International Journal of Mathematics and Physics

VIRTUAL STATE

Makoto Ito, Kiyoshi Katô — Mon, 08 Jun 2026 00:00:00 +0000

This review article explains the properties of virtual states and discusses their impact on realistic nuclear
structure and nuclear reaction problems. The first half of the paper defines virtual states as poles of the scattering matrix,
i.e., zeros of the Jost function, and discusses their similarities and differences with bound and (zero energy) resonant states. The second half of the paper provides concrete examples of the effects of virtual states in real nuclear systems. Regarding nuclear structure problems, we demonstrate the valence neutron occupying virtual state plays important roles in the formation of the anomalous structures in the binary and three-body systems: 9Li + neutron and α + α + neutron. On the other hand, in reaction problems, we address thermal neutron scattering by various targets and discuss the close relationship between the peak structure in the so-called S-wave strength function and the virtual states. By synthesizing the calculation about the neutron scattering, we propose a new reaction picture for thermal neutron absorption reactions.

Keywords: Virtual states, nuclear structure, neutron scattering, neutron capture, nuclear reactions.

PREPARATION OF TRANSPARENT SUPERHYDROPHOBIC COATINGS WITH ANTI-ICING, ANTI-FOGGING AND SELF-CLEANING PROPERTIES BY PLASMA POLYMERISATION AT ATMOSPHERIC PRESSURE

Mon, 08 Jun 2026 00:00:00 +0000

This study analyses the stability of superhydrophobic coatings produced by plasma polymerisation at atmospheric pressure using argon (Ar) as the base gas and hexamethyldisiloxane (HMDSO) as the precursor. The evaluation was aimed at determining the strength and durability of these coatings when exposed to various environmental factors such as fogging, anti-icing and temperature fluctuations. The superhydrophobic properties of the coatings were investigated by measuring contact angles and surface roughness values. The results show that the coatings obtained by the above mentioned method have significant water repellent property and retain their superhydrophobic characteristics for a long time. The results indicate that the combination of Ar and HMDSO in plasma polymerisation at atmospheric pressure is a promising approach to create stable and durable superhydrophobic surfaces suitable for various applications. The main focus is on the stability of coatings, their ability to resist icing and fogging. The study showed that the hydrophobic properties of the coatings can be improved by optimising the process parameters, resulting in coatings with a water contact angle of more than 154±2 degrees and high transparency of up to 98.5% in the visible range. The obtained results testify to the high efficiency of the proposed method of obtaining coatings, which opens up prospects for their application in various fields where high resistance and transparency to external influences are required.

Keywords: plasma polymerization, atmospheric pressure, superhydrophobic coatings.

INVESTIGATION OF THE EFFECT OF REACTIVE DILUENTS ON THE MECHANICAL PROPERTIES OF EPOXY BINDERS

Mon, 08 Jun 2026 00:00:00 +0000

The effect of various types of curing agents and reactive diluents on the rheological and mechanical properties of epoxy binders was investigated. “Etal Inject-T” and “Larit L-285” epoxy resins were used as matrices. “Etal Inject-T”, iso-MTHPA, dicyandiamide (DICY), and diaminodiphenylsulfone (DDS) were used as curing agents. The effect of reactive diluents – glycerol triglycidyl ether, pentaerythritol tetraglycidyl ether, and butyl glycidyl ether – was also studied. Maximum strength characteristics were achieved using DDS curing agent at 25%. For the “Etal Inject-T” system, compressive strength values of 140 MPa were obtained. It was shown that the addition of pentaerythritol tetraglycidyl ether at 10% simultaneously reduces the viscosity of the epoxy composition from 400 mPa·s to 280 mPa·s and increases compressive strength from 140 MPa to 155 MPa. The results demonstrate the high effectiveness of multifunctional glycidyl ethers for controlling the structure and mechanical properties of epoxy binders.

Keywords: epoxy resins, reactive diluents, curing agents, mechanical properties, viscosity, epoxy compositions.

AMMONIA SENSING PROPERTIES OF FLUORINATED SI@C CORESHELL HYBRIDS

Mon, 08 Jun 2026 00:00:00 +0000

Silicon nanoparticles encapsulated in carbon shells (Si@C) were synthesized via polymer-derived carbonization and subsequently fluorinated by gas-phase treatment to tailor their interfacial electronic properties. The resulting Si@C–F core–shell nanostructures were investigated as chemiresistive sensors for ammonia detection at room temperature. The fluorinated hybrids exhibit a 2–2.5-fold enhancement in response toward NH₃ in the 1–20 ppm range, while maintaining linear behavior (R²>0.99) at low concentrations. The enhanced performance is attributed to fluorination induced modulation of interfacial electronic states and the barrier height at the Si/SiO_x/C:F heterojunction. The introduction of electron-withdrawing C–F groups increases the work function of the carbon shell and strengthens interfacial dipole fields, leading to amplified resistance modulation under NH3 adsorption. Owing to the nanoscale dimensions of the silicon cores (20–40 nm), comparable to the Debye length, surface charge variations significantly influence charge transport. The sensors demonstrate high selectivity toward ammonia over alcohol vapors (ppm-normalized selectivity >10⁴) and stable operation under moderate humidity. These findings establish fluorination as an effective strategy for engineering interfacial charge transfer in Si–C hybrids for room-temperature gas sensing.

Keywords: Si@C hybrids; fluorinated carbon; ammonia sensing; coreshell nanostructures; chemiresistive gas sensor.

ELECTRONIC STATES IN ZnO/porousZnSe/ZnSe HETEROSTRUCTURES

A. Dyadenchuk, R. Oleksenko, E. Filipovich — Mon, 08 Jun 2026 00:00:00 +0000

ZnO nanowires have attracted considerable attention due to their wide band gap, high chemical stability, and pronounced quantumscale effects, making them promising components for optoelectronic and sensor devices. The electronic states of such nanostructures strongly depend on the properties of the substrate, especially in heterostructures containing porous materials. In this work, the formation of quantum levels and the electronic properties of ZnO nanowires in two systems ZnO/ZnSe(bulk) and ZnO/porousZnSe/ZnSe with porosity ranging from 20% to 80% were theoretically investigated. The base nanowire model, with a radius of 25 nm and a height of 500 nm, describes the structure as a cylindrical infinite potential well, while the influence of porous ZnSe is incorporated through porositydependent barrier parameters: dielectric constant, and electron affinity. Analytical solutions of the Schrödinger equation obtained using Bessel functions, together with numerical simulations in Matlab, revealed strong radial quantum confinement: the radial quantization energy significantly exceeds the longitudinal one for the first levels, and the groundstate energy is about 0.0015eV. To quantitatively analyze the effect of substrate porosity, a finite cylindrical potential well model is employed, in which the barrier heightV0(P)=χ_ZnO−χ_eff(P) explicitly depends on porosity through the dielectric constant and electron affinity of porous ZnSe, calculated using the Bruggeman effective medium equation and the Penn relation, respectively. Numerical simulations performed for nanowire radii in the range 5−20 nm showed that increasing ZnSe porosity leads to systematic upward shifts of the ground-state energy, with absolute changes reaching up to 3−4 meV for nanowires with radius R < 10 nm. The obtained results confirm that porous ZnSe is an effective tool for tuning the electronic states of ZnO nanowires and open up opportunities for optimizing UV photodetectors and photovoltaic converters by controlling substrate porosity.

Keywords: ZnO nanowires, porous ZnSe, quantum confinement, electronic states, optoelectronic applications.

LENSING IMAGES OF DILATONIC BLACK HOLES

Zh. Beisenbekova, A. Urazalina, M. Khassanov, D. Utepova, Hernando Quevedo — Mon, 08 Jun 2026 00:00:00 +0000

This paper investigates the optical characteristics of a static spherically symmetric dilatonic black hole. The primary objective of the study is to examine the effect of the dilatonic charge Q and the dilaton coupling parameter a on the shadow geometry and the structure of Einstein rings. The research methodology is based on numerical simulations using the backward ray-tracing method, employing the Lagrangian formalism for the photon equations of motion. The main results show that an increase in the dilatonic parameters leads to a significant "compactification" effect of the shadow, the diameter of which can decrease by 31% relative to the Schwarzschild limit at extreme parameter values. Furthermore, a characteristic visual thickening of higher-order photon rings is observed, while maintaining complete topological stability of the image. The scientific value of this work lies in identifying specific optical signatures that allow distinguishing dilatonic black holes from the classical objects of General Relativity. The practical significance of the results is related to their potential application in interpreting observational data from the Event Horizon Telescope (EHT) and searching for manifestations of physics beyond standard models.

Keywords: Dilatonic Black holes, Ray tracing, Lensing images, Shadow geometry.

NUMERICAL STUDY OF GIMBAL JOINT GAP INFLUENCE ON NOZZLE FLOW

Mon, 08 Jun 2026 00:00:00 +0000

Gimbaled thrust vector control (TVC) systems are widely employed in modern launch vehicles to provide attitude control during powered flight. However, the aerodynamic influence of the circumferential geometric discontinuity introduced by the gimbal joint gap on nozzle internal and external flow remains insufficiently studied in open literature. The purpose of this study is to evaluate aerodynamic losses and flow field modifications of bell-shaped rocket nozzles with the presence of a gimbal joint gap using computational fluid dynamics (CFD) simulation. These calculations were done using the Reynolds-Averaged Navier–Stokes (RANS) model in 2D axisymmetric flow in ANSYS Fluent software. For modelling the flow properties in compressible separated flows, the k-ω SST turbulence model was selected. Two nozzle configurations, with and without the gap of the gimbal joint, were compared. The Sutherland viscosity law and the NASA polynomial thermodynamic data were used for the working fluid and it was modeled as an ideal compressible gas representative of the combustion products of LOX/Kerosene. The exit to throat area expansion ratio for nozzle geometry is 8.97, which means that the nozzle is designed to have a supersonic exit condition. The CFD results showed a good agreement with the theoretical results, showing the validity of the numerical approach. The nozzle studied here operates under overexpanded conditions at sea level, where the nozzle exit static pressure falls below ambient pressure, giving rise to oblique shock waves in the exhaust plume and making the accurate characterisation of flow disturbances particularly important. The presence of the gimbal joint gap was found to introduce aerodynamic losses in Mach number of 6.74%, providing quantitative design-relevant data for gimbaled nozzle systems in launch vehicles.
Keywords: gimbal joint gap, bell nozzle, TVC, CFD.