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Gravitational Potential Energy (gravitational + potential_energy)

Distribution by Scientific Domains

Earth and Environmental Science	50%

Selected Abstracts

Minimum work paths in elevated networks

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 2 2008
Takeshi Shirabe
Abstract A new variant of the shortest path problem involves a bicycle traveling from an origin to a destination through a network situated on a hilly geography. Determining a path that takes the least amount of pedaling work involves a conservative force, gravity, and a nonconservative force, friction, acting on the bicycle. The cyclist's pedaling work to overcome the friction of each arc varies with the bicycle's kinetic and gravitational potential energies, which transform to one another. Although geometric characteristics of the network are invariable, arc weights representing required pedaling work are variable. This problem is formulated as a quadratic integer program and an approximation procedure is presented. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008 [source]

Contribution of gravitational potential energy differences to the global stress field

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2009
Attreyee Ghosh
SUMMARY Modelling the lithospheric stress field has proved to be an efficient means of determining the role of lithospheric versus sublithospheric buoyancies and also of constraining the driving forces behind plate tectonics. Both these sources of buoyancies are important in generating the lithospheric stress field. However, these sources and the contribution that they make are dependent on a number of variables, such as the role of lateral strength variation in the lithosphere, the reference level for computing the gravitational potential energy per unit area (GPE) of the lithosphere, and even the definition of deviatoric stress. For the mantle contribution, much depends on the mantle convection model, including the role of lateral and radial viscosity variations, the spatial distribution of density buoyancies, and the resolution of the convection model. GPE differences are influenced by both lithosphere density buoyancies and by radial basal tractions that produce dynamic topography. The global lithospheric stress field can thus be divided into (1) stresses associated with GPE differences (including the contribution from radial basal tractions) and (2) stresses associated with the contribution of horizontal basal tractions. In this paper, we investigate only the contribution of GPE differences, both with and without the inferred contribution of radial basal tractions. We use the Crust 2.0 model to compute GPE values and show that these GPE differences are not sufficient alone to match all the directions and relative magnitudes of principal strain rate axes, as inferred from the comparison of our depth integrated deviatoric stress tensor field with the velocity gradient tensor field within the Earth's plate boundary zones. We argue that GPE differences calibrate the absolute magnitudes of depth integrated deviatoric stresses within the lithosphere; shortcomings of this contribution in matching the stress indicators within the plate boundary zones can be corrected by considering the contribution from horizontal tractions associated with density buoyancy driven mantle convection. Deviatoric stress magnitudes arising from GPE differences are in the range of 1,4 TN m,1, a part of which is contributed by dynamic topography. The EGM96 geoid data set is also used as a rough proxy for GPE values in the lithosphere. However, GPE differences from the geoid fail to yield depth integrated deviatoric stresses that can provide a good match to the deformation indicators. GPE values inferred from the geoid have significant shortcomings when used on a global scale due to the role of dynamically support of topography. Another important factor in estimating the depth integrated deviatoric stresses is the use of the correct level of reference in calculating GPE. We also elucidate the importance of understanding the reference pressure for calculating deviatoric stress and show that overestimates of deviatoric stress may result from either simplified 2-D approximations of the thin sheet equations or the assumption that the mean stress is equal to the vertical stress. [source]

Why are the continents just so,?

JOURNAL OF METAMORPHIC GEOLOGY, Issue 6 2010
M. SANDIFORD
Abstract Variations in gravitational potential energy contribute to the intraplate stress field thereby providing the means by which lithospheric density structure is communicated at the plate scale. In this light, the near equivalence in the gravitational potential energy of typical continental lithosphere with the mid-ocean ridges is particularly intriguing. Assuming this equivalence is not simply a chance outcome of continental growth, it then probably involves long-term modulation of the density configuration of the continents via stress regimes that are able to induce significant strains over geological time. Following this notion, this work explores the possibility that the emergence of a chemically, thermally and mechanically structured continental lithosphere reflects a set of thermally sensitive feedback mechanisms in response to Wilson cycle oscillatory forcing about an ambient stress state set by the mid-ocean ridge system. Such a hypothesis requires the continents are weak enough to sustain long-term (108 years) strain rates of the order of ,10,17 s,1 as suggested by observations that continental lithosphere is almost everywhere critically stressed, by estimates of seismogenic strain rates in stable continental interiors such as Australia and by the low-temperature thermochronological record of the continents that requires significant relief generation on the 108 year time-scale. Furthermore, this notion provides a mechanism that helps explain interpretations of recently published heat flow data that imply the distribution of heat-producing elements within the continents may be tuned to produce a characteristic thermal regime at Moho depths. [source]

Equilibria of a self-gravitating, rotating disc around a magnetized compact object

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2004
J. Ghanbari
ABSTRACT We examine the effect of self-gravity in a rotating thick-disc equilibrium in the presence of a dipolar magnetic field. First, we find a self-similar solution for non-self-gravitating discs. The solution that we have found shows that the pressure and density equilibrium profiles are strongly modified by a self-consistent toroidal magnetic field. We introduce three dimensionless variables, CB, Cc and Ct, which indicate the relative importance of toroidal component of the magnetic field (CB), and centrifugal (Cc) and thermal (Ct) energy with respect to the gravitational potential energy of the central object. We study the effect of each of these on the structure of the disc. Secondly, we investigate the effect of self-gravity on the discs; thus, we introduce another dimensionless variable (Cg) which shows the importance of self-gravity. We find a self-similar solution for the equations of the system. Our solution shows that the structure of the disc is modified by the self-gravitation of the disc, the magnetic field of the central object and the azimuthal velocity of the gas disc. We find that self-gravity and magnetism from the central object can change the thickness and the shape of the disc. We show that as the effect of self-gravity increases the disc becomes thinner. We also show that, for different values of the star's magnetic field and of the disc's azimuthal velocity, the disc's shape and its density and pressure profiles are strongly modified. [source]