Superparamagnetic colloids gather depending on the magnitude of the magnetic field applied, forming chains and ribbons in a quasi-two-dimensional chamber. The results presented in this work are in good agreement with recent experimental multistable data for the mean length of the aggregates in thermodynamic equilibrium.

A long time ago, Brochard and de Gennes predicted the possibility of significantly decreasing the critical magnetic field of the Fredericksz transition (the magnetic Fredericksz threshold) in a mixture of nematic liquid crystals and ferromagnetic particles, the so-called ferronematics. This phenomenon is rarely measured to be large, due to soft homeotropic anchoring induced at the nanoparticle surface. Here we present an optical study of the magnetic Fredericksz transition combined with a light scattering study of the classical nematic liquid crystal: the pentylcyanobiphenyl (5CB), doped with 6 nm diameter magnetic and nonmagnetic nanoparticles. Surprisingly, for both nanoparticles, we observe at room temperature a net decrease of the threshold field of the Fredericksz transition at low nanoparticle concentrations, which appears associated with a coating of the nanoparticles by a brush of polydimethylsiloxane copolymer chains inducing planar anchoring of the director on the nanoparticle surface. Moreover, the magnetic Fredericksz threshold exhibits nonmonotonic behavior as a function of the nanoparticle concentration for both types of nanoparticles, first decreasing down to a value from 23% to 31% below that of pure 5CB, then increasing with a further increase of nanoparticle concentration. This is interpreted as an aggregation starting at around 0.02 weight fraction that consumes more isolated nanoparticles than those introduced when the concentration is increased above $c=0.05$ weight fraction (volume fraction $3.5\times {10}^{-2}$). This shows the larger effect of isolated nanoparticles on the threshold with respect to aggregates. From dynamic light scattering measurements we deduced that, if the decrease of the magnetic threshold when the nanoparticle concentration increases is similar for both kinds of nanoparticles, the origin of this decrease is different for magnetic and nonmagnetic nanoparticles. For nonmagnetic nanoparticles, the behavior may be associated with a decrease of the elastic constant due to weak planar anchoring. For magnetic nanoparticles there are non-negligible local magnetic interactions between liquid crystal molecules and magnetic nanoparticles, leading to an increase of the average order parameter. This magnetic interaction thus favors an easier liquid crystal director rotation in the presence of external magnetic field, able to reorient the magnetic moments of the nanoparticles along with the molecules.

The spreading of a cap-shaped spherical droplet of non-Newtonian power-law liquids, both shear-thickening and shear-thinning liquids, that completely wet a spherical substrate is theoretically investigated in the capillary-controlled spreading regime. The crater-shaped droplet model with the wedge-shaped meniscus near the three-phase contact line is used to calculate the viscous dissipation near the contact line. Then the energy balance approach is adopted to derive the equation that governs the evolution of the contact line. The time evolution of the dynamic contact angle $\theta$ of a droplet obeys a power law $\theta \sim t^{-\alpha }$ with the spreading exponent $\alpha$, which is different from Tanner's law for Newtonian liquids and those for non-Newtonian liquids on a flat substrate. Furthermore, the line-tension dominated spreading, which could be realized on a spherical substrate for late-stage of spreading when the contact angle becomes low and the curvature of the contact line becomes large, is also investigated.

We study the effect of hindered aggregation on the island formation process in a one- (1D) and two-dimensional (2D) point-island model for epitaxial growth with arbitrary critical nucleus size $i$. In our model, the attachment of monomers to preexisting islands is hindered by an additional attachment barrier, characterized by length $l_a$. For $l_a=0$ the islands behave as perfect sinks while for $l_a\to \infty$ they behave as reflecting boundaries. For intermediate values of $l_a$, the system exhibits a crossover between two different kinds of processes, diffusion-limited aggregation and attachment-limited aggregation. We calculate the growth exponents of the density of islands and monomers for the low coverage and aggregation regimes. The capture-zone (CZ) distributions are also calculated for different values of $i$ and $l_a$. In order to obtain a good spatial description of the nucleation process, we propose a fragmentation model, which is based on an approximate description of nucleation inside of the gaps for 1D and the CZs for 2D. In both cases, the nucleation is described by using two different physically rooted probabilities, which are related with the microscopic parameters of the model ($i$ and $l_a$). We test our analytical model with extensive numerical simulations and previously established results. The proposed model describes excellently the statistical behavior of the system for arbitrary values of $l_a$ and $i=1$, 2, and 3.

We performed experiments combining three-dimensional x-ray diffraction and x-ray computed tomography to explore the relationship between microstructure and local force and strain during quasistatic granular compaction. We found that initial void space around a grain and contact coordination number before compaction can be used to predict regions vulnerable to above-average local force and strain at later stages of compaction. We also found correlations between void space around a grain and coordination number, and between grain stress and maximum interparticle force, at all stages of compaction. Finally, we observed grains that fracture to have an above-average initial local void space and a below-average initial coordination number. Our findings provide (1) a detailed description of microstructure evolution during quasistatic granular compaction, (2) an approach for identifying regions vulnerable to large values of strain and interparticle force, and (3) methods for identifying regions of a material with large interparticle forces and coordination numbers from measurements of grain stress and local porosity.

Stress concentration at a crack tip generates a solid structural transformation in its vicinity, the process zone. We argue that its formation represents a local phase transition described by a multicomponent order parameter. We derive a system of equations describing the dynamics of the order parameter driven by an inhomogeneous, time-dependent stress field in the solid and show that it exhibits a bifurcation. The latter corresponds to the emergence of a process zone characterized by the distribution of the order parameter localized in the vicinity of the crack tip. The emergence temperature $T_{*}$ considerably differs from the temperature of the bulk phase transformation $T_{\text{c}}$. We demonstrate that $T_{*}$ exhibits a universal behavior $T_{*}-T_{\text{c}}\sim K_I^{4/3}$, in terms of the stress intensity factor $K_I$, and that the zone universally vanishes upon achieving a critical velocity. These facts together give rise to a universal dynamic phase diagram.

Advent of nematic liquid crystal flows has attracted renewed attention in view of microfluidic transport phenomena. Among various transport processes, electro-osmosis stands as one of the efficient flow actuation mechanisms through narrow confinements. In the present study, we explore the electrically actuated flow of an ordered nematic fluid with ionic inclusions, taking into account the influences from surface-induced elasticity and electrical double layer (EDL) phenomena. Toward this, we devise the coupled flow governing equations from fundamental free-energy analysis, considering the contributions from first- and second-order elastic, dielectric, flexoelectric, charged surface polarization, ionic and entropic energies. The present study focuses on the influence of surface charge and elasticity effects in the resulting linear electro-osmosis through a slit-type microchannel whose surfaces are chemically treated to display a homeotropic-type weak anchoring state. An optical periodic stripe configuration of the nematic director has been observed, especially for higher electric fields, wherein the Ericksen number for the dynamic study is restricted to the order of unity. Contrary to the isotropic electrolytes, the EDL potential in this case was found to be dependent on the external field strength. Through a systematic investigation, we brought out the fact that the wavelength of the oscillating patterns is dictated mainly by the external field, while the amplitude depends on most of the physical variables ranging from the anchoring strength and the flexoelectric coefficients to the surface charge density and electrical double layer thickness.

We studied the nonequilibrium aging behavior of the random-field Ising model in three dimensions for various values of the disorder strength. This allowed us to investigate how the aging behavior changes across the ferromagnetic-paramagnetic phase transition. We investigated a large system size of $N={256}^3$ spins and up to ${10}^8$ Monte Carlo sweeps. To reach these necessary long simulation times, we employed an implementation running on Intel Xeon Phi coprocessors, reaching single-spin-flip times as short as 6 ps. We measured typical correlation functions in space and time to extract a growing length scale and corresponding exponents.

The scaling function $F\left(s\right)$ in detrended fluctuation analysis (DFA) scales as $F\left(s\right)\sim s^H$ for stochastic processes with Hurst exponent $H$. This scaling law is proven for stationary stochastic processes with $0<H<1$ and nonstationary stochastic processes with $1<H<2$. For $H<0.5$, it is observed that the asymptotic (power-law) autocorrelation function (ACF) scales as $\sim s^{1/2}$. It is also demonstrated that the fluctuation function in DFA is equal in expectation to (i) a weighted sum of the ACF and (ii) a weighted sum of the second-order structure function. These results enable us to compute the exact finite-size bias for signals that are scaling and to employ DFA in a meaningful sense for signals that do not exhibit power-law statistics. The usefulness is illustrated by examples where it is demonstrated that a previous suggested modified DFA will increase the bias for signals with Hurst exponents $1<H\le 1.5$. As a final application of these developments, an estimator $\widehat{F}\left(s\right)$ is proposed. This estimator can handle missing data in regularly sampled time series without the need of interpolation schemes. Under mild regularity conditions, $\widehat{F}\left(s\right)$ is equal in expectation to the fluctuation function $F\left(s\right)$ in the gap-free case.

We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a larger one, and also one trail may split into two. In addition, trails move diffusively. The model is defined by two parameters which quantify the fragmentation rate and the fragment size. In the long-time limit, the system reaches a steady state, and our focus is the limiting distribution of trail weights. We find that the density of trail weight has power-law tail $P\left(w\right)\sim w^{-\gamma }$ for small weight $w$. We obtain the exponent $\gamma$ analytically and find that it varies continuously with the two model parameters. The exponent $\gamma$ can be positive or negative, so that in one range of parameters small-weight trails are abundant and in the complementary range they are rare.

We study a random target searching performed by $N$ independent searchers in a $d$-dimensional domain of a large but finite volume. Considering the two initial distributions of searchers where searchers are either uniformly or point distributed, we estimate the mean time for the first of the searchers to reach the target and refer to it as searching time. The searching time for the uniformly distributed searchers exhibits a universal power-law dependence on $N$, irrespective of dimensionality and the target-to-domain size ratio. For point-distributed searching, the searching time has a logarithmic dependence on $N$ in the large $N$ limit, while in the small $N$ limit, it shows qualitatively different behaviors depending upon $r_0$, the initial distance of the searchers from a target. We obtain a diagram by comparing the searching times of the two initial distributions in the parameter space ($r_0,N$) and therein present the asymptotic lines separating three characteristic regions to explain numerical simulation results.

We extend the family of visibility algorithms to map scalar fields of arbitrary dimension into graphs, enabling the analysis of spatially extended data structures as networks. We introduce several possible extensions and provide analytical results on the topological properties of the graphs associated to different types of real-valued matrices, which can be understood as the high and low disorder limits of real-valued scalar fields. In particular, we find a closed expression for the degree distribution of these graphs associated to uncorrelated random fields of generic dimension. This result holds independently of the field's marginal distribution and it directly yields a statistical randomness test, applicable in any dimension. We showcase its usefulness by discriminating spatial snapshots of two-dimensional white noise from snapshots of a two-dimensional lattice of diffusively coupled chaotic maps, a system that generates high dimensional spatiotemporal chaos. The range of potential applications of this combinatorial framework includes image processing in engineering, the description of surface growth in material science, soft matter or medicine, and the characterization of potential energy surfaces in chemistry, disordered systems, and high energy physics. An illustration on the applicability of this method for the classification of the different stages involved in carcinogenesis is briefly discussed.

Many physical, biological, and social phenomena can be described by cascades taking place on a network. Often, the activity can be empirically observed, but not the underlying network of interactions. In this paper we offer three topological methods to infer the structure of any directed network given a set of cascade arrival times. Our formulas hold for a very general class of models where the activation probability of a node is a generic function of its degree and the number of its active neighbors. We report high success rates for synthetic and real networks, for several different cascade models.

We propose a mechanism for the homeostatic control of synapses along the ventral cord of Caenorhabditis elegans during development, based on a form of Turing pattern formation on a growing domain. C. elegans is an important animal model for understanding cellular mechanisms underlying learning and memory. Our mathematical model consists of two interacting chemical species, where one is passively diffusing and the other is actively trafficked by molecular motors, which switch between forward and backward moving states (bidirectional transport). This differs significantly from the standard mechanism for Turing pattern formation based on the interaction between fast and slow diffusing species. We derive evolution equations for the chemical concentrations on a slowly growing one-dimensional domain, and use numerical simulations to demonstrate the insertion of new concentration peaks as the length increases. Taking the passive component to be the protein kinase CaMKII and the active component to be the glutamate receptor GLR-1, we interpret the concentration peaks as sites of new synapses along the length of C. elegans, and thus show how the density of synaptic sites can be maintained.

We investigated pressure-driven transport of an immiscible binary system, constituted by two electrically conducting liquids, in a narrow fluidic channel under the influence of an externally applied magnetic field. The surface wettability was taken into account in the analysis considering that the walls of the channel are chemically treated to obtain various predefined contact angles as required for the study. Alterations in the capillary filling and wetting dynamics in the channel stemming from a complex interplay among different forces acting over the interface were investigated. It was shown that an alteration in the strength of the magnetic field leads to an alteration in the dynamics of the interface, which in turn, alters the filling and wetting dynamics nontrivially upon interaction with the surface tension force due to the wetted walls of the channel. It is emphasized that a contrast in properties of constituents of the binary system gives rise to an alteration in the forces being applied across the interface, leading to an intricate control over the filling and wetting dynamics for a given flow configuration and an applied field strength. We believe that the results obtained from this analysis may aid the design of microfluidic devices used for multiphase transport.

In this paper, to predict the dynamics behaviors of flow and mass transfer with adsorption phenomena in porous media at the representative elementary volume (REV) scale, a multiple-relaxation-time (MRT) lattice Boltzmann (LB) model for the convection-diffusion equation is developed to solve the transfer problem with an unsteady source term in porous media. Utilizing the Chapman-Enskog analysis, the modified MRT-LB model can recover the macroscopic governing equations at the REV scale. The coupled MRT-LB model for momentum and mass transfer is validated by comparing with the finite-difference method and the analytical solution. Moreover, using the MRT-LB method coupled with the linear driving force model, the fluid transfer and adsorption behaviors of the carbon dioxide in a porous fixed bed are explored. The breakthrough curve of adsorption from MRT-LB simulation is compared with the experimental data and the finite-element solution, and the transient concentration distributions of the carbon dioxide along the porous fixed bed are elaborated upon in detail. In addition, the MRT-LB simulation results show that the appearance time of the breakthrough point in the breakthrough curve is advanced as the mass transfer resistance in the linear driving force model increases; however, the saturation point is prolonged inversely.

We introduce a lattice gas implementation that is based on coarse-graining a molecular dynamics (MD) simulation. Such a lattice gas is similar to standard lattice gases, but its collision operator is informed by an underlying MD simulation. This can be considered an optimal lattice gas implementation because it allows for the representation of any system that can be simulated with MD. We show here that equilibrium behavior of the popular lattice Boltzmann algorithm is consistent with this optimal lattice gas. This comparison allows us to make a more accurate identification of the expressions for temperature and pressure in lattice Boltzmann simulations, which turn out to be related not only to the physical temperature and pressure but also to the lattice discretization. We show that for any spatial discretization, we need to choose a particular temporal discretization to recover the lattice Boltzmann equilibrium.

We develop statistical mechanics for stochastic growth processes and apply it to Laplacian growth by using its remarkable connection with a random matrix theory. The Laplacian growth equation is obtained from the variation principle and describes adiabatic (quasistatic) thermodynamic processes in the two-dimensional Dyson gas. By using Einstein's theory of thermodynamic fluctuations we consider transitional probabilities between thermodynamic states, which are in a one-to-one correspondence with simply connected domains occupied by gas. Transitions between these domains are described by the stochastic Laplacian growth equation, while the transitional probabilities coincide with a free-particle propagator on an infinite-dimensional complex manifold with a Kähler metric.

A mixture of hard squares, dimers, and vacancies on a square lattice is known to undergo a transition from a low-density disordered phase to a high-density columnar ordered phase. Along the fully packed square-dimer line, the system undergoes a Kosterliz-Thouless-type transition to a phase with power law correlations. We estimate the phase boundary separating the ordered and disordered phases by calculating the interfacial tension between two differently ordered phases within two different approximation schemes. The analytically obtained phase boundary is in good agreement with Monte Carlo simulations.

In this paper, we present extensive numerical simulations of an excitable medium to study the long-term dynamics of knotted vortex strings for all torus knots up to crossing number 11. We demonstrate that FitzHugh-Nagumo evolution preserves the knot topology for all the examples presented, thereby providing a field theory approach to the study of knots. Furthermore, the evolution yields a well-defined minimal length for each knot that is comparable to the ropelength of ideal knots. We highlight the role of the medium boundary in stabilizing the length of the knot and discuss the implications beyond torus knots. We also show that there is not a unique attractor within a given knot topology.