Some Thoughts on Energy Conditions and Wormholes

This essay reviews some of the recent progress in the area of energy conditions and wormholes. Most of the discussion centers on the subject of ``quantum inequality'' restrictions on negative energy. These are bounds on the magnitude and duration of negative energy which put rather severe constraints on its possible macroscopic effects. Such effects might include the construction of wormholes and warp drives for faster-than-light travel, and violations of the second law of thermodynamics. Open problems and future directions are also discussed.Comment: 24 pages; to appear in the Proceedings of the Tenth Marcel Grossmann Meeting on General Relativity and Gravitatio

A randomized Kaczmarz algorithm with exponential convergence

The Kaczmarz method for solving linear systems of equations is an iterative algorithm that has found many applications ranging from computer tomography to digital signal processing. Despite the popularity of this method, useful theoretical estimates for its rate of convergence are still scarce. We introduce a randomized version of the Kaczmarz method for consistent, overdetermined linear systems and we prove that it converges with expected exponential rate. Furthermore, this is the first solver whose rate does not depend on the number of equations in the system. The solver does not even need to know the whole system, but only a small random part of it. It thus outperforms all previously known methods on general extremely overdetermined systems. Even for moderately overdetermined systems, numerical simulations as well as theoretical analysis reveal that our algorithm can converge faster than the celebrated conjugate gradient algorithm. Furthermore, our theory and numerical simulations confirm a prediction of Feichtinger et al. in the context of reconstructing bandlimited functions from nonuniform sampling

Minkowski Vacuum Stress Tensor Fluctuations

We study the fluctuations of the stress tensor for a massless scalar field in two and four-dimensional Minkowski spacetime in the vacuum state. Covariant expressions for the stress tensor correlation function are obtained as sums of derivatives of a scalar function. These expressions allow one to express spacetime averages of the correlation function as finite integrals. We also study the correlation between measurements of the energy density along a worldline. We find that these measurements may be either positively correlated or anticorrelated. The anticorrelated measurements can be interpreted as telling us that if one measurement yields one sign for the averaged energy density, a successive measurement with a suitable time delay is likely to yield a result with the opposite sign.Comment: 24 pages, 5 figures; Some additional comments added in Sect. IIB and a more compact argument given in App.

Construction of multi-instantons in eight dimensions

We consider an eight-dimensional local octonionic theory with the seven-sphere playing the role of the gauge group. Duality conditions for two- and four-forms in eight dimensions are related. Dual fields--octonionic instantons--solve an 8D generalization of the Yang-Mills equation. Modifying the ADHM construction of 4D instantons, we find general $k$-instanton 8D solutions which depends on $16k-7$ effective parameters

Low-rank Linear Fluid-structure Interaction Discretizations

Fluid-structure interaction models involve parameters that describe the solid and the fluid behavior. In simulations, there often is a need to vary these parameters to examine the behavior of a fluid-structure interaction model for different solids and different fluids. For instance, a shipping company wants to know how the material, a ship's hull is made of, interacts with fluids at different Reynolds and Strouhal numbers before the building process takes place. Also, the behavior of such models for solids with different properties is considered before the prototype phase. A parameter-dependent linear fluid-structure interaction discretization provides approximations for a bundle of different parameters at one step. Such a discretization with respect to different material parameters leads to a big block-diagonal system matrix that is equivalent to a matrix equation as discussed in [KressnerTobler 2011]. The unknown is then a matrix which can be approximated using a low-rank approach that represents the iterate by a tensor. This paper discusses a low-rank GMRES variant and a truncated variant of the Chebyshev iteration. Bounds for the error resulting from the truncation operations are derived. Numerical experiments show that such truncated methods applied to parameter-dependent discretizations provide approximations with relative residual norms smaller than $10^{-8}$ within a twentieth of the time used by individual standard approaches.Comment: 30 pages, 7 figure

The Poverty Impacts of Global Commodity Trade Liberalization

This paper examines the poverty impacts of global merchandise trade reform by looking at a wide range of developing countries in Africa, Asia and Latin America. Overall, we find that trade reform tends to reduce poverty primarily through the inclusion of agricultural components. The majority of our developing country sample experiences small poverty increases from non-agricultural reforms. We explore the relative poverty-friendliness of agricultural trade reforms in detail, examining the differential impacts on real after-tax factor returns of agricultural versus non-agricultural reforms. This analysis is extended to the distribution of households by looking at stratum-specific poverty changes. Our findings indicate that the more favorable impacts of agricultural reforms are driven by increased returns to peasant farm households’ labor as well as higher returns for unskilled wage labor. Finally, we examine the commodity-specific poverty impacts of trade reform for this sample of countries. We find that liberalization of food grains and other processed foods represent the largest contributions to poverty reduction. More specifically, it is tariff reform in these commodity markets that dominates the poverty increasing impacts of wealthy country subsidy removal.Distorted incentives, agricultural and trade policy reforms, national agricultural development, Agricultural and Food Policy, International Relations/Trade, F13, F14, Q17, Q18,