Energy Dissipation Via Coupling With a Finite Chaotic Environment

We study the flow of energy between a harmonic oscillator (HO) and an external environment consisting of N two-degrees of freedom non-linear oscillators, ranging from integrable to chaotic according to a control parameter. The coupling between the HO and the environment is bilinear in the coordinates and scales with system size with the inverse square root of N. We study the conditions for energy dissipation and thermalization as a function of N and of the dynamical regime of the non-linear oscillators. The study is classical and based on single realization of the dynamics, as opposed to ensemble averages over many realizations. We find that dissipation occurs in the chaotic regime for a fairly small N, leading to the thermalization of the HO and environment a Boltzmann distribution of energies for a well defined temperature. We develop a simple analytical treatment, based on the linear response theory, that justifies the coupling scaling and reproduces the numerical simulations when the environment is in the chaotic regime.Comment: 7 pages, 10 figure

Left atrial volume quantification using cardiac MRI in atrial fibrillation: comparison of the Simpson’s method with biplane area-length, ellipse, and three-dimensional methods

PURPOSELeft atrial volume is an important predictor of future arrhythmias, and it can be assessed by several different methods. Simpson’s method is well accepted as a reference standard, although no standardization exists for cardiac magnetic resonance (CMR). We aimed to compare the estimations of left atrial volumes obtained by the Simpson’s method with three other methods. MATERIALS AND METHODSEighty-one consecutive patients referred for CMR imaging between February 2007 and May 2010 were included in the study (47 males; mean age, 59.4±11.5 years; body mass index, 26.3±3.7 kg/m2). Left atrial volume measurements were performed using the Simpson’s, biplane area-length, ellipse, and three-dimensional methods. Results were correlated using a Bland-Altman plot and linear regression models and compared by two-tailed paired-sample t tests. Reader variability was also calculated. RESULTSLeft atrial volume measurements using the biplane area-length technique showed the best correlation with Simpson’s method (r=0.92; P 0.99). CONCLUSIONThe biplane area-length method can be used for left atrial volume measurement when the Simpson’s method cannot be performed. If these two methods are not feasible, then all methods are highly reproducible and can be used, but should not be used interchangeably for follow-up studies