We present microparticle image velocimetry measurements of suspended microparticles of diameters from $0.6$ to $10\mu \text{m}$ undergoing acoustophoresis in an ultrasound symmetry plane in a microchannel. The motion of the smallest particles is dominated by the Stokes drag from the induced acoustic streaming flow, while the motion of the largest particles is dominated by the acoustic radiation force. For all particle sizes we predict theoretically how much of the particle velocity is due to radiation and streaming, respectively. These predictions include corrections for particle-wall interactions and ultrasonic thermoviscous effects and match our measurements within the experimental uncertainty. Finally, we predict theoretically and confirm experimentally that the ratio between the acoustic radiation- and streaming-induced particle velocities is proportional to the actuation frequency, the acoustic contrast factor, and the square of the particle size, while it is inversely proportional to the kinematic viscosity.

Lateral migration and equilibrium shape and position of a single red blood cell (RBC) in bounded two-dimensional Poiseuille flows are investigated by using an immersed boundary method. An elastic spring model is applied to simulate the skeleton structure of a RBC membrane. We focus on studying the properties of lateral migration of a single RBC in Poiseuille flows by varying the initial position, the initial angle, the swelling ratio ($s^{*}$), the membrane bending stiffness of RBC ($k_b$), the maximum velocity of fluid flow ($u_{\max }$), and the degree of confinement. The combined effect of the deformability, the degree of confinement, and the shear gradient of the Poiseuille flow make the RBCs migrate toward a certain cross-sectional equilibrium position, which lies either on the center line of the channel or off center line. For $s^{*}>0.8$, the speed of the migration at the beginning decreases as one increases the swelling ratio $s^{*}$. But for $s^{*}<0.8$, the speed of the migration at the beginning is an increasing function of the swelling ratio $s^{*}$. Two motions of oscillation and vacillating breathing (swing) of RBCs are observed. The distance $Y_d$ between the cell mass center of the equilibrium position and the center line of the channel increases with increasing the Reynolds number Re and reaches a peak, then decreases with increasing Re. The peak of Re is a decreasing function of the swelling ratio ($s^{*}<1.0)$. The cell membrane energy of the equilibrium position is an increasing function as Re increases. The slipper-shaped cell is more stable than the parachute-shaped one in the sense that the energy stored in the former is lower than that in the latter. For a given Re, the bigger the swelling ratio ($s^{*}<1.0)$, the lower the cell membrane energy.

Using Langevin dynamics simulations we investigate the self-assembly of colloidal particles in two dimensions interacting via an isotropic potential, which comprises both a hard-core repulsion and an additional softened square-well potential of controllable width $\alpha$. In dilute concentrations, the particles assemble in small clusters with a well-defined crystalline order. For small values of $\alpha$ the particles form triangular lattices. As $\alpha$ is increased, more particles can be captured by the potential well giving rise to different crystalline symmetries and the structural phase transitions between them. The main structures observed are triangular, square, and a mixture of square and triangular cells forming an Archimedean tiling. In the concentrated regime the particles form a single percolated cluster with essentially the same orderings at the same ranges of $\alpha$ values as observed in the dilute regime, thus showing that cluster boundary effects have a minor influence on the cluster crystal symmetry. By using energy analysis and geometry arguments we discuss how the different observed structures minimize the system energy at different values of $\alpha$.

Large temperature discontinuities were recently measured at a solid-liquid interface during heat transport processes. These observations suggest that when heat flows between two phases, the interface is not well characterized by assuming thermal equilibrium. This can be of importance in rapid solidification processes. In this paper we consider a planar front model that solidifies from its undercooled melt. We use a generalized interfacial boundary condition that includes nonlinear kinetic effects and allows for a temperature discontinuity. The effects of the new boundary condition on the solidification rates and the temperature profile are reported as a function of time. Our analysis shows that the undercooling regime where constant phase-front velocities are observed at steady states (traveling-wave solutions) are unaffected by the new boundary conditions. These solutions arise when the Stephan number is larger than 1. On the other hand, the solidification rates and the steady-state velocities are greatly affected by the assumed conditions at the interface. Incorporation of an interface thermal resistance, or Kapitza resistance, generates temperature discontinuities at the interface, leads to reduced solidification rates and the Mullins-Sekerka instability arises at longer wavelengths deformation of the planar front.

For 4-cyano-3-fluorophenyl 4-butylbenzoate, a glass former giving glass of nematic phase at ambient pressure and after rapid pressurizing, isothermal studies of complex dielectric permittivity vs pressure were performed near room temperature. In the previous isobaric experiment, on cooling the nematic phase two super-Arrhenius α relaxations, ascribed to the reorientations of molecules around short axes (main process) and precession of long molecular axes, and β relaxation related to intramolecular motions were found. In the present isothermal experiments nematic-smectic phase transition was induced by increasing pressure. Linear pressure dependence of the logarithm of the dielectric relaxation time gives activation volume of about 70 cm${}^3$/mole for liquid crystalline phases and 50 cm${}^3$/mole for the isotropic phase. The time-temperature-pressure superposition principle for the α-relaxation process was found to be valid (i.e., a single master curve can be obtained by superpositioning dielectric loss curves measured at various temperatures and pressures).

We present a generalized approach to compute the shape and internal structure of two-dimensional nematic domains. By using conformal mappings, we are able to compute the director field for a given domain shape that we choose from a rich class, which includes drops with large and small aspect ratios and sharp domain tips as well as smooth ones. Results are assembled in a phase diagram that for given domain size, surface tension, anchoring strength, and elastic constant shows the transitions from a homogeneous to a bipolar director field, from circular to elongated droplets, and from sharp to smooth domain tips. We find a previously unaccounted for regime, where the drop is nearly circular, the director field bipolar, and the tip rounded. We also find that bicircular director fields, with foci that lie outside the domain, provide a remarkably accurate description of the optimal director field for a large range of values of the various shape parameters.

We present a Monte Carlo study of the dispersibility of nanoparticles in polymer melts based on the relative entropic contributions of particles and polymer chains. Our model predictions are in terms of the particle diameter $d$ and the chain statistical segment length $\ell$. In the limit of small ($d=\ell$) particles, a good dispersion is predicted, as the high entropy contribution of the small particles largely offsets the loss in polymer chain entropy. This is not the case, however, at larger $d\approx 3\ell$ and particle segregation at the surfaces of thin polymer films is observed. That model prediction is in good agreement with experimental observation for systems with little or no enthalpic interaction between polymer and particles.

By means of the concept of the balanced estimation of diffusion entropy, we evaluate the reliable scale invariance embedded in different sleep stages and stride records. Segments corresponding to waking, light sleep, rapid eye movement (REM) sleep, and deep sleep stages are extracted from long-term electroencephalogram signals. For each stage the scaling exponent value is distributed over a considerably wide range, which tell us that the scaling behavior is subject and sleep cycle dependent. The average of the scaling exponent values for waking segments is almost the same as that for REM segments ($\sim$$0.8$). The waking and REM stages have a significantly higher value of the average scaling exponent than that for light sleep stages ($\sim$$0.7$). For the stride series, the original diffusion entropy (DE) and the balanced estimation of diffusion entropy (BEDE) give almost the same results for detrended series. The evolutions of local scaling invariance show that the physiological states change abruptly, although in the experiments great efforts have been made to keep conditions unchanged. The global behavior of a single physiological signal may lose rich information on physiological states. Methodologically, the BEDE can evaluate with considerable precision the scale invariance in very short time series ($\sim$${10}^2$), while the original DE method sometimes may underestimate scale-invariance exponents or even fail in detecting scale-invariant behavior. The BEDE method is sensitive to trends in time series. The existence of trends may lead to an unreasonably high value of the scaling exponent and consequent mistaken conclusions.

An explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. The present paper reports on mean-field approximations to determine the critical coupling of such explosive synchronization. It has been verified that the equation obtained for the critical coupling has an inverse dependence on the network average degree. This expression differs from those whose frequency distributions are unimodal and even. In this case, the critical coupling depends on the ratio between the first and second statistical moments of the degree distribution. Numerical simulations were also conducted to verify our analytical results.

The transition to turbulence in a flow of semidilute shear-thinning viscoelastic solution with a moderate elasticity was investigated in the Taylor-Couette system with a fixed outer cylinder. As the cylinder rotation frequency increases, the base flow bifurcates to a pattern of ribbons and then to disordered oscillations (DOs). Within these DOs, we have identified two particular regimes of turbulence: spatiotemporal intermittency (STI) followed by inertioelastic turbulence (IET) with a net transition between them. This transition is evidenced by a sharp peak of a diffusion velocity and a Weissenberg number.

The dispersion of passive scalars and inertial particles in a turbulent flow can be described in terms of probability density functions (PDFs) defining the statistical distribution of relevant scalar or particle variables. The construction of transport equations governing the evolution of such PDFs has been the subject of numerous studies, and various authors have presented formulations for this type of equation, usually referred to as a kinetic equation. In the literature it is often stated, and widely assumed, that these PDF kinetic equation formulations are equivalent. In this paper it is shown that this is not the case, and the significance of differences among the various forms is considered. In particular, consideration is given to which form of equation is most appropriate for modeling dispersion in inhomogeneous turbulence and most consistent with the underlying particle equation of motion. In this regard the PDF equations for inertial particles are considered in the limit of zero particle Stokes number and assessed against the fully mixed (zero-drift) condition for fluid points. A long-standing question regarding the validity of kinetic equations in the fluid-point limit is answered; it is demonstrated formally that one version of the kinetic equation (derived using the Furutsu-Novikov method) provides a model that satisfies this zero-drift condition exactly in both homogeneous and inhomogeneous systems. In contrast, other forms of the kinetic equation do not satisfy this limit or apply only in a limited regime.

We present a theoretical polygon construction analysis of two-dimensional melting and freezing transitions in many-particle Yukawa systems. Two-dimensional melting transitions can be characterized as proliferation of geometrical defects—nontriangular polygons, obtained by removing unusually long bonds in the triangulation of particle positions. A liquid state is characterized by the temperature-independent number of quadrilaterals and linearly increasing number of pentagons. We analyze specific types of vertices, classified by the type and distribution of polygons surrounding them, and determine temperature dependencies of their concentrations. Solid-liquid phase transitions are followed by the peaks in the abundances of certain types of vertices.

We investigate the efficiency at the maximum power output (EMP) of an irreversible Carnot engine performing finite-time cycles between two reservoirs at constant temperatures $T_h$ and $T_c$ $(<T_h)$, taking into account the internally dissipative friction in two “adiabatic” processes. The EMP is retrieved to be situated between ${\eta }_{{}_C}/2$ and ${\eta }_{{}_C}/(2-{\eta }_{{}_C})$, with ${\eta }_{{}_C}=1-T_c/T_h$ being the Carnot efficiency, whether the internally dissipative friction is considered or not. When dissipations of two “isothermal” and two “adiabatic” processes are symmetric, respectively, and the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation, the Curzon-Ahlborn (CA) efficiency ${\eta }_{{}_{CA}}=1-\sqrt{T_c/T_h}$ is derived.

We study the spontaneous formation of granular towers produced when dry sand is poured on a wet sand bed. When the liquid content of the bed exceeds a threshold value $W^{☆}$, the impacting grains have a nonzero probability to stick on the wet grains due to instantaneous liquid bridges created during the impact. The trapped grains become wet by the capillary ascension of water and the process continues, giving rise to stable narrow towers. The growth velocity is determined by the surface liquid content which decreases exponentially as the tower height augments. This self-assembly mechanism (only observed in the funicular and capillary regimes) could theoretically last while the capillary rise of water is possible; however, the structure collapses before reaching this limit. The collapse occurs when the weight of the tower surpasses the cohesive stress at its base. The cohesive stress increases as the liquid content of the bed is reduced. Consequently, the highest towers are found just above $W^{☆}$.

A linear stability analysis is presented to understand the instabilities that arise in an elastic bilayer, consisting of a very thin bottom layer (thickness $<$ 100 nm) that acts as a wetting film and a top layer that acts as an adhesive film, when placed in contact proximity with an external rigid contactor. Depending on whichever layer is more compliant, “squeezing modes” of instability with a variety of length scales ranging from $\ll$$3h$ to $\gg$$3h$ ($h$: bilayer thickness) are found to be possible. The least length scales obtained are $0.1h$. The squeezing instabilities are, however, accompanied by delamination of the film-film interface. The instability length scales, the strength of interactions required, and the delamination decrease as the compliance of the top film increases. Surface tension effects are found to have a stabilizing influence which increases the instability length scales and decreases the degree of delamination at the cost of high interaction penalty.

We consider a discrete agent-based model on a one-dimensional lattice and a two-dimensional square lattice, where each agent is a dimer occupying two sites. Agents move by vacating one occupied site in favor of a nearest-neighbor site and obey either a strict simple exclusion rule or a weaker constraint that permits partial overlaps between dimers. Using indicator variables and careful probability arguments, a discrete-time master equation for these processes is derived systematically within a mean-field approximation. In the continuum limit, nonlinear diffusion equations that describe the average agent occupancy of the dimer population are obtained. In addition, we show that multiple species of interacting subpopulations give rise to advection-diffusion equations. Averaged discrete simulation data compares very well with the solution to the continuum partial differential equation models. Since many cell types are elongated rather than circular, this work offers insight into population-level behavior of collective cellular motion.

We study the statistical properties of the Kelvin waves propagating along quantized superfluid vortices driven by the Gross-Pitaevskii equation. No artificial forcing or dissipation is added. Vortex positions are accurately tracked. This procedure directly allows us to obtain the Kevin-wave occupation-number spectrum. Numerical data obtained from long time integration and ensemble average over initial conditions support the spectrum proposed in L'vov and Nazarenko [JETP Lett. 91, 428 (2010)]. Kelvin-wave modes in the inertial range are found to be Gaussian as expected by weak-turbulence predictions. Finally the dissipative range of the Kelvin-wave spectrum is studied. Strong non-Gaussian fluctuations are observed in this range.

In the spirit of behavioral finance, we study the process of opinion formation among investors using a variant of the two-dimensional voter model with a tunable social temperature. Further, a feedback acting on the temperature is introduced, such that social temperature reacts to market imbalances and thus becomes time dependent. In this toy market model, social temperature represents nervousness of agents toward market imbalances representing speculative risk. We use the knowledge about the discontinuous generalized voter model phase transition to determine critical fixed points. The system exhibits metastable phases around these fixed points characterized by structured lattice states, with intermittent excursions away from the fixed points. The statistical mechanics of the model is characterized, and its relation to dynamics of opinion formation among investors in real markets is discussed.

We report an experimental and numerical characterization of three-dimensional acoustic streaming behavior in small droplets of volumes (1–30 μl) induced by surface acoustic wave (SAW). We provide a quantitative evidence of the existence of strong nonlinear nature of the flow inertia in this SAW-driven flow over a range of the newly defined acoustic parameter $F_{\mathrm{NA}}=\frac{F\lambda }{(\sigma /R_d)}\ge 0.01$, which is a measure of the strength of the acoustic force to surface tension, where $F$ is the acoustic body force, λ is the SAW wavelength, σ is the surface tension, and $R_d$ is the droplet radius. In contrast to the widely used Stokes model of acoustic streaming, which generally ignores such a nonlinearity, we identify that the full Navier-Stokes equation must be applied to avoid errors up to 93$\%$ between the computed streaming velocities and those from experiments as in the nonlinear case. We suggest that the Stokes model is valid only for very small acoustic power of $\le 1$ μW ($F_{\mathrm{NA}}<0.002$). Furthermore, we demonstrate that the increase of $F_{\mathrm{NA}}$ above 0.45 induces not only internal streaming, but also the deformation of droplets.

The effective increase of the critical density associated with the interaction of relativistically intense laser pulses with overcritical plasmas, known as self-induced transparency, is revisited for the case of circular polarization. A comparison of particle-in-cell simulations to the predictions of a relativistic cold-fluid model for the transparency threshold demonstrates that kinetic effects, such as electron heating, can lead to a substantial increase of the effective critical density compared to cold-fluid theory. These results are interpreted by a study of separatrices in the single-electron phase space corresponding to dynamics in the stationary fields predicted by the cold-fluid model. It is shown that perturbations due to electron heating exceeding a certain finite threshold can force electrons to escape into the vacuum, leading to laser pulse propagation. The modification of the transparency threshold is linked to the temporal pulse profile, through its effect on electron heating.