Euler configurations and quasi-polynomial systems

Consider the problem of three point vortices (also called Helmholtz’ vortices) on a plane, with arbitrarily given vorticities. The interaction between vortices is proportional to 1/r, where r is the distance between two vortices. The problem has 2 equilateral and at most 3 collinear normalized relative equilibria. This 3 is the optimal upper bound. Our main result is that the above standard statements remain unchanged if we consider an interaction proportional to r ^b, for any b < 0. For 0 < b < 1, the optimal upper bound becomes 5. For positive vorticities and any b < 1, there are exactly 3 collinear normalized relative equilibria. The case b = −2 of this last statement is the well-known theorem due to Euler: in the Newtonian 3-body problem, for any choice of the 3 masses, there are 3 Euler configurations (also known as the 3 Euler points). These small upper bounds strengthen the belief of Kushnirenko and Khovanskii [18]: real varieties defined by simple systems should have a simple topology. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.     

Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds

This paper is devoted to the proof of almost global existence results for Klein‐Gordon equations on Zoll manifolds (e.g., spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof relies on Birkhoff normal form methods and on the specific distribution of eigenvalues of the Laplacian perturbed by a potential on Zoll manifolds. © 2007 Wiley Periodicals, Inc.     

Condensation film on an inclined rotating disk

The three dimensional problem of steady fluid deposition on an inclined rotating disk is solved by similarity transform. For a given spraying rate there may be one, two or no steady state solution. The inclination causes a downward draining flow and a lateral flow. Perturbation solutions compare well with exact similarity solutions when the fluid film is thin.     

Zn-doping effect on the energy barrier to magnetization reversal in superparamagnetic nickel ferrite nanoparticles

Measurements of ac-susceptibility and dc-magnetization were carried out on samples of Ni_1-xZn_xFe₂O₄ nanoparticles (x=0, 0.25, 0.5, 0.75) with average diameters 〈D〉≈7 nm. Values of the superparamagnetic blocking temperature T̄_B were obtained from the characteristic temperature behavior of the imaginary susceptibility χ_imag. An Arrhenius-type law, which accurately describes the relationship between the observation time τ_obs and the blocking temperature, was used to determine the effective energy barrier to magnetization reversal U_eff. A Zn-content dependence of the energy barrier is observed, where U_eff changes little for 0≤x≤0.25, it peaks at x=0.5, and decreases back upon further Zn-doping. The large increase of U_eff at x=0.5 is attributed to an enhanced magnetic anisotropy induced by the crossover between two spatial arrangements of spins in the A and B sub-lattices of the ferrimagnetic inverse spinel. PACS 75.50.Bb; 75.50.Gg; 75.30.Et     

Order conditions for linearly implicit fractional step Runge Kutta methods

^{In this paper, we study the consistency of a variant of fractionalstep Runge–Kutta methods. These methods are designed tointegrate efficiently semi-linear multidimensional parabolicproblems by means of linearly implicit time integration processes.Such time discretization procedures are also related to a splittingof the space differential operator (or the spatial discretizationof it) as a sum of ‘simpler’ linear differentialoperators and a nonlinear term.}     

A dynamic scorecard for monitoring baseline performance with application to tracking a mortgage portfolio

A principled technique for monitoring the performance of a consumer credit scorecard through time is derived from Kalman filtering. Standard approaches sporadically compare certain characteristics of the new applicants with those predicted from the scorecard. The new approach systematically updates the scorecard combining new applicant information with the previous best estimate. The dynamically updated scorecard is tracked through time and compared to limits calculated by sequential simulation from the baseline scorecard. The observation equation of the Kalman filter is tailored to take the results of fitting local scorecards by logistic regression to batches of new clients that arrive in the current time interval. The states in the Kalman filter represent the true or underlying score for each attribute in the card: the parameters of the logistic regression. Their progress in time is modelled by a random walk and the filter provides the best estimate of the scores using past and present information. We illustrate the technique using a commercial mortgage portfolio and the results indicate significant emerging deficiencies in the baseline scorecard.     

Einstein relation in chemically doped organic semiconductors

Based on the assumption of Gaussian energy distributions of the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO), analytical expressions of generalized Einstein relation in chemically doped organic semiconductor are developed, by approximation of Coulomb traps with a rectangle potential well. Numerical calculations show that traditional Einstein relations do not hold for chemically doped organic semiconductors. Similar to physical doping, the dependence of diffusion coefficient to mobility D/μ ratio on the carrier concentration has a maximum. An essential difference between chemical doping and physical doping is that, the D/μ ratio in chemically doped organic semiconductors depends not only on carrier concentration and doping concentration, but also on the applied electric field. PACS 71.20.Rv; 72.90.+y; 73.50.-h     

Non-aggregated Pd nanoparticles deposited onto catalytic supports

Nanostructured powders have shown great promise for a variety of applications including chemical gas sensors, high surface area supports for catalysis, tribology, chemical mechanical polishing, and optoelectronics. In this report, highly dispersed Pd nanoparticles with a narrow size distribution, and mean diameter of 2±0.2 nm, were deposited at room temperature onto amorphous carbon and oxide supports (TiO₂, Al₂O₃) by pulsed-laser ablation of a Pd sputtering target. Depositions were performed in Ar at a back-fill pressure of 3 mTorr after reaching a base pressure of 10^-7 Torr. Populations of uniformly dispersed particles with an interparticle spacing of 3 to 10 nm were observed by high-resolution transmission electron microscopy with little evidence of nanoparticle aggregation. The chemical compositions of individual nanoparticles were confirmed by high spatial resolution energy-dispersive X-ray spectroscopy.     

Directed and elliptic flow in 197Au+197Au at intermediate energies

Directed and elliptic flow for the ¹⁹⁷Au+¹⁹⁷Au system at incident energies between 40 and 150 MeV per nucleon has been measured using the INDRA 4π multi-detector. For semi-central collisions, the excitation function of elliptic flow shows a transition from in-plane to out-of-plane emission at around 100 MeV per nucleon. The directed flow changes sign at a bombarding energy between 50 and 60 MeV per nucleon and remains negative at lower energies. Molecular dynamics calculations (CHIMERA) indicate sensitivity of the global squeeze-out transition on the σ _NN and demonstrate the importance of angular momentum conservation in transport codes at low energies.     

System dependence of the correlation function of IMFs in Ar + Sn at 35 MeV/u

The inclusive reduced velocity correlation functions of the intermediate mass fragments were measured in the reactions of ³⁶Ar + ^112,124Sn at 35 MeV/u. The anti-correlation is observed to be stronger in ³⁶Ar + ¹²⁴Sn system than that in ³⁶Ar + ¹¹²Sn. The difference of the correlation functions between the two reactions is mainly contributed by the particle pairs with high momenta. A three body Coulomb repulsive trajectory model is employed to calculate the emission time scale of the IMFs for the two systems. The time scale is 150 fm/c in ³⁶Ar + ¹¹²Sn and 120 fm/c in the ³⁶Ar + ¹²⁴Sn, respectively.