Analysis of the Brinkman-Forchheimer equations with slip boundary conditions

In this work, we study the Brinkman-Forchheimer equations driven under slip boundary conditions of friction type. We prove the existence and uniqueness of weak solutions by means of regularization combined with the Faedo-Galerkin approach. Next we discuss the continuity of the solution with respect to Brinkman's and Forchheimer's coefficients. Finally, we show that the weak solution of the corresponding stationary problem is stable

Nonconservative Lagrangian mechanics II: purely causal equations of motion

This work builds on the Volterra series formalism presented in [D. W. Dreisigmeyer and P. M. Young, J. Phys. A \textbf{36}, 8297, (2003)] to model nonconservative systems. Here we treat Lagrangians and actions as `time dependent' Volterra series. We present a new family of kernels to be used in these Volterra series that allow us to derive a single retarded equation of motion using a variational principle

Negative discriminant states in N=4 supersymmetric string theories

Single centered BPS black hole solutions exist only when the charge carried by the black hole has positive discriminant. On the other hand the exact dyon spectrum in heterotic string theory compactified on T^6 is known to contain states with negative discriminant. We show that all of these negative discriminant states can be accounted for as two centered black holes. Thus after the contribution to the index from the two centered black holes is subtracted from the total microscopic index, the index for states with negative discriminant vanishes even for finite values of charges, in agreement with the results from the black hole side. Bound state metamorphosis -- which requires us to identify certain apparently different two centered configurations according to a specific set of rules -- plays a crucial role in this analysis. We also generalize these results to a class of CHL string theories.Comment: LaTeX file, 32 pages; v2: reference added; v3: added new section 3.

Homological Localisation of Model Categories

One of the most useful methods for studying the stable homotopy category is localising at some spectrum E. For an arbitrary stable model category we introduce a candidate for the E–localisation of this model category. We study the properties of this new construction and relate it to some well–known categories

Engineered swift equilibration of a Brownian particle

A fundamental and intrinsic property of any device or natural system is its relaxation time relax, which is the time it takes to return to equilibrium after the sudden change of a control parameter [1]. Reducing $tau$ relax , is frequently necessary, and is often obtained by a complex feedback process. To overcome the limitations of such an approach, alternative methods based on driving have been recently demonstrated [2, 3], for isolated quantum and classical systems [4--9]. Their extension to open systems in contact with a thermostat is a stumbling block for applications. Here, we design a protocol,named Engineered Swift Equilibration (ESE), that shortcuts time-consuming relaxations, and we apply it to a Brownian particle trapped in an optical potential whose properties can be controlled in time. We implement the process experimentally, showing that it allows the system to reach equilibrium times faster than the natural equilibration rate. We also estimate the increase of the dissipated energy needed to get such a time reduction. The method paves the way for applications in micro and nano devices, where the reduction of operation time represents as substantial a challenge as miniaturization [10]. The concepts of equilibrium and of transformations from an equilibrium state to another, are cornerstones of thermodynamics. A textbook illustration is provided by the expansion of a gas, starting at equilibrium and expanding to reach a new equilibrium in a larger vessel. This operation can be performed either very slowly by a piston, without dissipating energy into the environment, or alternatively quickly, letting the piston freely move to reach the new volume

Seed systems smallholder farmers use

Seed can be an important entry point for promoting productivity, nutrition and resilience among smallholder farmers. While investments have primarily focused on strengthening the formal sector, this article documents the degree to which the informal sector remains the core for seed acquisition, especially in Africa. Conclusions drawn from a uniquely comprehensive data set, 9660 observations across six countries and covering 40 crops, show that farmers access 90.2 % of their seed from informal systems with 50.9 % of that deriving from local markets. Further, 55 % of seed is paid for by cash, indicating that smallholders are already making important investments in this arena. Targeted interventions are proposed for rendering formal and informal seed sector more smallholder-responsive and for scaling up positive impacts

Discrete Information from CHL Black Holes

AdS_2/CFT_1 correspondence predicts that the logarithm of a Z_N twisted index over states carrying a fixed set of charges grows as 1/N times the entropy of the black hole carrying the same set of charges. In this paper we verify this explicitly by calculating the microscopic Z_N twisted index for a class of states in the CHL models. This demonstrates that black holes carry more information about the microstates than just the total degeneracy.Comment: LaTeX file, 24 pages; v2: references adde

Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function

We evaluate the one loop determinant of matter multiplet fields of N=4 supergravity in the near horizon geometry of quarter BPS black holes, and use it to calculate logarithmic corrections to the entropy of these black holes using the quantum entropy function formalism. We show that even though individual fields give non-vanishing logarithmic contribution to the entropy, the net contribution from all the fields in the matter multiplet vanishes. Thus logarithmic corrections to the entropy of quarter BPS black holes, if present, must be independent of the number of matter multiplet fields in the theory. This is consistent with the microscopic results. During our analysis we also determine the complete spectrum of small fluctuations of matter multiplet fields in the near horizon geometry.Comment: LaTeX file, 52 pages; v2: minor corrections, references adde

A rocky planet transiting a nearby low-mass star

M-dwarf stars -- hydrogen-burning stars that are smaller than 60 per cent of the size of the Sun -- are the most common class of star in our Galaxy and outnumber Sun-like stars by a ratio of 12:1. Recent results have shown that M dwarfs host Earth-sized planets in great numbers: the average number of M-dwarf planets that are between 0.5 to 1.5 times the size of Earth is at least 1.4 per star. The nearest such planets known to transit their star are 39 parsecs away, too distant for detailed follow-up observations to measure the planetary masses or to study their atmospheres. Here we report observations of GJ 1132b, a planet with a size of 1.2 Earth radii that is transiting a small star 12 parsecs away. Our Doppler mass measurement of GJ 1132b yields a density consistent with an Earth-like bulk composition, similar to the compositions of the six known exoplanets with masses less than six times that of the Earth and precisely measured densities. Receiving 19 times more stellar radiation than the Earth, the planet is too hot to be habitable but is cool enough to support a substantial atmosphere, one that has probably been considerably depleted of hydrogen. Because the host star is nearby and only 21 per cent the radius of the Sun, existing and upcoming telescopes will be able to observe the composition and dynamics of the planetary atmosphere.Comment: Published in Nature on 12 November 2015, available at http://dx.doi.org/10.1038/nature15762. This is the authors' version of the manuscrip