Hamiltonian structure for dispersive and dissipative dynamical systems

We develop a Hamiltonian theory of a time dispersive and dissipative inhomogeneous medium, as described by a linear response equation respecting causality and power dissipation. The proposed Hamiltonian couples the given system to auxiliary fields, in the universal form of a so-called canonical heat bath. After integrating out the heat bath the original dissipative evolution is exactly reproduced. Furthermore, we show that the dynamics associated to a minimal Hamiltonian are essentially unique, up to a natural class of isomorphisms. Using this formalism, we obtain closed form expressions for the energy density, energy flux, momentum density, and stress tensor involving the auxiliary fields, from which we derive an approximate, ``Brillouin-type,'' formula for the time averaged energy density and stress tensor associated to an almost mono-chromatic wave.Comment: 68 pages, 1 figure; introduction revised, typos correcte

Effects of a nine-month physical activity intervention on morphological characteristics and motor and cognitive skills of preschool children

(1) Background: Regular physical activity (PA) plays an important role during early childhood physical and psychological development. This study investigates the effects of a 9-month PA intervention on physiological characteristics and motor and cognitive skills in preschool children. (2) Methods: Preschool children (n = 132; age 4 to 7 years) attending regular preschool programs were nonrandomly assigned to PA intervention (n = 66; 60 min sessions twice per week) or a control group (n = 66; no additional organized PA program) for 9 months. Exercise training for the intervention group included various sports games, outdoor activities, martial arts, yoga, and dance. Anthropometry, motor skills (7 tests), and cognitive skills (Raven’s Colored Progressive Matrices and Cognitive Assessment System) were assessed before and after an intervention period in both groups. Data were analyzed using repeated-measures ANOVA. (3) Results: Body weight significantly increased in both groups over time. Compared to the changes observed in the control group, the intervention group significantly increased in chest circumference (p = 0.022). In contrast, the control group demonstrated an increase in waist circumference (p = 0.001), while these measures in the intervention group remained stable. Participants in the intervention group improved running speed (p = 0.016) and standing broad jump (p = 0.000). The flexibility level was maintained in the intervention group, while a significant decrease was observed in the control group (p = 0.010). Children from the intervention group demonstrated progress in the bent-arm hang test (p = 0.001), unlike the control group subjects. Varied improvements in cognitive skills were observed for different variables in both intervention and control groups, with no robust evidence for PA-intervention-related improvements. (4) Conclusions: Preschool children’s participation in a preschool PA intervention improves their motor skills

A meaningful expansion around detailed balance

We consider Markovian dynamics modeling open mesoscopic systems which are driven away from detailed balance by a nonconservative force. A systematic expansion is obtained of the stationary distribution around an equilibrium reference, in orders of the nonequilibrium forcing. The first order around equilibrium has been known since the work of McLennan (1959), and involves the transient irreversible entropy flux. The expansion generalizes the McLennan formula to higher orders, complementing the entropy flux with the dynamical activity. The latter is more kinetic than thermodynamic and is a possible realization of Landauer's insight (1975) that, for nonequilibrium, the relative occupation of states also depends on the noise along possible escape routes. In that way nonlinear response around equilibrium can be meaningfully discussed in terms of two main quantities only, the entropy flux and the dynamical activity. The expansion makes mathematical sense as shown in the simplest cases from exponential ergodicity.Comment: 19 page

Unique Aggregation of Sterigmatocystin in Water Yields Strong and Specific Circular Dichroism Response Allowing Highly Sensitive and Selective Monitoring of Bio-Relevant Interactions

We demonstrated the hitherto unknown property of the mycotoxin sterigmatocystin (STC) to provide homogeneous solutions in aqueous medium by forming a unique aggregate type (not formed by analogous aflatoxins), characterized by exceptionally strong circular dichroism (CD) bands in the 300-400 nm range. Results showed that these CD bands do not originate from intrinsic STC chirality but are a specific property of a peculiar aggregation process similar to psi-DNA CD response. Transmission electron microscopy (TEM) experiments revealed a fine fiber network resembling a supramolecular gel structure with helical fibers. Thermodynamic studies of aggregates by differential scanning calorimetry (DSC) revealed high reversibility of the dominant aggregation process. We demonstrated that the novel STC psi-CD band at 345 nm could be applied at biorelevant conditions (100 nanomolar concentration) and even in marine-salt content conditions for specific and quantitative monitoring of STC. Also, we showed that STC strongly non-covalently interacts with ds-DNA with likely toxic effects, thus contrary to the previous belief requiring prior enzyme epoxidation

Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems

We study the spectrum of a random Schroedinger operator for an electron submitted to a magnetic field in a finite but macroscopic two dimensional system of linear dimensions equal to L. The y direction is periodic and in the x direction the electron is confined by two smooth increasing boundary potentials. The eigenvalues of the Hamiltonian are classified according to their associated quantum mechanical current in the y direction. Here we look at an interval of energies inside the first Landau band of the random operator for the infinite plane. In this energy interval, with large probability, there exist O(L) eigenvalues with positive or negative currents of O(1). Between each of these there exist O(L^2) eigenvalues with infinitesimal current O(exp(-cB(log L)^2)). We explain what is the relevance of this analysis to the integer quantum Hall effect.Comment: 29 pages, no figure