It is shown that the strain field of an edge dislocation in a smectic crystal must be described in the framework of nonlinear theory, even far away from the core region. We present an exact solution of this nonlinear problem. The result of the linear theory is recovered in the limit of large bending rigidity.

Within nonlinear Poisson-Boltzmann theory we calculate the pair and triplet interactions between charged colloidal spheres, specifically in the nonlinear regime of low salt concentrations and high charges. We find repulsive pair interactions and attractive triplet interactions. Within a van der Waals-like mean-field theory we estimate in which parameter regime a gas-liquid coexistence is to be ...

A nonlinear scalar field theory from which an effective metric can be deduced is considered. This metric is shown to be compatible with requirements of general relativity. It is demonstrated that there is a class of solutions which fulfill both the nonlinear field equation as the Einstein equations for this metric.

A statistical model of self-organization in a generic class of one-dimensional nonlinear Schrödinger (NLS) equations on a bounded interval is developed. The main prediction of this model is that the statistically preferred state for such equations consists of a deterministic coherent structure coupled with fine-scale, random fluctuations, or radiation. The model is derived from equilibrium stat...

In the present work, effect of von Karman geometric nonlinearity on the vibration characteristics of a Y-shaped single walled carbon nanotube (Y-SWCNT) conveying viscose fluid is investigated based on Euler Bernoulli beam (EBB) model. The Y-SWCNT is also subjected to a longitudinal magnetic field which produces Lorentz force in transverse direction. In order to consider the small scale effects,...

We show that the classical non-abelian pure Chern-Simons action is related to nonrelativistic models in (2+1)-dimensions, via reductions of the gauge connection in Hermitian symmetric spaces. In such models the matter fields are coupled to gauge Chern-Simons fields, which are associated with the isotropy subgroup of the considered symmetric space. Moreover, they can be related to certain (integ...

We develop the effective field theory of density fluctuations for a Newtonian self-gravitating N -body system in quasi-equilibrium, apply it to a homogeneous universe with small density fluctuations. Keeping the density fluctuation up to the second order, we obtain the nonlinear field equation of the 2-pt correlation ξ(r), which contains the 3-pt correlation and formal ultra-violet divergences....

Phase field theory is developed for solids undergoing potentially large deformation and fracture. The elastic potential depends on a finite measure of elastic strain. Surface energy associated with fracture can be anisotropic, enabling description of preferred cleavage planes in single crystals, or isotropic, applicable to amorphous solids such as glass. Incremental solution of the Euler–Lagran...

In this work, the nonlinear buckling and post-buckling behavior of shallow arches made of Shape Memory Alloy (SMA) is investigated. Arches are susceptible to large deflections, due to their slenderness, especially when the external load exceeds the serviceability limit point. Beyond this, loss of stability may occur, the famous snap-through buckling. For this reason, curved beams can be used in...

We study the question of the Ward identity for “large” gauge invariance in 0+1 dimensional theories. We derive the relevant Ward identities for a single flavor fermion and a single flavor complex scalar field interacting with an Abelian gauge field. These identities are nonlinear. The Ward identity for any other complicated theory can be derived from these basic sets of identities. However, the...