618 research outputs found

    Nonequilibrium dynamics of piecewise-smooth stochastic systems

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    PhDPiecewise-smooth stochastic systems have attracted a lot of interest in the last decades in engineering science and mathematics. Many investigations have focused only on one-dimensional problems. This thesis deals with simple two-dimensional piecewise-smooth stochastic systems in the absence of detailed balance. We investigate the simplest example of such a system, which is a pure dry friction model subjected to coloured Gaussian noise. The nite correlation time of the noise establishes an additional dimension in the phase space and gives rise to a non-vanishing probability current. Our investigation focuses on stick-slip transitions, which can be related to a critical value of the noise correlation time. Analytical insight is provided by applying the uni ed coloured noise approximation. Afterwards, we extend our previous model by adding viscous friction and a constant force. Then we perform a similar analysis as for the pure dry friction case. With parameter values close to the deterministic stick-slip transition, we observe a non-monotonic behaviour of the probability of sticking by increasing the correlation time of the noise. As the eigenvalue spectrum is not accessible for the systems with coloured noise, we consider the eigenvalue problem of a dry friction model with displacement, velocity and Gaussian white noise. By imposing periodic boundary conditions on the displacement and using a Fourier ansatz, we can derive an eigenvalue equation, which has a similar form in comparison to the known one-dimensional problem for the velocity only. The eigenvalue analysis is done for the case without a constant force and with a constant force separately. Finally, we conclude our ndings and provide an outlook on related open problems.Queen Mary University of London and the School of Mathematical Science

    Passively mobile communicating machines that use restricted space

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    We propose a new theoretical model for passively mobile Wireless Sensor Networks, called PM, standing for Passively mobile Machines. The main modification w.r.t. the Population Protocol model [Angluin et al. 2006] is that the agents now, instead of being automata, are Turing Machines. We provide general definitions for unbounded memories, but we are mainly interested in computations upper-bounded by plausible space limitations. However, we prove that our results hold for more general cases. We focus on complete interaction graphs and define the complexity classes PM-SPACE(f(n)) parametrically, consisting of all predicates that are stably computable by some PM protocol that uses O(f(n)) memory in each agent. We provide a protocol that generates unique identifiers from scratch only by using O(log n) memory, and use it to provide an exact characterization of the classes PMSPACE(f(n)) when f(n) = ő©(log n): they are precisely the classes of all symmetric predicates in NSPACE(nf(n)). As a consequence, we obtain a space hierarchy of the PM model when the memory bounds are ő©(log n). Finally, we establish that the minimal space requirement for the computation of non-semilinear predicates is O(log log n). ¬© 2011 ACM.FOM

    Differential cross section measurements for the production of a W boson in association with jets in proton‚Äďproton collisions at ‚ąös = 7 TeV

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    Measurements are reported of differential cross sections for the production of a W boson, which decays into a muon and a neutrino, in association with jets, as a function of several variables, including the transverse momenta (pT) and pseudorapidities of the four leading jets, the scalar sum of jet transverse momenta (HT), and the difference in azimuthal angle between the directions of each jet and the muon. The data sample of pp collisions at a centre-of-mass energy of 7 TeV was collected with the CMS detector at the LHC and corresponds to an integrated luminosity of 5.0 fb[superscript ‚ąí1]. The measured cross sections are compared to predictions from Monte Carlo generators, MadGraph + pythia and sherpa, and to next-to-leading-order calculations from BlackHat + sherpa. The differential cross sections are found to be in agreement with the predictions, apart from the pT distributions of the leading jets at high pT values, the distributions of the HT at high-HT and low jet multiplicity, and the distribution of the difference in azimuthal angle between the leading jet and the muon at low values.United States. Dept. of EnergyNational Science Foundation (U.S.)Alfred P. Sloan Foundatio

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