Pub Date : 2019-06-01DOI: 10.1109/DD46733.2019.9016547
A. N. Bulygin, Y. Pavlov
Methods of construction of exact analytical solutions of the nonlinear nonautonomous Klein–Fock–Gordon (KFG) equation are proposed. The solutions are sought in the form of a composite function U = f(θ). The function f(θ) is found from an ordinary nonlinear differential equation of the second order. The argument (ansatz) θ(x, y, z, t) is a root of an algebraic equation (cubic or square). It is shown that as the algebraic equations it is possible to take equations of families of surfaces, determining various curvilinear coordinates. The found ansatzes are used to construct functions φ(θ) satisfying Laplace’s equation. This result allows us to develop a new method of the solution of the nonlinear nonautonomous KFG equation. The general ways of the solution of the KFG equation are illustrated by consideration of some special cases.
提出了非线性非自治Klein-Fock-Gordon (KFG)方程精确解析解的构造方法。解以复合函数U = f(θ)的形式求得。函数f(θ)是由一个二阶非线性微分方程求出的。参数(ansatz) θ(x, y, z, t)是一个代数方程(立方或平方)的根。结果表明，作为代数方程，可以取曲面族方程来确定各种曲线坐标。利用所得到的分析构造满足拉普拉斯方程的函数φ(θ)。这一结果为我们提供了一种求解非线性非自治KFG方程的新方法。通过考虑一些特殊情况，说明了解KFG方程的一般方法。
{"title":"Solutions of nonlinear nonautonomous Klein–Fock–Gordon equation. The choice of ansatz","authors":"A. N. Bulygin, Y. Pavlov","doi":"10.1109/DD46733.2019.9016547","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016547","url":null,"abstract":"Methods of construction of exact analytical solutions of the nonlinear nonautonomous Klein–Fock–Gordon (KFG) equation are proposed. The solutions are sought in the form of a composite function U = f(θ). The function f(θ) is found from an ordinary nonlinear differential equation of the second order. The argument (ansatz) θ(x, y, z, t) is a root of an algebraic equation (cubic or square). It is shown that as the algebraic equations it is possible to take equations of families of surfaces, determining various curvilinear coordinates. The found ansatzes are used to construct functions φ(θ) satisfying Laplace’s equation. This result allows us to develop a new method of the solution of the nonlinear nonautonomous KFG equation. The general ways of the solution of the KFG equation are illustrated by consideration of some special cases.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116670505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-01DOI: 10.1109/DD46733.2019.9016430
L. Pestov, D. Strelnikov
We consider acoustical tomography problem: to find a variable speed of sound in a bounded domain Ω by partial boundary measurements using the Boundary Control method. We use Neumann controls which are located at Σ × [0, T], where Σ is an open set of the boundary ∂Ω, T is a sufficiently large observation time. Boundary measurements are given at Σ × [0, 2T ]. The pressure at another part of the boundary is assumed to be zero.
我们考虑声学层析成像问题:利用边界控制方法通过局部边界测量在有界域Ω中找到可变声速。我们使用位于Σ x [0, T]的诺伊曼控制，其中Σ是边界∂Ω的开放集，T是一个足够大的观测时间。边界测量值在Σ × [0,2t]给出。假定边界另一部分的压强为零。
{"title":"Approximate boundary controllability of wave equation with mixed boundary conditions and sound-speed reconstruction","authors":"L. Pestov, D. Strelnikov","doi":"10.1109/DD46733.2019.9016430","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016430","url":null,"abstract":"We consider acoustical tomography problem: to find a variable speed of sound in a bounded domain Ω by partial boundary measurements using the Boundary Control method. We use Neumann controls which are located at Σ × [0, T], where Σ is an open set of the boundary ∂Ω, T is a sufficiently large observation time. Boundary measurements are given at Σ × [0, 2T ]. The pressure at another part of the boundary is assumed to be zero.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124574956","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-01DOI: 10.1109/DD46733.2019.9016622
A. Mikhaylov, V. Mikhaylov
We consider a dynamic inverse problem for a dynamical system describing propagation of waves in a Krein string. We reduce the dynamical system to the integral equation and consider the important special case when the density of a string is given by a finite number of point masses distributed on the interval. We derive the Krein-type equation and solve the dynamic inverse problem in this particular case. We also consider the approximation of constant density by point-mass densities uniformly distributed on the interval and the effect of appearing of the finite speed of a wave propagation in the dynamical system.
{"title":"Forward and inverse dynamic problems for a Krein string. Approximation by point-mass densities","authors":"A. Mikhaylov, V. Mikhaylov","doi":"10.1109/DD46733.2019.9016622","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016622","url":null,"abstract":"We consider a dynamic inverse problem for a dynamical system describing propagation of waves in a Krein string. We reduce the dynamical system to the integral equation and consider the important special case when the density of a string is given by a finite number of point masses distributed on the interval. We derive the Krein-type equation and solve the dynamic inverse problem in this particular case. We also consider the approximation of constant density by point-mass densities uniformly distributed on the interval and the effect of appearing of the finite speed of a wave propagation in the dynamical system.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130901058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-01DOI: 10.1109/DD46733.2019.9016421
V. Vasilchuk
We consider an ensemble of n × n Hermitian random matrices being a generalization of the additive and multiplicative deformed unitary invariant ensembles. We express the limiting normalized counting measure (NCM) of eigenvalues via the NCMs of operands, obtain explicitely the leading term of the asymptotic n−1-expansion of the covariance of traces of resolvents of the ensemble and prove the central limit theorem for sufficiently smooth linear eigenvalue statistics as n tends to infinity.
{"title":"Fluctuations of the spectrum of symmetrically deformed unitary invariant random matrix ensemble","authors":"V. Vasilchuk","doi":"10.1109/DD46733.2019.9016421","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016421","url":null,"abstract":"We consider an ensemble of n × n Hermitian random matrices being a generalization of the additive and multiplicative deformed unitary invariant ensembles. We express the limiting normalized counting measure (NCM) of eigenvalues via the NCMs of operands, obtain explicitely the leading term of the asymptotic n−1-expansion of the covariance of traces of resolvents of the ensemble and prove the central limit theorem for sufficiently smooth linear eigenvalue statistics as n tends to infinity.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"151 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124201263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-01DOI: 10.1109/DD46733.2019.9016628
N. Saburova, O. Post
We consider discrete Schrödinger operators with periodic potentials on periodic graphs perturbed by guided potentials, which are periodic in some directions and finitely supported in other ones. The spectrum of the perturbed operator consists of the spectrum of the unperturbed one and the additional so-called guided spectrum which is a union of a finite number of bands. We estimate the positions of the guided bands in gaps of the unperturbed operator in terms of eigenvalues of Schrödinger operators on some finite graphs. We also determine sufficient conditions for the guided potentials under which the guided bands do not appear in gaps of the unperturbed problem.
{"title":"Spectrum of Schrödinger operators with potential waveguides on periodic graphs","authors":"N. Saburova, O. Post","doi":"10.1109/DD46733.2019.9016628","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016628","url":null,"abstract":"We consider discrete Schrödinger operators with periodic potentials on periodic graphs perturbed by guided potentials, which are periodic in some directions and finitely supported in other ones. The spectrum of the perturbed operator consists of the spectrum of the unperturbed one and the additional so-called guided spectrum which is a union of a finite number of bands. We estimate the positions of the guided bands in gaps of the unperturbed operator in terms of eigenvalues of Schrödinger operators on some finite graphs. We also determine sufficient conditions for the guided potentials under which the guided bands do not appear in gaps of the unperturbed problem.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127808690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-01DOI: 10.1109/DD46733.2019.9016453
E. Barshak, C. Alexeyev, B. Lapin, M. Yavorsky
We demonstrate that there are three possible types of mode dispersion of optical vortices with topological charge |ℓ| ≥ 1 in step-index twisted fibers: polarization, topological and hybrid mode dispersion. We established that the values of these types of the dispersion are different for each pair of optical vortices with |ℓ| > 1, which is a result of the influence of twisted mechanical stress. We numerically obtained certain fiber parameters to minimize the dispersion.
我们证明了阶跃折射率扭曲光纤中具有拓扑电荷| r | r≥1的光旋涡存在三种可能的模式色散:偏振、拓扑和混合模式色散。我们发现，对于每一对> 1的光旋涡，这些色散的值是不同的，这是受扭曲机械应力影响的结果。我们通过数值计算得到了一定的光纤参数，使色散最小。
{"title":"Novel types of mode dispersion of optical vortices in twisted optical fibers","authors":"E. Barshak, C. Alexeyev, B. Lapin, M. Yavorsky","doi":"10.1109/DD46733.2019.9016453","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016453","url":null,"abstract":"We demonstrate that there are three possible types of mode dispersion of optical vortices with topological charge |ℓ| ≥ 1 in step-index twisted fibers: polarization, topological and hybrid mode dispersion. We established that the values of these types of the dispersion are different for each pair of optical vortices with |ℓ| > 1, which is a result of the influence of twisted mechanical stress. We numerically obtained certain fiber parameters to minimize the dispersion.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128585973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-01DOI: 10.1109/dd46733.2019.9016523
{"title":"DD 2019 Contents","authors":"","doi":"10.1109/dd46733.2019.9016523","DOIUrl":"https://doi.org/10.1109/dd46733.2019.9016523","url":null,"abstract":"","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127462486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-01DOI: 10.1109/DD46733.2019.9016569
A. Sushchenko, P. Vornovskikh
The paper considers the problem of remote sensing of the ocean by a point isotropic source. To determine the volume scattering coefficient in a weakly scattering medium, the inverse problem is formulated. For the calculation of the received signal taking into account acoustic noise, caused by a distributed sound source, an equation is obtained. Computational experiments are performed to analyze the solution of the inverse problem in the case when unaccounted acoustic objects are in the medium.
{"title":"Remote sensing applications to acoustical tomography: case of unaccounted objects","authors":"A. Sushchenko, P. Vornovskikh","doi":"10.1109/DD46733.2019.9016569","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016569","url":null,"abstract":"The paper considers the problem of remote sensing of the ocean by a point isotropic source. To determine the volume scattering coefficient in a weakly scattering medium, the inverse problem is formulated. For the calculation of the received signal taking into account acoustic noise, caused by a distributed sound source, an equation is obtained. Computational experiments are performed to analyze the solution of the inverse problem in the case when unaccounted acoustic objects are in the medium.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"153 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132664495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-01DOI: 10.1109/DD46733.2019.9016590
V. Polyanskiy, A. Belyaev, A. Porubov, Y. Yakovlev, A. Polyanskiy
The influence of internal hydrogen in metals is modeled using a bi-continual model. The internal medium is introduced in the bi-continuum for modeling the diffusion of mobile hydrogen. Study of the model equations was carried out under the assumption of a small fluctuation of the concentration of mobile hydrogen under the action of external mechanical load. The case of appearance of the nonlinear solitary waves exceeding the average concentration is considered. The conditions are obtained under which the appearance of a decaying solitary wave is possible.
{"title":"Nonlinear waves of the internal medium due to dynamic loading of bi-continuum","authors":"V. Polyanskiy, A. Belyaev, A. Porubov, Y. Yakovlev, A. Polyanskiy","doi":"10.1109/DD46733.2019.9016590","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016590","url":null,"abstract":"The influence of internal hydrogen in metals is modeled using a bi-continual model. The internal medium is introduced in the bi-continuum for modeling the diffusion of mobile hydrogen. Study of the model equations was carried out under the assumption of a small fluctuation of the concentration of mobile hydrogen under the action of external mechanical load. The case of appearance of the nonlinear solitary waves exceeding the average concentration is considered. The conditions are obtained under which the appearance of a decaying solitary wave is possible.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"228 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133145188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-06-01DOI: 10.1109/DD46733.2019.9016540
A. Oktyabrskaya, A. Spiridonov, E. Karchevskii
The current paper proposes a Galerkin method for calculating spectral characteristics of microcavity lasers with piercing holes. If boundaries of the cavity and holes are circles, then entries of the matrix have explicit expressions computed in the present work. Using the proposed algorithm, we calculate directivities, spectra, and thresholds of laser modes. Numerical experiments demonstrate that, by varying the location of the hole, we can increase the directivity, while the threshold gain stays low.
{"title":"Numerical modeling of active microcavities with piercing holes using the Muller boundary integral equations and the Galerkin method","authors":"A. Oktyabrskaya, A. Spiridonov, E. Karchevskii","doi":"10.1109/DD46733.2019.9016540","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016540","url":null,"abstract":"The current paper proposes a Galerkin method for calculating spectral characteristics of microcavity lasers with piercing holes. If boundaries of the cavity and holes are circles, then entries of the matrix have explicit expressions computed in the present work. Using the proposed algorithm, we calculate directivities, spectra, and thresholds of laser modes. Numerical experiments demonstrate that, by varying the location of the hole, we can increase the directivity, while the threshold gain stays low.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114284595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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