Non-equilibrium real-space condensation is a phenomenon in which a finite fraction of some conserved quantity (mass, particles, etc.) becomes spatially localised. We review two popular stochastic models of hopping particles that lead to condensation
and whose stationary states assume a factorized form: the zero-range process and the misanthrope process, and their various modifications. We also introduce a new model - a misanthrope process with parallel dynamics - that exhibits condensation and has a pair-factorized stationary state.
The quantity and quality of satellite photometric data strings is revealing details in Cepheid variation at very low levels. Specifically, we observed a Cepheid pulsating in the fundamental mode and one pulsating in the first overtone with the Canadi
an MOST satellite. The 3.7-d period fundamental mode pulsator (RT Aur) has a light curve that repeats precisely, and can be modeled by a Fourier series very accurately. The overtone pulsator (SZ Tau, 3.1 d period) on the other hand shows light curve variation from cycle to cycle which we characterize by the variations in the Fourier parameters. We present arguments that we are seeing instability in the pulsation cycle of the overtone pulsator, and that this is also a characteristic of the O-C curves of overtone pulsators. On the other hand, deviations from cycle to cycle as a function of pulsation phase follow a similar pattern in both stars, increasing after minimum radius. In summary, pulsation in the overtone pulsator is less stable than that of the fundamental mode pulsator at both long and short timescales.
We consider diffusion in arbitrary spatial dimension d with the addition of a resetting process wherein the diffusive particle stochastically resets to a fixed position at a constant rate $r$. We compute the non-equilibrium stationary state which exh
ibits non-Gaussian behaviour. We then consider the presence of an absorbing target centred at the origin and compute the survival probability and mean time to absorption of the diffusive particle by the target. The mean absorption time is finite and has a minimum value at an optimal resetting rate $r^*$ which depends on dimension. Finally we consider the problem of a finite density of diffusive particles, each resetting to its own initial position. While the typical survival probability of the target at the origin decays exponentially with time regardless of spatial dimension, the average survival probability decays asymptotically as $exp -A (log t)^d$ where $A$ is a constant. We explain these findings using an interpretation as a renewal process and arguments invoking extreme value statistics.
We consider an extension of the zero-range process to the case where the hop rate depends on the state of both departure and arrival sites. We recover the misanthrope and the target process as special cases for which the probability of the steady sta
te factorizes over sites. We discuss conditions which lead to the condensation of particles and show that although two different hop rates can lead to the same steady state, they do so with sharply contrasting dynamics. The first case resembles the dynamics of the zero-range process, whereas the second case, in which the hop rate increases with the occupation number of both sites, is similar to instantaneous gelation models. This new explosive condensation reveals surprisingly rich behaviour, in which the process of condensates formation goes through a series of collisions between clusters of particles moving through the system at increasing speed. We perform a detailed numerical and analytical study of the dynamics of condensation: we find the speed of the moving clusters, their scattering amplitude, and their growth time. We finally show that the time to reach steady state decreases with the size of the system.
Dramatic volume collapses under pressure are fundamental to geochemistry and of increasing importance to fields as diverse as hydrogen storage and high-temperature superconductivity. In transition metal materials, collapses are usually driven by so-c
alled spin-state transitions, the interplay between the single-ion crystal field and the size of the magnetic moment. Here we show that the classical S=5/2 mineral Hauerite undergoes an unprecedented 22 % collapse driven by a conceptually different magnetic mechanism. Using synchrotron x-ray diffraction we show that cold compression induces the formation of a disordered intermediate. However, using an evolutionary algorithm we predict a new structure with edge-sharing chains. This is confirmed as the thermodynamic groundstate using in situ laser heating. We show that magnetism is globally absent in the new phase, as low-spin quantum S=1/2 moments are quenched by dimerisation. Our results show how the emergence of metal-metal bonding can stabilise giant spin-lattice coupling in Earths minerals.
We study first-passage time problems for a diffusive particle with stochastic resetting with a finite rate $r$. The optimal search time is compared quantitatively with that of an effective equilibrium Langevin process with the same stationary distrib
ution. It is shown that the intermittent, nonequilibrium strategy with non-vanishing resetting rate is more efficient than the equilibrium dynamics. Our results are extended to multiparticle systems where a team of independent searchers, initially uniformly distributed with a given density, looks for a single immobile target. Both the average and the typical survival probability of the target are smaller in the case of nonequilibrium dynamics.
Through powder x-ray diffraction we have investigated the structural behavior of SmVO3, in which orbital and magnetic degrees of freedom are believed to be closely coupled to the crystal lattice. We have found, contrary to previous reports, that SmVO
3 exists in a single, monoclinic, phase below 200 K. The associated crystallographic distortion is then stabilized through the magnetostriction that occurs below 134 K. The crystal structure has been refined using synchrotron x-ray powder diffraction data measured throughout the structural phase diagram, showing a substantial Jahn-Teller distortion of the VO6 octahedra in the monoclinic phase, compatible with the expected G-type orbital order. Changes in the vanadium ion crystal field due to the structural and magnetic transitions have then been probed by resonant x-ray diffraction.
We consider the mean time to absorption by an absorbing target of a diffusive particle with the addition of a process whereby the particle is reset to its initial position with rate $r$. We consider several generalisations of the model of M. R. Evans
and S. N. Majumdar (2011), Diffusion with stochastic resetting, Phys. Rev. Lett. 106, 160601: (i) a space dependent resetting rate $r(x)$ ii) resetting to a random position $z$ drawn from a resetting distribution ${cal P}(z)$ iii) a spatial distribution for the absorbing target $P_T(x)$. As an example of (i) we show that the introduction of a non-resetting window around the initial position can reduce the mean time to absorption provided that the initial position is sufficiently far from the target. We address the problem of optimal resetting, that is, minimising the mean time to absorption for a given target distribution. For an exponentially decaying target distribution centred at the origin we show that a transition in the optimal resetting distribution occurs as the target distribution narrows.
We consider a large class of two-lane driven diffusive systems in contact with reservoirs at their boundaries and develop a stability analysis as a method to derive the phase diagrams of such systems. We illustrate the method by deriving phase diagra
ms for the asymmetric exclusion process coupled to various second lanes: a diffusive lane; an asymmetric exclusion process with advection in the same direction as the first lane, and an asymmetric exclusion process with advection in the opposite direction. The competing currents on the two lanes naturally lead to a very rich phenomenology and we find a variety of phase diagrams. It is shown that the stability analysis is equivalent to an `extremal current principle for the total current in the two lanes. We also point to classes of models where both the stability analysis and the extremal current principle fail.
We revisit the totally asymmetric simple exclusion process with open boundaries (TASEP), focussing on the recent discovery by de Gier and Essler that the model has a dynamical transition along a nontrivial line in the phase diagram. This line coincid
es neither with any change in the steady-state properties of the TASEP, nor the corresponding line predicted by domain wall theory. We provide numerical evidence that the TASEP indeed has a dynamical transition along the de Gier-Essler line, finding that the most convincing evidence was obtained from Density Matrix Renormalisation Group (DMRG) calculations. By contrast, we find that the dynamical transition is rather hard to see in direct Monte Carlo simulations of the TASEP. We furthermore discuss in general terms scenarios that admit a distinction between static and dynamic phase behaviour.
