On the surface tension of fluctuating quasi-spherical vesicles

We calculate the stress tensor for a quasi-spherical vesicle and we thermally average it in order to obtain the actual, mechanical, surface tension $\tau$ of the vesicle. Both closed and poked vesicles are considered. We recover our results for $\tau$ by differentiating the free-energy with respect to the proper projected area. We show that $\tau$ may become negative well before the transition to oblate shapes and that it may reach quite large negative values in the case of small vesicles. This implies that spherical vesicles may have an inner pressure lower than the outer one.Comment: To appear in Eur. Phys. J. E, revised versio

A quartet of fermionic expressions for M(k,2k±1)M(k,2k\pm1) Virasoro characters via half-lattice paths

We derive new fermionic expressions for the characters of the Virasoro minimal models $M(k,2k\pm1)$ by analysing the recently introduced half-lattice paths. These fermionic expressions display a quasiparticle formulation characteristic of the $\phi_{2,1}$ and $\phi_{1,5}$ integrable perturbations. We find that they arise by imposing a simple restriction on the RSOS quasiparticle states of the unitary models $M(p,p+1)$. In fact, four fermionic expressions are obtained for each generating function of half-lattice paths of finite length $L$, and these lead to four distinct expressions for most characters $\chi^{k,2k\pm1}_{r,s}$. These are direct analogues of Melzer's expressions for $M(p,p+1)$, and their proof entails revisiting, reworking and refining a proof of Melzer's identities which used combinatorial transforms on lattice paths. We also derive a bosonic version of the generating functions of length $L$ half-lattice paths, this expression being notable in that it involves $q$-trinomial coefficients. Taking the $L\to\infty$ limit shows that the generating functions for infinite length half-lattice paths are indeed the Virasoro characters $\chi^{k,2k\pm1}_{r,s}$.Comment: 29 pages. v2: minor improvements, references adde

Interactions of pure aluminium hydrolytic species Keggin polyoxocations and hydroxide with biologically relevant molecules

The general purpose of this thesis is concerned with the intricate interactions of pure aluminium species with biomolecules. Pure aluminium reference systems (aluminium monomers, Keggin aluminium polyoxocations - Al13 and Al30, and aluminium hydroxide suspensions) were used for systematic mechanistic studies of the sol-gel transformation of aqueous solutions of aluminium-ions into aluminium (oxy) hydroxides induced by the addition of a 'soft base' - Trizma-base, which does not ionize fully in an aqueous solution. The conversion proceeds via forced hydrolysis-condensation of aluminium-ions into molecular clusters, structural conversion of aluminium Keggin-like polynuclear clusters into nanoparticles of aluminium (oxy) hydroxide, aggregation of primary nuclei of aluminium (oxy) hydroxide into larger clusters and finally the 'arrested growth' of the aggregates with the formation of the three-dimensional gel network. The next part of the study concentrated on the development and the optimisation of a potentiometric method for the determination of the 'formal' hydrolysis ratio of aluminium-containing solutions. The method made it possible to establish the aluminium speciation of the selected systems

On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity

We prove an inequality on the Wasserstein distance with quadratic cost between two solutions of the spatially homogeneous Boltzmann equation without angular cutoff, from which we deduce some uniqueness results. In particular, we obtain a local (in time) well-posedness result in the case of (possibly very) soft potentials. A global well-posedeness result is shown for all regularized hard and soft potentials without angular cutoff. Our uniqueness result seems to be the first one applying to a strong angular singularity, except in the special case of Maxwell molecules. Our proof relies on the ideas of Tanaka: we give a probabilistic interpretation of the Boltzmann equation in terms of a stochastic process. Then we show how to couple two such processes started with two different initial conditions, in such a way that they almost surely remain close to each other

Aerodynamic characteristics in pitch of a 1/7-scale model of a two- and three-stage rocket configuration at Mach numbers of 0.4 to 4.63

Aerodynamic characteristics in pitch of scale model of two and three stage rocket configuration at Mach numbers of 0.4 to 4.6

What Happens in the Links? Framing Judgment in Context

Scholars of Chaucer’s Canterbury Tales have focused much of their research on the interpretation of individual tales in the collection. The meaning behind these tales is clearly important to the work as a whole, as the Tales discuss grand themes that run throughout human life. The choice of themes and arguments in each pilgrim’s tale can also reflect back on the pilgrim’s own motivations and ideas. However, in searching for some greater meaning for Chaucer’s collection, it is important not to leave out the framework within which the tales exist. The links that join the tales to one another, arguably the portions of the piece that are the most original to Chaucer, do not always receive the same kind of attention that is focused on the most popular tales. In a work that is so complex, with its layered narration and interactions between tale and teller, the tales cannot possibly stand on their own, containing all of the meaning behind the work. The links have the potential to be particularly revealing in terms of how the audience should read the entire story of Chaucer’s Canterbury pilgrimage, because they ground the tales in specific circumstances

Density Power Spectrum of Compressible Hydrodynamic Turbulent Flows

Turbulent flows are ubiquitous in astrophysical environments, and understanding density structures and their statistics in turbulent media is of great importance in astrophysics. In this paper, we study the density power spectra, $P_{\rho}$, of transonic and supersonic turbulent flows through one and three-dimensional simulations of driven, isothermal hydrodynamic turbulence with root-mean-square Mach number in the range of 1 \la M_{\rm rms} \la 10. From one-dimensional experiments we find that the slope of the density power spectra becomes gradually shallower as the rms Mach number increases. It is because the density distribution transforms from the profile with {\it discontinuities} having $P_{\rho} \propto k^{-2}$ for $M_{\rm rms} \sim 1$ to the profile with {\it peaks} having $P_{\rho} \propto k^0$ for $M_{\rm rms} \gg 1$. We also find that the same trend is carried to three-dimension; that is, the density power spectrum flattens as the Mach number increases. But the density power spectrum of the flow with $M_{\rm rms} \sim 1$ has the Kolmogorov slope. The flattening is the consequence of the dominant density structures of {\it filaments} and {\it sheets}. Observations have claimed different slopes of density power spectra for electron density and cold H I gas in the interstellar medium. We argue that while the Kolmogorov spectrum for electron density reflects the {\it transonic} turbulence of $M_{\rm rms} \sim 1$ in the warm ionized medium, the shallower spectrum of cold H I gas reflects the {\it supersonic} turbulence of $M_{\rm rms} \sim$ a few in the cold neutral medium.Comment: To appear in ApJ Lett. Pdf file with full resolution figures can be downloaded from http://canopus.cnu.ac.kr/ryu/kimryu.pd

Geothermal studies - Yellowstone National Park /test site 11/, Wyoming

Summary report of diamond drilling in thermal areas of Yellowstone National Park, and method for determining heat flow in thermal area