Coupled normal fluid and superfluid profiles of turbulent helium II in channels

We perform fully coupled two--dimensional numerical simulations of plane channel helium II counterflows with vortex--line density typical of experiments. The main features of our approach are the inclusion of the back reaction of the superfluid vortices on the normal fluid and the presence of solid boundaries. Despite the reduced dimensionality, our model is realistic enough to reproduce vortex density distributions across the channel recently calculated in three--dimensions. We focus on the coarse--grained superfluid and normal fluid velocity profiles, recovering the normal fluid profile recently observed employing a technique based on laser--induced fluorescence of metastable helium molecules.Comment: 26 pages, 8 Figures, accepted for publication in Phys. Rev.

Complex singularities and PDEs

In this paper we give a review on the computational methods used to characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the singularity tracking method based on the analysis of the Fourier spectrum. We then introduce other methods generally used to detect the hidden singularities. In particular we show some applications of the Pad\'e approximation, of the Kida method, and of Borel-Polya method. We apply these techniques to the study of the singularity formation of some nonlinear dispersive and dissipative one dimensional PDE of the 2D Prandtl equation, of the 2D KP equation, and to Navier-Stokes equation for high Reynolds number incompressible flows in the case of interaction with rigid boundaries

The saturation of decaying counterflow turbulence in helium II

We are concerned with the problem of the decay of a tangle of quantized vortices in He II generated by a heat current. Direct application of Vinen's equation yields the temporal scaling of vortex line density $L \sim t^{-1}$. Schwarz and Rozen [Phys. Rev. Lett. {\bf 66}, 1898 (1991); Phys. Rev. B {\bf 44}, 7563 (1991)] observed a faster decay followed by a slower decay. More recently, Skrbek and collaborators [Phys. Rev. E {\bf 67}, 047302 (2003)] found an initial transient followed by the same classical $t^{-3/2}$ scaling observed in the decay of grid-generated turbulence. We present a simple theoretical model which, we argue, contains the essential physical ingredients, and accounts for these apparently contradictory results.Comment: 19 pages, 5 figure

On the stability and convergence of a semi-discrete discontinuous Galerkin scheme to the kinetic Cucker–Smale model

We study analytical properties of a semi-discrete discontinuous Galerkin (DG) scheme for the kinetic Cucker–Smale (CS) equation. The kinetic CS equation appears in the mean-field limit of the particle CS model and it corresponds to the dissipative Vlasov type equation approximating the large particle CS system. For this proposed DG scheme, we show that it exhibits analytical properties such as the conservation of mass, L2 -stability and convergence to the sufficiently regular solution, as the mesh-size tends to zero. In particular, we verify that the convergence rate of the DG numerical solution to the sufficiently regular kinetic solution is dependent on the Sobolev regularity of the kinetic soluiton. We also present several numerical simulations for low-dimensional cases

Feeding the Dragon. An Eschatological Motif in Medieval Europe

This book consists of six original essays concerning two popular eschatological motifs of medieval Europe: the devouring devil, especially in the guise of a dragon, and the zoomorphic mouth of hell, arguably a distinctive English adaptation of the anthropomorphic mouth of hell of classical antiquity. Over a time span ranging from late antiquity to the late Middle Ages and stretching across three languages, Latin, Old English, and Old Norse, the topos of the devouring demonic monster, a veritable commonplace across cultures and ages, is investigated in a variety of texts, including the Holy Scripture, homiletic and hagiographic works by authors such as Augustine of Hippo, Gregory the Great, and Ælfric of Eynsham, and apocryphal writings, e.g. the Seven Heavens Apocryphon and the Gospel of Nicodemus, especially its latter section, the Descensus Christi ad inferos. By detailing the creative interaction of a wide range of influences and the various practices of appropriation and adaptation of a vast stock of source material, both ultimate and intermediate, the contributions afford relevant case studies of the densely interlingual and intertextual modes of textual production, transmission, and reception in the European Middle Ages. Advancing our understanding of the cultural and textual networks of the period, this book will prove an important resource for anyone interested in the dynamic process of mediation between past and present, pagan and Christian, orthodoxy and apocrypha, exotic and local that makes up medieval literary and figurative culture

Route to chaos in the weakly stratified Kolmogorov flow

We consider a two-dimensional fluid exposed to Kolmogorov’s forcing cos(ny) and heated from above. The stabilizing effects of temperature are taken into account using the Boussinesq approximation. The fluid with no temperature stratification has been widely studied and, although relying on strong simplifications, it is considered an important tool for the theoretical and experimental study of transition to turbulence. In this paper, we are interested in the set of transitions leading the temperature stratified fluid from the laminar solution [U∝cos(ny),0, T ∝ y] to more complex states until the onset of chaotic states. We will consider Reynolds numbers 0 < Re ≤ 30, while the Richardson numbers shall be kept in the regime of weak stratifications (Ri ≤ 5 × 10 −3 ). We shall first review the non-stratified Kolmogorov flow and find a new period-tripling bifurcation as the precursor of chaotic states. Introducing the stabilizing temperature gradient, we shall observe that higher Re are required to trigger instabilities. More importantly, we shall see new states and phenomena: the newly discovered period-tripling bifurcation is supercritical or subcritical according to Ri; more period-tripling and doubling bifurcations may depart from this new state; strong enough stratifications trigger new regions of chaotic solutions and, on the drifting solution branch, non-chaotic bursting solutions

Analysis of complex singularities in high-Reynolds-number Navier-Stokes solutions

Numerical solutions of the laminar Prandtl boundary-layer and Navier-Stokes equations are considered for the case of the two-dimensional uniform flow past an impulsively-started circular cylinder. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions that can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective

El compuesto humano en la filosofía de San Agustín

La sensación no es solamente passio corporis, sino también actividad del alma vivificadora del cuerpo (hay sensación sólo cuando el alma no ignora lo que el cuerpo padece): el sentir non est corporis, sed animae per corpus.

Radiation hardened transistor characteristics for applications at LHC and beyond

The high radiation environment at the LHC will require the use of radiation hardened microelectronics for the readout of inner detectors. Two such technologies are a Harris bulk CMOS process and the DMILL mixed technology process. Transistors have been fabricated in both of these and have been tested before and after irradiation to 10 Mrads, the total dose expected in the innermost silicon microstrip layers. Several processing runs of Harris transistors have been carried out and samples from one have also been irradiated to 100 Mrads. A preamplifier-shaper circuit, to be used for readout of the CMS microstrip tracker, has been tested and the noise performance is compared with individual transistors