Extending the functional equivalence of radial basis functionnetworks and fuzzy inference systems

We establish the functional equivalence of a generalized class of Gaussian radial basis function (RBFs) networks and the full Takagi-Sugeno model (1983) of fuzzy inference. This generalizes an existing result which applies to the standard Gaussian RBF network and a restricted form of the Takagi-Sugeno fuzzy system. The more general framework allows the removal of some of the restrictive conditions of the previous result

Ridge Formation and De-Spinning of Iapetus via an Impact-Generated Satellite

We present a scenario for building the equatorial ridge and de-spinning Iapetus through an impact-generated disk and satellite. This impact puts debris into orbit, forming a ring inside the Roche limit and a satellite outside. This satellite rapidly pushes the ring material down to the surface of Iapetus, and then itself tidally evolves outward, thereby helping to de-spin Iapetus. This scenario can de-spin Iapetus an order of magnitude faster than when tides due to Saturn act alone, almost independently of its interior geophysical evolution. Eventually, the satellite is stripped from its orbit by Saturn. The range of satellite and impactor masses required is compatible with the estimated impact history of Iapetus.Comment: 19 pages, 3 figures; Icarus, in pres

Enhanced stability of the square lattice of a classical bilayer Wigner crystal

The stability and melting transition of a single layer and a bilayer crystal consisting of charged particles interacting through a Coulomb or a screened Coulomb potential is studied using the Monte-Carlo technique. A new melting criterion is formulated which we show to be universal for bilayer as well as for single layer crystals in the case of (screened) Coulomb, Lennard--Jones and 1/r^{12} repulsive inter-particle interactions. The melting temperature for the five different lattice structures of the bilayer Wigner crystal is obtained, and a phase diagram is constructed as a function of the interlayer distance. We found the surprising result that the square lattice has a substantial larger melting temperature as compared to the other lattice structures. This is a consequence of the specific topology of the defects which are created with increasing temperature and which have a larger energy as compared to the defects in e.g. a hexagonal lattice.Comment: Accepted for publication in Physical Review

Single-grain and multi-grain OSL dating of river terrace sediments in the Tabernas Basin, SE Spain

River terraces represent important records of landscape response to e.g. base-level change and tectonic movement. Both these driving forces are important in the southern Iberian Peninsula. In this study, Optically Stimulated Luminescence (OSL) dating was used to date two principal river terraces in the Tabernas Basin, SE Spain. A total of 23 samples was collected from the fluvial terraces for dating using quartz OSL. Sixteen of the samples could not be dated because of low saturation levels (e.g. typical 2xD0 < 50 Gy). The remaining seven samples (5 fossil and 2 modern analogues) were investigated using both multi-grain and single-grain analysis. Single grain results show that: (i) measurements from multi-grain aliquots overestimate ages by up to ∼ 4 ka for modern analogues and young samples (<5 ka), presumably because (ii) the presence of many saturated grains has biased the multi-grain results to older ages. Despite the unfavourable luminescence characteristics we are able to present the first numerical ages for two terrace aggradation stages in the Tabernas Basin, one at ∼16 ka and the other within the last 2 ka

Vortices and dynamics in trapped Bose-Einstein condensates

I review the basic physics of ultracold dilute trapped atomic gases, with emphasis on Bose-Einstein condensation and quantized vortices. The hydrodynamic form of the Gross-Pitaevskii equation (a nonlinear Schr{\"o}dinger equation) illuminates the role of the density and the quantum-mechanical phase. One unique feature of these experimental systems is the opportunity to study the dynamics of vortices in real time, in contrast to typical experiments on superfluid $^4$He. I discuss three specific examples (precession of single vortices, motion of vortex dipoles, and Tkachenko oscillations of a vortex array). Other unusual features include the study of quantum turbulence and the behavior for rapid rotation, when the vortices form dense regular arrays. Ultimately, the system is predicted to make a quantum phase transition to various highly correlated many-body states (analogous to bosonic quantum Hall states) that are not superfluid and do not have condensate wave functions. At present, this transition remains elusive. Conceivably, laser-induced synthetic vector potentials can serve to reach this intriguing phase transition.Comment: Accepted for publication in Journal of Low Temperature Physics, conference proceedings: Symposia on Superfluids under Rotation (Lammi, Finland, April 2010

Strangeness Enhancement in p+Ap+A and S+AS+A Interactions at SPS Energies

The systematics of strangeness enhancement is calculated using the HIJING and VENUS models and compared to recent data on $\,pp\,$, $\,pA\,$ and $\,AA\,$ collisions at CERN/SPS energies ($200A\,\, GeV\,$). The HIJING model is used to perform a {\em linear} extrapolation from $pp$ to $AA$. VENUS is used to estimate the effects of final state cascading and possible non-conventional production mechanisms. This comparison shows that the large enhancement of strangeness observed in $S+Au$ collisions, interpreted previously as possible evidence for quark-gluon plasma formation, has its origins in non-equilibrium dynamics of few nucleon systems. % Strangeness enhancement %is therefore traced back to the change in the production dynamics %from $pp$ to minimum bias $pS$ and central $SS$ collisions. A factor of two enhancement of $\Lambda^{0}$ at mid-rapidity is indicated by recent $pS$ data, where on the average {\em one} projectile nucleon interacts with only {\em two} target nucleons. There appears to be another factor of two enhancement in the light ion reaction $SS$ relative to $pS$, when on the average only two projectile nucleons interact with two target ones.Comment: 29 pages, 8 figures in uuencoded postscript fil

Nonlinear multigrid methods for second order differential operators with nonlinear diffusion coefficient

Nonlinear multigrid methods such as the Full Approximation Scheme (FAS) and Newton-multigrid (Newton-MG) are well established as fast solvers for nonlinear PDEs of elliptic and parabolic type. In this paper we consider Newton-MG and FAS iterations applied to second order differential operators with nonlinear diffusion coefficient. Under mild assumptions arising in practical applications, an approximation (shown to be sharp) of the execution time of the algorithms is derived, which demonstrates that Newton-MG can be expected to be a faster iteration than a standard FAS iteration for a finite element discretisation. Results are provided for elliptic and parabolic problems, demonstrating a faster execution time as well as greater stability of the Newton-MG iteration. Results are explained using current theory for the convergence of multigrid methods, giving a qualitative insight into how the nonlinear multigrid methods can be expected to perform in practice