On gapped continuum resonance spectra

In this work, we study a warped five-dimensional (5D) model with ultraviolet (UV) and infrared (IR) branes, that solves the hierarchy problem with a fundamental 5D Planck scale [Formula: see text], and curvature parameter [Formula: see text], of the order of the 4D Planck mass [Formula: see text] TeV. The model exhibits a continuum of Kaluza–Klein (KK) modes with different mass gaps, at the TeV scale, for all fields. We have computed Green’s functions and spectral densities, and shown how the presence of a continuum KK spectrum can produce an enhancement in the cross-section of some Standard Model processes. The metric is linear near the IR, in conformal coordinates, as in the linear dilaton (LD) and 5D clockwork models, for which [Formula: see text] TeV. We also analyze a pure (continuum) LD scenario, solving the hierarchy problem with more conventional fundamental [Formula: see text] and [Formula: see text] scales of the order of [Formula: see text], and a continuum spectrum.

On Alfvén wave propagation along a circle on dipolar coordinates

The multipolar representation of the magnetic field has, for the lowest-order term, a magnetic dipole that dominates the far field. Thus the far-field representation of the magnetic field of the Earth, Sun and other celestial bodies is a dipole. Since these bodies consist of or are surrounded by plasma, which can support Alfvén waves, their propagation along dipole magnetic field lines is considered using a new coordinate system: dipolar coordinates. The present paper introduces multipolar coordinates, which are an example of conformal coordinates; conformal coordinates are orthogonal with equal scale factors, and can be extended from the plane to space, for instance as cylindrical or spherical dipolar coordinates. The application considered is to Alfvén waves propagating along a circle, that is a magnetic field line of a dipole, with transverse velocity and magnetic field perturbations; the various forms of the wave equation are linear second-order differential equations, with variable coefficients, specified by a background magnetic field, which is force free. The absence of a background magnetic force leads to a mean state of hydrostatic equilibrium, specified by the balance of gravity against the pressure gradient, for a perfect gas or incompressible liquid. The wave equation is simplified to a Gaussian hypergeometric type in the case of zero frequency, otherwise, for non-zero frequency, an extended Gaussian hypergeometric equation is obtained. The solution of the latter specifies the magnetic field perturbation spectrum, and also, via a polarisation relation, the velocity perturbation spectrum; both are plotted, over half a circle, for three values of the dimensionless frequency.

Application of Least Squares Estimation Techniques in 2D Conformal Coordinates Transformation from Local to National

A two-dimensional conformal coordinate transformation is a similarity transformation which is also known as the four parameter transformation since it maintains scale relationships between the two coordinates system. This transformation type uses a mathematical model that establish a geometrical relationship between coordinates of points in different reference frames. It gained wider acceptance because of its capability to retain the shape of an area represented. This paper utilizes three control points; PT02, PT03 and PT04 to compute the transformation parameters and later all validated the derived coordinates of point PT04 known in the local system to national system using manual computation check. The second approach was to derive the transformation parameters using four control points. The result obtained was validated and found to agree with the derived national coordinates system for point PT07. Subsequently, all other points within the areas covered in the scope of work were transformed by writing script and running it in MATLAB software environment. The total area covered was 457.457hectares.

Optimal convection cooling flows in general 2D geometries

We generalize a recent method for computing optimal 2D convection cooling flows in a horizontal layer to a wide range of geometries, including those relevant for technological applications. We write the problem in a conformal pair of coordinates which are the pure conduction temperature and its harmonic conjugate. We find optimal flows for cooling a cylinder in an annular domain, a hot plate embedded in a cold surface, and a channel with a hot interior and cold exterior. With a constraint of fixed kinetic energy, the optimal flows are all essentially the same in the conformal coordinates. In the physical coordinates, they consist of vortices ranging in size from the length of the hot surface to a small cutoff length at the interface of the hot and cold surfaces. With the constraint of fixed enstrophy (or fixed rate of viscous dissipation), a geometry-dependent metric factor appears in the equations. The conformal coordinates are useful here because they map the problems to a rectangular domain, facilitating numerical solutions. With a small enstrophy budget, the optimal flows are dominated by vortices that have the same size as the flow domain.

HOLOGRAPHIC DESCRIPTION OF A KERR–GÖDEL BLACK HOLE IN FIVE DIMENSIONS

In the present paper we study the holographic description of the five-dimensional Kerr–Gödel black holes. We find that if focusing on the near-horizon region, for the massless scalar scattering in the low-frequency limit, the radial equation could be rewritten as the SL (2, R)L × SL (2, R)R quadratic Casimir, suggesting the existence of dual two-dimensional description. We read the temperatures of the dual CFT from the conformal coordinates. We recover the macroscopic entropy from microscopic considerations by applying the Cardy formula for the putative dual CFT. We also show that the absorption cross-section of a near-region scalar field is matched to the universal behavior of the 2-point function of finite temperature CFT.