Pattern dynamics of density and velocity fields in segregation of fluid mixtures.

We present comprehensive numerical results from a study of model H, which describes phase separation kinetics in binary fluid mixtures. We study the pattern dynamics of both density and velocity fields in d = 2, 3. The density length scales show three distinct regimes, in accordance with analytical arguments. The velocity length scale shows a diffusive behavior. We also study the scaling behavior of the morphologies for density and velocity fields and observe dynamical scaling in the relevant correlation functions and structure factors. Finally, we study the effect of quenched random field disorder on spinodal decomposition in model H.

Segregation of fluids with polymer additives at domain interfaces: a dissipative particle dynamics study.

This paper investigates the phase separation kinetics of ternary fluid mixtures composed of a polymeric component (C) and two simple fluids (A and B) using dissipative particle dynamics simulations with a system dimensionality of d = 3. We model the affinities between the components to enable the settling of the polymeric component at the interface of fluids A and B. Thus, the system evolves to form polymer coated morphologies, enabling alteration of the fluids' interfacial properties. This manipulation can be utilized across various disciplines, such as the stabilization of emulsions and foams, rheological control, biomimetic design, and surface modification. We probe the effects of various parameters, such as the polymeric concentration, chain stiffness, and length, on the phase separation kinetics of the system. The simulation results show that changes in the concentration of flexible polymers exhibit perfect dynamic scaling for coated morphologies. The growth rate decreases as the polymeric composition is increased due to reduced surface tension and restricted connectivity between A- and B-rich clusters. Variations in the polymer chain rigidity at fixed composition ratios and degrees of polymerization slow the evolution kinetics of AB fluids marginally, although the effect is more pronounced for perfectly rigid chains. Whereas flexible polymer chain lengths at fixed composition ratios slow down the segregation kinetics of AB fluids slightly, varying the chain lengths of perfectly rigid polymers leads to a significant deviation in the length scale and dynamic scaling for the evolved coated morphologies. The characteristic length scale follows a power-law growth with a growth exponent ϕ that shows a crossover from the viscous to the inertial hydrodynamic regime, where the values of ϕ depend on the constraints imposed on the system.

Effect of amphiphilic polymers on phase separating binary mixtures: A DPD simulation study.

We present the phase separation dynamics of a binary (AB), simple fluid (SF), and amphiphilic polymer (AP) mixture using dissipative particle dynamics simulation at d = 3. We study the effect of different AP topologies, including block copolymers, ring block copolymers (RCP), and miktoarm star polymers, on the evolution morphologies, dynamic scaling functions, and length scale of the AB mixture. Our results demonstrate that the presence of APs leads to significantly different evolution morphologies in SF. However, the deviation from dynamical scaling is prominent, mainly for RCP. Typically, the characteristic length scale for SF follows the power law R(t) ∼ tϕ, where ϕ is the growth exponent. In the presence of high AP, we observe diffusive growth (ϕ → 1/3) at early times, followed by saturation in length scale (ϕ → 0) at late times. The extent of saturation varies with constraints imposed on the APs, such as topology, composition ratio, chain length, and stiffness. At lower composition ratios, the system exhibits inertial hydrodynamic growth (ϕ → 2/3) at asymptotic times without clearly exhibiting the viscous hydrodynamic regime (ϕ → 1) at earlier times in our simulations. Our results firmly establish the existence of hydrodynamic growth regimes in low surfactant-influenced phase separation kinetics of binary fluids and settle the related ambiguity in d = 3 systems.

Comparative study of functional outcomes of arthroscopic anterior cruciate ligament reconstruction using anteromedial portal and translateral all-inside technique.

Background: Anterior Cruciate Ligament (ACL) injuries are common in the active population of the Armed Forces. Symptomatic instability prompts individuals to seek a cure or a sheltered appointment. Despite the increasing numbers of ACL reconstructions performed, the outcomes have not been so spectacular with only a meager percentage of our patients returning to preinjury levels of activity. With the premise that an all-inside ACL reconstruction is likely to result in better functional outcomes, the aim of this study was to compare the short-term functional outcomes of a large consecutive series of patients undergoing ACL reconstruction using the translateral all-inside ACL reconstruction technique (AI) and standard anteromedial portal technique (AM) with a minimum follow-up of one year. Methods: A total of 240 patients with isolated ACL tear underwent ACL reconstruction via the AI or AM technique. Their preoperative and postoperative scores were compared to look for any significant differences in functional outcomes. Results: The two groups were matched for age, BMI, mechanism of injury, and interval from injury to surgery. There was no difference in their preoperative scores. Postoperatively, although there were significant improvements across both groups, there was no significant difference between the groups at any point of time. Conclusion: The AI technique has garnered interest in recent literature in addressing ACL injuries. This study found no discernible benefit of the AI technique when compared to the AM technique in terms of functionality following an ACL reconstruction at any point of time up to 1 year following surgery.

Domain growth in ferronematics: slaved coarsening, emergent morphologies and growth laws.

Ferronematics (FNs) are suspensions of magnetic nanoparticles in nematic liquid crystals (NLCs). They have attracted much experimental attention, and are of great interest both scientifically and technologically. There are very few theoretical studies of FNs, even in equilibrium. In this paper, we study the non-equilibrium phenomenon of domain growth after a thermal quench (or coarsening) in this coupled system. Our modeling is based on coupled time-dependent Ginzburg-Landau (TDGL) equations for two order parameters: the LC tensor order parameter Q, and the magnetization M. We consider both shallow and deep quenches from a high-temperature disordered phase. The system coarsens by the collision and annihilation of topological defects. We focus on slaved coarsening, where a disordered Q (or M) field is driven to coarsen by an ordered M (or Q) field. We present detailed results for the morphologies and growth laws, which exhibit unusual features purely due to the magneto-nematic coupling. To the best of our knowledge, this is the first study of non-equilibrium phenomena in FNs.

Photo-induced bond breaking during phase separation kinetics of block copolymer melts: a dissipative particle dynamics study.

Using a dissipative particle dynamics (DPD) simulation method, we study the phase separation dynamics in block copolymer (BCP) melts in d = 3, subjected to external stimuli such as light. An initial homogeneous BCP melt is rapidly quenched to a temperature T < Tc, where Tc is the critical temperature. We then allow the system to undergo alternate light "on" and "off" cycles. An on-cycle breaks the stimuli-sensitive bonds connecting both the blocks A and B in the BCP melt, and during the off-cycle, the broken bonds recombine. By simulating the effect of light, we isolate scenarios where phase separation begins with the light off (set 1); the cooperative interactions within the system allow it to undergo microphase separation. When the phase separation starts with the light on (set 2), the system undergoes macrophase separation due to bond breaking. Here, we report the role of alternate cycles on domain morphology by varying the bond-breaking probability for both set 1 and set 2, respectively. We observe that the scaling functions depend upon the conditions mentioned above that change the time scale of the evolving morphologies in various cycles. However, in all the cases, the average domain size respects the power-law growth: R(t) ∼tφ at late times, where φ is the dynamic growth exponent. After a short-lived diffusive growth (φ∼ 1/3) at early times, φ illustrates a crossover from the viscous hydrodynamic (φ∼ 1) to the inertial hydrodynamic (φ∼ 2/3) regimes at late times.

Coarsening dynamics in the Vicsek model of active matter.

We study the flocking model introduced by Vicsek et al. (Phys. Rev. Lett. 75, 1226 (1995)) in the "coarsening" regime. At standard self-propulsion speeds, we find two distinct growth laws for the coupled density and velocity fields. The characteristic length scale of the density domains grows as [Formula: see text] (with [Formula: see text] , while the velocity length scale grows much faster, viz., [Formula: see text] (with [Formula: see text] . The spatial fluctuations in the density and velocity fields are studied by calculating the two-point correlation function and the structure factor, which show deviations from the well-known Porod's law. This is a natural consequence of scattering from irregular morphologies that dynamically arise in the system. At large values of the scaled wave vector, the scaled structure factors for the density and velocity fields decay with powers -2.6 and -1.52 , respectively.

Kinetic Spinodal Instabilities in the Mott Transition in V_{2}O_{3}: Evidence from Hysteresis Scaling and Dissipative Phase Ordering.

We present the first systematic observation of scaling of thermal hysteresis with the temperature scanning rate around an abrupt thermodynamic transition in correlated electron systems. We show that the depth of supercooling and superheating in vanadium sesquioxide (V_{2}O_{3}) shifts with the temperature quench rates. The dynamic scaling exponent is close to the mean field prediction of 2/3. These observations, combined with the purely dissipative continuous ordering seen in "quench-and-hold" experiments, indicate departures from classical nucleation theory toward a barrier-free phase ordering associated with critical dynamics. Observation of critical-like features and scaling in a thermally induced abrupt phase transition suggests that the presence of a spinodal-like instability is not just an artifact of the mean field theories but can also exist in the transformation kinetics of real systems, surviving fluctuations.

Coarsening Dynamics of True Morphological Phase Separation in Unstable Thin Films.

Unstable thin films can spontaneously phase separate into two equilibrium flat-film morphologies of different thicknesses under the influence of gravity or favorable combinations of apolar and polar excess intermolecular forces. Two distinct pathways and associated dynamics of this morphological phase separation are presented based on numerical simulations of the 2-D thin film equation. The two pathways are (1) the "direct pathway" whereby the thicker phase forms directly and concurrently with the thinner phase and (2) the "defect pathway" whereby the thicker phase forms by the coarsening of defects of intermediate thickness and appears much later than the thinner phase. The defect pathway is favored by films whose initial thickness lies closer to the thickness of the thinner phase. Both pathways show an initial power law decay with exponent -1/4 in time followed by a plateau in the number density of domains/defects. Thereafter, the defect pathway shows another universal power law decay with exponent -1/3 and ends with a logarithmic decay, which is specific to the d = 2 case as there is no interfacial curvature in d = 2. The direct pathway skips the second power law decay and goes directly to the logarithmic decay.

Universality of domain growth in antiferromagnets with spin-exchange kinetics.

We study phase ordering kinetics in symmetric and asymmetric binary mixtures, undergoing an order-disorder transition below the critical temperature. Microscopically, we model the kinetics via the antiferromagnetic Ising model with Kawasaki spin-exchange kinetics. This conserves the composition while the order parameter (staggered magnetization) is not conserved. The order-parameter correlation function and structure factor show dynamical scaling, and the scaling functions are independent of the mixture composition. The average domain size shows a power-law growth: [Formula: see text]. The asymptotic growth regime has [Formula: see text], though there can be prolonged transients with [Formula: see text] for asymmetric mixtures. Our unambiguous observation of the asymptotic universal regime is facilitated by using an accelerated Monte Carlo technique. We also obtain the coarse-grained free energy from the Hamiltonian, as a function of two order parameters. The evolution of these order parameters is modeled by using Model C kinetics. As for the microscopic dynamics, the average domain size of the nonconserved order-parameter (staggered magnetization) field exhibits a power-law growth: [Formula: see text] at later times, irrespective of the mean value of the conserved order-parameter (composition) field.

Random field Ising model in a uniform magnetic field: Ground states, pinned clusters and scaling laws.

In this paper, we study the random field Ising model (RFIM) in an external magnetic field h . A computationally efficient graph-cut method is used to study ground state (GS) morphologies in this system for three different disorder types: Gaussian, uniform and bimodal. We obtain the critical properties of this system and find that they are independent of the disorder type. We also study GS morphologies via pinned-cluster distributions, which are scale-free at criticality. The spin-spin correlation functions (and structure factors) are characterized by a roughness exponent [Formula: see text]. The corresponding scaling function is universal for all disorder types and independent of h.

Single particle Brownian motion with solid friction.

We study the Brownian dynamics of a solid particle on a vibrating solid surface. Phenomenologically, the interaction between the two solid surfaces is modeled by solid friction, and the Gaussian white noise models the vibration of the solid surface. The solid friction force is proportional to the sign of relative velocity. We derive the Fokker-Planck (FP) equation for the time-dependent probability distribution to find the particle at a given location. We calculate analytically the steady state velocity distribution function, mean-square velocity and diffusion coefficient in d-dimensions. We present a generic method of calculating the autocorrelations in d-dimensions. This results in one dimension in an exact evaluation of the steady state velocity autocorrelation. In higher dimensions our exact general expression enables the analytic evaluation of the autocorrelation to any required approximation. We present approximate analytic expressions in two and three dimensions. Next, we numerically calculate the mean-square velocity and steady state velocity autocorrelation function up to d = 3 . Our numerical results are in good agreement with the analytically obtained results.

Phase separation in ternary fluid mixtures: a molecular dynamics study.

We present detailed results from molecular dynamics (MD) simulations of phase separation in ternary (ABC) fluid mixtures for d = 2 and d = 3 systems. Our MD simulations naturally incorporate hydrodynamic effects. The domain growth law is l(t) ∼ t(ϕ) with dynamic growth exponent ϕ. Our data clearly indicate that a ternary fluid mixture reaches a dynamical scaling regime at late times with a gradual crossover from ϕ = 1/3 → 1/2 → 2/3 in d = 2 and ϕ = 1/3 → 1 in d = 3 resulting from the hydrodynamic effect in the system. These MD simulations do not yet access the inertial hydrodynamic regime (with l(t) ∼ t(2/3)) of phase separation in ternary fluid mixtures in d = 3.

Non-Porod behavior in systems with rough morphologies.

Many experiments yield multi-scale morphologies which are smooth on some length scales and fractal on others. Accurate statements about morphological properties, e.g., roughness exponent, fractal dimension, domain size, interfacial width, etc. are obtained from the correlation function and structure factor. In this paper, we present structure factor data for two systems: (a) droplet-in-droplet morphologies of double-phase-separating mixtures; and (b) ground-state morphologies in dilute anti-ferromagnets. An important characteristic of the scattering data is a non-Porod tail, which is associated with scattering off rough domains and interfaces.

Ordering kinetics in liquid crystals with long-ranged interactions.

We present the results from comprehensive Monte Carlo (MC) simulations of ordering kinetics in d = 2 liquid crystals (LCs). Our LC system is described by the two-component Lebwohl-Lasher model with long-ranged interactions, V(r) ∼ r(-n). We find that systems with n ≥ 2 show the same dynamical behavior as the nearest-neighbor case (n = ∞). This contradicts available theoretical predictions.

Kinetics of phase separation in polymer mixtures: a molecular dynamics study.

We present detailed results from a molecular dynamics (MD) simulation of phase-separation kinetics in polymer mixtures. Our MD simulations naturally incorporate hydrodynamic effects. We find that polymeric phase separation (with dynamically symmetric components) is in the same universality class as segregation of simple fluids: the degree of polymerization only slows down the segregation kinetics. For d = 2 polymeric fluids, the domain growth law is L(t) ∼ t(ϕ) with ϕ showing a crossover from 1/3 → 1/2 → 2/3. For d = 3 polymeric fluids, we see the crossover ϕ = 1/3 → 1. Our MD simulations do not yet access the inertial hydrodynamic regime (with L ∼ t(2/3)) of phase separation in 3-d fluids.

Phase-ordering kinetics of the asymmetric Coulomb glass model.

We present results for phase-ordering kinetics in the Coulomb glass (CG) model, which describes electrons on a lattice with unscreened Coulombic repulsion. The filling factor is denoted by K∈[0,1]. For a square lattice with K=0.5 (symmetric CG), the ground state is a checkerboard with alternating electrons and holes. In this paper, we focus on the asymmetric CG where K≲0.5, i.e., the ground state is checkerboard-like with excess holes distributed uniformly. There is no explicit quenched disorder in our system, though the Coulombic interaction gives rise to frustration. We find that the evolution morphology is in the same dynamical universality class as the ordering ferromagnet. Further, the domain growth law is slightly slower than the Lifshitz-Cahn-Allen law, L(t)∼t^{1/2}, i.e., the growth exponent is underestimated. We speculate that this could be a signature of logarithmic growth in the asymptotic regime.

Phase separation in antisymmetric films: a molecular dynamics study.

We have used molecular dynamics (MD) simulations to study phase-separation kinetics in a binary fluid mixture (AB) confined in an antisymmetric thin film. One surface of the film (located at z = 0) attracts the A-atoms, and the other surface (located at z = D) attracts the B-atoms. We study the kinetic processes which lead to the formation of equilibrium morphologies subsequent to a deep quench below the miscibility gap. In the initial stages, one observes the formation of a layered structure, consisting of an A-rich layer followed by a B-rich layer at z = 0; and an analogous structure at z = D. This multi-layered morphology is time-dependent and propagates into the bulk, though it may break up into a laterally inhomogeneous structure at a later stage. We characterize the evolution morphologies via laterally averaged order parameter profiles; the growth laws for wetting-layer kinetics and layer-wise length scales; and the scaling properties of layer-wise correlation functions.

Symbiotic dynamics in living liquid crystals.

An amalgam of nematic liquid crystals and active matter, referred to as living liquid crystals, is a promising self-healing material with futuristic applications for targeted delivery of information and microcargo. We provide a phenomenological model to study the symbiotic pattern dynamics in this contemporary system using the Toner-Tu model for active matter (AM), the Landau-de Gennes free energy for liquid crystals (LCs), and an experimentally motivated coupling term that favours coalignment of the active and nematic components. Our extensive theoretical studies unfold two novel steady states, chimeras and solitons, with sharp regions of distinct orientational order that sweep through the coupled system in synchrony. The induced dynamics in the passive nematic is unprecedented. We show that the symbiotic dynamics of the AM and LC components can be exploited to induce and manipulate order in an otherwise disordered system.

Phase ordering dynamics of the random-field long-range Ising model in one dimension.

We investigate the influence of long-range (LR) interactions on the phase ordering dynamics of the one-dimensional random-field Ising model (RFIM). Unlike the usual RFIM, a spin interacts with all other spins through a ferromagnetic coupling that decays as r^{-(1+σ)}, where r is the distance between two spins. In the absence of LR interactions, the size of coarsening domains R(t) exhibits a crossover from pure system behavior R(t)∼t^{1/2} to an asymptotic regime characterized by logarithmic growth: R(t)∼(lnt)^{2}. The LR interactions affect the preasymptotic regime, which now exhibits ballistic growth R(t)∼t, followed by σ-dependent growth R(t)∼t^{1/(1+σ)}. Additionally, the LR interactions also affect the asymptotic logarithmic growth, which becomes R(t)∼(lnt)^{α(σ)} with α(σ)<2. Thus, LR interactions lead to faster growth than for the nearest-neighbor system at short times. Unexpectedly, this driving force causes a slowing down of the dynamics (α<2) in the asymptotic logarithmic regime. This is explained in terms of a nontrivial competition between the pinning force caused by the random field and the driving force introduced by LR interactions. We also study the spatial correlation function and the autocorrelation function of the magnetization field. The former exhibits superuniversality for all σ, i.e., a scaling function that is independent of the disorder strength. The same holds for the autocorrelation function when σ<1, whereas a signature of the violation of superuniversality is seen for σ>1.