verify our approach we synthesized the MLP neural network and trained it. The training technique was performed with the sets formed both with and without clustering. A comparative analysis of the effectiveness of clustering algorithms was carried out in relation to the problem of representative sample formation.

A toy quantum model of the inflationary universe is considered in which the role of cosmic time is played by the inflaton scalar field (its logarithm). Based on a variant of the positive energy theorem in General Relativity for the case of a closed universe, a strictly positive energy of space is introduced. The principle of minimum of the energy of space is proposed which determines a ground state as well as the excited states of the universe in quantum cosmology. According to this principle, the Beginning of the universe does exist as a state of minimal excitation of the energy of space. The initial proto-inflation quantum state of the universe is defined as a state of minimal excitation of the energy of space provided that the potential energy of the inflaton scalar field is large at the Beginning. Simultaneously, quanta of space energy excitation are introduced and the expansion of the universe can be considered as the birth of these quanta. Quantum birth of the ordinary matter becomes significant when the potential energy of the inflaton scalar field comes down to zero value.

The concentration dependencies of dielectric permittivity and dielectric loss factor have been studied for the water suspensions of nanogel films of bacterial cellulose Gluconacetobacter xylinus (BC) disintegrated with the blade rotation rates of 15,000 and 20,000 rpm. The dipole moments of BC colloids have been evaluated using Buckingham's statistical theory of dielectric polarization modified for binary polar systems. The number of monomer units of cellobiose in the BC colloid being equal to 113, the volume and the characteristic rotation time of the colloid particles were calculated. The difference between the values of dielectric parameters for BC samples disintegrated at 15,000 and 20,000 rpm were within experimental error. The constant stoichiometry of BC colloids and the identity of orientation ordering of microfibrills in colloids to that of the BC nanogel films have been shown by dielectric and X-ray studies.

It is necessary to provide the separation of the eigenmodes of elastic objects from the sensor signals and to make it possible to independently affect the modes with the use of actuators when realizing the modal system of controlling an elastic object with distributed parameters. The present paper puts forward an identification procedure which allows separating the vibration modes of the object in measured and control signals in the absence of the object model simulation. The control operability of this procedure was verified by experiment through making a system of active suppression of forced bending vibrations of a metal beam. The experiment showed the high control efficiency of the realized modal system.