scholarly journals Mathematical model of SPOC with a time dependent reactive field

2006 ◽  
Vol 31 ◽  
pp. 185-186
Author(s):  
Masako Ohtaki
Keyword(s):  
Mathematical Model ◽  
Time Dependent ◽  
Reactive Field

Modal Analysis of the Axial Compressor Blade: Advanced Time-Dependent Electronic Interferometry and Finite Element Method

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mykhaylo Tkach ◽  
Serhii Morhun ◽  
Yuri Zolotoy ◽  
Irina Zhuk
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Finite Element ◽  
High Reliability ◽  
Axial Compressor ◽  
Time Dependent ◽  
Experimental Setup ◽  
Vibration Modes ◽  
Compressor Blades ◽  
Isoparametric Finite Element

AbstractNatural frequencies and vibration modes of axial compressor blades are investigated. A refined mathematical model based on the usage of an eight-nodal curvilinear isoparametric finite element was applied. The verification of the model is carried out by finding the frequencies and vibration modes of a smooth cylindrical shell and comparing them with experimental data. A high-precision experimental setup based on an advanced method of time-dependent electronic interferometry was developed for this aim. Thus, the objective of the study is to verify the adequacy of the refined mathematical model by means of the advanced time-dependent electronic interferometry experimental method. The divergence of the results of frequency measurements between numerical calculations and experimental data does not exceed 5 % that indicates the adequacy and high reliability of the developed mathematical model. The developed mathematical model and experimental setup can be used later in the study of blades with more complex geometric and strength characteristics or in cases when the real boundary conditions or mechanical characteristics of material are uncertain.

scholarly journals C2 Continuous Blending of Time-Dependent Parametric Surfaces

2019 ◽  
Vol 19 (4) ◽  
Author(s):  
Xiangyu You ◽  
Feng Tian ◽  
Wen Tang
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
High Efficiency ◽  
Approximate Analytical Solution ◽  
Time Dependent ◽  
Order Partial Differential Equation ◽  
Parametric Surfaces ◽  
Boundary Constraints ◽  
Surface Blending ◽  
C2 Continuity

Surface blending is widely applied in mechanical engineering. Creating a smooth transition surface of C2 continuity between time-dependent parametric surfaces that change their positions and shapes with time is an important and unsolved topic in surface blending. In order to address this issue, this paper develops a new approach to unify both time-dependent and time-independent surface blending with C2 continuity. It proposes a new surface blending mathematical model consisting of a vector-valued sixth-order partial differential equation and blending boundary constraints and investigates a simple and efficient approximate analytical solution of the mathematical model. A number of examples are presented to demonstrate the effectiveness and applications. The proposed approach has the advantages of (1) unifying time-independent and time-dependent surface blending, (2) always maintaining C2 continuity at trimlines when parametric surfaces change their positions and shapes with time, (3) providing effective shape control handles to achieve the expected shapes of blending surfaces but still exactly satisfy the given blending boundary constraints, and (4) quickly generating C2 continuous blending surfaces from the approximate analytical solution with easiness, good accuracy, and high efficiency.

Modulatory effect of calmodulin-dependent kinase II (CaMKII) on sarcoplasmic reticulum Ca 2+ handling and interval–force relations: a modelling study

2006 ◽  
Vol 364 (1842) ◽  
pp. 1107-1133 ◽  
Author(s):  
Gentaro Iribe ◽  
Peter Kohl ◽  
Denis Noble
Keyword(s):  
Mathematical Model ◽  
Sarcoplasmic Reticulum ◽  
Ryanodine Receptor ◽  
Time Dependent ◽  
Kinetic Properties ◽  
Slow Inactivation ◽  
Slow Time ◽  
Key Factor ◽  
Amplifying Effect ◽  
Dependent Factor

We hypothesize that slow inactivation of Ca 2+ /calmodulin-dependent kinase II (CaMKII) and its modulatory effect on sarcoplasmic reticulum (SR) Ca 2+ handling are important for various interval–force (I–F) relations, in particular for the beat interval dependency in transient alternans during the decay of post-extrasystolic potentiation. We have developed a mathematical model of a single cardiomyocyte to integrate various I–F relations, including alternans, by incorporating a conceptual CaMKII kinetics model into the SR Ca 2+ handling model. Our model integrates I–F relations, such as the beat interval-dependent twitch force duration, restitution and potentiation, positive staircase phenomenon and alternans. We found that CaMKII affects more or less all I–F relations, and it is a key factor for integration of the various I–F relations in our model. Alternans arises, in the model, out of a steep relation between SR Ca 2+ load and release, owing to SR load-dependent changes in the releasability of Ca 2+ via the ryanodine receptor. Beat interval-dependent CaMKII activity, owing to its kinetic properties and amplifying effect on SR Ca 2+ load dependency of Ca 2+ release, replicated the beat interval dependency of alternans, as observed experimentally. Additionally, our model enabled reproduction of the effects of various interventions on alternans, such as the slowing or accelerating of Ca 2+ release and/or uptake. We conclude that a slow time-dependent factor, represented in the model by CaMKII, is important for the integration of I–F relations, including alternans, and that our model offers a useful tool for further analysis of the roles of integrative Ca 2+ handling in myocardial I–F relations.

Vibrational nitrogen concentration in the ionosphere and its dependence on season and solar cycle

1995 ◽  
Vol 13 (11) ◽  
pp. 1164-1171 ◽  
Author(s):  
A. E. Ennis ◽  
G. J. Bailey ◽  
R. J. Moffett
Keyword(s):  
Mathematical Model ◽  
Solar Cycle ◽  
Electron Density ◽  
Geomagnetic Field ◽  
Nitrogen Concentration ◽  
Time Dependent ◽  
Electron Content ◽  
Vibrationally Excited ◽  
F Region ◽  
Excited Nitrogen

Abstract. A fully time-dependent mathematical model, SUPIM, of the Earth's plasmasphere is used in this investigation. The model solves coupled time-dependent equations of continuity, momentum and energy balance for the O+, H+, He+, N+2, O+2, NO+ ions and electrons; in the present study, the geomagnetic field is represented by an axial-centred dipole. Calculation of vibrationally excited nitrogen molecules, which has been incorporated into the model, is presented here. The enhanced model is then used to investigate the behaviour of vibrationally excited nitrogen molecules with F10.7 and solar EUV flux, during summer, winter and equinox conditions. The presence of vibrational nitrogen causes a reduction in the electron content. The diurnal peak in electron content increases linearly up to a certain value of F10.7, and above this value increases at a lesser rate, in agreement with previous observations and modelling work. The value of F10.7 at which this change in gradient occurs is reduced by the presence of vibrational nitrogen. Vibrational nitrogen is most effective at F-region altitudes during summer daytime conditions when a reduction in the electron density is seen. A lesser effect is seen at equinox, and in winter the effect is negligible. The summer reduction in electron density due to vibrational nitrogen therefore reinforces the seasonal anomaly.

Large-scale flow in turbulent convection: a mathematical model

1986 ◽  
Vol 170 ◽  
pp. 385-410 ◽  
Author(s):  
L. N. Howard ◽  
R. Krishnamurti
Keyword(s):  
Mathematical Model ◽  
Large Scale ◽  
Laboratory Experiments ◽  
Boussinesq Equations ◽  
Time Dependent ◽  
Heteroclinic Orbits ◽  
Turbulent Convection ◽  
Mean Flow ◽  
Dependent Flow ◽  
Large Scale Flow

A mathematical model of convection, obtained by truncation from the two-dimensional Boussinesq equations, is shown to exhibit a bifurcation from symmetrical cells to tilted non-symmetrical ones. A subsequent bifurcation leads to time-dependent flow with similarly tilted transient plumes and a large-scale Lagrangian mean flow. This change of symmetry is similar to that occurring with the advent of a large-scale flow and transient tilted plumes seen in laboratory experiments on turbulent convection at high Rayleigh number. Though not intended as a description of turbulent convection, the model does bring out in a theoretically tractable context the possibility of the spontaneous change of symmetry suggested by the experiments.Further bifurcations of the model lead to stable chaotic phenomena as well. These are numerically found to occur in association with heteroclinic orbits. Some mathematical results clarifying this association are also presented.

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