Canonical solution of a system of long-range interacting rotators on a lattice

The canonical partition function of a system of rotators (classical X-Y spins) on a lattice, coupled by terms decaying as the inverse of their distance to the power alpha, is analytically computed. It is also shown how to compute a rescaling function that allows to reduce the model, for any d-dimensional lattice and for any alpha<d, to the mean field (alpha=0) model.Comment: Initially submitted to Physical Review Letters: following referees' Comments it has been transferred to Phys. Rev. E, because of supposed no general interest. Divided into sections, corrections in (5) and (20), reference 5 updated. 8 pages 1 figur

On "Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions" by Figueiredo et al

In the present paper we refute the criticism advanced in a recent preprint by Figueiredo et al [1] about the possible application of the $q$-generalized Central Limit Theorem (CLT) to a paradigmatic long-range-interacting many-body classical Hamiltonian system, the so-called Hamiltonian Mean Field (HMF) model. We exhibit that, contrary to what is claimed by these authors and in accordance with our previous results, $q$-Gaussian-like curves are possible and real attractors for a certain class of initial conditions, namely the one which produces nontrivial longstanding quasi-stationary states before the arrival, only for finite size, to the thermal equilibrium.Comment: 2 pages, 2 figures. Short version of the paper, accepted for publication in Europhysics Letters, (2009) in pres

Invariant measures of the 2D Euler and Vlasov equations

We discuss invariant measures of partial differential equations such as the 2D Euler or Vlasov equations. For the 2D Euler equations, starting from the Liouville theorem, valid for N-dimensional approximations of the dynamics, we define the microcanonical measure as a limit measure where N goes to infinity. When only the energy and enstrophy invariants are taken into account, we give an explicit computation to prove the following result: the microcanonical measure is actually a Young measure corresponding to the maximization of a mean-field entropy. We explain why this result remains true for more general microcanonical measures, when all the dynamical invariants are taken into account. We give an explicit proof that these microcanonical measures are invariant measures for the dynamics of the 2D Euler equations. We describe a more general set of invariant measures, and discuss briefly their stability and their consequence for the ergodicity of the 2D Euler equations. The extension of these results to the Vlasov equations is also discussed, together with a proof of the uniqueness of statistical equilibria, for Vlasov equations with repulsive convex potentials. Even if we consider, in this paper, invariant measures only for Hamiltonian equations, with no fluxes of conserved quantities, we think this work is an important step towards the description of non-equilibrium invariant measures with fluxes.Comment: 40 page

Fluorescence properties of the Na+/H+ exchanger inhibitor HMA (5-(N,N-hexamethylene) amiloride) are modulated by intracellular Ph

HMA (5-(N,N-hexamethylene)amiloride), which belongs to a family of novel amiloride derivatives, is one of the most effective inhibitors of Na+/H+ exchangers, while uneffective against Na+ channels and Na+/Ca2+ exchangers. In this study, we provided evidence that HMA can act as a fluorescent probe. In fact, human retinal ARPE19 cells incubated with HMA show an intense bluish fluorescence in the cytoplasm when observed at microscope under conventional UV-excitation conditions. Interestingly, a prolonged observation under continuous exposure to excitation lightdoes not induce great changes in cells incubated with HMA for times up to about 5 min, while an unexpected rapid increase in fluorescence signal is observed in cells incubated for longer times. The latter phenomenon is particularly evident in the perinuclear region and in discrete spots in the cytoplasm. Since HMA modulates intracellular acidity, the dependence of its fluorescence properties on medium pH and response upon irradiation have been investigated in solution, at pH 5.0 and pH 7.2. The changes in both spectral shape and amplitude emission indicate a marked pH influence on HMA fluorescence properties, making HMA exploitable as a self biomarker of pH alterations in cell studies, in the absence of perturbations induced by the administration of other exogenous dyes

Inclusion of new 5-fluorouracil amphiphilic derivatives in liposome formulation for cancer treatment

Correction for 'Inclusion of new 5-fluorouracil amphiphilic derivatives in liposome formulation for cancer treatment' by M. Petaccia et al., Med. Chem. Commun., 2015, 6, 1639–1642

Canonical Solution of Classical Magnetic Models with Long-Range Couplings

We study the canonical solution of a family of classical $n-vector$ spin models on a generic $d$-dimensional lattice; the couplings between two spins decay as the inverse of their distance raised to the power $\alpha$, with $\alpha<d$. The control of the thermodynamic limit requires the introduction of a rescaling factor in the potential energy, which makes the model extensive but not additive. A detailed analysis of the asymptotic spectral properties of the matrix of couplings was necessary to justify the saddle point method applied to the integration of functions depending on a diverging number of variables. The properties of a class of functions related to the modified Bessel functions had to be investigated. For given $n$, and for any $\alpha$, $d$ and lattice geometry, the solution is equivalent to that of the $\alpha=0$ model, where the dimensionality $d$ and the geometry of the lattice are irrelevant.Comment: Submitted for publication in Journal of Statistical Physic