On the Definition of Temperature in FPU Systems

It is usually assumed, in classical statistical mechanics, that the temperature should coincide, apart from a suitable constant factor, with the mean kinetic energy of the particles. We show that this is not the case for Fermi–Pasta–Ulam systems, in conditions in which energy equipartition between the modes is not attained. We find that the temperature should be rather identified with the mean value of the energy of the low frequency modes.     

On the Landau-Teller approximation for energy exchanges with fast degrees of freedom

We revisit the Landau-Teller heuristic approach to adiabatic invariants and, following Rapp, use it to investigate the energy exchanges between the different degrees of freedom, in simple Hamiltonian systems describing the collision of fast rotating or vibrating molecules with a fixed wall. We critically compare the theoretical results with particularly accurate numerical computations (quite small energy exchanges, namely of one part over 10³⁰, are measured).     

Influence and role of metal ions in enzymatic catalysis with e.c. 1.2.3.2. xanthine oxidase Application to trace analysis

The effect of metal ions on the reductive half-reaction of xanthine oxidase (XOD) in the catalytic conversion of xanthine into uric acid has been studied spectrophotometrically in Tris-HCl buffer at pH 7.4, 37 +/- 0.1 degrees and ionic strength 0.04M. Some metal ions display inhibitor properties, the sequence of inhibiting efficiency being Ag(I) > Hg(II) > Cu(II) > Cr(VI) > V(V) > Au(III) > Tl(I) and for these the I(50) values were determined. Only Tl(I), V(V) and Cu(II) showed reversible inhibition and therefore for these the mechanisms were assessed [competitive for V(V) and Tl(I); uncompetitive for Cu(II)]. The conditional inhibition constants (K(i)) were also determined. The effect of EDTA for protection of the enzyme against metal inhibition, and for its reactivation after inhibition, was also investigated. Utilization of the linear relationship between relative enzyme activity and inhibitor concentration allowed sensitive and selective (though not specific) determination of Ag(I) and Hg(II) (10(-9)-10(-8)M), and of Cu(II) and Cr(VI) (10(-7)-10(-6)M), the maximum relative error being +/- 4%. For a few metal ions, e.g., Ag(I) and Cr(VI), in the presence of EDTA, a certain specificity is observed.     

Towards a rigorous treatment of the Jeans-Landau-Teller method for the energy exchanges of harmonic oscillators

For classical Hamiltonian systems containing an harmonic oscillator of high frequency, one has the problem of controlling the energy exchange between the oscillator and the remaining slow degrees of freedom; under very general conditions, such an exchange turns out to be exponentially small with the frequency of the oscillator. In the Jeans-Landau-Teller method, one aims to prove the exponential dependence, and to estimate the coefficient of the exponential, by exploiting the analyticity properties of the solution of the differential equations describing the motion of the system. However, in practice, since the exact solution is not known, such properties are inferred from those of an approximate solution, with no control of the difference; this fact might a priori even invalidate the exponential dependence itself. In the present paper a rigorous treatment is given, for a particular model of interest in the domain of atomic collisions, by keeping control of the difference between the exact and the approximate solution.     

On the Specific Heat of Fermi–Pasta–Ulam Systems and Their Glassy Behavior

The specific heat of Fermi–Pasta–Ulam systems has until now been estimated through the energy fluctuations of a suitable subsystem, and opposite answers were apparently provided concerning its possible vanishing for vanishing temperatures. In the present paper a more realistic numerical implementation of the specific heat measurement is discussed, which mimics the interaction of the FPU system with a calorimeter. It is found that there exists a freezing critical temperature below which the relaxation times to equilibrium between FPU system and calorimeter become relevant, so that the system presents aging and hysteresis features very similar to those familiar in glasses and spin glasses. In particular, in the framework of such a point of view involving finite long times, the specific heat appears to vanish for vanishing temperatures.     

The Fermi-Pasta-Ulam problem as a challenge for the foundations of physics

The Fermi-Pasta-Ulam (FPU) problem is discussed in connection with its physical relevance, and it is shown how apparently there exist only two possibilities: either the FPU problem is just a curiosity, or it has a fundamental role for the foundations of physics, casting a new light on the relations between classical and quantum mechanics. To this end, a short review is given of the main conceptual proposals that have been advanced. Particular emphasis is given to the perspective of a metaequilibrium scenario, which appears to be the only possible one for the FPU paradox to survive in the physically relevant case of infinitely many particles.     

Chopping Time of the FPU $${\alpha }$$-Model

We study, both numerically and analytically, the time needed to observe the breaking of an FPU \(\alpha \)-chain in two or more pieces, starting from an unbroken configuration at a given temperature. It is found that such a “chopping” time is given by a formula that, at low temperatures, is of the Arrhenius–Kramers form, so that the chain does not break up on an observable time-scale. The result explains why the study of the FPU problem is meaningful also in the ill-posed case of the \(\alpha \)-model.     

A highly crystalline microporous hybrid organic-inorganic aluminosilicate resembling the AFI-type zeolite

ECS-14, a crystalline microporous hybrid organic-inorganic aluminosilicate, has been synthesized by using 1,4-bis-(triethoxysilyl)-benzene (BTEB) as a source of silica. Its structure contains a system of linear channels with 12-membered ring openings, running along the [001] direction, resembling the pore architecture of the AFI framework type.     

An Averaging Theorem for Hamiltonian Dynamical Systems in the Thermodynamic Limit

It is shown how to perform some steps of perturbation theory if one assumes a measure-theoretic point of view, i.e. if one renounces to control the evolution of the single trajectories, and the attention is restricted to controlling the evolution of the measure of some meaningful subsets of phase–space. For a system of coupled rotators, estimates uniform in N for finite specific energy can be obtained in quite a direct way. This is achieved by making reference not to the sup norm, but rather, following Koopman and von Neumann, to the much weaker L ² norm.