Abstract The problem of potential predictability of the temperature of the upper layer of the Arctic Ocean for the data of pre-industrial climate modelling run by the INM-CM5 Earth system model developed at the INM RAS is considered. The main attention is paid to the analysis of predictability of the phases of the dominant modes of low-frequency variability of the Arctic Ocean circulation. The initial estimate of its predictability is made by using the method of analogues and calculating the resonances of the invariant measure. Then this estimate is verified by direct ensemble calculations with the model. The results obtained indicate that the maximum predictability time interval reaches ten years for 15-year average values of heat content and corresponds to the states with maximum positive anomalies along the leading low-frequency variability modes.
{"title":"Predictability of the low-frequency modes of the Arctic Ocean heat content variability: a perfect model approach","authors":"A. Gritsun","doi":"10.1515/rnam-2022-0008","DOIUrl":"https://doi.org/10.1515/rnam-2022-0008","url":null,"abstract":"Abstract The problem of potential predictability of the temperature of the upper layer of the Arctic Ocean for the data of pre-industrial climate modelling run by the INM-CM5 Earth system model developed at the INM RAS is considered. The main attention is paid to the analysis of predictability of the phases of the dominant modes of low-frequency variability of the Arctic Ocean circulation. The initial estimate of its predictability is made by using the method of analogues and calculating the resonances of the invariant measure. Then this estimate is verified by direct ensemble calculations with the model. The results obtained indicate that the maximum predictability time interval reaches ten years for 15-year average values of heat content and corresponds to the states with maximum positive anomalies along the leading low-frequency variability modes.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"37 1","pages":"99 - 109"},"PeriodicalIF":0.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46346036","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 devoted to the construction of optimal stochastic forcings for studying the sensitivity of linear dynamical systems to external perturbations. The optimal forcings are sought to maximize the Schatten norms of the response. As an example,we consider the problem of constructing the optimal stochastic forcing for the linear dynamical system arising from the analysis of large-scale structures in a stratified turbulent Couette flow.
{"title":"Optimal stochastic forcings for sensitivity analysis of linear dynamical systems","authors":"Y. Nechepurenko, G. Zasko","doi":"10.1515/rnam-2022-0009","DOIUrl":"https://doi.org/10.1515/rnam-2022-0009","url":null,"abstract":"Abstract The paper is devoted to the construction of optimal stochastic forcings for studying the sensitivity of linear dynamical systems to external perturbations. The optimal forcings are sought to maximize the Schatten norms of the response. As an example,we consider the problem of constructing the optimal stochastic forcing for the linear dynamical system arising from the analysis of large-scale structures in a stratified turbulent Couette flow.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"37 1","pages":"111 - 118"},"PeriodicalIF":0.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44229731","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 Monte Carlo algorithm based on the use of transfer matrices is developed to describe the stochastic dynamics of the rotational--translational motion of aerosol clusters taking into account fluctuations in the molecular fluxes of the gas medium. In the general case, the cluster is immersed into a rarefied gas medium, the temperatures of its surfaces may differ from the temperature of the surrounding gas, for example, due to absorption of visible and infrared radiation. The motion of the cluster is described based on Langevin motion equations. The algorithm allows one to calculate parameters of the probability distribution of a six-dimensional vector consisting of components of the momentum and angular momentum vectors transmitted to the cluster by molecular flows. The numerical method allows one to apply preliminary analytical averaging modulo velocities of molecules for both the average values of the components of momentum and angular momentum and their correlation characteristics, which significantly reduces the calculation time.
{"title":"Transfer matrices and solution of the problem of stochastic dynamics of aerosol clusters by Monte Carlo method","authors":"A. Cheremisin","doi":"10.1515/rnam-2022-0001","DOIUrl":"https://doi.org/10.1515/rnam-2022-0001","url":null,"abstract":"Abstract A Monte Carlo algorithm based on the use of transfer matrices is developed to describe the stochastic dynamics of the rotational--translational motion of aerosol clusters taking into account fluctuations in the molecular fluxes of the gas medium. In the general case, the cluster is immersed into a rarefied gas medium, the temperatures of its surfaces may differ from the temperature of the surrounding gas, for example, due to absorption of visible and infrared radiation. The motion of the cluster is described based on Langevin motion equations. The algorithm allows one to calculate parameters of the probability distribution of a six-dimensional vector consisting of components of the momentum and angular momentum vectors transmitted to the cluster by molecular flows. The numerical method allows one to apply preliminary analytical averaging modulo velocities of molecules for both the average values of the components of momentum and angular momentum and their correlation characteristics, which significantly reduces the calculation time.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"37 1","pages":"1 - 14"},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44597766","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 New methods for constructing an approximation of the diffusion operator for the two-dimensional equation of the ambipolar diffusion process in the F layer of the Earth's ionosphere are presented. This equation is solved in the framework of modelling the global thermosphere and ionosphere dynamics (for the altitudes from 90 to 500 km). The proposed schemes have finite-difference versions of the integral identity, which is a property of differential diffusion equation and which represents the geometric properties of the process (diffusion proceeds along the magnetic field lines of the Earth). The stability of the proposed schemes is analyzed, as well as the accuracy estimates are obtained on the base of the model analytical solution and during the calculations with physically realistic data. A comparison is made with the second-order finite-difference scheme developed earlier for solving the same problem.
{"title":"On the approximation of the diffusion operator in the ionosphere model with conserving the direction of geomagnetic field","authors":"P. A. Ostanin","doi":"10.1515/rnam-2022-0003","DOIUrl":"https://doi.org/10.1515/rnam-2022-0003","url":null,"abstract":"Abstract New methods for constructing an approximation of the diffusion operator for the two-dimensional equation of the ambipolar diffusion process in the F layer of the Earth's ionosphere are presented. This equation is solved in the framework of modelling the global thermosphere and ionosphere dynamics (for the altitudes from 90 to 500 km). The proposed schemes have finite-difference versions of the integral identity, which is a property of differential diffusion equation and which represents the geometric properties of the process (diffusion proceeds along the magnetic field lines of the Earth). The stability of the proposed schemes is analyzed, as well as the accuracy estimates are obtained on the base of the model analytical solution and during the calculations with physically realistic data. A comparison is made with the second-order finite-difference scheme developed earlier for solving the same problem.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"37 1","pages":"25 - 39"},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48801876","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 constant (time-independent) upper bounds on the function ∥ exp(tA)∥2 where t ⩾ 0 and A is a square matrix whose eigenvalues have negative real parts. Along with some constant upper bounds obtained from known time-dependent exponential upper bounds based on the solutions of Lyapunov equations, a new constant upper bound is proposed that has significant advantages. A detailed comparison of all these constant upper bounds is carried out using 2 × 2 matrices and matrices of medium size from the well-known NEP collection.
{"title":"Constant upper bounds on the matrix exponential norm","authors":"Y. Nechepurenko, G. Zasko","doi":"10.1515/rnam-2022-0002","DOIUrl":"https://doi.org/10.1515/rnam-2022-0002","url":null,"abstract":"Abstract This work is devoted to the constant (time-independent) upper bounds on the function ∥ exp(tA)∥2 where t ⩾ 0 and A is a square matrix whose eigenvalues have negative real parts. Along with some constant upper bounds obtained from known time-dependent exponential upper bounds based on the solutions of Lyapunov equations, a new constant upper bound is proposed that has significant advantages. A detailed comparison of all these constant upper bounds is carried out using 2 × 2 matrices and matrices of medium size from the well-known NEP collection.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"37 1","pages":"15 - 23"},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47556151","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}
Pub Date : 2022-02-01DOI: 10.1515/rnam-2022-frontmatter1
Article Frontmatter was published on February 1, 2022 in the journal Russian Journal of Numerical Analysis and Mathematical Modelling (volume 37, issue 1).
{"title":"Frontmatter","authors":"","doi":"10.1515/rnam-2022-frontmatter1","DOIUrl":"https://doi.org/10.1515/rnam-2022-frontmatter1","url":null,"abstract":"Article Frontmatter was published on February 1, 2022 in the journal Russian Journal of Numerical Analysis and Mathematical Modelling (volume 37, issue 1).","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"28 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495406","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}
V. Shutyaev, T. T. Hà, F. Le Dimet, H. S. Hoang, N. H. Phong
Abstract Prediction of pollution in water flow is a very important task. To this end, it is imperative to be able to define the uncertainty in a model prediction. This is the purpose of sensitivity analysis whose role is to identify what uncertainty in the model outputs is attributable to the model inputs (parameters in this case). Traditionally, this is achieved by running the model perturbed by many random samples in the parameter space to determine their impact on the model outputs. It provides information on how much of the output variance is controlled by each parameter of the inputs. The theoretical results related to the procedure based adjoint approach for computing a sensitivity of the response function (RF) to changes in the input source are presented in the paper. It is shown that this approach allows to compute, by one single integration of the adjoint equation over a given time interval, a sensitivity of the RF to any source located in the domain of interest. The proposed approach is applied to the 2D Saint-Venant flow equations for modelling the water pollution problem. A numerical experiment is formulated and implemented for the Thanh Nhan Lake in Hanoi for studying a sensitivity of some RF to observations. The numerical model is constructed by applying the well-known finite-volume method. Two appropriate optimization problems are introduced and solved on the basis of the BFGS algorithm. The numerical results show the efficiency of the proposed method and confirm the theoretical findings.
{"title":"On numerical computation of sensitivity of response functions to system inputs in variational data assimilation problems","authors":"V. Shutyaev, T. T. Hà, F. Le Dimet, H. S. Hoang, N. H. Phong","doi":"10.1515/rnam-2022-0004","DOIUrl":"https://doi.org/10.1515/rnam-2022-0004","url":null,"abstract":"Abstract Prediction of pollution in water flow is a very important task. To this end, it is imperative to be able to define the uncertainty in a model prediction. This is the purpose of sensitivity analysis whose role is to identify what uncertainty in the model outputs is attributable to the model inputs (parameters in this case). Traditionally, this is achieved by running the model perturbed by many random samples in the parameter space to determine their impact on the model outputs. It provides information on how much of the output variance is controlled by each parameter of the inputs. The theoretical results related to the procedure based adjoint approach for computing a sensitivity of the response function (RF) to changes in the input source are presented in the paper. It is shown that this approach allows to compute, by one single integration of the adjoint equation over a given time interval, a sensitivity of the RF to any source located in the domain of interest. The proposed approach is applied to the 2D Saint-Venant flow equations for modelling the water pollution problem. A numerical experiment is formulated and implemented for the Thanh Nhan Lake in Hanoi for studying a sensitivity of some RF to observations. The numerical model is constructed by applying the well-known finite-volume method. Two appropriate optimization problems are introduced and solved on the basis of the BFGS algorithm. The numerical results show the efficiency of the proposed method and confirm the theoretical findings.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"37 1","pages":"41 - 61"},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48246963","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 propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose factors can be arbitrary. We calculate the computational complexities of the proposed methods and evaluate their performance in numerical experiments. The comparison with the known deterministic alternating projection methods shows that the randomized approaches are faster and exhibit similar convergence properties.
{"title":"Sketching for a low-rank nonnegative matrix approximation: Numerical study","authors":"S. Matveev, S. Budzinskiy","doi":"10.1515/rnam-2023-0009","DOIUrl":"https://doi.org/10.1515/rnam-2023-0009","url":null,"abstract":"Abstract We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose factors can be arbitrary. We calculate the computational complexities of the proposed methods and evaluate their performance in numerical experiments. The comparison with the known deterministic alternating projection methods shows that the randomized approaches are faster and exhibit similar convergence properties.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"38 1","pages":"99 - 114"},"PeriodicalIF":0.6,"publicationDate":"2022-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42931067","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}
Pub Date : 2021-12-01DOI: 10.1515/rnam-2021-frontmatter6
{"title":"Frontmatter","authors":"","doi":"10.1515/rnam-2021-frontmatter6","DOIUrl":"https://doi.org/10.1515/rnam-2021-frontmatter6","url":null,"abstract":"","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43713542","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}
G. Lotova, V. Lukinov, M. Marchenko, G. Mikhailov, D. Smirnov
Abstract A comparative analysis of the differential and the corresponding stochastic Poisson SEIR-models is performed for the test problem of COVID-19 epidemic in Novosibirsk modelling the period from March 23, 2020 to June 21, 2020 with the initial population N = 2 798 170. Varying the initial population in the form N = n m with m ⩾ 2, we show that the average numbers of identified sick patients is less (beginning from April 7, 2020) than the corresponding differential values by the quantity that does not differ statistically from C(t)/m, with C ≈ 27.3 on June 21, 2020. This relationship allows us to use the stochastic model for big population N. The practically useful ‘two sigma’ confidential interval for the time interval from June 1, 2020 to June 21, 2020 is about 108% (as to the statistical average) and involves the corresponding real statistical estimates. The influence of the introduction of delay on the prognosis, i.e., the incubation period corresponding to Poisson model is also studied.
{"title":"Numerical-statistical study of the prognostic efficiency of the SEIR model","authors":"G. Lotova, V. Lukinov, M. Marchenko, G. Mikhailov, D. Smirnov","doi":"10.1515/rnam-2021-0027","DOIUrl":"https://doi.org/10.1515/rnam-2021-0027","url":null,"abstract":"Abstract A comparative analysis of the differential and the corresponding stochastic Poisson SEIR-models is performed for the test problem of COVID-19 epidemic in Novosibirsk modelling the period from March 23, 2020 to June 21, 2020 with the initial population N = 2 798 170. Varying the initial population in the form N = n m with m ⩾ 2, we show that the average numbers of identified sick patients is less (beginning from April 7, 2020) than the corresponding differential values by the quantity that does not differ statistically from C(t)/m, with C ≈ 27.3 on June 21, 2020. This relationship allows us to use the stochastic model for big population N. The practically useful ‘two sigma’ confidential interval for the time interval from June 1, 2020 to June 21, 2020 is about 108% (as to the statistical average) and involves the corresponding real statistical estimates. The influence of the introduction of delay on the prognosis, i.e., the incubation period corresponding to Poisson model is also studied.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"36 1","pages":"337 - 345"},"PeriodicalIF":0.6,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43771417","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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