The kinetic separation of repulsive active Brownian particles into a dense and a dilute phase is analyzed using a systematic coarse-graining strategy. We derive an effective Cahn-Hilliard equation on large length and time scales, which implies that the separation process can be mapped onto that of passive particles. A lower density threshold for clustering is found, and using our approach we demonstrate that clustering first proceeds via a hysteretic nucleation scenario and above a higher threshold changes into a spinodal-like instability. Our results are in agreement with particle-resolved computer simulations and can be verified in experiments of artificial or biological microswimmers.PACS numbers: 82.70. Dd,64.60.Cn The collective behavior of living "active" matter has recently attracted considerable interest from the statistical physics community (for reviews, see Refs. 1, 2). Even if the mutual interactions of the individual units are following simple rules, complex spatiotemporal patterns can emerge. Examples in nature occur on a wide range of scales from flocks of birds [3] to bacterial turbulence [4]. A basic physical model is obtained by describing the individual entities as particles with internal degrees of freedom (in the simplest case just an orientation) that consume energy and are thus driven out of thermal equilibrium. Consequently, shaken granular particles [5] and phoretically propelled colloidal particles [6-9] have been investigated in detail. Moreover, the observed collective behavior might find applications in, e.g., the sorting [10] and transport of cargo [11].Here we are interested in the phase behavior of repulsive particles below the freezing density. While in equilibrium only one fluid phase exists, sufficiently dense suspensions of repulsive self-propelled disks undergo an "active phase separation", i.e., particles aggregate into a dense, transiently ordered cluster surrounded by a dilute gas phase. This has been observed first [12,13] in computer simulations of a minimal model [14][15][16]. Clustering has also been reported in experiments using colloidal suspensions of active Brownian particles, in which the particles are phoretically propelled along their orientations due to the catalytic decomposition of hydrogen peroxide on a platinum hemisphere [7], or due to lightactivated hematite [8]. In these experiments, phoretic attractive forces play an important role. A closer realization of ideally repulsive particles is possible through the reversible local demixing of a near-critical water-lutidine mixture [17]. Colloidal particles propelled due to the ensuing local density gradients show indeed the predicted phase separation [9]. While in passive suspensions phaseseparation occurs only for sufficiently strong attractive forces, the microscopic mechanism for repulsive active particles is due to self-trapping: colliding particles block each other due to the persistence of their orientation [9]. In sufficiently dense suspensions, the "pressure" of the free, fast particles leads to the...

One characteristic feature of soft matter systems is their strong response to external stimuli. As a consequence they are comparatively easily driven out of their ground state and out of equilibrium, which leads to many of their fascinating properties. Here, we review illustrative examples. This review is structured by an increasing distance from the equilibrium ground state. On each level, examples of increasing degree of complexity are considered. In detail, we first consider systems that are quasi-statically tuned or switched to a new state by applying external fields. These are common liquid crystals, liquid crystalline elastomers, or ferrogels and magnetic elastomers. Next, we concentrate on systems steadily driven from outside e.g. by an imposed flow field. In our case, we review the reaction of nematic liquid crystals, of bulk-filling periodically modulated structures such as block copolymers, and of localized vesicular objects to an imposed shear flow. Finally, we focus on systems that are "active" and "self-driven". Here our range spans from idealized self-propelled point particles, via sterically interacting particles like granular hoppers, via microswimmers such as self-phoretically driven artificial Janus particles or biological microorganisms, via deformable self-propelled particles like droplets, up to the collective behavior of insects, fish, and birds. As we emphasize, similarities emerge in the features and behavior of systems that at first glance may not necessarily appear related. We thus hope that our overview will further stimulate the search for basic unifying principles underlying the physics of these soft materials out of their equilibrium ground state.Comment: 84 pages, 30 figure

This article summarises the status of the global fit of the CKM parameters within the Standard Model performed by the CKMfitter group. Special attention is paid to the inputs for the CKM angles α and γ and the status of Bs → µµ and B d → µµ decays. We illustrate the current situation for other unitarity triangles. We also discuss the constraints on generic ∆F = 2 New Physics. All results have been obtained with the CKMfitter analysis package, featuring the frequentist statistical approach and using Rfit to handle theoretical uncertainties.

A microscopic field theory for crystallization in active systems is proposed which unifies the phase-field-crystal model of freezing with the Toner-Tu theory for self-propelled particles. A wealth of different active crystalline states are predicted and characterized. In particular, for increasing strength of self-propulsion, a transition from a resting crystal to a traveling crystalline state is found where the particles migrate collectively while keeping their crystalline order. Our predictions, which are verifiable in experiments and in particle-resolved computer simulations, provide a starting point for the design of new active materials. PACS numbers: 64.70.dm,87.18.Gh,82.70.Dd Self-propelled particles [1] exhibit fascinating collective phenomena like swarming, swirling and laning which have been intensely explored by theory, simulation and experiment, for recent reviews see [2][3][4]. In marked contrast to passive particles, self-propelled "active" particles have an internal motor of propulsion, dissipate energy and are therefore intrinsically in nonequilibrium. Examples of active particles include living systems, like bacteria and microbes [5], as well as man-made microswimmers, catalytically driven colloids [6,7] and granular hoppers [8].If, at high densities, the particle interaction dominates the propulsion, crystallization in an active system is conceivable. It is expected that such "active crystals" have structural and dynamical properties largely different from equilibrium crystals due to the intrinsic drive. In fact, there is experimental evidence for active crystals, both from observations of hexagonal structures for catalytically-driven colloids [9] and honeycomb-like textures for flagellated marine bacteria [10,11]. Moreover, recent computer simulations have confirmed crystallization [12][13][14] and proved that melting of active crystals differs from its equilibrium counterpart. However, though field-theoretical modelling of active systems has been widely applied to orientational ordering phenomena [2,15], there is no such theory for translational ordering of active crystals nor has a systematic classification of active crystals been achieved.Here we present a microscopic field-theoretical approach to crystallization in active systems and we propose a minimal model which has the necessary ingredients for both, crystallization and activity. In doing so, we combine the phase-field crystal model of freezing [16] with the Toner-Tu model for active systems [17] using the concept of dynamical density functional theory [18,19]. On the one hand, the phase-field-crystal (PFC) model as originally introduced by Elder and coworkers [16,20] describes crystallization of passive particles on microscopic length and diffusive time scales. When brought into connection with dynamical density functional theory [21][22][23][24], the PFC model represents in principle a microscopic theory for crystallization, and it has been successfully applied to a plethora of solidification phenomena [16,20,[25][26][27][28][29]...

Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Phys. Rev. Lett. 112, 218304 (2014)]. Here we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, meanfield description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (mobility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the dynamics. We finally discuss results from numerical simulations corroborating the analytical results.