Phase separation on surfaces in the presence of matter exchange.

We present a field theory to describe the composition of a surface spontaneously exchanging matter with its bulk environment. By only assuming matter conservation in the system, we show with extensive numerical simulations that, depending on the matter exchange rates, a complex patterned composition distribution emerges on the surface. For one-dimensional systems we show analytically and numerically that coarsening is arrested and as a consequence domains have a characteristic length scale. Our results show that the causes of heterogeneous lipid composition in cellular membranes may be justified in simple physical terms.

Microscopic interplay of temperature and disorder of a one-dimensional elastic interface.

Elastic interfaces display scale-invariant geometrical fluctuations at sufficiently large lengthscales. Their asymptotic static roughness then follows a power-law behavior, whose associated exponent provides a robust signature of the universality class to which they belong. The associated prefactor has instead a nonuniversal amplitude fixed by the microscopic interplay between thermal fluctuations and disorder, usually hidden below experimental resolution. Here we compute numerically the roughness of a one-dimensional elastic interface subject to both thermal fluctuations and a quenched disorder with a finite correlation length. We evidence the existence of a power-law regime at short lengthscales. We determine the corresponding exponent ζ_{dis} and find compelling numerical evidence that, contrarily to available analytic predictions, one has ζ_{dis}<1. We discuss the consequences on the temperature dependence of the roughness and the connection with the asymptotic random-manifold regime at large lengthscales. We also discuss the implications of our findings for other systems such as the Kardar-Parisi-Zhang equation and the Burgers turbulence.

Local Probe Comparison of Ferroelectric Switching Event Statistics in the Creep and Depinning Regimes in Pb(Zr_{0.2}Ti_{0.8})O_{3} Thin Films.

Ferroelectric materials provide a useful model system to explore the jerky, highly nonlinear dynamics of elastic interfaces in disordered media. The distribution of nanoscale switching event sizes is studied in two Pb(Zr_{0.2}Ti_{0.8})O_{3} thin films with different disorder landscapes using piezoresponse force microscopy. While the switching event statistics show the expected power-law scaling, significant variations in the value of the scaling exponent τ are seen, possibly as a consequence of the different intrinsic disorder landscapes in the samples and of further alterations under high tip bias applied during domain writing. Importantly, higher exponent values (1.98-2.87) are observed when crackling statistics are acquired only for events occurring in the creep regime. The exponents are systematically lowered when all events across both creep and depinning regimes are considered-the first time such a distinction is made in studies of ferroelectric materials. These results show that distinguishing the two regimes is of crucial importance, significantly affecting the exponent value and potentially leading to incorrect assignment of universality class.

Roughness and dynamics of proliferating cell fronts as a probe of cell-cell interactions.

Juxtacellular interactions play an essential but still not fully understood role in both normal tissue development and tumour invasion. Using proliferating cell fronts as a model system, we explore the effects of cell-cell interactions on the geometry and dynamics of these one-dimensional biological interfaces. We observe two distinct scaling regimes of the steady state roughness of in-vitro propagating Rat1 fibroblast cell fronts, suggesting different hierarchies of interactions at sub-cell lengthscales and at a lengthscale of 2-10 cells. Pharmacological modulation significantly affects the proliferation speed of the cell fronts, and those modulators that promote cell mobility or division also lead to the most rapid evolution of cell front roughness. By comparing our experimental observations to numerical simulations of elastic cell fronts with purely short-range interactions, we demonstrate that the interactions at few-cell lengthscales play a key role. Our methodology provides a simple framework to measure and characterise the biological effects of such interactions, and could be useful in tumour phenotyping.

Magnetic domain wall creep and depinning: A scalar field model approach.

Magnetic domain wall motion is at the heart of new magnetoelectronic technologies and hence the need for a deeper understanding of domain wall dynamics in magnetic systems. In this context, numerical simulations using simple models can capture the main ingredients responsible for the complex observed domain wall behavior. We present a scalar field model for the magnetization dynamics of quasi-two-dimensional systems with a perpendicular easy axis of magnetization which allows a direct comparison with typical experimental protocols, used in polar magneto-optical Kerr effect microscopy experiments. We show that the thermally activated creep and depinning regimes of domain wall motion can be reached and the effect of different quenched disorder implementations can be assessed with the model. In particular, we show that the depinning field increases with the mean grain size of a Voronoi tessellation model for the disorder.

Dynamic heterogeneity in an orientational glass.

The family of compounds CBrnCl4-n has been proven helpful in unraveling microscopic mechanisms responsible for glassy behavior. Some of the family members show translational ordered phases with minimal disorder which appears to reveal glassy features, thus deserving special attention in the search for universal glass anomalies. In this work, we studied CBrCl3 dynamics by performing extensive molecular dynamics simulations. Molecules of this compound perform reorientational discrete jumps, where the atoms exchange equivalent positions among each other revealing a cage-orientational jump motion fully comparable to the cage-rototranslational jump motion in supercooled liquids. Correlation times were calculated from rotational autocorrelation functions showing good agreement with previous reported dielectric results. From mean waiting and persistence times calculated directly from trajectory results, we are able to explain which microscopic mechanisms lead to characteristic times associated with α- and ß-relaxation times measured experimentally. We found that two nonequivalent groups of molecules have a longer characteristic time than the other two nonequivalent groups, both of them belonging to the asymmetric unit of the monoclinic (C2/c) lattice.

Dynamic Heterogeneity in the Monoclinic Phase of CCl4.

Carbon tetrachloride (CCl4) is one of the simplest compounds having a translationally stable monoclinic phase while exhibiting a rich rotational dynamics below 226 K. Recent nuclear quadrupolar resonance experiments revealed that the dynamics of CCl4 is similar to that of the other members of the isostructural series CBrnCl4-n, suggesting that the universal relaxation features of canonical glasses such as α and ß relaxation are also present in nonglass formers. Using molecular dynamics simulations we studied the rotational dynamics in the monoclinic phase of CCl4. The molecules undergo C3-type jump-like rotations around each one of the four C-Cl bonds. The rotational dynamics is very well described with a master equation using as the only input the rotational rates measured from the simulated trajectories. It is found that the heterogeneous dynamics emerges from faster and slower modes associated with different rotational axes, which have fixed orientations relative to the crystal and are distributed among the four nonequivalent molecules of the unit cell.

The plastic and liquid phases of CCl3Br studied by molecular dynamics simulations.

We present a molecular dynamics study of the liquid and plastic crystalline phases of CCl(3)Br. We investigated the short-range orientational order using a recently developed classification method and we found that both phases behave in a very similar way. The only differences occur at very short molecular separations, which are shown to be very rare. The rotational dynamics was explored using time correlation functions of the molecular bonds. We found that the relaxation dynamics corresponds to an isotropic diffusive mode for the liquid phase but departs from this behavior as the temperature is decreased and the system transitions into the plastic phase.