The Vlasov-Poisson-Landau System in Rx3\R^3_x

For the Landau-Poisson system with Coulomb interaction in $\R^3_x$, we prove the global existence, uniqueness, and large time convergence rates to the Maxwellian equilibrium for solutions which start out sufficiently close.Comment: 50 page

Optimal time decay of the non cut-off Boltzmann equation in the whole space

In this paper we study the large-time behavior of perturbative classical solutions to the hard and soft potential Boltzmann equation without the angular cut-off assumption in the whole space \threed_x with \DgE. We use the existence theory of global in time nearby Maxwellian solutions from \cite{gsNonCutA,gsNonCut0}. It has been a longstanding open problem to determine the large time decay rates for the soft potential Boltzmann equation in the whole space, with or without the angular cut-off assumption \cite{MR677262,MR2847536}. For perturbative initial data, we prove that solutions converge to the global Maxwellian with the optimal large-time decay rate of O(t^{-\frac{\Ndim}{2}+\frac{\Ndim}{2r}}) in the L^2_\vel(L^r_x)-norm for any $2\leq r\leq \infty$.Comment: 31 pages, final version to appear in KR

Global Newtonian limit for the Relativistic Boltzmann Equation near Vacuum

We study the Cauchy Problem for the relativistic Boltzmann equation with near Vacuum initial data. Unique global in time "mild" solutions are obtained uniformly in the speed of light parameter $c \ge 1$. We furthermore prove that solutions to the relativistic Boltzmann equation converge to solutions of the Newtonian Boltzmann equation in the limit as $c\to\infty$ on arbitrary time intervals $[0,T]$, with convergence rate $1/c^{2-\epsilon}$ for any $\epsilon \in(0,2)$. This may be the first proof of unique global in time validity of the Newtonian limit for a Kinetic equation.Comment: 35 page

Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials

In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out sufficiently close in $L^\infty_\ell$. If the initial data are continuous then so is the corresponding solution. We work in the case of a spatially periodic box. Conditions on the collision kernel are generic in the sense of (Dudy{\'n}ski and Ekiel-Je{\.z}ewska, Comm. Math. Phys., 1988); this resolves the open question of global existence for the soft potentials.Comment: 64 page

Physical instrumental vetoes for gravitational-wave burst triggers

We present a robust strategy to \emph{veto} certain classes of instrumental glitches that appear at the output of interferometric gravitational-wave (GW) detectors.This veto method is `physical' in the sense that, in order to veto a burst trigger, we make use of our knowledge of the coupling of different detector subsystems to the main detector output. The main idea behind this method is that the noise in an instrumental channel X can be \emph{transferred} to the detector output (channel H) using the \emph{transfer function} from X to H, provided the noise coupling is \emph{linear} and the transfer function is \emph{unique}. If a non-stationarity in channel H is causally related to one in channel X, the two have to be consistent with the transfer function. We formulate two methods for testing the consistency between the burst triggers in channel X and channel H. One method makes use of the \emph{null-stream} constructed from channel H and the \emph{transferred} channel X, and the second involves cross-correlating the two. We demonstrate the efficiency of the veto by `injecting' instrumental glitches in the hardware of the GEO 600 detector. The \emph{veto safety} is demonstrated by performing GW-like hardware injections. We also show an example application of this method using 5 days of data from the fifth science run of GEO 600. The method is found to have very high veto efficiency with a very low accidental veto rate.Comment: Minor changes, To appear in Phys. Rev.

Deep three-dimensional solid-state qubit arrays with long-lived spin coherence

Nitrogen-vacancy centers (NVCs) in diamond show promise for quantum computing, communication, and sensing. However, the best current method for entangling two NVCs requires that each one is in a separate cryostat, which is not scalable. We show that single NVCs can be laser written 6–15-µm deep inside of a diamond with spin coherence times that are an order of magnitude longer than previous laser-written NVCs and at least as long as naturally occurring NVCs. This depth is suitable for integration with solid immersion lenses or optical cavities and we present depth-dependent T2 measurements. 200 000 of these NVCs would fit into one diamond

How hosts control worms

No abstract available

DePaul University Centennial Essays and Images

A collection of eight essays honoring DePaul University’s centennial. The book has three parts: Mission and Governance; Campus Culture and Student Life; and Making the Modern University.https://via.library.depaul.edu/vincentian_ebooks/1020/thumbnail.jp

High precision integrated photonic thermometry enabled by a transfer printed diamond resonator on GaN waveguide chip

We demonstrate a dual-material integrated photonic thermometer, fabricated by high accuracy micro-transfer printing. A freestanding diamond micro-disk resonator is printed in close proximity to a gallium nitride on a sapphire racetrack resonator, and respective loaded Q factors of 9.1 × 104 and 2.9 × 104 are measured. We show that by using two independent wide-bandgap materials, tracking the thermally induced shifts in multiple resonances, and using optimized curve fitting tools the measurement error can be reduced to 9.2 mK. Finally, for the GaN, in a continuous acquisition measurement we record an improvement in minimum Allan variance, occurring at an averaging time four times greater than a comparative silicon device, indicating better performance over longer time scales

Global existence and full regularity of the Boltzmann equation without angular cutoff

We prove the global existence and uniqueness of classical solutions around an equilibrium to the Boltzmann equation without angular cutoff in some Sobolev spaces. In addition, the solutions thus obtained are shown to be non-negative and $C^\infty$ in all variables for any positive time. In this paper, we study the Maxwellian molecule type collision operator with mild singularity. One of the key observations is the introduction of a new important norm related to the singular behavior of the cross section in the collision operator. This norm captures the essential properties of the singularity and yields precisely the dissipation of the linearized collision operator through the celebrated H-theorem