Considering a Skyrme model with a peculiar gauging of the symmetry, monopole-like solutions exist through a topological lower bound. However, it was recently shown that these objects cannot form bound states in the limit of vanishing Skyrme coupling. Here we consider these monopoles in scalar-tensor gravity. A numerical study of the equations reveals that neither the coupling to gravity nor to ...

A nonlinear theory of pattern selection in parametric surface waves (Faraday waves) is presented that is not restricted to small viscous dissipation. By using a multiple scale asymptotic expansion near threshold, a standing wave amplitude equation is derived from the governing equations. The amplitude equation is of gradient form, and the coefficients of the associated Lyapunov function are com...

The evolution of scale-invariant gravity waves from the early universe is analyzed using an equation of state which smoothly interpolates between the radiation dominated era and the present matter dominated era. We find that for large wavenumbers the standard scale-invarant wavefunction for the gravity wave severely underestimates the actual size of the gravity wave. Moreover, there is a defini...

We discuss the global properties of static, spherically symmetric configurations of a self-gravitating real scalar field φ in general relativity (GR), scalar-tensor and high-order (curvature-nonlinear) theories of gravity in various dimensions. In GR, for scalar fields with an arbitrary potential V (φ) , not necessarily positive-definite, it is shown that the list of all possible types of space...

Considering a Skyrme model with a peculiar gauging of the symmetry, monopole-like solutions exist through a topological lower bound. However, it was recently shown that these objects cannot form bound states in the limit of vanishing Skyrme coupling. Here we consider these monopoles in scalar-tensor gravity. A numerical study of the equations reveals that neither the coupling to gravity nor to ...

We consider renormalizability of topologically massive gravity in three space-time dimensions. With a usual parametrization of the metric tensor, we establish the statement that topologically massive gravity is in fact renormalizable. In this proof, we make use of not only a recently found, new infrared regularization method of scalar mode but also a covariant ultraviolet regulator with a speci...

We want to correct the misunderstandings on the tetrad (or veilbeins in general) appeared in many text books or review articles. The tetrad should be defined without any condition. eμa = ∂μXa with local Lorentz coordinates Xa ia wrong in many sences: it gives the condition ∂μeνa = ∂νeμa, which leads us to the trivial result that the cyclic coefficients vanish identically and to the null Riemann...

cp heat capacity dx distance between two points after time t dX original infinitesimal distance between two points D stretching tensor Di dissipation number ĝ gravity vector h depth of convecting layer H(r) two-particle correlation function P dynamic pressure Ra thermal Rayleigh number t time T temperature ui components of the velocity tensor v velocity w upward velocity a thermal expansivity _...

In diffusion tensor imaging (DTI) an effective diffusion tensor in each voxel is measured by using a set of diffusion-weighted images (DWIs) in which diffusion gradients are applied in a multiplicity of oblique directions. However, to estimate the diffusion tensor accurately, one must account for the effects of all imaging and diffusion gradient pulses on each signal echo, which are embodied in...

This paper proposes a geometric approach for comparing tensor-valued images (tensor fields) that is based on the idea of matching intrinsically low-dimensional shapes embedded in a higher-dimensional ambient space. More specifically, instead of regarding the tensor fields as tensor-valued functions defined on a given (image) domain, we consider their image graphs. These tensorial image graphs c...