arXiv subjects

Rastko Sknepnek

Publications and source records attributed to Rastko Sknepnek.

At least 37 records · Page 2Linked to original sources

arXiv2017

Cell division and death inhibit glassy behaviour of confluent tissues

We investigate the effects of cell division and apopotosis on collective dynamics in two-dimensional epithelial tissues. Our model includes three key ingredients observed across many epithelia, namely cell-cell adhesion, cell death and a cell division process that depends on the surrounding environment. We show a rich non-equilibrium phase diagram depending on the ratio of cell death to cell division and on the adhesion strength. For large apopotosis rates, cells die out and the tissue disintegrates. As the death rate decreases, however, we show, consecutively, the existence of a gas-like phase, a gel-like phase, and a dense confluent (tissue) phase. Most striking is the observation that the tissue is self-melting through its own internal activity, ruling out the existence of any glassy phase.

cond-mat.soft↗

arXiv2017

Non-Hookean statistical mechanics of clamped graphene ribbons

Thermally fluctuating sheets and ribbons provide an intriguing forum in which to investigate strong violations of Hooke's Law: large distance elastic parameters are in fact not constant, but instead depend on the macroscopic dimensions. Inspired by recent experiments on free-standing graphene cantilevers, we combine the statistical mechanics of thin elastic plates and large-scale numerical simulations to investigate the thermal renormalization of the bending rigidity of graphene ribbons clamped at one end. For ribbons of dimensions $W\times L$ (with $L\geq W$), the macroscopic bending rigidity $κ_R$ determined from cantilever deformations is independent of the width when $W<\ell_\textrm{th}$, where $\ell_\textrm{th}$ is a thermal length scale, as expected. When $W>\ell_\textrm{th}$, however, this thermally renormalized bending rigidity begins to systematically increase, in agreement with the scaling theory, although in our simulations we were not quite able to reach the system sizes necessary to determine the fully developed power law dependence on $W$. When the ribbon length $L > \ell_p$, where $\ell_p$ is the $W$-dependent thermally renormalized ribbon persistence length, we observe a scaling collapse and the beginnings of large scale random walk behavior.

cond-mat.soft↗

arXiv2016

Active Vertex Model for Cell-Resolution Description of Epithelial Tissue Mechanics

We introduce an Active Vertex Model (AVM) for cell-resolution studies of the mechanics of confluent epithelial tissues consisting of tens of thousands of cells, with a level of detail inaccessible to similar methods. The AVM combines the Vertex Model for confluent epithelial tissues with active matter dynamics. This introduces a natural description of the cell motion and accounts for motion patterns observed on multiple scales. Furthermore, cell contacts are generated dynamically from positions of cell centres. This not only enables efficient numerical implementation, but provides a natural description of the T1 transition events responsible for local tissue rearrangements. The AVM also includes cell alignment, cell-specific mechanical properties, cell growth, division and apoptosis. In addition, the AVM introduces a flexible, dynamically changing boundary of the epithelial sheet allowing for studies of phenomena such as the fingering instability or wound healing. We illustrate these capabilities with a number of case studies.

physics.bio-ph↗

arXiv2014

Effects of scars on crystalline shell stability under external pressure

We study how the stability of spherical crystalline shells under external pressure is influenced by the defect structure. In particular, we compare stability for shells with a minimal set of topologically-required defects to shells with extended defect arrays (grain boundary "scars" with non-vanishing net disclination charge). We perform Monte Carlo simulations to compare how shells with and without scars deform quasi-statically under external hydrostatic pressure. We find that the critical pressure at which shells collapse is lowered for scarred configurations that break icosahedral symmetry and raised for scars that preserve icosahedral symmetry. The particular shapes which arise from breaking of an initial icosahedrally-symmetric shell depend on the Föppl-von Kármán number.

cond-mat.soft↗

arXiv2014

Active swarms on a sphere

Here we show that coupling to curvature has profound effects on collective motion in active systems, leading to patterns not observed in flat space. Biological examples of such active motion in curved environments are numerous: curvature and tissue folding are crucial during gastrulation, epithelial and endothelial cells move on constantly growing, curved crypts and vili in the gut, and the mammalian corneal epithelium grows in a steady-state vortex pattern. On the physics side, droplets coated with actively driven microtubule bundles show active nematic patterns. We study a model of self-propelled particles with polar alignment on a sphere. Hallmarks of these motion patterns are a polar vortex and a circulating band arising due to the incompatibility between spherical topology and uniform motion - a consequence of the hairy ball theorem. We present analytical results showing that frustration due to curvature leads to stable elastic distortions storing energy in the band.

cond-mat.soft↗

arXiv2014

Defect dynamics in active nematics

Topological defects are distinctive signatures of liquid crystals. They profoundly affect the viscoelastic behavior of the fluid by constraining the orientational structure in a way that inevitably requires global changes not achievable with any set of local deformations. In active nematic liquid crystals topological defects not only dictate the global structure of the director, but also act as local sources of motion, behaving as self-propelled particles. In this article we present a detailed analytical and numerical study of the mechanics of topological defects in active nematic liquid crystals.

cond-mat.soft↗

arXiv2013

Optimal shapes and stresses of adherent cells on patterned substrates

We investigate a continuum mechanical model for an adherent cell on two dimensional adhesive micropatterned substrates. The cell is modeled as an isotropic and homogeneous elastic material subject to uniform internal contractile stresses. The build-up of tension from cortical actin bundles at the cell periphery is incorporated by introducing an energy cost for bending of the cell boundary, resulting to a resistance to changes in local curvature. Integrin-based adhesions are modeled as harmonic springs, that pin the cell to adhesive patches of a predefined geometry. Using Monte Carlo simulations and analytical techniques we investigate the competing effects of bulk contractility and cortical bending rigidity in regulating cell shapes on non-adherent regions. We show that the crossover from convex to concave cell edges is controlled by the interplay between contractile stresses and boundary bending rigidity. In particular, the cell boundary becomes concave beyond a critical value of the contractile stress that is proportional to the cortical bending rigidity. Furthermore, the intracellular stresses are found largely concentrated at the concave edge of the cell. The model can be used to generate a cell-shape phase diagram for each specific adhesion geometry.

physics.bio-ph↗

arXiv2013

Pathways to faceting of vesicles

The interplay between geometry, topology and order can lead to geometric frustration that profoundly affects the shape and structure of a curved surface. In this commentary we show how frustration in this context can result in the faceting of elastic vesicles. We show that, under the right conditions, an assortment of regular and irregular polyhedral structures may be the low energy states of elastic membranes with spherical topology. In particular, we show how topological defects, necessarily present in any crystalline lattice confined to spherical topology, naturally lead to the formation of icosahedra in a homogeneous elastic vesicle. Furthermore, we show that introducing heterogeneities in the elastic properties, or allowing for non-linear bending response of a homogeneous system, opens non-trivial pathways to the formation of faceted, yet non-icosahedral, structures.

cond-mat.soft↗

arXiv2013

Shapes of pored membranes

We study the shapes of pored membranes within the framework of the Helfrich theory under the constraints of fixed area and pore size. We show that the mean curvature term leads to a budding- like structure, while the Gaussian curvature term tends to flatten the membrane near the pore; this is corroborated by simulation. We propose a scheme to deduce the ratio of the Gaussian rigidity to the bending rigidity simply by observing the shape of the pored membrane. This ratio is usually difficult to measure experimentally. In addition, we briefly discuss the stability of a pore by relaxing the constraint of a fixed pore size and adding the line tension. Finally, the flattening effect due to the Gaussian curvature as found in studying pored membranes is extended to two-component membranes. We find that sufficiently high contrast between the components' Gaussian rigidities leads to budding which is distinct from that due to the line tension.

cond-mat.soft↗

arXiv2012

Planar sheets meet negative curvature liquid interfaces

If an inextensible thin sheet is adhered to a substrate with a negative Gaussian curvature it will experience stress due to geometric frustration. We analyze the consequences of such geometric frustration using analytic arguments and numerical simulations. Both concentric wrinkles and eye-like folds are shown to be compatible with negative curvatures. Which pattern will be realized depends on the curvature of the substrate. We discuss both types of folding patterns and determine the phase diagram governing their appearance.

cond-mat.soft↗

arXiv2012

A curvature-driven effective attraction in multicomponent membranes

We study closed liquid membranes that segregate into three phases due to differences in the chemical and physical properties of its components. The shape and in-plane membrane arrangement of the phases are coupled through phase-specific bending energies and line tensions. We use simulated annealing Monte Carlo simulations to find low-energy structures, allowing both phase arrangement and membrane shape to relax. The three-phase system is the simplest one in which there are multiple interface pairs, allowing us to analyze interfacial preferences and pairwise distinct line tensions. We observe the system's preference for interface pairs that maximize differences in spontaneous curvature. From a pattern selection perspective, this acts as an effective attraction between phases of most disparate spontaneous curvature. We show that this effective attraction is robust enough to persist even when the interface between these phases is the most penalized by line tension. This effect is driven by geometry and not by any explicit component-component interaction.

cond-mat.soft↗

arXiv2012

Nonlinear elastic model for faceting of vesicles with soft grain boundaries

We use an elastic model to explore faceting of solid-wall vesicles with elastic heterogeneities. We show that faceting occurs in regions where the vesicle wall is softer, such as areas of reduced wall thicknesses or concentrated in crystalline defects. The elastic heterogeneities are modeled as a second component with reduced elastic parameters. Using simulated annealing Monte Carlo simulations we obtain the vesicle shape by optimizing the distributions of facets and boundaries. Our model allows us to reduce the effects of the residual stress generated by crystalline defects, and reveals a robust faceting mechanism into polyhedra other than the icosahedron.

cond-mat.soft↗

arXiv2010

Spectral analysis for the iron-based superconductors: Anisotropic spin fluctuations and fully gapped s^{\pm}-wave superconductivity

Spin fluctuations are considered to be one of the candidates that drive a sign-reversed s^{\pm} superconducting state in the iron pnictides. In the magnetic scenario, whether the spin fluctuation spectrum exhibits certain unique fine structures is an interesting aspect for theoretical study in order to understand experimental observations. We investigate the detailed momentum dependence of the short-range spin fluctuations using a 2-orbital model in the self-consistent fluctuation exchange approximation and find that a common feature of those fluctuations that are capable of inducing a fully gapped s^{\pm} state is the momentum anisotropy with lengthened span along the direction transverse to the antiferromagnetic momentum transfer. Performing a qualitative analysis based on the orbital character and the deviation from perfect nesting of the electronic structure for the 2-orbital and a more complete 5-orbital model, we gain the insight that this type of anisotropic spin fluctuations favor superconductivity due to their enhancement of intra-orbital, but inter-band, pair scattering processes. The momentum anisotropy leads to elliptically shaped magnetic responses which have been observed in inelastic neutron scattering measurements. Meanwhile, our detailed study on the magnetic and the electronic spectrum shows that the dispersion of the magnetic resonance mode in the nearly isotropic s^{\pm} superconducting state exhibits anisotropic propagating behavior in an upward pattern and the coupling of the resonance mode to fermions leads to a dip feature in the spectral function.

cond-mat.supr-con↗

arXiv2009

Orbital coupling and superconductivity in the iron pnictides

We demonstrate that strong inter-orbital interaction is very efficient to achieve superconductivity due to magnetic fluctuations in the iron pnictides. Fermi surface states that are coupled by the antiferromagnetic wave vector are often of different orbital nature, causing pair-hopping interactions between distinct Fe-3d orbitals to become important. Performing a self-consistent FLEX calculation below $T_{c}$ we determine the superconducting order parameter as function of intra- and inter-orbital couplings. We find an $s^{\pm}$-pairing state with $T_{c}\simeq80\mathrm{K}$ for realistic parameters.

cond-mat.supr-con↗

arXiv2009

Anisotropic pairing in the iron pnictides

We determine the anisotropy of the spin fluctuation induced pairing gap on the Fermi surface of the FeAs based superconductors as function of the exchange and Hund's coupling $J_{H}$. We find that for sufficiently large $J_{H}$, nearly commensurate magnetic fluctuations yield a fully gapped $s^{\pm}$-pairing state with small anisotropy of the gap amplitude on each Fermi surface sheet, but significant variations of the gap amplitude for different sheets of the Fermi surface. In particular, we obtain the large variation of the gap amplitude on different Fermi surface sheets, as seen in ARPES experiments. For smaller values of Hund's coupling incommensurate magnetic fluctuations yield an $s^{\pm}$-pairing state with line nodes. Such a state is also possible once the anisotropy of the material is reduced and three dimensional effects come into play.

cond-mat.supr-con↗

arXiv2007

Universality of liquid-gas Mott transitions at finite temperatures

We explain in a consistent manner the set of seemingly conflicting experiments on the finite temperature Mott critical point, and demonstrate that the Mott transition is in the Ising universality class. We show that, even though the thermodynamic behavior of the system near such critical point is described by an Ising order parameter, the global conductivity can depend on other singular observables and, in particular, on the energy density. Finally, we show that in the presence of weak disorder the dimensionality of the system has crucial effects on the size of the critical region that is probed experimentally.

cond-mat.str-el↗

arXiv2006

Quantum phase transitions of the diluted O(3) rotor model

We study the phase diagram and the quantum phase transitions of a site-diluted two-dimensional O(3) quantum rotor model by means of large-scale Monte-Carlo simulations. This system has two quantum phase transitions, a generic one for small dilutions, and a percolation transition across the lattice percolation threshold. We determine the critical behavior for both transitions and for the multicritical point that separates them. In contrast to the exotic scaling scenarios found in other random quantum systems, all these transitions are characterized by finite-disorder fixed points with power-law scaling. We relate our findings to a recent classification of phase transitions with quenched disorder according to the rare region dimensionality, and we discuss experiments in disordered quantum magnets.

cond-mat.str-el↗

arXiv2006

Spin Structure Factor of the Frustrated Quantum Magnet Cs_2CuCl_4

The ground state properties and neutron structure factor for the two-dimensional antiferromagnet on the triangular lattice, with uni-directional anisotropy in the nearest-neighbor exchange couplings and a weak Dzyaloshinskii-Moriya (DM) interaction, are studied. This Hamiltonian has been used to interpret neutron scattering measurements on the spin 1/2 spiral spin-density-wave system, Cs_2CuCl_4, [R. Coldea, et al., Phys. Rev. B 68, 134424 (2003)]. Calculations are performed using a 1/S expansion, taking into account interactions between spin-waves. The ground state energy, the shift of the ordering wave-vector, Q, and the local magnetization are all calculated to order 1/S^2. The neutron structure factor, obtained using anharmonic spin-wave Green's functions to order 1/S, is shown to be in reasonable agreement with published neutron data, provided that slightly different parameters are used for the exchange and DM interactions than those inferred from measurements in high magnetic field.

cond-mat.str-el↗