The blockage problem

We investigate the totally asymmetric exclusion process on Z, with the jump rate at site i given by r_i=1 for i nonzero, r_0=r. It is easy to see that the maximal stationary current j(r) is nondecreasing in r and that j(r)=1/4 for r>=1; it is a long outstanding problem to determine whether or not the critical value r_c of r such that j(r)=1/4 for r>r_c is strictly less than 1. Here we present a heuristic argument, based on the analysis of the first sixteen terms in a formal power series expansion of j(r) obtained from finite volume systems, that r_c=1 and that for r less than 1 and near 1, j(r) behaves as 1/4-\gamma\exp[-{a/(1-r)}] with a approximately equal to 2. We also give some new exact results about this system; in particular we prove that j(r)=J_max(r), with J_max(r) the hydrodynamic maximal current defined by Seppalainen, and thus establish continuity of j(r). Finally we describe a related exactly solvable model, a semi-infinite system in which the site i=0 is always occupied. For that system, the critical r is 1/2 and the analogue j_s(r) of j(r) satisfies j_s(r)=r(1-r) for r<=1/2; j_s(r) is the limit of finite volume currents inside the curve |r(1-r)|=1/4 in the complex r plane and we suggest that analogous behavior may hold for the original system.Comment: 23 pages, 6 figure

Derivation of a Matrix Product Representation for the Asymmetric Exclusion Process from Algebraic Bethe Ansatz

We derive, using the algebraic Bethe Ansatz, a generalized Matrix Product Ansatz for the asymmetric exclusion process (ASEP) on a one-dimensional periodic lattice. In this Matrix Product Ansatz, the components of the eigenvectors of the ASEP Markov matrix can be expressed as traces of products of non-commuting operators. We derive the relations between the operators involved and show that they generate a quadratic algebra. Our construction provides explicit finite dimensional representations for the generators of this algebra.Comment: 16 page

Design considerations of scheduling systems suitable for PCB manufacturing

This paper identifies five key design characteristics of production scheduling software systems in printed circuit board (PCB) manufacturing. The authors consider that, in addition to an effective scheduling engine, a scheduling system should be able to process a preventative maintenance calendar, to give the user the flexibility to handle data using a variety of electronic sources, to run simulations to support decision-making, and to have simple and customisable graphical user interfaces. These design considerations were the result of a review of academic literature, the evaluation of commercial applications and a compilation of requirements of a PCB manufacturer. It was found that, from those systems that were evaluated, those that effectively addressed all five characteristics outlined in this paper were the most robust of all and could be used in PCB manufacturing

Comparison of thromboelastometry (ROTEM®) with standard plasmatic coagulation testing in paediatric surgery

Background Thromboelastometry (ROTEM®) might be useful to detect intraoperative coagulation disorders early in major paediatric surgery. This observational trial compares this technique to standard coagulation tests. Methods Intraoperative blood sampling was obtained in children undergoing elective major surgery. At each time point, standard coagulation tests [activated partial thromboplastin time (aPTT), prothrombin time (PT), and fibrinogen level] and ROTEM® analyses (InTEM, ExTEM, and FibTEM) were performed simultaneously by trained hospital laboratory staff. Results A total of 288 blood samples from 50 subjects were analysed. While there was a poor correlation between PT and aPTT to ExTEM clotting time (CT) and InTEM CT, respectively, a good correlation was detected between PT and aPTT to clot formation time, and a very good correlation between fibrinogen level and FibTEM assay (r=0.882, P<0.001). Notably, 64% of PT and 94% of aPTT measurements were outside the reference range, while impaired CT was observed in 13% and 6.3%, respectively. Standard coagulation test results were available after a median of 53 min [inter-quartile range (IQR): 45-63 min], whereas 10 min values of ROTEM® results were available online after 23 min (IQR: 21-24 min). Conclusions PT and aPTT cannot be interchangeably used with ROTEM® CT. Based on the results of ROTEM®, recommended thresholds for PT and aPTT might overestimate the need for coagulation therapy. A good correlation was found between the fibrinogen level and the FibTEM assay. In addition, ROTEM® offered faster turnaround time

New procedures in estimating feed substitution rates and in determining economic efficiency in pork production II. Replacement rates of corn and soybean oilmeal in fortified rations for growing-fattening swine on pasture

A previous bulletin reported results from an experiment designed to predict substitution rates and economic optima in corn/soybean oilmeal rations for growing and fattening hogs in drylot.2 Principles and analytical models were included which illustrate that the least-cost ration depends both on (1) the marginal rate of substitution between feeds and (2) the ratio of feed prices. These basic concepts will not be repeated in this bulletin. Since more hogs are farrowed in spring than in fall, the research reported in this study was conducted for growing and fattening hogs raised on pasture. Like the drylot study, the objectives of the pasture experiment were to estimate: (1) the production function, (2) the substitution rate between corn and soybean oilmeal at different points on the production surface, (3) the least-cost ration for different soybean oilmeal/corn price ratios, (4) the relationship between the rate of hog gains and the input of corn and soybean oilmeal and (5) the proportion of the years in which a least-cost feeding system results in greater profits than a least-time feeding system. Substitution between major classes of feed such as corn and soybean oilmeal is possible mainly where the rations are fortified with appropriate quantities of trace minerals (as well as antibiotics in the case of drylot feeding). These fortifying elements have been included in the rations of this study

Spectral Degeneracies in the Totally Asymmetric Exclusion Process

We study the spectrum of the Markov matrix of the totally asymmetric exclusion process (TASEP) on a one-dimensional periodic lattice at ARBITRARY filling. Although the system does not possess obvious symmetries except translation invariance, the spectrum presents many multiplets with degeneracies of high order. This behaviour is explained by a hidden symmetry property of the Bethe Ansatz. Combinatorial formulae for the orders of degeneracy and the corresponding number of multiplets are derived and compared with numerical results obtained from exact diagonalisation of small size systems. This unexpected structure of the TASEP spectrum suggests the existence of an underlying large invariance group. Keywords: ASEP, Markov matrix, Bethe Ansatz, Symmetries.Comment: 19 pages, 1 figur

Continuity of the four-point function of massive ϕ44\phi_4^4-theory above threshold

In this paper we prove that the four-point function of massive \vp_4^4-theory is continuous as a function of its independent external momenta when posing the renormalization condition for the (physical) mass on-shell. The proof is based on integral representations derived inductively from the perturbative flow equations of the renormalization group. It closes a longstanding loophole in rigorous renormalization theory in so far as it shows the feasibility of a physical definition of the renormalized coupling.Comment: 23 pages; to appear in Rev. Math. Physics few corrections, two explanatory paragraphs adde

The grand canonical ABC model: a reflection asymmetric mean field Potts model

We investigate the phase diagram of a three-component system of particles on a one-dimensional filled lattice, or equivalently of a one-dimensional three-state Potts model, with reflection asymmetric mean field interactions. The three types of particles are designated as $A$, $B$, and $C$. The system is described by a grand canonical ensemble with temperature $T$ and chemical potentials $T\lambda_A$, $T\lambda_B$, and $T\lambda_C$. We find that for $\lambda_A=\lambda_B=\lambda_C$ the system undergoes a phase transition from a uniform density to a continuum of phases at a critical temperature $\hat T_c=(2\pi/\sqrt3)^{-1}$. For other values of the chemical potentials the system has a unique equilibrium state. As is the case for the canonical ensemble for this $ABC$ model, the grand canonical ensemble is the stationary measure satisfying detailed balance for a natural dynamics. We note that $\hat T_c=3T_c$, where $T_c$ is the critical temperature for a similar transition in the canonical ensemble at fixed equal densities $r_A=r_B=r_C=1/3$.Comment: 24 pages, 3 figure

Phase diagram of the ABC model with nonconserving processes

The three species ABC model of driven particles on a ring is generalized to include vacancies and particle-nonconserving processes. The model exhibits phase separation at high densities. For equal average densities of the three species, it is shown that although the dynamics is {\it local}, it obeys detailed balance with respect to a Hamiltonian with {\it long-range interactions}, yielding a nonadditive free energy. The phase diagrams of the conserving and nonconserving models, corresponding to the canonical and grand-canonical ensembles, respectively, are calculated in the thermodynamic limit. Both models exhibit a transition from a homogeneous to a phase-separated state, although the phase diagrams are shown to differ from each other. This conforms with the expected inequivalence of ensembles in equilibrium systems with long-range interactions. These results are based on a stability analysis of the homogeneous phase and exact solution of the hydrodynamic equations of the models. They are supported by Monte-Carlo simulations. This study may serve as a useful starting point for analyzing the phase diagram for unequal densities, where detailed balance is not satisfied and thus a Hamiltonian cannot be defined.Comment: 32 page, 7 figures. The paper was presented at Statphys24, held in Cairns, Australia, July 201

Four-dimensional integration by parts with differential renormalization as a method of evaluation of Feynman diagrams

It is shown how strictly four-dimensional integration by parts combined with differential renormalization and its infrared analogue can be applied for calculation of Feynman diagrams.Comment: 6 pages, late