An empirical test of the gravity p-median model

A customer is presumed to gravitate to a facility by the distance to it and the attractiveness of it. However regarding the location of the facility, the presumption is that the customer opts for the shortest route to the nearest facility.This paradox was recently solved by the introduction of the gravity p-median model. The model is yet to be implemented and tested empirically. We implemented the model in an empirical problem of locating locksmiths, vehicle inspections, and retail stores ofv ehicle spare-parts, and we compared the solutions with those of the p-median model. We found the gravity p-median model to be of limited use for the problem of locating facilities as it either gives solutions similar to the p-median model, or it gives unstable solutions due to a non-concave objective function.

Testing the gravity p-median model empirically

Regarding the location of a facility, the presumption in the widely used p-median model is that the customer opts for the shortest route to the nearest facility. However, this assumption is problematic on free markets since the customer is presumed to gravitate to a facility by the distance to and the attractiveness of it. The recently introduced gravity p-median model offers an extension to the p-median model that account for this. The model is therefore potentially interesting, although it has not yet been implemented and tested empirically. In this paper, we have implemented the model in an empirical problem of locating vehicle inspections, locksmiths, and retail stores of vehicle spare-parts for the purpose of investigating its superiority to the p-median model. We found, however, the gravity p-median model to be of limited use for the problem of locating facilities as it either gives solutions similar to the p-median model, or it gives unstable solutions due to a non-concave objective function.

Gravity: a new play by Greg Belanger

Gravity was first performed at Strider Theatre, Colby College in Waterville, Maine. It was directed by the author with the following cast: STEVEN: Harold Withee PAMELA: Sue Larsen JEREMY: Jason Reifler IXXTOR: Amanda Starr MOTHER: Catherine C. Coyne BREIT: Scott W. Cole TONI: Laura Smishkiss

Brazilian international and inter-state trade flows: an exploratory analysis using the gravity model

Recent efforts toward a world with freer trade, like WTO/GATT or regional Preferential Trade Agreements(PTAs), were put in doubt after McCallum's(1995) finding of a large border effect between US and Canadian provinces. Since then, there has been a great amount of research on this topic employing the gravity equation. This dissertation has two goals. The first goal is to review comprehensively the recent literature about the gravity equation, including its usages, econometric specifications, and the efforts to provide it with microeconomic foundations. The second goal is the estimation of the Brazilian border effect (or 'home-bias trade puzzle') using inter-state and international trade flow data. It is used a pooled cross-section Tobit model. The lowest border effect estimated was 15, which implies that Brazilian states trade among themselves 15 times more than they trade with foreign countries. Further research using industry disaggregated data is needed to qualify the estimated border effect with respect to which part of that effect can be attributed to actual trade costs and which part is the outcome of the endogenous location problem of the firm.

g-acceleration of gravity: its measurement from the shape of water by using a computerized rotational system

This paper proposes a different experimental setup compared with the traditional ones, in order to determine the acceleration of gravity, which is carried out by using a fluid at a constant rotation. A computerized rotational system-by using a data acquisition system with specific software, a power amplifier and a rotary motion sensor-is employed in order to evaluate the angular velocity and g. An equation to determine g is inferred from fluid mechanics. For this purpose, the fluid's parabolic shape inside a cylindrical receptacle is considered using a rotational movement.

Aggregates in the strength and gravity regime: Particles sizes in Saturn's rings

Particles in Saturn's main rings range in size from dust to kilometer-sized objects. Their size distribution is thought to be a result of competing accretion and fragmentation processes. While growth is naturally limited in tidal environments, frequent collisions among these objects may contribute to both accretion and fragmentation. As ring particles are primarily made of water ice attractive surface forces like adhesion could significantly influence these processes, finally determining the resulting size distribution. Here, we derive analytic expressions for the specific self-energy Q and related specific break-up energy Q(star) of aggregates. These expressions can be used for any aggregate type composed of monomeric constituents. We compare these expressions to numerical experiments where we create aggregates of various types including: regular packings like the face-centered cubic (fcc), Ballistic Particle Cluster Aggregates (BPCA), and modified BPCAs including e.g. different constituent size distributions. We show that accounting for attractive surface forces such as adhesion a simple approach is able to: (a) generally account for the size dependence of the specific break-up energy for fragmentation to occur reported in the literature, namely the division into "strength" and "gravity" regimes and (b) estimate the maximum aggregate size in a collisional ensemble to be on the order of a few tens of meters, consistent with the maximum particle size observed in Saturn's rings of about 10 m. (c) 2012 Elsevier B.V. All rights reserved.

Attitude stability of artificial satellites subject to gravity gradient torque

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Frequency and gravity of human envenomations caused by marine catfish (suborder siluroidei): a clinical and epidemiological study

Introduction and objectives: Catfish occur in marine and freshwater environments worldwide. They have three serrated venomous bony stings in the dorsal and pectoral fins that are used for defence against predators and are refilled by glandular tissues under the epithelium. However, some catfishes do not have poisonous glands next to the sting and cause traumatic wounds without poisoning. The objective of this study was to provide data for, and comment on, the epidemiological and clinical problems caused by marine catfish.Patients and methods: the authors have observed, followed and documented 127 injuries caused by marine catfish stings during different phases of the envenoming over a time period of 8 years at three points along the Western Atlantic Ocean coast.Results: the patients presented intense pain during the acute phase of envenoming and complications, such as bacterial and fungi infections and retention of bony fragments, in the later phase. Immersion of the affected extremity in hot water was used in about 20% of cases with excellent results.Discussion: Injuries caused by marine catfish are common (about 20% of injuries caused by marine animals in a series of more than 700 injuries recorded by the author) and cause intense pain and later complications. Immersion of the affected extremity in hot water results in improvement in the acute phase, but does not prevent the appearance of secondary infection or foreign body reactions. (c) 2006 Elsevier Ltd. All rights reserved.

On the symplectic two-form of gravity in terms of Dirac eigenvalues

The Dirac eigenvalues form a subset of observables of the Euclidean gravity. The symplectic two-form in the covariant phase space could be expressed, in principle, in terms of the Dirac eigenvalues. We discuss the existence of the formal solution of the equations defining the components of the symplectic form in this framework. (C) 2002 Published by Elsevier B.V. B.V.

Quadratic gravity in (2+1)D with a topological Chern-Simons term

Three-dimensional quadratic gravity, unlike general relativity in (2+1)D, is dynamically nontrivial and has a well behaved nonrelativistic potential. Here we analyse the changes that occur when a topological Chem-Simons term is added to this theory. It is found that the harmless massive scalar mode of the latter gives rise to a troublesome massive spin-0 ghost, while the massive spin-2 ghost is replaced by two massive physical particles both of spin 2. We also found that light deflection does not have the 'wrong sign' such as in the framework of three-dimensional quadratic gravity.

Propagator, tree-level unitarity and effective nonrelativistic potential for higher-derivative gravity theories in D dimensions

A prescription for computing the propagator for D-dimensional higher-derivative gravity theories, based on the Barnes-Rivers operators, is presented. A systematic study of the tree-level unitarity of these theories is developed and the agreement of their linearized versions with Newton's law is investigated by computing the corresponding effective nonrelativistic potential. Three-dimensional quadratic gravity with a gravitational Chern-Simons term is also analyzed. A discussion on the issue of light bending within the framework of both D-dimensional quadratic gravity and three-dimensional quadratic gravity with a Chern-Simons term is provided as well. (C) 2002 American Institute of Physics.

Can one cure the nommitarity of three-dimensional quadratic gravity using a topological Chern-Simons term?

Quadratic gravity in (2+1)D is nonunitarity at the tree level. When a topological Chern-Simons term is added to this theory, the harmless massive scalar mode of the former gives rise to a troublesome massive spin-0 ghost, while the massive spin-2 ghost is replaced by two massive physical particles both of spin-2. Therefore, unlike what it is claimed in the literature, quadratic Chern-Simons gravity in (2+1)D is nonunitary at the tree level.

The energy of the universe in teleparallel gravity

The teleparallel versions of the Einstein and the Landau-Lifshitz energy-momentum complexes of the gravitational field are obtained. By using these complexes, the total energy of the universe, which includes the energy of both the matter and the gravitational fields, is then obtained. It is shown that in the case of a closed universe, the total energy vanishes independently of the pseudotensor used, as well as of the three dimensionless coupling constants of teleparallel gravity.

Consistent modified gravity: dark energy, acceleration and the absence of cosmic doomsday

We discuss modified gravity which includes negative and positive powers of curvature and provides gravitational dark energy. It is shown that in GR plus a term containing a negative power of curvature, cosmic speed-up may be achieved while the effective phantom phase (with w less than -1) follows when such a term contains a fractional positive power of curvature. Minimal coupling with matter makes the situation more interesting: even 1/R theory coupled with the usual ideal fluid may describe the (effective phantom) dark energy. The account of the R(2) term (consistent modified gravity) may help to escape cosmic doomsday.

Prediction of R plus R-2 gravity for the deflection of a photon passing close to the Sun

The cross-section for the scattering of a photon by the Sun's gravitational field, treated as an external field, is computed in the framework of R + R-2 gravity. Using this result, we found that for a photon just grazing the Sun's surface the deflection is 1.75 which is exactly the same as that given by Einstein's theory. An explanation for this pseudo-paradox is provided.