The main purpose of this paper is to show that ideas of deformation theory can be applied to “infinite dimensional geometry”. We develop the deformation theory of Brody curves. Brody curve is a kind of holomorphic map from the complex plane to the projective space. Since the complex plane is not compact, the parameter space of the deformation can be infinite dimensional. As an application we pr...

A theory of associative deformations is developed for general complex analytic spaces. Deformation quantization and commutative deformation are particular cases of this concept. Deformation cohomology and obstruction are studied. It is proved that any compact analytic space has a formal versal associative deformation. Mathematics Subject Classi…cation (2000). 53D55, 13D10, 16S80, 81T70.

Buckling analysis of a functionally graded (FG) nanobeam resting on two-parameter elastic foundation is presented based on third-order shear deformation beam theory (TOSDBT). The in-plane displacement of TOSDBT has parabolic variation through the beam thickness. Also, TOSDBT accounts for shear deformation effect and verifies stress-free boundary conditions on upper and lower faces of FG nanobea...

To determine flow curves of a material, whose plastic deformation is produced by martensitic transformation, transformation strains of a martensite plate must be characterized [1–3]. Most studies along this line adopt results obtained by the phenomenological crystallographic theory of martensitic transformation [4,5]. The theory is based on finite deformation analysis, which needs involved comp...

Buckling analysis of a functionally graded (FG) nanobeam resting on two-parameter elastic foundation is presented based on third-order shear deformation beam theory (TOSDBT). The in-plane displacement of TOSDBT has parabolic variation through the beam thickness. Also, TOSDBT accounts for shear deformation effect and verifies stress-free boundary conditions on upper and lower faces of FG nanobea...

This article investigates the static behavior of functionally graded plate under mechanical loads by using a new quasi 3D model. The theory is designated as fifth-order shear and normal deformation theory (FOSNDT). Properties of functionally graded material are graded across the transverse direction by using the rule of mixture i.e. power-law. The effect of thickness stretching is considered to...

We study SL(3, R) deformations of a type IIB background based on D5 branes that is conjectured to be dual to N = 1 SYM. We argue that this deformation of the geometry correspond to turning on a dipole deformation in the field theory on the D5 branes. We give evidence that this deformation only affects the KK-sector of the dual field theory and helps decoupling the KK dynamics from the pure gaug...

The search for scale-bridging relations in the deformation of amorphous materials presents a current challenge with tremendous applications in material science, engineering and geology. While generic features in the flow and microscopic dynamics support the idea of a universal scaling theory of deformation, direct microscopic evidence remains poor. Here, we provide the first measurement of inte...

In this paper, we demonstrate how deformation patterns of leaves and fruits in growing and drying processes can be described via the inhomogeneous field theory. The distorted deformation of ribbed leaves and the ridge formation on fruit surfaces can be understood as the energy-minimizing mechanical buckling patterns. The swelling and de-swelling induced instabilities of various membrane structu...