Thermodynamics of Ising model with infinite-range interactions by generalized canonical ensemble

In this work we present the idea of how generalized ensembles can be used to simplify the operational study of non-additive physical systems. As alternative of the usual methods of direct integration or mean-field theory, we show how the solution of the Ising model with infinite-range interactions is obtained by using a generalized canonical ensemble. We describe how the thermodynamical properties of this model in the presence of an external magnetic field are founded by simple parametric equations. Without impairing the usual interpretation, we obtain an identical critical behaviour as observed in traditional approaches.

Instrumental activities of daily living performance in healthy and cognitively intact seniors from a Brazilian sample and its relation to age and other socio-demographic variables

Background: Studies on functional capacity in community-dwelling older people have shown associations between declines in instrumental activities of daily living (IADL) and several factors. Among these, age has been the most consistently related to functional capacity independent of other variables. We aimed at evaluating the performance of a sample of healthy and cognitively intact Brazilian older people on activities of daily living and to analyze its relation to social-demographic variables. Methods: We conducted a secondary analysis of data collected for previous epidemiological studies with community-dwelling subjects aged 60 years or more. We selected subjects who did not have dementia or depression, and with no history of neurological diseases, heart attack, HIV, hepatitis or arthritis (n = 1,111). Functional capacity was assessed using the Brazilian version of the Older American Resources and Services Questionnaire (BOMFAQ). ADL performance was analyzed according to age, gender, education, and marital status (Pearson's chi(2), logistic regression). Results: IADL difficulties were present in our sample, especially in subjects aged 80 years or more, with lower levels of education, or widowed. The logistic regression analysis results indicated that "higher age" and "lower education" (p <= 0.001) remained significantly associated with IADL difficulty. Conclusions: Functional decline was present in older subjects even in the absence of medical conditions and cognitive impairment. Clinicians and researchers could benefit from knowing what to expect from older people regarding IADL performance in the absence of medical conditions.

Stabilization for an ensemble of half-spin systems

Feedback stabilization of an ensemble of non interacting half spins described by the Bloch equations is considered. This system may be seen as an interesting example for infinite dimensional systems with continuous spectra. We propose an explicit feedback law that stabilizes asymptotically the system around a uniform state of spin +1/2 or -1/2. The proof of the convergence is done locally around the equilibrium in the H-1 topology. This local convergence is shown to be a weak asymptotic convergence for the H-1 topology and thus a strong convergence for the C topology. The proof relies on an adaptation of the LaSalle invariance principle to infinite dimensional systems. Numerical simulations illustrate the efficiency of these feedback laws, even for initial conditions far from the equilibrium. (C) 2011 Elsevier Ltd. All rights reserved.