A model of self-driven particles similar to the Vicsek model [Phys. Rev. Lett. 75 (1995) 1226] but with metric-free interactions is studied by means of a novel Enskog-type kinetic theory. In this model, N particles of constant speed v0 try to align their travel directions with the average direction of a fixed number of closest neighbors. At strong alignment a global flocking state forms. The alignment is defined by a stochastic rule, not by a Hamiltonian. The corresponding interactions are of genuine multi-body nature. The theory is based on a Master equation in 3N-dimensional phase space, which is made tractable by means of the molecular chaos approximation. The phase diagram for the transition to collective motion is calculated and compared to direct numerical simulations. A linear stability analysis of a homogeneous ordered state is performed using the kinetic but not the hydrodynamic equations in order to achieve high accuracy. In contrast to the regular metric Vicsek-model no instabilities occur. This confirms previous direct simulations that for Vicsek-like models with metric-free interactions, there is no formation of density bands and that the flocking transition is continuous.

In order to characterise non-equilibrium growth processes, we study the behaviour of global quantities that depend in a non-trivial way on two different times. We discuss the dynamical scaling forms of global correlation and response functions and show that the scaling behaviour of the global response can depend on how the system is perturbed. On the one hand we derive exact expressions for systems characterised by linear Langevin equations (as for example the Edwards-Wilkinson and the noisy Mullins-Herring equations), on the other hand we discuss the influence of non-linearities on the scaling behaviour of global quantities by integrating numerically the Kardar-Parisi-Zhang equation. We also discuss global fluctuation-dissipation ratios and how to use them for the characterisation of non-equilibrium growth processes.

Recently, Hanke et al. [Phys.Rev. E 88, 052309 (2013)] showed that mean-field kinetic theory fails to describe collective motion in soft active colloids and that correlations must not be neglected.Correlation effects are also expected to be essential in systems of biofilaments driven by molecular motors and in swarms of midges. To obtain correlations in an active matter system from first principles, we derive a ring-kinetic theory for Vicsek-style models of self-propelled agents from the exact N -particle evolution equation in phase space. The theory goes beyond mean-field and does not rely on Boltzmann's approximation of molecular chaos. It can handle pre-collisional correlations and cluster formation which both seem important to understand the phase transition to collective motion. We propose a diagrammatic technique to perform a small density expansion of the collision operator and derive the first two equations of the BBGKY-hierarchy. An algorithm is presented that numerically solves the evolution equation for the two-particle correlations on a lattice. Agent-based simulations are performed and informative quantities such as orientational and density correlation functions are compared with those obtained by ring-kinetic theory. Excellent quantitative agreement between simulations and theory is found at not too small noises and mean free paths. This shows that there is parameter ranges in Vicsek-like models where the correlated closure of the BBGKY-hierarchy gives correct and nontrivial results. We calculate the dependence of the orientational correlations on distance in the disordered phase and find that it seems to be consistent with a power law with exponent around -1.8, followed by an exponential decay. General limitations of the kinetic theory and its numerical solution are discussed.

We discuss a parameter free scaling relation that yields a complete data collapse for large classes of nonequilibrium growth processes. We illustrate the power of this new scaling relation through various growth models, as for example the competitive growth model RD/RDSR (random deposition/random deposition with surface diffusion) and the RSOS (restricted solid-on-solid) model with different nearest-neighbor height differences, as well as through a new deposition model with temperature dependent diffusion. The new scaling relation is compared to the familiar Family-Vicsek relation and the limitations of the latter are highlighted.PACS numbers: 64.60.Ht,68.35.Ct,05.70.Np The study of growing interfaces has been a very active field for many years [1,2,3]. Many studies focus on the technologically relevant growth of thin films or nanostructures, but growing interfaces are also encountered in various other physical, chemical, or biological systems, ranging from bacterial growth to diffusion fronts. Over the years important insights into the behavior of nonequilibrium growth processes have been gained through the study of simple model systems that capture the most important aspects of real experimental systems [4,5].In their seminal work, Edwards and Wilkinson investigated surface growth phenomena generated by particle sedimentation under the influence of gravity [6]. They proposed to describe this process in (d + 1) dimensions by the following stochastic equation of motion for the surface height h(x, t), now called the Edwards-Wilkinson (EW) equation,where ν is the diffusion constant (surface tension), whereas η(x, t) is a Gaussian white noise with zero mean and covariance η(x, t)η(y, s) = Dδ d (x − y)δ(t − s). Since Eq. 1 is linear, it can be solved exactly by Fourier transformations [2,4,6]. Later, Family [7] discussed the random deposition (RD) and random deposition with surface relaxation (RDSR) processes. RD [3,7] is one of the simplest surface growth processes. In this lattice model particles drop from randomly chosen sites over the surface and stick directly on the top of the selected surface site. Since there is no surface diffusion, the independently growing columns yield an uncorrelated and never-saturated surface. The RDSR process is realized by adding surface diffusion which allows particles just deposited on the surface to jump to the neighboring site with lowest height. This diffusion step smoothes the surface and limits the maximum interface width W (t), defined at deposition time t as the standard deviation of the surface height h from its mean value h: W (t) = h − h 2 . Starting from an initially flat surface, RDSR yields at very early times, with t < t 1 ∼ 1 (we assume here that one layer is deposited per unit time), a surface growing in the same way as for the RD process since no (or only very few) diffusion steps occur in that regime. For t > t 1 the width increases as a power law of time with a growth exponent β before entering a saturation regime after a crossover time t 2 , see Fig. 1. Both...

Motivated by a series of experiments that revealed a temperature dependence of the dynamic scaling regime of growing surfaces, we investigate theoretically how a nonequilibrium growth process reacts to a sudden change of system parameters. We discuss quenches between correlated regimes through exact expressions derived from the stochastic Edwards-Wilkinson equation with a variable diffusion constant. Our study reveals that a sudden change of the diffusion constant leads to remarkable changes in the surface roughness. Different dynamic regimes, characterized by a power-law or by an exponential relaxation, are identified, and a dynamic phase diagram is constructed. We conclude that growth processes provide one of the rare instances where quenches between correlated regimes yield a power-law relaxation.