A non-relativistic limit of M-theory and 11-dimensional membrane Newton-Cartan geometry

We consider a non-relativistic limit of the bosonic sector of eleven-dimensional supergravity, leading to a theory based on a covariant ‘membrane Newton-Cartan’ (MNC) geometry. The local tangent space is split into three ‘longitudinal’ and eight ‘transverse’ directions, related only by Galilean rather than Lorentzian symmetries. This generalises the ten-dimensional stringy Newton-Cartan (SNC) theory. In order to obtain a finite limit, the field strength of the eleven-dimensional four-form is required to obey a transverse self-duality constraint, ultimately due to the presence of the Chern-Simons term in eleven dimensions. The finite action then gives a set of equations that is invariant under longitudinal and transverse rotations, Galilean boosts and local dilatations. We supplement these equations with an extra Poisson equation, coming from the subleading action. Reduction along a longitudinal direction gives the known SNC theory with the addition of RR gauge fields, while reducing along a transverse direction yields a new non-relativistic theory associated to D2 branes. We further show that the MNC theory can be embedded in the U-duality symmetric formulation of exceptional field theory, demonstrating that it shares the same exceptional Lie algebraic symmetries as the relativistic supergravity, and providing an alternative derivation of the extra Poisson equation.

W-infinity symmetry in the quantum hall effect beyond the edge

The description of chiral quantum incompressible fluids by the W∞ symmetry can be extended from the edge, where it encompasses the conformal field theory approach, to the non-conformal bulk. The two regimes are characterized by excitations with different sizes, energies and momenta within the disk geometry. In particular, the bulk quantities have a finite limit for large droplets. We obtain analytic results for the radial shape of excitations, the edge reconstruction phenomenon and the energy spectrum of density fluctuations in Laughlin states.

Weak-anisotropy approximation of P-wave geometrical spreading in horizontally layered anisotropic media of arbitrary symmetry: TTI specification

Understanding the role of geometrical spreading and estimating its effects on seismic wave propagation play an important role in several techniques used in seismic exploration. The spreading can be estimated through dynamic ray tracing or determined from reflection traveltime derivatives. In the latter case, derivatives of non-hyperbolic moveout approximations are often used. We offer an alternative approach based on the weak-anisotropy approximation. The resulting formula is applicable to P-waves reflected from the bottom of a stack of horizontal layers, in which each layer can be of arbitrary anisotropy. At an arbitrary surface point, the formula depends, in each layer, on the thickness of the layer, on the P-wave reference velocity used for the construction of reference rays, and on nine P-wave weak-anisotropy (WA) parameters specifying the layer anisotropy. Along an arbitrary surface profile, the number of WA parameters reduces to five parameters related to the profile. WA parameters represent an alternative to the elastic moduli, and as such can be used for the description of any anisotropy. The relative error of the approximate formula for a multilayered structure consisting of layers of anisotropy between 8% and 20% is, at most, 10%. For models including layers of anisotropy stronger than 20%, the relative errors may reach, locally, even 30%. For any offset, relative errors remain under a finite limit, which varies with anisotropy strength.

Performance Testing of a Large-Format X-ray Reflection Grating Prototype for a Suborbital Rocket Payload

The soft X-ray grating spectrometer on board the Off-plane Grating Rocket Experiment (OGRE) hopes to achieve the highest resolution soft X-ray spectrum of an astrophysical object when it is launched via suborbital rocket. Paramount to the success of the spectrometer are the performance of the [Formula: see text] reflection gratings populating its reflection grating assembly. To test current grating fabrication capabilities, a grating prototype for the payload was fabricated via electron-beam lithography at The Pennsylvania State University’s Materials Research Institute and was subsequently tested for performance at Max Planck Institute for Extraterrestrial Physics’ PANTER X-ray Test Facility. Bayesian modeling of the resulting data via Markov chain Monte Carlo (MCMC) sampling indicated that the grating achieved the OGRE single-grating resolution requirement of [Formula: see text] at the 94% confidence level. The resulting [Formula: see text] posterior probability distribution suggests that this confidence level is likely a conservative estimate though, since only a finite [Formula: see text] parameter space was sampled and the model could not constrain the upper bound of [Formula: see text] to less than infinity. Raytrace simulations of the tested system found that the observed data can be reproduced with a grating performing at [Formula: see text]. It is therefore postulated that the behavior of the obtained [Formula: see text] posterior probability distribution can be explained by a finite measurement limit of the system and not a finite limit on [Formula: see text]. Implications of these results and improvements to the test setup are discussed.

Liouville Results and Asymptotics of Solutions of a Quasilinear Elliptic Equation with Supercritical Source Gradient Term

We consider the elliptic quasilinear equation - Δ m ⁢ u = u p ⁢ | ∇ ⁡ u | q {-\Delta_{m}u=u^{p}\lvert\nabla u\rvert^{q}} in ℝ N {\mathbb{R}^{N}} , q ≥ m {q\geq m} and p > 0 {p>0} , 1 < m < N {1<m<N} . Our main result is a Liouville-type property, namely, all the positive C 1 {C^{1}} solutions in ℝ N {\mathbb{R}^{N}} are constant. We also give their asymptotic behaviour; all the solutions in an exterior domain ℝ N ∖ B r 0 {\mathbb{R}^{N}\setminus B_{r_{0}}} are bounded. The solutions in B r 0 ∖ { 0 } {B_{r_{0}}\setminus\{0\}} can be extended as continuous functions in B r 0 {B_{r_{0}}} . The solutions in ℝ N ∖ { 0 } {\mathbb{R}^{N}\setminus\{0\}} has a finite limit l ≥ 0 {l\geq 0} as | x | → ∞ {\lvert x\rvert\to\infty} . Our main argument is a Bernstein estimate of the gradient of a power of the solution, combined with a precise Osserman-type estimate for the equation satisfied by the gradient.

Limit drift for complex Feigenbaum mappings

We study the dynamics of towers defined by fixed points of renormalization for Feigenbaum polynomials in the complex plane with varying order $\ell $ of the critical point. It is known that the measure of the Julia set of the Feigenbaum polynomial is positive if and only if almost every point tends to $0$ under the dynamics of the tower for corresponding $\ell $ . That in turn depends on the sign of a quantity called the drift. We prove the existence and key properties of absolutely continuous invariant measures for tower dynamics as well as their convergence when $\ell $ tends to $\infty $ . We also prove the convergence of the drifts to a finite limit, which can be expressed purely in terms of the limiting tower, which corresponds to a Feigenbaum map with a flat critical point.

General Collective Intelligence, Human-Centric Functional Modeling and the Current Limitations on Collective Design Cognition

This paper explores the limits to the size and complexity of designs that can be created by humans. Beginning with the existence of a finite limit to the design output of any single individual, as a result, some design efforts require teams. However, anecdotally, when it comes to contributing to a single design objective, there is a limit to the size of groups, a limit to the diversity of skill sets, a limit to the diversity of design techniques and other problem-solving tools, and there is a limit to the range of objectives, at which the group can remain effective. Design processes are cognitive (reasoning or understanding) processes. And design tools are an automation of cognitive processes. Therefore design techniques and other problem-solving tools can be represented as the cognitive processes by which design problems are solved. The execution of these cognitive processes is then design cognition. Equating the term objective with the problem that has been defined, equating design techniques and other problem-solving tools with the cognitive processes by which those problems are solved, and defining the execution of these cognitive processes as design cognition, then since large complex designs must be created by teams, the limit to the capacity of groups for this cognition imposes a limit on the size and complexity of designs that can be created by humans. General Collective Intelligence has been defined as a system that organizes groups into a single collective intelligence with vastly greater general problem solving ability. Design based on General Collective Intelligence has been suggested to have the capacity to expand current limits to collective design cognition that might take certain classes of problems outside the capacity of groups to reliably define or solve. In any GCI based design process, Human-Centric Functional Modeling is a critical requirement in defining design problems as well as in creating the designs that solve those problems. This paper explores GCI based design, and the classes of problems that can’t reliably be defined or solved without it.

Entropy Law, Sustainability, and Third Industrial Revolution

In mankind’s relentless quest for prosperity, Nature has suffered great damage. It has been treated as an inexhaustible reserve of resources. The indefinite scale of global expansion is still continuing and now the earth’s very survival is under threat. But against this exploitation of nature, there is the concept of entropy, which places a finite limit on the extent to which resources can be used in any closed system, such as our planet. Considering the impact of entropy, this book examines the key issues of sustainability—social, economic, and environmental. It discusses the social dimension of sustainability, showing how it is impacted by issues of economic inequality, poverty, and other socio-economic and infrastructural factors in the Indian context. It also highlights how Indian households suffer from clean energy poverty and points to the inequality in distribution of different fuels and of fuel cost among households. It assesses India’s power sector and its potential to be a significant player in bringing the Third Industrial Revolution to India by replacing fossil fuels with new renewables. It concludes by projecting power sector scenarios till 2041–42 achievable through alternative, realizable policy with respect to energy conservation and fuel substitution, and thus paves the way for the green power.