arXiv subjects

Razvan-Dumitru Ceuca

Publications and source records attributed to Razvan-Dumitru Ceuca.

3 recordsLinked to original sources

arXiv2026

Effective Complexity Reduction of the Landau-de Gennes Elastic Energy: A Quantitative Framework and Numerical Validation

We revisit the elastic energy formulation of the Landau-de Gennes model for nematic liquid crystals, focusing on quantitative reductions of the multi-constant elastic energy. Building on the generalized optimal scaling procedure (GOS) introduced by Rusconi et al. in 2025, we identify explicit parameter regimes in which the three-constant model $(L_1,L_2,L_3)$ can be reduced to $(L_1,L_2,0)$ and how the two-constant model $(L_1,L_2,0)$ can be reduced to the commonly used one-constant configuration $(L_1,0,0)$. The analytical scaling predictions are tested numerically using the openQmin simulation framework, confirming that below a critical threshold for $L_3$ or $L_2$, given by GOS, the deviation from the reduced model remains of the same order of magnitude as predicted by the scaling theory. These results provide a quantitative criterion for the validity of reduced elastic models and establish a direct connection between optimal scaling arguments and numerical observations within the Landau-de Gennes framework.

cond-mat.soft↗

arXiv2021

Effective surface energies in nematic liquid crystals as homogenised rugosity effects

We study the effect of boundary rugosity in nematic liquid crystalline systems. We consider a highly general formulation of the problem, able to simultaneously deal with several liquid crystal theories. We use techniques of Gamma convergence and demonstrate that the effect of fine-scale surface oscillations may be replaced by an effective homogenised surface energy on a simpler domain. The homogenisation limit is then quantitatively studied in a simplified setting, obtaining convergence rates.

math.AP↗

arXiv2020

Cubic microlattices embedded in nematic liquid crystals: a Landau de-Gennes study

We consider a Landau-de Gennes model for a connected cubic lattice scaffold in a nematic host, in a dilute regime. We analyse the homogenised limit for both cases in which the lattice of embedded particles presents or not cubic symmetry and then we compute the free effective energy of the composite material. In the cubic symmetry case, we impose different types of surface anchoring energy densities, such as quartic, Rapini-Papoular or more general versions, and, in this case, we show that we can tune any coefficient from the corresponding bulk potential, especially the phase transition temperature. In the case with loss of cubic symmetry, we prove similar results in which the effective free energy functional has now an additional term, which describes a change in the preferred alignment of the liquid crystal particles inside the domain. Moreover, we compute the rate of convergence for how fast the surface energies converge to the homogenised one and also for how fast the minimisers of the free energies tend to the minimiser of the homogenised free energy.

math.AP↗