Development of drainage assessment procedures based on physical features in Illinois

The objectives of this study were to identify the physical features of the land in a drainage district which influence benefits accruing from drainage improvements, and to formulate a method for distributing assessments based upon the relative importance of these physical features. The significant physical features discovered in the study were: (1) the distance from the tract of land to the main drain, (2) the distance from the tract of land to the main outlet, and (3) the permeability of the soil on the tract of land. An equation was developed to determine the assessment for any tract: An = 1,4845 - 0,3476 (Ln/L*) - 0.4680 (Dn/D*) - 0.4434 (Kn/K*). The equation provides a procedure and a computer program to equitably distribute drainage assessments with a savings in labor and time in the preparation of the assessment roll. This unbiased procedure should reduce the present objection of landowners of unfair assessments based upon p.ersona1 judgment. Although the present equation is limited to the geographic area that supplied the data for the coefficients, the procedure developed may be used to calculate coefficients for other soil and morphological areas.U.S. Department of the InteriorU.S. Geological SurveyOpe

The General Warped Solution with Conical Branes in Six-dimensional Supergravity

We present the general regular warped solution with 4D Minkowski spacetime in six-dimensional gauged supergravity. In this framework, we can easily embed multiple conical branes into the warped geometry by choosing an undetermined holomorphic function. As an example, for the holomorphic function with many zeroes, we find warped solutions with multi-branes and discuss the generalized flux quantization in this case.Comment: 1+19 pages, no figure, JHEP style, version to appear in JHE

Resolving Curvature Singularities in Holomorphic Gravity

We formulate holomorphic theory of gravity and study how the holomorphy symmetry alters the two most important singular solutions of general relativity: black holes and cosmology. We show that typical observers (freely) falling into a holomorphic black hole do not encounter a curvature singularity. Likewise, typical observers do not experience Big Bang singularity. Unlike Hermitian gravity \cite{MantzHermitianGravity}, Holomorphic gravity does not respect the reciprocity symmetry and thus it is mainly a toy model for a gravity theory formulated on complex space-times. Yet it is a model that deserves a closer investigation since in many aspects it resembles Hermitian gravity and yet calculations are simpler. We have indications that holomorphic gravity reduces to the laws of general relativity correctly at large distance scales.Comment: 14 pages, 7 figure

Probing Yukawian Gravitational Potential by Numerical Simulations. II. Elliptical Galaxies

Since the Newtonian gravitation is largely used to model with success the structures of the universe, such as galaxies and clusters of galaxies, for example, a way to probe and constrain alternative theories, in the weak field limit, is to apply them to model the structures of the universe. We then modified the well known Gadget-2 code to probe alternative theories of gravitation through galactic dynamics. In particular, we modified the Gadget-2 code to probe alternatives theories whose weak field limits have a Yukawa-like gravitational potential. As a first application of this modified Gadget-2 code we simulate the evolution of elliptical galaxies. These simulations show that galactic dynamics can be used to constrain the parameters associated with alternative theories of gravitation.Comment: 6 pages, 5 figures - To appear in General Relativity and Gravitatio

Quantum corrections to the entropy of charged rotating black holes

Hawking radiation from a black hole can be viewed as quantum tunneling of particles through the event horizon. Using this approach we provide a general framework for studying corrections to the entropy of black holes beyond semiclassical approximations. Applying the properties of exact differentials for three variables to the first law thermodynamics, we study charged rotating black holes and explicitly work out the corrections to entropy and horizon area for the Kerr-Newman and charged rotating BTZ black holes. It is shown that the results for other geometries like the Schwarzschild, Reissner-Nordstr\"{o}m and anti-de Sitter Schwarzschild spacetimes follow easily

Gravity on codimension 2 brane worlds

We compute the matching conditions for a general thick codimension 2 brane, a necessary previous step towards the investigation of gravitational phenomena in codimension 2 braneworlds. We show that, provided the brane is weakly curved, they are specified by the integral in the extra dimensions of the brane energy-momentum, independently of its detailed internal structure. These general matching conditions can then be used as boundary conditions for the bulk solution. By evaluating Einstein equations at the brane boundary we are able to write an evolution equation for the induced metric on the brane depending only on physical brane parameters and the bulk energy-momentum tensor. We particularise to a cosmological metric and show that a realistic cosmology can be obtained in the simplest case of having just a non-zero cosmological constant in the bulk. We point out several parallelisms between this case and the codimension 1 brane worlds in an AdS space.Comment: 24 page

Electromagnetic Polarization Effects due to Axion Photon Mixing

We investigate the effect of axions on the polarization of electromagnetic waves as they propagate through astronomical distances. We analyze the change in the dispersion of the electromagnetic wave due to its mixing with axions. We find that this leads to a shift in polarization and turns out to be the dominant effect for a wide range of frequencies. We analyze whether this effect or the decay of photons into axions can explain the large scale anisotropies which have been observed in the polarizations of quasars and radio galaxies. We also comment on the possibility that the axion-photon mixing can explain the dimming of distant supernovae.Comment: 18 pages, 1 figur

Modified Gravity via Spontaneous Symmetry Breaking

We construct effective field theories in which gravity is modified via spontaneous breaking of local Lorentz invariance. This is a gravitational analogue of the Higgs mechanism. These theories possess additional graviton modes and modified dispersion relations. They are manifestly well-behaved in the UV and free of discontinuities of the van Dam-Veltman-Zakharov type, ensuring compatibility with standard tests of gravity. They may have important phenomenological effects on large distance scales, offering an alternative to dark energy. For the case in which the symmetry is broken by a vector field with the wrong sign mass term, we identify four massless graviton modes (all with positive-definite norm for a suitable choice of a parameter) and show the absence of the discontinuity.Comment: 5 pages; revised versio

Exact Black Holes and Gravitational Shockwaves on Codimension-2 Branes

We derive exact gravitational fields of a black hole and a relativistic particle stuck on a codimension-2 brane in $D$ dimensions when gravity is ruled by the bulk $D$-dimensional Einstein-Hilbert action. The black hole is locally the higher-dimensional Schwarzschild solution, which is threaded by a tensional brane yielding a deficit angle and includes the first explicit example of a `small' black hole on a tensional 3-brane. The shockwaves allow us to study the large distance limits of gravity on codimension-2 branes. In an infinite locally flat bulk, they extinguish as $1/r^{D-4}$, i.e. as $1/r^2$ on a 3-brane in $6D$, manifestly displaying the full dimensionality of spacetime. We check that when we compactify the bulk, this special case correctly reduces to the 4D Aichelburg-Sexl solution at large distances. Our examples show that gravity does not really obstruct having general matter stress-energy on codimension-2 branes, although its mathematical description may be more involved.Comment: 18 pages, LaTeX; v2: added references, version to appear in JHE

Loop-Generated Bounds on Changes to the Graviton Dispersion Relation

We identify the effective theory appropriate to the propagation of massless bulk fields in brane-world scenarios, to show that the dominant low-energy effect of asymmetric warping in the bulk is to modify the dispersion relation of the effective 4-dimensional modes. We show how such changes to the graviton dispersion relation may be bounded through the effects they imply, through loops, for the propagation of standard model particles. We compute these bounds and show that they provide, in some cases, the strongest constraints on nonstandard gravitational dispersions. The bounds obtained in this way are the strongest for the fewest extra dimensions and when the extra-dimensional Planck mass is the smallest. Although the best bounds come for warped 5-D scenarios, for which the 5D Planck Mass is O(TeV), even in 4 dimensions the graviton loop can lead to a bound on the graviton speed which is comparable with other constraints.Comment: 18 pages, LaTeX, 4 figures, uses revte