Abstract The kinetic formulation of the model problem of plasma waves excitation by a powerful short laser pulse is numerically studied for the first time. Kinetic and simplest hydrodynamic plasma models are also compared for the problem under consideration. It is shown that the considered hydrodynamic models do not provide good approximations to the solution to the Vlasov kinetic equation, namely, one leads to discontinuous solutions and the other has a significant qualitative distinction. At a low plasma temperature, the effect of non-isothermicity of the process is small, but it can lead to significant distortions of the solution during further heating. The results obtained here imply that the first two moments of the distribution function are not enough to describe the plasma hydrodynamics; higher-order moments should be used.
{"title":"Effect of electron temperature on formation of travelling waves in plasma: Kinetic and hydrodynamic models","authors":"E. V. Chizhonkov, A. A. Frolov","doi":"10.1515/rnam-2023-0006","DOIUrl":"https://doi.org/10.1515/rnam-2023-0006","url":null,"abstract":"Abstract The kinetic formulation of the model problem of plasma waves excitation by a powerful short laser pulse is numerically studied for the first time. Kinetic and simplest hydrodynamic plasma models are also compared for the problem under consideration. It is shown that the considered hydrodynamic models do not provide good approximations to the solution to the Vlasov kinetic equation, namely, one leads to discontinuous solutions and the other has a significant qualitative distinction. At a low plasma temperature, the effect of non-isothermicity of the process is small, but it can lead to significant distortions of the solution during further heating. The results obtained here imply that the first two moments of the distribution function are not enough to describe the plasma hydrodynamics; higher-order moments should be used.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"63 - 74"},"PeriodicalIF":0.6,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46035987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The paper is focused on the dependence of optimal disturbances of stable periodic solutions of time-delay systems on phases of such solutions. The results of numerical experiments with the well-known model of the dynamics of infection caused by lymphocytic choriomeningitis virus are presented and discussed. A new more efficient method for computing the optimal disturbances of periodic solutions is proposed and used.
{"title":"Dependence of optimal disturbances on periodic solution phases for time-delay systems","authors":"M. Y. Khristichenko, Y. Nechepurenko, G. Bocharov","doi":"10.1515/rnam-2023-0008","DOIUrl":"https://doi.org/10.1515/rnam-2023-0008","url":null,"abstract":"Abstract The paper is focused on the dependence of optimal disturbances of stable periodic solutions of time-delay systems on phases of such solutions. The results of numerical experiments with the well-known model of the dynamics of infection caused by lymphocytic choriomeningitis virus are presented and discussed. A new more efficient method for computing the optimal disturbances of periodic solutions is proposed and used.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"89 - 98"},"PeriodicalIF":0.6,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41743164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The article is devoted to the construction and study of a finite-difference scheme for a one-dimensional diffusion–convection equation with a fractional derivative with respect to the characteristic of the convection operator. It develops the previous results of the authors from [5, 6] in the following ways: the differential equation contains a fractional derivative of variable order along the characteristics of the convection operator and a quasi-linear diffusion operator; a new accuracy estimate is proved, which singles out the dependence of the accuracy of mesh scheme on the curvature of the characteristics.
{"title":"Finite difference scheme for a non-linear subdiffusion problem with a fractional derivative along the trajectory of motion","authors":"A. Lapin, V. Shaydurov, R. Yanbarisov","doi":"10.1515/rnam-2023-0003","DOIUrl":"https://doi.org/10.1515/rnam-2023-0003","url":null,"abstract":"Abstract The article is devoted to the construction and study of a finite-difference scheme for a one-dimensional diffusion–convection equation with a fractional derivative with respect to the characteristic of the convection operator. It develops the previous results of the authors from [5, 6] in the following ways: the differential equation contains a fractional derivative of variable order along the characteristics of the convection operator and a quasi-linear diffusion operator; a new accuracy estimate is proved, which singles out the dependence of the accuracy of mesh scheme on the curvature of the characteristics.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"23 - 35"},"PeriodicalIF":0.6,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48692854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We present a new approach for multidimensional surface–subsurface flow coupling. The method does not require mesh-to-canal refinement or alignment and is based on numerical characteristics of the intersection of one-dimensional hydraulic object beds and the surface faces of the 3D tetrahedral mesh. The method is validated using widely recognized tilted v-catchment with subsurface and Borden catchment benchmarks.
{"title":"Mesh-independent multidimensional coupling of surface and subsurface water flow models","authors":"K. Novikov","doi":"10.1515/rnam-2023-0004","DOIUrl":"https://doi.org/10.1515/rnam-2023-0004","url":null,"abstract":"Abstract We present a new approach for multidimensional surface–subsurface flow coupling. The method does not require mesh-to-canal refinement or alignment and is based on numerical characteristics of the intersection of one-dimensional hydraulic object beds and the surface faces of the 3D tetrahedral mesh. The method is validated using widely recognized tilted v-catchment with subsurface and Borden catchment benchmarks.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"37 - 45"},"PeriodicalIF":0.6,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47999520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This work is devoted to the comparison of one- (1-D) and zero-dimensional (0-D) models of sea ice thermodynamics. 1-D thermodynamics solvers imply the solution of the diffusion equation with penetrating radiation in the moving domain (moving boundary problem), while 0-D implementations neglect the heat capacity of ice and penetrating radiation, that leads to a linear temperature profile by the construction. So far, some climate models use 0-D implementation of thermodynamics in a block of sea ice, while other models use 1-D implementation with a small number of nodes. In this work we present our fully implicit 0-D and 1-D version of snow–ice thermodynamics, which relieves the model of Courant-type time step constraints. Implicitness is achieved by the relaxation method for nonlinear heat capacity and thermal conductivity coefficients with simultaneous search for the temperature that satisfies the boundary conditions. We introduce the experiment with analytical forcing to compare evolution of temperature profiles. This model experiment shows that 0-D model underestimates ice thickness and overestimates the amplitude of temperature profile variation compared to 1-D solution. Despite the large differences in thickness and internal temperatures, the surface temperatures are very close. The models were also validated on the data of the SHEBA field experiment. According to comparison with observation data, the 0-D model predicts ice thickness and spatiotemporal temperature distribution much worse compared to 1-D model, but the amplitude of error in surface temperature is slightly greater for 0-D code. It can be concluded that 0-D model of sea ice thermodynamics is a good tool for predicting surface temperature, but it gives a large error in thickness and temperature distribution.
{"title":"The new sea ice thermodynamics code for the INM RAS Earth System model: The design and comparison of one- and zero-dimensional approaches with the observational data","authors":"Sergey S. Petrov, Vladimir K. Zyuzin, N. Iakovlev","doi":"10.1515/rnam-2023-0005","DOIUrl":"https://doi.org/10.1515/rnam-2023-0005","url":null,"abstract":"Abstract This work is devoted to the comparison of one- (1-D) and zero-dimensional (0-D) models of sea ice thermodynamics. 1-D thermodynamics solvers imply the solution of the diffusion equation with penetrating radiation in the moving domain (moving boundary problem), while 0-D implementations neglect the heat capacity of ice and penetrating radiation, that leads to a linear temperature profile by the construction. So far, some climate models use 0-D implementation of thermodynamics in a block of sea ice, while other models use 1-D implementation with a small number of nodes. In this work we present our fully implicit 0-D and 1-D version of snow–ice thermodynamics, which relieves the model of Courant-type time step constraints. Implicitness is achieved by the relaxation method for nonlinear heat capacity and thermal conductivity coefficients with simultaneous search for the temperature that satisfies the boundary conditions. We introduce the experiment with analytical forcing to compare evolution of temperature profiles. This model experiment shows that 0-D model underestimates ice thickness and overestimates the amplitude of temperature profile variation compared to 1-D solution. Despite the large differences in thickness and internal temperatures, the surface temperatures are very close. The models were also validated on the data of the SHEBA field experiment. According to comparison with observation data, the 0-D model predicts ice thickness and spatiotemporal temperature distribution much worse compared to 1-D model, but the amplitude of error in surface temperature is slightly greater for 0-D code. It can be concluded that 0-D model of sea ice thermodynamics is a good tool for predicting surface temperature, but it gives a large error in thickness and temperature distribution.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"47 - 61"},"PeriodicalIF":0.6,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44103749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Algorithms for stochastic simulation of the signal arriving at the photodetector matrix of the aircraft navigation system are constructed. During the operation of the aircraft landing navigation system, the laser beam of the navigation system coincides in its direction with the glide path determining safe landing. Two photodetector units placed on board of the aircraft determine the glide path position in the coordinate system of the aircraft, which allows one to adjust the position of the touch point on the runway in poor visibility conditions. In this case, the estimation of the power and angular distributions of radiation recorded by the receiver of the navigation system is a relevant problem. In addition, it is interesting to study the effect of scattering of various multiplicities on the recorded signal. The algorithms developed here are based on direct statistical modelling (estimation over collisions) and local estimates of the Monte Carlo method. The calculations show that the proposed methods allow us to evaluate the efficiency of the laser navigation system in various conditions.
{"title":"Stochastic simulation of a signal on a photodetector matrix of a laser navigation system","authors":"E. Kablukova, V. Oshlakov, S. Prigarin","doi":"10.1515/rnam-2023-0002","DOIUrl":"https://doi.org/10.1515/rnam-2023-0002","url":null,"abstract":"Abstract Algorithms for stochastic simulation of the signal arriving at the photodetector matrix of the aircraft navigation system are constructed. During the operation of the aircraft landing navigation system, the laser beam of the navigation system coincides in its direction with the glide path determining safe landing. Two photodetector units placed on board of the aircraft determine the glide path position in the coordinate system of the aircraft, which allows one to adjust the position of the touch point on the runway in poor visibility conditions. In this case, the estimation of the power and angular distributions of radiation recorded by the receiver of the navigation system is a relevant problem. In addition, it is interesting to study the effect of scattering of various multiplicities on the recorded signal. The algorithms developed here are based on direct statistical modelling (estimation over collisions) and local estimates of the Monte Carlo method. The calculations show that the proposed methods allow us to evaluate the efficiency of the laser navigation system in various conditions.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"13 - 21"},"PeriodicalIF":0.6,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46798847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The problem of variational observation data assimilation is considered for the mathematical thermodynamics model developed at the Marchuk Institute of Numerical Mathematics of RAS with the aim to reconstruct the sea surface heat flux. The sensitivity of functionals of solutions to observation data is studied for the considered variational assimilation problem and the results of numerical experiments for the Black Sea dynamics problem are presented.
{"title":"Sensitivity of functionals of the solution to a variational data assimilation problem with heat flux reconstruction for the sea thermodynamics model","authors":"V. Shutyaev, E. Parmuzin","doi":"10.1515/rnam-2022-0030","DOIUrl":"https://doi.org/10.1515/rnam-2022-0030","url":null,"abstract":"Abstract The problem of variational observation data assimilation is considered for the mathematical thermodynamics model developed at the Marchuk Institute of Numerical Mathematics of RAS with the aim to reconstruct the sea surface heat flux. The sensitivity of functionals of solutions to observation data is studied for the considered variational assimilation problem and the results of numerical experiments for the Black Sea dynamics problem are presented.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"37 1","pages":"373 - 382"},"PeriodicalIF":0.6,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48081967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The paper is focused on the study of the superexponential growth of the average number of particles in a stochastically homogeneous propagating medium. A mosaic Voronoi field (‘mosaic’) is considered as a random density model. The notion of ‘effective’ correlation radius is introduced to compare the results with previously obtained estimates of superexponential parameters for a spherically symmetric layered mosaic. It is shown that transition from the layered random density model to a chaotic one preserving the correlation scale and one-dimensional distribution weakens the ‘superexponential’ property of the particle flux.
{"title":"Estimation of the average particle flux in a stochastically homogeneous medium by Monte Carlo method","authors":"G. Lotova, G. A. Mikhailov","doi":"10.1515/rnam-2022-0029","DOIUrl":"https://doi.org/10.1515/rnam-2022-0029","url":null,"abstract":"Abstract The paper is focused on the study of the superexponential growth of the average number of particles in a stochastically homogeneous propagating medium. A mosaic Voronoi field (‘mosaic’) is considered as a random density model. The notion of ‘effective’ correlation radius is introduced to compare the results with previously obtained estimates of superexponential parameters for a spherically symmetric layered mosaic. It is shown that transition from the layered random density model to a chaotic one preserving the correlation scale and one-dimensional distribution weakens the ‘superexponential’ property of the particle flux.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"37 1","pages":"363 - 371"},"PeriodicalIF":0.6,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43159781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
K. Alipova, G. Goyman, M. Tolstykh, V. G. Mizyak, V. Rogutov
Abstract Algorithms for stochastic perturbation of parameters and tendencies of physical parameterizations for subgrid-scale processes are implemented into the ensemble prediction system. This system is based on the global semi-Lagrangian atmospheric model SL-AV with the resolution of 0.9 × 0.72 degrees in longitude and latitude, respectively, 96 vertical levels, and our implementation of the Local Ensemble Tranform Kalman Filter (LETKF). The use of stochastically perturbed parameterizations allows to generate ensembles with a significantly larger spread compared to one obtained with the method of static parameter perturbation. An improvement in the probabilistic estimates of the ensemble forecast for different seasons is shown.
{"title":"Stochastic perturbation of tendencies and parameters of parameterizations in the global ensemble prediction system based on the SL-AV model","authors":"K. Alipova, G. Goyman, M. Tolstykh, V. G. Mizyak, V. Rogutov","doi":"10.1515/rnam-2022-0027","DOIUrl":"https://doi.org/10.1515/rnam-2022-0027","url":null,"abstract":"Abstract Algorithms for stochastic perturbation of parameters and tendencies of physical parameterizations for subgrid-scale processes are implemented into the ensemble prediction system. This system is based on the global semi-Lagrangian atmospheric model SL-AV with the resolution of 0.9 × 0.72 degrees in longitude and latitude, respectively, 96 vertical levels, and our implementation of the Local Ensemble Tranform Kalman Filter (LETKF). The use of stochastically perturbed parameterizations allows to generate ensembles with a significantly larger spread compared to one obtained with the method of static parameter perturbation. An improvement in the probabilistic estimates of the ensemble forecast for different seasons is shown.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"37 1","pages":"331 - 347"},"PeriodicalIF":0.6,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49323596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A new INM RAS global dynamical model of Earth’s ionosphere F region (100–500 km), which takes into account plasma-chemical processes, ambipolar diffusion, and advective ion transport due to electromagnetic drifts and neutral wind is presented. The model includes parameterizations of polar electric fields induced by magnetospheric convection and simplified equatorial drifts considerations. The focus of the paper is directed on the description of specific methods developed and utilized in the ionospheric model. Key processes responsible for the formation of global ionospheric features are outlined and their representation in the model is evaluated. The main global ionospheric characteristic features, such as seasonal and diurnal cycles, the equatorial ionization anomaly (EIA), polar ionization caps and the main trough have been adequately reproduced based on this model.
{"title":"INM-IM: INM RAS Earth ionosphere F region dynamical model","authors":"D. Kulyamin, P. A. Ostanin, V. Dymnikov","doi":"10.1515/rnam-2022-0028","DOIUrl":"https://doi.org/10.1515/rnam-2022-0028","url":null,"abstract":"Abstract A new INM RAS global dynamical model of Earth’s ionosphere F region (100–500 km), which takes into account plasma-chemical processes, ambipolar diffusion, and advective ion transport due to electromagnetic drifts and neutral wind is presented. The model includes parameterizations of polar electric fields induced by magnetospheric convection and simplified equatorial drifts considerations. The focus of the paper is directed on the description of specific methods developed and utilized in the ionospheric model. Key processes responsible for the formation of global ionospheric features are outlined and their representation in the model is evaluated. The main global ionospheric characteristic features, such as seasonal and diurnal cycles, the equatorial ionization anomaly (EIA), polar ionization caps and the main trough have been adequately reproduced based on this model.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"37 1","pages":"349 - 362"},"PeriodicalIF":0.6,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45188900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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