We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate by duplication of columns. Despite the null global curvature, we show that all investigated models have asymptotic height distributions and spatial covariances in agreement with those expected for the KPZ subclass for curved surfaces. In 1 + 1 dimensions, the height distribution and covariance are given by the GUE Tracy-Widom distribution and the Airy 2 process instead of the GOE and Airy 1 foreseen for flat interfaces. These results imply that when the KPZ class splits into curved and flat subclasses, as conventionally considered, the expanding substrate may play a role equivalent to, or perhaps more important than, the global curvature. Moreover, the translational invariance of the interfaces evolving on growing domains allowed us to accurately determine, in 2 + 1 dimensions, the analog of the GUE Tracy-Widom distribution for height distribution and that of the Airy 2 process for spatial covariance. Temporal covariance is also calculated and shown to be universal in each dimension and in each of the two subclasses. A logarithmic correction associated with the duplication of columns is observed and theoretically elucidated. Finally, crossover between regimes with fixed-size and enlarging substrates is also investigated.

Binding of ligands to DNA can be studied by measuring the change of the persistence length of the complex formed, in single-molecule assays. We propose a methodology for persistence length data analysis based on a quenched disorder statistical model and describing the binding isotherm by a Hill-type equation. We obtain an expression for the effective persistence length as a function of the total ligand concentration, which we apply to our data of the DNA-cationic β-cyclodextrin and to the DNA-HU protein data available in the literature, determining the values of the local persistence lengths, the dissociation constant, and the degree of cooperativity for each set of data. In both cases the persistence length behaves nonmonotonically as a function of ligand concentration and based on the results obtained we discuss some physical aspects of the interplay between DNA elasticity and cooperative binding of ligands.

We report extensive numerical simulations of growth models belonging to the nonlinear molecular beam epitaxy (nMBE) class, on flat (fixed-size) and expanding substrates (ES). In both d=1+1 and 2+1, we find that growth regime height distributions (HDs), and spatial and temporal covariances are universal, but are dependent on the initial conditions, while the critical exponents are the same for flat and ES systems. Thus, the nMBE class does split into subclasses, as does the Kardar-Parisi-Zhang (KPZ) class. Applying the "KPZ ansatz" to nMBE models, we estimate the cumulants of the 1+1 HDs. Spatial covariance for the flat subclass is hallmarked by a minimum, which is not present in the ES one. Temporal correlations are shown to decay following well-known conjectures.

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Circular KPZ interfaces spreading radially in the plane have GUE Tracy-Widom (TW) height distribution (HD) and Airy2 spatial covariance, but what are their statistics if they evolve on the surface of a different background space, such as a bowl, a cup, or any surface of revolution? To give an answer to this, we report here extensive numerical analyses of several one-dimensional KPZ models on substrates whose size enlarges as L(t) = L0 + ωt γ , while their mean height h increases as usual [ h ∼ t]. We show that the competition between the L enlargement and the correlation length (ξ ct 1/z ) plays a key role in the asymptotic statistics of the interfaces. While systems with γ > 1/z have HDs given by GUE and the interface width increasing as w ∼ t β , for γ < 1/z the HDs are Gaussian, in a correlated regime where w ∼ t αγ . For the special case γ = 1/z, a continuous class of distributions exists, which interpolate between Gaussian (for small ω/c) and GUE (for ω/c 1). Interestingly, the HD seems to agree with the Gaussian symplectic ensemble (GSE) TW distribution for ω/c ≈ 10. Despite the GUE HDs for γ > 1/z, the spatial covariances present a strong dependence on the parameters ω and γ, agreeing with Airy2 only for ω 1, for a given γ, or when γ = 1, for a fixed ω. These results considerably generalize our knowledge on the 1D KPZ systems, unveiling the importance of the background space in their statistics.