Modelling crystal aggregation and deposition\ud in the catheterised lower urinary tract

Urethral catheters often become encrusted with crystals of magnesium struvite and calcium phosphate. The encrustation can block the catheter, which can cause urine retention in the bladder and reflux into the kidneys. We develop a mathematical model to investigate crystal deposition on the catheter surface, modelling the bladder as a reservoir of fluid and the urethral catheter as a rigid channel. At a constant rate, fluid containing crystal particles of unit size enters the reservoir, and flows from the reservoir through the channel and out of the system. The crystal particles aggregate, which we model using Becker–Döring coagulation theory, and are advected through the channel, where they continue to aggregate and are deposited on the channel’s walls. Inhibitor particles also enter the reservoir, and can bind to the crystals, preventing further aggregation and deposition. The crystal concentrations are spatially homogeneous in the reservoir, whereas the channel concentrations vary spatially as a result of advection, diffusion and deposition. We investigate the effect of inhibitor particles on the amount of deposition. For all parameter values, we find that crystals deposit along the full length of the channel, with maximum deposition close to the channel’s entrance

Many-body effects on adiabatic passage through Feshbach resonances

We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting semiclassical phase space is investigated, highlighting the dynamical instability of the system towards association, for sufficiently small detuning from resonance. It is shown that this instability significantly modifies the finite-rate efficiency of the sweep, transforming the single-pair exponential Landau-Zener behavior of the remnant fraction of atoms Gamma on sweep rate alpha, into a power-law dependence as the number of atoms increases. The obtained nonadiabaticity is determined from the interplay of characteristic time scales for the motion of adiabatic eigenstates and for fast periodic motion around them. Critical slowing-down of these precessions near the instability leads to the power-law dependence. A linear power law $Gamma\propto alpha$ is obtained when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and a cubic-root power law $Gamma\propto alpha^{1/3}$ is attained when it is larger. Our mean-field analysis is confirmed by exact calculations, using Fock-space expansions. Finally, we fit experimental low temperature Feshbach sweep data with a power-law dependence. While the agreement with the experimental data is well within experimental error bars, similar accuracy can be obtained with an exponential fit, making additional data highly desirable.Comment: 9 pages, 9 figure

Sensitivity of a high‐elevation rocky mountain watershed to altered climate and CO2

We explored the hydrologic and ecological responses of a headwater mountain catchment, Loch Vale watershed, to climate change and doubling of atmospheric CO2 scenarios using the Regional Hydro‐Ecological Simulation System (RHESSys). A slight (2°C) cooling, comparable to conditions observed over the past 40 years, led to greater snowpack and slightly less runoff, evaporation, transpiration, and plant productivity. An increase of 2°C yielded the opposite response, but model output for an increase of 4°C showed dramatic changes in timing of hydrologic responses. The snowpack was reduced by 50%, and runoff and soil water increased and occurred 4–5 weeks earlier with 4°C warming. Alpine tundra photosynthetic rates responded more to warmer and wetter conditions than subalpine forest, but subalpine forest showed a greater response to doubling of atmospheric CO2 than tundra. Even though water use efficiency increased with the double CO2 scenario, this had little effect on basin‐wide runoff because the catchment is largely unvegetated. Changes in winter and spring climate conditions were more important to hydrologic and vegetation dynamics than changes that occurred during summer

On the conversion efficiency of ultracold fermionic atoms to bosonic molecules via Feshbach resonances

We explain why the experimental efficiency observed in the conversion of ultracold Fermi gases of $^{40}$K and $^{6}$Li atoms into diatomic Bose gases is limited to 0.5 when the Feshbach resonance sweep rate is sufficiently slow to pass adiabatically through the Landau Zener transition but faster than ``the collision rate'' in the gas, and increases beyond 0.5 when it is slower. The 0.5 efficiency limit is due to the preparation of a statistical mixture of two spin-states, required to enable s-wave scattering. By constructing the many-body state of the system we show that this preparation yields a mixture of even and odd parity pair-states, where only even parity can produce molecules. The odd parity spin-symmetric states must decorrelate before the constituent atoms can further Feshbach scatter thereby increasing the conversion efficiency; ``the collision rate'' is the pair decorrelation rate.Comment: 4 pages, 3 figures, final version accepted to Phys. Rev. Let

Nonlinear adiabatic passage from fermion atoms to boson molecules

We study the dynamics of an adiabatic sweep through a Feshbach resonance in a quantum gas of fermionic atoms. Analysis of the dynamical equations, supported by mean-field and many-body numerical results, shows that the dependence of the remaining atomic fraction $\Gamma$ on the sweep rate $\alpha$ varies from exponential Landau-Zener behavior for a single pair of particles to a power-law dependence for large particle number $N$. The power-law is linear, $\Gamma \propto \alpha$, when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and $\Gamma \propto \alpha^{1/3}$ when it is larger. Experimental data agree better with a linear dependence than with an exponential Landau-Zener fit, indicating that many-body effects are significant in the atom-molecule conversion process.Comment: 5 pages, 4 figure

Redshifts and Luminosities for 112 Gamma Ray Bursts

Two different luminosity indicators have recently been proposed for Gamma Ray Bursts that use gamma-ray observations alone. They relate the burst luminosity (L) with the time lag between peaks in hard and soft energies, and the spikiness or variability of the burst's light curve (V). These relations are currently justified and calibrated with only 6 or 7 bursts with known red shifts. We have examined BATSE data for the lag and V for 112 bursts. (1) A strong correlation between the lag and V exists, and it is exactly as predicted from the two proposed relations. This is proof that both luminosity indicators are reliable. (2) GRB830801 is the all-time brightest burst, yet with a small V and a large lag, and hence is likely the closest known event being perhaps as close as 3.2 Mpc. (3) We have combined the luminosities as derived from both indicators as a means to improve the statistical and systematic accuracy when compared with the accuracy from either method alone. The result is a list of 112 bursts with good luminosities and hence red shifts. (4) The burst averaged hardness ratio rises strongly with the luminosity of the burst. (5) The burst luminosity function is a broken power law, with the break at L = 2x10^{52} erg/s. The luminosity function has power law indices of -2.8+-0.2 above the break and -1.7+-0.1 below the break. (6) The number density of GRBs varies with red shift roughly as (1+z)^(2.5+-0.3) between 0.2<z<5. Excitingly, this result also provides a measure of the star formation rate out to z~5 with no effects from reddening, and the rate is rising uniformly for red shifts above 2.Comment: 13 pages, 4 figures, submitted to ApJLet

Testing the Gamma-Ray Burst Energy Relationships

Building on Nakar & Piran's analysis of the Amati relation relating gamma-ray burst peak energies E_p and isotropic energies E_iso, we test the consistency of a large sample of BATSE bursts with the Amati and Ghirlanda (which relates peak energies and actual gamma-ray energies E_gamma) relations. Each of these relations can be expressed as a ratio of the different energies that is a function of redshift (for both the Amati and Ghirlanda relations) and beaming fraction f_B (for the Ghirlanda relation). The most rigorous test, which allows bursts to be at any redshift, corroborates Nakar & Piran's result--88% of the BATSE bursts are inconsistent with the Amati relation--while only 1.6% of the bursts are inconsistent with the Ghirlanda relation if f_B=1. Even when we allow for a real dispersion in the Amati relation we find an inconsistency. Modelling the redshift distribution results in an energy ratio distribution for the Amati relation that is shifted by an order of magnitude relative to the observed distribution; any sub-population satisfying the Amati relation can comprise at most ~18% of our burst sample. A similar analysis of the Ghirlanda relation depends sensitively on the beaming fraction distribution for small values of f_B; for reasonable estimates of this distribution about a third of the burst sample is inconsistent with the Ghirlanda relation. Our results indicate that these relations are an artifact of the selection effects of the burst sample in which they were found; these selection effects may favor sub-populations for which these relations are valid.Comment: 17 pages, 4 figures. To appear in ApJ, 627, #2 (10 July 2005