The concept of swim pressure quantifies the average force exerted by microswimmers on confining walls in nonequilibrium. Here we explore how the swim pressure depends on the wall curvature and on the presence of sharp corners in the wall. For active Brownian particles at high dilution, we present a coherent framework which describes the force and torque on passive particles of arbitrary shape, in the limit of large particles compared to the persistence length of the swimmer trajectories. The resulting forces can be used to derive, for example, the activity-induced depletion interaction between two disks, as well as to optimize the shape of a tracer particle for high swimming velocity. Our predictions are verifiable in experiments on passive obstacles exposed to a bath of bacteria or artificial microswimmers.

A model for one-dimensional convection is proposed by adding a buoyancy term to the Burgers' equation and including an equation for the temperature perturbation. A linear stability analysis shows onset of instability at a critical Rayleigh number. Computation in the unstable region shows steady convection with only one convection cell. Computations up to ${10}^5$ times the critical Rayleigh number do not show transition to an oscillatory state or to turbulence. Using a large Rayleigh number approximation, closed form solutions for the spectrum and the scaling for the heat transport due to nonlinear convection are obtained up to two orders. These are shown to be in good agreement with numerical results at high Rayleigh number.

We investigate, via both asymptotic analysis and direct numerical simulation, precessionally driven flow of a homogeneous fluid confined in fluid-filled circular cylinders that rotate rapidly about their symmetry axis and precess about a different axis and that are marked by radius-height aspect ratios $\mathrm{\Gamma }=1.045945$ and $\mathrm{\Gamma }=1.611089$. At these radius-height aspect ratios, the Poincaré force resonates directly with the two special inertial modes that have the simplest vertical structure. An asymptotic analytical solution in closed form describing weakly precessing flow is derived in the mantle frame of reference for asymptotically small Ekman numbers, showing quantitative agreement with the result of direct nonlinear numerical simulation. Our numerical simulation makes use of a finite-element method with the three-dimensional tetrahedralization of a cylindrical cavity that allows the construction of dense nodes in the vicinity of the bounding surface of the cavity for resolving the thin viscous boundary layer. It is found that axisymmetric geostrophic flow in the alternating eastward and westward direction can be generated and maintained by nonlinear and viscous effects in the viscous boundary layer. It is also found that, when the precessing rate is moderate and, consequently, the geostrophic flow is weak, nonlinear interaction between the resonant inertial mode and the nonesonant inertial modes driven by the Poincaré force and the boundary-layer influx leads to strongly turbulent flow with irregular temporal-spatial fluctuation. When the cylinders are strongly precessing such that the geostrophic flow becomes predominant, however, the effect of the geostrophic flow controls/stabilizes its nonlinear dynamics, leading to weakly turbulent flow that can be largely described by a dominant quasisteady geostrophic component and a weak nonaxisymmetric component localized in the region where the geostrophic flow is weak.

Analytical expressions describing the electron energy distribution function (EEDF) in a dusty plasma are obtained from the homogeneous Boltzmann equation for electrons. The expressions are derived neglecting electron-electron collisions, as well as transformation of high-energy electrons into low-energy electrons at inelastic electron-atom collisions. At large electron energies, the quasiclassical approach for calculation of the EEDF is applied. For the moderate energies, we account for inelastic electron-atom collisions in the dust-free case and both inelastic electron-atom and electron-dust collisions in the dusty plasma case. Using these analytical expressions and the balance equation for dust charging, the electron energy distribution function, the effective electron temperature, the dust charge, and the dust surface potential are obtained for different dust radii and densities, as well as for different electron densities and radio-frequency (rf) field amplitudes and frequencies. The dusty plasma parameters are compared with those calculated numerically by a finite-difference method taking into account electron-electron collisions and the transformation of high-energy electrons at inelastic electron-neutral collisions. It is shown that the analytical expressions can be used for calculation of the EEDF and dusty plasma parameters at typical experimental conditions, in particular, in the positive column of a direct-current glow discharge and in the case of an rf plasma maintained by an electric field with frequency $f=13.56\mathrm{MHz}$.

We investigate experimentally the steady flows in a cylinder containing two immiscible liquids, with the primary fluid being driven by the upper boundary rotating at constant speeds. The system exhibits interesting interplays between the flow fields and the morphology of the interface, with evidence showing that the remarkable flattop structure is a consequence of the vortex breakdown discovered decades ago, and that the deformability of the interface also feedbacks positively to the development of the vortices. Monitoring the topological structure of the flow fields defines the base states and transitions behind the morphology, whereas our survey over different aspect ratios also reveals rich phenomena of surface instabilities accompanying these steady states.

We address the dispersion properties of overdamped Brownian particles migrating in a two-dimensional acoustophoretic microchannel, where a pressure-driven axial Stokes flow coexists with a transverse acoustophoretic potential. Depending on the number and symmetries of the stable nodal points of the acoustophoretic force with respect to the axial velocity profile, different convection-enhanced dispersion regimes can be observed. Among these regimes, an anomalous scaling, for which the axial dispersion increases exponentially with the particle Peclét number, is observed whenever two or more stable acoustophoretic nodes are associated with different axial velocities. A theoretical explanation of this regime is derived, based on exact moment homogenization. Attention is also focused on transient dispersion, which can exhibit superballistic behavior $\langle {(x-\langle x\rangle )}^2\rangle \sim t^3,x$ being the axial coordinate.

We study the efficiency of a single-particle Szilard and Carnot engine. Within a first order correction to the quasistatic limit, the work distribution is found to be Gaussian and the correction factor to average work and efficiency only depends on the piston speed. The stochastic efficiency is studied for both models and the recent findings on efficiency fluctuations are confirmed numerically. Special features are revealed in the zero-temperature limit.

We compute critical properties of a general class of quantum spin chains which are quadratic in the Fermi operators and can be solved exactly under certain symmetry constraints related to the classical compact groups $\text{U}\left(N\right),\text{O}\left(N\right)$, and $\text{Sp}\left(2N\right)$. In particular we calculate critical exponents $s,\nu$, and $z$, corresponding to the energy gap, correlation length, and dynamic exponent, respectively. We also compute the ground state correlators ${〈{\sigma }_i^x{\sigma }_{i+n}^x〉}_g,{〈{\sigma }_i^y{\sigma }_{i+n}^y〉}_g$, and ${〈{\prod }_{i=1}^n{\sigma }_i^z〉}_g$, all of which display quasi-long-range order with a critical exponent dependent upon system parameters. Our approach establishes universality of the exponents for the class of systems in question.

The coffee-ring effect for particle deposition near the three-phase line after drying a pinned sessile colloidal droplet has been suppressed or attenuated in many recent studies. However, there have been few attempts to simulate the mitigation of the effect in the presence of strong particle-particle attraction forces. We develop a three-dimensional stochastic model to investigate the drying process of a pinned colloidal sessile droplet by considering the sticking between particles, which was observed in the experiments. The Monte Carlo simulation results show that by solely promoting the particle-particle attraction in the model, the final deposit shape is transformed from the coffee ring to the uniform film deposition. This phenomenon is modeled using the colloidal aggregation technique and explained by the “Tetris principle,” meaning that unevenly shaped or branched particle clusters rapidly build up a sparse structure spanning throughout the entire domain in the drying process. The influence of the controlled parameters is analyzed as well. The simulation is reflected by the drying patterns of the nanofluid droplets through the surfactant control in the experiments.

We present numerical results from phase-field simulations of the buoyancy-driven detachment of an isolated, wall-bound pendant emulsion droplet acted upon by surface tension and wall-normal buoyancy forces alone. Our theoretical approach follows a diffuse-interface model for partially miscible binary mixtures which has been extended to include the influence of static contact angles other than ${90}^{\circ }$, based on a Hermite interpolation formulation of the Cahn boundary condition as first proposed by Jacqmin [J. Fluid Mech. 402, 57 (2000)]. In a previous work, this model has been successfully employed for simulating triphase contact line problems in stable emulsions with nearly immiscible components, and, in particular, applied to the determination of critical Bond numbers for buoyancy-driven detachment as a function of static contact angle. Herein, the shapes of interfaces at pinchoff are investigated as a function of static contact angle and distance to the critical condition. Furthermore, we show numerical results on the nonequilibrium surface tension that help to explain the discrepancy between our numerically determined static contact angle dependence of the critical Bond number and its sharp-interface counterpart based on a static stability analysis of equilibrium shapes after numerical integration of the Young-Laplace equation. Finally, we show the influence of static contact angle and distance to the critical condition on the temporal evolution of the minimum neck radius in the necking regime of drop detachment.

The temperature dependence of the ionic conductivity is studied in a series of poly(propylene glycol) diacrylate monomers. The experimental data are analyzed by means of the approach recently proposed by Petrowsky et al. [J. Phys. Chem. B. 113, 5996 (2009)]. This so-called compensated Arrhenius formalism (CAF) approach takes into account the influence of the dielectric permittivity on the exponential prefactor in the classical Arrhenius equation. The experimental data presented in this paper show a good agreement with the CAF; this means that the exponential prefactor is principally dielectric permittivity dependent. The compensated data revealed two conduction processes with different activation energies; they correspond to low and high temperature ranges, respectively.

A butterfly with broad wings, flapping at a small frequency, flies an erratic trajectory at an inconstant speed. A large variation of speed within a cycle is observed in the forward flight of a butterfly. A self-propulsion model to simulate a butterfly is thus created to investigate the transient translation of the body; the results, which are in accordance with experimental data, show that the shape of the variation of the flight speed is similar to a sinusoidal wave with a maximum $(J=0.89)$ at the beginning of the downstroke, and a decrease to a minimum $(J=0.17)$ during a transition from downstroke to upstroke; the difference between the extrema of the flight speed is enormous in a flapping cycle. At a high speed, a clapping motion of the butterfly wings decreases the generation of drag. At a small speed, a butterfly is able to capture the induced wakes generated in a downstroke, and effectively generates a thrust at the beginning of an upstroke. The wing motion of a butterfly skillfully interacts with its speed so as to enable an increased speed with the same motion. Considering a butterfly to fly in a constant inflow leads to either an underestimate of its speed or an overestimate of its generated lift, which yields an inaccurate interpretation of the insect's flight. Our results reveal the effect of transient translation on a butterfly in forward flight, which is especially important for an insect with a small flapping frequency.

We have analyzed long-term wind speed time series from five field sites up to a height of 300 m from the ground. Structure function-based scaling analysis has revealed that the scaling exponents in the mesoscale regime systematically depend on height. This anomalous behavior is likely caused by the buoyancy effects. In the framework of the extended self-similarity, the relative scaling exponents portray quasiuniversal behavior.

We study a class of nonequilibrium lattice models on a ring where particles hop in a particular direction, from a site to one of its (say, right) nearest neighbors, with a rate that depends on the occupation of all the neighboring sites within a range $R$. This finite-range process (FRP) for $R=0$ reduces to the well-known zero-range process (ZRP), giving rise to a factorized steady state (FSS) for any arbitrary hop rate. We show that, provided the hop rates satisfy a specific condition, the steady state of FRP can be written as a product of a cluster-weight function of $(R+1)$ occupation variables. We show that, for a large class of cluster-weight functions, the cluster-factorized steady state admits a finite dimensional transfer-matrix formulation, which helps in calculating the spatial correlation functions and subsystem mass distributions exactly. We also discuss a criterion for which the FRP undergoes a condensation transition.

A general theory of the dielectric constant of nematic liquid crystal mixtures is presented including the particular case of nematics doped with polar nanoparticles. The results are used to estimate the contribution of chains of polar nanoparticles to the static dielectric anisotropy and birefringence of the nematic composite taking into account contributions from chains of different lengths. The dependence of the dielectric anisotropy on the dipolar interaction strength is considered in detail and it is shown that formation of polar chains of nanoparticles enables one to explain a significant increase of the dielectric constant of the composite as observed experimentally.

Many organisms form colonies for a transient period of time to withstand environmental pressure. Bacterial biofilms are a prototypical example of such behavior. Despite significant interest across disciplines, physical mechanisms governing the formation and dissolution of bacterial colonies are still poorly understood. Starting from a kinetic description of motile and interacting cells we derive a hydrodynamic equation for their density on a surface, where most of the kinetic coefficients are estimated from experimental data for N. gonorrhoeae bacteria. We use it to describe the formation of multiple colonies with sizes consistent with experimental observations. Finally, we show how the changes in the cell-to-cell interactions lead to the dissolution of the bacterial colonies. The successful application of kinetic theory to a complex far from equilibrium system such as formation and dissolution of living bacterial colonies potentially paves the way for the physical quantification of the initial stages of biofilm formation.