Finite-size effects in roughness distribution scaling

We study numerically finite-size corrections in scaling relations for roughness distributions of various interface growth models. The most common relation, which considers the average roughness $$as scaling factor, is not obeyed in the steady states of a group of ballistic-like models in 2+1 dimensions, even when very large system sizes are considered. On the other hand, good collapse of the same data is obtained with a scaling relation that involves the root mean square fluctuation of the roughness, which can be explained by finite-size effects on second moments of the scaling functions. We also obtain data collapse with an alternative scaling relation that accounts for the effect of the intrinsic width, which is a constant correction term previously proposed for the scaling of$$. This illustrates how finite-size corrections can be obtained from roughness distributions scaling. However, we discard the usual interpretation that the intrinsic width is a consequence of high surface steps by analyzing data of restricted solid-on-solid models with various maximal height differences between neighboring columns. We also observe that large finite-size corrections in the roughness distributions are usually accompanied by huge corrections in height distributions and average local slopes, as well as in estimates of scaling exponents. The molecular-beam epitaxy model of Das Sarma and Tamborenea in 1+1 dimensions is a case example in which none of the proposed scaling relations works properly, while the other measured quantities do not converge to the expected asymptotic values. Thus, although roughness distributions are clearly better than other quantities to determine the universality class of a growing system, it is not the final solution for this task.Comment: 25 pages, including 9 figures and 1 tabl

Cluster growth in far-from-equilibrium particle models with diffusion, detachment, reattachment and deposition

Monolayer cluster growth in far-from-equilibrium systems is investigated by applying simulation and analytic techniques to minimal hard core particle (exclusion) models. The first model (I), for post-deposition coarsening dynamics, contains mechanisms of diffusion, attachment, and slow activated detachment (at rate epsilon<<1) of particles on a line. Simulation shows three successive regimes of cluster growth: fast attachment of isolated particles; detachment allowing further (epsilon t)^(1/3) coarsening of average cluster size; and t^(-1/2) approach to a saturation size going like epsilon^(-1/2). Model II generalizes the first one in having an additional mechanism of particle deposition into cluster gaps, suppressed for the smallest gaps. This model exhibits early rapid filling, leading to slowing deposition due to the increasing scarcity of deposition sites, and then continued power law (epsilon t)^(1/2) cluster size coarsening through the redistribution allowed by slow detachment. The basic (epsilon t)^(1/3) domain growth laws and epsilon^(-1/2) saturation in model I are explained by a simple scaling picture. A second, fuller approach is presented which employs a mapping of cluster configurations to a column picture and an approximate factorization of the cluster configuration probability within the resulting master equation. This allows quantitative results for the saturation of model I in excellent agreement with the simulation results. For model II, it provides a one-variable scaling function solution for the coarsening probability distribution, and in particular quantitative agreement with the cluster length scaling and its amplitude.Comment: Accepted in Phys. Rev. E; 9 pages with figure

Non-universal coarsening and universal distributions in far-from equilibrium systems

Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates epsilon<<1, particle deposition into cluster gaps, but suppressed for the smallest gaps, and breakup of clusters which are adjacent to large gaps. Cluster breakup rates vary with the cluster length x as kx^alpha. The domain growth law x ~ (epsilon t)^z, with z=1/(2+alpha) for alpha>0, is explained by a scaling picture, as well as the scaling of the density of double vacancies (at which deposition and cluster breakup are allowed) as 1/[t(epsilon t)^z]. Numerical simulations for several values of alpha and epsilon confirm these results. An approximate factorization of the cluster configuration probability is performed within the master equation resulting from the mapping to a column picture. The equation for a one-variable scaling function explains the above results. The probability distributions of cluster lengths scale as P(x)= 1/(epsilon t)^z g(y), with y=x/(epsilon t)^z. However, those distributions show a universal tail with the form g(y) ~ exp(-y^{3/2}), which disagrees with the prediction of the independent cluster approximation. This result is explained by the connection of the vacancy dynamics with the problem of particle trapping in an infinite sea of traps and is confirmed by simulation.Comment: 30 pages (10 figures included), to appear in Phys. Rev.

Extracellular matrix mimics using hyaluronan-based biomaterials

Hyaluronan (HA) is a critical element of the extracellular matrix (ECM). The regulated synthesis and degradation of HA modulates the ECM chemical and physical properties that, in turn, influence cellular behavior. HA triggers signaling pathways associated with the adhesion, proliferation, migration, and differentiation of cells, mediated by its interaction with specific cellular receptors or by tuning the mechanical properties of the ECM. This review summarizes the recent advances on strategies used to mimic the HA present in the ECM to study healthy or pathological cellular behavior. This includes the development of HA-based 2D and 3D in vitro tissue models for the seeding and encapsulation of cells, respectively, and HA particles as carriers for the targeted delivery of therapeutic agents.The authors acknowledge thefinancial support from the European Commission’s H2020 programme, under grantagreements H2020-WIDESPREAD-2014-668983-FORECAST, and H2020-MSCA-RISE-2019-872648-MEPHOS. S.A.acknowledges the Portuguese Foundation for Science and Technology (FCT) for her PhD grant (SFRH/BD/112075/2015)

Modeling one-dimensional island growth with mass-dependent detachment rates

We study one-dimensional models of particle diffusion and attachment/detachment from islands where the detachment rates gamma(m) of particles at the cluster edges increase with cluster mass m. They are expected to mimic the effects of lattice mismatch with the substrate and/or long-range repulsive interactions that work against the formation of long islands. Short-range attraction is represented by an overall factor epsilon<<1 in the detachment rates relatively to isolated particle hopping rates [epsilon ~ exp(-E/T), with binding energy E and temperature T]. We consider various gamma(m), from rapidly increasing forms such as gamma(m) ~ m to slowly increasing ones, such as gamma(m) ~ [m/(m+1)]^b. A mapping onto a column problem shows that these systems are zero-range processes, whose steady states properties are exactly calculated under the assumption of independent column heights in the Master equation. Simulation provides island size distributions which confirm analytic reductions and are useful whenever the analytical tools cannot provide results in closed form. The shape of island size distributions can be changed from monomodal to monotonically decreasing by tuning the temperature or changing the particle density rho. Small values of the scaling variable X=epsilon^{-1}rho/(1-rho) favour the monotonically decreasing ones. However, for large X, rapidly increasing gamma(m) lead to distributions with peaks very close to and rapidly decreasing tails, while slowly increasing gamma(m) provide peaks close to /2$ and fat right tails.Comment: 16 pages, 6 figure

Ultrasonic Fatigue Analysis on Steel Specimen with Temperature Control : Evaluation of Variable Temperature Effect

Non peer reviewe