First-order directional ordering transition in the three-dimensional compass model

We study the low-temperature properties of the classical three-dimensional compass or $t_{2g}$ orbital model on simple-cubic lattices by means of comprehensive large-scale Monte Carlo simulations. Our numerical results give evidence for a directionally ordered phase that is reached via a first-order transition at the temperature $T_0 = 0.098328(3) J / k_{\mathrm{B}}$. To obtain our results we employ local and cluster update algorithms, parallel tempering and multiple histogram reweighting as well as model-specific screw-periodic boundary conditions, which help counteract severe finite-size effects.Comment: 8.5 pages, 7 figures, 2 table

For-Profit Public Enforcement

This Article investigates an important yet undertheorized phenomenon: financial incentives in public enforcement. Each year, public enforcers assess billions of dollars in penalties and other financial sanctions for violations of state and federal law. Why? If the awards in question were the result of private lawsuits, the answer would be obvious. We expect that private enforcers—the victims of law violations and their fee-seeking attorneys—will attempt to maximize financial recoveries. Record recoveries come as no surprise in private class actions, for example. But dollar signs are harder to explain in the context of public enforcement. Unlike private attorneys, public enforcers are paid by salary. They have no direct financial stake in successful enforcement efforts. We assume that public enforcers pursue financial awards only for their deterrent value, not for the benefits that such recoveries can bring the enforcement agency itself. Or do they? This Article argues, contrary to the conventional wisdom on the division between public and private enforcement, that public enforcers often seek large monetary awards for self-interested reasons divorced from the public interest in deterrence. The incentives are strongest when enforcement agencies are permitted to retain all or some of the proceeds of enforcement—an institutional arrangement that is common at the state level and beginning to crop up in federal law. Yet even when public enforcers must turn over their winnings to the general treasury, they may have reputational incentives to focus their efforts on measurable units like dollars earned. Financially motivated public enforcers are likely to behave more like private enforcers than is commonly appreciated: they will undertake more enforcement actions, focus on maximizing financial recoveries rather than securing injunctive relief, and compete with other would-be enforcers for lucrative cases. Those effects will often be undesirable, particularly in circumstances where the risk of over-enforcement is high. But financial incentives might provide a valuable spur to action for agencies that currently are performing well below optimal levels. Policymakers recognize as much when they seek to boost private enforcement by promising prevailing plaintiffs supra-compensatory damages. We show that financial incentives can serve a similar purpose in the public sphere, offering policymakers an additional tool for calibrating the level of public enforcement

Strong Nash Equilibria in Games with the Lexicographical Improvement Property

We introduce a class of finite strategic games with the property that every deviation of a coalition of players that is profitable to each of its members strictly decreases the lexicographical order of a certain function defined on the set of strategy profiles. We call this property the Lexicographical Improvement Property (LIP) and show that it implies the existence of a generalized strong ordinal potential function. We use this characterization to derive existence, efficiency and fairness properties of strong Nash equilibria. We then study a class of games that generalizes congestion games with bottleneck objectives that we call bottleneck congestion games. We show that these games possess the LIP and thus the above mentioned properties. For bottleneck congestion games in networks, we identify cases in which the potential function associated with the LIP leads to polynomial time algorithms computing a strong Nash equilibrium. Finally, we investigate the LIP for infinite games. We show that the LIP does not imply the existence of a generalized strong ordinal potential, thus, the existence of SNE does not follow. Assuming that the function associated with the LIP is continuous, however, we prove existence of SNE. As a consequence, we prove that bottleneck congestion games with infinite strategy spaces and continuous cost functions possess a strong Nash equilibrium

Discontinuous Galerkin Methods for Mass Transfer through Semi-Permeable Membranes

A discontinuous Galerkin (dG) method for the numerical solution of initial/boundary value multi-compartment partial differential equation (PDE) models, interconnected with interface conditions, is presented and analysed. The study of interface problems is motivated by models of mass transfer of solutes through semi-permeable membranes. More specifically, a model problem consisting of a system of semilinear parabolic advection-diffusion-reaction partial differential equations in each compartment, equipped with respective initial and boundary conditions, is considered. Nonlinear interface conditions modelling selective permeability, congestion and partial reflection are applied to the compartment interfaces. An interior penalty dG method is presented for this problem and it is analysed in the space-discrete setting. The a priori analysis shows that the method yields optimal a priori bounds, provided the exact solution is sufficiently smooth. Numerical experiments indicate agreement with the theoretical bounds and highlight the stability of the numerical method in the advection-dominated regime

Pastures in Vanuatu

Livestock Production/Industries,

Optimal dividend policies with random profitability

We study an optimal dividend problem under a bankruptcy constraint. Firms face a trade-off between potential bankruptcy and extraction of profits. In contrast to previous works, general cash flow drifts, including Ornstein--Uhlenbeck and CIR processes, are considered. We provide rigorous proofs of continuity of the value function, whence dynamic programming, as well as comparison between the sub- and supersolutions of the Hamilton--Jacobi--Bellman equation, and we provide an efficient and convergent numerical scheme for finding the solution. The value function is given by a nonlinear PDE with a gradient constraint from below in one dimension. We find that the optimal strategy is both a barrier and a band strategy and that it includes voluntary liquidation in parts of the state space. Finally, we present and numerically study extensions of the model, including equity issuance and credit lines