External control strategies for self-propelled particles: optimizing navigational efficiency in the presence of limited resources

We experimentally and numerically study the dependence of different navigation strategies regarding the effectivity of an active particle to reach a predefined target area. As the only control parameter, we vary the particle's propulsion velocity depending on its position and orientation relative to the target site. By introducing different figures of merit, e.g. the time to target or the total consumed propulsion energy, we are able to quantify and compare the efficiency of different strategies. Our results suggest, that each strategy to navigate towards a target, has its strengths and weaknesses and none of them outperforms the other in all regards. Accordingly, the choice of an ideal navigation strategy will strongly depend on the specific conditions and the figure of merit which should be optimized

Noninvasive Measurement of Dissipation in Colloidal Systems

According to Harada and Sasa [Phys. Rev. Lett. 95, 130602 (2005)], heat production generated in a non-equilibrium steady state can be inferred from measuring response and correlation functions. In many colloidal systems, however, it is a nontrivial task to determine response functions, whereas details about spatial steady state trajectories are easily accessible. Using a simple conditional averaging procedure, we show how this fact can be exploited to reliably evaluate average heat production. We test this method using Brownian dynamics simulations, and apply it to experimental data of an interacting driven colloidal system

Critical Casimir forces in colloidal suspensions on chemically patterned surfaces

We investigate the behavior of colloidal particles immersed in a binary liquid mixture of water and 2,6-lutidine in the presence of a chemically patterned substrate. Close to the critical point of the mixture, the particles are subjected to critical Casimir interactions with force components normal and parallel to the surface. Because the strength and sign of these interactions can be tuned by variations in the surface properties and the mixtures temperature, critical Casimir forces allow the formation of highly ordered monolayers but also extend the use of colloids as model systems.Comment: 4 papges, 4 figures, accepted at Phys. Rev. Let

Theory of orientational ordering in colloidal molecular crystals

Freezing of charged colloids on square or triangular two-dimensional periodic substrates has been recently shown to realize a rich variety of orientational orders. We propose a theoretical framework to analyze the corresponding structures. A fundamental ingredient is that a non spherical charged object in an electrolyte creates a screened electrostatic potential that is anisotropic at any distance. Our approach is in excellent agreement with the known experimental and numerical results, and explains in simple terms the reentrant orientational melting observed in these so called colloidal molecular crystals. We also investigate the case of a rectangular periodic substrate and predict an unusual phase transition between orientationnaly ordered states, as the aspect ratio of the unit cell is changed.Comment: 4 pages, to appear in Phys. Rev. Let

Phase Transitions of Soft Disks in External Periodic Potentials: A Monte Carlo Study

The nature of freezing and melting transitions for a system of model colloids interacting by a DLVO potential in a spatially periodic external potential is studied using extensive Monte Carlo simulations. Detailed finite size scaling analyses of various thermodynamic quantities like the order parameter, its cumulants etc. are used to map the phase diagram of the system for various values of the reduced screening length $\kappa a_{s}$ and the amplitude of the external potential. We find clear indication of a reentrant liquid phase over a significant region of the parameter space. Our simulations therefore show that the system of soft disks behaves in a fashion similar to charge stabilized colloids which are known to undergo an initial freezing, followed by a re-melting transition as the amplitude of the imposed, modulating field produced by crossed laser beams is steadily increased. Detailed analysis of our data shows several features consistent with a recent dislocation unbinding theory of laser induced melting

Understanding depletion forces beyond entropy

The effective interaction energy of a colloidal sphere in a suspension containing small amounts of non-ionic polymers and a flat glass surface has been measured and calculated using total internal reflection microscopy (TIRM) and a novel approach within density functional theory (DFT), respectively. Quantitative agreement between experiment and theory demonstrates that the resulting repulsive part of the depletion forces cannot be interpreted entirely in terms of entropic arguments but that particularly at small distances ($\lesssim$ 100 nm) attractive dispersion forces have to be taken into account

Normal and lateral critical Casimir forces between colloids and patterned substrates

We study the normal and lateral effective critical Casimir forces acting on a spherical colloid immersed in a critical binary solvent and close to a chemically structured substrate with alternating adsorption preference. We calculate the universal scaling function for the corresponding potential and compare our results with recent experimental data [Soyka F., Zvyagolskaya O., Hertlein C., Helden L., and Bechinger C., Phys. Rev. Lett., 101, 208301 (2008)]. The experimental potentials are properly captured by our predictions only by accounting for geometrical details of the substrate pattern for which, according to our theory, critical Casimir forces turn out to be a sensitive probe.Comment: 6 pages, 3 figure

Dirac Leptogenesis with a Non-anomalous U(1)′U(1)^{\prime} Family Symmetry

We propose a model for Dirac leptogenesis based on a non-anomalous $U(1)^{\prime}$ gauged family symmetry. The anomaly cancellation conditions are satisfied with no new chiral fermions other than the three right-handed neutrinos, giving rise to stringent constraints among the charges. Realistic masses and mixing angles are obtained for all fermions. The model predicts neutrinos of the Dirac type with naturally suppressed masses. Dirac leptogenesis is achieved through the decay of the flavon fields. The cascade decays of the vector-like heavy fermions in the Froggatt-Nielsen mechanism play a crucial role in the separation of the primodial lepton numbers. We find that a large region of parameter space of the model gives rise to a sufficient cosmological baryon number asymmetry through Dirac leptogenesis.Comment: 8 pages, 8 figures, version to appear in JHE

Brownian motion exhibiting absolute negative mobility

We consider a single Brownian particle in a spatially symmetric, periodic system far from thermal equilibrium. This setup can be readily realized experimentally. Upon application of an external static force F, the average particle velocity is negative for F>0 and positive for F<0 (absolute negative mobility).Comment: 4 pages, 3 figures, to be published in PR

Critical Casimir effect in classical binary liquid mixtures

If a fluctuating medium is confined, the ensuing perturbation of its fluctuation spectrum generates Casimir-like effective forces acting on its confining surfaces. Near a continuous phase transition of such a medium the corresponding order parameter fluctuations occur on all length scales and therefore close to the critical point this effect acquires a universal character, i.e., to a large extent it is independent of the microscopic details of the actual system. Accordingly it can be calculated theoretically by studying suitable representative model systems. We report on the direct measurement of critical Casimir forces by total internal reflection microscopy (TIRM), with femto-Newton resolution. The corresponding potentials are determined for individual colloidal particles floating above a substrate under the action of the critical thermal noise in the solvent medium, constituted by a binary liquid mixture of water and 2,6-lutidine near its lower consolute point. Depending on the relative adsorption preferences of the colloid and substrate surfaces with respect to the two components of the binary liquid mixture, we observe that, upon approaching the critical point of the solvent, attractive or repulsive forces emerge and supersede those prevailing away from it. Based on the knowledge of the critical Casimir forces acting in film geometries within the Ising universality class and with equal or opposing boundary conditions, we provide the corresponding theoretical predictions for the sphere-planar wall geometry of the experiment. The experimental data for the effective potential can be interpreted consistently in terms of these predictions and a remarkable quantitative agreement is observed.Comment: 30 pages, 17 figure