Kinetics of first-order phase transitions from microcanonical thermostatistics

More than a century has passed since van't Hoff and Arrhenius formulated their celebrated rate theories, but there are still elusive aspects in the temperature-dependent phase transition kinetics of molecular systems. Here I present a theory based on microcanonical thermostatistics that establishes a simple and direct temperature dependence for all rate constants, including the forward and the reverse rate constants, the equilibrium constant, and the nucleation rate. By considering a generic model that mimic the microcanonical temperature of molecular systems in a region close to a first-order phase transition, I obtain shape-free relations between kinetics and thermodynamics physical quantities which are validated through stochastic simulations. Additionally, the rate theory is applied to results obtained from protein folding and ice nucleation experiments, demonstrating that the expressions derived here can be used to describe the experimental data of a wide range of molecular systems.Comment: 22 pages, 5 figure

Spacetime geometries and light trapping in travelling refractive index perturbations

In the framework of transformation optics, we show that the propagation of a locally superluminal refractive index perturbation (RIP) in a Kerr medium can be described, in the eikonal approximation, by means of a stationary metric, which we prove to be of Gordon type. Under suitable hypotheses on the RIP, we obtain a stationary but not static metric, which is characterized by an ergosphere and by a peculiar behaviour of the geodesics, which are studied numerically, also accounting for material dispersion. Finally, the equation to be satisfied by an event horizon is also displayed and briefly discussed.Comment: 14 pages, 7 figure

Space geometry of rotating platforms: an operational approach

We study the space geometry of a rotating disk both from a theoretical and operational approach, in particular we give a precise definition of the space of the disk, which is not clearly defined in the literature. To this end we define an extended 3-space, which we call relative space: it is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the 'physical space of the rotating platform'. Then, the geometry of the space of the disk turns out to be non Euclidean, according to the early Einstein's intuition; in particular the Born metric is recovered, in a clear and self consistent context. Furthermore, the relativistic kinematics reveals to be self consistent, and able to solve the Ehrenfest's paradox without any need of dynamical considerations or ad hoc assumptions

Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames of Minkowski Spacetime: I. Admissible 3+1 Splittings of Minkowski Spacetime and the Non-Inertial Rest Frames

By using the 3+1 point of view and parametrized Minkowski theories we develop the theory of {\it non-inertial} frames in Minkowski space-time. The transition from a non-inertial frame to another one is a gauge transformation connecting the respective notions of instantaneous 3-space (clock synchronization convention) and of the 3-coordinates inside them. As a particular case we get the extension of the inertial rest-frame instant form of dynamics to the non-inertial rest-frame one. We show that every isolated system can be described as an external decoupled non-covariant canonical center of mass (described by frozen Jacobi data) carrying a pole-dipole structure: the invariant mass and an effective spin. Moreover we identify the constraints eliminating the internal 3-center of mass inside the instantaneous 3-spaces. In the case of the isolated system of positive-energy scalar particles with Grassmann-valued electric charges plus the electro-magnetic field we obtain both Maxwell equations and their Hamiltonian description in non-inertial frames. Then by means of a non-covariant decomposition we define the non-inertial radiation gauge and we find the form of the non-covariant Coulomb potential. We identify the coordinate-dependent relativistic inertial potentials and we show that they have the correct Newtonian limit. In the second paper we will study properties of Maxwell equations in non-inertial frames like the wrap-up effect and the Faraday rotation in astrophysics. Also the 3+1 description without coordinate-singularities of the rotating disk and the Sagnac effect will be given, with added comments on pulsar magnetosphere and on a relativistic extension of the Earth-fixed coordinate system.Comment: This paper and the second one are an adaptation of arXiv 0812.3057 for publication on Int.J.Geom. Methods in Modern Phys. 77

On the origin of the negative energy-related contribution to the elastic modulus of rubber-like gels

We consider a coarse-grained polymer model in order to investigate the origin of a recently discovered negative energy-related contribution to the elastic modulus $G(T)$ of rubber-like gels. From this model, we are able to compute an exact expression for the free energy of the system, which allows us to evaluate a stress-strain relationship that displays a non-trivial dependence on the temperature $T$. We validate our approach through comparisons between the theoretical results and the experimental data obtained for tetra-PEG hydrogels, which indicate that, although simple, the present model works well to describe the experiments. Importantly, our approach unveiled aspects of the experimental analysis which turned out to be different from the conventional entropic and energetic analysis broadly used in the literature. Also, in contrast to the linear dependence predicted by the traditional, {\it i.e.}, purely entropic, models, our results suggest that the general expression of the elastic modulus should be of the form $G(T) \propto k_BT w(T)$, with $w(T)$ being a temperature-dependent correction factor that could be related to the interaction between the chains in the network and the solvent. Accordingly, the correction factor allows the expression found for the elastic modulus to describe both rubber and rubber-like gels.Comment: 14 pages, 5 figure