1,720,987 research outputs found
The delamination of a growing elastic sheet with adhesion
Full text linkWe study the onset of delamination blisters in a growing elastic sheet adhered to a flat stiff substrate. When the ends of the sheet are kept fixed, its growth causes residual stresses that lead to delamination. This instability can be viewed as a discontinuous buckling between the complete adhered solution and the buckled solution. We provide an analytic expression for the critical deformation at which the instability occurs. We show that the critical threshold scales with a single dimensionless parameter that comprises information from the geometry of the sheet, the mechanical parameters of material and the adhesive features of the substrate
Active viscoelastic nematics with partial degree of order
Full text linkContinuum models of active nematic gels have proved successful to describe a
number of biological systems consisting of a population of rodlike motile
subunits in a fluid environment. However, in order to get a thorough
understanding of the collective processes underlying the behaviour of active
biosystems, the theoretical underpinnings of these models still need to be
critically examined. To this end, we derive a minimal model based on a nematic
elastomer energy, where the key parameters have a simple physical
interpretation and the irreversible nature of activity emerges clearly. The
interplay between viscoelastic material response and active dynamics of the
microscopic constituents is accounted for by material remodelling. Partial
degree of order and defect dynamics is included as a result of the kinematic
coupling between the nematic elastomer shape-tensor and the orientational
ordering tensor \bQ. In a simple one-dimensional channel geometry, we use
linear stability analysis to show that even in the isotropic phase the
interaction between flow-induced local nematic order and activity results in a
spontaneous flow of particles
Drift-Diffusion Transport in a Randomly Inhomogeneous One-Dimensional Medium
Full text linkOrganic semiconductors are intrinsic randomly inhomogeneous materials where charge transport occurs by hopping of the carriers between localized sites having a distribution of energy levels. However, the average carrier density seems to be accurately described by a simple drift-diffusion equation. We investigate the reasons for the effectiveness of the drift-diffusion model in a random material and show that the key assumption for its validity is that the correlation lengths of the randomly perturbed coefficients are much smaller than any other characteristic length of the problem. As a byproduct, we find how the effective drift and diffusion coefficients depend on the randomness
Landau-like theory for buckling phenomena and its application to the elastica hypoarealis
Full text linkBifurcation phenomena are ubiquitous in elasticity, but their study is often limited to linear perturbation or numerical analysis since second or higher variations are often beyond an analytic treatment. Here, we review two key mathematical ideas, namely, the splitting lemma and the determinacy of a function, and show how they can be fruitfully used to derive a reduced function, named Landau expansion in the paper, that allows us to give a simple but rigorous description of the bifurcation scenario, including the stability of the equilibrium solutions. We apply these ideas to a paradigmatic example with potential applications to various softly constrained physical systems and biological tissues: a stretchable elastic ring under pressure. We prove the existence of a tricritical point and find bistability effects and hysteresis when the stretching modulus is sufficiently small. These results seem to be in qualitative agreement with some recent experiments on heart cells
Determination of the symmetry classes of orientational ordering tensors
Full text linkThe orientational order of nematic liquid crystals is traditionally studied by
means of the second-rank ordering tensor S. When this is calculated through
experiments or simulations, the symmetry group of the phase is not known
a priori, but needs to be deduced from the numerical realisation of S, which
is affected by numerical errors. There is no generally accepted procedure to
perform this analysis. Here, we provide a new algorithm suited to identifying
the symmetry group of the phase. As a by product, we prove that there are
only five phase-symmetry classes of the second-rank ordering tensor and
give a canonical representation of S for each class. The nearest tensor of the
assigned symmetry is determined by group-projection. In order to test our
procedure, we generate uniaxial and biaxial phases in a system of interacting
particles, endowed with D_{\infty h} or D_{2h} symmetry, which mimic the outcome
of Monte–Carlo simulations. The actual symmetry of the phases is correctly
identified, along with the optimal choice of laboratory frame
Asymptotic director fields of moving defects in nematic liquid crystals
No full textThis paper deals with the detailed structure of the order-parameter field
both close and far from a moving singularity in nematic liquid crystals. We put forward asymptotic expansions that allow to extract from the exact solution the necessary analytical details, at any prescribed order. We also present a simple uniform approximation, which captures the qualitative features of the exact solution in all the domain
A Catastrophe-Theoretic Approach to Tricritical Points with Application to Liquid Crystals
No full textBoundary-roughness effects in nematic liquid crystals
No full textWe study the equilibrium configuration of a nematic liquid crystal bounded by a rough surface. The wrinkling of the surface induces a partial melting in the degree of orientation. This softened region penetrates the bulk up to a length scale which turns out to coincide with the characteristic wavelength of the corrugation. Within the boundary layer where the nematic degree of orientation decreases, the tilt angle steepens and gives rise to a nontrivial structure, which may be interpreted in terms of an effective weak anchoring potential. We determine how the effective surface extrapolation length is related to the microscopic anchoring parameters. We also analyze the crucial role played by the boundary conditions assumed on the degree of orientation. Quite different features emerge depending on whether they are Neumann‐ or Dirichlet‐like. These features may be useful to ascertain experimentally how the degree of orientation interacts with an external boundary
Identification of low-symmetry phases in nematic liquid crystals
Full text linkMesophases of nematic liquid crystals (NLC) are traditionally identified by building a second-rank ordering tensor S that efficiently describes the average orientation of nematogenic molecules with respect to a fixed laboratory/reference frame. In general, both in experiments and in simulations, the symmetry group of the molecules is known a-priori, contrary to the symmetry group of the phase; this latter has to be determined by analysing the numerical realisation of S, possibly affected by numerical errors. Furthermore, when a mesophase has a simple symmetric structure, as is the case of uniaxial nematics, the identification of the preferred direction is relatively an easy task. However, this task becomes less straightforward when the symmetry group of a mesophase is more complex. There is no generally accepted procedure to perform this analysis, but we have provided in a previous paper a new algorithm suited to identifying the symmetry group of the phase. We implement here such algorithm which gives a canonical representation of S for each of the classes that can be distinguished with a second-rank ordering tensor, and determines the nearest tensor of the assigned symmetry by group averaging
- …
