In this paper we consider the electrophoresis of a functionalized nanoparticle in electrolyte solution. The undertaken particle is comprised of a rigid inner core encapsulated with a layer of dielectric liquid (e.g., oil or lipid layer), which is immiscible to the bulk aqueous medium. The peripheral liquid layer of the undertaken nanoparticle contains mobile charges due to presence of solubilized surfactants. The mobile electrolyte ions can penetrate across the peripheral layer depending on the difference in the Born energy of the both phases. Such types of nanoparticles have received substantial attention due to their widespread applications in biomedical research. The electric double layer (EDL) is governed by the linearized Poisson-Boltzmann equation under a low potential limit and the electroosmotic flow field is governed by modified Stokes equation. We adopt the flat-plate formalism to obtain the closed analytical expression for the electrophoretic mobility of the undertaken particle under a thin EDL approximation. The dependence of electrophoretic mobility on the pertinent parameters is also illustrated.

Both ${}^1\mathrm{H}$ and ${}^{13}\mathrm{C}$ NMR spectra have been obtained in a static magnetic field of 23.5 T on a bent-shaped dimer molecule, $1^{\prime \prime },7^{\prime \prime }$-bis(4-cyanobiphenyl-4′-yl) nonane (CB9CB), which shows the sequence of liquid crystal phases twist-bend nematic, $N_{\mathrm{TB}}$, and uniaxial nematic, $N_{\mathrm{U}}$, before entering the isotropic phase. The ${}^1\mathrm{H}$ spectra are used to locate the temperature at which the sample melts to form a twist-bend nematic, $T_{Cr{N}_{\mathrm{TB}}}$, and then $T_{N_{U}I}$ when the isotropic phase is entered, both in a magnetic field of 23.5 T, and to compare these with those measured at the Earth's field. The differences between these transition temperatures are found to be zero within the error in their measurement, in stark contrast to previous measurements by Salili et al. [Phys. Rev. Lett. 116, 217801 (2016)]. In the isotropic phase in the presence of the field the sample exists in a paranematic phase in which the molecules of CB9CB are partially ordered. The ${}^1\mathrm{H}$ and ${}^{13}\mathrm{C}$ NMR spectra in the paranematic phase are used to measure the critical temperature T* below which this phase is unstable. The spectra are also used to study the structure, molecular orientational order, and distribution of molecular conformations in the paranematic phase.

Thin film deposition with particle transport mixing collimated and diffusive components and with barriers for adsorption are studied using numerical simulations and scaling approaches. Biased random walks on lattices are used to model the particle flux and the analogy with advective-diffusive transport is used to define a Peclet number $\mathcal{P}$ that represents the effect of the bias towards the substrate. An aggregation probability that relates the rates of adsorption and of the dominant transport mechanism plays the role of a Damkohler number $\mathcal{D}$, where $\mathcal{D}\lesssim 1$ is set to describe moderate to low adsorption rates. Very porous deposits with sparse branches are obtained with $\mathcal{P}\ll 1$, whereas low porosity deposits with large height fluctuations at short scales are obtained with $\mathcal{P}\gg 1$. For $\mathcal{P}\gtrsim 1$ in which the field bias is intense, an initial random deposition is followed by Kardar-Parisi-Zhang (KPZ) roughening. As the transport is displaced from those limiting conditions, the interplay of the transport and adsorption mechanisms establishes a condition to produce films with the smoothest surfaces for a constant deposited mass: with low adsorption barriers, a balance of random and collimated flux is required, whereas for high barriers the smoothest surfaces are obtained with $\mathcal{P}\sim {\mathcal{D}}^{1/2}$. For intense bias, the roughness is shown to be a power law of $\mathcal{P}/\mathcal{D}$, whose exponent depends on the growth exponent $\beta$ of the KPZ class, and the porosity has a superuniversal scaling as ${\left(\mathcal{P}/\mathcal{D}\right)}^{-1/3}$. We also study a generalized ballistic deposition model with slippery particle aggregation that shows the universality of these relations in growth with dominant collimated flux, particle adsorption at any point of the deposit, and negligible adsorbate diffusion, in contrast with the models where aggregation is restricted to the outer surface.

Acoustic waves can generate steady streaming within a fluid owing to the generation of viscous boundary layers near walls of typical thickness $\delta$. In microchannels, the acoustic wavelength $\lambda$ is adjusted to twice the channel width $w$ to ensure a resonance condition, which implies the use of MHz transducers. Recently, though, intense acoustic streaming was generated by acoustic waves of a few kHz (hence with $\lambda \gg w$), owing to the presence of sharp-tipped structures of curvature radius at the tip $r_c$ smaller than $\delta$. The present study quantitatively investigates this sharp-edge acoustic streaming via the direct resolution of the full Navier-Stokes equation using the finite element method. The influence of $\delta ,r_c$, and viscosity $\nu$ on the acoustic streaming performance is quantified. Our results suggest choices of operating conditions and geometrical parameters, in particular the dimensionless tip radius of curvature $r_c/\delta$ and the liquid viscosity.

Microorganisms and artificial microswimmers often need to swim through environments that are more complex than purely viscous liquids in their natural habitats or operational environments, such as gel-like mucus, wet soil, and aquifers. The question of how the properties of these complex environments affect locomotion has attracted considerable recent attention. In this paper, we present a theoretical model to examine how the additional resistance due to the network of stationary obstacles in a porous medium affects helical locomotion. Here, we focus on helical locomotion for its ubiquity as a propulsion mechanism adopted by many swimming bacteria and artificial microswimmers. We show that the additional resistance can have qualitatively different effects on various scenarios of helical locomotion: (1) a helical propeller driven by an external torque, (2) a free swimming bacterium consisting of a helical flagellum and a head, and (3) a cargo-carrying helical propeller driven by an external torque. Our results elucidate the subtle and significant differences between torqued helical propulsion versus force-free and torque-free swimming in a porous medium. We also remark on the limitations as well as potential connections of our results with experimental measurements of bacterial swimming speeds in polymeric solutions.

Dusty plasma experiments can be performed quite easily in a strong coupling regime. In our previous work [V. S. Dharodi, S. K. Tiwari, and A. Das, Physics of Plasmas 21, 073705 (2014)], we numerically explored such plasmas with constant density and observed the transverse shear (TS) waves from the rotating vortex. Laboratory dusty plasmas are good examples of homogeneous plasmas; however, heterogeneity (e.g., density, temperature, and charge) may be due to the existence of voids, different domains with different orientations, presence of external forces like magnetic and/or electric, size or charge imbalance, etc. Here, we examine how the density heterogeneity in dusty plasmas responds to the circularly rotating vortex monopoles, specifically, smooth and sharp cutoff. For this purpose, we have carried out a series of two-dimensional fluid simulations in the framework of the incompressible generalized hydrodynamics fluid model. The rotating vortices are placed at the interface of two incompressible fluids with different densities. The smooth rotating vortex causes two effects: First, the regions are stretched to form the spiral density waves; second, there is a shear in flows which consequently induces the TS waves. The TS waves move slower in the denser side than in the lighter side. The difference in speeds of the waves induces the net flow of the medium towards the lower density side. We notice that the spiral density arms are distinguishable in the early time while later they get smeared out. In sharp flows, the interplay between the TS waves and the vortices of Kelvin-Helmholtz instability distorts the formation of the regular spiral density arms around the rotor.

Two-dimensional three-vector ($d=2,n=3$) lattice model of a liquid crystal (LC) system with order parameter space ($\mathcal{R}$) described by the fundamental group ${\mathrm{\Pi }}_1\left(\mathcal{R}\right)=Z_2$ was recently investigated based on non-Boltzmann Monte Carlo simulations. Its results indicated that the system did not undergo a topological transition condensing to a low temperature critical state as was reported earlier. Instead, a crossover to a nematic phase was observed, induced by the onset of a competing relevant length scale. This mechanism is further probed here by assigning a more restrictive $\mathcal{R}$ symmetry with ${\mathrm{\Pi }}_1\left(\mathcal{R}\right)=\mathbb{Q}$ (the discrete and non-Abelian group of quaternions), thus engaging the three spin degrees in the formation of point topological defects (disclinations). The results reported here indicate that such a choice of symmetry of the Hamiltonian with suitable model parameters leads to a defect-mediated transition to a low-temperature phase with topological order. It is characterized by a line of critical points with quasi-long-range order of its three spin degrees. The associated temperature-dependent power-law exponent decreases progressively and vanishes linearly as temperature tends to zero. The high-temperature disordered phase shows exponential spin correlations and their temperature-dependent lengths exhibit an essential singular divergence as the system approaches the topological transition point. Biaxial LC models have the required $\mathcal{R}$ symmetry owing to their tensor orientational orders and are suggested to serve as prototype examples to exhibit topological transition in ($d=2,n=3$) lattice models.

The Kitaev model on the honeycomb lattice has been receiving substantial attention due to the discovery of quantum spin liquid state associated with this model. Consequently, its classical partners such as the Kitaev-Heisenberg (KH) model and associated phase transitions become concerned. Specifically, an intermediate Kosterlitz-Thouless (KT) phase engaged in the transition from the high-temperature ($T$) disordered state to the low-$T$ sixfold degenerate state is predicted in the isotropic KH model [Phys. Rev. Lett. 109, 187201 (2012)], but so far no sufficient experimental proof has been reported. In this work, we consider an essential extension of this KH model on the honeycomb lattice by including the Kitaev exchange anisotropy that is non-negligible in realistic materials. The associated phase transitions are thus investigated using the Monte Carlo simulations. It is found that such an anisotropy will result in a degradation of the sixfold degeneracy of the ground state in the isotropic KH model down to the fourfold or twofold degenerate ground state, and the finite-$T$ phase transitions will also be modified remarkably. Interestingly, the intermediate KT phase can be suppressed by this Kitaev exchange anisotropy. This work thus provides a more realistic description of the physics ingredient with the KH model and presents a possible explanation on absence of the intermediate phase in real materials where the Kitaev exchange anisotropy can be more or less available.

Soft matter systems are renowned for being able to display complex emerging phenomena such as clustering phases. Recently, a surprising quantum phase transition has been revealed in a one-dimensional (1D) system composed of bosons interacting via a pairwise soft potential in the continuum. It was shown that the spatial coordinates undergoing two-particle clustering could be mapped into quantum spin variables of a 1D transverse Ising model. In this work we investigate the manifestation of an analogous critical phenomenon in 1D classical fluids of soft particles in the continuum. In particular, we study the low-temperature behavior of three different classical models of 1D soft matter, whose interparticle interactions allow for clustering. The same string variables highlight that, at the commensurate density for the two-particle cluster phase, the peculiar pairing of neighboring soft particles can be nontrivially mapped onto a 1D discrete classical Ising model. We also observe a related phenomenon, namely the presence of an anomalous peak in the low-temperature specific heat, thus indicating the emergence of Schottky phenomenology in a nonmagnetic fluid.

The Kuramoto model, which serves as a paradigm for investigating synchronization phenomena of oscillatory systems, is known to exhibit second-order, i.e., continuous, phase transitions in the macroscopic order parameter. Here we generalize a number of classical results by presenting a general framework for analytically capturing the critical scaling properties of the order parameter at the onset of synchronization. Using a self-consistent approach and constructing a characteristic function, we identify various phase transitions toward synchrony and establish scaling relations describing the asymptotic dependence of the order parameter on the coupling strength near the critical point. We find that the geometric properties of the characteristic function, which depends on the natural frequency distribution, determine the scaling properties of order parameter above criticality.

Directional locking occurs when a particle moving over a periodic substrate becomes constrained to travel along certain substrate symmetry directions. Such locking effects arise for colloids and superconducting vortices moving over ordered substrates when the direction of the external drive is varied. Here we study the directional locking of run-and-tumble active matter particles interacting with a periodic array of obstacles. In the absence of an external biasing force, we find that the active particle motion locks to various symmetry directions of the substrate when the run time between tumbles is large. The number of possible locking directions depends on the array density and on the relative sizes of the particles and the obstacles. For a square array of large obstacles, the active particle only locks to the $x$, $y$, and ${45}^{\circ }$ directions, while for smaller obstacles, the number of locking angles increases. Each locking angle satisfies $\theta =arctan(p/q)$, where $p$ and $q$ are integers, and the angle of motion can be measured using the ratio of the velocities or the velocity distributions in the $x$ and $y$ directions. When a biasing driving force is applied, the directional locking behavior is affected by the ratio of the self-propulsion force to the biasing force. For large biasing, the behavior resembles that found for directional locking in passive systems. For large obstacles under biased driving, a trapping behavior occurs that is nonmonotonic as a function of increasing run length or increasing self-propulsion force, and the trapping diminishes when the run length is sufficiently large.

It is now well established that microswimmers can be sorted or segregated fabricating suitable microfluidic devices or using external fields. A natural question is how these techniques can be employed for dividing swimmers of different motility. In this paper, using numerical simulations in the dilute limit, we investigate how motility parameters (time of persistence and velocity) impact the narrow-escape time of active particles from circular domains. We show that the escape time undergoes a crossover between two asymptotic regimes. The control parameters of the crossover is the ratio between the persistence length of the active motion and the typical length scale of the circular domain. We explore the possibility of taking advantage of this finding for sorting active particles by motility parameters.

Turbulent mixing is studied in the Lagrangian framework with an approach based on the complex network formalism. We consider the motion of passive, noninertial particles inside a turbulent channel simulated at ${\text{Re}}_{\tau }=950$. The time-dependent network is built to evaluate the transfer of tracers between thin wall-parallel layers which partition the channel in the wall-normal direction. By doing so, we are able to assess the spatial and temporal complexities arising from turbulence dynamics and their influence on the mixing process. This approach highlights the effects of small-scale features of turbulent flow structures and also the larger scale effects determined by wall-induced anisotropy. Complex networks, coupled to the Lagrangian description of turbulence, are effective in providing novel insights into inhomogeneous turbulence and mixing.

Statistical properties of circulation encode relevant information about the multiscale structure of turbulent cascades. Recent massive computational efforts have posed challenging theoretical issues, such as the dependence of circulation moments upon Reynolds numbers and length scales, and the specific shape of the heavy-tailed circulation probability distribution functions. We address these focal points in an investigation of circulation statistics for planar cuts of three-dimensional flows. The model introduced here borrows ideas from the structural approach to turbulence, whereby turbulent flows are depicted as dilute vortex gases, combined with the standard Obukhov-Kolmogorov phenomenological framework of small-scale intermittency. We are able to reproduce, in this way, key statistical features of circulation, in close agreement with empirical observations compiled from direct numerical simulations.

We use computer simulations to investigate the extended phase diagram of a supercooled liquid linearly coupled to a quenched reference configuration. An extensive finite-size scaling analysis demonstrates the existence of a random-field Ising model (RFIM) critical point and of a first-order transition line, in agreement with recent field-theoretical approaches. The dynamics in the vicinity of this critical point resembles the peculiar activated scaling of RFIM-like systems, and the overlap autocorrelation displays a logarithmic stretching. Our study demonstrates RFIM criticality in the thermodynamic limit for a three-dimensional supercooled liquid at equilibrium.

On the basis of the latest advances in Mayer's cluster-based approach, the reduced forms of the well-known virial expansions are derived in terms of scaled reducible and irreducible cluster integrals. This transformation minimizes the dependence on temperature and the effect of parameters specific for each thermodynamic system, thus making the resulting reduced expansions indeed universal on the quantitative level. In particular, the scaling of isotherms and saturation curves for various systems (the Lennard-Jones model, different lattice gases, and real substances with simple nonpolar molecules as well as complex polar ones) confirms the approximate universality of the proposed reduced variables for temperature, pressure, and density at subcritical gaseous states up to the saturation point. In addition, the temperature dependence of the correspondingly scaled second virial coefficients also appears similar for various systems.

Thermoremanent magnetization data for the three-dimensional Edwards-Anderson (EA) spin glass are generated using the waiting time method as a simulational tool and interpreted using record dynamics. We verify that clusters of contiguous spins are overturned by quakes, nonequilibrium events linked to record-sized energy fluctuations, and we show that quaking is a log-Poisson process, i.e., a Poisson process whose average depends on the logarithm of the system age, counted from the initial quench. Our findings compare favorably with experimental thermoremanent magnetization findings and with the spontaneous fluctuation dynamics of the EA model. The logarithmic growth of the size of overturned clusters is related to similar experimental results and to the growing length scale of the spin-spin spatial correlation function. The analysis buttresses the applicability of the waiting time method as a simulational tool, and of record dynamics as a coarse-graining method for aging dynamics.

We study how a chimera state in a one-dimensional medium of nonlocally coupled oscillators responds to a homogeneous in space periodic in time external force. On a macroscopic level, where a chimera can be considered as an oscillating object, forcing leads to entrainment of the chimera's basic frequency inside an Arnold tongue. On a mesoscopic level, where a chimera can be viewed as an inhomogeneous, stationary, or nonstationary pattern, strong forcing can lead to regularization of an unstationary chimera. On a microscopic level of the dynamics of individual oscillators, forcing outside of the Arnold tongue leads to a multiplateau state with nontrivial locking properties.

Inferring causal relations from time series measurements is an ill-posed mathematical problem, where typically an infinite number of potential solutions can reproduce the given data. We explore in depth a strategy to disambiguate between possible underlying causal networks by perturbing the network, where the forcings are either targeted or applied at random. The resulting transient dynamics provide the critical information necessary to infer causality. Two methods are shown to provide accurate causal reconstructions: Granger causality (GC) with perturbations, and our proposed perturbation cascade inference (PCI). Perturbed GC is capable of inferring smaller networks under low coupling strength regimes. Our proposed PCI method demonstrated consistently strong performance in inferring causal relations for small (2–5 node) and large (10–20 node) networks, with both linear and nonlinear dynamics. Thus, the ability to apply a large and diverse set of perturbations to the network is critical for successfully and accurately determining causal relations and disambiguating between various viable networks.