Related papers: Curved geometries from planar director fields - So…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
We derive basic differential geometric formulae for surfaces in hyperbolic space represented as envelopes of horospheres. The dual notion of parallel hypersurfaces is also studied. The representation is applied to prove existence and…
The director configuration of disclination lines in nematic liquid crystals in the presence of an external magnetic field is evaluated. Our method is a combination of a polynomial expansion for the director and of further analytical…
The accelerated inverse design of complex material properties - such as identifying a material with a given stress-strain response over a nonlinear deformation path - holds great potential for addressing challenges from soft robotics to…
Holographic renormalization is a systematic procedure for regulating divergences in observables in asymptotically locally AdS spacetimes. For dual boundary field theories which are supersymmetric it is natural to ask whether this defines a…
We develop a theory for distributed branch points and investigate their role in determining the shape and influencing the mechanics of thin hyperbolic objects. We show that branch points are the natural topological defects in hyperbolic…
A mechanical strain field applied to a monodomain cholesteric elastomer will unwind the helical director distribution. There is an analogy with the classical problem of an electric field applied to a cholesteric liquid crystal, but with…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
We discuss infinitesimal isometries of the middle surfaces and present some characteristic conditions for a function to be the normal component of an infinitesimal isometry. Our results show that those characteristic conditions depend on…
Given a distribution of defects on a structured surface, such as those represented by 2-dimensional crystalline materials, liquid crystalline surfaces, and thin sandwiched shells, what is the resulting stress field and the deformed shape?…
Free interfaces of liquid crystals tend to minimise both capillarity and anchoring forces. Here we study nematic films in planar and radial geometries with antagonistic anchoring boundary conditions and one deformable interface. Assuming a…
Engineering problems frequently require solution of governing equations with spatially-varying discontinuous coefficients. Even for linear elliptic problems, mapping large ensembles of coefficient fields to solutions can become a major…
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
In this paper we show that any static and spherically symmetric anisotropic solution of the Einstein field equations can be thought as a system sourced by certain deformed isotropic system in the context of Minimal Geometric…
We present an inverse problem which uses the renormalized area functional on minimal submanifolds to recover the expansion of asymptotically hyperbolic, conformally compact metrics which are partially even to high order. We use a rigidity…
This paper presents an adaptation of recently developed algorithms for quadratic forms over number fields in arXiv:1304.0708 to global function fields of odd characteristics. First, we present algorithm for checking if a given…
The properties of liquid crystals can be modelled using an order parameter which describes the variability of the local orientation of rod-like molecules. Defects in the director field can arise due to external factors such as applied…
In this paper, we will show that a periodic nonlinear, time-varying dissipative system that is defined on a genus-p surface contains one or more invariant sets which act as attractors. Moreover, we shall generalize a result in [Martins,…
In liquid crystal elastomers, the orientational order of liquid crystals is coupled with elastic distortions of crosslinked polymer networks. Previous theoretical research has described these materials through two different approaches: a…
Invariants of general linear system of two hyperbolic partial differential equations (PDEs) are derived under transformations of the dependent and independent variables by real infinitesimal method earlier. Here a subclass of the general…