Mathematical models for fluid–solid interaction and their numerical solutions

2014 ◽  
Vol 50 ◽  
pp. 184-216 ◽  
Author(s):  
K.S. Surana ◽  
B. Blackwell ◽  
M. Powell ◽  
J.N. Reddy
Keyword(s):  
Mathematical Models ◽  
Numerical Solutions ◽  
Fluid Solid Interaction

scholarly journals Application of hybrid asymptotic methods and modern software for mathematical models developing for nonlinear dynamics of structures with variables in time parameters

2021 ◽  
pp. 66-70
Author(s):  
S. Homeniuk ◽  
S. Grebenyuk ◽  
D. Gristchak
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Methods ◽  
Nonlinear Systems ◽  
Analytical Solution ◽  
Mathematical Models ◽  
Nonlinear Dynamic ◽  
Numerical Solutions ◽  
Hybrid Approach ◽  
Time Dependent ◽  
Forced Oscillations

The relevance. The aerospace domain requires studies of mathematical models of nonlinear dynamic structures with time-varying parameters. The aim of the work. To obtain an approximate analytical solution of nonlinear forced oscillations of the designed models with time-dependent parameters. The research methods. A hybrid approach based on perturbation methods, phase integrals, Galorkin orthogonalization criterion is used to obtain solutions. Results. Nonlocal investigation of nonlinear systems behavior is done using results of analytical and numerical methods and developed software. Despite the existence of sufficiently powerful numerical software systems, qualitative analysis of nonlinear systems with variable parameters requires improved mathematical models based on effective analytical, including approximate, solutions, which using numerical methods allow to provide a reliable analysis of the studied structures at the stage designing. An approximate solution in analytical form is obtained with constant coefficients that depend on the initial conditions. Conclusions. The approximate analytical results and direct numerical solutions of the basic equation were compared which showed a sufficient correlation of the obtained analytical solution. The proposed algorithm and program for visualization of a nonlinear dynamic process could be implemented in nonlinear dynamics problems of systems with time-dependent parameters.

Application of minimal mathematical models for the dynamics of the signaling pathway of the p53 - miRNA to the analysis of laboratory data

2021 ◽  
pp. 4-49
Author(s):  
Софья Дмитриевна Сенотрусова ◽  
Ольга Фалалеевна Воропаева ◽  
Юрий Иванович Шокин
Keyword(s):  
Mathematical Models ◽  
Signaling Pathway ◽  
Numerical Solutions ◽  
Laboratory Data ◽  
Minimal Models ◽  
Basic Model ◽  
P53 Signaling ◽  
Wide Range ◽  
P53 Signaling Pathway

Работа посвящена практическому использованию минимальных математических моделей динамики сигнального пути p53 для описания достаточно широкого круга лабораторных экспериментов, в которых взаимодействие p53 и белковингибиторов p53 опосредуется микроРНК, образующими с p53 петлю положительной обратной связи. Представлены базовая модель, разработанные на ее основе новые минимальные модели, алгоритм численного решения прямых и обратных коэффициентных задач и результаты сопоставления полученных численных решений с экспериментальными данными о динамике уровней белков p53, p21, Bax, белков-ингибиторов Mdm2, Wip1, Sirt1 и различных микроРНК (miR-16, miR-34a, miR-192, miR-194, miR-215) в условиях стрессовых воздействий. С привлечением полученных математических моделей исследованы базовые механизмы функционирования сигнального пути p53 в условиях, приближенных к условиям конкретных лабораторных экспериментов in vitro и in vivo. Продемонстрированы синергический эффект гиперактивации сигнального пути p53, в котором задействованы микроРНК, и механизмы бимодального переключения. Показана ключевая роль p53-зависимых микроРНК в реализации некоторых гипотетических терапевтических стратегий, связанных с управлением механизмом активации апоптоза клеток. В рамках принятой базовой модели даны оценки вероятности рассогласования в диагностике дегенеративных заболеваний, основанной на анализе уровня p53зависимых микроРНК и p53, при слабой и умеренной дерегуляции микроРНК. This study addresses the practical use of minimal mathematical models of the dynamics of a hypothetical system of the p53 signaling pathway to describe a fairly wide range of laboratory experiments. In such system, the interaction of p53 and p53 inhibitor proteins is mediated by microRNAs that form a positive feedback loop with p53. A basic model, new minimal models developed on its basis, an algorithm for the numerical solution of direct and inverse coefficient problems, and the results of comparing the obtained numerical solutions with experimental data on the dynamics of the levels of p53, p21, Bax proteins, inhibitor proteins Mdm2, Wip1, Sirt1, and various microRNAs (miR-16, miR-34a, miR-192, miR-194, miR-215) under stress conditions are presented. In numerical experiments, the main mechanisms of the p53 signaling pathway were investigated. A synergistic effect of hyperactivation of the p53 signaling pathway and bimodal switching mechanisms has been demonstrated. We show the key role of p53-dependent microRNAs in the implementation of some hypothetical therapeutic strategies associated with the control mechanism for activation of cells apoptosis. Within the framework of the accepted basic model, we estimated the probability of mismatch in the diagnosis of the patient’s status. The status is based on the analysis of the level of p53-dependent microRNAs and p53, with weak and moderate deregulation of microRNAs.

scholarly journals A Partial Lagrangian Approach to Mathematical Models of Epidemiology

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
R. Naz ◽  
I. Naeem ◽  
F. M. Mahomed
Keyword(s):  
Mathematical Models ◽  
Exact Solutions ◽  
Numerical Solutions ◽  
First Integrals ◽  
Order Equation ◽  
Second Order ◽  
Lagrangian Approach ◽  
Hiv Model ◽  
First Order ◽  
Partial Lagrangian

This paper analyzes the first integrals and exact solutions of mathematical models of epidemiology via the partial Lagrangian approach by replacing the three first-order nonlinear ordinary differential equations by an equivalent system containing one second-order equation and a first-order equation. The partial Lagrangian approach is then utilized for the second-order ODE to construct the first integrals of the underlying system. We investigate the SIR and HIV models. We obtain two first integrals for the SIR model with and without demographic growth. For the HIV model without demography, five first integrals are established and two first integrals are deduced for the HIV model with demography. Then we utilize the derived first integrals to construct exact solutions to the models under investigation. The dynamic properties of these models are studied too. Numerical solutions are derived for SIR models by finite difference method and are compared with exact solutions.

Numerical analysis of hemivariational inequalities in contact mechanics

Acta Numerica ◽  
2019 ◽  
Vol 28 ◽  
pp. 175-286 ◽  
Author(s):  
Weimin Han ◽  
Mircea Sofonea
Keyword(s):  
Numerical Analysis ◽  
Mathematical Models ◽  
Contact Mechanics ◽  
Numerical Solutions ◽  
Deformable Body ◽  
Industrial Process ◽  
Contact Problems ◽  
Hemivariational Inequalities ◽  
Uniqueness Results ◽  
Simulation Results

Contact phenomena arise in a variety of industrial process and engineering applications. For this reason, contact mechanics has attracted substantial attention from research communities. Mathematical problems from contact mechanics have been studied extensively for over half a century. Effort was initially focused on variational inequality formulations, and in the past ten years considerable effort has been devoted to contact problems in the form of hemivariational inequalities. This article surveys recent development in studies of hemivariational inequalities arising in contact mechanics. We focus on contact problems with elastic and viscoelastic materials, in the framework of linearized strain theory, with a particular emphasis on their numerical analysis. We begin by introducing three representative mathematical models which describe the contact between a deformable body in contact with a foundation, in static, history-dependent and dynamic cases. In weak formulations, the models we consider lead to various forms of hemivariational inequalities in which the unknown is either the displacement or the velocity field. Based on these examples, we introduce and study three abstract hemivariational inequalities for which we present existence and uniqueness results, together with convergence analysis and error estimates for numerical solutions. The results on the abstract hemivariational inequalities are general and can be applied to the study of a variety of problems in contact mechanics; in particular, they are applied to the three representative mathematical models. We present numerical simulation results giving numerical evidence on the theoretically predicted optimal convergence order; we also provide mechanical interpretations of simulation results.

scholarly journals On mathematical models and numerical solutions of gas stirred ladle systems

1993 ◽  
Vol 17 (5) ◽  
pp. 255-262 ◽  
Author(s):  
Dipak Mazumdar ◽  
R.I.L. Guthrie ◽  
Y. Sahai
Keyword(s):  
Mathematical Models ◽  
Numerical Solutions

On The Fluid-Solid Interaction in Reference to Thermoelastohydrodynamic Analysis of Journal Bearings

1991 ◽  
Vol 113 (2) ◽  
pp. 398-404 ◽  
Author(s):  
M. M. Khonsari ◽  
S. H. Wang
Keyword(s):  
Finite Element ◽  
Thermal Expansion ◽  
Finite Difference ◽  
Numerical Solutions ◽  
Journal Bearings ◽  
Collective Effect ◽  
Thermoelastic Deformation ◽  
Simulation Results ◽  
Thermal Dilation ◽  
Fluid Solid Interaction

Thermohydrodynamic analysis of journal bearings is extended to include provisions for the shaft thermal dilation as well as the bush thermoelastic deformation. Numerical solutions using a combination of the finite difference and finite element methods are presented. Comparison of the simulation results with those obtained experimentally yielded satisfactory agreement. It was found that while the shaft and bush thermal expansion and the bush elastic deformation are individually important, the collective effect of these factors must be considered for meaningful end results.

scholarly journals Mathematical modelling of soil massifs strained-deformed state under soil water level decreasing

2018 ◽  
Vol 2 (51) ◽  
pp. 73-78
Author(s):  
Mykola Kuzlo
Keyword(s):  
Mathematical Models ◽  
Numerical Solutions ◽  
Single Layer ◽  
Filtration Flow ◽  
Curvilinear Boundary ◽  
Vertical Displacements ◽  
Deformed State ◽  
Water Saturated ◽  
Soil Filtration ◽  
Saline Solutions

The analytical solutions for the determination of vertical displacements at any point of single-layer and multilayer soil compositions under filtration water flow influence, saline solutions presence and filtration considering soil changing filtration and deformation characteristics have been obtained. The mathematical models of soil filtration and the stress-deformed state from water-saturated ground massifs and bases deformations forecast under internal volumetric forces influence (hydrodynamic forces of the filtration flow, changes in the soils own weight) have been developed and substantiated. Numerical solutions of the corresponding boundary filtration problems and SDS of soil in regions with time-varying curvilinear boundary have been obtained for these mathematical models. They have enabled to perform water-saturated soils and bases deformations forecast under the change of hydrogeological conditions and man-made factors effect.

scholarly journals Laminar and weakly turbulent oceanic gravity currents performing inertial oscillations

2011 ◽  
Vol 8 (5) ◽  
pp. 2001-2045
Author(s):  
A. Wirth
Keyword(s):  
Mathematical Models ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Gravity Current ◽  
Boussinesq Approximation ◽  
Turbulent Fluxes ◽  
Navier Stokes ◽  
Small Scale ◽  
Mean Flow ◽  
Inertial Oscillations

Abstract. The small scale dynamics of a weakly turbulent oceanic gravity current is determined. The gravity current considered is initially at rest and adjusts by performing inertial oscillations to a geostrophic mean flow. The dynamics is explored with a hierarchy of mathematical models. The most involved are the fully 3-D Navier-Stokes equations subject to the Boussinesq approximation. A 1-D and 0-D mathematical model of the same gravity current dynamics are systematically derived. Using this hierarchy and the numerical solutions of the mathematical models, the turbulent dynamics at the bottom and the interface is explored and their interaction investigated. Three different regimes of the small scale dynamics of the gravity current are identified, they are characterised by laminar flow, coherent roll vortices and turbulent dynamics with coherent streaks and bursts. The problem of the rectification of the turbulent fluxes, that is how to average out the fluctuations and calculate their average influence on the flow is considered. It is shown that two different regimes of friction are superposed, an Ekman friction applies to the average geostrophic flow and a linear friction, not influenced by rotation, to the inertial oscillations. The combination of the two makes the bulk friction non-local in time for the 0-D model. The implications of the results for parametrisations of the Ekman dynamics and the small scale turbulent fluxes in the planetary boundary layer are discussed.

scholarly journals Computational Experiments to Evaluate the Approaches to the Modeling of Viscoelastic Plates Motion Based on Various Theories

2018 ◽  
pp. 15-33
Author(s):  
B. A. Khudayarov
Keyword(s):  
Differential Equations ◽  
Mathematical Models ◽  
Viscoelastic Properties ◽  
Numerical Solutions ◽  
Aircraft Design ◽  
Panel Flutter ◽  
Scientific Problem ◽  
Wide Range ◽  
Hereditary Theory ◽  
Theory Of Viscoelasticity

Mathematical and computer modeling of the flutter of elements and units of the aircraft design is an actual scientific problem; its study is stimulated by the failure of aircraft elements, parts of space and jet engines. In view of the complexity of the flutter phenomenon of aircraft elements, simplifying assumptions are used in many studies. However, these assumptions, as a rule, turn out to be so restrictive that the mathematical model ceases to reflect the real conditions with sufficient accuracy. Therefore, results of theoretical and experimental studies are in bad agreement.At present, the problem of panel flutter is very relevant. Improvement of characteristics of military and civil aircraft inevitably requires reducing their weight, and consequently, the rigidity of paneling, which increases the possibility of a panel flutter. The concept of creating the aircraft with a variable shape, which would inevitably lead to a reduction in paneling thickness are actively discussed. Finally, the use of new materials and, in particular, composites, changes physical properties of the panels and can also lead to a flutter.The above-mentioned scientific problem gives grounds to assert that the development of adequate mathematical models, numerical methods and algorithms for solving nonlinear integral-differential equations of dynamic problems of the hereditary theory of viscoelasticity is actual.In connection with this, the development of mathematical models of individual elements of aircraft made of composite material is becoming very important.Generalized mathematical models of non-linear problems of the flutter of viscoelastic isotropic plates, streamlined by a supersonic gas flow, are constructed in the paper on the basis of integral models. To study oscillation processes in plates, a numerical algorithm is proposed for solving nonlinear integro-differential equations with singular kernels. Based on the developed computational algorithm, a package of applied programs is created. The effect of the singularity parameter in heredity kernels on the vibrations of structures with viscoelastic properties is numerically investigated. In a wide range of changes in plate parameters, critical flutter velocities are determined. Numerical solutions of the problem of viscoelastic plate flutter are compared for different models. It is shown that the most adequate theory for investigating a wide class of problems of the hereditary theory of viscoelasticity is the geometric nonlinear Kirchhoff-Love theory with consideration of elastic waves propagation. It is established that an account of viscoelastic properties of plate material leads to 40-60% decrease in the critical flutter velocity.

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