Heuristic explanation of journal bearing instability

A fluid-filled journal bearing is viewed as a powerful pump circulating fluid around the annular space between the journal and the bearing. A small whirling motion of the journal generates a wave of thickness variation progressing around the channel. The hypothesis that the fluid flow drives the whirl whenever the mean of the pumped fluid velocity is greater than the peripheral speed of the thickness variation wave is discussed and compared with other simple explanations of journal bearing instability. It is shown that for non-cavitation long bearings the hypothesis predicts instability onset correctly for unloaded bearings but gradually overpredicts the onset speed as the load is increased

Physical explanations of the destabilizing effect of damping in rotating parts

The destabilizing effect of rotating damping was investigated. When the rotation was faster than the whirl, rotating damping drags the orbiting particle forward. When stationary damping was also present, the stability borderline was readily determined by balancing the backward and forward drags. A key notion was that a forward whirl at rate omega a sub n with respect to stationary axes appears to be a backward whirl at rate Omega - omega sub n with respect to a system rotating supercritically at rate Omega. The growth rate of unstable whirls (or the decay rate of stable whirls was readily estimated by a simple energy balance

ON SCALING LAWS FOR MATERIAL DAMPING

Scaling laws for dampin

Enhancement of Wigner crystallization in quasi low-dimensional solids

The crystallization of electrons in quasi low-dimensional solids is studied in a model which retains the full three-dimensional nature of the Coulomb interactions. We show that restricting the electron motion to layers (or chains) gives rise to a rich sequence of structural transitions upon varying the particle density. In addition, the concurrence of low-dimensional electron motion and isotropic Coulomb interactions leads to a sizeable stabilization of the Wigner crystal, which could be one of the mechanisms at the origin of the charge ordered phases frequently observed in such compounds

The Cosmological Time Function

Let $(M,g)$ be a time oriented Lorentzian manifold and $d$ the Lorentzian distance on $M$. The function $\tau(q):=\sup_{p< q} d(p,q)$ is the cosmological time function of $M$, where as usual $p< q$ means that $p$ is in the causal past of $q$. This function is called regular iff $\tau(q) < \infty$ for all $q$ and also $\tau \to 0$ along every past inextendible causal curve. If the cosmological time function $\tau$ of a space time $(M,g)$ is regular it has several pleasant consequences: (1) It forces $(M,g)$ to be globally hyperbolic, (2) every point of $(M,g)$ can be connected to the initial singularity by a rest curve (i.e., a timelike geodesic ray that maximizes the distance to the singularity), (3) the function $\tau$ is a time function in the usual sense, in particular (4) $\tau$ is continuous, in fact locally Lipschitz and the second derivatives of $\tau$ exist almost everywhere.Comment: 19 pages, AEI preprint, latex2e with amsmath and amsth

Energy solutions to one-dimensional singular parabolic problems with BVBV data are viscosity solutions

We study one-dimensional very singular parabolic equations with periodic boundary conditions and initial data in $BV$, which is the energy space. We show existence of solutions in this energy space and then we prove that they are viscosity solutions in the sense of Giga-Giga.Comment: 15 page

Dynamical response of the "GGG" rotor to test the Equivalence Principle: theory, simulation and experiment. Part I: the normal modes

Recent theoretical work suggests that violation of the Equivalence Principle might be revealed in a measurement of the fractional differential acceleration $\eta$ between two test bodies -of different composition, falling in the gravitational field of a source mass- if the measurement is made to the level of $\eta\simeq 10^{-13}$ or better. This being within the reach of ground based experiments, gives them a new impetus. However, while slowly rotating torsion balances in ground laboratories are close to reaching this level, only an experiment performed in low orbit around the Earth is likely to provide a much better accuracy. We report on the progress made with the "Galileo Galilei on the Ground" (GGG) experiment, which aims to compete with torsion balances using an instrument design also capable of being converted into a much higher sensitivity space test. In the present and following paper (Part I and Part II), we demonstrate that the dynamical response of the GGG differential accelerometer set into supercritical rotation -in particular its normal modes (Part I) and rejection of common mode effects (Part II)- can be predicted by means of a simple but effective model that embodies all the relevant physics. Analytical solutions are obtained under special limits, which provide the theoretical understanding. A simulation environment is set up, obtaining quantitative agreement with the available experimental data on the frequencies of the normal modes, and on the whirling behavior. This is a needed and reliable tool for controlling and separating perturbative effects from the expected signal, as well as for planning the optimization of the apparatus.Comment: Accepted for publication by "Review of Scientific Instruments" on Jan 16, 2006. 16 2-column pages, 9 figure

Expansion Dating: Calibrating Molecular Clocks in Marine Species from Expansions onto the Sunda Shelf Following the Last Glacial Maximum

The rate of change in DNA is an important parameter for understanding molecular evolution and hence for inferences drawn from studies of phylogeography and phylogenetics. Most rate calibrations for mitochondrial coding regions in marine species have been made from divergence dating for fossils and vicariant events older than 1-2 My and are typically 0.5-2% per lineage per million years. Recently, calibrations made with ancient DNA (aDNA) from younger dates have yielded faster rates, suggesting that estimates of the molecular rate of change depend on the time of calibration, decaying from the instantaneous mutation rate to the phylogenetic substitution rate. aDNA methods for recent calibrations are not available for most marine taxa so instead we use radiometric dates for sea-level rise onto the Sunda Shelf following the Last Glacial Maximum (starting similar to 18,000 years ago), which led to massive population expansions for marine species. Instead of divergence dating, we use a two-epoch coalescent model of logistic population growth preceded by a constant population size to infer a time in mutational units for the beginning of these expansion events. This model compares favorably to simpler coalescent models of constant population size, and exponential or logistic growth, and is far more precise than estimates from the mismatch distribution. Mean rates estimated with this method for mitochondrial coding genes in three invertebrate species are elevated in comparison to older calibration points (2.3-6.6% per lineage per million years), lending additional support to the hypothesis of calibration time dependency for molecular rates

Necrotic tumor growth: an analytic approach

The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine the linearization of our model at such an equilibrium. Finally, we compute the solutions of the stationary linearized problem and comment on bifurcation.Comment: 14 pages, 3 figure

Expansion Dating: Calibrating Molecular Clocks in Marine Species from Expansions onto the Sunda Shelf following the Last Glacial Maximum

The rate of change in DNA is an important parameter for understanding molecular evolution, and hence for inferences drawn from studies of phylogeography and phylogenetics. Most rate calibrations for mitochondrial coding regions in marine species have been made from divergence dating for fossils and vicariant events older than 1-2 million years, and are typically 0.5% - 2% per lineage per million years. Recently, calibrations made with ancient DNA from younger dates have yielded faster rates, suggesting that estimates of the molecular rate of change depend on the time of calibration, decaying from the instantaneous mutation rate to the phylogenetic substitution rate. Ancient DNA methods for recent calibrations are not available for most marine taxa so instead we use radiometric dates for sea-level rise onto the Sunda Shelf following the Last Glacial Maximum (starting ~18,000 years ago), which led to massive population expansions for marine species. Instead of divergence dating, we use a two epoch coalescent model of logistic population growth preceded by a constant population size to infer a time in mutational units for the beginning of these expansion events. This model compares favorably to simpler coalescent models of constant population size, and exponential or logistic growth, and is far more precise than estimates from the mismatch distribution. Mean rates estimated with this method for mitochondrial coding genes in three invertebrate species are elevated in comparison to older calibration points (2.3% - 6.6% per lineage per million years), lending additional support to the hypothesis of calibration time-dependency for molecular rates