We show that new massless Dirac fermions are generated when a slowly varying periodic potential is applied to graphene. These quasiparticles, generated near the supercell Brillouin zone boundaries with anisotropic group velocity, are different from the original massless Dirac fermions. The quasiparticle wave vector (measured from the new Dirac point), the generalized pseudospin vector, and the ...

1. The Fundamental Assumptions.-Denote by Sap the components of the deviation s of the stress tensor a. Let va be the components of the velocity vector v and efa the components of the rate of strain tensor e derived from the velocity vector. We impose the usual condition that the flow is incompressible, i.e., eaa = 0, which appears to be in agreement with experimental evidence. Hence e is ident...

Consider a vicous incompressible fluid occupying a bounded domain Ω ⊂ R. In the Eulerean reference system, the motion of the fluid is completely determined by the velocity field u = u(t, x) a vector valued function of the time t and the spatial position x ∈ Ω. Under the hypothesis of impermeability of the boundary, the velocity satisfies u · n|∂Ω = 0, (1.1) where the symbol n stands for the out...

this paper deals with three-dimensional evaluation of the slopes on the basis of limit analysis. an upper-bound technique of limit analysis is used in this paper to determine either the bearing capacity of a shallow foundation near a slope or the safety factor of the slope. the theorems of limit analysis (upper and lower bound) provide a powerful tool for solving problems in which limit loads n...

This paper presents a novel method to determine the complete velocity vector of a moving target using a single Synthetic Aperture Radar (SAR) sensor. The method exploits the structure of the returned echo from a moving target: in the slow-time frequency domain, it is a scaled and shifted replica of the antenna radiation pattern immersed in Gaussian noise; the scale and the shift are related wit...

This paper presents an embedding framework for myocardial velocity processing with MRI based on a hollow, semi-spherical template. The relationship between vector bundle and manifold mapping is analysed and three different mapping methods that include tangent mapping, normal mapping, and normal-tangent mapping are assessed for their practical value of myocardial contractility analysis. The prop...

Here u, b describe the flow velocity vector and the magnetic field vector respectively, p is a scalar pressure, ν > 0 is the kinematic viscosity and η > 0 is the magnetic diffusivity, while u0 and b0 are the given initial velocity and initial magnetic field respectively, with ∇ · u0 = ∇ · b0 = 0. If ν = η = 0, (1.1) is called the ideal MHD equations. Using the standard energy method, it can be ...

Background One-directionally-encoded cine 2D Phase-Contrast MRI (PC MRI) of basal short axial image is generally used for the evaluation of diastolic function, but has potential limitations due to the longitudinal cardiac motion and inflow direction. Time-resolved 3D PC MRI is not affected by the flow direction and left ventricular motion, however, requires long acquisition time. In theory, thr...

In this paper, we point out that the Coulomb’s force and gravitational force on a particle always act in the direction orthogonal to the 4-vector velocity of the particle in 4-dimensional space-time, rather than along the line joining a couple of particles. This inference is obviously supported from the fact that the magnitude of the 4-vector velocity is kept constant.This orthogonal relation t...

Here u, b describe the flow velocity vector and the magnetic field vector respectively, p is a scalar pressure, ν > 0 is the kinematic viscosity, η > 0 is the magnetic diffusivity, while u0 and b0 are the given initial velocity and initial magnetic field with ∇ · u0 = ∇ · b0 = 0. If ν = η = 0, (1.1) is called the ideal MHD equations. As same as the 3D Navier-Stokes equations, the regularity of ...