Two-dimensional shear modulus of a Langmuir foam

We deform a two-dimensional (2D) foam, created in a Langmuir monolayer, by applying a mechanical perturbation, and simultaneously image it by Brewster angle microscopy. We determine the foam stress tensor (through a determination of the 2D gas-liquid line tension, 2.35 $\pm$ 0.4 pJ$\cdot$m$^{-1}$) and the statistical strain tensor, by analyzing the images of the deformed structure. We deduce the 2D shear modulus of the foam, $\mu= 38 \pm 3 \mathrm{nN}\cdot \mathrm{m}^{-1}$. The foam effective rigidity is predicted to be $35 \pm 3 \mathrm {nN}\cdot \mathrm {m}^{- 1}$, which agrees with the value $37.5 \pm 0.8 \mathrm {nN}\cdot \mathrm {m}^{-1}$ obtained in an independent mechanical measurement.Comment: submitted May 12, 2003 ; resubmitted Sept 9, 200

Analysis of Compound Synergy in High-Throughput Cellular Screens by Population-Based Lifetime Modeling

Despite the successful introduction of potent anti-cancer therapeutics, most of these drugs lead to only modest tumor-shrinkage or transient responses, followed by re-growth of tumors. Combining different compounds has resulted in enhanced tumor control and prolonged survival. However, methods querying the efficacy of such combinations have been hampered by limited scalability, analytical resolution, statistical feasibility, or a combination thereof. We have developed a theoretical framework modeling cellular viability as a stochastic lifetime process to determine synergistic compound combinations from high-throughput cellular screens. We apply our method to data derived from chemical perturbations of 65 cancer cell lines with two inhibitors. Our analysis revealed synergy for the combination of both compounds in subsets of cell lines. By contrast, in cell lines in which inhibition of one of both targets was sufficient to induce cell death, no synergy was detected, compatible with the topology of the oncogenically activated signaling network. In summary, we provide a tool for the measurement of synergy strength for combination perturbation experiments that might help define pathway topologies and direct clinical trials

Noncommutative generalizations of theorems of Cohen and Kaplansky

This paper investigates situations where a property of a ring can be tested on a set of "prime right ideals." Generalizing theorems of Cohen and Kaplansky, we show that every right ideal of a ring is finitely generated (resp. principal) iff every "prime right ideal" is finitely generated (resp. principal), where the phrase "prime right ideal" can be interpreted in one of many different ways. We also use our methods to show that other properties can be tested on special sets of right ideals, such as the right artinian property and various homological properties. Applying these methods, we prove the following noncommutative generalization of a result of Kaplansky: a (left and right) noetherian ring is a principal right ideal ring iff all of its maximal right ideals are principal. A counterexample shows that the left noetherian hypothesis cannot be dropped. Finally, we compare our results to earlier generalizations of Cohen's and Kaplansky's theorems in the literature.Comment: 41 pages. To appear in Algebras and Representation Theory. Minor changes were made to the numbering system, in order to remain consistent with the published versio

Palaeomagnetic field intensity variations suggest Mesoproterozoic inner-core nucleation

The Earth’s inner core grows by the freezing of liquid iron at its surface. The point in history at which this process initiated marks a step-change in the thermal evolution of the planet. Recent computational and experimental studies1,2,3,4,5 have presented radically differing estimates of the thermal conductivity of the Earth’s core, resulting in estimates of the timing of inner-core nucleation ranging from less than half a billion to nearly two billion years ago. Recent inner-core nucleation (high thermal conductivity) requires high outer-core temperatures in the early Earth that complicate models of thermal evolution. The nucleation of the core leads to a different convective regime6 and potentially different magnetic field structures that produce an observable signal in the palaeomagnetic record and allow the date of inner-core nucleation to be estimated directly. Previous studies searching for this signature have been hampered by the paucity of palaeomagnetic intensity measurements, by the lack of an effective means of assessing their reliability, and by shorter-timescale geomagnetic variations. Here we examine results from an expanded Precambrian database of palaeomagnetic intensity measurements7 selected using a new set of reliability criteria8. Our analysis provides intensity-based support for the dominant dipolarity of the time-averaged Precambrian field, a crucial requirement for palaeomagnetic reconstructions of continents. We also present firm evidence for the existence of very long-term variations in geomagnetic strength. The most prominent and robust transition in the record is an increase in both average field strength and variability that is observed to occur between a billion and 1.5 billion years ago. This observation is most readily explained by the nucleation of the inner core occurring during this interval9; the timing would tend to favour a modest value of core thermal conductivity and supports a simple thermal evolution model for the Earth

On the influence of a translating inner core in models of outer core convection

It has recently been proposed that the hemispheric seismic structure of the inner core can be explained by a self-sustained rigid-body translation of the inner core material, resulting in melting of the solid at the leading face and a compensating crystallisation at the trailing face. This process induces a hemispherical variation in the release of light elements and latent heat at the inner-core boundary, the two main sources of thermochemical buoyancy thought to drive convection in the outer core. However, the effect of a translating inner core on outer core convection is presently unknown. In this paper we model convection in the outer core with a nonmagnetic Boussinesq fluid in a rotating spherical shell driven by purely thermal buoyancy, incorporating the effect of a translating inner core by a time-independent spherical harmonic degree and order 1 (View the MathML sourceY11) pattern of heat-flux imposed at the inner boundary. The analysis considers Rayleigh numbers up to 10 times the critical value for onset of nonmagnetic convection, a parameter regime where the effects of the inhomogeneous boundary condition are expected to be most pronounced, and focuses on varying q∗q∗, the amplitude of the imposed boundary anomalies. The presence of inner boundary anomalies significantly affects the behaviour of the model system. Increasing q∗q∗ leads to flow patterns dominated by azimuthal jets that span large regions of the shell where radial motion is significantly inhibited. Vigorous convection becomes increasingly confined to isolated regions as q∗q∗ increases; these regions do not drift and always occur in the hemisphere subjected to a higher than average boundary heat-flux. Effects of the inner boundary anomalies are visible at the outer boundary in all inhomogeneous models considered. At low q∗q∗ the expression of inner boundary effects at the core surface is a difference in the flow speed between the two hemispheres. As q∗q∗ increases the spiralling azimuthal jets driven from the inner boundary are clearly visible at the outer boundary. Finally, our results suggest that, when the system is heated from below, a View the MathML sourceY11 heat-flux pattern imposed on the inner boundary has a greater overall influence on the spatio-temporal behaviour of the flow than the same pattern imposed at the outer boundary