Pub Date : 2019-06-01DOI: 10.1109/DD46733.2019.9016443
A. Kovtanyuk, A. Chebotarev, Anastasiya A. Dekalchuk, N. Botkin, R. Lampe
A non-stationary model of oxygen transport in brain is studied. The model comprises two coupled, non-linear partial differential equations describing the oxygen concentration in the blood and tissue phases. Thus, the model is the so-called continuum one, where the blood and tissue fractions occupy the same spatial domain. A priori estimates of solutions are obtained, and an iterative procedure for finding them is proposed. The convergence of this method to a unique weak solution of the problem is proven. A numerical example illustrates the theoretical analysis.
{"title":"An iterative algorithm for solving an initial boundary value problem of oxygen transport in brain","authors":"A. Kovtanyuk, A. Chebotarev, Anastasiya A. Dekalchuk, N. Botkin, R. Lampe","doi":"10.1109/DD46733.2019.9016443","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016443","url":null,"abstract":"A non-stationary model of oxygen transport in brain is studied. The model comprises two coupled, non-linear partial differential equations describing the oxygen concentration in the blood and tissue phases. Thus, the model is the so-called continuum one, where the blood and tissue fractions occupy the same spatial domain. A priori estimates of solutions are obtained, and an iterative procedure for finding them is proposed. The convergence of this method to a unique weak solution of the problem is proven. A numerical example illustrates the theoretical analysis.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"1 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":"128865387","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/DD46733.2019.9016614
V.V. Kuydin, M. Perel
Gaussian beams for the stationary 2D Dirac equation with inhomogeneous electric and magnetic fields are constructed. Gaussian beams (GB) are such asymptotic solutions of this equation that are exponentially localized near semiclassical trajectories. To derive formulas for the GB, we found the leading term of semiclassical asymptotic solutions of this equation by elementary methods. The results are given in such a form that can be applied to another vector problems.
{"title":"Gaussian beams for 2D Dirac equation with electromagnetic field","authors":"V.V. Kuydin, M. Perel","doi":"10.1109/DD46733.2019.9016614","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016614","url":null,"abstract":"Gaussian beams for the stationary 2D Dirac equation with inhomogeneous electric and magnetic fields are constructed. Gaussian beams (GB) are such asymptotic solutions of this equation that are exponentially localized near semiclassical trajectories. To derive formulas for the GB, we found the leading term of semiclassical asymptotic solutions of this equation by elementary methods. The results are given in such a form that can be applied to another vector problems.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"15 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":"131748695","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/DD46733.2019.9016616
R. Gaydukov, V. Danilov
Equations describing the double- and triple-deck structure are demonstrated for the case of compressible flows along a small perturbed plate for large Reynolds numbers. Numerical and analytical investigations of the influence of the upstream flow on the behavior of the flow in the near-wall region are presented.
{"title":"Multideck structures of boundary layers in compressible flows","authors":"R. Gaydukov, V. Danilov","doi":"10.1109/DD46733.2019.9016616","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016616","url":null,"abstract":"Equations describing the double- and triple-deck structure are demonstrated for the case of compressible flows along a small perturbed plate for large Reynolds numbers. Numerical and analytical investigations of the influence of the upstream flow on the behavior of the flow in the near-wall region are presented.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"83 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":"114312484","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/DD46733.2019.9016499
D. Razumov, M. Salin
We consider the scattering of a plane sound wave at a rough water-air interface using numerical simulations. We describe our method in detail and demonstrate its functionality with simple examples. The main advantage of the method is that there are no limitations on the relation between the shape of the surface and the incident wave. This allows us to consider large Rayleigh parameters, shading, and multiple scattering. In the method, the solution of the Helmholtz equation in the form of an integral over the domain boundary is used only in the inner domain. In the outer domain, separation of variables is used to obtain a non-local integral boundary condition on an artificial boundary.
{"title":"Numerical simulations of sound scattering on a partly rough pressure-release surface using the boundary element method","authors":"D. Razumov, M. Salin","doi":"10.1109/DD46733.2019.9016499","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016499","url":null,"abstract":"We consider the scattering of a plane sound wave at a rough water-air interface using numerical simulations. We describe our method in detail and demonstrate its functionality with simple examples. The main advantage of the method is that there are no limitations on the relation between the shape of the surface and the incident wave. This allows us to consider large Rayleigh parameters, shading, and multiple scattering. In the method, the solution of the Helmholtz equation in the form of an integral over the domain boundary is used only in the inner domain. In the outer domain, separation of variables is used to obtain a non-local integral boundary condition on an artificial boundary.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"17 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":"125510845","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/DD46733.2019.9016424
E. Korotyaev, D. Mokeev
We consider the dislocation problem for the Dirac operator with a periodic potential on the real line. The dislocation is parameterized by a real parameter. For each parameter value, the absolutely continuous spectrum has a band structure and there are open gaps between spectral bands. We show that in each open gap there exist exactly two distinct “states” (eigenvalues or resonances) of the dislocated operator, such that they runs clockwise around the gap. These states are separated from each other by the Dirichlet eigenvalue and they make half as many revolutions as the Dirichlet eigenvalue does in unit time. We find asymptotic of this motion for the cases when a state is near the gaps boundary and collides with the Dirichlet eigenvalue.
{"title":"Dislocation problem for the Dirac operator","authors":"E. Korotyaev, D. Mokeev","doi":"10.1109/DD46733.2019.9016424","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016424","url":null,"abstract":"We consider the dislocation problem for the Dirac operator with a periodic potential on the real line. The dislocation is parameterized by a real parameter. For each parameter value, the absolutely continuous spectrum has a band structure and there are open gaps between spectral bands. We show that in each open gap there exist exactly two distinct “states” (eigenvalues or resonances) of the dislocated operator, such that they runs clockwise around the gap. These states are separated from each other by the Dirichlet eigenvalue and they make half as many revolutions as the Dirichlet eigenvalue does in unit time. We find asymptotic of this motion for the cases when a state is near the gaps boundary and collides with the Dirichlet eigenvalue.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"48 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":"121679271","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/DD46733.2019.9016612
O. Motygin
The classical linear problem of ship waves, describing forward motion of rigid bodies with a constant speed in an unbounded heavy fluid having a free surface, is studied. A two-dimensional statement of the boundary value problem is considered in the case when the fluid consists of two layers of different density and the bodies are totally submerged in one of the layers. For an arbitrary geometry of bodies, it is known that the problem is uniquely solvable almost everywhere in the set of physically meaningful values of speed and a parameter characterizing stratification. In this paper, the existence of exceptional values is numerically confirmed by constructing examples of non-uniqueness. For this, the ideas suggested by Motygin & McIver (2009) for the case of homogeneous fluid are developed.
{"title":"Non-uniqueness in the problem of forward motion of bodies in a two-layer fluid","authors":"O. Motygin","doi":"10.1109/DD46733.2019.9016612","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016612","url":null,"abstract":"The classical linear problem of ship waves, describing forward motion of rigid bodies with a constant speed in an unbounded heavy fluid having a free surface, is studied. A two-dimensional statement of the boundary value problem is considered in the case when the fluid consists of two layers of different density and the bodies are totally submerged in one of the layers. For an arbitrary geometry of bodies, it is known that the problem is uniquely solvable almost everywhere in the set of physically meaningful values of speed and a parameter characterizing stratification. In this paper, the existence of exceptional values is numerically confirmed by constructing examples of non-uniqueness. For this, the ideas suggested by Motygin & McIver (2009) for the case of homogeneous fluid are developed.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"87 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":"132924119","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/DD46733.2019.9016514
E. Zlobina
High-frequency diffraction of a plane wave by a contour with a Hölder-type discontinuity in otherwise smooth curvature is addressed. Aiming at explicit construction of asymptotic formulas, a systematic version of boundary layer approach is applied. An expression for the outgoing wavefield is presented.
{"title":"High-frequency diffraction by a contour with a Hölder discontinuity of curvature","authors":"E. Zlobina","doi":"10.1109/DD46733.2019.9016514","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016514","url":null,"abstract":"High-frequency diffraction of a plane wave by a contour with a Hölder-type discontinuity in otherwise smooth curvature is addressed. Aiming at explicit construction of asymptotic formulas, a systematic version of boundary layer approach is applied. An expression for the outgoing wavefield is presented.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"66 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":"122770295","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/DD46733.2019.9016581
A. Plachenov, G. Dyakova
We describe a new class of localized solutions of the paraxial parabolic equation, which can be represented as a product of two functions. One of them is a Gauss-type axisymmetric function different from a fundamental mode, the other one can be expressed in terms of an arbitrary solution of a certain Helmholtz equation on an auxiliary two-sheet complex surface. Some examples are considered.
{"title":"Quadratic Helmholtz–Gauss beams","authors":"A. Plachenov, G. Dyakova","doi":"10.1109/DD46733.2019.9016581","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016581","url":null,"abstract":"We describe a new class of localized solutions of the paraxial parabolic equation, which can be represented as a product of two functions. One of them is a Gauss-type axisymmetric function different from a fundamental mode, the other one can be expressed in terms of an arbitrary solution of a certain Helmholtz equation on an auxiliary two-sheet complex surface. Some examples are considered.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"18 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":"123447359","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/dd46733.2019.9016497
{"title":"DD 2019 Author Index","authors":"","doi":"10.1109/dd46733.2019.9016497","DOIUrl":"https://doi.org/10.1109/dd46733.2019.9016497","url":null,"abstract":"","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"3 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":"114625147","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/DD46733.2019.9016562
S. Kozitskiy
In this work a mode parabolic equation method for resonantly interacting modes accounting for the weak elasticity in the bottom is developed. The proposed method is tested numerically. The test calculations carried out for the ASA wedge benchmark prove an excellent agreement with the source images method for sufficiently small values of shear waves speed that are typical for soft sediments of the sea bottom.
{"title":"Examples of test calculations by the acoustic mode parabolic equation with the mode interaction and the elastic bottom","authors":"S. Kozitskiy","doi":"10.1109/DD46733.2019.9016562","DOIUrl":"https://doi.org/10.1109/DD46733.2019.9016562","url":null,"abstract":"In this work a mode parabolic equation method for resonantly interacting modes accounting for the weak elasticity in the bottom is developed. The proposed method is tested numerically. The test calculations carried out for the ASA wedge benchmark prove an excellent agreement with the source images method for sufficiently small values of shear waves speed that are typical for soft sediments of the sea bottom.","PeriodicalId":319575,"journal":{"name":"2019 Days on Diffraction (DD)","volume":"33 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":"126931058","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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