On a problem of Pillai with k-generalized Fibonacci numbers and powers of 2

For an integer $k\geq 2$, let $\{F^{(k)}_{n} \}_{n\geq 0}$ be the $k$--generalized Fibonacci sequence which starts with $0, \ldots, 0, 1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we find all integers $c$ having at least two presentations as a difference between a $k$--generalized Fibonacci number and a powers of 2 for any fixed $k \geqslant 4$. This paper extends previous work from [9] for the case $k=2$ and [6] for the case $k=3$

Estimation of unsteady aerodynamic forces using pointwise velocity data

A novel method to estimate unsteady aerodynamic force coefficients from pointwise velocity measurements is presented. The methodology is based on a resolvent-based reduced-order model which requires the mean flow to obtain physical flow structures and pointwise measurement to calibrate their amplitudes. A computationally-affordable time-stepping methodology to obtain resolvent modes in non-trivial flow domains is introduced and compared to previous existing matrix-free and matrix-forming strategies. The technique is applied to the unsteady flow around an inclined square cylinder at low Reynolds number. The potential of the methodology is demonstrated through good agreement between the fluctuating pressure distribution on the cylinder and the temporal evolution of the unsteady lift and drag coefficients predicted by the model and those computed by direct numerical simulation.Comment: In revie

Magnetization plateaux and jumps in a frustrated four-leg spin tube under a magnetic field

We study the ground state phase diagram of a frustrated spin-1/2 four-leg spin tube in an external magnetic field. We explore the parameter space of this model in the regime of all-antiferromagnetic exchange couplings by means of three different approaches: analysis of low-energy effective Hamiltonian (LEH), a Hartree variational approach (HVA) and density matrix renormalization group (DMRG) for finite clusters. We find that in the limit of weakly interacting plaquettes, low-energy singlet, triplet and quintuplet states play an important role in the formation of fractional magnetization plateaux. We study the transition regions numerically and analytically, and find that they are described, at first order in a strong- coupling expansion, by an XXZ spin-1/2 chain in a magnetic field; the second-order terms give corrections to the XXZ model. All techniques provide consistent results which allow us to predict the existence of fractional plateaux in an important region in the space of parameters of the model.Comment: 10 pages, 7 figures. Accepted for publication in Physical Review

A reduced-order model of three-dimensional unsteady flow in a cavity based on the resolvent operator

A novel reduced-order model for nonlinear flows is presented. The model arises from a resolvent decomposition in which the nonlinear advection terms of the Navier-Stokes equation are considered as the input to a linear system in Fourier space. Results show that Taylor-G\"ortler-like vortices can be represented from a low-order resolvent decomposition of a nonlinear lid-driven cavity flow. The present approach provides an approximation of the fluctuating velocity given the time-mean and the time history of a single velocity probe

Metastable and scaling regimes of a one-dimensional Kawasaki dynamics

We investigate the large-time scaling regimes arising from a variety of metastable structures in a chain of Ising spins with both first- and second-neighbor couplings while subject to a Kawasaki dynamics. Depending on the ratio and sign of these former, different dynamic exponents are suggested by finite-size scaling analyses of relaxation times. At low but nonzero-temperatures these are calculated via exact diagonalizations of the evolution operator in finite chains under several activation barriers. In the absence of metastability the dynamics is always diffusive.Comment: 18 pages, 8 figures. Brief additions. To appear in Phys. Rev.

Steady streamwise transpiration control in turbulent pipe flow

A study of the the main features of low- and high amplitude steady streamwise wall transpiration applied to pipe flow is presented. The effect of the two transpiration parameters, amplitude and wavenumber, on the flow have been investigated by means of direct numerical simulation at a moderate turbulent Reynolds number. The behaviour of the three identified mechanisms that act in the flow: modification of Reynolds shear stress, steady streaming and generation of non-zero mean streamwise gradients, have been linked to the transpiration parameters. The observed trends have permitted the identification of wall transpiration configurations able to reduce or increase the overall flow rate in -36.1% and 19.3% respectively. A resolvent analysis has been carried out to obtain a description of the reorganization of the flow structures induced by the transpiration

The quantum double well anharmonic oscillator in an external field

The aim of this paper is twofold. First of all, we study the behaviour of the lowest eigenvalues of the quantum anharmonic oscillator under influence of an external field. We try to understand this behaviour using perturbation theory and compare the results with numerical calculations. This brings us to the second aim of selecting the best method to carry out the numerical calculations accurately.Comment: 9 pages, 6 figure

Radio interferometric observations of candidate water-maser-emitting planetary nebulae

We present Very Large Array (VLA) observations of H2O and OH masers, as well as radio continuum emission at 1.3 and 18 cm toward three sources previously cataloged as planetary nebulae (PNe) and in which single-dish detections of H2O masers have been reported: IRAS 17443-2949, IRAS 17580-3111, and IRAS 18061-2505. Our goal was to unambiguously confirm their nature as water-maser-emitting PNe, a class of objects of which only two bona-fide members were previously known. We detected and mapped H2O maser emission toward all three sources, while OH maser emission is detected in IRAS 17443-2949 and IRAS 17580-3111 as well as in other two objects within the observed fields: IRAS 17442-2942 (unknown nature) and IRAS 17579-3121 (also cataloged as a possible PN). We found radio continuum emission associated only with IRAS 18061-2505. Our results confirm IRAS 18061-2505 as the third known case of a PN associated with H2O maser emission. The three known water-maser-emitting PNe have clear bipolar morphologies, which suggests that water maser emission in these objects is related to non-spherical mass-loss episodes. We speculate that these bipolar PNe would have ``water-fountain'' Asymptotic Giant Branch (AGB) and post-AGB stars as their precursors. A note of caution is given for other objects that have been classified as OHPNe (objects with both OH maser and radio continuum emission, that could be extremely young PNe) based on single-dish observations, since interferometric data of both OH masers and continuum are necessary for a proper identification as members of this class.Comment: 33 pages, 10 figures. Accepted by The Astronomical Journa