We discuss the phase structure (in the 1/N -expansion) of the Nambu-Jona-Lasinio model in curved spacetime with non-trivial topology M3 × S. The evaluation of the effective potential of the composite field ψ̄ψ is presented in the linear curvature approximation (topology is treated exactly) and in the leading order of the 1/N -expansion. The combined influence of topology and curvature to the pha...

We give lower bounds estimates for the first Dirichilet eigenvalues for domains Ω in submanifolds M ⊂ N with locally bounded mean curvature. These lower bounds depend on the local injectivity radius, local upper bound for sectional curvature of N and local bound for the mean cuvature of M . For sumanifolds with bounded mean curvature of Hadamard manifolds these lower bounds depends only on the ...

The study of wood diameter is needed for the understanding of wood supply management. This type of approach, which was launched in the 1990s, has improved considerably as radius of curvature measurement has gained in precision through the introduction of new equipment: stereomicroscope equipped with a camera, and image analysis software. This paper focuses on the first step of the wood diameter...

We review recent work on the local geometry and optimal regularity of Lorentzian manifolds with bounded curvature. Our main results provide an estimate of the injectivity radius of an observer, and a local canonical foliations by CMC (Constant Mean Curvature) hypersurfaces, together with spatially harmonic coordinates. In contrast with earlier results based on a global bound for derivatives of ...

Article history: Received 1 December 2015 Received in revised form 19 January 2016 Accepted 20 January 2016 Available online 22 January 2016 The design and fabrication of large radii of curvature micro-lenses in single crystal chemical vapour deposition diamond is described. An optimised photoresist reflow process and low selectivity inductively coupled plasma etching are used to actualize a un...

A non-linear theory is presented for stretching and inplane-bending of isotropic beams which have constant initial curvature and lie in their plane of symmetry. For the kinematics, the geometrically exact one-dimensional (1-D) measures of deformation are specialized for small strain. The 1-D constitutive law is developed in terms of these measures via an asymptotically correct dimensional reduc...

The study of shape processing in the human visual system has frequently employed radial frequency (RF) patterns as conveniently manipulable stimuli. This study uses an adaptation paradigm to investigate how local shape information is sampled in the processing of RF contour shapes. Experiment 1 measured thresholds for detecting a fixed mean radius RF contour following adaptation to RF patterns w...

Precision measurements of a nanoscale sample surface using an atomic force microscope (AFM) require a precise quantitative knowledge of the 3D tip shape. Blind tip reconstruction (BTR), established by Villarrubia, gives an outer bound with larger errors if the tip characterizer is not appropriate. In order to explore the errors of BTR, a series of simulation experiments based on a conical model...