Hamiltonian formulation of SL(3) Ur-KdV equation

We give a unified view of the relation between the $SL(2)$ KdV, the mKdV, and the Ur-KdV equations through the Fr\'{e}chet derivatives and their inverses. For this we introduce a new procedure of obtaining the Ur-KdV equation, where we require that it has no non-local operators. We extend this method to the $SL(3)$ KdV equation, i.e., Boussinesq(Bsq) equation and obtain the hamiltonian structure of Ur-Bsq equationin a simple form. In particular, we explicitly construct the hamiltonian operator of the Ur-Bsq system which defines the poisson structure of the system, through the Fr\'{e}chet derivative and its inverse.Comment: 12 pages, KHTP-93-03 SNUTP-93-2

A pairwise maximum entropy model describes energy landscape for spiral wave dynamics of cardiac fibrillation

Heart is an electrically-connected network. Spiral wave dynamics of cardiac fibrillation shows chaotic and disintegrated patterns while sinus rhythm shows synchronized excitation patterns. To determine functional interactions between cardiomyocytes during complex fibrillation states, we applied a pairwise maximum entropy model (MEM) to the sequential electrical activity maps acquired from the 2D computational simulation of human atrial fibrillation. Then, we constructed energy landscape and estimated hierarchical structure among the different local minima (attractors) to explain the dynamic properties of cardiac fibrillation. Four types of the wave dynamics were considered: sinus rhythm; single stable rotor; single rotor with wavebreak; and multiple wavelet. The MEM could describe all types of wave dynamics (both accuracy and reliability>0.9) except the multiple random wavelet. Both of the sinus rhythm and the single stable rotor showed relatively high pairwise interaction coefficients among the cardiomyocytes. Also, the local energy minima had relatively large basins and high energy barrier, showing stable attractor properties. However, in the single rotor with wavebreak, there were relatively low pairwise interaction coefficients and a similar number of the local minima separated by a relatively low energy barrier compared with the single stable rotor case. The energy landscape of the multiple wavelet consisted of a large number of the local minima separated by a relatively low energy barrier, showing unstable dynamics. These results indicate that the MEM provides information about local and global coherence among the cardiomyocytes beyond the simple structural connectivity. Energy landscape analysis can explain stability and transitional properties of complex dynamics of cardiac fibrillation, which might be determined by the presence of 'driver' such as sinus node or rotor.Comment: Presented at the 62nd Biophysical Society Annual Meeting, San Francisco, California, 201

Extended nonlocal chiral-quark model for the heavy-light quark systems

In this talk, we report the recent progress on constructing a phenomenological effective model for the heavy-light quark systems, which consist of (u,d,s,c,b) quarks, i.e. extended nonlocal chiral-quark model (ExNLChQM). We compute the heavy-meson weak-decay constants to verify the validity of the model. From the numerical results, it turns out that (f_D, f_B, f_{D_s}, f_{B_s})=(207.54,208.13,262.56,262.39) MeV. These values are in relatively good agreement with experimental data and various theoretical estimations.Comment: 3 pages, 4 figures, Talk given at the 20th International IUPAP Conference on Few-Body Problems in Physics (FB20), 20~25 August 2012, Fukuoka, Japa