A Variational Method in Out of Equilibrium Physical Systems

A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same formal symplectic structure shared by classical mechanics, fluid mechanics and thermodynamics. In particular, it is obtained an extended equation of motion for a rotating dynamical system, from where it emerges a kind of topological torsion current of the form $\epsilon_{ijk} A_j \omega_k$, with $A_j$ and $\omega_k$ denoting components of the vector potential (gravitational or/and electromagnetic) and $\omega$ is the angular velocity of the accelerated frame. In addition, it is derived a special form of Umov-Poynting's theorem for rotating gravito-electromagnetic systems, and obtained a general condition of equilibrium for a rotating plasma. The variational method is then applied to clarify the working mechanism of some particular devices, such as the Bennett pinch and vacuum arcs, to calculate the power extraction from an hurricane, and to discuss the effect of transport angular momentum on the radiactive heating of planetary atmospheres. This development is seen to be advantageous and opens options for systematic improvements.Comment: 22 pages, 1 figure, submitted to review, added one referenc

Reversals in nature and the nature of reversals

The asymmetric shape of reversals of the Earth's magnetic field indicates a possible connection with relaxation oscillations as they were early discussed by van der Pol. A simple mean-field dynamo model with a spherically symmetric $\alpha$ coefficient is analysed with view on this similarity, and a comparison of the time series and the phase space trajectories with those of paleomagnetic measurements is carried out. For highly supercritical dynamos a very good agreement with the data is achieved. Deviations of numerical reversal sequences from Poisson statistics are analysed and compared with paleomagnetic data. The role of the inner core is discussed in a spectral theoretical context and arguments and numerical evidence is compiled that the growth of the inner core might be important for the long term changes of the reversal rate and the occurrence of superchrons.Comment: 24 pages, 12 figure

Abnormal Distracter Processing in Adults with Attention-Deficit-Hyperactivity Disorder

Background: Subjects with Attention-Deficit Hyperactivity Disorder (ADHD) are overdistractible by stimuli out of the intended focus of attention. This control deficit could be due to primarily reduced attentional capacities or, e. g., to overshooting orienting to unexpected events. Here, we aimed at identifying disease-related abnormalities of novelty processing and, therefore, studied event-related potentials (ERP) to respective stimuli in adult ADHD patients compared to healthy subjects. Methods: Fifteen unmedicated subjects with ADHD and fifteen matched controls engaged in a visual oddball task (OT) under simultaneous EEG recordings. A target stimulus, upon which a motor response was required, and non-target stimuli, which did not demand a specific reaction, were presented in random order. Target and most non-target stimuli were presented repeatedly, but some non-target stimuli occurred only once (‘novels’). These unique stimuli were either ‘relative novels ’ with which a meaning could be associated, or ‘complete novels’, if no association was available. Results: In frontal recordings, a positive component with a peak latency of some 400 ms became maximal after novels. In healthy subjects, this novelty-P3 (or ‘orienting response’) was of higher magnitude after complete than after relative novels, in contrast to the patients with an undifferentially high frontal responsivity. Instead, ADHD patients tended to smaller centro-parietal P3 responses after target signals and, on a behavioural level, responded slower than controls

Altered mRNA expression of genes related to nerve cell activity in the fracture callus of older rats: A randomized, controlled, microarray study

BACKGROUND: The time required for radiographic union following femoral fracture increases with age in both humans and rats for unknown reasons. Since abnormalities in fracture innervation will slow skeletal healing, we explored whether abnormal mRNA expression of genes related to nerve cell activity in the older rats was associated with the slowing of skeletal repair. METHODS: Simple, transverse, mid-shaft, femoral fractures with intramedullary rod fixation were induced in anaesthetized female Sprague-Dawley rats at 6, 26, and 52 weeks of age. At 0, 0.4, 1, 2, 4, and 6 weeks after fracture, a bony segment, one-third the length of the femur, centered on the fracture site, including the external callus, cortical bone, and marrow elements, was harvested. cRNA was prepared and hybridized to 54 Affymetrix U34A microarrays (3/age/time point). RESULTS: The mRNA levels of 62 genes related to neural function were affected by fracture. Of the total, 38 genes were altered by fracture to a similar extent at the three ages. In contrast, eight neural genes showed prolonged down-regulation in the older rats compared to the more rapid return to pre-fracture levels in younger rats. Seven genes were up-regulated by fracture more in the younger rats than in the older rats, while nine genes were up-regulated more in the older rats than in the younger. CONCLUSIONS: mRNA of 24 nerve-related genes responded differently to fracture in older rats compared to young rats. This differential expression may reflect altered cell function at the fracture site that may be causally related to the slowing of fracture healing with age or may be an effect of the delayed healing