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Stochastic perturbations in the semi-Lagrangian advection algorithm of the SL-AV global atmosphere model Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2024-02-10 Kseniya A. Alipova, Vasiliy G. Mizyak, Mikhail A. Tolstykh, Gordey S. Goyman
An algorithm for stochastic perturbation of the semi-Lagrangian trajectories is implemented in the ensemble weather prediction system based on the global atmosphere model SL-AV20 with a horizontal resolution of approximately 20 km, 51 vertical levels, and Local Ensemble Transform Kalman Filter (LETKF). The combined use of methods for stochastic perturbation of trajectories and the parameters and tendencies
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Simulating the propagation of boundary-layer disturbances by solving boundary-value and initial-value problems Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2024-02-10 Grigory V. Zasko, Andrey V. Boiko, Kirill V. Demyanko, Yuri M. Nechepurenko
The article deals with the downstream propagation of small–amplitude disturbances of viscous incompressible laminar boundary layers, using the linearized equations for disturbance amplitudes. Two different methods are proposed. The first one solves a two-dimensional boundary-value problem, using a buffer-domain technique to mimic the outflow boundary condition. The second one solves a streamwise initial-value
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ENSO phase locking, asymmetry and predictability in the INMCM Earth system model Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2024-02-10 Aleksei F. Seleznev, Andrey S. Gavrilov, Dmitry N. Mukhin, Andrey S. Gritsun, Evgenii M. Volodin
Advanced numerical climate models are known to exhibit biases in simulating some features of El Niño–Southern Oscillation (ENSO), which is a key mode of interannual climate variability. In this study we analyze how two fundamental features of observed ENSO – asymmetry between hot and cold states and phase-locking to the annual cycle – are reflected in two different versions of the INMCM Earth system
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On a 1D-electrostatic test problem for the PIC method Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2024-02-10 Eugene V. Chizhonkov
A test problem for the ‘particle-in-cell’ method is proposed which allows one to check individual errors on each stage of numerical implementation of the method. General testing usually controls only total (final) error. Using the test problem, we analyze errors of a difference method of MacCormack type and the CIC method being the most popular version of the ‘particle-in-cell’ method. It is shown
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A new tool for studying seasonality and spatio-temporal structure of ENSO cycles in data and ESM simulations Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2024-02-10 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
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Multiresolution approximation for shallow water equations using summation-by-parts finite differences Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-12-05 Ilya D. Tretyak, Gordey S. Goyman, Vladimir V. Shashkin
We present spatial approximation for shallow water equations on a mesh of multiple rectangular blocks with different resolution in Cartesian geometry. The approximation is based on finite-difference operators that fulfill Summation By Parts (SBP) property – a discrete analogue of integration by parts. The solution continuity conditions between mesh blocks are imposed in a weak form using Simultaneous
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Extracting connectivity paths in digital core images using solution of partial minimum eigenvalue problem Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-12-05 Serguei Yu. Maliassov, Yuri V. Vassilevski
We show theoretically and numerically that the lowest non-trivial eigenvector function for a specific eigenproblem has almost constant values in high conductivity channels, which are different in separate channels. Therefore, based on these distinct values, all separate connected clusters of open pores can be identified in digital cores.
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Explaining breakthrough behaviour in shale rock: influence of capillary effects and geomechanics Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-12-05 Denis Anuprienko, Valentina Svitelman
Shale rock, being a common caprock for carbon dioxide reservoirs, is subject to extensive research. One of the topics is breakthrough phenomena during injection of supercritical carbon dioxide in shale, the nature of which is still to be fully understood. In the present paper, a two-phase flow model, which may possibly be used to explain the breakthrough behaviour is examined. Capillary effects and
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The study of the local sensitivity of functionals of the optimal solution to observational data and the heat flux input data in a variational assimilation problem for the sea thermodynamics model Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-12-05 Victor P. Shutyaev, Eugene I. Parmuzin, Igor Yu. Gejadze
The problem of variational assimilation of observational data for the sea thermodynamics model is considered with the aim to reconstruct heat fluxes on the sea surface. The local sensitivity of functionals of the solution to the observational data and input data for heat fluxes is studied in the considered problem and the results of numerical experiments are presented for the Black Sea dynamics model
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Non-local discretization of the isoneutral diffusion operator in a terrain-following climate ocean model Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-12-05 Dmitry V. Blagodatskikh, Nikolay G. Iakovlev, Evgenii M. Volodin, Andrey S. Gritsun
The present paper considers numerical properties of two different approaches to discretization of the isoneutral diffusion. The necessity of an alternative treatment of the isoneutral diffusion in a terrain-following climate ocean model as opposed to the more convenient rotated tensor formalism is studied. A new method of the approximation of the isoneutral diffusion based on a non-local computational
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Numerical model of Earth ionosphere F region based on three-dimensional transport and ambipolar diffusion equations Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-12-05 Dmitry V. Kulyamin, Sergey V. Kostrykin, Pavel A. Ostanin, Valentin P. Dymnikov
The paper provides a detailed description of the numerical implementation of the transport scheme in the Earth’s ionosphere three-dimensional dynamical model of the Institute of Numerical Mathematics (INMIM). The presented version of INM-IM model takes into account the global dynamical processes of ion transport and ambipolar diffusion in the altitude range between 100 and 500 km (corresponding to
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One-dimensional haemodynamic model of a vascular network with fractional-order viscoelasticity Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-11-08 Ruslan Yanbarisov, Timur Gamilov
We propose a computational framework for a one-dimensional haemodynamic model with the arterial walls described by the fractional-order viscoelastic material constitutive law. This framework is used to compare blood flow characteristics for simulations with elastic and fractional-order viscoelastic walls. We use three well-established benchmark tests: a single pulse wave in a long vessel, flow in a
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Myocardial perfusion segmentation and partitioning methods in personalized models of coronary blood flow Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-11-08 Alexander A. Danilov, Timur M. Gamilov, Fuyou Liang, Alina A. Rebrova, Petr Sh. Chomakhidze, Philipp Yu. Kopylov, Yan R. Bravyy, Sergey S. Simakov
In this work we present methods and algorithms for construction of a personalized model of coronary haemodynamics based on computed tomography images. This model provides estimations of fractional flow reserve, coronary flow reserve, and instantaneous wave-free ratio taking into account transmural perfusion ratio indices obtained from perfusion images. The presented pipeline consists of the following
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Mathematical modelling for spatial optimization of irradiation during proton radiotherapy with nanosensitizers Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-11-08 Maxim Kuznetsov, Andrey Kolobov
A spatially distributed mathematical model is presented that simulates the growth of a non-invasive tumour undergoing treatment by fractionated proton therapy with the use of non-radioactive tumour-specific nanosensitizers. Nanosensitizers are injected intravenously before each irradiation to increase the locally deposited dose via a chain of reactions with therapeutic protons. Modelling simulations
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Multiphysics modelling of immune processes using distributed parameter systems Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-11-08 Gennady A. Bocharov, Dmitry S. Grebennikov, Rostislav S. Savinkov
The immune system is a complex distributed system consisting of cells, which circulate through the body, communicate and turnover in response to antigenic perturbations. We discuss new approaches to modelling the functioning of the immune system of humans and experimental animals with a focus on its ‘complexity’. Emerging mathematical and computer models are reviewed to describe the immune system diversity
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Study of performance of low-rank nonnegative tensor factorization methods Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-08-08 Elena M. Shcherbakova, Sergey A. Matveev, Alexander P. Smirnov, Eugene E. Tyrtyshnikov
In the present paper we compare two different iterative approaches to constructing nonnegative tensor train and Tucker decompositions. The first approach is based on idea of alternating projections and randomized sketching for factorization of tensors with nonnegative elements. This approach can be useful for both TT and Tucker formats. The second approach consists of two stages. At the first stage
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Operator-difference schemes on non-uniform grids for second-order evolutionary equations Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-08-08 Petr N. Vabishchevich
The approximate solution of the Cauchy problem for second-order evolution equations is performed, first of all, using three-level time approximations. Such approximations are easily constructed and relatively uncomplicated to investigate when using uniform time grids. When solving applied problems numerically, we should focus on approximations with variable time steps. When using multilevel schemes
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Pressure-correction projection method for modelling the incompressible fluid flow in porous media Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-08-08 Kirill M. Terekhov
This work is dedicated to the pressure-correction projection method for the volume-averaged Navier–Stokes system for porous media. A set of parameters controlling the presence of inertia and viscosity is introduced into the system. Switching parameters allows us to reduce the system to either the Brinkman system or the Darcy equation. Considering the jump in the parameters between mesh cells allows
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The group behaviour modelling of workers in the labor market Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-08-08 Alexander Shananin, Nikolai Trusov
We describe the mathematical modelling of the group behaviour of workers in the labor market. The worker receives the salary and seeks to improve his qualifications in order to receive higher wages. The worker enlarges his qualification by the investments in human capital. At a random moment of time, a vacancy appears that provides a jump in the worker’s salary. The mathematical model of the worker’s
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Multicontinuum homogenization for Richards’ equation: The derivation and numerical experiments Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-08-08 Dmitry Ammosov, Sergei Stepanov, Denis Spiridonov, Wenyuan Li
In the present paper, the authors rigorously derive Richards’ multicontinuum model using the multicontinuum homogenization approach. This approach is based on formulating constraint cell problems and a homogenization-like expansion. We present numerical results for the two continua case with separable coefficients. First, we explore the relationships between the effective coefficients and the hydraulic
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CarNum: parallel numerical framework for computational cardiac electromechanics Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-06-15 Alexey A. Liogky, Alexey Yu. Chernyshenko, Alexander A. Danilov, Fyodor A. Syomin
A new parallel numerical framework CarNum is presented for efficient coupling of mathematical models in multiphysics problems such as computational cardiac electromechanics. This framework is based on open source projects, which provide the core functionality of the platform. Computational cardiac electromechanics requires a complex pipeline of solving different types of ordinary and partial differential
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Neural networks singular evolutive interpolated Kalman filter and its application to data assimilation for 2D water pollution model Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-06-15 Thu Ha Tran, Victor Shutyaev, Hong Son Hoang, Shuai Li, Chinh Kien Nguyen, Hong Phong Nguyen, Thi Thanh Huong Duong
The present study promotes a new algorithm for estimating the water pollution propagation with the primary goal of providing more reliable and high quality estimates to decision makers. To date, the widely used variational method suffers from the large computational burden, which limits its application in practice. Moreover, this method, considering the initial state as a control variable, is very
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Validation of boundary conditions for coronary circulation model based on a lumped parameter approach Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-06-15 Sergey S. Simakov, Timur M. Gamilov, Fuyou Liang, Petr Sh. Chomakhidze, Philipp Yu. Kopylov
In the present work, we construct a model of coronary flow, which utilizes both CT scans of large coronary arteries and coronary CT perfusion. The model describes pulsatile flow in the patient’s network of coronary vessels and takes into account a number of physiological effects: myocardium contractions, stenoses, impairment of microvascular perfusion. The main novelty of this model is the new smooth
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Ensemble-based statistical verification of INM RAS Earth system model Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-06-15 Maria A. Tarasevich, Ivan V. Tsybulin, Vladimir A. Onoprienko, Dmitry V. Kulyamin, Evgeny M. Volodin
Modern numerical models of the Earth system are complex and inherit its natural chaotic behaviour. The numerical results depend on various specifications of the simulation process, including computing systems, compilers, etc. Due to the chaotic behaviour, these minor differences lead to significant and unpredictable deviations. Therefore, some procedure verifying that simulation results describe the
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SIMUG – finite element model of sea ice dynamics on triangular grid in local Cartesian basis Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-06-15 Sergey S. Petrov, Nikolay G. Iakovlev
The paper presents the dynamical core of the new sea ice model SIMUG (Sea Ice Model on Unstructured Grid) on the A- and CD-types of unstructured triangular grids in the local-element basis on sphere. Three standardized box tests to reproduce the Linear Kinematic Features (LKFs), and the short-term forecast in the real Arctic Ocean geometry with the realistic atmosphere and ocean forcing demonstrate
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Particle tracking for face-based flux data on general polyhedral grids with applications to groundwater flow modelling Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-06-15 Ivan V. Kapyrin
A particle tracking method based on face fluxes data calculated using finite volume methods is developed for unstructured three-dimensional polyhedral grids. The flow velocity field reconstruction on grid cells using a mixed finite element method is proposed. Cases of sinks and sources in cells as well as different cell partitionings are considered. Algorithms for streamlines and time of flight calculation
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Sketching for a low-rank nonnegative matrix approximation: Numerical study Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-04-11 Sergey Matveev, Stanislav Budzinskiy
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
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Effect of electron temperature on formation of travelling waves in plasma: Kinetic and hydrodynamic models Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-04-11 Eugene V. Chizhonkov, Alexander A. Frolov
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
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Computational methods for multiscale modelling of virus infection dynamics Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-04-11 Dmitry S. Grebennikov
Virus infection dynamics is governed by the processes on multiple scales: on the whole organism level, tissue level, and intracellular level. In this paper, we develop a multi-scale multi-compartment model of HIV infection in a simplified setting and the computational methods for numerical realization of the model. The multiscale model describes the processes from various scales and of different nature
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Dependence of optimal disturbances on periodic solution phases for time-delay systems Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-04-11 Michael Yu. Khristichenko, Yuri M. Nechepurenko, Gennady A. Bocharov
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
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Finite difference scheme for a non-linear subdiffusion problem with a fractional derivative along the trajectory of motion Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-02-16 Alexander V. Lapin, Vladimir V. Shaydurov, Ruslan M. Yanbarisov
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
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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 Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-02-16 Sergey S. Petrov, Vladimir K. Zyuzin, Nikolay G. Iakovlev
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
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Mesh-independent multidimensional coupling of surface and subsurface water flow models Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-02-16 Konstantin Novikov
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
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Stochastic simulation of a signal on a photodetector matrix of a laser navigation system Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-02-16 Evgeniya G. Kablukova, Victor G. Oshlakov, Sergei M. Prigarin
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
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Growing axons: greedy learning of neural networks with application to function approximation Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2023-02-16 Daria Fokina, Ivan Oseledets
We propose a new method for learning deep neural network models, which is based on a greedy learning approach: we add one basis function at a time, and a new basis function is generated as a non-linear activation function applied to a linear combination of the previous basis functions. Such a method (growing deep neural network by one neuron at a time) allows us to compute much more accurate approximants
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INM-IM: INM RAS Earth ionosphere F region dynamical model Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-12-06 Dmitry V. Kulyamin, Pavel A. Ostanin, Valentin P. Dymnikov
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
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Sensitivity of functionals of the solution to a variational data assimilation problem with heat flux reconstruction for the sea thermodynamics model Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-12-06 Victor P. Shutyaev, Eugene I. Parmuzin
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
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Estimation of the average particle flux in a stochastically homogeneous medium by Monte Carlo method Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-12-06 Galiya Z. Lotova, Gennady A. Mikhailov
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
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Stochastic perturbation of tendencies and parameters of parameterizations in the global ensemble prediction system based on the SL-AV model Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-12-06 Kseniya A. Alipova, Gordey S. Goyman, Mikhail A. Tolstykh, Vasiliy G. Mizyak, Vladimir S. Rogutov
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
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Computational mimicking of surgical leaflet suturing for virtual aortic valve neocuspidization Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-11-07 Alexey A. Liogky
The aortic valve neocuspidization (AVNeo) procedure requires the design of patient-specific neo-cusps which can be made numerically through the neovalve closure modelling. Prior the simulation, it is required to ‘suture virtually’ the neocusps into the patient’s aortic geometry, i.e., to find such state in which the neocusps are placed in the aortic root lumen without intersections of physical surfaces
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Algorithms and methodological challenges in the development and application of quantitative systems pharmacology models: a case study in type 2 diabetes Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-11-07 Victor Sokolov
Quantitative systems pharmacology (QSP) is a relatively new modelling discipline, formed within the ever-growing domain of model-informed drug development and actively evolving throughout the last decade. This modelling technique is based on the systems analysis and is used to get a quantitative rather than qualitative understanding of systems dynamics and explore the mechanisms of action of a drug
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Computational analysis of the impact of aortic bifurcation geometry to AAA haemodynamics Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-11-07 Denis V. Tikhvinskii, Lema R. Merzhoeva, Alexander P. Chupakhin, Andrey A. Karpenko, Daniil V. Parshin
Abdominal aortic aneurysm is a widespread disease of cardiovascular system. Predicting a moment of its rupture is an important task for modern vascular surgery. At the same time, little attention is paid to the comorbidities, which are often the causes of severe postoperative complications or even death. This work is devoted to a numerical study of the haemodynamics of the model geometry for possible
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Application of minimum description length criterion to assess the complexity of models in mathematical immunology Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-11-07 Dmitry S. Grebennikov, Valerya V. Zheltkova, Gennady A. Bocharov
Mathematical models in immunology differ enormously in the dimensionality of the state space, the number of parameters and the parameterizations used to describe the immune processes. The ongoing diversification of the models needs to be complemented by rigorous ways to evaluate their complexity and select the parsimonious ones in relation to the data available/used for their calibration. A broadly
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Personalized computational estimation of relative change in coronary blood flow after percutaneous coronary intervention in short-term and long-term perspectives Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-11-07 Sergey S. Simakov, Timur M. Gamilov, Alexander A. Danilov, Fuyou Liang, Petr Sh. Chomakhidze, Mariam K. Gappoeva, Alina A. Rebrova, Philipp Yu. Kopylov
Coronary artery disease is the leading cause of mortality worldwide, accounting for 12.8% of all deaths. Although the clinical benefits of treating stenosis with percutaneous coronary intervention (PCI) have been extensively demonstrated, residual myocardial ischemia remains in about 30–50% of patients even after a formally successful PCI. We apply previously developed and validated 1D model of haemodynamics
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Glacier parameterization in SLAV numerical weather prediction model Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-08-18 Rostislav Yu. Fadeev, Kseniya A. Alipova, Anna S. Koshkina, Timofey E. Lapin, Nadezhda A. Ozerova, Alina E. Pereladova, Andrey V. Sakhno, Mikhail A. Tolstykh
In the present paper, we describe a one-dimensional glacier parameterization for use in the numerical weather prediction models. The proposed scheme is implemented into the global atmospheric model SLAV. To avoid inconsistency of surface temperature and turbulent heat fluxes in the lower troposphere, glacier parameterization has been iteratively coupled with both planetary boundary layer and land surface
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Construction and optimization of numerically-statistical projection algorithms for solving integral equations Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-08-18 Anna S. Korda, Gennady A. Mikhailov, Sergey V. Rogasinsky
The problem of minimizing the root-mean-square error of the numerical-statistical projection estimation of the solution to an integral equation is solved. It is shown that the optimal estimator in this sense can be obtained by equalizing deterministic and stochastic components of the error in the case when the norm of the remainder of the utilized decomposition decreases inversely proportional to its
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Error identities for the reaction–convection–diffusion problem and applications to a posteriori error control Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-08-18 Sergey I. Repin
The paper is devoted to a posteriori error identities for the stationary reaction–convection–diffusion problem with mixed Dirichlét–Neumann boundary conditions. They reflect the most general relations between deviations of approximations from the exact solutions and those values that can be observed in a numerical experiment. The identities contain no mesh dependent constants and are valid for any
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On the efficiency of using correlative randomized algorithms for solving problems of gamma radiation transfer in stochastic medium Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-08-18 Ilia N. Medvedev
To solve problems of radiation balance, optical sounding, and tomography, it may be necessary to take into account multiple scattering of radiation in a stochastically inhomogeneous medium. In real radiation models, for this purpose, the numerical-statistical ‘majorant cross-section method’ (MCM, delta-Woodcock tracking) is used based on the alignment of the optical density field by adding an artificial
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Optimal disturbances for periodic solutions of time-delay differential equations Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-08-18 Michael Yu. Khristichenko, Yuri M. Nechepurenko
A concept of optimal disturbances of periodic solutions for a system of time-delay differential equations is defined. An algorithm for computing the optimal disturbances is proposed and justified. This algorithm is tested on the known system of four nonlinear time-delay differential equations modelling the dynamics of the experimental infection caused by the lymphocytic choriomeningitis virus. The
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Linear regularized finite difference scheme for the quasilinear subdiffusion equation Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-08-18 Alexander Lapin, Erkki Laitinen
A homogeneous Dirichlet initial-boundary value problem for a quasilinear parabolic equation with a time-fractional derivative and coefficients at the elliptic part that depend on the gradient of the solution is considered. Conditions on the coefficients ensure the monotonicity and Lipschitz property of the elliptic operator on the set of functions whose gradients in space variables are uniformly bounded
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Variational data assimilation for a sea dynamics model Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-06-14 Valery Agoshkov, Vladimir Zalesny, Victor Shutyaev, Eugene Parmuzin, Natalia Zakharova
The 4D variational data assimilation technique is presented for modelling the sea dynamics problems, developed at the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS). The approach is based on the splitting method for the mathematical model of sea dynamics and the minimization of cost functionals related to the observation data by solving an optimality system
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Mesh scheme for a phase transition problem with time-fractional derivative Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-06-14 Alexander Lapin
The time-fractional phase transition problem, formulated in enthalpy form, is studied. This nonlinear problem with an unknown moving boundary includes, as an example, a mathematical model of one-phase Stefan problem with the latent heat accumulation memory. The posed problem is approximated by the backward Euler mesh scheme. The unique solvability of the mesh scheme is proved and a priori estimates
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A finite element scheme for the numerical solution of the Navier–Stokes/Biot coupled problem Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-06-14 Alexander Lozovskiy, Maxim A. Olshanskii, Yuri V. Vassilevski
A finite element method for a monolithic quasi-Lagrangian formulation of a fluid–porous structure interaction problem with a corrected balance of stresses on the fluid–structure interface is considered. Deformations of the elastic medium are not necessarily small and are modelled using Saint Venant–Kirchhoff (SVK) constitutive relation. The stability of the method is proved in a form of energy bound
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Difference schemes for second-order ordinary differential equations with corrector and predictor properties Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-06-14 Vladimir V. Shaidurov, Anton E. Novikov
A technique for constructing a sequence of difference schemes with the properties of a corrector and a predictor for integrating systems of the second-order ordinary differential equations is presented. The sequence of schemes begins with the explicit three-point Störmer method of the second order of approximation. Each subsequent scheme also implements the Störmer method corrected with additional
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Connection between the existence of a priori estimate for a flux and the convergence of iterative methods for diffusion equation with highly varying coefficients Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-06-14 George M. Kobelkov, Eckart Schnack
An iterative method with the number of iterations independent of the coefficient jumps is proposed for the boundary value problem for a diffusion equation with highly varying coefficient. The method applies one solution of the Poisson equation at each step of iteration. In the present paper we extend the class of domains the iterative method is justified for.
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Development of a numerical stochastic model of joint spatio-temporal fields of weather parameters for the south part of the Baikal natural territory Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-04-20 Marina S. Akenteva, Nina A. Kargapolova, Vasily A. Ogorodnikov
The paper is focused on the construction of a numerical stochastic model of the joint spatio-temporal fields of air temperature, wind speed vector with three-hour resolution, and semidiurnal precipitation amounts according to observation data at a group of weather stations located in the south of the Baikal natural territory. The model also takes into account the dependence of one-dimensional distributions
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Predictability of the low-frequency modes of the Arctic Ocean heat content variability: a perfect model approach Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-04-20 Andrey S. Gritsun
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
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Discrete curvatures for planar curves based on Archimedes’ duality principle Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-04-20 Vladimir A. Garanzha, Liudmila N. Kudryavtseva, Dmitry A. Makarov
We introduce discrete curvatures for planar curves based on the construction of sequences of pairs of mutually dual polylines. For piecewise-regular curves consisting of a finite number of fragments of regular generalized spirals with definite (positive or negative) curvatures our discrete curvatures approximate the exact averaged curvature from below and from above. In order to derive these estimates
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On the multi-annual potential predictability of the Arctic Ocean climate state in the INM RAS climate model Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-04-20 Evgeny M. Volodin, Vasilisa V. Vorobyeva
Idealized numerical experiments with the INM RAS climate model are used to study the potential predictability of the temperature in the upper 300-meter layer of the Arctic Ocean. It is shown that the heat content can be predictable for up to 4–6 years. Positive anomalies of the temperature and salinity are preceded for several years by a state in which the influx of Atlantic water into the Arctic Ocean
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Optimal stochastic forcings for sensitivity analysis of linear dynamical systems Russ. J. Numer. Anal. Math. Model. (IF 0.6) Pub Date : 2022-04-20 Yuri M. Nechepurenko, Grigory V. Zasko
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