Regularization of point vortices for the Euler equation in dimension two

In this paper, we construct stationary classical solutions of the incompressible Euler equation approximating singular stationary solutions of this equation. This procedure is carried out by constructing solutions to the following elliptic problem [ -\ep^2 \Delta u=(u-q-\frac{\kappa}{2\pi}\ln\frac{1}{\ep})_+^p, \quad & x\in\Omega, u=0, \quad & x\in\partial\Omega, ] where $p>1$, $\Omega\subset\mathbb{R}^2$ is a bounded domain, $q$ is a harmonic function. We showed that if $\Omega$ is simply-connected smooth domain, then for any given non-degenerate critical point of Kirchhoff-Routh function $\mathcal{W}(x_1,...,x_m)$ with the same strength $\kappa>0$, there is a stationary classical solution approximating stationary $m$ points vortex solution of incompressible Euler equations with vorticity $m\kappa$. Existence and asymptotic behavior of single point non-vanishing vortex solutions were studied by D. Smets and J. Van Schaftingen (2010).Comment: 32page

Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor

In this paper we provide a sufficient condition, in terms of only one of the nine entries of the gradient tensor, i.e., the Jacobian matrix of the velocity vector field, for the global regularity of strong solutions to the three-dimensional Navier-Stokes equations in the whole space, as well as for the case of periodic boundary conditions

The effect of the annealing temperature on the local distortion of La0.67_{0.67}Ca0.33_{0.33}MnO3_3 thin films

Mn $K$-edge fluorescence data are presented for thin film samples (3000~\AA) of Colossal Magnetoresistive (CMR) La$_{0.67}$Ca$_{0.33}$MnO$_3$: as-deposited, and post-annealed at 1000 K and 1200 K. The local distortion is analyzed in terms of three contributions: static, phonon, and an extra, temperature-dependent, polaron term. The polaron distortion is very small for the as-deposited sample and increases with the annealing temperature. In contrast, the static distortion in the samples decreases with the annealing temperature. Although the local structure of the as-deposited sample shows very little temperature dependence, the change in resistivity with temperature is the largest of these three thin film samples. The as-deposited sample also has the highest magnetoresistance (MR), which indicates some other mechanism may also contribute to the transport properties of CMR samples. We also discuss the relationship between local distortion and the magnetization of the sample.Comment: 11 pages of Preprint format, 8 figures in one tar fil

Brain functional and effective connectivity based on electroencephalography recordings: A review.

Functional connectivity and effective connectivity of the human brain, representing statistical dependence and directed information flow between cortical regions, significantly contribute to the study of the intrinsic brain network and its functional mechanism. Many recent studies on electroencephalography (EEG) have been focusing on modeling and estimating brain connectivity due to increasing evidence that it can help better understand various brain neurological conditions. However, there is a lack of a comprehensive updated review on studies of EEG-based brain connectivity, particularly on visualization options and associated machine learning applications, aiming to translate those techniques into useful clinical tools. This article reviews EEG-based functional and effective connectivity studies undertaken over the last few years, in terms of estimation, visualization, and applications associated with machine learning classifiers. Methods are explored and discussed from various dimensions, such as either linear or nonlinear, parametric or nonparametric, time-based, and frequency-based or time-frequency-based. Then it is followed by a novel review of brain connectivity visualization methods, grouped by Heat Map, data statistics, and Head Map, aiming to explore the variation of connectivity across different brain regions. Finally, the current challenges of related research and a roadmap for future related research are presented

Spin-triplet superconducting pairing due to local (Hund's rule, Dirac) exchange

We discuss general implications of the local spin-triplet pairing among fermions induced by local ferromagnetic exchange, example of which is the Hund's rule coupling. The quasiparticle energy and their wave function are determined for the three principal phases with the gap, which is momentum independent. We utilize the Bogolyubov-Nambu-De Gennes approach, which in the case of triplet pairing in the two-band case leads to the four-components wave function. Both gapless modes and those with an isotropic gap appear in the quasiparticle spectrum. A striking analogy with the Dirac equation is briefly explored. This type of pairing is relevant to relativistic fermions as well, since it reflects the fundamental discrete symmetry-particle interchange. A comparison with the local interband spin-singlet pairing is also made.Comment: 16 pages, LaTex, submitted to Phys. Rev.

Generalized quantum Fokker-Planck, diffusion and Smoluchowski equations with true probability distribution functions

Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using {\it true probability distribution functions} is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their co-ordinates and momenta we derive a generalized quantum Langevin equation in $c$-numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion and the Smoluchowski equations are the {\it exact} quantum analogues of their classical counterparts. The present work is {\it independent} of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (Smoluchowski equation being considered in the overdamped limit).Comment: RevTex, 16 pages, 7 figures, To appear in Physical Review E (minor revision

Stochastic generation of synthetic minutely irradiance time series derived from mean hourly weather observation data

Synthetic minutely irradiance time series are utilised in non-spatial solar energy system research simulations. It is necessary that they accurately capture irradiance fluctuations and variability inherent in the solar resource. This article describes a methodology to generate a synthetic minutely irradiance time series from widely available hourly weather observation data. The weather observation data are used to produce a set of Markov chains taking into account seasonal, diurnal, and pressure influences on transition probabilities of cloud cover. Cloud dynamics are based on a power-law probability distribution, from which cloud length and duration are derived. Atmospheric transmission losses are simulated with minutely variability, using atmospheric profiles from meteorological reanalysis data and cloud attenuation derived real-world observations. Both direct and diffuse irradiance are calculated, from which total irradiance is determined on an arbitrary plane. The method is applied to the city of Leeds, UK, and validated using independent hourly radiation measurements from the same site. Variability and ramp rate are validated using 1-min resolution irradiance data from the town of Cambourne, Cornwall, UK. The hourly irradiance frequency distribution correlates with R2=0.996 whilst the mean hourly irradiance correlates with R2=0.971, the daily variability indices cumulative probability distribution function (CDF), 1-min irradiance ramp rate CDF and 1-min irradiance frequency CDF are also shown to correlate with R2=0.9903, 1.000, and 0.9994 respectively. Kolmogorov-Smirnov tests on 1-min data for each day show that the ramp rate frequency of occurrence is captured with a high significance level of 99.99%, whilst the irradiance frequency distribution and minutely variability indices are captured at significances of 99% and 97.5% respectively. The use of multiple Markov chains and detailed consideration of the atmospheric losses are shown to be essential elements for the generation of realistic minutely irradiance time series over a typical meteorological year. A freely downloadable example of the model is made available and may be configured to the particular requirements of users or incorporated into other models

Associated charged Higgs and W boson production in the MSSM at the CERN Large Hadron Collider

We investigate the viability of observing charged Higgs bosons (H^+/-) produced in association with W bosons at the CERN Large Hadron Collider, using the leptonic decay H^+ -> tau^+ nu_tau and hadronic W-decay, within different scenarios of the Minimal Supersymmetric Standard Model (MSSM) with both real and complex parameters. Performing a parton level study we show how the irreducible Standard Model background from W+2 jets can be controlled by applying appropriate cuts and find that the size of a possible signal depends on the cuts needed to suppress QCD backgrounds and misidentifications. In the standard maximal mixing scenario of the MSSM we find a viable signal for large tan(beta) and intermediate H^+/- masses (~m_t) when using optimistic cuts whereas for more pessimistic ones we only find a viable signal for very large tan(beta) (>~50). We have also investigated a special class of MSSM scenarios with large mass-splittings among the heavy Higgs bosons where the cross-section can be resonantly enhanced by factors up to one hundred, with a strong dependence on the CP-violating phases. Even so we find that the signal after cuts remains small except for small masses (~< m_t) with optimistic cuts. Finally, in all the scenarios we have investigated we have only found small CP-asymmetries.Comment: 28 pages, 12 figures, version to appear in Euro. Phys. J.

Search for a W' boson decaying to a bottom quark and a top quark in pp collisions at sqrt(s) = 7 TeV

Results are presented from a search for a W' boson using a dataset corresponding to 5.0 inverse femtobarns of integrated luminosity collected during 2011 by the CMS experiment at the LHC in pp collisions at sqrt(s)=7 TeV. The W' boson is modeled as a heavy W boson, but different scenarios for the couplings to fermions are considered, involving both left-handed and right-handed chiral projections of the fermions, as well as an arbitrary mixture of the two. The search is performed in the decay channel W' to t b, leading to a final state signature with a single lepton (e, mu), missing transverse energy, and jets, at least one of which is tagged as a b-jet. A W' boson that couples to fermions with the same coupling constant as the W, but to the right-handed rather than left-handed chiral projections, is excluded for masses below 1.85 TeV at the 95% confidence level. For the first time using LHC data, constraints on the W' gauge coupling for a set of left- and right-handed coupling combinations have been placed. These results represent a significant improvement over previously published limits.Comment: Submitted to Physics Letters B. Replaced with version publishe

Knowledge network modelling to support decision-making for strategic intervention in IT project-oriented change management

This is the Accepted Manuscript version of an article published by Taylor & Francis in Journal of Decision Systems on 20 March 2014, available online: http://www.tandfonline.com/doi/abs/10.1080/12460125.2014.886499.This paper focuses on knowledge management to enhance decision support systems for strategic intervention in information technology (IT) project-oriented change management. It proposes a model of change management knowledge networks (CMKNM) to support decision by tackling three existing issues: insufficient knowledge traceability based on the relationships between knowledge elements and key factors, lack of procedural knowledge to provide adequate policies to guide changes, and lack of ‘lessons learned’ documentation in knowledge bases. A qualitative method was used to investigate issues surrounding knowledge mobilisation and knowledge networks. Empirical study was undertaken with industries to test the CMKNM. Results are presented from the empirical study on the key factors influencing knowledge mobilisation in IT project-oriented change management, knowledge networks and connections. The CMKNM model allows key knowledge mobilisation factors to be aligned with each other; it also defines the connections between knowledge networks allowing knowledge to be mobilised by tracing knowledge channels to support decision.Peer reviewe