Spiral order by disorder and lattice nematic order in a frustrated Heisenberg antiferromagnet on the honeycomb lattice

Motivated by recent experiments on Bi$_3$Mn$_4$O$_{12}$(NO$_3$), we study a frustrated $J_1$-$J_2$ Heisenberg model on the two dimensional (2D) honeycomb lattice. The classical $J_1$-$J_2$ Heisenberg model on the two dimensional (2D) honeycomb lattice has N\'eel order for $J_2 J_1/6$, it exhibits a one-parameter family of degenerate incommensurate spin spiral ground states where the spiral wave vector can point in any direction. Spin wave fluctuations at leading order lift this accidental degeneracy in favor of specific wave vectors, leading to spiral order by disorder. For spin $S=1/2$, quantum fluctuations are, however, likely to be strong enough to melt the spiral order parameter over a wide range of $J_2/J_1$. Over a part of this range, we argue that the resulting state is a valence bond solid (VBS) with staggered dimer order - this VBS is a nematic which breaks lattice rotational symmetry. Our arguments are supported by comparing the spin wave energy with the energy of the dimer solid obtained using a bond operator formalism. Turning to the effect of thermal fluctuations on the spiral ordered state, any nonzero temperature destroys the magnetic order, but the discrete rotational symmetry of the lattice remains broken resulting in a thermal analogue of the nematic VBS. We present arguments, supported by classical Monte Carlo simulations, that this nematic transforms into the high temperature symmetric paramagnet via a thermal phase transition which is in the universality class of the classical 3-state Potts (clock) model in 2D. We discuss the possible relevance of our results for honeycomb magnets, such as Bi$_3$M$_4$O$_{12}$(NO$_3$) (with M=Mn,V,Cr), and bilayer triangular lattice magnets.Comment: Slightly revise

Optimization of a charge-state analyzer for ECRIS beams

A detailed experimental and simulation study of the extraction of a 24 keV He-ion beam from an ECR ion source and the subsequent beam transport through an analyzing magnet is presented. We find that such a slow ion beam is very sensitive to space-charge forces, but also that the neutralization of the beam's space charge by secondary electrons is virtually complete for beam currents up to at least 0.5 mA. The beam emittance directly behind the extraction system is 65 pi mm mrad and is determined by the fact that the ion beam is extracted in the strong magnetic fringe field of the ion source. The relatively large emittance of the beam and its non-paraxiality lead, in combination with a relatively small magnet gap, to significant beam losses and a five-fold increase of the effective beam emittance during its transport through the analyzing magnet. The calculated beam profile and phase-space distributions in the image plane of the analyzing magnet agree well with measurements. The kinematic and magnet aberrations have been studied using the calculated second-order transfer map of the analyzing magnet, with which we can reproduce the phase-space distributions of the ion beam behind the analyzing magnet. Using the transfer map and trajectory calculations we have worked out an aberration compensation scheme based on the addition of compensating hexapole components to the main dipole field by modifying the shape of the poles. The simulations predict that by compensating the kinematic and geometric aberrations in this way and enlarging the pole gap the overall beam transport efficiency can be increased from 16 to 45%

Will liner ships make fewer port calls per route?

Traditional liner shipping route networks consists of many port calls per route. However, container ship sizes have increased substantially over the past few years. These large container ships benefit from economies of scale at sea, but might suffer diseconomies of scale in ports. Therefore, we investigate whether larger container ships will lead to fewer port calls per route. First, we discuss the influence of fewer port visits on some aspects that are difficult to include in a mathematical analysis. Thereafter, we propose a mathematical approach to obtain networks with fewer port calls per route. Liner shipping route networks are generated by distinguishing between hub routes and regional routes. Hub routes are used to connect a small number of hubs, while regional routes connect all other ports with its nearest hub. An iterative approach is used to generate networks, which are evaluated using a mixed integer program in which the joint ship allocation and cargo routing is solved. A case study is performed with different combinations of seven hub ports. In the case study, three capacity scenarios are considered: low, base and high capacity. Our networks generate profits that are more than 25% higher compared with the best known networks in literature

Designing liner shipping networks

In this paper the combined fleet-design, ship-scheduling and cargo-routing problem with limited availability of ships in liner shipping is considered. A genetic algorithm based solution method is proposed in which the ports are first aggregated into port cluster to reduce the problem size. When the cargo flows are disaggregated, a feeder service network is introduced to ship the cargo within a port cluster. The solution method is tested on a problem instance containing 58 ports on the Asia-Europe trade lane of Maersk. The best obtained profit gives an improvement of almost 20% compared to the reference network based on the Maersk network

Optimization in container liner shipping

We will give an overview of several decision problem encountered in liner shipping. We will cover problems on the strategic, tactical and operational planning levels as well as problems that can be considered at two planning levels simultaneously. Furthermore, we will shortly discuss some related problems in terminals, geographical bottlenecks for container ships and provide an overview of operations research methods used in liner shipping problems. Thereafter, the decision problems will be illustrated using a case study for six Indonesian ports

Methods for strategic liner shipping network design

In this paper the combined fleet-design, ship-scheduling and cargo-routing problem with limited availability of ships in liner shipping is considered. A composite solution approach is proposed in which the ports are first aggregated into port clusters to reduce the problem size. When the cargo flows are disaggregated, a feeder service network is introduced to ship the cargo within a port cluster. The solution method is tested on a problem instance containing 58 ports on the Asia-Europe trade lane of Maersk. The best obtained profit gives an improvement of more than 10% compared to the reference network based on the Maersk network

The Effect of the Outer Lindblad Resonance of the Galactic Bar on the Local Stellar Velocity Distribution

Hydro-dynamical modeling of the inner Galaxy suggest that the radius of the outer Lindblad resonance (OLR) of the Galactic bar lies in the vicinity of the Sun. How does this resonance affect the distribution function in the outer parts of a barred disk, and can we identify any effect of the resonance in the velocity distribution f(v) actually observed in the solar neighborhood? To answer these questions, detailed simulations of f(v) in the outer parts of an exponential stellar disks with nearly flat rotation curves and a rotating central bar have been performed. For a model resembling the old stellar disk, the OLR causes a distinct feature in f(v) over a significant fraction of the outer disk. For positions <2kpc outside the OLR radius and at bar angles of \~10-70 degrees, f(v) inhibits a bi-modality between the low-velocity stars moving like the local standard of rest (LSR) and a secondary mode of stars predominantly moving outward and rotating more slowly than the LSR. Such a bi-modality is indeed present in f(v) inferred from the Hipparcos data for late-type stars in the solar neighborhood. If one interpretes this observed bi-modality as induced by the OLR -- and there are hardly any viable alternatives -- then one is forced to deduce that the OLR radius is slightly smaller than Ro. Moreover, by a quantitative comparison of the observed with the simulated distributions one finds that the pattern speed of the bar is 1.85+/-0.15 times the local circular frequency, where the error is dominated by the uncertainty in bar angle and local circular speed. Also other, less prominent but still significant, features in the observed f(v) resemble properties of the simulated velocity distributions, in particular a ripple caused by orbits trapped in the outer 1:1 resonance.Comment: 14 pages, 10 figures (Fig.2 in full resolution available upon request), accepted for publication in A

Soil moisture control of NO turnover and N₂O release in nitrogen-saturated subtropical forest soils

Acid forest soils in South China experience a chronically elevated input of atmospheric nitrogen (N), turning them into hot spots for gaseous N emissions. Soil moisture is known to be a major controller for the partitioning of gaseous N loss to nitric (NO) and nitrous oxide (N2O), which may be of particular relevance in the monsoonal climate of South China. To study this partitioning in more detail, we determined gas phase kinetics of NO and N2O release during laboratory dry-out of acidic surface soils from the headwater catchment TieShanPing (TSP), situated close to Chongqing, SW China. Soils were sampled from two hydrologically distinct environments, a well-drained hill slope (HS), and a periodically flooded groundwater discharge zone (GDZ). Production and consumption of NO were studied in an automated flow-through system purged with NO-free or NO-spiked air. Production rates peaked at 21% and 18% water filled pore space (WFPS) in HS and GDZ soils, respectively, suggesting nitrification as the dominant process of NO formation in both landscape units. In HS soils, maximum production and consumption occurred at the same WFPS, whereas GDZ soils displayed maximum NO consumption at higher WFPS than maximum production, suggesting that denitrification is an important NO sink in GDZ soils. Net N2O release was largest at 100% WFPS and declined steadily during drying. Integrated over the entire range of soil moisture, potential NO-N loss outweighed potential N2O-N loss, suggesting that N-saturated, acid forest soil is an important NO source

Axiomatic Characterization of the Mean Function on Trees

A mean of a sequence π = (x1, x2, . . . , xk) of elements of a finite metric space (X, d) is an element x for which is minimum. The function Mean whose domain is the set of all finite sequences on X and is defined by Mean(π) = { x | x is a mean of π } is called the mean function on X. In this paper the mean function on finite trees is characterized axiomatically