The impact of anticipation in dynamical systems

Collective motion in biology is often modelled as a dynamical system, in which individuals are represented as particles whose interactions are determined by the current state of the system. Many animals, however, including humans, have predictive capabilities, and presumably base their behavioural decisions---at least partially---upon an anticipated state of their environment. We explore a minimal version of this idea in the context of particles that interact according to a pairwise potential. Anticipation enters the picture by calculating the interparticle forces from linear extrapolations of the particle positions some time $\tau$ into the future. Simulations show that for intermediate values of $\tau$, compared to a transient time scale defined by the potential and the initial conditions, the particles form rotating clusters in which the particles are arranged in a hexagonal pattern. Analysis of the system shows that anticipation induces energy dissipation and we show that the kinetic energy asymptotically decays as $1/t$. Furthermore, we show that the angular momentum is not necessarily conserved for $\tau >0$, and that asymmetries in the initial condition therefore can cause rotational movement. These results suggest that anticipation could play an important role in collective behaviour, since it induces pattern formation and stabilises the dynamics of the system.Comment: Major revision compared to previous version. All figures replaced. Only introduction and discussion remain intac

Interband physics in an ultra-cold Fermi gas in an optical lattice

We study a gas of strongly polarized cold fermions in an optical lattice when the excited p-bands are populated. We derive the relevant Hamiltonian and discuss the expected phase diagram for both repulsive and attractive interactions. In the parameter regime covered here, checkerboard anti-ferromagnetic ordering is found to be possible for repulsive interactions while for attractive interactions, transitions between different types of paired phases are predicted.Comment: 5 pages, 2 figure

Long-term lead elimination from plasma and whole blood after poisoning

OBJECTIVE: Blood lead (B-Pb), one of the most used toxicological biomarker all kind, has serious limitations. Thus, the objective is to evaluate whether plasma lead (P-Pb) is more adequate. METHODS: A long-term follow-up study of five cases of lead poisoning. P-Pb was analysed by inductively coupled plasma mass spectrometry. Kinetics after end of exposure was modelled. RESULTS: P-Pb at severe poisoning was about 20 μg/L; haematological effects at about 5 μg/L. Biological half-time of P-Pb was about 1 month; B-Pb decay was much slower. CONCLUSION: P-Pb is a valuable biomarker of exposure to and risk, particularly at high exposure

Multiple‑point statistical modeling of three‑dimensional glacial aquifer heterogeneity for improved groundwater management

Quaternary glacial aquifers are important water sources for irrigation in many agricultural regions, including eastern Nebraska, USA. Quaternary glacial aquifers are heterogeneous, with juxtaposed low-permeability and high-permeability hydrofacies. Managing groundwater in such aquifers requires a realistic groundwater-flow model parameterization, and characterization of the aquifer geometry, spatial distribution of aquifer properties, and local aquifer interconnectedness. Despite its importance in considering uncertainty during decision-making, hydrofacies probabilities generated from multiple-point statistics (MPS) are not widely applied for groundwater model parameterization and groundwater management zone delineation. This study used a combination of soft data, a cognitive training image, and hard data to generate 100 three-dimensional (3D) conditional aquifer heterogeneity realizations. The most probable model (probability of hydrofacies) was then computed at node spacing of 200 × 200 × 3 m and validated using groundwater-level hydrographs. The resulting hydrofacies probability grids revealed variations in aquifer geometry, locally disconnected aquifer systems, recharge pathways, and hydrologic barriers. The profiles from hydrofacies probability at various locations show spatial variability of the streambed and aquifer connectivity. Groundwater-level hydrographs show evidence of these aquifer characteristics, verifying the general structure of the model. Using the MPS-generated 3D hydrofacies probability and hydrologic data, a novel workflow was developed in order to better define high-resolution groundwater management zones and strategies. In general, the conditional probability of hydrofacies helps improve the understanding of glacial aquifer heterogeneity, the characterization of aquifer-to-aquifer and streambed-aquifer connections, and the delineation of groundwater management zones. This MPS workflow can be adapted to other areas for modeling 3D aquifer heterogeneity using multisource data

Multiply quantized vortices in trapped Bose-Einstein condensates

Vortex configurations in rotating Bose-Einstein condensed gases trapped in power-law and anharmonic potentials are studied. When the confining potential is steeper than harmonic in the plane perpendicular to the axis of rotation, vortices with quantum numbers larger than one are energetically favorable if the interaction is weak enough. Features of the wave function for small and intermediate rotation frequencies are investigated numerically.Comment: 9 pages, 6 figures. Revised and extended article following referee repor

Finite temperature theory of the scissors mode in a Bose gas using the moment method

We use a generalized Gross-Pitaevskii equation for the condensate and a semi-classical kinetic equation for the noncondensate atoms to discuss the scissors mode in a trapped Bose-condensed gas at finite temperatures. Both equations include the effect of $C_{12}$ collisions between the condensate and noncondensate atoms. We solve the coupled moment equations describing oscillations of the quadrupole moments of the condensate and noncondensate components to find the collective mode frequencies and collisional damping rates as a function of temperature. Our calculations extend those of Gu\'ery-Odelin and Stringari at T=0 and in the normal phase. They complement the numerical results of Jackson and Zaremba, although Landau damping is left out of our approach. Our results are also used to calculate the quadrupole response function, which is related to the moment of inertia. It is shown explicitly that the moment of inertia of a trapped Bose gas at finite temperatures involves a sum of an irrotational component from the condensate and a rotational component from the thermal cloud atoms.Comment: 18 pages, 8 figure

A developmentally descriptive method for quantifying shape in gastropod shells

The growth of snail shells can be described by simple mathematical rules. Variation in a few parameters can explain much of the diversity of shell shapes seen in nature. However, empirical studies of gastropod shell shape variation typically use geometric morphometric approaches, which do not capture this growth pattern. We have developed a way to infer a set of developmentally descriptive shape parameters based on three-dimensional logarithmic helicospiral growth and using landmarks from two-dimensional shell images as input. We demonstrate the utility of this approach, and compare it to the geometric morphometric approach, using a large set of Littorina saxatilis shells in which locally adapted populations differ in shape. Our method can be modified easily to make it applicable to a wide range of shell forms, which would allow for investigations of the similarities and differences between and within many different species of gastropods

Splitting of a doubly quantized vortex through intertwining in Bose-Einstein condensates

The stability of doubly quantized vortices in dilute Bose-Einstein condensates of 23Na is examined at zero temperature. The eigenmode spectrum of the Bogoliubov equations for a harmonically trapped cigar-shaped condensate is computed and it is found that the doubly quantized vortex is spectrally unstable towards dissection into two singly quantized vortices. By numerically solving the full three-dimensional time-dependent Gross-Pitaevskii equation, it is found that the two singly quantized vortices intertwine before decaying. This work provides an interpretation of recent experiments [A. E. Leanhardt et al. Phys. Rev. Lett. 89, 190403 (2002)].Comment: 4 pages, 3 figures (to be published in PRA

Presynaptic actions of 4-Aminopyridine and γ-aminobutyric acid on rat sympathetic ganglia in vitro

Responses to bath-applications of 4-aminopyridine (4-AP) and -aminobutyric acid (GABA) were recorded intracellularly from neurones in the rat isolated superior cervical ganglion. 4-aminopyridine (0.1–1.0 mmol/l) usually induced spontaneous action potentials and excitatory postsynaptic potentials (EPSPs), which were blocked by hexamethonium. Membrane potential was unchanged; spike duration was slightly increased. Vagus nerve B-and C-fibre potentials were prolonged. In 4-AP solution (0.1–0.3 mmol/l), GABA (0.1 mmol/l), 3-aminopropanesulphonic acid or muscimol evoked bursts of spikes and EPSPs in addition to a neuronal depolarization. These bursts, which were not elicited by glycine, glutamate, taurine or (±)-baclofen, were completely antagonised by hexamethonium, tetrodotoxin or bicuculline methochloride. It is concluded that: (a) 4-AP has a potent presynaptic action on sympathetic ganglia; (b) presynaptic actions of GABA can be recorded postsynaptically in the presence of 4-AP; and (c) the presynaptic GABA-receptors revealed in this condition are similar to those on the postsynaptic membrane