First-passage and extreme-value statistics of a particle subject to a constant force plus a random force

We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point $x_1$ of a particle which starts at $x_0$ with velocity $v_0$. The probability that the particle has not yet arrived at $x_1$ after a time $t$, the mean time of first arrival, and the velocity distribution at first arrival are all considered. We also study the statistics of the first return of the particle to its starting point. Finally, we point out that the extreme-value statistics of the particle and the first-passage statistics are closely related, and we derive the distribution of the maximum displacement $m={\rm max}_t[x(t)]$.Comment: Contains an analysis of the extreme-value statistics not included in first versio

Osteoarthritis prevalence in retired national football league players with a history of ankle injuries and surgery

Context: Ankle injuries are common at all levels of American football, and retired National Football League (NFL) players have a high prevalence of osteoarthritis (OA), but little is known about how ankle injuries influence OA prevalence and daily activities in this population or how surgical interventions for such injuries alter the risk of OA. Objective: To examine (1) the association of ankle-injury history with OA prevalence, (2) the association of surgical intervention after ankle injury with OA prevalence, and (3) the relationships among ankle injuries, reported OA, and daily activities in retired NFL players. Design: Case-control study. Setting: Survey. Patients or Other Participants: Data from the Retired NFL Players General Health Survey. Main Outcome Measure(s): We created a 7-category main exposure variable that differentiated respondents by football-related ankle injury and surgical intervention. Multivariable binomial regression models were used to estimate prevalence ratios and 95% confidence intervals. Among those reporting OA, we examined the distribution of responses regarding whether OA affected daily activities. Results: Among the 2446 respondents, 920 participants experienced OA in any joint during their lifetime. Compared with those reporting no ankle injuries, the prevalence of OA was higher among those with a history of ankle injury. Also, the prevalence of OA was higher among those who had undergone surgery versus those who had not. The number of retired NFL players who reported that OA often affected their daily activities increased with the number of ankle injuries. Conclusions: Among former NFL players, a history of ankle injury increased the prevalence of OA. More ankle injuries increased the probability that OA negatively affected daily activities. Future prospective research is needed to better determine the influence of surgical intervention at the ankle or foot on OA

Spin-1/2 J1-J2 model on the body-centered cubic lattice

Using exact diagonalization (ED) and linear spin wave theory (LSWT) we study the influence of frustration and quantum fluctuations on the magnetic ordering in the ground state of the spin-1/2 J1-J2 Heisenberg antiferromagnet (J1-J2 model) on the body-centered cubic (bcc) lattice. Contrary to the J1-J2 model on the square lattice, we find for the bcc lattice that frustration and quantum fluctuations do not lead to a quantum disordered phase for strong frustration. The results of both approaches (ED, LSWT) suggest a first order transition at J2/J1 $\approx$ 0.7 from the two-sublattice Neel phase at low J2 to a collinear phase at large J2.Comment: 6.1 pages 7 figure

Variational Approximations in a Path-Integral Description of Potential Scattering

Using a recent path integral representation for the T-matrix in nonrelativistic potential scattering we investigate new variational approximations in this framework. By means of the Feynman-Jensen variational principle and the most general ansatz quadratic in the velocity variables -- over which one has to integrate functionally -- we obtain variational equations which contain classical elements (trajectories) as well as quantum-mechanical ones (wave spreading).We analyse these equations and solve them numerically by iteration, a procedure best suited at high energy. The first correction to the variational result arising from a cumulant expansion is also evaluated. Comparison is made with exact partial-wave results for scattering from a Gaussian potential and better agreement is found at large scattering angles where the standard eikonal-type approximations fail.Comment: 35 pages, 3 figures, 6 tables, Latex with amsmath, amssymb; v2: 28 pages, EPJ style, misprints corrected, note added about correct treatment of complex Gaussian integrals with the theory of "pencils", matches published versio

Statistical properties of the Burgers equation with Brownian initial velocity

We study the one-dimensional Burgers equation in the inviscid limit for Brownian initial velocity (i.e. the initial velocity is a two-sided Brownian motion that starts from the origin x=0). We obtain the one-point distribution of the velocity field in closed analytical form. In the limit where we are far from the origin, we also obtain the two-point and higher-order distributions. We show how they factorize and recover the statistical invariance through translations for the distributions of velocity increments and Lagrangian increments. We also derive the velocity structure functions and we recover the bifractality of the inverse Lagrangian map. Then, for the case where the initial density is uniform, we obtain the distribution of the density field and its $n$-point correlations. In the same limit, we derive the $n-$point distributions of the Lagrangian displacement field and the properties of shocks. We note that both the stable-clustering ansatz and the Press-Schechter mass function, that are widely used in the cosmological context, happen to be exact for this one-dimensional version of the adhesion model.Comment: 42 pages, published in J. Stat. Phy

Coupling of acoustic cavitation with DEM-based particle solvers for modeling de-agglomeration of particle clusters in liquid metals

The aerospace and automotive industries are seeking advanced materials with low weight yet high strength and durability. Aluminum and magnesium-based metal matrix composites with ceramic micro- and nano-reinforcements promise the desirable properties. However, larger surface-area-to-volume ratio in micro- and especially nanoparticles gives rise to van der Waals and adhesion forces that cause the particles to agglomerate in clusters. Such clusters lead to adverse effects on final properties, no longer acting as dislocation anchors but instead becoming defects. Also, agglomeration causes the particle distribution to become uneven, leading to inconsistent properties. To break up clusters, ultrasonic processing may be used via an immersed sonotrode, or alternatively via electromagnetic vibration. This paper combines a fundamental study of acoustic cavitation in liquid aluminum with a study of the interaction forces causing particles to agglomerate, as well as mechanisms of cluster breakup. A non-linear acoustic cavitation model utilizing pressure waves produced by an immersed horn is presented, and then applied to cavitation in liquid aluminum. Physical quantities related to fluid flow and quantities specific to the cavitation solver are passed to a discrete element method particles model. The coupled system is then used for a detailed study of clusters’ breakup by cavitation

Master Sculptor at Work: Enteropathogenic Escherichia coli Infection Uniquely Modifies Mitochondrial Proteolysis during Its Control of Human Cell Death

Enteropathogenic Escherichia coli (EPEC) causes severe diarrheal disease and is present globally. EPEC virulence requires a bacterial type III secretion system to inject 20 effector proteins into human intestinal cells. Three effectors travel to mitochondria and modulate apoptosis; however, the mechanisms by which effectors control apoptosis from within mitochondria are unknown. To identify and quantify global changes in mitochondrial proteolysis during infection, we applied the mitochondrial terminal proteomics technique mitochondrial stable isotope labeling by amino acids in cell culture-terminal amine isotopic labeling of substrates (MS-TAILS). MS-TAILS identified 1,695 amino N-terminal peptides from 1,060 unique proteins and 390 N-terminal peptides from 215 mitochondrial proteins at a false discovery rate of 0.01. Infection modified 230 cellular and 40 mitochondrial proteins, generating 27 cleaved mitochondrial neo-N termini, demonstrating altered proteolytic processing within mitochondria. To distinguish proteolytic events specific to EPEC from those of canonical apoptosis, we compared mitochondrial changes during infection with those reported from chemically induced apoptosis. During infection, fewer than half of all mitochondrial cleavages were previously described for canonical apoptosis, and we identified nine mitochondrial proteolytic sites not previously reported, including several in proteins with an annotated role in apoptosis, although none occurred at canonical Asp-Glu-Val-Asp (DEVD) sites associated with caspase cleavage. The identification and quantification of novel neo-N termini evidences the involvement of noncaspase human or EPEC protease(s) resulting from mitochondrialtargeting effectors that modulate cell death upon infection. All proteomics data are available via ProteomeXchange with identifier PXD016994. IMPORTANCE To our knowledge, this is the first study of the mitochondrial proteome or N-terminome during bacterial infection. Identified cleavage sites that had not been previously reported in the mitochondrial N-terminome and that were not generated in canonical apoptosis revealed a pathogen-specific strategy to control human cell apoptosis. These data inform new mechanisms of virulence factors targeting mitochondria and apoptosis during infection and highlight how enteropathogenic Escherichia coli (EPEC) manipulates human cell death pathways during infection, including candidate substrates of an EPEC protease within mitochondria. This understanding informs the development of new antivirulence strategies against the many human pathogens that targe

Quantum magnetism in two dimensions: From semi-classical N\'eel order to magnetic disorder

This is a review of ground-state features of the s=1/2 Heisenberg antiferromagnet on two-dimensional lattices. A central issue is the interplay of lattice topology (e.g. coordination number, non-equivalent nearest-neighbor bonds, geometric frustration) and quantum fluctuations and their impact on possible long-range order. This article presents a unified summary of all 11 two-dimensional uniform Archimedean lattices which include e.g. the square, triangular and kagome lattice. We find that the ground state of the spin-1/2 Heisenberg antiferromagnet is likely to be semi-classically ordered in most cases. However, the interplay of geometric frustration and quantum fluctuations gives rise to a quantum paramagnetic ground state without semi-classical long-range order on two lattices which are precisely those among the 11 uniform Archimedean lattices with a highly degenerate ground state in the classical limit. The first one is the famous kagome lattice where many low-lying singlet excitations are known to arise in the spin gap. The second lattice is called star lattice and has a clear gap to all excitations. Modification of certain bonds leads to quantum phase transitions which are also discussed briefly. Furthermore, we discuss the magnetization process of the Heisenberg antiferromagnet on the 11 Archimedean lattices, focusing on anomalies like plateaus and a magnetization jump just below the saturation field. As an illustration we discuss the two-dimensional Shastry-Sutherland model which is used to describe SrCu2(BO3)2.Comment: This is now the complete 72-page preprint version of the 2004 review article. This version corrects two further typographic errors (three total with respect to the published version), see page 2 for detail

Coordination in multiagent systems and Laplacian spectra of digraphs

Constructing and studying distributed control systems requires the analysis of the Laplacian spectra and the forest structure of directed graphs. In this paper, we present some basic results of this analysis partially obtained by the present authors. We also discuss the application of these results to decentralized control and touch upon some problems of spectral graph theory.Comment: 15 pages, 2 figures, 40 references. To appear in Automation and Remote Control, Vol.70, No.3, 200

Measurement of the polarisation of W bosons produced with large transverse momentum in pp collisions at sqrt(s) = 7 TeV with the ATLAS experiment

This paper describes an analysis of the angular distribution of W->enu and W->munu decays, using data from pp collisions at sqrt(s) = 7 TeV recorded with the ATLAS detector at the LHC in 2010, corresponding to an integrated luminosity of about 35 pb^-1. Using the decay lepton transverse momentum and the missing transverse energy, the W decay angular distribution projected onto the transverse plane is obtained and analysed in terms of helicity fractions f0, fL and fR over two ranges of W transverse momentum (ptw): 35 < ptw < 50 GeV and ptw > 50 GeV. Good agreement is found with theoretical predictions. For ptw > 50 GeV, the values of f0 and fL-fR, averaged over charge and lepton flavour, are measured to be : f0 = 0.127 +/- 0.030 +/- 0.108 and fL-fR = 0.252 +/- 0.017 +/- 0.030, where the first uncertainties are statistical, and the second include all systematic effects.Comment: 19 pages plus author list (34 pages total), 9 figures, 11 tables, revised author list, matches European Journal of Physics C versio