Mean square Hyers-Ulam stability for a system of stochastic differential equations
Mean square Hyers-Ulam stability for a system of stochastic differential equations
E. P. Georgievskaia, N. T. Levashova
This paper presents the results of a study of the stochastic differential equation stability used in the model of accumulation of gene mutations during the evolution of organisms. In the course of numerical implementation, the need was revealed to obtain a criterion that the parameters of the problem must be in order for the solution to remain within the boundaries determined by the physical meaning. To solve this problem, a study of the stochastic equation for stability according to Hyers-Ulam was carried out. The resulting criterion corresponds well with the numerical experiment.
Show AbstractSpherically symmetrical singular hypersurfaces in conformal gravity
Spherically symmetrical singular hypersurfaces in conformal gravity
I. D. Ivanova
The surface energy-momentum tensor was obtained for the action of an ideal fluid with a variable number of particles in Euler variables. It is shown that in the absence of external fields, “external pressure” and “external flow” are associated with the production of particles in a double layer. The equations of motion along with the Lichnerowicz conditions are expressed using invariants of spherical geometry for timelike and spacelike spherically symmetric singular hypersurfaces. It is shown that for spherically symmetric thin shells the two-dimensional scalar curvature and the two-dimensional Laplacian of the radius are continuous. Spherically symmetric timelike and spacelike singular hypersurfaces separating two solutions of spherically symmetric conformal gravity are investigated as applications, in particular, various vacua and Vaidya-type solutions are used.
Show AbstractScanning capillary microscopy in the study of tumor and blood cells
Scanning capillary microscopy in the study of tumor and blood cells
T. O. Sovetnikov$^{1,4}$, I. V. Yaminsky$^{1,4}$, A. I. Akhmetova$^{2,4}$, M. A. Tikhomirova$^{2,3}$
Scanning ion-conductance microscopy or scanning capillary microscopy (SICM) is one of the methods of scanning probe microscopy (SPM) based on the use of nanocapillaries. The main advantages of SICM over other SPM methods are a non–violent action on an object under study in the course of measurements and a possibility to conduct studies in the natural environment (in liquid). Therefore, this method has become widely used in biological and medical research. Today SICM can be used for multiparametric analysis of the object’s surface and processes occurring near it. In SICM bioapplications the most relevant areas of work are studies of living systems with a wide time resolution (from minutes to days) and development of methods for targeted agent delivery to the surface of the subject in order to study its response to external influences. This paper presents the results of a study of the morphology of human carcinoma cells and the life cycle of human blood cells using ion-conductance microscopy. SICM allows not only the visualization in a three-dimensional scale, but also provides an opportunity to process a number of experimental data for diagnostic purposes.
Show AbstractStudy of the dependence of mechanical losses in silicon disc resonators caused by electric field on the silicon resistivity
Study of the dependence of mechanical losses in silicon disc resonators caused by electric field on the silicon resistivity
Y. Yu. Klochkov
Silicon is considered as perspective material for test masses in some projects of future gravitational-wave detectors. Electrostatic actuators are suggested for precise correction of test masses' position. Electric field of actuators will cause additional mechanical loss and corresponding thermal noise of their position, because of finite value of silicon resistivity. The experimental setup developed allows us to investigate this loss in temperature range 100-300 K via a model comprises silicon disc resonator and an electrode plate situated nearby. The dependence of additional mechanical losses induced by electrostatic field on the resistivity of silicon was obtained. These results would be useful while estimating additional losses, arising from action of actuator's electric field on test masses and corresponding noise.
Show AbstractRaman spectroscopy of human hair: the influence of sample orientation
Raman spectroscopy of human hair: the influence of sample orientation
N. N. Brandt, E. I. Travkina
Despite the large number of works on Raman spectroscopy of human hair, there is a lack of information about the methodology of experiments and the reliability of the data obtained. There are various experimental configurations in which the sample is positioned differently relative to the exciting radiation, and the published spectral data differ from each other. The question arises about the influence of the sample orientation on the measured Raman spectra. We compare the Raman spectra of a human hair measured in horizontal (exciting beam is perpendicular to the hair axis) and vertical (exciting beam and hair are coaxial) configurations. Along with the differences in the spectra, which result from molecular changes, the differences related to the polarization sensitivity of hairs were identified. To obtain cross-sections of the hair, we have developed the method based on freezing the sample in liquid nitrogen, which does not require microtomes and fixing agents.
Show AbstractCorrelation of magnetic and magnetothermal properties of ZnMn ferrite nanoparticles
Correlation of magnetic and magnetothermal properties of ZnMn ferrite nanoparticles
N. N. Liu$^1$, Yu. A. Alekhina$^1$, V. I. Zverev$^1$, M. N. Zharkov$^2$, N. A. Pyataev$^2$, V. I. Zverev$^1$, G. B. Sukhorukov$^{3,4}$, A. M. Tishin$^{1,5}$
The specific absorption rate of electromagnetic energy is the most important parameter to characterize the efficiency of the heating process during magnetic hyperthermia. Further improvements in the efficiency of converting electromagnetic energy into thermal energy are not possible without a deep understanding of the physical mechanisms of energy conversion and the development of new methods to increase SAR values. The purpose of this work is to experimentally investigate the dependence of the SAR value on the magnetic field amplitude of ZnMn ferrite magnetic nanoparticles (MNPs) and reveal the contribution of the non-zero hysteresis loop width to the heating of the MNPs. MNPs of ZnMn ferrite were obtained by chemical co-precipitation. Experimental studies conducted have shown that in large MNPs, the behavior of SAR values changes significantly with increasing electromagnetic field (EM) amplitude, which is related to the change in the rate of area increase. The hysteresis loop increases with increasing EM field amplitude. This allows us to conclude that the hysteresis heating mechanism dominates in large MNPs, and that MNPs larger than 13 nm are not less promising than small superparamagnetic particles (<10 nm). Considering the Brezovich limitation, choosing a field value at the 100 Oe level is more suitable for clinical practice using MNP data.
Show AbstractAssociated quarkonia production in a single boson $e^{+}e^{−}$~annihilation
Associated quarkonia production in a single boson $e^{+}e^{−}$~annihilation
E. A. Leshchenko$^1$, I. N. Belov$^2$
We present the preliminary results on the study of the cross sections for charmonium pair and bottomonium pair production in a single boson $e^+e^-$~annihilation. Processes have been studied in a wide range of energies, which are to be achieved at future $e^+e^-$~colliders, such as ILC and FCC. The contribution of color singlets states to production of vector and pseudoscalar states have been taken into account. Both QCD and EW production mechanisms have been considered including their interference and one-loop QCD correction. Cases of both intermediate bosons have been investigated: $\gamma$ and $Z$. All the calculations were performed in terms of perturbative technique and NRQCD-factorization.
Show AbstractModeling the interaction of solar radiation with vegetation elements using the Monte Carlo method
Modeling the interaction of solar radiation with vegetation elements using the Monte Carlo method
I. D. Sergeev, N. T. Levashova
The aim of this work is mathematical modeling of radiation transfer in vegetation cover elements, the geometry of which is close to real, using a software implementation of the Monte Carlo method. Information about the radiation reflected by a plant is needed to model the photosynthetic activity of trees, and consequently to model the carbon dioxide fluxes absorbed or released by plants, which is one of the most important tasks of ecology. By definition, the Monte Carlo method is a method for modeling random variables and processes to calculate the characteristics of their distributions. The process of radiation transfer in inhomogeneous media is modeled as a random Markov chain of collisions of photons with matter, and the purpose of the Monte Carlo method is to find the average statistical characteristics of this process. In this work, a small branch of birch is used as an object. In connection with the possibility of using modern multiprocessor systems for calculations it becomes necessary to distribute calculations, which can significantly reduce the time of realization.
Show AbstractFully heavy tetraquark spectroscopy in relativistic quark model
Fully heavy tetraquark spectroscopy in relativistic quark model
V. O. Galkin$^1$, E. M. Savchenko$^2$, R. N. Faustov$^1$
Masses of the ground and excited states of tetraquarks, composed of charm $c$ and bottom $b$ quarks and antiquarks, are calculated in the relativistic quark model based on the quasipotential approach and quantum chromodynamics. Relativistic effects are consistently taken into account. A tetraquark is considered as a bound state of a diquark and an antidiquark. The finite size of the diquark is taken into account, using the form factors of the diquark-gluon interaction. It is shown that most of the investigated states of tetraquarks lie above the decay thresholds into a pair of quarkonia, as a result they can be observed as broad resonances. The narrow state in the $J/\psi$ meson pair production spectrum recently discovered by the LHCb collaboration at Large Hadron Collider corresponds to the excited state of a fully charmed tetraquark.
Show AbstractThe method of equivalent substitutions, applied for the exact analytical solution of multilayer periodic structures with coupled wave thicknesses and specified amplitude-phase characteristics synthesis.
The method of equivalent substitutions, applied for the exact analytical solution of multilayer periodic structures with coupled wave thicknesses and specified amplitude-phase characteristics synthesis.
A. E. Zhitelev, A. V. Kozar
Based on the method of equivalent substitutions and the method of coupled wave thicknesses, a numerical analytical solution to the problem of calculations of the thickness values of the interference anti-reflective structure ("π structure") for an arbitrary number of layers is obtained. Exact algorithm is obtained that make it possible to synthesize antireflection structures providing a predefined reflection coefficient on the entire continuous set of values from 0 to 1 for any real values of the refractive indices of both matched media and materials of layers of such structures. The correctness of the obtained algorithm and the efficiency of the method are confirmed by a numerical experiment.
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