A thickness transition in evaporating water films

When a thin water film evaporates from a clean cleaved mica substrate, two films of different thickness can coexist, one of them being stable and the other metastable. As the evaporation proceeds, a phase transition occurs between them. The edge between the two films becomes unstable and the patterns which develop are reminiscent of diffusion-limited solidification. Experimental results and a theory are presented. The theory suggests that remaining drops evaporate in an unusual manner, whereby the largest drops evaporate fastest, and also shows how the instability in a linear edge coarsens. These predictions were confirmed.     

Gregarious versus individualistic behavior in Vicsek swarms and the onset of first-order phase transitions

The standard Vicsek model (SVM) is a minimal non-equilibrium model of self-propelled particles that appears to capture the essential ingredients of critical flocking phenomena. In the SVM, particles tend to align with each other and form ordered flocks of collective motion; however, perturbations controlled by a noise term lead to a noise-driven continuous order–disorder phase transition. In this work, we extend the SVM by introducing a parameter α$\alpha$ that allows particles to be individualistic instead of gregarious, i.e. to choose a direction of motion independently of their neighbors. By focusing on the small-noise regime, we show that a relatively small probability of individualistic motion (around 10%$10\%$) is sufficient to drive the system from a Vicsek-like ordered phase to a disordered phase. Despite the fact that the α$\alpha$-extended model preserves the O(n)$O\left(n\right)$ symmetry and the interaction range, as well as the dimensionality of the underlying SVM, this novel phase transition is found to be discontinuous (first order), an intriguing manifestation of the richness of the non-equilibrium flocking/swarming phenomenon.     

On the relation between Vicsek and Kuramoto models of spontaneous synchronization

The Vicsek model for self-propelling particles in 2D is investigated with respect to the addition of the stochastic perturbation of dynamic equations. We show that this model represents in essence the same type of bifurcations under a different type of noise as the celebrated Kuramoto model of spontaneous synchronization. These models demonstrate similar behavior at least within the mean-field approach. To prove this we consider two types of noise for the Vicsek model which are commonly considered in the literature: the intrinsic and the extrinsic ones (according to the terminology of Pimentel et al. [J.A. Pimentel, M. Aldana, C. Huepe, H. Larralde, Intrinsic and extrinsic noise effects on phase transitions of network models with applications to swarming systems, Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 77 (6) (2008) doi:10.1103/PhysRevE.77.061138. URL: http://dx.doi.org/10.1103/PhysRevE.77.061138]). The qualitative correspondence with the bifurcation of stationary states in the Kuramoto model is stated. A new type of stochastic perturbation—the “mixed” noise is proposed. It is constructed as the weighted superposition of the intrinsic and the extrinsic noises. The corresponding phase diagram “noise amplitude vs. interaction strength” is obtained. The possibility of the tricritical behavior for the Vicsek model is predicted.     

Noise induced patterning in periodic systems with conserved dynamics

We study pattern formation in periodic systems with conserved dynamics driven by both thermally sustained flux and external (athermal) flux. Assuming the stochastic nature of each kind of flux we discuss noise induced patterning with competing stochastic dynamics in the framework of the modulated phase field method. Analytical results obtained within the mean field theory are compared with computer simulations.     

Motility-induced phase separation and coarsening in active matter

Active systems, or active matter, are self-driven systems that live, or function, far from equilibrium – a paradigmatic example that we focus on here is provided by a suspension of self-motile particles. Active systems are far from equilibrium because their microscopic constituents constantly consume energy from the environment in order to do work, for instance to propel themselves. The non-equilibrium nature of active matter leads to a variety of non-trivial intriguing phenomena. An important one, which has recently been the subject of intense interest among biological and soft matter physicists, is that of the so-called “motility-induced phase separation”, whereby self-propelled particles accumulate into clusters in the absence of any explicit attractive interactions between them. Here we review the physics of motility-induced phase separation, and discuss this phenomenon within the framework of the classic physics of phase separation and coarsening. We also discuss theories for bacterial colonies where coarsening may be arrested. Most of this work will focus on the case of run-and-tumble and active Brownian particles in the absence of solvent-mediated hydrodynamic interactions – we will briefly discuss at the end their role, which is not currently fully understood in this context.     

Solid-liquid transition induced by the anisotropic diffusion of colloidal particles

We numerically study the phase behaviors of colloids with anisotropic diffusion in two dimensions. It is found that the diffusion anisotropy of colloidal particles plays an important role in the phase transitions. A strong diffusion anisotropy induces the large vibration of particles, subsequently, the system goes into a disordered state. In the presence of the strong-coupling, particles with weak diffusion anisotropy can freeze into hexagonal crystals. Thus, there exists a solid-liquid transition. With the degree of diffusion anisotropy increasing, the transition points are shifted to the stronger-coupled region. A competition between the degree of diffusion anisotropy and coupling strength widens the transition region where the heterogeneous structures coexist, which results in a broad-peak probability distribution curve for the local order parameter. Our study may be helpful for the experiments related to the phase behavior in statistical physics, materials science and biophysical systems.     

Spiral tip meandering induced by excitability modulation

In this work, we introduce a spatiotemporal modulation for excitability into an excitable medium, the Barkley model. The modulation can make the spiral wave tip meandering. Various types of periodic spiral and quasiperiodic meandering spiral motions can be observed numerically by varying the modulation. And the theoretical analysis for the conditions of Hopf bifurcation, based on an ordinary-differential-equation (ODE) model, is applied to well explain the rich behaviors of numerical simulations.     

Ion beam induced chemical vapor deposition (IBICVD) of cobalt particles

A novel method aiming at fabricating submicron-scale particles utilizing dicobalt octacarbonyl as a precursor for cobalt, formed upon localized ion beam induced decomposition, is presented. Patterns of deposited particles are fabricated through vector scan rastering. Measurements of cumulative magnetic properties (arrays of 2 μm–size dots) show coercivity of about 100 Oe and the saturation magnetization of approximately 1000 emu/cm³.     

Exploiting the Hamiltonian structure of a neural field model

We study the unexpected disappearance of stable homoclinic orbits in regions of parameter space in a neural field model with one spatial dimension. The usual approach of using numerical continuation techniques and local bifurcation theory is insufficient to explain the qualitative change in the model’s behaviour. The lack of robustness of the model to small perturbations in parameters is surprising, and the phenomenon may be of broader significance than just our model. By exploiting the Hamiltonian structure of the time-independent system, we develop a numerical technique with which we discover that a small, separate solution curve exists for a range of parameter values. As the firing rate function steepens, the small curve causes the main curve to break and stable homoclinic orbits are destroyed in a region of parameter space. Numerically, we use level set analysis to find that a codimension-one heteroclinic bifurcation occurs at the terminating ends of the solution curves. By replacing the firing rate function with a step function, we show analytically that the bifurcation is related to the value of the firing threshold. We also show the existence of heteroclinic orbits at the breakpoints using a travelling front analysis in the time-dependent system.     

Pattern formation in a simple chemical system with general orders of autocatalysis and decay. I. Stability analysis

In this preliminary paper we introduce a mathematical model based on an autocatalytic reaction scheme with termination, and general reaction orders. Rigorous stability analysis and numerical solutions are presented which illustrate that the problem can for certain parameter values admit a stable stationary pattern in the concentration of the autocatalyst and reactant. This pattern forms at the rear of a permanent form travelling wave or pulse solution.     

Stabilizing transient nanopatterns in heterogeneous catalysis: A comprehensive explanation of the phenomenon

A pattern-formation mechanism driven by attractive forces—previously studied in the context of lateral interactions between adsorbates—is reassessed through a simplified model. In its original version, such a mechanism needed an additional chemical reaction to stabilize the pattern. Recently, that goal has been achieved by means of a particular multiplicative noise. However, many details of the mechanism have remained obscure. In order to clarify them, we resorted to a simplified model that reproduces qualitatively the results of the studies carried out on the complete model. Our analysis reveals that such a mechanism may largely transcend the context in which it was found.     

Radial fingering in a Hele-Shaw cell: a weakly nonlinear analysis

The Saffman-Taylor viscous fingering instability occurs when a less viscous fluid displaces a more viscous one between narrowly spaced parallel plates in a Hele-Shaw cell. Experiments in radial flow geometry form fan-like patterns, in which fingers of different lengths compete, spread and split. Our weakly nonlinear analysis of the instability predicts these phenomena, which are beyond the scope of linear stability theory. Finger competition arises through enhanced growth of sub-harmonic perturbations, while spreading and splitting occur through the growth of harmonic modes. Nonlinear mode-coupling enhances the growth of these specific perturbations with appropriate relative phases, as we demonstrate through a symmetry analysis of the mode coupling equations. We contrast mode coupling in radial flow with rectangular flow geometry.     

Density dependence of the transition temperature in a homogeneous bose-einstein condensate

Transition temperature data obtained as a function of particle density in the 4He-Vycor system are compared with recent theoretical calculations for 3D Bose-condensed systems. In the low density dilute Bose gas regime we find, in agreement with theory, a positive shift in the transition temperature of the form DeltaT/T0 = gamma(na(3))(1/3). At higher densities a maximum is found in the ratio of T(c)/T0 for a value of the interaction parameter, na(3), that is in agreement with path-integral Monte Carlo calculations.     

Polymorphic and regular localized activity structures in a two-dimensional two-component reaction-diffusion lattice with complex threshold excitation

Space-time dynamics of the system modeling collective behaviour of electrically coupled nonlinear units is investigated. The dynamics of a local cell is described by the FitzHugh-Nagumo system with complex threshold excitation. It is shown that such a system supports formation of two distinct kinds of stable two-dimensional spatially localized moving structures without any external stabilizing actions. These are regular and polymorphic structures. The regular structures preserve their shape and velocity under propagation while the shape and velocity as well as other integral characteristics of polymorphic structures show rather complex temporal behaviour. Both kinds of structures represent novel sorts of spatially temporal patterns which have not been observed before in typical two-component reaction-diffusion type systems. It is demonstrated that there exist two types of regular structures: single and bound states and three types of polymorphic structures: periodic, quasiperiodic and even chaotic ones. The partition of the parameter plane into regions corresponding to the existence of these different types of structures is carried out. High multistability of regular structures is indicated. The interaction of regular structures is investigated. The correspondence between the structures and trajectories in multidimensional phase space associated with the system is given. Bifurcation mechanisms leading to the loss of stability of regular structures as well as to a transition from one type of polymorphic structure to another are indicated. The mechanisms of formation of regular and polymorphic structures are discussed.     

Turing instability for a semi-discrete Gierer-Meinhardt system

In this paper, we investigate the spatial patterns of a Gierer-Meinhardt system where the space is discrete in two dimensions with the periodic boundary condition and time is continuous, in contrast to the continuum models. The conditions of Turing instability are obtained by linear analysis and a series of numerical simulations are performed. In the instability region, we have shown that this system can produce a number of different patterns such as stripes and snowflake pattern, other than ubiquitous fix-spotted patterns. As mentioned, the results are substantiated only by means of snapshots of the apatial grid. However, we also give some analysis by using the time series at three random grids and of the average value of states, that is, the stable state patterns can be observed. On the other hand, the effects of varying parameters on pattern formation are also discussed. Moreover, simulations for fixed parameters and special initial conditions indicate that the initial conditions can alter the structure of patterns. The patterns can form as a consequence of cellular interaction. So patterns arising from a semi-discrete model can present simulations on a geometrically accurate representation in biology. As a result, our work is interesting and important in ecology.     

Accelerating consensus of self-driven swarm via a weighted model

In this paper, we study a weighted self-propelled agent system, wherein each agent’s direction is affected by its spatial neighbors with different impacts. In the model, a tunable parameter α≥0$\alpha \ge 0$ is introduced to weight the different impacts of spatial neighbors: if α=0$\alpha =0$, the agent’s direction is updated by averaging all of neighbors directions and own direction, i.e., Vicsek model. Otherwise, with the increase of the value of α$\alpha$, the agent’s direction is more affected by the agent who has small view angle between them. Interestingly, simulation results show that there exists an optimal α$\alpha$ leading to the shortest convergence time. Thus, our findings provide a powerful mechanism for collective motions in biological and technological multiagent systems.     

Forward-facing steps induced transition in a subsonic boundary layer

A forward-facing step (FFS) immersed in a subsonic boundary layer is studied through a high-order flux reconstruction (FR) method to highlight the flow transition induced by the step. The step height is a third of the local boundary-layer thickness. The Reynolds number based on the step height is 720. Inlet disturbances are introduced giving rise to streamwise vortices upstream of the step. It is observed that these small-scale streamwise structures interact with the step and hairpin vortices are quickly developed after the step leading to flow transition in the boundary layer.     

Magnetic-field induced orientational transition in a helicoidal liquid-crystalline antiferromagnet

The magnetic-field induced orientational transition in helicoidal liquid-crystalline antiferromagnets representing compensated suspensions of magnetic nanoparticles in cholesteric liquid crystals is theoretically studied. The untwisting of a helicoidal structure and the behavior of mean magnetization as a function of the field strength and material parameters are investigated. It is shown that the magnetic subsystems in the field-untwisted ferronematic phase are not completely compensated, and the ferronematic phase is ferrimagnetic.     

Peierls-like transition induced by frustration in a two-dimensional antiferromagnet

We show that the introduction of frustration into the spin- 1/2 two-dimensional (2D) antiferromagnetic Heisenberg model on a square lattice via a next-nearest-neighbor exchange interaction can lead to a Peierls-like transition, from a tetragonal to an orthorhombic phase, when the spins are coupled to adiabatic phonons. The two different orthorhombic ground states define an Ising order parameter, which is expected to lead to a finite temperature transition. Implications for Li(2)VOSiO(4), the first realization of that model, will be discussed.     

Density correlations induced by temperature fluctuations in a photon gas

The impact of angular temperature variations on the thermodynamic variables and real-space correlation functions of black-body radiation are analyzed. In particular, the effect of temperature fluctuations on the number density and energy density correlations of the cosmic microwave background (CMB) is studied. The angular temperature fluctuations are modeled by an isotropic and homogeneous Gaussian random field, whose autocorrelation function is defined on the unit sphere in momentum space. This temperature correlation function admits an angular Fourier transform which determines the density correlations in real space induced by temperature fluctuations. In the case of the CMB radiation, the multipole coefficients of the angular power spectrum defining the temperature correlation function have been measured by the Planck satellite. The fluctuation-induced perturbation of the equilibrium variables (internal energy, entropy, heat capacity and compressibility) can be quantified in terms of the measured multipole coefficients by expanding the partition function around the equilibrium state in powers of the temperature random field. The real-space density correlations can also be extracted from the measured temperature power spectrum. Both the number density and energy density correlations of the electromagnetic field are long-range, admitting power-law decay; in the case of the energy density correlation, the fluctuation-induced correlation overpowers the isotropic equilibrium correlation in the long-distance limit.