Ultrasonic oil-film thickness measurement: An angular spectrum approach to assess performance limits

The performance of ultrasonic oil-film thickness measurement in a ball bearing is quantified. A range of different viscosity oils (Shell T68, VG15, and VG5) are used to explore the lowest reflection coefficient and hence the thinnest oil-film thickness that the system can measure. The results show a minimum reflection coefficient of 0.07 for both oil VG15 and VG5 and 0.09 for oil T68 at 50 MHz. This corresponds to an oil-film thickness of 0.4 μm for T68 oil. An angular spectrum (or Fourier decomposition) approach is used to analyze the performance of this configuration. This models the interaction of component plane waves with the measurement system and quantifies the effect of the key parameters (transducer aperture, focal length, and center frequency). The simulation shows that for a focused transducer the reflection coefficient tends to a limiting value at small oil-film thickness. For the transducer used in this paper it is shown that the limiting reflection coefficient is 0.05 and the oil-film measurement errors increase as the reflection coefficient approaches this value. The implications for improved measurement systems are then discussed

Surface Dynamics of Crude and Weathered Oil in the Presence of Dispersants: Laboratory Experiment and Numerical Simulation

Marine oil spills can have dire consequences for the environment. Research on their dynamics is important for the well-being of coastal communities and their economies. Propagation of oil spills is a very complex physical-chemical process. As seen during the Deepwater Horizon event in the Gulf of Mexico during 2010, one of the critical problems remaining for prediction of oil transport and dispersion in the marine environment is the small-scale structure and dynamics of surface oil spills. The laboratory experiments conducted in this work were focused on understanding the differences between the dynamics of crude and weathered oil spills and the effect of dispersants. After deposition on the still water surface, a drop of crude oil quickly spread into a thin slick; while at the same time, a drop of machine (proxy for weathered) oil did not show significant evolution. Subsequent application of dispersant to the crude oil slick resulted in a quick contraction or fragmentation of the slick into narrow wedges and tiny drops. Notably, the slick of machine oil did not show significant change in size or topology after spraying dispersant. An advanced multi-phase, volume of fluid computational fluid dynamics model, incorporating capillary forces, was able to explain some of the features observed in the laboratory experiment. As a result of the laboratory and modeling experiments, the new interpretation of the effect of dispersant on the oil dispersion process including capillary effects has been proposed, which is expected to lead to improved oil spill models and response strategies

Classical big-bounce cosmology: dynamical analysis of a homogeneous and irrotational Weyssenhoff fluid

A dynamical analysis of an effective homogeneous and irrotational Weyssenhoff fluid in general relativity is performed using the 1+3 covariant approach that enables the dynamics of the fluid to be determined without assuming any particular form for the space-time metric. The spin contributions to the field equations produce a bounce that averts an initial singularity, provided that the spin density exceeds the rate of shear. At later times, when the spin contribution can be neglected, a Weyssenhoff fluid reduces to a standard cosmological fluid in general relativity. Numerical solutions for the time evolution of the generalised scale factor in spatially-curved models are presented, some of which exhibit eternal oscillatory behaviour without any singularities. In spatially-flat models, analytical solutions for particular values of the equation-of-state parameter are derived. Although the scale factor of a Weyssenhoff fluid generically has a positive temporal curvature near a bounce, it requires unreasonable fine tuning of the equation-of-state parameter to produce a sufficiently extended period of inflation to fit the current observational data.Comment: 34 pages, 18 figure

New Isotropic and Anisotropic Sudden Singularities

We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong, and dominant energy conditions. We show what new type of energy condition is needed to exclude them ab initio. We also determine the conditions under which finite-time future singularities can arise in a wide class of anisotropic cosmological models. New types of finite-time singularity are possible which are characterised by divergences in the time-rate of change of the anisotropic-pressure tensor. We investigate the conditions for the formation of finite-time singularities in a Bianchi type $VII_{0}$ universe with anisotropic pressures and construct specific examples of anisotropic sudden singularities in these universes.Comment: Typos corrected. Published versio

In-situ measurement of journal bearing lubricant viscosity by means of a novel ultrasonic measurement technique using matching layer

An ultrasonic viscometer was used to measure the circumferential viscosity variation in a journal bearing non-invasively. This sensing technique is based on the reflection of a shear wave at a solid-liquid boundary that depends on the viscosity of the liquid and the acoustic properties of the solid. Very little ultrasonic energy can propagate into the oil at a metal-oil interface because the acoustic mismatch is significant. Interleaving a matching layer between the metal and the lubricant enables accurate ultrasonic viscosity measurements [1] Schirru, M., Mills, R., Dwyer-Joyce, R., Smith, O., and Sutton, M. (2015). Viscosity Measurement in a Lubricant Film Using an Ultrasonically Resonating Matching Layer. Tribology Letters, 60(3) pp. 1–11. [CrossRef], [Web of Science ®] . This technique has been used to build a miniaturized ultrasonic viscometer that is accommodated inside a journal to obtain the circumferential viscosity profile. Four viscosity regions are identified due to the variations in the localized temperatures and loads. The results are compared with the isothermal solution of the Reynolds equations for hydrodynamic lubricated bearings. The ultrasonic viscometer locates the angle at which the maximum load occurs and the length of the loaded contact with good accuracy. Finally, the viscosity results are used to estimate the frictional power losses. It is shown that over 70% of the total losses in the journal bearing occur in the region where the load is maximum

Can dark matter be a Bose-Einstein condensate?

We consider the possibility that the dark matter, which is required to explain the dynamics of the neutral hydrogen clouds at large distances from the galactic center, could be in the form of a Bose-Einstein condensate. To study the condensate we use the non-relativistic Gross-Pitaevskii equation. By introducing the Madelung representation of the wave function, we formulate the dynamics of the system in terms of the continuity equation and of the hydrodynamic Euler equations. Hence dark matter can be described as a non-relativistic, Newtonian Bose-Einstein gravitational condensate gas, whose density and pressure are related by a barotropic equation of state. In the case of a condensate with quartic non-linearity, the equation of state is polytropic with index $n=1$. To test the validity of the model we fit the Newtonian tangential velocity equation of the model with a sample of rotation curves of low surface brightness and dwarf galaxies, respectively. We find a very good agreement between the theoretical rotation curves and the observational data for the low surface brightness galaxies. The deflection of photons passing through the dark matter halos is also analyzed, and the bending angle of light is computed. The bending angle obtained for the Bose-Einstein condensate is larger than that predicted by standard general relativistic and dark matter models. Therefore the study of the light deflection by galaxies and the gravitational lensing could discriminate between the Bose-Einstein condensate dark matter model and other dark matter models.Comment: 20 pages, 7 figures, accepted for publication in JCAP, references adde

Dark energy problem: from phantom theory to modified Gauss-Bonnet gravity

The solution of dark energy problem in the models without scalars is presented. It is shown that late-time accelerating cosmology may be generated by the ideal fluid with some implicit equation of state. The universe evolution within modified Gauss-Bonnet gravity is considered. It is demonstrated that such gravitational approach may predict the (quintessential, cosmological constant or transient phantom) acceleration of the late-time universe with natural transiton from deceleration to acceleration (or from non-phantom to phantom era in the last case).Comment: LaTeX 8 pages, prepared for the Proceedings of QFEXT'05, minor correctons, references adde

Friction and wear phenomena of vegetable oil based lubricants with additives at severe sliding wear conditions

The tribological responses of palm oil and soybean oil, combined with two commercial antiwear additives (zinc dialkyl dithiophosphate and boron compound), were investigated at a lubricant temperature of 100 °C and under severe contact conditions in a reciprocating sliding contact. The friction coefficient of palm oil with zinc dialkyl dithiophosphate was closest to the commercial mineral engine oil, with a 2% difference. The soybean oil with zinc dialkyl dithiophosphate produced a 57% improvement in wear resistance compared to its pure oil state. The existence of boron nitride in vegetable oils was only responsive in reduction of wear rather than friction. The response of commercial antiwear additives with vegetable oils showed a potential for the future improvement in the performance of vegetable oils

Variational Methods for Biomolecular Modeling

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the identification of essential energetic components, the optimal parametrization of energies, and the efficient computational implementation of energy variation or minimization. Given the fact that complex biomolecular systems are structurally non-uniform and their interactions occur through contact interfaces, their free energies are associated with various interfaces as well, such as solute-solvent interface, molecular binding interface, lipid domain interface, and membrane surfaces. This fact motivates the inclusion of interface geometry, particular its curvatures, to the parametrization of free energies. Applications of such interface geometry based energetic variational principles are illustrated through three concrete topics: the multiscale modeling of biomolecular electrostatics and solvation that includes the curvature energy of the molecular surface, the formation of microdomains on lipid membrane due to the geometric and molecular mechanics at the lipid interface, and the mean curvature driven protein localization on membrane surfaces. By further implicitly representing the interface using a phase field function over the entire domain, one can simulate the dynamics of the interface and the corresponding energy variation by evolving the phase field function, achieving significant reduction of the number of degrees of freedom and computational complexity. Strategies for improving the efficiency of computational implementations and for extending applications to coarse-graining or multiscale molecular simulations are outlined.Comment: 36 page

Almost optimal asynchronous rendezvous in infinite multidimensional grids

Two anonymous mobile agents (robots) moving in an asynchronous manner have to meet in an infinite grid of dimension δ> 0, starting from two arbitrary positions at distance at most d. Since the problem is clearly infeasible in such general setting, we assume that the grid is embedded in a δ-dimensional Euclidean space and that each agent knows the Cartesian coordinates of its own initial position (but not the one of the other agent). We design an algorithm permitting the agents to meet after traversing a trajectory of length O(d δ polylog d). This bound for the case of 2d-grids subsumes the main result of [12]. The algorithm is almost optimal, since the Ω(d δ) lower bound is straightforward. Further, we apply our rendezvous method to the following network design problem. The ports of the δ-dimensional grid have to be set such that two anonymous agents starting at distance at most d from each other will always meet, moving in an asynchronous manner, after traversing a O(d δ polylog d) length trajectory. We can also apply our method to a version of the geometric rendezvous problem. Two anonymous agents move asynchronously in the δ-dimensional Euclidean space. The agents have the radii of visibility of r1 and r2, respectively. Each agent knows only its own initial position and its own radius of visibility. The agents meet when one agent is visible to the other one. We propose an algorithm designing the trajectory of each agent, so that they always meet after traveling a total distance of O( ( d)), where r = min(r1, r2) and for r ≥ 1. r)δpolylog ( d r