Based on classical density functional theory (DFT), we investigate the demixing phase transition of a two-dimensional, binary Heisenberg fluid mixture. The particles in the mixture are modeled as Gaussian soft spheres, where one component is characterized by an additional classical spin-spin interaction of Heisenberg type. Within the DFT we treat the particle interactions using a mean-field approximation. For certain magnetic coupling strengths we calculate phase diagrams in the density-concentration plane. For sufficiently large coupling strengths and densities, we find a demixing phase transition driven by the ferromagnetic interactions of the magnetic species. We also provide a microscopic description (i.e., density profiles) of the resulting non-magnetic/magnetic fluid-fluid interface. Finally, we investigate the phase separation using dynamical density functional theory (DDFT), considering both nucleation processes and spinodal demixing.Comment: 15 pages, 10 figure

Abstract. -Based on dynamical density functional theory (DDFT) we consider a non-equilibrium system of interacting colloidal particles driven by a constant tilting force through a periodic, symmetric "washboard" potential. We demonstrate that, despite of pronounced spatio-temporal correlations, the particle current can be reversed by adding suitable feedback control terms to the DDFT equation of motion. We explore two distinct control protocols with time delay, focussing on either the particle positions or the density profile. Our study shows that the DDFT is an appropriate framework to implement time-delayed feedback control strategies widely used in other fields of nonlinear physics.Introduction. -Transport phenomena of Brownian particles in complex geometries are a topic receiving intense and continuos attention since decades [1][2][3]. A large number of studies has been devoted to transport in structured 1D systems such as colloids or biomolecules in microchannels [4], colloids in optical potentials [5,6], or cold atoms in optical lattices [7]. Theoretical studies of such systems have predicted spectacular effects such as ratchet mechanisms in systems with asymmetric spatial potential [1], giant diffusion [5,6,8,9] and dispersionless transport [10] in symmetric systems under constant external bias ("tilted washboards"), and the negative mobility effect [4,11]. Many of these effects have also been observed experimentally (see, e.g., [5,6,11,12]), often involving colloidal systems. A related topic is how these non-equilibrium phenomena can be manipulated by control forces [13]. Particularly promising are feedback control schemes which depend on the state of the system. A special case is the time-delayed feedback control method suggested by Pyragas [14], where the control term involves the difference between an output variable (the control target) at time t and its value at time t − τ , with τ being the delay time. This method is particularly suitable to stabilize certain, otherwise unstable (periodic) states. Moreover, a time delay naturally occurs in experiments involving feedback control due to the lag between the collection of information and the feedback. Indeed, time-delayed feedback control is nowadays used in a broad variety of non-linear systems such as lasers, neural dynamics, and excitable

We investigate the self-organization of a binary mixture of similar sized rods and dipolar soft spheres by means of Monte-Carlo simulations. We model interparticle interactions by employing anisotropic Gay-Berne, dipolar and soft-sphere interactions. In the limit of vanishing magnetic moments we obtain a variety of fully miscible liquid crystalline phases including nematic, smectic and lamellar phases. For the magnetic mixture, we find that the liquid crystalline matrix supports the formation of orientationally ordered ferromagnetic chains. Depending on the relative size of the species the chains align parallel or perpendicular to the director of the rods forming uniaxial or biaxial nematic, smectic and lamellar phases. As an exemplary external perturbation we apply a homogeneous magnetic field causing uniaxial or biaxial ordering to an otherwise isotropic state.

We investigate a driven, one-dimensional system of colloidal particles in a periodically corrugated narrow channel subject to a time-delayed feedback control. Our goal is to identify conditions under which the control induces oscillatory, time-periodic states. The investigations are based on the Fokker-Planck equation involving the density distribution of the system. First, by using the numerical continuation technique, we determine the linear stability of a stationary density. Second, the nonlinear regimes are analyzed by studying numerically the temporal evolution of the first moment of the density distribution. In this way we construct a bifurcation diagram revealing the nature of the instability. Apart from the case of a system with periodic boundary conditions, we also consider a microchannel of finite length. Finally, we study the influence of (repulsive) particle interactions based on dynamical density functional theory.

PACS 64.75.Xc -Phase separation and segregation in colloidal systems PACS 47.54.-r -Pattern selection; pattern formation PACS 64.70.Nd -Structural transitions in nanoscale materials Abstract -Based on Dynamical Density Functional Theory (DDFT) we investigate a binary mixture of interacting Brownian particles driven over a substrate via a one-dimensional ratchet potential. The particles are modeled as soft spheres where one component carries a classical Heisenberg spin. In the absence of a substrate field, the system undergoes a first-order fluidfluid demixing transition driven by the spin-spin interaction. We demonstrate that the interplay between the intrinsic spinodal decomposition and time-dependent external forces leads to a novel dynamical instability where stripes against the symmetry of the external potential form. This structural transition is observed for a broad range of parameters related to the ratchet potential. Moreover, we find intriguing effects for the particle transport.Introduction. -Understanding the dynamics of particles in complex geometry is an ubiquitary problem throughout non-equilibrium statistical physics with applications in diverse fields such as biology, condensed matter and nanotechnology [1,2]. Paradigm examples are colloidal particles in periodic optical (or otherwise modulated) potentials [3][4][5], which display a variety of fascinating transport phenomena including giant diffusion [6], subdiffusive motion [7], and ratchet effects, i.e., fluctuatinginduced transport in the absence of a biasing deterministic force [8]. Indeed, ratchet-driven transport of Brownian (overdamped) particles has been studied in a variety of optical [9,10], magnetic [11][12][13][14][15][16], and biological systems [17][18][19]. The advantage of studying colloids, which are typically of the size of nano-to micrometer, is that many of these effects can be monitored by real-space experiments (see, e.g.,). In the present letter we study the impact of ratchet potentials on the collective behavior, specifically the phase separation dynamics, of a colloidal suspension. As a model system we consider systems involving magnetic colloids subject to magnetic ratchet potentials. Indeed, recent experimental and theoretical research has shown that magnetic colloidal systems are ideally suited to study transport in complex geometries. Static, magnetic periodic potentials can be created, e.g., by using ferrite garnet films

In our previous work [J. Chem. Phys. 136, 024502 (2012)], we reported a demixing phase transition of a quasi-two-dimensional, binary Heisenberg fluid mixture driven by the ferromagnetic interactions of the magnetic species. Here, we present a theoretical study for the time-dependent coarsening occurring within the two-phase region in the density-concentration plane, also known as spinodal decomposition. Our investigations are based on dynamical density functional theory (DDFT). The particles in the mixture are modeled as Gaussian soft spheres on a two-dimensional surface, where one component carries a classical spin of Heisenberg type. To investigate the two-phase region, we first present a linear stability analysis with respect to small, harmonic density perturbations. Second, to capture nonlinear effects, we calculate time-dependent structure factors by combining DDFT with Percus' test particle method. For the growth of the average domain size l during spinodal decomposition with time t, we observe a power-law behavior l∝t^{δ_{α}} with δ_{m}≃0.333 for the magnetic species and δ_{n}≃0.323 for the nonmagnetic species.

We review recent work on feedback control of one-dimensional colloidal systems, both with instantaneous feedback and with time delay. The feedback schemes are based on measurement of the average particle position, a natural control target for an ensemble of colloidal particles, and the systems are investigated via the Fokker-Planck equation for overdamped Brownian particles. Topics include the reversal of current and the emergence of current oscillations, transport in ratchet systems, and the enhancement of mobility by a co-moving trap. Beyond the commonly considered case of non-interacting systems, we also discuss the treatment of colloidal interactions via (dynamical) density functional theory and provide new results for systems with attractive interactions.

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