Phenomenological model for a novel melt-freeze phase of sliding bilayers

Simulations show that sliding bilayers of colloidal particles can exhibit a new phase, the ``melt-freeze'' phase, where the layers stochastically alternate between solidlike and liquidlike states. We introduce a mean field phenomenological model with two order parameters to understand the interplay of two adjacent layers while the system is in this remarkable phase. Predictions from our numerical simulations of a system in the melt-freeze phase include the tendency of two adjacent layers to be in opposite states (solid and liquid) and the difference between the fluctuation of the order parameter in one layer while the other layer is in the same phase compared to the fluctuation while the other layer is in the opposite phase. We expect this behavior to be seen in future simulations and experiments.Comment: 6 Pages, 6 figure

Properties of Dynamic Earthquake Ruptures With Heterogeneous Stress Drop

Earthquake rupture is a notoriously complex process, at all observable scales. We introduce a simplified semi-dynamic crack model to investigate the connection between the statistical properties of stress and those of macroscopic source parameters such as rupture size, seismic moment, apparent stress drop and radiated energy. Rupture initiation is treated consistently with nucleation on a linear slip-weakening fault, whereas rupture propagation and arrest are treated according to the Griffith criterion. The available stress drop is prescribed as a spatially correlated random field and is shown to potentially sustain a broad range of magnitudes. By decreasing the amplitude of the stress heterogeneities or increasing their correlation length the distribution of earthquake sizes presents a transition from Gutenberg- Richter to characteristic earthquake behavior. This transition is studied through a mean-field analysis. The bifurcation to characteristic earthquake behavior is sharp, reminiscent of a first-order phase transition. A lower roll-off magnitude observed in the Gutenberg-Richter regime is shown to depend on the correlation length of the available stress drop, rather than being a direct signature of the nucleation process. More generally, we highlight the possible role of the stress correlation length scale on deviations from earthquake source self-similarity. The present reduced model is a building block towards understanding the effect of structural and dynamic fault heterogeneities on the scaling of source parameters and on basic properties of seismicity

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.Comment: 36 pages, 1 tabl

Micro heat exchanger by using MEMS impinging jets

A micro impinging-jet heat exchanger is presented here. Heat transfer is studied for single jet, slot arrays and jet arrays. In order to facilitate micro heat transfer measurements with these devices, a MEMS sensor chip, which has an 8 x 8 temperature-sensor array on one side, and an integrated heater on the other side has been designed and fabricated. This sensor chip allows 2-D surface temperature measurement with various jets impinging on it. It is found that micro impinging jets can be highly efficient when compared to existing macro impinging-jet microelectronics packages such as IBM 4381. For example, using a single nozzle jet (500-μm diameter driven by 5 psig pressure), the sensor chip (2 x 2 cm^2) temperature can be cooled down from 70 to 33°C. The cooling becomes more efficient when nozzle arrays (4x5 over 1 cm^2 area) are used under the same driving pressure. Interestingly, although higher driving pressure gives better cooling (lower surface temperature), the cooling efficiency, defined as h/0.5pv^2, is actually higher for lower driving pressure

Comparing different accelerometer cut-points for sedentary time in children

Actigraph accelerometers are hypothesized to be valid measurements for assessing children\u27s sedentary time. However, there is considerable variation in accelerometer cut-points used. Therefore, we compared the most common accelerometer sedentary cut-points of children performing sedentary behaviors. Actigraph Actitrainer uniaxial accelerometers were used to measure children\u27s activity intensity (29 children, 5-11 years old) during different activities, namely playing computer games, nonelectronic sedentary games, watching television and playing outdoors. A structured protocol was the criterion for assessing the validity of four common cut-points (100, 300, 800, 1100 counts/minute). The median counts during all sedentary behaviors were below the lowest comparison cut-point of 100 cpm. The 75th percentile values for the sedentary behaviors were always below the cut-point of 300 cpm. Our results suggest that the cut-point of <100 cpm is the most appropriate