The motion of an axisymmetric body falling in a tube at moderate Reynolds numbers

This study concerns the rectilinear and periodic paths of an axisymmetric solid body (short-length cylinder and disk of diameter d and thickness h) falling in a vertical tube of diameter D. We investigated experimentally the influence of the confinement ratio (S=d/D<0.8) on the motion of the body, for different aspect ratios (χ=d/h=3, 6 and 10), Reynolds numbers (80<Re<320) and a density ratio between the fluid and the body close to unity. For a given body, the Reynolds number based on its mean vertical velocity is observed to decrease when S increases. The critical Reynolds number for the onset of the periodic motion decreases with S in the case of thin bodies (χ=10), whereas it appears unaffected by S for thicker bodies (χ=3 and 6). The characteristics of the periodic motion are also strongly modified by the confinement ratio. A thick body (χ=3) tends to go back to a rectilinear path when S increases, while a thin body (χ=10) displays oscillations of growing amplitude with S until it touches the tube (at about S=0.5). For a given aspect ratio, however, the amplitudes of the oscillations follow a unique curve for all S, which depends only on the relative distance of the Reynolds number to the threshold of path instability. In parallel, numerical simulations of the wake of a body held fixed in a uniform confined flow were carried out. The simulations allowed us to determine in this configuration the effect of the confinement ratio on the thresholds for wake instability (loss of axial symmetry at Rec₁ and loss of stationarity at Rec₂) and on the maximal velocity Vw in the recirculating region of the stationary axisymmetric wake. The evolution with χ and S of Vw at Rec₁ was used to define a Reynolds number Re*. Remarkably, for a freely moving body, Re* remains almost constant when S varies, regardless of the nature of the path

Phase transitions related to the pigeonhole principle

Since Paris introduced them in the late seventies (Paris1978), densities turned out to be useful for studying independence results. Motivated by their simplicity and surprising strength we investigate the combinatorial complexity of two such densities which are strongly related to the pigeonhole principle. The aim is to miniaturise Ramsey's Theorem for $1$-tuples. The first principle uses an unlimited amount of colours, whereas the second has a fixed number of two colours. We show that these principles give rise to Ackermannian growth. After parameterising these statements with respect to a function f:N->N, we investigate for which functions f Ackermannian growth is still preserved

Pygmy dipole strength close to particle-separation energies - the case of the Mo isotopes

The distribution of electromagnetic dipole strength in 92, 98, 100 Mo has been investigated by photon scattering using bremsstrahlung from the new ELBE facility. The experimental data for well separated nuclear resonances indicate a transition from a regular to a chaotic behaviour above 4 MeV of excitation energy. As the strength distributions follow a Porter-Thomas distribution much of the dipole strength is found in weak and in unresolved resonances appearing as fluctuating cross section. An analysis of this quasi-continuum - here applied to nuclear resonance fluorescence in a novel way - delivers dipole strength functions, which are combining smoothly to those obtained from (g,n)-data. Enhancements at 6.5 MeV and at ~9 MeV are linked to the pygmy dipole resonances postulated to occur in heavy nuclei.Comment: 6 pages, 5 figures, proceedings Nuclear Physics in Astrophysics II, May 16-20, Debrecen, Hungary. The original publication is available at www.eurphysj.or

Percolation on an infinitely generated group

We give an example of a long range Bernoulli percolation process on a group non-quasi-isometric with $\mathbb{Z}$, in which clusters are almost surely finite for all values of the parameter. This random graph admits diverse equivalent definitions, and we study their ramifications. We also study its expected size and point out certain phase transitions.Comment: 23 page

Super-Radiant Dynamics, Doorways, and Resonances in Nuclei and Other Open Mesoscopic Systems

The phenomenon of super-radiance (Dicke effect, coherent spontaneous radiation by a gas of atoms coupled through the common radiation field) is well known in quantum optics. The review discusses similar physics that emerges in open and marginally stable quantum many-body systems. In the presence of open decay channels, the intrinsic states are coupled through the continuum. At sufficiently strong continuum coupling, the spectrum of resonances undergoes the restructuring with segregation of very broad super-radiant states and trapping of remaining long-lived compound states. The appropriate formalism describing this phenomenon is based on the Feshbach projection method and effective non-Hermitian Hamiltonian. A broader generalization is related to the idea of doorway states connecting quantum states of different structure. The method is explained in detail and the examples of applications are given to nuclear, atomic and particle physics. The interrelation of the collective dynamics through continuum and possible intrinsic many-body chaos is studied, including universal mesoscopic conductance fluctuations. The theory serves as a natural framework for general description of a quantum signal transmission through an open mesoscopic system.Comment: 85 pages, 10 figure

Theories and quantification of thymic selection

The peripheral T cell repertoire is sculpted from prototypic T cells in the thymus bearing randomly generated T cell receptors (TCR) and by a series of developmental and selection steps that remove cells that are unresponsive or overly reactive to self-peptide–MHC complexes. The challenge of understanding how the kinetics of T cell development and the statistics of the selection processes combine to provide a diverse but self-tolerant T cell repertoire has invited quantitative modeling approaches, which are reviewed here