Equivalence of two sets of Hamiltonians associated with the rational BCn Ruijsenaars–Schneider–van Diejen system

The equivalence of two complete sets of Poisson commuting Hamiltonians of the (super)integrable rational BCn Ruijsenaars–Schneider–van Diejen system is established. Specifically, the commuting Hamiltonians constructed by van Diejen are shown to be linear combinations of the Hamiltonians generated by the characteristic polynomial of the Lax matrix obtained recently by Pusztai, and the explicit formula of this invertible linear transformation is found

On a Poisson–Lie deformation of the BCn Sutherland system

A deformation of the classical trigonometric BCn Sutherland system is derived via Hamiltonian reduction of the Heisenberg double of SU (2n). We apply a natural Poisson–Lie analogue of the Kazhdan–Kostant–Sternberg type reduction of the free particle on SU (2n) that leads to the BCn Sutherland system. We prove that this yields a Liouville integrable Hamiltonian system and construct a globally valid model of the smooth reduced phase space wherein the commuting flows are complete. We point out that the reduced system, which contains 3 independent coupling constants besides the deformation parameter, can be recovered (at least on a dense submanifold) as a singular limit of the standard 5-coupling deformation due to van Diejen. Our findings complement and further develop those obtained recently by Marshall on the hyperbolic case by reduction of the Heisenberg double of SU (n,n)

Spatial Representation and Navigation in a Bio-inspired Robot

A biologically inspired computational model of rodent repre-sentation?based (locale) navigation is presented. The model combines visual input in the form of realistic two dimensional grey-scale images and odometer signals to drive the firing of simulated place and head direction cells via Hebbian synapses. The space representation is built incrementally and on-line without any prior information about the environment and consists of a large population of location-sensitive units (place cells) with overlapping receptive fields. Goal navigation is performed using reinforcement learning in continuous state and action spaces, where the state space is represented by population activity of the place cells. The model is able to reproduce a number of behavioral and neuro-physiological data on rodents. Performance of the model was tested on both simulated and real mobile Khepera robots in a set of behavioral tasks and is comparable to the performance of animals in similar tasks

The calibration of optical backscatter sensors for suspended sediment of varying darkness levels

A series of calibration experiments were run in order to determine the effect of the colour of suspended sediment on the response of optical backscatter sensors (OBS). Munsell notation describes the properties of soil and sediment colour using the three parameters, hue, chroma, and value, which represent, respectively, the spectral position, lightness level, and amount of pure chromatic colour present. The exposure of the OBS to Munsell Soil Chart patches revealed that the OBS is sensitive to variations in Munsell value and not Munsell hue or chroma. Since OBS output decreased with darkness level (and increased with lightness level and Munsell value), it is suggested that the level of blackness of particles acts to absorb the near-infrared (IR) signal of the OBS, modifying its output. A strong correlation (r2=0.984) was found between the observed and predicted OBS outputs of varying concentrations and ratios of black and white suspended sediment. The OBS output was predicted using a linear mixture-model incorporating end-member calibrations of black and white sediment (similar to Green and Boon [Green, M.O., Boon, J.D., III, 1993. The measurement of constituent concentrations in nonhomogeneous sediment suspensions using optical backscatter sensors. Marine Geology, 110, pp. 73–81.]). A strong correlation (r2=0.907) was also observed between luminance factor and IR reflectance for various minerals, suggesting a link between Munsell notation and OBS output. Formulae were developed to predict the IR reflectance of sediment of known Munsell value, concentration, and size. Models predicting sediment transport should consider the effect of the level of blackness of particles on the OBS response

Pigments of marine animals. Iii. The synthesis of some substituted polyhydroxy-anthraquinones

Synthetic specimens of 1, 3, 6, 8-tetramethoxyanthraquinone and its 4-methoxy and 4-methoxycarbonyl derivatives have been prepared for comparison with products derived from the degradation of the pigments of the crinoids, Comatula pectinata and C. cratera

Corrasion of a remoulded cohesive bed by saltating littorinid shells

Corrasion of a standard cohesive bed due to saltating gastropod shells of the species Littorina has been examined in a laboratory mini flume. The purpose of the study was to examine the effects of shell size and number on bed erosion rate. The movement of shells by flows explain why intertidal, glacial clays in the Bay of Fundy (which are covered in places with Littorinid shells) suffer erosion because bed erosion rate increased up to 20-fold with the introduction of a single shell to the flume (27 m?2). The standard bed was made of potters clay which had an erosion threshold of 0.19 Pa and a fluid-induced erosion rate Eo=0.072(Uy?Ucrit) gm?2 s?1, where Uy is the azimuthal current speed at height y=0.10 m. Shells of seven differing sizes (ds) were used to define the process of erosion by shell impacts. The threshold for shell motion (Ugcrit) was linearly related to shell size in the form: Ugcrit=9.17×10?3 ds?0.22 m s?1. Motion began by intermittent rolling, followed by continuous rolling and then by saltation. The shell speed in saltation was 68% that of Uy, thus 32% of the horizontal shell momentum was transmitted to the bed. The length/height ratio of saltations was 6.3, and was constant for all sizes, and the mean saltation frequency was 1.7 s?1. The shell erosion rate (Es) increased with shell diameter for both the rolling and saltating phases. During the rolling phase, Es was up to 5 times greater than Eo at the same current speed. During saltation, Es was up to 20 times greater than Eo at the same current speed. The effect of shell number (1–7) was examined for the 7–10 mm size class. During rolling, Es increased linearly with shell number. For the saltating phase, Es increased in an asymptotic fashion, suggesting that groups of saltating shells affect the erosion process differently than single shells. The ballistic momentum flux (T) of saltating shells is highly dependent on the area of impact (Ag), which in the case of the littorinids, is along the rounded outer lip of the aperture (measured to be 0.5% of the nominal cross-sectional area of the shell). T increased with shell mass (Mg) and current speed (Uy). Below 0.29 m s?1, T<?o; for 0.29<Uy<0.35 m s?1, T??o; and for Uy>0.35 m s?1, T>?o where ?o is the fluid-induced shear stress. The total erosion rate (Etot=Es+Eo) was compared to the excess total bed shear stress (?tot??crit) and found to be linearly related in the form: gm?2 s?1. Es appeared to be in linear continuity with Eo if the impact area was set to 0.05% of the estimated shell nominal cross-sectional area

Sea Surface Temperature Trends in the Coastal Zone of British Columbia, Canada

Coastal sea surface temperature (SST), measured daily at the British Columbia (BC) Lighthouse network of stations, has been analyzed in this paper. A network of 14 of the 27 stations had (near) continuous data sets. These stations were clustered previously into exposed (northern/outer) and sheltered (southern/inner) sites. SST trends, evaluated between 1973 and 2010, show that the temperature contrast between these clusters is becoming greater: The northern/exposed stations are strongly influenced by interdecadal (Pacific Decadal oscillation [PDO]) and multidecadal oscillations in the north Pacific that are coherent with HadISST1.1 data for the region. There is no statistically significant warming trend for this region. The stations in the Strait of Georgia are much less influenced by the PDO and show a statistically significant mean increase in SST of up to 0.56°C/decade (Anomaly 1). This is higher than the global average and contrasts markedly with the trends from the northern stations. The warming trends of the southern stations are significant at all months of the year but are most evident during summer (July–September). The summertime anomalies in temperature at Active Pass are significantly correlated (p < 0.001) with the temperature of the Fraser River water. Temperature differences between the Strait of Georgia and the outer shelf (Anomaly 2) are increasing in time; this is particularly evident since 2000. Monthly averaged MODIS satellite data (4×4-km resolution) show that trends in SST at two selected sites in the Strait of Georgia are very similar to the BC Lighthouse measurements and support the spatial extrapolation of the Lighthouse measurements. At present rates of SST rise, the southern coastal waters of BC will be about 3°C warmer by the end of the 21st century