How to squeeze the toothpaste back into the tube

We consider "bridges" for the simple exclusion process on Z, either symmetric or asymmetric, in which particles jump to the right at rate p and to the left at rate 1-p. The initial state O has all negative sites occupied and all non-negative sites empty. We study the probability that the process is again in state O at time t, and the behaviour of the process on [0,t] conditioned on being in state O at time t. In the case p=1/2, we find that such a bridge typically goes a distance of order t (in the sense of graph distance) from the initial state. For the asymmetric systems, we note an interesting duality which shows that bridges with parameters p and 1-p have the same distribution; the maximal distance of the process from the original state behaves like c(p)log(t) for some constant c(p) depending on p. (For p>1/2, the front particle therefore travels much less far than the bridge of the corresponding random walk, even though in the unconditioned process the path of the front particle dominates a random walk.) We mention various further questions.Comment: 15 page

Stationary distributions of multi-type totally asymmetric exclusion processes

We consider totally asymmetric simple exclusion processes with n types of particle and holes ($n$-TASEPs) on $\mathbb {Z}$ and on the cycle $\mathbb {Z}_N$. Angel recently gave an elegant construction of the stationary measures for the 2-TASEP, based on a pair of independent product measures. We show that Angel's construction can be interpreted in terms of the operation of a discrete-time $M/M/1$ queueing server; the two product measures correspond to the arrival and service processes of the queue. We extend this construction to represent the stationary measures of an n-TASEP in terms of a system of queues in tandem. The proof of stationarity involves a system of n 1-TASEPs, whose evolutions are coupled but whose distributions at any fixed time are independent. Using the queueing representation, we give quantitative results for stationary probabilities of states of the n-TASEP on $\mathbb {Z}_N$, and simple proofs of various independence and regeneration properties for systems on $\mathbb {Z}$.Comment: Published at http://dx.doi.org/10.1214/009117906000000944 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Testing isomorphism of graded algebras

We present a new algorithm to decide isomorphism between finite graded algebras. For a broad class of nilpotent Lie algebras, we demonstrate that it runs in time polynomial in the order of the input algebras. We introduce heuristics that often dramatically improve the performance of the algorithm and report on an implementation in Magma

Coronal--Temporal Correlations in GX339-4: Hysteresis, Possible Reflection Changes, and Implications for ADAFs

We present spectral fits and timing analysis of Rossi X-ray Timing Explorer observations of GX339-4. These observations were carried out over a span of more than two years and encompassed both the soft/high and hard/low states. Hysteresis in the soft state/hard state transition is observed. The hard state exhibits a possible anti-correlation between coronal compactness (i.e., spectral hardness) and the covering fraction of cold, reflecting material. The correlation between `reflection fraction' and soft X-ray flux, however, appears to be more universal. Furthermore, low flux, hard state observations - taken over a decline into quiescence- show that the Fe line, independent of `reflection fraction', remains broad and at a roughly constant equivalent width, counter to expectations from ADAF models. All power spectral densities (PSD) of the hard state X-ray lightcurves are describable as the sum of just a few broad, quasi-periodic features with frequencies that roughly scale as coronal compactness to the -3/2 power. Similar to observations of Cyg X-1, time lags between soft and hard variability anti-correlate with coronal compactness. A stronger correlation is seen between the time lags and the `reflection fraction'.Comment: 29 Pages, 17 Figures, 6 Tables. Accepted for Publication in MNRAS. (Abstract Abridged

Aircraft interior noise reduction by alternate resonance tuning

Model problem development and analysis continues with the Alternate Resonance Tuning (ART) concept. The various topics described are presently at different stages of completion: investigation of the effectiveness of the ART concept under an external propagating pressure field associated with propeller passage by the fuselage; analysis of ART performance with a double panel wall mounted in a flexible frame model; development of a data fitting scheme using a branch analysis with a Newton-Raphson scheme in multiple dimensions to determine values of critical parameters in the actual experimental apparatus; and investigation of the ART effect with real panels as opposed to the spring-mass-damper systems currently used in much of the theory

Aircraft interior noise reduction by alternate resonance tuning

Model problem development and analysis continues with the Alternate Resonance Tuning concept. Various topics are presently at different stages of completion and are described. These topics included optimization of panel mass ratios, panel computer code verification and agreement with experimental data, and flexible frame modeling

Aircraft interior noise reduction by alternate resonance tuning

The focus is on a noise control method which considers aircraft fuselages lined with panels alternately tuned to frequencies above and below the frequency that must be attenuated. An interior noise reduction called alternate resonance tuning (ART) is described both theoretically and experimentally. Problems dealing with tuning single paneled wall structures for optimum noise reduction using the ART methodology are presented, and three theoretical problems are analyzed. The first analysis is a three dimensional, full acoustic solution for tuning a panel wall composed of repeating sections with four different panel tunings within that section, where the panels are modeled as idealized spring-mass-damper systems. The second analysis is a two dimensional, full acoustic solution for a panel geometry influenced by the effect of a propagating external pressure field such as that which might be associated with propeller passage by a fuselage. To reduce the analysis complexity, idealized spring-mass-damper panels are again employed. The final theoretical analysis presents the general four panel problem with real panel sections, where the effect of higher structural modes is discussed. Results from an experimental program highlight real applications of the ART concept and show the effectiveness of the tuning on real structures