arXiv subjects

C. Nadir Kaplan

Publications and source records attributed to C. Nadir Kaplan.

14 recordsLinked to original sources

arXiv2026

Geometric theory of elastic curves constrained on rigid curved surfaces

Slender elastic objects constrained to curved surfaces are ubiquitous in soft systems, with examples ranging from DNA wrapping around histones to actin filaments forming contractile rings on the cell membrane during cytokinesis. In the continuum limit, the conformation of these effectively one-dimensional (1D) objects is governed by both the geometry and mechanics of the embedding surface, and the elasticity of the object. Existing phenomenological typically describe such behavior through elastic energy minimization that incorporates bending and twisting, but neglect stretching that may be important for filaments with finite cross-section or are highly incompatible with the underlying surface. Here we present a coarse-grained geometric theory of 1D elastic curves constrained on rigid surfaces, derived from the first principles. For an isotropic material, our model emerges naturally in terms of the Young's modulus, Poisson's ratio, and area moments of inertia. The resulting effective energy functional explicitly includes stretching in addition to bending and twisting. We minimize it to determine the equilibrium curve conformations on different zero, positive, or negative Gaussian rigid surfaces. Our theory provides a general framework for analyzing the equilibrium configurations of surface-bound elastic curves in biologically and physically relevant settings.

cond-mat.soft↗

arXiv2026

A hyperelastic theory for nonlinear hydrogel diffusiophoresis

Hydrogel diffusiophoresis is the deformation of a hydrogel due to a solute gradient that leads to a gradient of pairwise interactions between the solute particles and the hydrogel polymers to trigger osmotic flux. Unlike typical osmosis, it occurs without any interface selectivity of the gel to the solute and can overcome the diffusive swelling without any structural modifications to the gel. We have recently shown this effect for linear deformations of a chemically responsive polyacrylic acid (PAA) hydrogel that releases ions upon arrival of a stimulus (acid), thus internally generating the solute gradient required for diffusiophoresis [Phys. Rev. Lett. 132, 208201 (2024)]. Here we develop a nonlinear poroelastic theory for large diffusiophoretic gel strains in two models: Model I considers deformations of a generic gel when an external solute gradient is imposed and indicates that deformations can be stored while the stimulus gradient persists. Model II is concerned with the internal generation of the solute gradient within the gel, motivated by the coupled PAA gel, solute (copper), and stimulus (acid) system. In Model II, we investigate the nonlinear deformations for high stimulus concentrations or by changing the solute particle size to boost steric polymer-solute interactions, as well as under a stimulus flow through the gel. Compared to the experimental strain rates in Katke [Phys. Rev. Lett. 132, 208201 (2024)], Model II demonstrates that varying the stimulus concentration can increase the strain rate up to four times, changing the solute particle size up to $\sim 25$ times, and imposed flow up to $\sim 40$ times. Our theory couples nonlinear poroelasticity, polymer-solute interactions, and reaction-transport dynamics to predict large and fast diffusiophoretic gel deformations, which may find applications in hydrogel-based soft robotics and drug delivery.

cond-mat.soft↗

arXiv2024

Diffusio-phoretic fast swelling of chemically responsive hydrogels

Acid-induced release of stored ions from polyacrylic acid hydrogels (with a free surface fully permeable to the ion and acid flux) was observed to increase the gel osmotic pressure that leads to rapid, temporary swelling faster than the characteristic solvent absorption rate of the gel. Here we develop a continuum poroelastic theory that quantitatively explains the experiments by introducing a "gel diffusio-phoresis" mechanism: Steric repulsion between the gel polymers and released ions can induce a diffusio-osmotic solvent intake counteracted by the diffusio-phoretic expansion of the gel network. For applications ranging from drug delivery to soft robotics, engineering the gel diffusio-phoresis may enable stimuli-responsive hydrogels with amplified strain rates and power output.

cond-mat.soft↗

arXiv2023

Dynamic, viscoelasticity-driven shape change of elastomer bilayers

Thin bilayers made of elastic sheets with different strain recoveries can be used for dynamic shape morphing through ambient stimuli, such as temperature, mass diffusion, and light. As a fundamentally different approach to designing temporal shape change, constituent polymer molecular features (rather than external fields) are leveraged, specifically the viscoelasticity of gelatin bilayers, to achieve dynamic three-dimensional (3D) curls and helical twists. After stretching and releasing, the acquired 3D shape recovers its original flat shape on a timescale originating from the polymer viscoelasticity. The bilayer time-dependent curvature can be accurately predicted from hyperelastic and viscoelastic functions using finite element analysis (FEA). FEA reveals the nonlinear shape dynamics in space and time in quantitative agreement with experiments. The findings present a new frontier in dynamic biomimetic shape-morphing by exploiting intrinsic material properties in contrast with state-of-the-art methods relying on external field variations, moving one step closer to acquiring autonomous shape-shifting capabilities of biological systems.

cond-mat.soft↗

arXiv2021

Geometrical dynamics of edge-driven surface growth

Accretion of mineralized thin wall-like structures via localized growth along their edges is observed in a range of physical and biological systems ranging from molluscan and brachiopod shells to carbonate-silica composite precipitates. To understand the shape of these mineralized structures, we develop a mathematical framework that treats the thin-walled shells as a smooth surface left in the wake of the growth front that can be described as an evolving space curve. Our theory then takes an explicit geometric form for the prescription of the velocity of the growth front curve, along with some compatibility relations and a closure equation related to the nature of surface curling. The result is a set of equations for the geometrical dynamics of a curve that leaves behind a compatible surface. Solutions of these equations capture a range of geometric precipitate patterns seen in abiotic and biotic forms across scales. In addition to providing a framework for the growth and form of these thin-walled morphologies, our theory suggests a new class of dynamical systems involving moving space curves that are compatible with non-Euclidean embeddings of surfaces.

cond-mat.soft↗

arXiv2016

Achiral symmetry breaking and positive Gaussian modulus lead to scalloped colloidal membranes

In the presence of a non-adsorbing polymer, monodisperse rod-like particles assemble into colloidal membranes, which are one rod-length thick liquid-like monolayers of aligned rods. Unlike 3D edgeless bilayer vesicles, colloidal monolayer membranes form open structures with an exposed edge, thus presenting an opportunity to study physics of thin elastic sheets. Membranes assembled from single-component chiral rods form flat disks with uniform edge twist. In comparison, membranes comprised of mixture of rods with opposite chiralities can have the edge twist of either handedness. In this limit disk-shaped membranes become unstable, instead forming structures with scalloped edges, where two adjacent lobes with opposite handedness are separated by a cusp-shaped point defect. Such membranes adopt a 3D configuration, with cusp defects alternatively located above and below the membrane plane. In the achiral regime the cusp defects have repulsive interactions, but away from this limit we measure effective long-ranged attractive binding. A phenomenological model shows that the increase in the edge energy of scalloped membranes is compensated by concomitant decrease in the deformation energy due to Gaussian curvature associated with scalloped edges, demonstrating that colloidal membranes have positive Gaussian modulus. A simple excluded volume argument predicts the sign and magnitude of the Gaussian curvature modulus that is in agreement with experimental measurements. Our results provide insight into how the interplay between membrane elasticity, geometrical frustration and achiral symmetry breaking can be used to fold colloidal membranes into 3D shapes.

cond-mat.soft↗

arXiv2014

Dynamics of evaporative colloidal patterning

Drying suspensions often leave behind complex patterns of particulates, as might be seen in the coffee stains on a table. Here we consider the dynamics of periodic band or uniform solid film formation on a vertical plate suspended partially in a drying colloidal solution. Direct observations allow us to visualize the dynamics of the band and film deposition, and the transition in between when the colloidal concentration is varied. A minimal theory of the liquid meniscus motion along the plate reveals the dynamics of the banding and its transition to the filming as a function of the ratio of deposition and evaporation rates. We also provide a complementary multiphase model of colloids dissolved in the liquid, which couples the inhomogeneous evaporation at the evolving meniscus to the fluid and particulate flows and the transition from a dilute suspension to a porous plug. This allows us to determine the concentration dependence of the bandwidth and the deposition rate. Together, our findings allow for the control of drying-induced patterning as a function of the colloidal concentration and evaporation rate.

cond-mat.soft↗

arXiv2014

Evaporation-driven ring and film deposition from colloidal droplets

Evaporating suspensions of colloidal particles lead to the formation of a variety of patterns, ranging from a left-over ring of a dried coffee drop to uniformly distributed solid pigments left behind wet paint. To characterize the transition between single rings, multiple concentric rings, broad bands, and uniform deposits, we investigate the dynamics of a drying droplet via a multiphase model of colloidal particles in a solvent. Our theory couples the inhomogeneous evaporation at the evolving droplet interface to the dynamics inside the drop, i.e. the liquid flow, local variations of the particle concentration, and the propagation of the deposition front where the solute forms an incompressible porous medium at high concentrations. A dimensionless parameter combining the capillary number and the droplet aspect ratio captures the formation conditions of different pattern types.

cond-mat.soft↗

arXiv2014

Chiral smectic A membranes: Unified theory of free edge structure and twist walls

Monodisperse suspensions of rodlike chiral $fd$ viruses are condensed into a rod-length thick colloidal monolayers of aligned rods by depletion forces. Twist deformations of the molecules are expelled to the monolayer edge as in a chiral smectic $A$ liquid crystal, and a cholesteric band forms at the edge. Coalescence of two such isolated membranes results in a twist wall sandwiched between two regions of aligned rods, dubbed $π$-walls. By modeling the membrane as a binary fluid of coexisting cholesteric and chiral smectic $A$ liquid-crystalline regions, we develop a unified theory of the $π$-walls and the monolayer edge. The mean-field analysis of our model yields the molecular tilt profiles, the local thickness change, and the crossover from smectic to cholesteric behavior at the monolayer edge and across the $π$-wall. Furthermore, we calculate the line tension associated with the formation of these interfaces. Our model offers insights regarding the stability and the detailed structure of the $π$-wall and the monolayer edge.

cond-mat.soft↗

arXiv2013

Intrinsic curvature determines the crinkled edges of "crenellated disks"

Elastic curvature constants determine many structural and functional properties of fluid membranes. Methods to measure the mean curvature modulus have proved to be robust. In contrast, Gaussian curvature is an intrinsic property of a surface. Thus, measuring the relevant modulus $\bar{k}$ in fluid membranes remains a challenging task. Inspired from colloidal "crenellated disks" observed in a model system composed of hard rods, we propose a concise relation between the two curvature moduli and the parameters associated with the free, crinkled edges. Our approach offers a straightforward way to determine $\bar{k}$ of these reconfigurable membranes, where various complex topologies can be nanosculpted. Further, we reveal the structure and stability of the "crenellated disks."

cond-mat.soft↗

arXiv2010

Theory of depletion induced phase transition from chiral smectic A twisted ribbons to semi-infinite flat membranes

We consider a theoretical model for the chiral smectic A twisted ribbons observed in assemblies of fd viruses condensed by depletion forces. The depletion interaction is modeled by an edge energy assumed to be proportional to the depletant polymer in solution. Our model is based on the Helfrich energy for surface bending and the de Gennes model of chiral smectic A liquid crystals with twist penetration at the edge. We consider two variants of this model, one with the conventional Helfrich Gaussian curvature term, and a second with saddle-splay energy. A mean field analysis of both models yields a first-order phase transition between ribbons and semi-infinite flat membranes as the edge energy is varied. The phase transition line and tilt angle profile are found to be nearly identical for the two models; the pitch of the ribbon, however, does show some differences. Our model yields good qualitative agreement with experimental observations if the sign of the Gaussian curvature or saddle-splay modulus is chosen to favor negative Gaussian curvature.

cond-mat.soft↗

arXiv2010

Frustrated Further-Neighbor Antiferromagnetic and Electron-Hopping Interactions in the d=3 tJ Model: Finite-Temperature Global Phase Diagrams from Renormalization-Group Theory

The renormalization-group theory of the d=3 tJ model is extended to further-neighbor antiferromagnetic or electron-hopping interactions, including the ranges of frustration. The global phase diagram of each model is calculated for the entire ranges of temperatures, electron densities, and further/first-neighbor interaction strength ratios. In addition to the τ_{tJ} phase seen in earlier studies of the nearest-neighbor d=3 tJ model, the τ_{Hb} phase seen before in the d=3 Hubbard model appears both near and away from half-filling. These distinct τphases potentially correspond to different (BEC-like and BCS-like) superconducting phases.

cond-mat.supr-con↗

arXiv2009

Infinitely Robust Order and Local Order-Parameter Tulips in Apollonian Networks with Quenched Disorder

For a variety of quenched random spin systems on an Apollonian network, including ferromagnetic and antiferromagnetic bond percolation and the Ising spin glass, we find the persistence of ordered phases up to infinite temperature over the entire range of disorder. We develop a renormalization-group technique that yields highly detailed information, including the exact distributions of local magnetizations and local spin-glass order parameters, which turn out to exhibit, as function of temperature, complex and distinctive tulip patterns.

cond-mat.dis-nn↗

arXiv2008

Quantum-Mechanically Induced Asymmetry in the Phase Diagrams of Spin-Glass Systems

The spin-1/2 quantum Heisenberg model is studied in all spatial dimensions d by renormalization-group theory. Strongly asymmetric phase diagrams in temperature and antiferromagnetic bond probability p are obtained in dimensions d \geq 3. The asymmetry at high temperatures approaching the pure ferromagnetic and antiferromagnetic systems disappears as d is increased. However, the asymmetry at low but finite temperatures remains in all dimensions, with the antiferromagnetic phase receding to the ferromagnetic phase. A finite-temperature second-order phase boundary directly between the ferromagnetic and antiferromagnetic phases occurs in d \geq 6, resulting in a new multicritical point at its meeting with the boundaries to the paramagnetic phase. In d=3,4,5, a paramagnetic phase reaching zero temperature intervenes asymmetrically between the ferromagnetic and reentrant antiferromagnetic phases. There is no spin-glass phase in any dimension.

cond-mat.dis-nn↗