Alexey Yu. Chernenkov, Evgeny M. Volodin, Victor M. Stepanenko
Nitrogen is one of the most abundant chemical elements on the Earth and plays an important role in global environmental change. Leading Earth system models include coupled carbon and nitrogen cycle modules of varying complexity, but the INM RAS climate model family has not yet included an explicit N-cycle description. This paper presents a parameterization of the terrestrial N-cycle based on a simplification of the JULES-CN model, adapted for coupled use with the INM-CM land C-cycle module. Numerical simulations were carried out with a standalone carbon cycle model with nitrogen feedback disabled and enabled versions for the period 1850–2100. The simulated global pools show good agreement with results of other models with an implemented N-cycle. Taking into account the N-limitation of the C-cycle, the modelled dynamics of total carbon storage in terrestrial ecosystems from 1850 to the mid-20th century is specified.
{"title":"Nitrogen cycle module for INM RAS climate model","authors":"Alexey Yu. Chernenkov, Evgeny M. Volodin, Victor M. Stepanenko","doi":"10.1515/rnam-2024-0018","DOIUrl":"https://doi.org/10.1515/rnam-2024-0018","url":null,"abstract":"Nitrogen is one of the most abundant chemical elements on the Earth and plays an important role in global environmental change. Leading Earth system models include coupled carbon and nitrogen cycle modules of varying complexity, but the INM RAS climate model family has not yet included an explicit N-cycle description. This paper presents a parameterization of the terrestrial N-cycle based on a simplification of the JULES-CN model, adapted for coupled use with the INM-CM land C-cycle module. Numerical simulations were carried out with a standalone carbon cycle model with nitrogen feedback disabled and enabled versions for the period 1850–2100. The simulated global pools show good agreement with results of other models with an implemented N-cycle. Taking into account the N-limitation of the C-cycle, the modelled dynamics of total carbon storage in terrestrial ecosystems from 1850 to the mid-20th century is specified.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"30 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936427","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}
SLNE is the coupled model, that was developed in 2023. SL and NE here are the first two letters from SLAV (Semi-Lagrangian, based on Absolute Vorticity equation) model of the atmosphere and NEMO (Nucleus for European Modelling of the Ocean) ocean model that have been coupled using OASIS3-MCT software. The initial conditions for SLAV and NEMO are specified from an atmospheric and ocean analyses produced in Hydrometcentre of Russia. The 2010–2021 hindcast accuracy study shows, that SLNE has comparable errors to the operational SLAV model on a sub-seasonal time scale. The SLNE model has improved prediction skill of the 2010 heatwave features in comparison to SLAV, that is a motivation for further work to improve the coupled model.
{"title":"Evaluation of 2010 heatwave prediction skill by SLNE coupled model","authors":"Rostislav Yu. Fadeev","doi":"10.1515/rnam-2024-0019","DOIUrl":"https://doi.org/10.1515/rnam-2024-0019","url":null,"abstract":"SLNE is the coupled model, that was developed in 2023. SL and NE here are the first two letters from SLAV (Semi-Lagrangian, based on Absolute Vorticity equation) model of the atmosphere and NEMO (Nucleus for European Modelling of the Ocean) ocean model that have been coupled using OASIS3-MCT software. The initial conditions for SLAV and NEMO are specified from an atmospheric and ocean analyses produced in Hydrometcentre of Russia. The 2010–2021 hindcast accuracy study shows, that SLNE has comparable errors to the operational SLAV model on a sub-seasonal time scale. The SLNE model has improved prediction skill of the 2010 heatwave features in comparison to SLAV, that is a motivation for further work to improve the coupled model.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"44 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936429","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}
Tatyana S. Khachkova, Vadim V. Lisitsa, Elena A. Gondul, Dmiriy I. Prokhorov, Viktor I. Kostin
The paper presents an algorithm for three-dimensional modelling of two-phase flows on the scale of pore size order for numerical evaluation of relative phase permeability curves of porous materials. Such an evaluation is performed based on the results of numerical simulation of primary drainage with subsequent waterflooding. In this case, models of porous materials based on three-dimensional tomographic images of rocks are used. The simulation of the flow considers the Stokes equation and the Cahn–Hilliard equation for modelling phase transfer, which allows us to determine phases using the concentration function. The combination of the phase field method and finite difference method makes it possible to correctly take into account the contact angle and stably calculate surface tension forces in domains with complex topology.
{"title":"Two-phase flow simulation algorithm for numerical estimation of relative phase permeability curves of porous materials","authors":"Tatyana S. Khachkova, Vadim V. Lisitsa, Elena A. Gondul, Dmiriy I. Prokhorov, Viktor I. Kostin","doi":"10.1515/rnam-2024-0020","DOIUrl":"https://doi.org/10.1515/rnam-2024-0020","url":null,"abstract":"The paper presents an algorithm for three-dimensional modelling of two-phase flows on the scale of pore size order for numerical evaluation of relative phase permeability curves of porous materials. Such an evaluation is performed based on the results of numerical simulation of primary drainage with subsequent waterflooding. In this case, models of porous materials based on three-dimensional tomographic images of rocks are used. The simulation of the flow considers the Stokes equation and the Cahn–Hilliard equation for modelling phase transfer, which allows us to determine phases using the concentration function. The combination of the phase field method and finite difference method makes it possible to correctly take into account the contact angle and stably calculate surface tension forces in domains with complex topology.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"15 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936467","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}
Ivan G. Chechkin, Kirill V. Demyanko, Yuri M. Nechepurenko
An original numerical matrix algorithm aimed at solving the optimal control problems for linear systems of ordinary differential equations with constant coefficients is proposed. The work of the algorithm is demonstrated with the problem, which consists in generating a given small disturbance of the Poiseuille flow in an infinite duct by blowing and suction through the walls. The costs of creating the leading modes and optimal disturbances are compared, which is of independent interest.
{"title":"Numerical solution of optimal control problems for linear systems of ordinary differential equations","authors":"Ivan G. Chechkin, Kirill V. Demyanko, Yuri M. Nechepurenko","doi":"10.1515/rnam-2024-0017","DOIUrl":"https://doi.org/10.1515/rnam-2024-0017","url":null,"abstract":"An original numerical matrix algorithm aimed at solving the optimal control problems for linear systems of ordinary differential equations with constant coefficients is proposed. The work of the algorithm is demonstrated with the problem, which consists in generating a given small disturbance of the Poiseuille flow in an infinite duct by blowing and suction through the walls. The costs of creating the leading modes and optimal disturbances are compared, which is of independent interest.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"77 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141936440","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}
We study the accuracy of shock-capturing schemes for the shallow water Cauchy problems with piecewise smooth discontinuous initial data. We consider the second order balance-characteristic (CABARETM) scheme, the third order finite-difference Rusanov–Burstein–Mirin (RBM) scheme and the fifth order in space, the third order in time weighted essentially non-oscillatory (WENO5) scheme. We have shown that the maximum loss of accuracy occurs in the centered rarefaction waves of the exact solutions, where all these schemes have the first order of convergence and fairly close values of the numerical disbalances (errors), regardless of their formal approximation order on the smooth solutions. In the same time, inside the shock influence areas the considered schemes can have different convergence orders and, as a result, significantly different accuracy. In particular, when solving the Cauchy problem with periodic initial data, when the exact solution has no centered rarefaction waves, the RBM scheme has a significantly higher accuracy inside the shock influence areas, compared to the CABARETM and WENO5 schemes. It means that the combined scheme, in which the RBM scheme is a basic scheme and the CABARETM scheme is an internal one, can be effectively used to compute weak solutions of such type Cauchy problems.
{"title":"On the accuracy of shock-capturing schemes when calculating Cauchy problems with periodic discontinuous initial data","authors":"Olyana A. Kovyrkina, Vladimir V. Ostapenko","doi":"10.1515/rnam-2024-0009","DOIUrl":"https://doi.org/10.1515/rnam-2024-0009","url":null,"abstract":"We study the accuracy of shock-capturing schemes for the shallow water Cauchy problems with piecewise smooth discontinuous initial data. We consider the second order balance-characteristic (CABARETM) scheme, the third order finite-difference Rusanov–Burstein–Mirin (RBM) scheme and the fifth order in space, the third order in time weighted essentially non-oscillatory (WENO5) scheme. We have shown that the maximum loss of accuracy occurs in the centered rarefaction waves of the exact solutions, where all these schemes have the first order of convergence and fairly close values of the numerical disbalances (errors), regardless of their formal approximation order on the smooth solutions. In the same time, inside the shock influence areas the considered schemes can have different convergence orders and, as a result, significantly different accuracy. In particular, when solving the Cauchy problem with periodic initial data, when the exact solution has no centered rarefaction waves, the RBM scheme has a significantly higher accuracy inside the shock influence areas, compared to the CABARETM and WENO5 schemes. It means that the combined scheme, in which the RBM scheme is a basic scheme and the CABARETM scheme is an internal one, can be effectively used to compute weak solutions of such type Cauchy problems.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"29 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140560495","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}
The projected gradient method for matrix completion is generalized towards the higher-dimensional case of low-rank Tucker tensors. It is shown that an operation order rearrangement in the common projected gradient approach provides a complexity improvement. An even better algorithm complexity can be obtained by replacing the completion operator by a general operator that satisfies restricted isometry property; however, such a replacement transforms the completion algorithm into an approximation algorithm.
{"title":"Constructing low-rank Tucker tensor approximations using generalized completion","authors":"Sergey Petrov","doi":"10.1515/rnam-2024-0010","DOIUrl":"https://doi.org/10.1515/rnam-2024-0010","url":null,"abstract":"The projected gradient method for matrix completion is generalized towards the higher-dimensional case of low-rank Tucker tensors. It is shown that an operation order rearrangement in the common projected gradient approach provides a complexity improvement. An even better algorithm complexity can be obtained by replacing the completion operator by a general operator that satisfies restricted isometry property; however, such a replacement transforms the completion algorithm into an approximation algorithm.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"91 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140560605","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}
Vladimir P. Golubyatnikov, Natalia B. Ayupova, Natalia E. Bondarenko, Alina V. Glubokikh
We study periodic trajectories of nonlinear dynamical systems considered as models of the simplest molecular repressilator. In the phase portraits of these systems, we find hidden attractors and nonlocal oscillations. The cases of nonuniqueness of cycles in these portraits are described as well.
{"title":"Hidden attractors and nonlocal oscillations in gene networks models","authors":"Vladimir P. Golubyatnikov, Natalia B. Ayupova, Natalia E. Bondarenko, Alina V. Glubokikh","doi":"10.1515/rnam-2024-0007","DOIUrl":"https://doi.org/10.1515/rnam-2024-0007","url":null,"abstract":"We study periodic trajectories of nonlinear dynamical systems considered as models of the simplest molecular repressilator. In the phase portraits of these systems, we find hidden attractors and nonlocal oscillations. The cases of nonuniqueness of cycles in these portraits are described as well.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"11 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140560595","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}
Michael Yu. Khristichenko, Yuri M. Nechepurenko, Ilya V. Mironov, Dmitry S. Grebennikov, Gennady A. Bocharov
Optimal disturbances of a number of typical stationary solutions of the hepatitis B virus infection dynamics model have been found. Specifically optimal disturbances have been found for stationary solutions corresponding to various forms of the chronic course of the disease, including those corresponding to the regime of low-level virus persistence. The influence of small optimal disturbances of individual groups of variables on the stationary solution is studied. The possibility of transition from stable stationary solutions corresponding to chronic forms of hepatitis B to stable stationary solutions corresponding to the state of functional recovery or a healthy organism using optimal disturbances is studied. Optimal disturbances in this study were constructed on the basis of generalized therapeutic drugs characterized by one-compartment and two-compartment pharmacokinetics.
{"title":"Computation and analysis of optimal disturbances of stationary solutions of the hepatitis B dynamics model","authors":"Michael Yu. Khristichenko, Yuri M. Nechepurenko, Ilya V. Mironov, Dmitry S. Grebennikov, Gennady A. Bocharov","doi":"10.1515/rnam-2024-0008","DOIUrl":"https://doi.org/10.1515/rnam-2024-0008","url":null,"abstract":"Optimal disturbances of a number of typical stationary solutions of the hepatitis B virus infection dynamics model have been found. Specifically optimal disturbances have been found for stationary solutions corresponding to various forms of the chronic course of the disease, including those corresponding to the regime of low-level virus persistence. The influence of small optimal disturbances of individual groups of variables on the stationary solution is studied. The possibility of transition from stable stationary solutions corresponding to chronic forms of hepatitis B to stable stationary solutions corresponding to the state of functional recovery or a healthy organism using optimal disturbances is studied. Optimal disturbances in this study were constructed on the basis of generalized therapeutic drugs characterized by one-compartment and two-compartment pharmacokinetics.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"249 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140560680","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}
Vladimir Bening, Victor Korolev, Natalia Sukhareva, Hong Xiaoyang, Ruslan Khaydarpashich
The representability of the Burr distribution as a mixture of Weibull distribution is studied in order to justify its utility for modelling the statistical regularities in extreme values registered in non-stationary flows of informative events. A result of [24] is improved by extending the domain of admissible values of the parameters which provide the representability of the (generalized) Burr distribution as a scale mixture of the Weibull distribution. This result gives an argument in favour of application of the Burr distribution as a model of statistical regularities of extreme values registered within moderate regular time intervals, say, daily (short-term) extremes. In turn, if we are interested in the statistical regularities of the behaviour of the absolute extreme observation over a long period, say, a decade (the long-term extreme), then it can be noted that the daily extreme values form a sample of the Burr-distributed random variables. As is known, the Burr distribution belongs to the domain of max-attraction of the Fréchet distribution. The problem of improving the accuracy of the approximation of the distribution of the absolute extreme by the Fréchet distribution by the construction of an asymptotic expansion for the distribution of the extreme order statistics in the sample of independent identically Burr-distributed random variables is also considered. These results are illustrated by an example of fitting the Burr distribution to the data representing the extreme values of characteristics of the interplanetary magnetic field.
{"title":"The Burr distribution as an asymptotic law for extreme order statistics and its application to the analysis of statistical regularities in the interplanetary magnetic field","authors":"Vladimir Bening, Victor Korolev, Natalia Sukhareva, Hong Xiaoyang, Ruslan Khaydarpashich","doi":"10.1515/rnam-2024-0006","DOIUrl":"https://doi.org/10.1515/rnam-2024-0006","url":null,"abstract":"The representability of the Burr distribution as a mixture of Weibull distribution is studied in order to justify its utility for modelling the statistical regularities in extreme values registered in non-stationary flows of informative events. A result of [24] is improved by extending the domain of admissible values of the parameters which provide the representability of the (generalized) Burr distribution as a scale mixture of the Weibull distribution. This result gives an argument in favour of application of the Burr distribution as a model of statistical regularities of extreme values registered within moderate regular time intervals, say, daily (<jats:italic>short-term</jats:italic>) extremes. In turn, if we are interested in the statistical regularities of the behaviour of the absolute extreme observation over a long period, say, a decade (the <jats:italic>long-term</jats:italic> extreme), then it can be noted that the daily extreme values form a sample of the Burr-distributed random variables. As is known, the Burr distribution belongs to the domain of max-attraction of the Fréchet distribution. The problem of improving the accuracy of the approximation of the distribution of the absolute extreme by the Fréchet distribution by the construction of an asymptotic expansion for the distribution of the extreme order statistics in the sample of independent identically Burr-distributed random variables is also considered. These results are illustrated by an example of fitting the Burr distribution to the data representing the extreme values of characteristics of the interplanetary magnetic field.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"45 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140560679","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}
Dmitry Mukhin, Semen Safonov, Andrey Gavrilov, Andrey Gritsun, Alexander Feigin
In this work, we present a new diagnostic tool for El Niño Southern Oscillation (ENSO) simulations in Earth System Models (ESMs) based on the analysis of upper ocean heat content data. It allows us to identify the seasonally dependent structure of temperature anomalies in the equatorial Pacific Ocean in the form of a dominant spatio-temporal pattern. We demonstrate the results of applying a tool to analysis of real data as well as climate simulations in two versions of the Institute of Numerical Mathematics ESM. We find that the latest version of the model, with improved parameterizations of clouds, large-scale condensation, and aerosols, provides significantly better reproduction of ENSO-related structure of anomalies, as well as the phase locking of ENSO to the annual cycle. We recommend to use the tool for diagnostic analysis of ESMs regarding simulation of climate phenomena with strong seasonality.
{"title":"A new tool for studying seasonality and spatio-temporal structure of ENSO cycles in data and ESM simulations","authors":"Dmitry Mukhin, Semen Safonov, Andrey Gavrilov, Andrey Gritsun, Alexander Feigin","doi":"10.1515/rnam-2024-0003","DOIUrl":"https://doi.org/10.1515/rnam-2024-0003","url":null,"abstract":"In this work, we present a new diagnostic tool for El Niño Southern Oscillation (ENSO) simulations in Earth System Models (ESMs) based on the analysis of upper ocean heat content data. It allows us to identify the seasonally dependent structure of temperature anomalies in the equatorial Pacific Ocean in the form of a dominant spatio-temporal pattern. We demonstrate the results of applying a tool to analysis of real data as well as climate simulations in two versions of the Institute of Numerical Mathematics ESM. We find that the latest version of the model, with improved parameterizations of clouds, large-scale condensation, and aerosols, provides significantly better reproduction of ENSO-related structure of anomalies, as well as the phase locking of ENSO to the annual cycle. We recommend to use the tool for diagnostic analysis of ESMs regarding simulation of climate phenomena with strong seasonality.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"17 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139756789","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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