Linear oscillations of a compressible hemispherical bubble on a solid substrate

The linear natural and forced oscillations of a hemispherical bubble on a solid substrate are under theoretical consideration. The contact line dynamics is taken into account with the Hocking condition, which eventually leads to interaction of the shape and volume oscillations. Resonant phenomena, mostly pronounced for the bubble with the fixed contact line or with the fixed contact angle, are found out. The limiting case of weakly compressible bubble is studied. The general criterion identifying whether the compressibility of a bubble can be neglected is obtained.Comment: new slightly extended version with some minor changes, added journal reference and DOI information; 12 pages, 8 figures, published in Physics of Fluid

Orion Flight Performance Design Trades

A significant portion of the Orion pre-PDR design effort has focused on balancing mass with performance. High level performance metrics include abort success rates, lunar surface coverage, landing accuracy and touchdown loads. These metrics may be converted to parameters that affect mass, such as ballast for stabilizing the abort vehicle, propellant to achieve increased lunar coverage or extended missions, or ballast to increase the lift-to-drag ratio to improve entry and landing performance. The Orion Flight Dynamics team was tasked to perform analyses to evaluate many of these trades. These analyses not only provide insight into the physics of each particular trade but, in aggregate, they illustrate the processes used by Orion to balance performance and mass margins, and thereby make design decisions. Lessons learned can be gleaned from a review of these studies which will be useful to other spacecraft system designers. These lessons fall into several categories, including: appropriate application of Monte Carlo analysis in design trades, managing margin in a highly mass-constrained environment, and the use of requirements to balance margin between subsystems and components. This paper provides a review of some of the trades and analyses conducted by the Flight Dynamics team, as well as systems engineering lessons learned

‘‘Lozenge’’ contour plots in scattering from polymer networks

We present a consistent explanation for the appearance of “lozenge” shapes in contour plots of the two dimensional scattering intensity from stretched polymer networks. By explicitly averaging over quenched variables in a tube model, we show that lozenge patterns arise as a result of chain material that is not directly deformed by the stretch. We obtain excellent agreement with experimental data

Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtolitres. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small sub-cellular compartment. This is achieved by applying a mesoscopic version of the quasi-steady state assumption to the exact Fokker-Planck equation associated with the Poisson Representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing sub-cellular volume, decreasing Michaelis-Menten constants and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.Comment: 13 pages, 4 figures; published in The Journal of Chemical Physic

Cryopyrin-associated periodic fever syndrome manifesting as Tolosa-Hunt syndrome

Background Tolosa-Hunt syndrome (THS) is characterized by unilateral orbital pain, ipsilateral oculomotor paresis and a prompt response to treatment with corticosteroids. Several reports have demonstrated that the clinical features of THS are not specific to one causal aetiology and can lead to misdiagnosis. Case report We report the case of a patient diagnosed with THS after an episode of unilateral orbital pain and diplopia with demonstration of granulomatous inflammation of both cavernous sinus on cerebral magnetic resonance imaging and an immediate response to treatment with corticosteroids. Progression of the disease over the following years, accompanied by increasing signs of inflammation on cerebral magnetic resonance imaging and cerebrospinal fluid pleocytosis, led to further diagnostic tests. Genetic analyses revealed a heterozygote low-penetrance mutation (Q703K) of the cryopyrin/NLRP3 gene compatible with a cryopyrin-associated periodic fever syndrome. Discussion This case report demonstrates that THS can be a central nervous system manifestation of cryopyrin-associated periodic fever syndrome, which therefore represents a differential diagnosis of THS, even in elderly patients

MAT-734: INCREASING THE DURABILITY AND RESILIENCE OF TALL BUILDINGS WITH PRECAST CONCRETE ENCLOSURE SYSTEMS

In this paper precast concrete wall systems are compared to curtain wall and window wall systems in terms of durability and disaster resilience of multi-story buildings. Window wall systems are currently the enclosure system of choice for tall residential buildings in most parts of North America. Precast concrete wall systems can be expected to last the lifetime of a building with routine seal replacement. These are highly durable systems. Windows within precast concrete wall systems will require replacement in 25-35 years but represent a limited portion of the wall area and hence are less costly and have less impact on building use interruption. The impact of façade choice on passive survivability and security are also considered. Maintaining livable temperatures in a space in Toronto, Ontario (a city with a climate similar to many Northern U.S. cities) during a power outage is shown to mostly depend on having little heat loss, reducing solar gains, and provision of thermal mass. A whole wall metric is also introduced which combines various vision and non-vision wall system heat loss components. A similar metric for solar gain is introduced. The most significant factor affecting this heat loss and solar gain (and thereby affecting thermal resilience) is to avoid high Window to Wall Ratios (WWR). This will apply for most wall systems but is most significant for systems like precast concrete where there is minimal thermal bridging through the insulation. In terms of security, precast concrete walls will protect occupants from projectiles and endure little damage during disasters. These impacts make precast concrete wall systems significantly more disaster resilient

How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?

The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokker-Planck estimates of the mean concentrations and of the variance of the concentration fluctuations about the mean are accurate to order $\Omega^{-3/2}$ for reaction systems which do not obey detailed balance and at least accurate to order $\Omega^{-2}$ for systems obeying detailed balance, where $\Omega$ is the characteristic size of the system. Hence the chemical Fokker-Planck equation turns out to be more accurate than the linear-noise approximation of the chemical master equation (the linear Fokker-Planck equation) which leads to mean concentration estimates accurate to order $\Omega^{-1/2}$ and variance estimates accurate to order $\Omega^{-3/2}$. This higher accuracy is particularly conspicuous for chemical systems realized in small volumes such as biochemical reactions inside cells. A formula is also obtained for the approximate size of the relative errors in the concentration and variance predictions of the chemical Fokker-Planck equation, where the relative error is defined as the difference between the predictions of the chemical Fokker-Planck equation and the master equation divided by the prediction of the master equation. For dimerization and enzyme-catalyzed reactions, the errors are typically less than few percent even when the steady-state is characterized by merely few tens of molecules.Comment: 39 pages, 3 figures, accepted for publication in J. Chem. Phy