Convexity and potential sums for Salpeter-like Hamiltonians

The semirelativistic Hamiltonian H = \beta\sqrt{m^2 + p^2} + V(r), where V(r) is a central potential in R^3, is concave in p^2 and convex in p. This fact enables us to obtain complementary energy bounds for the discrete spectrum of H. By extending the notion of 'kinetic potential' we are able to find general energy bounds on the ground-state energy E corresponding to potentials with the form V = sum_{i}a_{i}f^{(i)}(r). In the case of sums of powers and the log potential, where V(r) = sum_{q\ne 0} a(q) sgn(q)r^q + a(0)ln(r), the bounds can all be expressed in the semi-classical form E \approx \min_{r}{\beta\sqrt{m^2 + 1/r^2} + sum_{q\ne 0} a(q)sgn(q)(rP(q))^q + a(0)ln(rP(0))}. 'Upper' and 'lower' P-numbers are provided for q = -1,1,2, and for the log potential q = 0. Some specific examples are discussed, to show the quality of the bounds.Comment: 21 pages, 4 figure

An experimental study on a motion sensing system for sports training

In sports science, motion data collected from athletes is used to derive key performance characteristics, such as stride length and stride frequency, that are vital coaching support information. The sensors for use must be more accurate, must capture more vigorous events, and have strict weight and size requirements, since they must not themselves affect performance. These requirements mean each wireless sensor device is necessarily resource poor and yet must be capable of communicating a considerable amount of data, contending for the bandwidth with other sensors on the body. This paper analyses the results of a set of network traffic experiments that were designed to investigate the suitability of conventional wireless motion sensing system design � which generally assumes in-network processing - as an efficient and scalable design for use in sports training

Quantum Information Approach to Bose-Einstein Condensate in a Tilted Double-Well System

We study the ground state properties of bosons in a tilted double-well system. We use fidelity susceptibility to identify the possible ground state transitions under different tilt values. For a very small tilt (for example $10^{-10}$), two transitions are found. For a moderate tilt (for example $10^{-3}$), only one transition is found. For a large tilt (for example $10^{-1}$), no transition is found. We explain this by analyzing the spectrum of the ground state. The quantum discord and total correlation of the ground state under different tilts are also calculated to indicate those transitions. In the transition region, both quantities have peaks decaying exponentially with particle number $N$. This means for a finite-size system the transition region cannot be explained by the mean-field theory, but in the large-$N$ limit it can be.Comment: 5 pages, 5 figures, slightly different from the published versio

Influence of the characteristics of soluble algal organic matter released from Microcystis aeruginosa on the fouling of a ceramic microfiltration membrane

The influence of the characteristics of soluble algal organic matter (AOM) on the fouling of a 7-channel tubular ceramic microfiltration membrane (ZrO2-TiO2, 0.1 mm) was investigated at lab scale. The AOM (3 mg DOC/L) extracted from a Microcystis aeruginosa culture at three phases of growth (10, 20 and 35 days) all caused severe flux decline, and its fouling potential increased with increasing growth time. Size exclusion chromatography, fluorescence excitation-emission matrix spectra and organic matter fractionation showed that the high MW biopolymers were the major component determining the severity of the AOM fouling of the ceramic membrane. For the AOM at stationary phase (35 days), 0.45 and 1 mm pre-filtration gave greater flux decline and hydraulically irreversible fouling than 5 mm prefiltration due to the denser foulant layer formed and greater amounts of small organic molecules entering membrane pores. However, the non-pre-filtered AOM (with algal cells) caused the greatest flux decline which was likely due to the presence of the high fouling potential cell surface organic matter. The addition of calcium to the feed solutions led to a marked improvement in flux and reduction in membrane irreversible fouling due to the lower fouling potential of the AOM-calcium complexes formed

Feedwater coagulation to mitigate the fouling of a ceramic MF membrane caused by soluble algal organic matter

Soluble algal organic matter (AOM) resulting from the cyanobacterial blooms in water catchments can cause severe fouling of ceramic membranes in water treatment. The effect of feedwater coagulation using alum, aluminium, ACH, ferric sulphate and ferric chloride for reducing the fouling of a commercial ceramic MF membrane (ZrO2-TiO2) caused by the AOM released from Microcystis aeruginosa was investigated. At their optimum dosages (i.e., 5 mg Al3+/L and 10 mg Fe3+/L), all coagulants could significantly mitigate the membrane fouling, with the hydraulically reversible and irreversible fouling resistance reduced by over 90% and 65%, respectively. ACH, ferric chloride and ferric sulphate performed similarly in reducing the flux decline, and considerably better than alum did. The reduction in AOM fouling of the membrane was primarily due to the effective removal of the very high MW biopolymers (20,000 Da). There were much greater removals in carbohydrate (74-77%) than protein content (15-28%) by the coagulation. The hydrophobic compounds in the AOM solution were more susceptible to the coagulation treatment than the hydrophilic and transphilic compounds. Among the tested coagulants, ACH appeared to be more cost-effective in maintaining the permeate flux and minimising the irreversible fouling for the ceramic MF membrane