Electro-Optic Modulation of Higher-Order Poincaré Beam Based on Nonlinear Optical Crystal

Vector beams (VBs) have spatially inhomogeneous polarization states distribution and have been widely used in many fields. In this paper, we proposed a method to modulate polarization states of higher-order Poincaré (HOP) beams and designed a system based on Mach-Zehnder interferometers, in which polarization state (include azimuth and ellipticity) of generated HOP beams were modulated by linear electro-optic (EO) effect of nonlinear optical crystals. Using this method, the polarization state of generated HOP beams could be controlled by voltage signal applied on EO crystals, which makes the process of the polarization state change with no optical element moving and mechanical vibrations. Besides, due to the flexibility of the voltage signal, the polarization state could be switched directly and immediately.

Photoacoustic effect in micro- and nanostructures: numerical simulations of Lagrange equations

The work provides the description of theoretical and numerical modeling techniques of thermomechanical effects that take place in absorbing micro- and nanostructures of different materials under the action of pulsed laser radiation. A proposed technique of the numerical simulation is based on the solution of equations of motion of continuous media in the form of Lagrange for spatially inhomogeneous media. This model allows calculating fields of temperature, pressure, density, and velocity of the medium depending on the parameters of laser pulses and the characteristics of micro- and nanostructures.

The Spatially Inhomogeneous Influence of Snow on the Radial Growth of Schrenk Spruce (Picea schrenkiana Fisch. et Mey.) in the Ili-Balkhash Basin, Central Asia

Snow has an important impact on forest ecosystems in mountainous areas. In this study, we developed 14 tree-ring-width chronologies of Schrenk spruce (Picea schrenkiana Fisch. et Mey.) for the Ili-Balkhash Basin (IBB), Central Asia. We analyzed the response of radial growth to temperature, precipitation and snow parameters. The results show that previous winter and current summer precipitation have an important influence on the radial growth of P. schrenkiana. Further, we find spatially inhomogeneous effects of snow on subsequent growing-season tree growth in IBB. The radial growth response of P. schrenkiana to snow shows a weak–strong–weak trend from west to east across the Ili-Balkhash Basin. This spatial difference is mainly related to precipitation, as snow has little effect on tree growth in regions that receive more precipitation. Thus, winter snow has an important influence on the radial growth of trees in regions that receive limited amounts of precipitation.

GEODYNAMICS

In order to study the deep structure of the southwestern Ukrainian Carpathians, where the Carpathian conductivity anomaly is located, in 2015 and 2020, modern synchronous magnetotelluric studies were carried out on the profiles of Mukachevo-Skole, Seredne-Borynya and Karpatsky at twenty-three points and the spatiotemporal distribution and the electric field on the Earth's surface, which can be used to assess the conductivity and geoelectrical structure of the region, was obtained. Processing of experimental data was performed using the software PRC_MTMV, which provides a common noise-canceling impedance estimation for synchronous magnetotellurical recordings. Curves of apparent electrical resistivity (amplitude values and phases of impedance) from 10 to 10000 s were obtained reliably. A joint analysis of the apparent resistivity and impedance phases and the formal interpretation of the deep magnetotellurical sounding curves using the Niblett transformation indicate the presence of the spatially inhomogeneous conductor both in the earth's crust and in the upper part of the upper mantle. The chain of local conductive sections in the earth's crust coincides with the axial part of the Carpathian conductivity anomaly. High conductivity of the upper mantle was recorded in the Ukrainian Carpathians from the Transcarpathian Depression to the Skiba cover. It is shown that it is not a homogeneous layer, there is a general deepening of the upper edge to the northeast from 40-60 km (Transcarpathian depression) to 90-100 km (Krosno cover). Sharp deepening along the Porkulets and Dukla covers is revealed. Information about the existence of a deep conductor and its parameters should be the basis for quantitative interpretation and construction of the 3D deep geoelectrical model.

Inhomogeneous spatial patterns in diffusive predator-prey system with spatial memory and predator-taxis

In this paper, we consider a diffusive predator-prey system with spatial memory and predator-taxis. Since in this system, the memory delay appears in the diffusion term, and the diffusion term is nonlinear, the classical normal form of Hopf bifurcation in the reaction-diffusion system with delay can't be applied to this system. Thus, in this paper, we first derive an algorithm for calculating the normal form of Hopf bifurcation in this system. Then in order to illustrate the effectiveness of our newly developed algorithm, we consider the diffusive Holling-Tanner model with spatial memory and predator-taxis. The stability and Hopf bifurcation analysis of this model are investigated, and the direction and stability of Hopf bifurcation periodic solution are also researched by using our newly developed algorithm for calculating the normal form of Hopf bifurcation. At last, we carry out some numerical simulations, two stable spatially inhomogeneous periodic solutions corresponding to the mode-1 and mode-2 Hopf bifurcations are found, which verifies our theoretical analysis results.

Numerical Modeling of Self-Consistent Dynamics of Shallow and Ground Waters

A mathematical and numerical model of the joint dynamics of shallow and ground waters has been built, which takes into account the nonlinear dynamics of a liquid, water absorption from the surface into the ground, filtration currents in the ground, and water seepage from the ground back to the surface. The dynamics of shallow waters is described by the Saint-Venant equations, taking into account the spatially inhomogeneous distributions of the terrain, the coefficients of bottom friction and infiltration, as well as non-stationary sources and flows of water. For the numerical integration of Saint-Venant’s equations, the well-tested CSPH-TVD method of the second order of accuracy is used, the parallel CUDA algorithm of which is implemented as a software package “EcoGIS-Simulation” for high-performance computing on supercomputers with graphic coprocessors (GPU). The dynamics of groundwater is described by the nonlinear Bussensk equation, generalized to the case of a spatially inhomogeneous distribution of the parameters of the porous medium and the surface of the aquiclude (the boundary between water-permeable and low-permeable soils). The numerical solution of this equation is built on the basis of a finite-difference scheme of the second order of accuracy, the CUDA algorithm of which is integrated into the calculation module of the “EcoGIS-Simulation” software package and is consistent with the main stages of the CSPH-TVD method. The relative deviation of the numerical solution from the exact solution of the nonlinear Boussinesq equation does not exceed 10−4–10−5. The paper compares the results of numerical modeling of the dynamics of groundwater with analytical solutions of the linearized Bussensk equation used as calculation formulas in the methods for predicting the level of groundwater in the vicinity of water bodies. It is shown that the error of these methods is several percent even for the simplest case of a plane-parallel flow of groundwater with a constant backwater. Based on the results obtained, it was concluded that the proposed method for numerical modeling of the joint dynamics of surface and ground waters can be more versatile and efficient (it has significantly better accuracy and productivity) in comparison with the existing methods for calculating flooding zones, especially for hydrodynamic flows with complex geometry and nonlinear interaction of counter fluid flows arising during seasonal floods during flooding of vast land areas.