CALCULATION OF SCATTERING WAVE FUNCTIONS FOR METASTABLE STATES OF A DIATOMIC BERYLLIUM MOLECULE

Trong bài báo này chúng tôi trình bày sơ đồ thuật toán và kết quả tính toán hàm sóng tán xạ đối với các trạng thái siêu bền của phân tử lưỡng nguyên tử Beryli trong quang phổ laser. Nghiệm của bài toán biên được tính toán bằng chương trình phần mềm được biên soạn bởi tác giả bài báo cùng các cộng sự khoa học ở Viện Liên hiệp Nghiên cứu Hạt nhân Dubna, Thành phố Dubna, Liên bang Nga. Các thuật toán của chương trình tính toán này dựa trên phương pháp phần tử hữu hạn với độ chính xác cao. Hàm thế năng được cho ở dạng bảng giá trị được nối với hàm thế năng tiệm cận Waals bằng cách sử dụng đa thức nội suy Hermite và đảm bảo tính liên tục của nghiệm hàm cùng đạo hàm của nó. Sự hiệu quả của chương trình tính toán này được thể hiện bằng việc tính toán các giá trị năng lượng cộng hưởng ở dạng phức của các trạng thái siêu bền trong phổ xung động quay của phân tử lưỡng nguyên tử Beryli. Với các trạng thái siêu bền này, các hàm sóng tán xạ tương ứng với năng lượng cộng hưởng mang giá trị thực được tính toán và biểu diễn dưới dạng đồ thị.

Fixed-distance multipoint formulas for the scattering amplitude from phaseless measurements

We give new formulas for finding the complex (phased) scattering amplitude at fixed frequency and angles from absolute values of the scattering wave function at several points $x_1,..., x_m$. In dimension $d\geq 2$, for $m>2$, we significantly improve previous results in the following two respects. First, geometrical constraints on the points needed in previous results are significantly simplified. Essentially, the measurement points $x_j$ are assumed to be on a ray from the origin with fixed distance $\tau=|x_{j+1}- x_j|$, and high order convergence (linearly related to $m$) is achieved as the points move to infinity with fixed $\tau$. Second, our new asymptotic reconstruction formulas are significantly simpler than previous ones. In particular, we continue studies going back to [Novikov, Bull. Sci. Math. 139(8), 923-936, 2015].

SIMULATION OF COMPACT POLARIZERS FOR SATELLITE TELECOMMUNICATION SYSTEMS WITH THE ACCOUNT OF THICKNESS OF IRISES

Background. One of the main problems in modern satellite telecommunication systems is to increase the volume of information transmission with simultaneous preservation of its quality. Key element of such systems is antenna systems with polarization processing, which is carried out using polarizers. Therefore, development of new polarizers and simple techniques for their analysis and optimization are important problems. The most simple, effective, technological and actual for analysis are polarizers based on waveguides with irises.Objective. The purpose of the paper is to create a mathematical model of the polarizer based on a square waveguide with irises, which allows analyzing the influence of polarizer’s design parameters on its electromagnetic characteristics.Methods. A mathematical model of the waveguide polarizer with irises is created by decomposition technique using transfer and scattering wave matrices. To take into account the irises’ thickness their equivalent T- and Π-shaped circuits were used.Results. We have developed mathematical model of the waveguide polarizer with irises, which takes into account their thickness and is based on the complete scattering wave matrix of the waveguide polarizer. The matrix has been obtained using the microwave circuit theory. The main characteristics of the waveguide polarizer were defined using matrix elements. The optimization of characteristics of a polarizer was carried out in the operating Ku-band 10.7–12.8 GHz.Conclusions. Suggested mathematical model of a waveguide polarizer with irises provides the account of heights of irises, distances between them and their thickness. The results obtained show that this model is simpler and faster for the calculation of electromagnetic characteristics compared to finite elements method, which is often used for analysis of microwave devices for various applications.

SIMULATION OF COMPACT POLARIZERS FOR SATELLITE TELECOMMUNICATION SYSTEMS WITH THE ACCOUNT OF THICKNESS OF IRISES

Background. One of the main problems in modern satellite telecommunication systems is to increase the volume of information transmission with simultaneous preservation of its quality. Key element of such systems is antenna systems with polarization processing, which is carried out using polarizers. Therefore, development of new polarizers and simple techniques for their analysis and optimization are important problems. The most simple, effective, technological and actual for analysis are polarizers based on waveguides with irises. Objective. The purpose of the paper is to create a mathematical model of the polarizer based on a square waveguide with irises, which allows analyzing the influence of polarizer’s design parameters on its electromagnetic characteristics. Methods. A mathematical model of the waveguide polarizer with irises is created by decomposition technique using transfer and scattering wave matrices. To take into account the irises’ thickness their equivalent T- and Π-shaped circuits were used. Results. We have developed mathematical model of the waveguide polarizer with irises, which takes into account their thickness and is based on the complete scattering wave matrix of the waveguide polarizer. The matrix has been obtained using the microwave circuit theory. The main characteristics of the waveguide polarizer were defined using matrix elements. The optimization of characteristics of a polarizer was carried out in the operating Ku-band 10.7–12.8 GHz. Conclusions. Suggested mathematical model of a waveguide polarizer with irises provides the account of heights of irises, distances between them and their thickness. The results obtained show that this model is simpler and faster for the calculation of electromagnetic characteristics compared to finite elements method, which is often used for analysis of microwave devices for various applications.

Consistent Theory of Alpha-Decay

In the framework of the Goldberger–Watson decay theory, we consider the a-decay of nuclei as a transition between the initial bound state of the nucleus and scattering states of the continuum spectrum with a-particle. The scattering wave functions for the a-decay with arbitrary orbital angular momentum are derived in the quasiclassical approximation. The a-particle is described by the square-integrable wave packet formed by these functions, whose amplitude exponentially grows outside the nucleus up to the wave front. The Moshinsky’s distortions of the a-wave front are analyzed. The derived general expression for the decay rate is approximated by the quasiclassical formula.

Infrared Problem vs Gauge Choice: Scattering of Classical Dirac Field

We consider the Dirac equation for the classical spinor field placed in an external, time-dependent electromagnetic field of the form typical for scattering settings: $$F=F^\mathrm{ret}+F^\mathrm{in}=F^\mathrm{adv}+F^\mathrm{out}$$ F = F ret + F in = F adv + F out , where the current producing $$F^{\mathrm{ret}/\mathrm{adv}}$$ F ret / adv has past and future asymptotes homogeneous of degree $$-3$$ - 3 , and the free fields $$F^{\mathrm{in}/\mathrm{out}}$$ F in / out are radiation fields produced by currents with similar asymptotic behavior. We show the existence of the electromagnetic gauges in which the particle has ‘in’ and ‘out’ asymptotic states approaching free field states, with no long-time corrections of the free dynamics. Using a special Cauchy foliation of the spacetime, we show in this context the existence and asymptotic completeness of the wave operators. Moreover, we define a special ‘evolution picture’ in which the free evolution operator has well-defined limits for $$t\rightarrow \pm \infty $$ t → ± ∞ ; thus the scattering wave operators do not need the free evolution counteraction.

Dynamic Stress Analysis of a Circular-Lined Tunnel in Composite Strata-SH Wave Incidence

It is necessary to study the problem of seismic wave scattering in composite stratum for tunnel engineering because the existence of composite strata will make the stress of tunnels more complicated during earthquakes. In this thesis, a series solution of the scattering wave field of the composite strata and lining is obtained using the complex function method. According to the stress and displacement boundary conditions between the composite stratum and the lining, a series of equations are established and are solved by means of Fourier transformation and finite term truncation, and the calculation errors are also discussed. Through programming calculations, the dynamic stress concentration factor (DSCF) of circular tunnels in the two types of composite strata, “hard-over-soft” and “soft-over-hard,” is analyzed when SH waves propagate, and certain conclusions on the scattering of SH waves that are distinguished from the case of single homogeneous layers are reached. The research in this article reveals some phenomena. For the Q345 steel lining in the calculation examples, it is found in this paper that increasing the thickness of the lining is effective to reduce the influence of the DSCF. But, for C30 concrete, increasing the thickness of the lining reduces the DSCF of the outer surface while increasing the DSCF of the inner surface.

Application of Instantaneous Parameter Characteristic in Active Lamb Wave Based Monitoring of Plate Structural Health

In the active Lamb wave based monitoring of plate structural health, it is difficult to extract damage information from active Lamb waves based on single sensor collection. Based on the Hilbert–Huang transform (HHT) instantaneous processing method, this paper proposes to study the damage information carried by a single sensor monitoring signal from the instantaneous parameter characteristics of the signal. The instantaneous phase change caused by the phase difference between the damage scattering wave and the direct wave is studied. The change of the marginal spectrum amplitude in the effective range caused by the damage scattering wave is studied in continuous multiple frequency bands. Finally, the damage information extraction based on a single sensor monitoring signal is realized. From the model analysis and experimental results, it is reliable and feasible to realize the active Lamb wave based monitoring of plate structural health according to the instantaneous parameter change characteristics from a single sensor signal.