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Driven granular gases with gravity.

We study fluidized granular gases in a stationary state determined by the balance between external driving and bulk dissipation. The two considered situations are inspired by recent experiments, where gravity plays a major role as a driving mechanism: in the first case, gravity acts only in one direction and the bottom wall is vibrated; in the second case, gravity acts in both directions and no vibrating walls are present. Simulations performed under the molecular chaos assumption show averaged profiles of density, velocity, and granular temperature that are in good agreement with the experiments. Moreover, we measure velocity distributions that show strong non-Gaussian behavior, as experiments pointed out, but also density correlations accounting for clustering, at odds with the experimental results. The hydrodynamics of the first model is discussed and an exact solution is found for the density and granular temperature as functions of the distance from the vibrating wall. The limitations of such a solution, in particular in a broad layer near the wall injecting energy, are discussed.

Journal Article↗

Thermal collapse of a granular gas under gravity.

Free cooling of a gas of inelastically colliding hard spheres represents a central paradigm of kinetic theory of granular gases. At zero gravity the temperature of a freely cooling homogeneous granular gas follows a power law in time. How does gravity, which brings inhomogeneity, affect the cooling? We combine molecular dynamics simulations, a numerical solution of hydrodynamic equations and an analytic theory to show that a granular gas cooling under gravity undergoes thermal collapse: it cools down to zero temperature and condenses on the bottom of the container in a finite time.

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Renormalization-group calculation of the dependence on gravity of the surface tension and bending rigidity of a fluid interface.

The surface tension and the bending rigidity of a planar liquid-vapor interface in the presence of vanishing gravity are analyzed using the renormalization group. Based on the density functional theory of inhomogeneous fluids, we show that a term, quartic in the density fluctuations, can be added to the classical capillary-wave model so that a renormalization-group calculation can be performed. By comparing the outcome of such a calculation with rigorous results relating the direct correlation function with surface tension and bending rigidity, we find the scaling dependence of the latter on gravity. The results agree with the expected fact that the interface should become unstable as gravity vanishes.

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Primordial gravity waves and weak lensing.

Inflation produces a primordial spectrum of gravity waves in addition to the density perturbations which seed structure formation. We compute the signature of these gravity waves in the large scale shear field. The shear can be divided into a gradient mode (G or E) and a curl mode (C or B). The latter is produced only by gravity waves, so the observations of a nonzero curl mode could be seen as evidence for inflation. We find that the expected signal from inflation is small, peaking on the largest scales at l(l+1)C(l)/2pi<10(-11) at l=2 and falling rapidly thereafter. Even for an all-sky deep survey, this signal would be below noise at all multipoles.

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Cosmogenic neutrinos and signals of TeV gravity in air showers and neutrino telescopes.

The existence of extra dimensions allows the possibility that the fundamental scale of gravity is at the TeV. If that is the case, gravity could dominate the interactions of ultrahigh energy cosmic rays. In particular, the production of microscopic black holes by cosmogenic neutrinos has been estimated in a number of papers. We consider here gravity-mediated interactions at larger distances, where they can be calculated in the eikonal approximation. We show that for the expected flux of cosmogenic neutrinos these elastic processes give a stronger signal than black hole production in neutrino telescopes. Taking the bounds on the higher-dimensional Planck mass M(D) (D=4 + n) from current air shower experiments, for n=2(6) elastic collisions could produce up to 118 (34) events per year at IceCube. On the other hand, the absence of any signal would imply a bound of M(D) > or approximately 5 TeV.

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Feynman propagator for spin foam quantum gravity.

We link the notion causality with the orientation of the spin foam 2-complex. We show that all current spin foam models are orientation independent. Using the technology of evolution kernels for quantum fields on Lie groups, we construct a generalized version of spin foam models, introducing an extra proper time variable. We prove that different ranges of integration for this variable lead to different classes of spin foam models: the usual ones, interpreted as the quantum gravity analogue of the Hadamard function of quantum field theory (QFT) or as inner products between quantum gravity states; and a new class of causal models, the quantum gravity analogue of the Feynman propagator in QFT, nontrivial function of the orientation data, and implying a notion of "timeless ordering".

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Model-updated image guidance: initial clinical experiences with gravity-induced brain deformation.

Image-guided neurosurgery relies on accurate registration of the patient, the preoperative image series, and the surgical instruments in the same coordinate space. Recent clinical reports have documented the magnitude of gravity-induced brain deformation in the operating room and suggest these levels of tissue motion may compromise the integrity of such systems. We are investigating a model-based strategy which exploits the wealth of readily-available preoperative information in conjunction with intraoperatively acquired data to construct and drive a three dimensional (3-D) computational model which estimates volumetric displacements in order to update the neuronavigational image set. Using model calculations, the preoperative image database can be deformed to generate a more accurate representation of the surgical focus during an operation. In this paper, we present a preliminary study of four patients that experienced substantial brain deformation from gravity and correlate cortical shift measurements with model predictions. Additionally, we illustrate our image deforming algorithm and demonstrate that preoperative image resolution is maintained. Results over the four cases show that the brain shifted, on average, 5.7 mm in the direction of gravity and that model predictions could reduce this misregistration error to an average of 1.2 mm.

Adolescent↗

Theory and design of an orthotic device for full or partial gravity-balancing of a human leg during motion.

Gravity balancing is often used in industrial machines to decrease the required actuator efforts during motion. In the literature, a number of methods have been proposed for gravity balancing that include counterweights, springs, and auxiliary parallelograms that determine the center of mass. However, these concepts have not yet been seriously applied to rehabilitation machines. This paper presents the underlying theory and design of an orthosis for the human leg that can fully or partially balance the human leg over the range of its motion. This design combines the use of auxiliary parallelograms to determine the center of mass along with springs to achieve a full or partial gravity balanced orthosis design. A first prototype has been constructed to demonstrate the effectiveness of the idea. Future prototypes will have parameters that will be tuned to the geometry and inertia of a human subject and be tailored to an individual's needs.

Computer-Aided Design↗

Gravity cavernosometry--a simple diagnostic test for cavernosal incompetence.

The papaverine test has been widely used as a diagnostic procedure in erectile impotence. However, when patients do not achieve full erection on the test, it is necessary to differentiate between insufficient inflow and excessive outflow. Gravity cavernosometry is a method designed to evaluate the pressure responses in the corpora when they are subjected to a constant infusion pressure. The infusion flow is of minor significance. The intracavernous pressure (ICP) was measured in cadavers, in psychogenically impotent patients and in patients with arteriogenic impotence, following administration of papaverine and gravity perfusion. During perfusion in cadavers and in psychogenic patients, the ICP showed values above 110 cm H2O, while in arteriogenic patients the values ranged from 30 to 141 cm H2O. In the arteriogenic group, 11/20 patients had an ICP lower than 110 during perfusion. There was no correlation between the pre-perfusion pressure and the final pressure with perfusion. Gravity cavernosometry is a simple, cost-effective and reliable method for the assessment of corporeal competence.

Adult↗

Isokinetic hamstring/quadriceps strength ratio: influence from joint angular velocity, gravity correction and contraction mode.

This study investigated isokinetic peak- and angle-specific hamstring/quadriceps strength ratios (conventional H/Q ratio) obtained during concentric and eccentric muscle contraction and examined the influence of joint angular velocity and the effect of gravity correction on these ratios. Also, a 'functional' H/Q ratio was defined by calculating eccentric hamstring strength relative to concentric quadriceps strength (Hecc/Qcon' representative for knee extension) and calculating concentric hamstring strength relative to eccentric quadriceps strength (Hcon/Qecc' representative for knee flexion). The H/Q ratio was calculated based on isokinetic peak moment and 50 degree-moment (0 degree = full extension) obtained at joint angular velocities 30, 120 and 240 degrees s-1. Gravity corrected conventional H/Q ratio remained constant across speeds and contraction mode, ranging from 0.47 to 0.54 and from 0.49 to 0.56 based on peak and 50 degree moment, respectively. In contrast, non-corrected H/Q ratio increased during concentric contraction from 0.58 at 30 degrees s-1 to 0.74 at 240 degree s-1 (P < 0.01). For knee extension at 240 degrees s-1 an Hecc/Qcon of 1.05 (peak) and 0.89 (50 degrees) was observed while for flexion at 240 degrees s-1 an Hcon/Qecc of 0.27 (peak) and 0.28 (50 degrees) was observed. In conclusion, gravity correction had high influence on the change in H/Q ratio with variation in extension velocity. A potential 1:1 hamstring/quadriceps strength relationship was demonstrated for fast knee extension, indicating a significant functional capacity of the hamstring muscles for providing muscular stability at the knee joint in such situations.

Adult↗

Somatic versus vestibular gravity reception in man.

In order to assess the effect of extravestibular gravity receptors on perception and control of body position against that of the otoliths, the subject (S) is exposed to gravitoinertial forces along the spinal (Z) axis on a tiltable board and on a sled centrifuge. It turns out that (1) both effects, on average, are equally strong, although with considerable variance between Ss; (2) the centroid of the mass(es) governing the somatic receptors lies near the centroid of the body; and (3) somatic gravity reception contains two distinctly different systems. Both appear unimpaired in paraplegic Ss with total bilateral sensory loss (TSL) from the 5th to the 1st lumbar spinal segment. One, the truncal system, is eliminated with TSL from the 11th thoracic segment upwards. Yet another is still functioning with TSL up to and including the 6th cervical segment, with the same effectiveness throughout this range. Hence it must be mediated by vagal or, less likely, sympathetic afference, that is, probably, by the influence of gravity on the cardiovascular system. That the afference of the truncal system appears to enter the cord at the last two thoracic segments supports earlier conjectures about a supererogatory static function of the kidneys. In fact, on the tiltable board, 7 bilaterally nephrectomized Ss behaved like paraplegics with TSL between T11 and C6, yet differed significantly in the predicted direction from the normal controls.

Gravitation↗

Vestibular discrimination of gravity and translational acceleration.

According to Einstein's equivalence principle, linear accelerations experienced during translational motion are physically indistinguishable from changes in orientation relative to gravity experienced during tilting movements. Nevertheless, despite these ambiguous sensory cues provided by the primary otolith afferents, perceptual and motor responses discriminate between gravity and translational acceleration. There is growing evidence to suggest that the brain resolves this ambiguity primarily by combining signals from multiple sensors, the semicircular canals being a main extra otolith contributor. Here, we summarize the experimental evidence in support of the canal influences on the neural processing of otolith cues, provide specific experimental results in rhesus monkeys, and discuss and compare previously proposed models that combine otolith and semicircular-canal signals in order to provide neural estimates of gravity and linear acceleration.

Animals↗

Gravity-induced anomalies in interphase spacing reported for binary eutectics.

It has been reasoned that desirable microstructural refinement in binary eutectics could result from freezing in reduced-gravity. It is recognized that the interphase spacing in a binary eutectic is controlled by solute transport and that, on Earth, buoyancy-driven convection may enhance this. Hence, it has been presumed that the interphase spacing ought to decrease when a eutectic alloy is frozen under conditions of much-reduced gravity, where such buoyancy effects would be largely absent. The result of such speculation has been that many workers have frozen various eutectics under reduced gravity and have reported that, although some eutectics became finer, others showed no change, and some even became coarser. This reported varied behavior will be reviewed in the light of long term studies by the author at Queen's University, including recent microgravity studies in which samples of two eutectic alloy systems, MnBi-Bi and MnSb-Sb, were frozen under very stable conditions and showed no change in interphase spacing.

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Sliding-cavity fluid contactors in low-gravity fluids, materials, and biotechnology research.

The well-known method of sliding-cavity fluid contactors used by Gosting for diffusion measurements and by Tiselius in electrophoresis has found considerable use in low-gravity research. To date, sliding-cavity contactors have been used in liquid diffusion experiments, interfacial transport experiments, biomolecular crystal growth, biphasic extraction, multistage extraction, microencapsulation, seed germination, invertebrate development, and thin-film casting. Sliding-cavity technology has several advantages for spaceflight: it is simple, it accommodates small samples, samples can be fully enclosed, phases can be combined, multiple samples can be processed at high sample density, real-time observations can be made, and mixed and diffused samples can be compared. An analysis of the transport phenomena that govern the sliding-cavity method is offered. During sliding of one liquid over another flow rates between 0.001 and 0.1m/sec are developed, giving Reynolds numbers in the range 0.1-100. Assuming no slip at liquid-solid boundaries shear rates are of the order 1sec(-1). The measured consequence is the transfer of 2-5% of the content of a cavity to the opposite cavity. In the absence of gravity, buoyancy-driven transport is assumed absent. Transport processes are limited to (1) molecular diffusion, in which reactants diffuse toward one another at rates that depend on their diffusion coefficient and concentration gradient (Fick's second law), (2) solutocapillary (Marangoni) flow driven by surface-tension gradients, (3) capillary flow (drop spreading) at liquid-solid three-phase lines leading to immiscible phase demixing, and (4) vapor-phase diffusive mass transfer in evaporative processes. Quantitative treatment of these phenomena has been accomplished over the past few years in low-gravity research in space and on aircraft.

Biotechnology↗

Heart rate and blood pressure variability in subjects exposed to simulated increases in gravity.

The effect of simulated increases in gravity (G) force on blood pressure and heart rate variability was investigated in seven normal healthy subjects using a man-carrying centrifuge. Subjects were exposed to G forces up to 3.6 times the gravity at the earth's surface (3.6 G). Blood pressure was measured non-invasively using a finger cuff (Finapres), while the subjects breathed at a fixed rate and depth. The blood pressure waveform was digitized and systolic blood pressure, diastolic blood pressure and beat-to-beat intervals were extracted from these data. Power spectra were produced from these values. Increases in G force produced increases in spectral power of systolic blood pressure and diastolic blood pressure at the respiratory frequency (0.2 Hz) and less conspicuous but significant increases in spectral power at lower frequencies (0.045-0.15 Hz). The spectral power of beat-to-beat interval did not change. It is postulated that the reduction in central blood volume produced by increased gravity is affecting blood pressure control in a similar way to that seen in hypovolaemic animals. The marked increase in blood pressure fluctuations induced by respiration at the higher G levels may be a result of the alteration in venous return to the right atrium, ultimately reflected as fluctuating left ventricular output and pressure.

Acceleration↗

Antarctic Tectonics: Constraints From an ERS-1 Satellite Marine Gravity Field

A high-resolution gravity field of poorly charted and ice-covered ocean near West Antarctica, from the Ross Sea east to the Weddell Sea, has been derived with the use of satellite altimetry, including ERS-1 geodetic phase, wave-form data. This gravity field reveals regional tectonic fabric, such as gravity lineations, which are the expression of fracture zones left by early (65 to 83 million years ago) Pacific-Antarctic sea-floor spreading that separated the Campbell Plateau and New Zealand continent from West Antarctica. These lineations constrain plate motion history and confirm the hypothesis that Antarctica behaved as two distinct plates, separated from each other by an extensional Bellingshausen plate boundary active in the Amundsen Sea before about 61 million years ago.

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Improved gravity field of the moon from lunar prospector

An improved gravity model from Doppler tracking of the Lunar Prospector (LP) spacecraft reveals three new large mass concentrations (mascons) on the nearside of the moon beneath the impact basins Mare Humboltianum, Mendel-Ryberg, and Schiller-Zucchius, where the latter basin has no visible mare fill. Although there is no direct measurement of the lunar farside gravity, LP partially resolves four mascons in the large farside basins of Hertzsprung, Coulomb-Sarton, Freundlich-Sharonov, and Mare Moscoviense. The center of each of these basins contains a gravity maximum relative to the surrounding basin. The improved normalized polar moment of inertia (0.3932 +/- 0.0002) is consistent with an iron core with a radius of 220 to 450 kilometers.

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Thermal undulations of quasi-spherical vesicles stabilized by gravity.

The classical treatment of quasi-spherical vesicle undulations has, in the present work, been reviewed and extended to systems, which are affected by a gravitational field caused by a density difference across the membrane. The effects have been studied by the use of perturbation theory leading to corrections to the mean shape and the fluctuation correlation matrix. These corrections have been included in an analytical expression for the flicker spectrum to probe how the experimentally accessible spectrum changes with gravity. The results are represented in terms of the gravitational parameter, g(0) = Delta(rho)g R(4)/kappa. The contributions from gravity are in most experimental situations small and thus negligible, but for values of g(0) above a certain limit, the perturbational corrections must be included. Expressions for the relative error on the flicker spectrum have been worked out, so that it is possible to define the regime where gravity is negligible. An upper limit of g(0) has also been identified, where the error in all modes of the flicker spectrum is significant due to distortion of the mean shape.

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