In bistable systems, the stability of front structures often influences the dynamics of extended patterns. We show how the combined effect of an instability to curvature modulations and proximity to a pitchfork front bifurcation leads to spontaneous nucleation of spiral waves along the front. This effect is demonstrated by direct simulations of a FitzHugh-Nagumo (FHN) model and by simulations o...

We study the effect of quenched randomness in the arc-length dependent spontaneous curvature of a wormlike chain under tension. In the weakly bending approximation in two dimensions, we obtain analytic results for the force-elongation curve and the width of transverse fluctuations. We compare quenched and annealed disorder and conclude that the former cannot always be reduced to a simple change...

In this paper energy bands and Berry curvature of graphene was studied. Desired Hamiltonian regarding the next-nearest neighbors obtained by tight binding model. By using the second quantization approach, the transformation matrix is calculated and the Hamiltonian of system is diagonalized. With this Hamiltonian, the band structure and wave function can be calculated. By using calculated wave f...

PURPOSE To explore the potential effect of ageing on the corneal curvature and corrected visual acuity in patients with long-term keratoconus because of the paucity of these patients older than 50 years. METHODS Records of keratoconic patients, who had initially presented to a specialized contact lens clinic and followed for more than 20 years after disease onset, were reviewed. Collected inf...

which is sharp as indicated in the Euclidean case. However even if M contains a small compact region where the Ricci curvature is not nonnegative, estimate (1.1) becomes very much different from (1.2) when r is large, due to the presence of the √ k term. Whether estimate (1.2) is stable under perturbation has been an open question for some time, in light of the known stability results on weaker...

We analyze 2-dimensional Ginzburg-Landau vortices at critical coupling, and establish asymptotic formulas for the tangent vectors of the vortex moduli space using theorems of Taubes and Bradlow. We then compute the corresponding Berry curvature and holonomy in the large area limit.

In bistable systems, the stability of front structures often influences the dynamics of extended patterns. We show how the combined effect of an instability to curvature modulations and proximity to a pitchfork front bifurcation leads to spontaneous nucleation of spiral waves along the front. This effect is demonstrated by direct simulations of a FitzHugh-Nagumo (FHN) model and by simulations o...

We study the effects of a small curvature of the middle plane of a thickness-shear mode crystal plate resonator on its vibration frequencies, modes and acceleration sensitivity. Two-dimensional equations for coupled thickness-shear, flexural and extensional vibrations of a shallow shell are used. The equations are simplified to a single equation for thickness-shear, and two equations for couple...

In the static field limit, the vibrational hyperpolarizability consists of two contributions due to: ~1! the shift in the equilibrium geometry ~known as nuclear relaxation!, and ~2! the change in the shape of the potential energy surface ~known as curvature!. Simple finite field methods have previously been developed for evaluating these static field contributions and also for determining the e...

A type of super-hydrophobic surface consists of a solid plane boundary with an array of grooves which, due to the effect of surface tension, prevent a complete wetting of the wall. The effect is greatest when the grooves are aligned with the flow. The pressure difference between the liquid and the gas in the grooves causes a curvature of the liquid surface resisted by surface tension. The effec...