Inflation Band Targeting and Optimal Inflation Contracts

In this paper we examine how target ranges work in the context of a Barro-Gordon (1983) type model, in which the time-inconsistency problem stems from political pressures from the government. We show that target ranges turn out to be an excellent way to cope with the time-inconsistency problem, and achieve many of the benefits that arise under practically less attractive solutions such as the conservative central banker and optimal inflation contracts. Our theoretical model also shows how an inflation targeting range should be set and how it should respond to changes in the nature of shocks to the economy.

The timing and magnitude of exchange rate overshooting

Empirical evidence suggests that a monetary shock induces the exchange rate to overshoot its long-run level. The estimated magnitude and timing of the overshooting, however, varies across studies. This paper generates delayed overshooting in a new Keynesian model of a small open economy by incorporating incomplete information about the true nature of the monetary shock. The framework allows for a sensitivity analysis of the overshooting result to underlying structural parameters. It is shown that policy objectives and measures of the economy's sensitivity to exchange rate dynamic affect the timing and magnitude of the overshooting in a predictable manner, suggesting a possible rationale for the cross-study variation of the delayed overshooting Phenomenon. --Exchange rate overshooting,Partial information,Learning

Leonardo's rule, self-similarity and wind-induced stresses in trees

Examining botanical trees, Leonardo da Vinci noted that the total cross-section of branches is conserved across branching nodes. In this Letter, it is proposed that this rule is a consequence of the tree skeleton having a self-similar structure and the branch diameters being adjusted to resist wind-induced loads

An entropy stable discontinuous Galerkin method for the shallow water equations on curvilinear meshes with wet/dry fronts accelerated by GPUs

We extend the entropy stable high order nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations presented by Wintermeyer et al. [N. Wintermeyer, A. R. Winters, G. J. Gassner, and D. A. Kopriva. An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry. Journal of Computational Physics, 340:200-242, 2017] with a shock capturing technique and a positivity preservation capability to handle dry areas. The scheme preserves the entropy inequality, is well-balanced and works on unstructured, possibly curved, quadrilateral meshes. For the shock capturing, we introduce an artificial viscosity to the equations and prove that the numerical scheme remains entropy stable. We add a positivity preserving limiter to guarantee non-negative water heights as long as the mean water height is non-negative. We prove that non-negative mean water heights are guaranteed under a certain additional time step restriction for the entropy stable numerical interface flux. We implement the method on GPU architectures using the abstract language OCCA, a unified approach to multi-threading languages. We show that the entropy stable scheme is well suited to GPUs as the necessary extra calculations do not negatively impact the runtime up to reasonably high polynomial degrees (around $N=7$). We provide numerical examples that challenge the shock capturing and positivity properties of our scheme to verify our theoretical findings

An Entropy Stable Nodal Discontinuous Galerkin Method for the Two Dimensional Shallow Water Equations on Unstructured Curvilinear Meshes with Discontinuous Bathymetry

We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the nonlinear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretisation exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretisation of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem

Supercontinuum generation in media with sign-alternated dispersion

When an ultrafast optical pulse with high intensity is propagating through transparent material a supercontinuum can be coherently generated by self-phase modulation, which is essential to many photonic applications in fibers and integrated waveguides. However, the presence of dispersion causes stagnation of spectral broadening past a certain propagation length, requiring an increased input peak power for further broadening. We present a concept to drive supercontinuum generation with significantly lower input power by counteracting spectral stagnation via alternating the sign of group velocity dispersion along the propagation. We demonstrate the effect experimentally in dispersion alternating fiber in excellent agreement with modeling, revealing almost an order of magnitude reduced peak power compared to uniform dispersion. Calculations reveal a similar power reduction also with integrated optical waveguides, simultaneously with a significant increase of flat bandwidth, which is important for on-chip broadband photonics.Comment: Main text and supplementary informatio

Holograms of Conformal Chern-Simons Gravity

We show that conformal Chern-Simons gravity in three dimensions has various holographic descriptions. They depend on the boundary conditions on the conformal equivalence class and the Weyl factor, even when the former is restricted to asymptotic Anti-deSitter behavior. For constant or fixed Weyl factor our results agree with a suitable scaling limit of topologically massive gravity results. For varying Weyl factor we find an enhancement of the asymptotic symmetry group, the details of which depend on certain choices. We focus on a particular example where an affine u(1) algebra related to holomorphic Weyl rescalings shifts one of the central charges by 1. The Weyl factor then behaves as a free chiral boson in the dual conformal field theory.Comment: 5