We study the dynamics of a system of coupled oscillators of distributed natural frequencies, by including the features of both thermal noise, parametrized by a temperature, and inertial terms, parametrized by a moment of inertia. For a general unimodal frequency distribution, we report here the complete phase diagram of the model in the space of dimensionless moment of inertia, temperature, and width of the frequency distribution. We demonstrate that the system undergoes a nonequilibrium first-order phase transition from a synchronized phase at low parameter values to an incoherent phase at high values. We provide strong numerical evidence for the existence of both the synchronized and the incoherent phase, treating the latter analytically to obtain the corresponding linear stability threshold that bounds the first-order transition point from below. In the limit of zero noise and inertia, when the dynamics reduces to the one of the Kuramoto model, we recover the associated known continuous transition. At finite noise and inertia but in the absence of natural frequencies, the dynamics becomes that of a well-studied model of long-range interactions, the Hamiltonian mean-field model. Close to the first-order phase transition, we show that the escape time out of metastable states scales exponentially with the number of oscillators, which we explain to be stemming from the long-range nature of the interaction between the oscillators.

DNA fragmentation was studied in the fragment size range 0.023-5.7 Mbp after irradiation of human fibroblasts with iron-ion beams of four different energies, i.e., 200 MeV/nucleon, 500 MeV/nucleon, 1 GeV/nucleon and 5 GeV/nucleon, with gamma rays used as the reference radiation. The double-strand break (DSB) yield (and thus the RBE for DNA DSB induction) of the four iron-ion beams, which have LETs ranging from 135 to 442 keV/mum, does not vary greatly as a function of LET. As a consequence, the variation of the cross section for DSB induction mainly reflects the variation in LET. However, when the fragmentation spectra were analyzed with a simple theoretical tool that we recently introduced, the results showed that spatially correlated DSBs, which are absent after gamma irradiation, increased markedly with LET for the iron-ion beams. This occurred because iron ions produce DNA fragments smaller than 0.75 Mbp with a higher probability than gamma rays (a probability that increases with LET). These sizes include those expected from fragmentation of the chromatin loops with Mbp dimensions. This result does not exclude a correlation at distances smaller than the lower size analyzed here, i.e. 23 kbp. Moreover, the DSB correlation is dependent on dose, decreasing when dose increases; this can be explained with the argument that at increasing dose there is an increasing fraction of fragments produced by DSBs caused by separate, uncorrelated tracks.

The canonical phase diagram of the Blume-Emery-Griffiths model with infinite-range interactions is known to exhibit a fourth-order critical point at some negative value of the biquadratic interaction $K<0$. Here we study the microcanonical phase diagram of this model for $K<0$, extending previous studies which were restricted to positive $K$. A fourth-order critical point is found to exist at coupling parameters which are different from those of the canonical ensemble. The microcanonical phase diagram of the model close to the fourth-order critical point is studied in detail revealing some distinct features from the canonical counterpart.

In this paper we study an Ising spin chain with short-range competing interactions in the presence of long-range ferromagnetic interactions in the canonical ensemble. The simultaneous presence of the frustration induced by the short-range couplings together with their competition with the long-range term gives rise to a rich thermodynamic-phase diagram. We compare our results with the limit in which one of two local interactions is turned off, which was previously studied in the literature. Eight regions of parameters with qualitatively distinct properties are featured, with different first- and second-order phase transition lines and critical points.

In nonadditive systems, like small systems or like long-range interacting systems even in the thermodynamic limit, ensemble inequivalence can be related to the occurrence of negative response functions, this in turn being connected with anomalous concavity properties of the thermodynamic potentials associated with the various ensembles. We show how the type and number of negative response functions depend on which of the quantities E, V and N (energy, volume and number of particles) are constrained in the ensemble. In particular, we consider the unconstrained ensemble in which E, V and N fluctuate, which is physically meaningful only for nonadditive systems. In fact, its partition function is associated with the replica energy, a thermodynamic function that identically vanishes when additivity holds, but that contains relevant information in nonadditive systems.

We study the properties of large systems of globally coupled oscillators in the presence of noise. When the distribution of the natural frequencies of the oscillators is bimodal and its analytical continuation in the complex plane has only a few poles in the lower half plane, the dynamics of the system, governed by a Fokker–Planck equation for the single particle distribution function, can be reduced to a system of ordinary differential equations describing the dynamics of suitably defined order parameters, the first ones of which are related to the usual synchronization order parameter. We obtain the full phase diagram of the oscillator system, that shows a very rich behaviour, with regions characterized by synchronized states, regions with periodic states, and others with bi-stability, associated to the presence of hysteresis. The latter phenomenon is confirmed by numerical simulations ot the full system of coupled oscillators. We compare our results with those previously obtained for noiseless systems, and we show that for increasing noise the phase diagram changes qualitatively, tending to the simple diagram that is found for systems with unimodal frequency distributions.