36 citations · 189 across the 19 of their papers we have counts for
20 papers
Fractional is Better: Learnable Derivative Orders in Neural Operator Learning
Fares B. Mehouachi, Saif Eddin Jabari
Neural operators learn mappings between function spaces, enabling fast surrogate solutions to partial differential equations. Despite remarkable architectural diversity, these meth…
Fractal signatures of strong universality in the disordered Ising model
Henrique A Lima, Kaue Hermann, Ismael S. S. Carrasco +2
Disordered systems are very rich laboratories for exploring complex systems. In particular, disordered magnetic systems have been extremely important in the last five decades for u…
Dimensional crossover in surface growth on rectangular substrates
Ismael S. S. Carrasco, Tiago J. Oliveira
In a recent work [Phys. Rev. E 109, L042102 (2024)], interesting dimensional crossovers [from two- to one-dimensional (2D to 1D) scaling] were found in the growth of Kardar-Parisi-…
Non-monotonic roughness evolution in film growth on weakly interacting substrates
Dmitry Lapkin, Ismael S. S. Carrasco, Catherine Cruz Luukkonen +5
Thin film deposition on weakly interacting substrates exhibits a unique growth mode characterized by initially strong island formation and rapidly increasing roughness, which reach…
A new Fractal Mean-Field analysis in phase transition
Ismael S. S. Carrasco, Henrique A. de Lima, Fernando A. Oliveira
Understanding phase transitions requires not only identifying order parameters but also characterizing how their correlations behave across scales. By quantifying how fluctuations…
Scaling, Fractal Dynamics and Critical Exponents: Application in a non-integer dimensional Ising model
Henrique A. de Lima, Ismael S. S. Carrasco, Marcio Santos +1
Moving beyond simple associations, researchers need tools to quantify how variables influence each other in space and time. Correlation functions provide a mathematical framework f…
Island formation in heteroepitaxial growth
Frederik Munko, Catherine Cruz Luukkonen, Ismael S. S. Carrasco +2
Island formation in strain-free heteroepitaxial deposition of thin films is analyzed using kinetic Monte Carlo simulations of two minimal lattice models and scaling approaches. The…
Dimensional crossover in Kardar-Parisi-Zhang growth
Ismael S. S. Carrasco, Tiago J. Oliveira
Two-dimensional (2D) KPZ growth is usually investigated on substrates of lateral sizes , so that and the correlation length () are the only relevant lengths deter…
A geometrical interpretation of critical exponents
Henrique A. Lima, Edwin E. Mozo Luis, Ismael S. S. Carrasco +2
We develop the hypothesis that the dynamics of a given system may lead to the activity being constricted to a subset of space, characterized by a fractal dimension smaller than the…
One-point height fluctuations and two-point correlators of cylindrical KPZ systems
Ismael S. S. Carrasco, Tiago J. Oliveira
While the 1-point height distributions (HDs) and 2-point covariances of KPZ systems have been investigated in several recent works for flat and spherical geometries, for th…
Kardar-Parisi-Zhang growth on square domains that enlarge nonlinearly in time
Ismael S. S. Carrasco, Tiago J. Oliveira
We study discrete KPZ growth models deposited on square lattice substrates, whose (average) lateral size enlarges as . Our numerical simulations reveal that the comp…
Time increasing rates of infiltration and reaction in porous media at the percolation thresholds
Ismael S. S. Carrasco, Fábio D. A. Aarão Reis
The infiltration of a solute in a fractal porous medium is usually anomalous, but chemical reactions of the solute and that material may increase the porosity and affect the evolut…
Statistics of adatom diffusion in a model of thin film growth
Edwin E. Mozo Luis, Ismael S. S. Carrasco, Thiago A. de Assis +1
We study the statistics of the number of executed hops of adatoms at the surface of films grown with the Clarke-Vvedensky (CV) model in simple cubic lattices. The distributions of…
Height fluctuations in homoepitaxial thin film growth: A numerical study
I. S. S. Carrasco, T. J. Oliveira
We report on the investigation of height distributions (HDs) and spatial covariances of two-dimensional surfaces obtained from extensive numerical simulations of the celebrated Cla…
Geometry dependence in linear interface growth
I. S. S. Carrasco, T. J. Oliveira
The effect of geometry in the statistics of \textit{nonlinear} universality classes for interface growth has been widely investigated in recent years and it is well known to yield…
Circular Kardar-Parisi-Zhang interfaces evolving out of the plane
I. S. S. Carrasco, T. J. Oliveira
Circular KPZ interfaces spreading radially in the plane have GUE Tracy-Widom (TW) height distribution (HD) and Airy spatial covariance, but what are their statistics if they ev…
Kardar-Parisi-Zhang growth on one-dimensional decreasing substrates
Ismael S. S. Carrasco, Tiago J. Oliveira
Recent experimental works on one-dimensional (1D) circular Kardar-Parisi-Zhang (KPZ) systems whose radii decrease in time have reported controversial conclusions about the statisti…
Universality and dependence on initial conditions in the class of the nonlinear molecular beam epitaxy equation
I. S. S. Carrasco, T. J. Oliveira
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 bo…
Width and extremal height distributions of fluctuating interfaces with window boundary conditions
I. S. S. Carrasco, T. J. Oliveira
We present a detailed study of squared local roughness (SLRDs) and local extremal height distributions (LEHDs), calculated in windows of lateral size , for interfaces in several…
Interface fluctuations for deposition on enlarging flat substrates
I. S. S. Carrasco, K. A. Takeuchi, S. C. Ferreira +1
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 column…