Exponentially growing solutions in homogeneous Rayleigh-Benard convection

It is shown that homogeneous Rayleigh-Benard flow, i.e., Rayleigh-Benard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient, has a family of exact, exponentially growing, separable solutions of the full non-linear system of equations. These solutions are clearly manifest in numerical simulations above a computable critical value of the Rayleigh number. In our numerical simulations they are subject to secondary numerical noise and resolution dependent instabilities that limit their growth to produce statistically steady turbulent transport.Comment: 4 pages, 3 figures, to be published in Phys. Rev. E - rapid communication

Variational bounds on the energy dissipation rate in body-forced shear flow

A new variational problem for upper bounds on the rate of energy dissipation in body-forced shear flows is formulated by including a balance parameter in the derivation from the Navier-Stokes equations. The resulting min-max problem is investigated computationally, producing new estimates that quantitatively improve previously obtained rigorous bounds. The results are compared with data from direct numerical simulations.Comment: 15 pages, 7 figure

Law Is in the Bin: New Frontiers in Conceptual Art and Legal Liability

Part I of this Note begins with a discussion of who Banksy is and why his work is important to this legal debate, finishing with a detailed description of the features of conceptual art that are relevant for legal analysis and an argument that the shredding stunt—the event itself, not the partially shredded canvas—is a work of conceptual art. Part II argues that the unique features of the shredding stunt, and of future works in the same artistic category, present a novel legal problem both for artists and for buyers. This novel problem is explored through the lens of the legal recourse available to buyers of modern art who become aware at the time of purchase that the artist had different plans for the tangible elements of the work than were communicated prior to purchase. Whether the court adopts the artist’s or the buyer’s definition of the “artwork” is crucial to the resolution of these disputes. Existing law governing sales of artwork indicates that a reviewing court is more likely to side with the buyer. In light of the ramifications of the shredding stunt and the new questions it raises, Part III issues recommendations for artists seeking to realize their creative goals and buyers seeking to avoid harm to themselves and liability to third parties. In the absence of formal copyright protection for conceptual artworks, artists can avoid legal action from potential buyers by ensuring they only sell to willing buyers. While this option has adverse consequences for artistic integrity, as risk mitigation is antithetical to the element of surprise at the heart of works like the shredding stunt, artists might need to voluntarily accept this reality as a limitation on their ability to pursue any concepts they desire. Buyers, on the other hand, need to begin scrutinizing art transactions with more caution if they want to avoid becoming unwilling participants in conceptual artworks. In fully evaluating risk, buyers may also be able to rely on industry norms to incentivize artists to be mindful of their interests

Distribution of label spacings for genome mapping in nanochannels

In genome mapping experiments, long DNA molecules are stretched by confining them to very narrow channels, so that the locations of sequence-specific fluorescent labels along the channel axis provide large-scale genomic information. It is difficult, however, to make the channels narrow enough so that the DNA molecule is fully stretched. In practice its conformations may form hairpins that change the spacings between internal segments of the DNA molecule, and thus the label locations along the channel axis. Here we describe a theory for the distribution of label spacings that explains the heavy tails observed in distributions of label spacings in genome mapping experiments.Comment: 18 pages, 4 figures, 1 tabl

CHICAGO MEDICAL SOCIETY.: Stated Meeting, Oct. 18, 1886.

n/

Fuel quality/processing study. Volume 4: On site processing studies

Fuel treated at the turbine and the turbine exhaust gas processed at the turbine site are studied. Fuel treatments protect the turbine from contaminants or impurities either in the upgrading fuel as produced or picked up by the fuel during normal transportation. Exhaust gas treatments provide for the reduction of NOx and SOx to environmentally acceptable levels. The impact of fuel quality upon turbine maintenance and deterioration is considered. On site costs include not only the fuel treatment costs as such, but also incremental costs incurred by the turbine operator if a turbine fuel of low quality is not acceptably upgraded

Entrance and exit at infinity for stable jump diffusions

In his seminal work from the 1950s, William Feller classified all one-dimensional diffusions on $-\infty\leq a<b\leq \infty$ in terms of their ability to access the boundary (Feller's test for explosions) and to enter the interior from the boundary. Feller's technique is restricted to diffusion processes as the corresponding differential generators allow explicit computations and the use of Hille-Yosida theory. In the present article we study exit and entrance from infinity for the most natural generalization, that is, jump diffusions of the form $$dZ_t=\sigma(Z_{t-})\,dX_t,$$ driven by stable L\'evy processes for $\alpha\in (0,2)$. Many results have been proved for jump diffusions, employing a variety of techniques developed after Feller's work but exit and entrance from infinite boundaries has long remained open. We show that the presence of jumps implies features not seen in the diffusive setting without drift. Finite time explosion is possible for $\alpha\in (0,1)$, whereas entrance from different kinds of infinity is possible for $\alpha\in [1,2)$. We derive necessary and sufficient conditions on $\sigma$ so that (i) non-exploding solutions exist and (ii) the corresponding transition semigroup extends to an entrance point at `infinity'. Our proofs are based on very recent developments for path transformations of stable processes via the Lamperti-Kiu representation and new Wiener-Hopf factorisations for L\'evy processes that lie therein. The arguments draw together original and intricate applications of results using the Riesz-Bogdan--\.Zak transformation, entrance laws for self-similar Markov processes, perpetual integrals of L\'evy processes and fluctuation theory, which have not been used before in the SDE setting, thereby allowing us to employ classical theory such as Hunt-Nagasawa duality and Getoor's characterisation of transience and recurrence

Resonant Activation Phenomenon for Non-Markovian Potential-Fluctuation Processes

We consider a generalization of the model by Doering and Gadoua to non-Markovian potential-switching generated by arbitrary renewal processes. For the Markovian switching process, we extend the original results by Doering and Gadoua by giving a complete description of the absorption process. For all non-Markovian processes having the first moment of the waiting time distributions, we get qualitatively the same results as in the Markovian case. However, for distributions without the first moment, the mean first passage time curves do not exhibit the resonant activation minimum. We thus come to the conjecture that the generic mechanism of the resonant activation fails for fluctuating processes widely deviating from Markovian.Comment: RevTeX 4, 5 pages, 4 figures; considerably shortened version accepted as a brief report to Phys. Rev.