Decay of quantised vorticity by sound emission

It is thought that in a quantum fluid sound generation is the ultimate sink of turbulent kinetic energy in the absence of any other dissipation mechanism near absolute zero. We show that a suitably trapped Bose-Einstein condensate provides a model system to study the sound emitted by accelerating vortices in a controlled way.Comment: 6 pages, 3 figure

Ultrasonic study of the gelation of gelatin: phase diagram, hysteresis and kinetics

We map the ultrasonic (8 MHz) speed and attenuation of edible-grade gelatin in water, exploring the key dependencies on temperature, concentration and time. The ultrasonic signatures of the sol-gel transition, confirmed by rheological measurements, and incomplete gel formation at low concentrations, enable a phase diagram of the system to be constructed. Sensitivity is also demonstrated to the kinetics of gel formation and melting, and associated hysteresis effects upon cyclic temperature sweeps. Furthermore, simple acoustic models of the sol and gel state enable estimation of the speed of sound and compressibility of gelatin. Our results demonstrate the potential of ultrasonic measurements to characterise the structure and visco-elasticity of gelatin hydrogels.Comment: 15 pages, 8 figure

Thermodynamics of an interacting trapped Bose-Einstein gas in the classical field approximation

We present a convenient technique describing the condensate in dynamical equilibrium with the thermal cloud, at temperatures close to the critical one. We show that the whole isolated system may be viewed as a single classical field undergoing nonlinear dynamics leading to a steady state. In our procedure it is the observation process and the finite detection time that allow for splitting the system into the condensate and the thermal cloud.Comment: 4 pages, 4 eps figures, final versio

An horizon scan of biogeography

The opportunity to reflect broadly on the accomplishments, prospects, and reach of a field may present itself relatively infrequently. Each biennial meeting of the International Biogeography Society showcases ideas solicited and developed largely during the preceding year, by individuals or teams from across the breadth of the discipline. Here, we highlight challenges, developments, and opportunities in biogeography from that biennial synthesis. We note the realized and potential impact of rapid data accumulation in several fields, a renaissance for inter-disciplinary research, the importance of recognizing the evolution-ecology continuum across spatial and temporal scales and at different taxonomic, phylogenetic and functional levels, and re-exploration of classical assumptions and hypotheses using new tools. However, advances are taxonomically and geographically biased, and key theoretical frameworks await tools to handle, or strategies to simplify, the biological complexity seen in empirical systems. Current threats to biodiversity require unprecedented integration of knowledge and development of predictive capacity that may enable biogeography to unite its descriptive and hypothetico-deductive branches and establish a greater role within and outside academia

Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals

High-order derivatives of analytic functions are expressible as Cauchy integrals over circular contours, which can very effectively be approximated, e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius of convergence is equal, numerical stability strongly depends on r. We give a comprehensive study of this effect; in particular we show that there is a unique radius that minimizes the loss of accuracy caused by round-off errors. For large classes of functions, though not for all, this radius actually gives about full accuracy; a remarkable fact that we explain by the theory of Hardy spaces, by the Wiman-Valiron and Levin-Pfluger theory of entire functions, and by the saddle-point method of asymptotic analysis. Many examples and non-trivial applications are discussed in detail.Comment: Version 4 has some references and a discussion of other quadrature rules added; 57 pages, 7 figures, 6 tables; to appear in Found. Comput. Mat

Stability and collapse of localized solutions of the controlled three-dimensional Gross-Pitaevskii equation

On the basis of recent investigations, a newly developed analytical procedure is used for constructing a wide class of localized solutions of the controlled three-dimensional (3D) Gross-Pitaevskii equation (GPE) that governs the dynamics of Bose-Einstein condensates (BECs). The controlled 3D GPE is decomposed into a two-dimensional (2D) linear Schr\"{o}dinger equation and a one-dimensional (1D) nonlinear Schr\"{o}dinger equation, constrained by a variational condition for the controlling potential. Then, the above class of localized solutions are constructed as the product of the solutions of the transverse and longitudinal equations. On the basis of these exact 3D analytical solutions, a stability analysis is carried out, focusing our attention on the physical conditions for having collapsing or non-collapsing solutions.Comment: 21 pages, 14 figure

A Phenomenological Analysis of Heavy Hadron Lifetimes

A phenomenological analysis of lifetimes of bottom and charmed hadrons within the framework of the heavy quark expansion is performed. The baryon matrix element is evaluated using the bag model and the nonrelativistic quark model. We find that bottom-baryon lifetimes follow the pattern $\tau(\Omega_b)\simeq\tau(\Xi_b^-)>\tau(\Lambda_b)\simeq\tau(\Xi_b^0)$. However, neither the lifetime ratio $\tau(\Lambda_b)/\tau( B_d)$ nor the absolute decay rates of the $\Lambda_b$ baryon and $B$ mesons can be explained. One way of solving both difficulties is to allow the presence of linear $1/m_Q$ corrections by scaling the inclusive nonleptonic width with the fifth power of the hadron mass $m_{H_Q}$ rather than the heavy quark mass $m_Q$. The hierarchy of bottom baryon lifetimes is dramatically modified to $\tau(\Lambda_b)>\tau(\Xi_b^-)>\tau(\Xi_b^0)>\tau( \Omega_b)$: The longest-lived $\Omega_b$ among bottom baryons in the OPE prescription now becomes shortest-lived. The replacement of $m_Q$ by $m_{H_Q}$ in nonleptonic widths is natural and justified in the PQCD-based factorization approach formulated in terms of hadron-level kinematics. For inclusive charmed baryon decays, we argue that since the heavy quark expansion does not converge, local duality cannot be tested in this case. We show that while the ansatz of substituting the heavy quark mass by the hadron mass provides a much better description of the charmed-baryon lifetime {\it ratios}, it appears unnatural and unpredictive for describing the {\it absolute} inclusive decay rates of charmed baryons, contrary to the bottom case.Comment: 35 pages, to appear in Phys. Rev. The CDF result on the lifetime ratio of Lambda_b and B_d is discusse

Quantum Kinetic Theory III: Quantum kinetic master equation for strongly condensed trapped systems

We extend quantum kinetic theory to deal with a strongly Bose-condensed atomic vapor in a trap. The method assumes that the majority of the vapor is not condensed, and acts as a bath of heat and atoms for the condensate. The condensate is described by the particle number conserving Bogoliubov method developed by one of the authors. We derive equations which describe the fluctuations of particle number and phase, and the growth of the Bose-Einstein condensate. The equilibrium state of the condensate is a mixture of states with different numbers of particles and quasiparticles. It is not a quantum superposition of states with different numbers of particles---nevertheless, the stationary state exhibits the property of off-diagonal long range order, to the extent that this concept makes sense in a tightly trapped condensate.Comment: 3 figures submitted to Physical Review

Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale

In the context of Markov evolution, we present two original approaches to obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the language of stochastic derivatives and by using a family of exponential martingales functionals. We show that GFDT are perturbative versions of relations verified by these exponential martingales. Along the way, we prove GFDT and Fluctuation Relations (FR) for general Markov processes, beyond the usual proof for diffusion and pure jump processes. Finally, we relate the FR to a family of backward and forward exponential martingales.Comment: 41 pages, 7 figures; version2: 45 pages, 7 figures, minor revisions, new results in Section

Selecting the best candidates for resurrecting extinct-in-the-wild plants from herbaria

Resurrecting extinct species is a fascinating and challenging idea for scientists and the general public. Whereas some theoretical progress has been made for animals, the resurrection of extinct plants (de-extinction sensu lato) is a relatively recently discussed topic. In this context, the term ‘de-extinction’ is used sensu lato to refer to the resurrection of ‘extinct in the wild’ species from seeds or tissues preserved in herbaria, as we acknowledge the current impossibility of knowing a priori whether a herbarium seed is alive and can germinate. In plants, this could be achieved by germinating or in vitro tissue-culturing old diaspores such as seeds or spores available in herbarium specimens. This paper reports the first list of plant de-extinction candidates based on the actual availability of seeds in herbarium specimens of globally extinct plants. We reviewed globally extinct seed plants using online resources and additional literature on national red lists, resulting in a list of 361 extinct taxa. We then proposed a method of prioritizing candidates for seed-plant de-extinction from diaspores found in herbarium specimens and complemented this with a phylogenetic approach to identify species that may maximize evolutionarily distinct features. Finally, combining data on seed storage behaviour and longevity, as well as specimen age in the novel ‘best de-extinction candidate’ score (DEXSCO), we identified 556 herbarium specimens belonging to 161 extinct species with available seeds. We expect that this list of de-extinction candidates and the novel approach to rank them will boost research efforts towards the first-ever plant de-extinction