Volume 25, Nº 2 (2025)

Background and Objectives: In problems where the model of dynamical system is known and the parameters need to be determined, researchers most often encounter the problem of ”getting stuck” in local minima of the cost function. Most known methods do not guarantee finding the global minimum, although they increase the probability of finding it. A known method of avoiding local maxima, which consists of simultaneously using several cost functions that behave differently in the vicinity of local minima, detecting the minimum as local, in some cases does not find a way to leave the region of the local minimum of the cost function. In this paper, we propose an improvement in the latter method, which allows finding the global minimum with a higher probability. Materials and Methods: In this paper, 4 different error values were calculated at each iteration of the parameter selection algorithm. The parameter values were saved when at least one of the cost functions reaches a new minimum value. Both the parameters were varied, and the random choice between the saved sets of parameters corresponding to the smallest value of at least one of the cost functions was made, when the procedure is “getting stuck” in local minima. Results: An improved algorithm for estimating the values of control parameters of ordinary differential equation models has been presented. The method demonstrates good results in restoring the parameters of the considered dynamical system both in the case of steady-state solutions different from the equilibrium state and in the case of transient processes. Conclusion: As the results of numerical modeling using the described algorithm have shown, preserving several sets of parameters that correspond to the best values of error values allows us to avoid local minima of cost functions with a higher probability in the presence of noise.

Background and Objectives: The emergence of sources of ultrashort high-intensity laser pulses has made it possible to subject various materials to a strong electric field without the risk of irreversible damage. Nonlinear effects observed under these conditions, such as the generation of high-frequency harmonics, have great potential for practical application. Graphene is considered one of the most promising materials due to the specificity of its band structure. The aim of the work is to demonstrate the applicability of the model based on the quantum kinetic equation in describing the results of the action of an external electric field with frequencies close to the lower limit of the IR range on the electronic subsystem of a material. Comparison of the model behavior at different values of temperature, relaxation time of nonequilibrium population and decoherence time with experimental data will allow us to estimate possible values of these parameters. Materials and Method: The work uses a quantum kinetic equation for the charge carrier distribution function in the state space. It allows one to reproduce the behavior of the electron subsystem of the material in an external classical electric field with an arbitrary time dependence. The spectrum of single-electron states is determined using the tight-binding approximation of nearest neighbors. The model parameters are the sample temperature, which determines the initial equilibrium distribution, the relaxation time of the nonequilibrium population of excited states, and the decoherence time. The implemented efficient computational procedure allows one to reproduce the characteristics of radiation induced by the action of an external field and analyze its spectral composition. The subject of comparison was the published results of experiments on the generation of high-frequency harmonics by far-infrared pulses at the TELBE facility. Results: The results presented in the work confirm the applicability of the used model for the frequency range near the lower boundary of the IR. It has been shown that under such conditions the external electric field forms a strongly anisotropic distribution in the conduction band with the population of states with high, up to several eV, energy values. In this case, the initial population of the conduction band, determined by the temperature of the sample at zero chemical potential, is much smaller than that created by the external field and does not significantly affect the observed results of the external field action. On the contrary, the relaxation time of the nonequilibrium population turns out to be the most important parameter determining the achieved values of the carrier density and conduction current. This is due to the fact that its value is small compared to the duration of the half-period of the external field. The estimate of this parameter made on the basis of the comparison with the experimental data is in good agreement with the expected values. Due to the insignificant role of the polarization current reflecting the dynamics of interband transitions, a comparison of the model behavior with the available experimental data does not provide criteria for estimating the decoherence time. Conclusion: The results of the work have shown the promise of new tools for modeling, studying, and qualitatively and quantitatively reproducing the characteristics of nonlinear effects under the action of an external electric field on graphene with frequencies close to the lower limit of the IR range. It has been shown that the distinguished role of the conduction current in this frequency range allows one to obtain an independent estimate of the relaxation time of the nonequilibrium population of excited states by comparing the behavior of the model with the experimental results.

Background and Objectives: Optical differentiation of pathologies is a promising tool for biomedical diagnostics, primarily due to its non-invasiveness and ease of implementation. The values of optical parameters andthe kinetics oftheir changes differ in healthy and pathological tissues due to changes in the tissue structure. In diabetes mellitus, such changes are especially noticeable. This requires detailed studies and the development of quantitative criteria for differentiating pathological (glycated) tissues. Materials and Methods: This paper presents an ex vivo experimental study of the optical and geometric parameters of rat head tissue samples under the action of an immersion liquid in the form of an aqueous 70% glycerol solution. Results: Optical and volumetric-weight characteristics were measured for rat head tissue samples (scalp skin, skull bone, dura mater, gray and white matter of the brain) in health and in model diabetes mellitus. Collimated transmission spectra of tissue samples were measured in the wavelength range of 450–900 nm. Conclusion: Analysis of optical transmittance kinetics over time up to 60 minutes has shown that all types of head tissue in diabetic rats exhibited impaired diffusion of test glycerol molecules compared to healthy rats.

Background and Objectives: The relaxation of internal stresses in pressed carbon and fiberglass plastics under the action of bending loads after modification by heating in a thermal chamber and exposure to a microwave electromagnetic field has been studied. It is shown that for pressed carbon and fiberglass plastics under the influence of bending loads, relaxation processes of internal stresses are characteristic, the intensity of which is determined by the initial state of the material. Materials and Methods: In the experiment, three groups of carbon and fiberglass samples produced by Eurocomplant LLC in Kaluga were used in the form of plane-parallel plates with dimensions of 75x10x5 mm, cut from a panel with dimensions of 500x500x5 mm in the state of delivery. Experiments with the first group of samples were carried out using a special microwave technological installation assembled on the basis of the Zhuk-2–02 radiator (NPP Agroecotech LLC, Obninsk, Kaluga region, Russia) with a horn-type radiator. The time of microwave exposure was recorded upon reaching the set surface temperature determined by the Flir E-40 thermal imager (FLIR, USA). The second group of samples was heated in an artificial light-weather chamber Solarbox 522 model 1500e RH (COFOMEGRA SRL, Italy). The study of internal stress relaxation was carried out according to the three-point bending scheme on a laboratory computer installation with LabVIEW software (IP Mayorov, Orel, Russia). Results: Microwave exposure to carbon and fiberglass contributes to stress relaxation by (5.1–7.2)% and (6.5–9.8)%, respectively, depending on the magnitude of the external load. After heating in the thermal chamber, stress relaxation was noted by(4.4–6.8)% and (5.2–9.0)%. For control samples, the degree of relaxation is(4.3–6.5)% and (4.9–8.55)%, the process stops almost 3 times earlier than for experimental samples. On average, the degree of stress relaxation in samples after exposure to a microwave electromagnetic field is 18.5% and 12.8% higher for carbon fiber and fiberglass, respectively, compared with heating in a thermal chamber. Conclusion: Тhis indicates a greater effectiveness of the microwave method of heat treatment in order to stabilize the properties of PCM.