Emergent orbitals in the cluster Mott insulator on a breathing Kagome lattice

Motivated by the recent developments on cluster Mott insulating materials such as the cluster magnet LiZn$_2$Mo$_3$O$_8$, we consider the strong plaquette charge ordered regime of the extended Hubbard model on a breathing Kagome lattice and reveal the properties of the cluster Mottness. The plaquette charge order arises from the inter-site charge interaction and the collective motion of three localized electrons on the hexagon plaquettes. This model leads naturally to a reduction of the local moments by 2/3 as observed in LiZn$_2$Mo$_3$O$_8$. Furthermore, at low temperatures each hexagon plaquette contains an extra orbital-like degree of freedom in addition to the remaining spin 1/2. We explore the consequence of this emergent orbital degree of freedom. We point out the interaction between the local moments is naturally described by a Kugel-Khomskii spin-orbital model. We develop a parton approach and suggest a spin liquid ground state with spinon Fermi surfaces for this model. We further predict an emergent orbital order when the system is under a strong magnetic field. Various experimental consequences for LiZn$_2$Mo$_3$O$_8$ are discussed, including an argument that the charge ordering much be short ranged if the charge per Mo is slightly off stoichiometry.Comment: 12 pages, 13 figure

Loss Leading as an Exploitative Practice

Large retailers, enjoying substantial market power in some local markets, often compete with smaller retailers who carry a narrower range of products in a more efficient way. We find that these large retailers can exercise their market power by adopting a loss-leading pricing strategy, which consists of pricing below cost some of the products also offered by smaller rivals, and raising the prices on the other products. In this way, the large retailers can better discriminate multi-stop shoppers from one-stop shoppers — and may even earn more profit than in the absence of the more efficient rivals. Loss leading thus appears as an exploitative device, designed to extract additional surplus from multi-stop shoppers, rather than as an exclusionary instrument to foreclose the market, although the small rivals are hurt as a by-product of exploitation. We show further that banning below-cost pricing increases consumer surplus, small rivals’ profits, and social welfare. Our insights apply generally to industries where a firm, enjoying substantial market power in one segment, competes with more efficient rivals in other segments, and procuring these products from the same supplier generates customer-specific benefits. They also apply to complementary products, such as platforms and applications. There as well, our analysis provides a rationale for below-cost pricing based on exploitation rather than exclusion.loss leading, exploitative practice, retail power

Pocketqube Deorbit Times: Susceptibility to the Solar Cycle

Nowadays, as a new kind of femto-satellite with a low cost, Pocketqube has been developed to finish the space research task within the LEO region. During its lifetime the pocketqube is exposed to a high risk of collision with space debris. Taking the solar cycle as a main factor, predicting its deorbit time and evaluating its collision probability before the launch is of great importance for the mission designers to choose a right orbit and determine the proper launch time. This article presents a combined atmospheric density model based on the data from CIRA-2012 to describe the effects of the solar cycle on air density in LEO, and shows how the model is applied to calculate orbital lifetimes of pocketqubes in essentially circular equatorial orbits below 800 km altitude. Then the classical fourth order Runge-Kutta method is utilized in integrating the first order differential equations, which express the rates of change of semi major axis and eccentricity, in order to calculate the orbital lifetimes of pocketqube in LEO. The launch date within the 11-year solar cycle has been chosen as an independent variable to present the influence on lifetime prediction and probability evaluation. The result of lifetime calculation shows that the pocketqube launched at the minimum solar activity year does not necessarily get its longest lifetime. Meanwhile if the pocketqube at some specific starting altitudes is launched at the maximum solar activity year, it may remain in orbit for the longest time period. It also demonstrates how the sensitivity of pocketqube deorbit time to the launch date varies with the initial altitudes. From the figures, it can be obtained that 450 km is the altitude at which the deorbit time is most sensitive to the launch date with the percentage amplitude of 180% over its average value. Furthermore, the collision risk from space debris whose diameter is larger than 1 mm and 10 cm are evaluated by using the same method to integrate through its whole lifetime. It illustrates that for those orbits whose initial altitude is over 700 km, no matter which date is chosen to launch a pocketqube, the debris collision risk grows sharply with the starting altitude rising. Finally, by comparison with the trend of lifetime and collision risk, the interesting thing is that at some orbits with higher altitudes, like 800km, when the lifetime of the pocketqube reaches its maximum, the collision risk inversely reaches its local minimum, which can be useful for its designers to balance these two considerations

Loss Leading as an Exploitative Practice

Large retailers, enjoying substantial market power in some local markets, often compete with smaller retailers who carry a narrower range of products in a more efficient way. We find that these large retailers can exercise their market power by adopting a loss-leading pricing strategy, which consists of pricing below cost some of the products also offered by smaller rivals, and raising the prices on the other products. In this way, the large retailers can better discriminate multi-stop shoppers from one-stop shoppers — and may even earn more profit than in the absence of the more efficient rivals. Loss leading thus appears as an exploitative device, designed to extract additional surplus from multi-stop shoppers, rather than as an exclusionary instrument to foreclose the market, although the small rivals are hurt as a by-product of exploitation. We show further that banning below-cost pricing increases consumer surplus, small rivals' profits, and social welfare. Our insights apply generally to industries where a firm, enjoying substantial market power in one segment, competes with more efficient rivals in other segments, and procuring these products from the same supplier generates customer-specific benefits. They also apply to complementary products, such as platforms and applications. There as well, our analysis provides a rationale for below-cost pricing based on exploitation rather than exclusion.loss leading, exploitative practice, retail power

Potential Vorticity Mixing in a Tangled Magnetic Field

A theory of potential vorticity (PV) mixing in a disordered (tangled) magnetic field is presented. The analysis is in the context of $\beta$-plane MHD, with a special focus on the physics of momentum transport in the stably stratified, quasi-2D solar tachocline. A physical picture of mean PV evolution by vorticity advection and tilting of magnetic fields is proposed. In the case of weak-field perturbations, quasi-linear theory predicts that the Reynolds and magnetic stresses balance as turbulence Alfv\'enizes for a larger mean magnetic field. Jet formation is explored quantitatively in the mean field-resistivity parameter space. However, since even a modest mean magnetic field leads to large magnetic perturbations for large magnetic Reynolds number, the physically relevant case is that of a strong but disordered field. We show that numerical calculations indicate that the Reynolds stress is modified well before Alfv\'enization -- i.e. before fluid and magnetic energies balance. To understand these trends, a double-average model of PV mixing in a stochastic magnetic field is developed. Calculations indicate that mean-square fields strongly modify Reynolds stress phase coherence and also induce a magnetic drag on zonal flows. The physics of transport reduction by tangled fields is elucidated and linked to the related quench of turbulent resistivity. We propose a physical picture of the system as a resisto-elastic medium threaded by a tangled magnetic network. Applications of the theory to momentum transport in the tachocline and other systems are discussed in detail.Comment: 17 pages, 10 figures, 2 table

Unified Formalism for calculating Polarization, Magnetization, and more in a Periodic Insulator

In this paper, we propose a unified formalism, using Green's functions, to integrate out the electrons in an insulator under uniform electromagnetic fields. We derive a perturbative formula for the Green's function in the presence of uniform magnetic or electric fields. Applying the formula, we derive the formula for the polarization, the orbital magnetization, and the orbital magneto-polarizability, without assuming time reversal symmetry. Specifically, we realize that the terms linear in the electric field can only be expressed in terms of the Green's functions in one extra dimension. This observation directly leads to the result that the coefficient of the $\theta$ term in any dimensions is given by a Wess-Zumino-Witten-type term, integrated in the extended space, interpolating between the original physical Brillouin zone and a trivial system, with the group element replaced by the Green's function. This generalizes an earlier result for the case of time reversal invariance [see Z. Wang, X.-L. Qi, and S.-C. Zhang, Phys. Rev. Lett. {\bf 105}, 256803 (2010)].Comment: 16 pages, 1 figure. The version accepted by PR

California Almond Yield Prediction at the Orchard Level With a Machine Learning Approach.

California's almond growers face challenges with nitrogen management as new legislatively mandated nitrogen management strategies for almond have been implemented. These regulations require that growers apply nitrogen to meet, but not exceed, the annual N demand for crop and tree growth and nut production. To accurately predict seasonal nitrogen demand, therefore, growers need to estimate block-level almond yield early in the growing season so that timely N management decisions can be made. However, methods to predict almond yield are not currently available. To fill this gap, we have developed statistical models using the Stochastic Gradient Boosting, a machine learning approach, for early season yield projection and mid-season yield update over individual orchard blocks. We collected yield records of 185 orchards, dating back to 2005, from the major almond growers in the Central Valley of California. A large set of variables were extracted as predictors, including weather and orchard characteristics from remote sensing imagery. Our results showed that the predicted orchard-level yield agreed well with the independent yield records. For both the early season (March) and mid-season (June) predictions, a coefficient of determination (R 2) of 0.71, and a ratio of performance to interquartile distance (RPIQ) of 2.6 were found on average. We also identified several key determinants of yield based on the modeling results. Almond yield increased dramatically with the orchard age until about 7 years old in general, and the higher long-term mean maximum temperature during April-June enhanced the yield in the southern orchards, while a larger amount of precipitation in March reduced the yield, especially in northern orchards. Remote sensing metrics such as annual maximum vegetation indices were also dominant variables for predicting the yield potential. While these results are promising, further refinement is needed; the availability of larger data sets and incorporation of additional variables and methodologies will be required for the model to be used as a fertilization decision support tool for growers. Our study has demonstrated the potential of automatic almond yield prediction to assist growers to manage N adaptively, comply with mandated requirements, and ensure industry sustainability