Modeling the transport of interacting matter waves in a disordered system by a nonlinear diffusion equation.

We model the expansion of an interacting atomic Bose-Einstein condensate in a disordered lattice with a nonlinear diffusion equation normally used for a variety of classical systems. We find approximate solutions of the diffusion equation that well reproduce the experimental observations for both short and asymptotic expansion times. Our study establishes a connection between the peculiar shape of the expanding density profiles and the microscopic nonlinear diffusion coefficients.

[Preclinical left ventricular diastolic dysfunction in insulin-dependent diabetes]. / Disfunzione diastolica ventricolare sinistra preclinica nel diabete insulino-dipendente.

BACKGROUND: Isolated alterations of the left ventricular diastolic function have been described in diabetic insulin-dependent patients (IDDM), even in the absence of old age, hypertension, ischemic heart disease, left ventricular hypertrophy. Such alterations have been associated with microangiopathy but it is not known whether it is reversible or if there is a relation with the way the therapy is given. METHODS: Fifty-five subjects have been studied, of which 15 were healthy, 30 recently diagnosed IDDM without microangiopathy and 10 IDDM with microangiopathy. All the patients were under 35 years old and did not present risk factors for coronary artery disease, hypertension or autonomic neuropathy. The maximal exercise stress test proved negative. The diastolic function was studied using the results of Doppler echocardiography of the mitral flow and of isovolumetric relaxation time, with continuous and discrete parameters. RESULTS: The velocity of wave A and E, the relationship between them and their integrals are significantly greater in diabetics with microangiopathy than in those without it and in healthy subjects. There are no significant differences between healthy and diabetic subjects without microangiopathy using continuous parameters. Using discrete parameters diastolic damage is absent in the healthy subjects and is present in 48% of diabetics without microangiopathy and in 90% of those with it. CONCLUSIONS: Slight preclinical diastolic dysfunction is present in young recently diagnosed IDDM without microangiopathy. More severe dysfunction is present when there is also microangiopathy.