We investigate a system with attracting δ-potential located along a straight line in 3D. It has constant intensity, except for a local region. We prove the existence of discrete spectrum and construct an upper bound on the number of bound states, using Birman-Schwinger method.

The transmission of an impulse through a neuron is provided by processes that occur at the nanoscale level. This paper will build a model for an oriented ring of connected neurons. To describe the process of impulse transmission through a neuron, the FitzHugh-Nagumo model is used, which allows one to set a higher abstraction level by simulating an impulse. In this case, when transmitting impulses between neurons, the delay is taken into account. For the constructed model, the dependence of the number of neurons on the dynamics of the network as a whole is studied, and local bifurcations are found. All results are verified numerically. It is shown that the period of self-oscillations of such a network depends on the number of neurons.

We consider a DNA as a configuration of HC Blume–Capel model and embed it on a path of Cayley tree. To study thermodynamic properties of the model of DNAs, we describe the corresponding translation-invariant Gibbs measures (TIGM) of the model on the Cayley tree. It is shown that, for k ≥ 2, for any temperature T > 0 there is a unique TIGM. Using these results, we study the distributions of the Holliday junctions DNA. For very high and very low temperatures, we give stationary distributions and typical configurations of the Holliday junctions.

It is important to study the effect of light intensity on the main photoelectric parameters of silicon solar cell with various metal nanoparticles because the intensity of sunlight is variable. In this paper, the effect of Cu, Pt, Au, Ag, Ti, Al, Co nanoparticles on dependence of main photoelectric parameters of silicon solar cell on light intensity has been studied by modeling with Sentaurus TCAD. The intensity coefficient of short circuit current densities of Pt and Ti nanoparticles induced silicon solar cells were found to be KJ,Pt = 0.0158 A/W and KJ,Ti = 0.0164 A/W.

For simple silicon solar cell, this value was found to be KJ = 0.0071 A/W. Thus, we have observed that was the two-fold greater the intensity coefficient of short circuit current density and output power for the silicon solar cells with Ti and Pt nanoparticles relative to that of a simple silicon solar cell.

The transmission of SARS-CoV-2, the novel severe acute respiratory syndrome corona virus have caused the corona virus disease (Covid-19) worldwide pandemic. Overcoming this pandemic requires identifying patients to avoid further spread of the disease. Real-time, sensitive, and costefficient methods for detecting the COVID-19 virus are crucial. Optical sensors provide one such means to achieve this, especially using surface plasmon resonance due to its advantages such as high sensitivity and excellent detection limits. In this paper, we propose a sensor for COVID-19 detection which is based on a simple Kretschmann configuration with gold layers and thiol-tethered DNA for the ligand layer. Angle interrogation was used to obtain the sensitivity of this structure using Matlab numerical analysis. The performance of the sensor was investigated with two types of prisms, SF10 and SF11, while varying the gold layer thickness between 45 – 60 nm. This information was then used to determine which combination of prism and gold thickness are ideal for detecting COVID-19 using thiol-tethered DNA. Thiol-tethered DNA layer sensor showed the highest sensitivity of 137 degree/RIU when a SF10 prism was used with a 50 – 60 nm gold layer and thiol tethered DNA layer.

A set of functions commonly used in basic circuits are defined as standard functions. They are so called because different combinations of different logic circuits are designed using these functions. They are also used to realize combinational logic circuits and most Boolean expressions. In this paper, 13 standard functions are discussed with their various applications using Quantum Dot Cellular Automata known as QCA which is currentlya familiar nanotechnology for its ultra-low power consumption and high speed operations. The designed functions are analyzed with area, latency and cell count. Energy calculations have been done with the suitable input for its stable operation. Algorithms are also established for the designed functions to realize in QCA technology.

In this paper, we consider relaxation processes in molecular systems containing single biomolecule and salt ions. The energy fluctuations in such systems were evaluated using computer simulations. The comparative analysis of the free energy dynamics of alanine, tryptophan, and albumin biomolecules in constructed molecular systems (aqueous solutions with different degrees of ionization) resulted in high influence of ionizing impurities on the full energy of the system and on the energy relaxation time. The results obtained can be used for development of hybrid micro and nanoelectronic devices with built-in biomolecular objects, for example, biochemical sensors, devices with microflow of liquids, technology for the preparation of molecular films, etc.

Surface nanobubbles are gaseous formations on solid-liquid interfaces. They are interesting in that their lifetime can reach several days, although initially it was assumed only a few nanoseconds. We built a mathematical and computer model of the nanobubble and performed a series of simulations to see how the nanobubble behaves when various external factors change.

By applying cyclooctaglycine model for cyclic peptide (CP) and cluster Au6 model for gold nanoparticles (GN), seven different configurations of cyclic peptide-gold nanoparticles (CPGN) with 5-fluorouracil (FU) were investigated. Binding energies, quantum molecular descriptors, and solvation energies in the aqueous solution and gas phase were studied at the density functional level of M06-2X/6-31g(d, p). Solvation energies indicate that the solubility of FU increases in CPGN/FU1-7. This subject is considered a key factor for drug transfer, so CPGNs can be used as an appropriate drug delivery system. The large negative values of calculated binding energies show the stability of CPGN/FU1-7 structures, and quantum molecular descriptors, such as electrophilicity (ω) and global hardness (η) indicate that the reactivity of FU in CPGN/FU1-7 structures increases. AIM calculations for all structures also show that intermolecular hydrogen bonding and Au-drug interactions play an important role for this drug delivery system.

The present study reports on energy modeling of morphological features of hydrosilicate nanoscrolls with chrysotile structure. It considers a possibility of scrolling direction change driven by difference in specific surface energies on the hydrosilicate layer edges. Specific surface energy estimation together with energy modeling of the scrolling process reveal several directions, which are preferable in comparison to the [010] or [100] directions of scrolling. The results obtained may help to better understand correlation between morphology, structural features, and mechanical behavior of hydrosilicate nanoscrolls.

We have shown for the first time that a platinum layer has been obtained on the surface of nickel foil as a result of Galvanic Replacement Reaction (GRR) when interacting with an aqueous solution of H₂PtCl₆, during drying in air, partially rolling up into incompletely formed microscrolls with a unique 3D morphology. Analysis of the wall of these microscrolls by FESEM, TEM, HR-TEM, and SAED methods showed that they are porous and formed by platinum nanocrystals with sizes of 5 – 10 nm, and their packing density over the wall thickness differs. Nickel foil samples with the layer of platinum microscrolls deposited on their surface exhibit high electrocatalytic activity in hydrogen evolution reaction (HER) during water electrolysis in the alkaline medium. In particular, the overpotential value is 32 mV and the Tafel slope is 32.5 mV/dec for an electrode with the platinum layer with a thickness of 120 – 140 nm.

Multicomponent zinc ferrites are of great applied value due to their functional features, due to which they are widely used in the production of microwave devices. In this regard, the development of new methods for obtaining initial pre-ceramic nanopowders in a nanostructured form is especially urgent. In this work, multicomponent zinc-manganese ferrites of the Zn1−xMnxFe2O4 (x = 0, 0.2, . . . , 1.0) composition were obtained by thermal treatment of X-ray amorphous products of solution combustion synthesis at a temperature of 750 ◦C and a holding time of 6 hours. The synthesized powders were analyzed by PXRD, FT-IR, and SEM methods. The magnetic characteristics were determined by vibration magnetometry. It was shown that the obtained samples contain one-phase spinel ferrite without any noticeable impurities. Depending on the number of Mn2+ cations in the crystal lattice, the unit cell parameters varied from 8.485(2) to 8.451(2) ˚A. The average crystallite size of the powders varied from 29.4 nm in the case of zinc ferrite to 36.8 nm in the case of MnFe2O4. Residual magnetization (Ms), saturation magnetization (Mr), and coercive force (Hc) also depend on the content of manganese cations in spinel and variedfrom 4.9 to 12.3 emu/g, from 22.4 to 76.4 emu/g, and from 47.5 to 81.3 Oe, respectively and these dependencies are almost linear. The highest magnetic parameters were found in simple manganese ferrite, which has the largest crystallite size.

Nanocompositions with “core-shell” structure are of interest in different areas of materials science and solid state chemistry, since, along with traditional refractory components in the form of carbides or nitrides and individual metals (Ni, Co), phases of mixed composition of the type Me11−xMe2xN (Me1 – a refractory element of IV-VIA subgroup, Me2 – Ni or Co) are formed during synthesis within one highly dispersed particle. It should be noted that such multicomponent phase components are metastable and cannot be obtained in an individual state. At the same time, phases of the Me11−xMe2xN type are formed in systems with participation of nitride compounds during extreme processing. In the present work, the technology of plasma-chemical synthesis with subsequent recondensation of gaseous nitrogen in a rotating cylinder was used.

The work is aimed at obtaining metastable complex-substituted titanium-cobalt nitride Ti0.7Co0.3N in the framework of nano- and ultradispersed Ti(Mo)C–Co “core-shell” structures. All phase components of the claimed compositions were determined by X-ray diffraction. Additionally, Ti(Mo)C–Co nanoparticles were studied by high-resolution transmission electron microscopy and electron diffraction. It was determined that Ti0.7Co0.3N has a strongly deformed stressed state, as evidenced by a single reflection (101) on the X-ray diffraction pattern. The paper also considers some aspects of crystal chemical design of Ti0.7Co0.3N obtained in the course of structural and morphological certification of the Ti(Mo)C–Co nanocomposition.