Asymptotics of solutions for a system of equations of surface waves for large times

1994 ◽  
pp. 235-260
Keyword(s):  
Surface Waves ◽  
System Of Equations ◽  
Asymptotics Of Solutions

THE ASYMPTOTIC STRUCTURE OF THE HODGKIN–HUXLEY EQUATIONS

2003 ◽  
Vol 13 (12) ◽  
pp. 3805-3825 ◽  
Author(s):  
REBECCA SUCKLEY ◽  
VADIM N. BIKTASHEV
Keyword(s):  
Differential Equations ◽  
Action Potential ◽  
Slow Manifold ◽  
System Of Equations ◽  
Asymptotic Structure ◽  
Asymptotics Of Solutions ◽  
Cusp Singularity ◽  
Systems Of Differential Equations ◽  
Characteristic Features

We analyze the asymptotic structure of the Hodgkin–Huxley system of equations, in terms of the concepts of slow manifold and fast foliation, based on Tikhonov's theorem on asymptotics of solutions of slow–fast systems of differential equations. We test Zeeman's conjecture that the jump onset–slow return structure of the action potential in realistic equations of biological excitability may be due to a cusp singularity of the slow manifold with respect to the fast foliation. We find that although the cusp singularity can appear in such equations, the characteristic features in question cannot be reproduced within the Tikhonov scheme and require development of different asymptotic approaches.

ON A SYSTEM OF EQUATIONS DESCRIBING SURFACE WAVES

1991 ◽  
Vol 37 (1) ◽  
pp. 119-156
Author(s):  
P I Naumkin ◽  
I A Shishmarëv
Keyword(s):  
Surface Waves ◽  
System Of Equations

Modeling of Sea Sea Surface Waves In Hurricane Basing On Self-Similarity Concept

2020 ◽  
Author(s):  
Mariya Yurovskaya ◽  
Vladimir Kudryavtsev ◽  
Bertrand Chapron
Keyword(s):  
Surface Waves ◽  
Wave Energy ◽  
Wind Field ◽  
Time Moment ◽  
Peak Frequency ◽  
Parametric Model ◽  
Spectral Peak ◽  
System Of Equations ◽  
Self Similarity ◽  
Wave Forecast

<p>The study is based on a simple parametric model, which is an extension of the self-similarity theory for surface waves generated by a wind field. According to the original similarity concept, the development of wind waves can be fully described using the scale of the fetch length (or time) and wind velocity. The aim of the work is to develop a parametric model to describe the wave generation in arbitrary spatio-temporal wind field. We assume that in this case similarity laws are also fulfilled, i.e., the rate of spectral the peak frequency and wave energy change is completely determined by the wave age. The source function is written in a form providing the stationary solution that corresponds to the well-known fetch law, confirmed in numerous experiments.</p><p>In order to extend the equations to the two-dimensional case, when the wind change occurs in both directions, it is assumed that the relations stay valid if the wind speed is replaced by its component in spectral peak direction. In this case, the system of equations should be supplemented by an expression for the evolution of spectral peak direction, describing its adaptating to the direction of non-uniform wind.</p><p>The algorithm for solving the complete system of equations describing the evolution of wave height, spectral peak frequency, its propagation direction and focusing/defocusing of wave energy, is based on the method of characteristics. To simulate the evolution of waves in a hurricane, we use the calculation in a non-stationary reference system associated with the hurricane. Coordinates, wave peak frequency, energy and direction are calculated along ray trajectory at every discrete time moment. To increase the stability of the numerical scheme, an implicit 4th-order Runge-Kutta method is used.</p><p>Test calculations were carried out for the case of the wave development from the coast with a uniform wind and then for an inhomogeneous cyclonic wind field for different hurricane speeds. The calculations reproduce the anisotropy of the energy distribution inside the hurricane and the effect of wave trapping by a moving cyclone. A comparison of the results with available field measurements of wave parameters in tropical cyclones showed their good agreement. The proposed algorithm can be used in wave forecast models and can serve for deeper understanding the wave field formation in extreme conditions.</p><p>The work was supported by Russian Science Foundation via grant 17-77-30019 and the Ministry of Education and Science of the Russian Federation under the State Assignment No. 0827-2018-0003.</p>

Pulsed discharges produced by surface waves

1998 ◽  
Vol 08 (PR7) ◽  
pp. Pr7-317-Pr7-326 ◽  
Author(s):  
O. A. Ivanov ◽  
A. M. Gorbachev ◽  
V. A. Koldanov ◽  
A. L. Kolisko ◽  
A. L. Vikharev
Keyword(s):  
Surface Waves ◽  
Pulsed Discharges

Canonical Submersion and Lie Homomorphisms Normal Subgroup

2020 ◽  
Vol 23 (1) ◽  
pp. 97-101
Author(s):  
Mikhail Petrichenko ◽  
Dmitry W. Serow
Keyword(s):  
Normal Subgroup ◽  
Canonical System ◽  
System Of Equations ◽  
Core Group ◽  
The Core ◽  
Switch Group

Normal subgroup module f (module over the ring F = [ f ] 1; 2-diffeomorphisms) coincides with the kernel Ker Lf derivations along the field. The core consists of the trivial homomorphism (integrals of the system v = x = f (t; x )) and bundles with zero switch group Lf , obtained from the condition ᐁ( ω × f ) = 0. There is the analog of the Liouville for trivial immersion. In this case, the core group Lf derivations along the field replenished elements V ( z ), such that ᐁz = ω × f. Hence, the core group Lf updated elements helicoid (spiral) bundles, in particular, such that f = ᐁU. System as an example Crocco shown that the canonical system does not permit the trivial embedding: the canonical system of equations are the closure of the class of systems that permit a submersion.

LIQUIDUS THERMO-BAROMETER FOR THE MODELING OF MAGNETITE — MELT EQUILIBRIUM

2018 ◽  
pp. 71-80
Author(s):  
N. S. Aryaeva ◽  
E. V. Koptev-Dvornikov ◽  
D. A. Bychkov
Keyword(s):  
Experimental Data ◽  
Liquidus Temperature ◽  
Vertical Structure ◽  
Maximum Error ◽  
Silicate Melt ◽  
System Of Equations ◽  
Wide Range ◽  
Basaltic Melts ◽  
Multidimensional Statistics

A system of equations of thermobarometer for magnetite-silicate melt equilibrium was obtained by method of multidimensional statistics of 93 experimental data of a magnetite solubility in basaltic melts. Equations reproduce experimental data in a wide range of basalt compositions, temperatures and pressures with small errors. Verification of thermobarometers showed the maximum error in liquidus temperature reproducing does not exceed ±7 °C. The level of cumulative magnetite appearance in the vertical structure of Tsypringa, Kivakka, Burakovsky intrusions predicted with errors from ±10 to ±50 m.

Magnetoacoustic surface waves in magnetic crystals near spin-reorientation phase transitions

1997 ◽  
Vol 167 (7) ◽  
pp. 735-750 ◽  
Author(s):  
Yurii V. Gulyaev ◽  
Igor E. Dikshtein ◽  
Vladimir G. Shavrov
Keyword(s):  
Phase Transitions ◽  
Surface Waves ◽  
Spin Reorientation
Sign in / Sign up

Export Citation Format

Share Document