1,460 research outputs found
Control of scroll wave turbulence using resonant perturbations
Turbulence of scroll waves is a sort of spatio-temporal chaos that exists in
three-dimensional excitable media. Cardiac tissue and the Belousov-Zhabotinsky
reaction are examples of such media. In cardiac tissue, chaotic behaviour is
believed to underlie fibrillation which, without intervention, precedes cardiac
death. In this study we investigate suppression of the turbulence using
stimulation of two different types, "modulation of excitability" and "extra
transmembrane current". With cardiac defibrillation in mind, we used a single
pulse as well as repetitive extra current with both constant and feedback
controlled frequency. We show that turbulence can be terminated using either a
resonant modulation of excitability or a resonant extra current. The turbulence
is terminated with much higher probability using a resonant frequency
perturbation than a non-resonant one. Suppression of the turbulence using a
resonant frequency is up to fifty times faster than using a non-resonant
frequency, in both the modulation of excitability and the extra current modes.
We also demonstrate that resonant perturbation requires strength one order of
magnitude lower than that of a single pulse, which is currently used in
clinical practice to terminate cardiac fibrillation. Our results provide a
robust method of controlling complex chaotic spatio-temporal processes.
Resonant drift of spiral waves has been studied extensively in two dimensions,
however, these results show for the first time that it also works in three
dimensions, despite the complex nature of the scroll wave turbulence.Comment: 13 pages, 12 figures, submitted to Phys Rev E 2008/06/13. Last
version: 2008/09/18, after revie
Semi-analytical Solution of Dirac equation in Schwarzschild Geometry
Separation of the Dirac equation in the spacetime around a Kerr black hole
into radial and angular coordinates was done by Chandrasekhar in 1976. In the
present paper, we solve the radial equations in a Schwarzschild geometry
semi-analytically using Wentzel-Kramers-Brillouin approximation (in short WKB)
method. Among other things, we present analytical expression of the
instantaneous reflection and transmission coefficients and the radial wave
functions of the Dirac particles. Complete physical parameter space was divided
into two parts depending on the height of the potential well and energy of the
incoming waves. We show the general solution for these two regions. We also
solve the equations by a Quantum Mechanical approach, in which the potential is
approximated by a series of steps and found that these two solutions agree. We
compare solutions of different initial parameters and show how the properties
of the scattered wave depend on these parameters.Comment: RevTex, 11 Latex pages and 12 Figures ; Classical and Quantum Gravity
(in Press) (1999
Phosphorylase kinase: Mathematical model
A mathematical model of the dynamic behavior of phosphorylase kinase was devised. Based on the results obtained, the function of this protein is discussed. It is suggested that phosphorylase kinase doses in a cAMP-dependent manner additional portions of glucoso-1-phosphate, which the muscle cell receives in response to contraction
Extension of Frohlich's method to 4-fermion interactions
Higher order terms of the transformed electron-phonon Hamiltonian, obtained
by performing the Frohlich's transformation, are investigated. The influence of
terms discarded by Frohlich (in particular those proportional to the third
power of electron-phonon coupling) on the effective Hamiltonian is examined. To
this end a second Frohlich-type transformation is performed, which yields,
among others, an effective 4-electron interaction. This interaction is reduced
to a form admitting solution of thermodynamics. The form of the coupling of the
4-electron interaction is found. By applying standard approximations, it is
shown that this interaction is attractive with interaction coupling given by -
D_{k_F}^6 / \omega_{k_F}^5, where D_{k} is electron-phonon coupling,
\omega_{k}$ is phonon energy and k_F is Fermi momentum.
The form of higher order terms of the original Frohlich-transformed H_{e-ph}
are also found, up to terms proportional to the 6-th power of the coupling,
that is up to those, which yield the effective 4-electron interactions.Comment: REVTeX4, 25 pages; major changes: added section and appendix about
the form of 4-fermion interaction coupling, typos correcte
Probing the Ternary Complexes of Indoleamine and Tryptophan 2,3-Dioxygenases by Cryoreduction EPR and ENDOR Spectroscopy
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