A construction of integer-valued polynomials with prescribed sets of lengths of factorizations

For an arbitrary finite set S of natural numbers greater 1, we construct an integer-valued polynomial f, whose set of lengths in Int(Z) is S. The set of lengths of f is the set of all natural numbers n, such that f has a factorization as a product of n irreducibles in Int(Z)={g in Q[x] | g(Z) contained in Z}.Comment: To appear in Monatshefte f\"ur Mathematik; 11 page

Comment on ``Lyapunov Exponent of a Many Body System and Its Transport Coefficients''

In a recent Letter, Barnett, Tajima, Nishihara, Ueshima and Furukawa obtained a theoretical expression for the maximum Lyapunov exponent $\lambda_1$ of a dilute gas. They conclude that $\lambda_1$ is proportional to the cube root of the self-diffusion coefficient $D$, independent of the range of the interaction potential. They validate their conjecture with numerical data for a dense one-component plasma, a system with long-range forces. We claim that their result is highly non-generic. We show in the following that it does not apply to a gas of hard spheres, neither in the dilute nor in the dense phase.Comment: 1 page, Revtex - 1 PS Figs - Submitted to Physical Review Letter

Orientation cues for high-flying nocturnal insect migrants: do turbulence-induced temperature and velocity fluctuations indicate the mean wind flow?

Migratory insects flying at high altitude at night often show a degree of common alignment, sometimes with quite small angular dispersions around the mean. The observed orientation directions are often close to the downwind direction and this would seemingly be adaptive in that large insects could add their self-propelled speed to the wind speed, thus maximising their displacement in a given time. There are increasing indications that high-altitude orientation may be maintained by some intrinsic property of the wind rather than by visual perception of relative ground movement. Therefore, we first examined whether migrating insects could deduce the mean wind direction from the turbulent fluctuations in temperature. Within the atmospheric boundary-layer, temperature records show characteristic ramp-cliff structures, and insects flying downwind would move through these ramps whilst those flying crosswind would not. However, analysis of vertical-looking radar data on the common orientations of nocturnally migrating insects in the UK produced no evidence that the migrants actually use temperature ramps as orientation cues. This suggests that insects rely on turbulent velocity and acceleration cues, and refocuses attention on how these can be detected, especially as small-scale turbulence is usually held to be directionally invariant (isotropic). In the second part of the paper we present a theoretical analysis and simulations showing that velocity fluctuations and accelerations felt by an insect are predicted to be anisotropic even when the small-scale turbulence (measured at a fixed point or along the trajectory of a fluid-particle) is isotropic. Our results thus provide further evidence that insects do indeed use turbulent velocity and acceleration cues as indicators of the mean wind direction

Shape oscillations in non-degenerate Bose gases - transition from the collisionless to the hydrodynamic regime

We investigate collective oscillations of non-degenerate clouds of Rb-87 atoms as a function of density in an elongated magnetic trap. For the low-lying M=0 monopole-quadrupole shape oscillation we measure the oscillation frequencies and damping rates. At the highest densities the mean-free-path is smaller than the axial dimension of the sample, which corresponds to collisionally hydrodynamic conditions. This allows us to cover the cross-over from the collisionless to the hydrodynamic regime. The experimental results show good agreement with theory. We also analyze the influence of trap anharmonicities on the oscillations in relation to observed temperature dependencies of the dipole and quadrupole oscillation frequencies. We present convenient expressions to quantify these effects.Comment: 10 pages, 5 figure

Possibility of culturing Pacific goliath grouper Epinephelus quinquefasciatus in water with different salinities

Objective. To assess the survival and growth of juvenile Pacific goliath grouper (Epinephelus quinquefasciatus) in captivity at low salinities. Materials and methods. We randomly selected twelve juvenile goliath groupers with an average standard length of 44.2 ± 6.1 cm and 1492 ± 476 g in body weight, and raised them for three months in the laboratory in waters of 32-26, 20, 10 and 5 parts per thousand of salinity. Results. All juvenile Pacific goliath groupers tolerated the initial gradual transfer from full strength seawater to salinities of 32-26, 20, 10, and 5 parts per thousand, which was done over a period of four days. All of them survived and grew in body weight and length during the course of the three-month experiment, in all the treatments of high and low salinity water. The body condition factor (K) for each fish was between 1.5 and 2.4. Conclusions. This is a first time trial that documents a randomized, controlled experiment demonstrating the ability of Pacific juvenile goliath grouper to gradually transfer from full strength seawater to water of lower salinity, and survive and grow well in these brackish waters.Key words: Aquaculture, euryhaline species, osmoregulation, water salinity (Source: BNA, NAL)

Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases I: Equilibrium Systems

We compute the Lyapunov spectrum and the Kolmogorov-Sinai entropy for a moving particle placed in a dilute, random array of hard disk or hard sphere scatterers - i.e. the dilute Lorentz gas model. This is carried out in two ways: First we use simple kinetic theory arguments to compute the Lyapunov spectrum for both two and three dimensional systems. In order to provide a method that can easily be generalized to non-uniform systems we then use a method based upon extensions of the Lorentz-Boltzmann (LB) equation to include variables that characterize the chaotic behavior of the system. The extended LB equations depend upon the number of dimensions and on whether one is computing positive or negative Lyapunov exponents. In the latter case the extended LB equation is closely related to an "anti-Lorentz-Boltzmann equation" where the collision operator has the opposite sign from the ordinary LB equation. Finally we compare our results with computer simulations of Dellago and Posch and find very good agreement.Comment: 48 pages, 3 ps fig

A random cell motility gradient downstream of FGF controls elongation of amniote embryos

Vertebrate embryos are characterized by an elongated antero-posterior (AP) body axis, which forms by progressive cell deposition from a posterior growth zone in the embryo. Here, we used tissue ablation in the chicken embryo to demonstrate that the caudal presomitic mesoderm (PSM) has a key role in axis elongation. Using time-lapse microscopy, we analysed the movements of fluorescently labelled cells in the PSM during embryo elongation, which revealed a clear posterior-to-anterior gradient of cell motility and directionality in the PSM. We tracked the movement of the PSM extracellular matrix in parallel with the labelled cells and subtracted the extracellular matrix movement from the global motion of cells. After subtraction, cell motility remained graded but lacked directionality, indicating that the posterior cell movements associated with axis elongation in the PSM are not intrinsic but reflect tissue deformation. The gradient of cell motion along the PSM parallels the fibroblast growth factor (FGF)/mitogen-activated protein kinase (MAPK) gradient1, which has been implicated in the control of cell motility in this tissue2. Both FGF signalling gain- and loss-of-function experiments lead to disruption of the motility gradient and a slowing down of axis elongation. Furthermore, embryos treated with cell movement inhibitors (blebbistatin or RhoK inhibitor), but not cell cycle inhibitors, show a slower axis elongation rate. We propose that the gradient of random cell motility downstream of FGF signalling in the PSM controls posterior elongation in the amniote embryo. Our data indicate that tissue elongation is an emergent property that arises from the collective regulation of graded, random cell motion rather than by the regulation of directionality of individual cellular movements

Transit Variability in Bow Shock-Hosting Planets

We investigate the formation of bow shocks around exoplanets as a result of the interaction of the planet with the coronal material of the host star, focusing on physical causes that can lead to temporal variations in the shock characteristics. We recently suggested that WASP-12b may host a bow shock around its magnetosphere, similarly to the one observed around the Earth. For WASP12b, the shock is detected in the near-UV transit light curve. Observational follow-up suggests that the near-UV light curve presents temporal variations, which may indicate that the stand-off distance between the shock and the planet is varying. This implies that the size of the planet's magnetosphere is adjusting itself in response to variations in the surrounding ambient medium. We investigate possible causes of shock variations for the known eccentric (e>0.3) transiting planets. We show that, because the distance from the star changes along the orbit of an eccentric planet, the shock characteristics are modulated by orbital phase. We predict time offsets between the beginnings of the near-UV and optical light curves that are, in general, less than the transit duration. Variations in shock characteristics caused in eccentric systems can only be probed if the shock is observed at different orbital phases, which is, in general, not the case for transit observations. However, non-thermal radio emission produced by the interaction of the star and planet should be modulated by orbital phase. We also quantify the response of the shock to variations in the coronal material itself due to, e.g., a non-axisymmetric stellar corona, planetary obliquity, intrinsic variations of the stellar magnetic field. Such variations do not depend on the system eccentricity. We conclude that, for systems where a shock is detectable through transit light curve observations, shock variations should be a common occurrence. (Abridged)Comment: 10 pages, 11 figures, 1 table. MNRAS accepte