How to orient polymers homeotropically in thin films has been a long-standing issue in polymer science because polymers intrinsically prefer to lie down. Here we provide a design principle for polymers that are processable into a 2D homeotropic order. The key to this achievement was a recognition that cylindrical polymers can be designed to possess oppositely directed local dipoles in their cro...

In this work, we address the problem of 3D circle detection in a hierarchical representation which contains 2D and 3D information in the form of multi-modal primitives and their perceptual organizations in terms of contours. Semantic reasoning on higher levels leads to hypotheses that then become verified on lower levels by feedback mechanisms. The effects of uncertainties in visually extracted...

Realistic 3D face model is more precise in representing pose, illumination, and expression of face than 2D face model so that it can be utilized usefully in various applications such as face recognition, games, avatars, animations, and etc. In this paper, we propose a 3D face modeling method based on 3D dense morphable shape model. The proposed 3D modeling method first constructs a 3D dense mor...

Extensions of singular spectrum analysis (SSA) for processing of non-rectangular images and time series with gaps are considered. A circular version is suggested, which allows application of the method to the data given on a circle or on a cylinder, e.g. cylindrical projection of a 3D ellipsoid. The constructed Shaped SSA method with planar or circular topology is able to produce low-rank appro...

We propose the use of two-dimensional (2D) photonic crystals (PhCs) with engineered defects for the generation of an arbitrary-profile beam from a focused input beam. The cylindrical harmonics expansion of complex-source beams is derived and used to compute the scattered wave function of a 2D PhC via the multiple scattering method. The beam shaping problem is then solved using a genetic algorit...

The forcing term in the lattice Boltzmann equation (LBE) is usually used to mimic Navier-Stokes equations with a body force. To derive axisymmetric model, forcing terms are incorporated into the two-dimensional (2D) LBE to mimic the additional axisymmetric contributions in 2D Navier-Stokes equations in cylindrical coordinates. Many axisymmetric lattice Boltzmann D2Q9 models were obtained throug...

In this paper, we propose a new numerical method to compute the ground state solution of trapped interacting Bose-Einstein condensation (BEC) at zero or very low temperature by directly minimizing the energy functional via finite element approximation. As preparatory steps we begin with the 3d Gross-Pitaevskii equation (GPE), scale it to get a three-parameter model and show how to reduce it to ...

In this paper, we propose a new numerical method to compute the ground-state solution of trapped interacting Bose–Einstein condensation at zero or very low temperature by directly minimizing the energy functional via finite element approximation. As preparatory steps we begin with the 3d Gross–Pitaevskii equation (GPE), scale it to get a three-parameter model and show how to reduce it to 2d and...

We describe broad new classes of three-dimensional (3D) structures which, when made of silicon, exhibit robust 3D photonic band gaps of up to 25% of the gap center frequency. The proposed photonic crystals are readily amenable to very high precision microfabrication using established techniques such as x-ray lithography and template inversion. Each architecture consists of a set of oriented cyl...