Non-crossing Brownian paths and Dyson Brownian motion under a moving boundary

We compute analytically the probability $S(t)$ that a set of $N$ Brownian paths do not cross each other and stay below a moving boundary $g(\tau)= W \sqrt{\tau}$ up to time $t$. We show that for large $t$ it decays as a power law $S(t) \sim t^{- \beta(N,W)}$. The decay exponent $\beta(N,W)$ is obtained as the ground state energy of a quantum system of $N$ non-interacting fermions in a harmonic well in the presence of an infinite hard wall at position $W$. Explicit expressions for $\beta(N,W)$ are obtained in various limits of $N$ and $W$, in particular for large $N$ and large $W$. We obtain the joint distribution of the positions of the walkers in the presence of the moving barrier $g(\tau) =W \sqrt{\tau}$ at large time. We extend our results to the case of $N$ Dyson Brownian motions (corresponding to the Gaussian Unitary Ensemble) in the presence of the same moving boundary $g(\tau)=W\sqrt{\tau}$. For $W=0$ we show that the system provides a realization of a Laguerre biorthogonal ensemble in random matrix theory. We obtain explicitly the average density near the barrier, as well as in the bulk far away from the barrier. Finally we apply our results to $N$ non-crossing Brownian bridges on the interval $[0,T]$ under a time-dependent barrier $g_B(\tau)= W \sqrt{\tau(1- \frac{\tau}{T})}$.Comment: 44 pages, 13 figure

Frictional dissipation of polymeric solids vs interfacial glass transition

We present single contact friction experiments between a glassy polymer and smooth silica substrates grafted with alkylsilane layers of different coverage densities and morphologies. This allows us to adjust the polymer/substrate interaction strength. We find that, when going from weak to strong interaction, the response of the interfacial junction where shear localizes evolves from that of a highly viscous threshold fluid to that of a plastically deformed glassy solid. This we analyse as resulting from an interaction-induced ``interfacial glass transition'' helped by pressure

Modal analysis as non-destructive testing technique for additively manufactured 304L stainless steel parts

“Non-Destructive Testing (NDT) methods for Additively Manufactured (AM) parts is an ongoing field of research in the additive community due to its ability to determine if a part can be deemed viable for field usage. This study presents modal analysis as a NDT method for AM parts. For production builds that have multiple copies of the same part, a correcting technique can be used such that the frequencies of the parts under test can be reliably compared against each other, which saves both time and money compared to other traditional NDT methods. This study was able to develop a novel method for quantifying the processing force that develops over the melt pool during the Selective Laser Melting (SLM) process. The processing force was found to be dependent on the laser power, Pulse Repetition Frequency (PRF), and scanning speed, which are the primary processing parameters of the SLM process. Modal analysis is shown to be a promising NDT method and future work will be done to look at an algorithmic framework for analyzing an arbitrary part with modal analysis”--Abstract, page iv

Analysis Of Textbooks For Beginning English Learners In Middle School

Research shows that it takes an average of 5-7 years for English learners to achieve academic English proficiency (Demie, 2013). Students who begin learning English in middle school have exactly 5-7 years remaining in school to achieve proficiency. This project analyzes three textbooks intended for beginning English learners in middle school in order to answer the question: Which textbook or textbooks can be recommended as a solid textbook for grammar instruction for beginning English learners in a middle school? The three textbooks were systematically analyzed for explicit instruction, samples of language, and activity types included, as well as the adherence to the scope of developmental stages of English acquisition (Fernandez, 2001; Dutro et al, 2005). Through the findings, one textbook is recommended above the others for grammar instruction

Evolution of Exoplanets and their Parent Stars

Studying exoplanets with their parent stars is crucial to understand their population, formation and history. We review some of the key questions regarding their evolution with particular emphasis on giant gaseous exoplanets orbiting close to solar-type stars. For masses above that of Saturn, transiting exoplanets have large radii indicative of the presence of a massive hydrogen-helium envelope. Theoretical models show that this envelope progressively cools and contracts with a rate of energy loss inversely proportional to the planetary age. The combined measurement of planetary mass, radius and a constraint on the (stellar) age enables a global determination of the amount of heavy elements present in the planet interior. The comparison with stellar metallicity shows a correlation between the two, indicating that accretion played a crucial role in the formation of planets. The dynamical evolution of exoplanets also depends on the properties of the central star. We show that the lack of massive giant planets and brown dwarfs in close orbit around G-dwarfs and their presence around F-dwarfs are probably tied to the different properties of dissipation in the stellar interiors. Both the evolution and the composition of stars and planets are intimately linked.Comment: appears in The age of stars - 23rd Evry Schatzman School on Stellar Astrophysics, Roscoff : France (2013

Improved limits on short-wavelength gravitational waves from the cosmic microwave background

The cosmic microwave background (CMB) is affected by the total radiation density around the time of decoupling. At that epoch, neutrinos comprised a significant fraction of the radiative energy, but there could also be a contribution from primordial gravitational waves with frequencies greater than ~ 10^-15 Hz. If this cosmological gravitational wave background (CGWB) were produced under adiabatic initial conditions, its effects on the CMB and matter power spectrum would mimic massless non-interacting neutrinos. However, with homogenous initial conditions, as one might expect from certain models of inflation, pre big-bang models, phase transitions and other scenarios, the effect on the CMB would be distinct. We present updated observational bounds for both initial conditions using the latest CMB data at small scales from the South Pole Telescope (SPT) in combination with Wilkinson Microwave Anisotropy Probe (WMAP), current measurements of the baryon acoustic oscillations, and the Hubble parameter. With the inclusion of the data from SPT the adiabatic bound on the CGWB density is improved by a factor of 1.7 to 10^6 Omega_gw < 8.7 at the 95% confidence level (C.L.), with weak evidence in favor of an additional radiation component consistent with previous analyses. The constraint can be converted into an upper limit on the tension of horizon-sized cosmic strings that could generate this gravitational wave component, with Gmu < 2 10^-7 at 95% C.L., for string tension Gmu. The homogeneous bound improves by a factor of 3.5 to 10^6 Omega_gw < 1.0 at 95% C.L., with no evidence for such a component from current data.Comment: 5 pages, 3 figure

Dynamic range and mass accuracy of wide-scan direct infusion nanoelectrospray fourier transform ion cyclotron resonance mass spectrometry-based metabolomics increased by the spectral stitching method

Direct infusion nanoelectrospray Fourier transform ion cyclotron resonance mass spectrometry (DI nESI FT-ICR MS)offers high mass accuracy and resolution for analyzing complex metabolite mixtures. High dynamic range across a wide mass range, however, can only be achieved at the expense of mass accuracy, since the large numbers of ions entering the ICR detector induce adverse spacecharge effects. Here we report an optimized strategy for wide-scan DI nESI FT-ICR MS that increases dynamic range but maintains high mass accuracy. It comprises the collection if multiple adjacent selected ion monitoring (SIM) windows that are stitched together using novel algorithms. The final SIM-stitching method, derived from several optimization experiments, comprises 21 adjoining SIM windows each of width m/z 30 (from m/z 70 to 500; adjacent windows overlap by m/z 10) with an automated gain control (AGC) target of 1 105 charges. SIMstitching and wide-scan range (WSR; Thermo Electron)were compared using a defined standard to assess mass accuracy and a liver extract to assess peak count and dynamic range. SIM-stitching decreased the maximum mass error by 1.3- and 4.3-fold, and increased the peak count by 5.3- and 1.8-fold, versus WSR (AGC targets of 1 x 105 and 5 x 105, respectively). SIM-stitching achieved an rms mass error of 0.18 ppm and detected over 3000 peaks in liver extract. This novel approach increases metabolome coverage, has very high mass accuracy, and at 5.5 min/sample is conducive for high- throughput metabolomics

Worldsheet Form Factors in AdS/CFT

We formulate a set of consistency conditions appropriate to worldsheet form factors in the massive, integrable but non-relativistic, light-cone gauge fixed AdS(5) x S**5 string theory. We then perturbatively verify that these conditions hold, at tree level in the near-plane-wave limit and to one loop in the near-flat (Maldacena-Swanson) limit, for a number of specific cases. We further study the form factors in the weakly coupled dual description, verifying that the relevant conditions naturally hold for the one-loop Heisenberg spin-chain. Finally, we note that the near-plane-wave expressions for the form factors, when further expanded in small momentum or, equivalently, large charge density, reproduce the thermodynamic limit of the spin-chain results at leading order.Comment: 30 pages, 12 figures, v3: typos fixed, improved discussion of bound states and bound state axio

Dark Before Light: Testing the Cosmic Expansion History through the Cosmic Microwave Background

The cosmic expansion history proceeds in broad terms from a radiation dominated epoch to matter domination to an accelerated, dark energy dominated epoch. We investigate whether intermittent periods of acceleration are possible in the early universe -- between Big Bang nucleosynthesis (BBN) and recombination and beyond. We establish that the standard picture is remarkably robust: observations of anisotropies in the cosmic microwave background exclude any extra period of accelerated expansion between 1 \leq z \lesssim 10^5 (corresponding to 5\times10^{-4}\ {\rm eV} \leq T \lesssim 25\ {\rm eV}).Comment: 7 pages, 5 figure