M. M. B. Sheraj | Searcharxiv

arXiv2026

Three-slab model for the dielectric permittivity of a lipid bilayer

A model for the tensorial dielectric permittivity of phospholipid membranes is presented here. The four-nanometer-thick membrane is treated as a composite made up of three dielectric slabs: one for each of the two phospholipid head-group regions, and one for the entire domain spanned by the lipid tails. Equal and opposite bound surface charge densities surround each head-group slab, and account for the membrane dipole potential. Three-slab model parameters are obtained from molecular dynamics simulations, and capture both the zero-field electric potential and the membrane response to applied electric fields. The tail region is well-approximated as having vacuum permittivity, while the head-group region is highly anisotropic due to the configurations of molecular dipoles. For the bilayers studied, the out-of-plane permittivity of the head-group region is 10--15 times that of the vacuum, while the in-plane permittivity is an order of magnitude larger. Membrane responses to applied electric fields up to 30 millivolts per nanometer are found to be in the linear regime. The model overcomes a fundamental limitation of microscopic theories---where the out-of-plane permittivity lacks a meaningful continuum interpretation in the head-group region due to large gradients in the local electric field---by averaging over slab widths, thereby introducing new length scales. Our approach can be extended to characterize general interfacial systems with similar microscopic permittivities.

cond-mat.soft↗

arXiv2025

Interplay of choice and topology in percolation on mediation-driven attachment networks

We investigate bond percolation on mediation-driven attachment (MDA) networks under the generalized Achlioptas process, where $M>1$ candidate bonds are sampled and the one that minimizes the resulting cluster size is selected the best-of-$M$ rule. This framework offers a systematic approach to investigate how network topology and choice mechanisms jointly shape percolation behavior. We analyze the effects of the degree exponent $ω$ and the choice parameter $M$ on the critical point $t_c$ and the critical exponents ($β,α,γ$), which define universality classes and obey the Rushbrooke inequality $α+ 2β+ γ\geq 2$. Using entropy, the order parameter, and their derivatives (representing specific heat and susceptibility respectively), we show that both $t_c$ and the universality class depend only weakly on $ω$ but strongly on $M$, while the Rushbrooke inequality remains valid throughout. For $M=2$, the order parameter varies continuously without a clear order-disorder transition. By contrast, $M=3$ and $M=4$ display explosive percolation that still corresponds to a continuous phase transition, with $M=4$ producing a significantly sharper and clearer order-disorder transition. This sharpening is traced to an enhanced powder-keg effect at larger $M$, underscoring the entropic origin of explosive percolation.

cond-mat.stat-mech↗