Shear dispersion along circular pipes is affected by bends, but the torsion of the pipe is negligible

The flow of a viscous fluid along a curving pipe of fixed radius is driven by a pressure gradient. For a generally curving pipe it is the fluid flux which is constant along the pipe and so I correct fluid flow solutions of Dean (1928) and Topakoglu (1967) which assume constant pressure gradient. When the pipe is straight, the fluid adopts the parabolic velocity profile of Poiseuille flow; the spread of any contaminant along the pipe is then described by the shear dispersion model of Taylor (1954) and its refinements by Mercer, Watt et al (1994,1996). However, two conflicting effects occur in a generally curving pipe: viscosity skews the velocity profile which enhances the shear dispersion; whereas in faster flow centrifugal effects establish secondary flows that reduce the shear dispersion. The two opposing effects cancel at a Reynolds number of about 15. Interestingly, the torsion of the pipe seems to have very little effect upon the flow or the dispersion, the curvature is by far the dominant influence. Lastly, curvature and torsion in the fluid flow significantly enhance the upstream tails of concentration profiles in qualitative agreement with observations of dispersion in river flow

Magnetic Phase Transitions in One-dimensional Strongly Attractive Three-Component Ultracold Fermions

We investigate the nature of trions, pairing and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions in external fields. Exact results for the groundstate energy, critical fields, magnetization and phase diagrams are obtained analytically from the Bethe ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of trions, bound pairs, a normal Fermi liquid and four mixtures of these states. Particularly, a smooth phase transition from a trionic phase into a pairing phase occurs as the highest hyperfine level separates from the two lower energy levels. In contrast, there is a smooth phase transition from the trionic phase into a normal Fermi liquid as the lowest level separates from the two higher levels.Comment: 4 pages, 3 figures, minor revisions to text, replacement figure, refs added and update

Phase diagram of the su(8) quantum spin tube

We calculate the phase diagram of an integrable anisotropic 3-leg quantum spin tube connected to the su(8) algebra. We find several quantum phase transitions for antiferromagnetic rung couplings. Their locations are calculated exactly from the Bethe Ansatz solution and we discuss the nature of each of the different phases.Comment: 10 pages, RevTeX, 1 postscript figur

Turbulent Pair Diffusion

Kinematic Simulations of turbulent pair diffusion in planar turbulence with a -5/3 energy spectrum reproduce the results of the laboratory measurements of Jullien Phys. Rev. Lett. 82, 2872 (1999), in particular the stretched exponential form of the PDF of pair separations and their correlation functions. The root mean square separation is found to be strongly dependent on initial conditions for very long stretches of times. This dependence is consistent with the topological picture of turbulent pair diffusion where pairs initially close enough travel together for long stretches of time and separate violently when they meet straining regions around hyperbolic points. A new argument based on the divergence of accelerations is given to support this picture

Wilson ratio of Fermi gases in one dimension

We calculate the Wilson ratio of the one-dimensional Fermi gas with spin imbalance. The Wilson ratio of attractively interacting fermions is solely determined by the density stiffness and sound velocity of pairs and of excess fermions for the two-component Tomonaga-Luttinger liquid (TLL) phase. The ratio exhibits anomalous enhancement at the two critical points due to the sudden change in the density of states. Despite a breakdown of the quasiparticle description in one dimension, two important features of the Fermi liquid are retained, namely the specific heat is linearly proportional to temperature whereas the susceptibility is independent of temperature. In contrast to the phenomenological TLL parameter, the Wilson ratio provides a powerful parameter for testing universal quantum liquids of interacting fermions in one, two and three dimensions.Comment: 5+2 pages, 4+1 figures, Eq. (4) is proved, figures were refine

Universal local pair correlations of Lieb-Liniger bosons at quantum criticality

The one-dimensional Lieb-Liniger Bose gas is a prototypical many-body system featuring universal Tomonaga-Luttinger liquid (TLL) physics and free fermion quantum criticality. We analytically calculate finite temperature local pair correlations for the strong coupling Bose gas at quantum criticality using the polylog function in the framework of the Yang-Yang thermodynamic equations. We show that the local pair correlation has the universal value $g^{(2)}(0)\approx 2 p/(n\varepsilon)$ in the quantum critical regime, the TLL phase and the quasi-classical region, where $p$ is the pressure per unit length rescaled by the interaction energy $\varepsilon=\frac{\hbar^2}{2m} c^2$ with interaction strength $c$ and linear density $n$. This suggests the possibility to test finite temperature local pair correlations for the TLL in the relativistic dispersion regime and to probe quantum criticality with the local correlations beyond the TLL phase. Furthermore, thermodynamic properties at high temperatures are obtained by both high temperature and virial expansion of the Yang-Yang thermodynamic equation.Comment: 8 pages, 6 figures, additional text and reference

European Paediatric Formulation Initiative (EuPFI)-Formulating Ideas for Better Medicines for Children.

© American Association of Pharmaceutical Scientists 2016, published by Springer US, available online at doi: https://doi.org/10.1208/s12249-016-0584-1The European Paediatric Formulation Initiative (EuPFI), founded in 2007, aims to promote and facilitate the preparation of better and safe medicines for children through linking research and information dissemination. It brings together the capabilities of the industry, academics, hospitals, and regulators within a common platform in order to scope the solid understanding of the major issues, which will underpin the progress towards the future of paediatric medicines we want.The EuPFI was formed in parallel to the adoption of regulations within the EU and USA and has served as a community that drives research and dissemination through publications and the organisation of annual conferences. The membership and reach of this group have grown since its inception in 2007 and continue to develop and evolve to meet the continuing needs and ambitions of research into and development of age appropriate medicines. Five diverse workstreams (age-appropriate medicines, Biopharmaceutics, Administration Devices, Excipients and Taste Assessment & Taste Masking (TATM)) direct specific workpackages on behalf of the EuPFI. Furthermore, EuPFI interacts with multiple diverse professional groups across the globe to ensure efficient working in the area of paediatric medicines. Strong commitment and active involvement of all EuPFI stakeholders have proved to be vital to effectively address knowledge gaps related to paediatric medicines, discuss potential areas for further research and identify issues that need more attention and analysis in the future.Peer reviewedFinal Accepted Versio

Temperley-Lieb Words as Valence-Bond Ground States

Based on the Temperley--Lieb algebra we define a class of one-dimensional Hamiltonians with nearest and next-nearest neighbour interactions. Using the regular representation we give ground states of this model as words of the algebra. Two point correlation functions can be computed employing the Temperley--Lieb relations. Choosing a spin-1/2 representation of the algebra we obtain a generalization of the (q-deformed) Majumdar--Ghosh model. The ground states become valence-bond states.Comment: 9 Pages, LaTeX (with included style files

Bethe Ansatz study of one-dimensional Bose and Fermi gases with periodic and hard wall boundary conditions

We extend the exact periodic Bethe Ansatz solution for one-dimensional bosons and fermions with delta-interaction and arbitrary internal degrees of freedom to the case of hard wall boundary conditions. We give an analysis of the ground state properties of fermionic systems with two internal degrees of freedom, including expansions of the ground state energy in the weak and strong coupling limits in the repulsive and attractive regimes.Comment: 27 pages, 6 figures, key reference added, typos correcte

Microscale swimming: The molecular dynamics approach

The self-propelled motion of microscopic bodies immersed in a fluid medium is studied using molecular dynamics simulation. The advantage of the atomistic approach is that the detailed level of description allows complete freedom in specifying the swimmer design and its coupling with the surrounding fluid. A series of two-dimensional swimming bodies employing a variety of propulsion mechanisms -- motivated by biological and microrobotic designs -- is investigated, including the use of moving limbs, changing body shapes and fluid jets. The swimming efficiency and the nature of the induced, time-dependent flow fields are found to differ widely among body designs and propulsion mechanisms.Comment: 5 pages, 3 figures (minor changes to text