Non-geometric string backgrounds were proposed to be related to a nonassociative deformation of the space-time geometry. In the flux formulation of double field theory (DFT), the structure of mathematically possible non-associative deformations is analyzed in detail. It is argued that on-shell there should not be any violation of associativity in the effective DFT action. For imposing either th...

We develop a meshless method for simulating soft organ deformation. The method is motivated by simple, automatic model creation for real-time simulation. Our method is meshless in the sense that deformation is calculated at nodes that are not part of an element mesh. Node placement is almost arbitrary. Fully geometrically nonlinear total Lagrangian formulation is used. Geometric integration is ...

A new analytical approach for bubble deformation was used for optimization of the electron acceleration in the 3D highly nonlinear laser wake-field regime. Injection of the electron bunch with initial velocity in the bubble was considered in the inhomogeneous plasma with linearly density ramp. The researchers show that deformation of the bubble shape has an efficient role on the trapping of the...

Recall that a smooth Riemannian metric on a simply connected domain can be realized as the pull-back metric of an orientation preserving deformation if and only if the associated Riemann curvature tensor vanishes identically. When this condition fails, one seeks a deformation yielding the closest metric realization. We set up a variational formulation of this problem by introducing the non-Eucl...

Based on a paper from Heeren et al. this report presents a method of finding a natural deformation between two shapes with a given correspondence. It is based on minimizing an energy function derived from results of elasticity theory. Different than other algorithms this energy has only parameters with concrete physical meanings. Furthermore proper discretization methods are presented. The resu...

We characterize through large-scale simulations the nonlinear elastic response of multiwalled carbon nanotubes (MWCNTs) in torsion and bending. We identify a unified law consisting of two distinct power law regimes in the energy-deformation relation. This law encapsulates the complex mechanics of rippling and is described in terms of elastic constants, a critical length scale, and an anharmonic...

This paper deals with the calculation of the elastic properties for single-walled carbon nanotubes (SWCNTs) under axial deformation and hydrostatic pressure using the atomistic-based continuum approach and the deformation mapping technique. A hyperelastic model based on the higher-order Cauchy-Born (HCB) rule being applicable at finite strains and accounting for the chirality and material nonli...

Motivated by nonlinear elasticity theory, we study deformations that are weakly approximately differentiable, orientation-preserving and one-to-one almost everywhere, and in addition have finite surface energy. This surface energy is a functional E introduced by the authors in a previous paper, and has connections with the theory of currents. In the present paper we prove that E measures exactl...

Based on a newly developed canonical dual transformation methodology, this paper presents a potentially useful duality theory and method for solving fully nonlinear distributed-parameter control problems. The extended Lagrange duality and the interesting triality theory proposed recently in finite deformation theory are generalized into nonconvex dissipative Hamiltonian systems. It is shown tha...

We address the question of bounds on the synchronization error for the case of nearly identical nonlinear systems. It is pointed out that negative largest conditional Lyapunov exponents of the synchronization manifold are not sufficient to guarantee a small synchronization error and that one has to find bounds for the deformation of the manifold due to perturbations. We present an analytic boun...