Monotone Volume Formulas for Geometric Flows

We consider a closed manifold M with a Riemannian metric g(t) evolving in direction -2S(t) where S(t) is a symmetric two-tensor on (M,g(t)). We prove that if S satisfies a certain tensor inequality, then one can construct a forwards and a backwards reduced volume quantity, the former being non-increasing, the latter being non-decreasing along the flow. In the case where S=Ric is the Ricci curvature of M, the result corresponds to Perelman's well-known reduced volume monotonicity for the Ricci flow. Some other examples are given in the second section of this article, the main examples and motivation for this work being List's extended Ricci flow system, the Ricci flow coupled with harmonic map heat flow and the mean curvature flow in Lorentzian manifolds with nonnegative sectional curvatures. With our approach, we find new monotonicity formulas for these flows.Comment: v2: final version (as published

Fear of the dark in children: is stationary night blindness the cause?

No abstract available

Pauli Spin Blockade of Heavy Holes in a Silicon Double Quantum Dot

In this work, we study hole transport in a planar silicon metal-oxide-semiconductor based double quantum dot. We demonstrate Pauli spin blockade in the few hole regime and map the spin relaxation induced leakage current as a function of inter-dot level spacing and magnetic field. With varied inter-dot tunnel coupling we can identify different dominant spin relaxation mechanisms. Applying a strong out-of-plane magnetic field causes an avoided singlet-triplet level crossing, from which the heavy hole g-factor $\sim$ 0.93, and the strength of spin-orbit interaction $\sim$ 110 $\mu$eV, can be obtained. The demonstrated strong spin-orbit interaction of heavy hole promises fast local spin manipulation using only electrical fields, which is of great interest for quantum information processing.Comment: 15 pages, 4 figure

How Does Wind Project Performance Change with Age in the United States?

Wind-plant performance declines with age, and the rate of decline varies between regions. The rate of performance decline is important when determining wind-plant financial viability and expected lifetime generation. We determine the rate of age-related performance decline in the United States wind fleet by evaluating generation records from 917 plants. We find the rate of performance decline to be 0.53%/year for older vintages of plants and 0.17%/year for newer vintages of plants on an energy basis for the first 10 years of operation, which is on the lower end of prior estimates in Europe. Unique to the United States, we find a significant drop in performance by 3.6% after 10 years, as plants lose eligibility for the production tax credit. Certain plant characteristics, such as the ratio of blade length to nameplate capacity, influence the rate of performance decline. These results indicate that the performance decline rate can be partially managed and influenced by policy

MECHANICAL DAMPING SYSTEM FOR STRUCTURES

A mechanical damping system for a structure is provided. The mechanical damping system comprises a tubular impact frame secured to the structure. A support frame is secured to the structure with the support frame spaced from the impact frame. An elongated member is provided having a first end and a second end. The first end is secured within the support frame and the second end is free from connection and extends into the impact frame. At least one impact mass is secured to the second end of the elongated member, the impact mass movable within and contactable with the impact frame

Comment on "Canonical formalism for Lagrangians with nonlocality of finite extent"

We show by some counterexamples that Lagrangian sysytems with nonlocality of finite extent are not necessarily unstable.Comment: 8 pages, 1 figure Submitted to Phys. Rev.

Generalized Tomonaga-Schwinger equation from the Hadamard formula

A generalized Tomonaga--Schwinger equation, holding on the entire boundary of a {\em finite} spacetime region, has recently been considered as a tool for studying particle scattering amplitudes in background-independent quantum field theory. The equation has been derived using lattice techniques under assumptions on the existence of the continuum limit. Here I show that in the context of continuous euclidean field theory the equation can be directly derived from the functional integral formalism, using a technique based on Hadamard's formula for the variation of the propagator.Comment: 11 pages, no figure

Power Spectrum Correlations Induced by Non-Linear Clustering

Gravitational clustering is an intrinsically non-linear process that generates significant non-Gaussian signatures in the density field. We consider how these affect power spectrum determinations from galaxy and weak-lensing surveys. Non-Gaussian effects not only increase the individual error bars compared to the Gaussian case but, most importantly, lead to non-trivial cross-correlations between different band-powers. We calculate the power-spectrum covariance matrix in non-linear perturbation theory (weakly non-linear regime), in the hierarchical model (strongly non-linear regime), and from numerical simulations in real and redshift space. We discuss the impact of these results on parameter estimation from power spectrum measurements and their dependence on the size of the survey and the choice of band-powers. We show that the non-Gaussian terms in the covariance matrix become dominant for scales smaller than the non-linear scale, depending somewhat on power normalization. Furthermore, we find that cross-correlations mostly deteriorate the determination of the amplitude of a rescaled power spectrum, whereas its shape is less affected. In weak lensing surveys the projection tends to reduce the importance of non-Gaussian effects. Even so, for background galaxies at redshift z=1, the non-Gaussian contribution rises significantly around l=1000, and could become comparable to the Gaussian terms depending upon the power spectrum normalization and cosmology. The projection has another interesting effect: the ratio between non-Gaussian and Gaussian contributions saturates and can even decrease at small enough angular scales if the power spectrum of the 3D field falls faster than 1/k^2.Comment: 34 pages, 15 figures. Revised version, includes a clearer explanation of why the hierarchical ansatz does not provide a good model of the covariance matrix in the non-linear regime, and new constraints on the amplitudes Ra and Rb for general 4-pt function configurations in the non-linear regim