Thermal fluctuations and boundary conditions in the lattice Boltzmann method

The lattice Boltzmann method is a popular approach for simulating hydrodynamic interactions in soft matter and complex fluids. The solvent is represented on a discrete lattice whose nodes are populated by particle distributions that propagate on the discrete links between the nodes and undergo local collisions. On large length and time scales, the microdynamics leads to a hydrodynamic flow field that satisfies the Navier-Stokes equation. In this thesis, several extensions to the lattice Boltzmann method are developed. In complex fluids, for example suspensions, Brownian motion of the solutes is of paramount importance. However, it can not be simulated with the original lattice Boltzmann method because the dynamics is completely deterministic. It is possible, though, to introduce thermal fluctuations in order to reproduce the equations of fluctuating hydrodynamics. In this work, a generalized lattice gas model is used to systematically derive the fluctuating lattice Boltzmann equation from statistical mechanics principles. The stochastic part of the dynamics is interpreted as a Monte Carlo process, which is then required to satisfy the condition of detailed balance. This leads to an expression for the thermal fluctuations which implies that it is essential to thermalize all degrees of freedom of the system, including the kinetic modes. The new formalism guarantees that the fluctuating lattice Boltzmann equation is simultaneously consistent with both fluctuating hydrodynamics and statistical mechanics. This establishes a foundation for future extensions, such as the treatment of multi-phase and thermal flows. An important range of applications for the lattice Boltzmann method is formed by microfluidics. Fostered by the "lab-on-a-chip" paradigm, there is an increasing need for computer simulations which are able to complement the achievements of theory and experiment. Microfluidic systems are characterized by a large surface-to-volume ratio and, therefore, boundary conditions are of special relevance. On the microscale, the standard no-slip boundary condition used in hydrodynamics has to be replaced by a slip boundary condition. In this work, a boundary condition for lattice Boltzmann is constructed that allows the slip length to be tuned by a single model parameter. Furthermore, a conceptually new approach for constructing boundary conditions is explored, where the reduced symmetry at the boundary is explicitly incorporated into the lattice model. The lattice Boltzmann method is systematically extended to the reduced symmetry model. In the case of a Poiseuille flow in a plane channel, it is shown that a special choice of the collision operator is required to reproduce the correct flow profile. This systematic approach sheds light on the consequences of the reduced symmetry at the boundary and leads to a deeper understanding of boundary conditions in the lattice Boltzmann method. This can help to develop improved boundary conditions that lead to more accurate simulation results.

Observation of Associated Near-Side and Away-Side Long-Range Correlations in √sNN=5.02 TeV Proton-Lead Collisions with the ATLAS Detector

Two-particle correlations in relative azimuthal angle (Delta phi) and pseudorapidity (Delta eta) are measured in root S-NN = 5.02 TeV p + Pb collisions using the ATLAS detector at the LHC. The measurements are performed using approximately 1 mu b(-1) of data as a function of transverse momentum (p(T)) and the transverse energy (Sigma E-T(Pb)) summed over 3.1 < eta < 4.9 in the direction of the Pb beam. The correlation function, constructed from charged particles, exhibits a long-range (2 < vertical bar Delta eta vertical bar < 5) "near-side" (Delta phi similar to 0) correlation that grows rapidly with increasing Sigma E-T(Pb). A long-range "away-side" (Delta phi similar to pi) correlation, obtained by subtracting the expected contributions from recoiling dijets and other sources estimated using events with small Sigma E-T(Pb), is found to match the near-side correlation in magnitude, shape (in Delta eta and Delta phi) and Sigma E-T(Pb) dependence. The resultant Delta phi correlation is approximately symmetric about pi/2, and is consistent with a dominant cos2 Delta phi modulation for all Sigma E-T(Pb) ranges and particle p(T).

Evaluating the Effectiveness of a Commercial Portable Air Purifier in Homes with Wood Burning Stoves: A Preliminary Study

Wood burning for residential heating is prevalent in the Rocky Mountain regions of the United States. Studies have shown that wood stoves can be a significant source of PM2.5 within homes. In this study, the effectiveness of an electrostatic filter portable air purifier was evaluated (1) in a home where a wood stove was the sole heat source and (2) in a home where a wood stove was used as a supplemental heat source. Particle count concentrations in six particle sizes and particle mass concentrations in two particle sizes weremeasured for ten 12-hour purifier on and ten purifier off trials in each home. Particle count concentrations were reduced by 61–85 percent. Similar reductions were observed in particle mass concentrations. These findings, although limited to one season, suggest that a portable air purifier may effectively reduce indoor particulate matter concentrations associated with wood combustion during home heating.

Measurement of long-range pseudorapidity correlations and azimuthal harmonics in √s_NN=5.02 TeV proton-lead collisions with the ATLAS detector

Measurements of two-particle correlation functions and the first five azimuthal harmonics, v 1 to v 5 , are presented, using 28 nb −1 of p+Pb collisions at a nucleon-nucleon center-of-mass energy of √s NN=5.02 TeV measured with the ATLAS detector at the LHC. Significant long-range “ridgelike” correlations are observed for pairs with small relative azimuthal angle (|Δϕ|<π/3 ) and back-to-back pairs (|Δϕ|>2π/3 ) over the transverse momentum range 0.4

4 GeV. The v 2 (p T ) , v 3 (p T ) , and v 4 (p T ) are compared to the v n coefficients in Pb+Pb collisions at √s NN=2.76 TeV with similar event multiplicities. Reasonable agreement is observed after accounting for the difference in the average p T of particles produced in the two collision systems.

Survival analysis of longevity in siblings

Do siblings of centenarians tend to have longer life spans? To answer this question, life spans of 184 siblings for 42 centenarians have been evaluated. Two important questions have been addressed in analyzing the sibling data. First, a standard needs to be established, to which the life spans of 184 siblings are compared. In this report, an external reference population is constructed from the U.S. life tables. Its estimated mortality rates are treated as baseline hazards from which the relative mortality of the siblings are estimated. Second, the standard survival models which assume independent observations are invalid when correlation within family exists, underestimating the true variance. Methods that allow correlations are illustrated by three different methods. First, the cumulative relative excess mortality between siblings and their comparison group is calculated and used as an effective graphic tool, along with the Product Limit estimator of the survival function. The variance estimator of the cumulative relative excess mortality is adjusted for the potential within family correlation using Taylor linearization approach. Second, approaches that adjust for the inflated variance are examined. They are adjusted one-sample log-rank test using design effect originally proposed by Rao and Scott in the correlated binomial or Poisson distribution setting and the robust variance estimator derived from the log-likelihood function of a multiplicative model. Nether of these two approaches provide correlation estimate within families, but the comparison with the comparison with the standard remains valid under dependence. Last, using the frailty model concept, the multiplicative model, where the baseline hazards are known, is extended by adding a random frailty term that is based on the positive stable or the gamma distribution. Comparisons between the two frailty distributions are performed by simulation. Based on the results from various approaches, it is concluded that the siblings of centenarians had significant lower mortality rates as compared to their cohorts. The frailty models also indicate significant correlations between the life spans of the siblings. ^

Texture analyses of ODP Site 131-808 sediments

The microfabric of 11 mudrock specimens from ODP Site 808 (Nankai accretionary prism) was quantitatively analyzed using X-ray texture goniometry and optical petrography. The objectives of the study were to learn about rock strain and to detect a component of bulk lateral shortening in the deformation of the mudstones. Strain evaluation is based on the predictions of March theory, and on distortions of initially homogeneous marker particle distributions (the Fry technique). The main results are as follows. The specimens underwent a strain path of progressive flattening, which is closely related to loss of pore space by vertical loading. A component of bulk lateral shortening is detectable in the top 550 mbsf at Site 808, but compared with the amount of uniaxial vertical shortening, its relative magnitude is probably small. Moreover, it cannot be said with confidence whether this is caused by toe contraction of the accretionary wedge or by gravitationally induced downslope movement of the sediment pile. The mudstones examined were deposited in a marine environment with an oxic bottom water column. Micropore collapse is an important fabric building mechanism, but below 400 mbsf its effects are at least partly overridden by recrystallization of smectite. We conclude that mud microfabrics are not very precise deformation gauges, but can be used for rough estimations of strain.

(Table 2) Comparison of annual mass fluxes measured with shallower and deeper sediment traps off Cape Blanc (CB)

The ocean off NW Africa is the second most important coastal upwelling system with a total annual primary production of 0.33 Gt of carbon per year (Carr in Deep Sea Res II 49:59-80, 2002). Deep ocean organic carbon fluxes measured by sediment traps are also fairly high despite low biogenic opal fluxes. Due to a low supply of dissolved silicate from subsurface waters, the ocean off NW Africa is characterized by predominantly carbonate-secreting primary producers, i.e. coccolithophorids. These algae which are key primary producers since millions of years are found in organic- and chlorophyll-rich zooplankton fecal pellets, which sink rapidly through the water column within a few days. Particle flux studies in the Mauretanian upwelling area (Cape Blanc) confirm the hypothesis of Armstrong et al. (Deep Sea Res II 49:219-236, 2002) who proposed that ballast availability, e.g. of carbonate particles, is essential to predict deep ocean organic carbon fluxes. The role of dust as ballast mineral for organic carbon, however, must be also taken into consideration in the coastal settings off NW Africa. There, high settling rates of larger particles approach 400 m day**-1, which may be due to a particular composition of mineral ballast. An assessment of particle settling rates from opal-production systems in the Southern Ocean of the Atlantic Sector, in contrast, provides lower values, consistent with the assumptions of Francois et al. (Global Biogeochem Cycles 16(4):1087, 2002). Satellite chlorophyll distributions, particle distributions and fluxes in the water column off NW Africa as well as modelling studies suggest a significant lateral flux component and export of particles from coastal shelf waters into the open ocean. These transport processes have implications for paleo-reconstructions from sediment cores retrieved at continental margin settings.

Exploring the folding free energy surface of a three-helix bundle protein

The multidimensional free energy surface for a small fast folding helical protein is explored based on first-principle calculations. The model represents the 46-residue segment from fragment B of staphylococcal protein A. The relationship between collapse and tertiary structure formation, and the order of collapse and secondary structure formation, are investigated. We find that the initial collapse process gives rise to a transition state with about 30% of the native tertiary structure and 50–70% of the native helix content. We also observe two distinct distributions of native helix in this collapsed state (Rg ≈ 12 Å), one with about 20% of the native helical hydrogen bonds, the other with near 70%. The former corresponds to a local minimum. The barrier from this metastable state to the native state is about 2 kBT. In the latter case, folding is essentially a downhill process involving topological assembly. In addition, the order of formation of secondary structure among the three helices is examined. We observe cooperative formation of the secondary structure in helix I and helix II. Secondary structure in helix III starts to form following the formation of certain secondary structure in both helix I and helix II. Comparisons of our results with those from theory and experiment are made.

JMPIERCE: Stata module to perform Juhn-Murphy-Pierce decomposition

jmpierce computes the decomposition of differences between two outcome distributions introduced by Juhn, Murphy and Pierce (1993). Examples are the decomposition of changes in the income distribution over time, the decomposition of male-female wage differentials, or the decomposition of wage inequality differences between countries. This routine was previously circulated as jmp.

Studies in three phase gas-liquid-solid fluidised systems

The work is a logical continuation of research started at Aston some years ago when studies were conducted on fermentations in bubble columns. The present work highlights typical design and operating problems that could arise in such systems as waste water, chemical, biochemical and petroleum operations involving three-phase, gas-liquid-solid fluidisation; such systems are in increasing use. It is believed that this is one of few studies concerned with `true' three-phase, gas-liquid-solid fluidised systems, and that this work will contribute significantly to closing some of the gaps in knowledge in this area. The research work was mainly experimentally based and involved studies of the hydrodynamic parameters, phase holdups (gas and solid), particle mixing and segregation, and phase flow dynamics (flow regime and circulation patterns). The studies have focused particularly on the solid behaviour and the influence of properties of solids present on the above parameters in three-phase, gas-liquid-solid fluidised systems containing single particle components and those containing binary and ternary mixtures of particles. All particles were near spherical in shape and two particle sizes and total concentration levels were used. Experiments were carried out in two- and three-dimensional bubble columns. Quantitative results are presented in graphical form and are supported by qualitative results from visual studies which are also shown as schematic diagrams and in photographic form. Gas and solid holdup results are compared for air-water containing single, binary and ternary component particle mixtures. It should be noted that the criteria for selection of the materials used are very important if true three-phase fluidisation is to be achieved: this is very evident when comparing the results with those in the literature. The fluid flow and circulation patterns observed were assessed for validation of the generally accepted patterns, and the author believes that the present work provides more accurate insight into the modelling of liquid circulation in bubble columns. The characteristic bubbly flow at low gas velocity in a two-phase system is suppressed in the three-phase system. The degree of mixing within the system is found to be dependent on flow regime, liquid circulation and the ratio of solid phase physical properties. Evidence of strong `trade-off' of properties is shown; the overall solid holdup is believed to be a major parameter influencing the gas holdup structure.

Exotic meson decay widths using lattice quantum chromodynamics

Most experiments in particle physics are scattering experiments, the analysis of which leads to masses, scattering phases, decay widths and other properties of one or multi-particle systems. Until the advent of Lattice Quantum Chromodynamics (LQCD) it was difficult to compare experimental results on low energy hadron-hadron scattering processes to the predictions of QCD, the current theory of strong interactions. The reason being, at low energies the QCD coupling constant becomes large and the perturbation expansion for scattering; amplitudes does not converge. To overcome this, one puts the theory onto a lattice, imposes a momentum cutoff, and computes the integral numerically. For particle masses, predictions of LQCD agree with experiment, but the area of decay widths is largely unexplored. ^ LQCD provides ab initio access to unusual hadrons like exotic mesons that are predicted to contain real gluonic structure. To study decays of these type resonances the energy spectra of a two-particle decay state in a finite volume of dimension L can be related to the associated scattering phase shift δ(k) at momentum k through exact formulae derived by Lüscher. Because the spectra can be computed using numerical Monte Carlo techniques, the scattering phases can thus be determined using Lüscher's formulae, and the corresponding decay widths can be found by fitting Breit-Wigner functions. ^ Results of such a decay width calculation for an exotic hybrid( h) meson (JPC = 1-+) are presented for the decay channel h → πa 1. This calculation employed Lüscher's formulae and an approximation of LQCD called the quenched approximation. Energy spectra for the h and πa1 systems were extracted using eigenvalues of a correlation matrix, and the corresponding scattering phase shifts were determined for a discrete set of πa1 momenta. Although the number of phase shift data points was sparse, fits to a Breit-Wigner model were made, resulting in a decay width of about 60 MeV. ^

(Table 3) Interannual variability of total mass flux at the deep sediment trap site CBmeso between 1988 and 2006

This article will review major features of the 'giant' Cape Blanc filament off Mauritania with regard to the transport of chlorophyll and organic carbon from the shelf to the open ocean. Within the filament, chlorophyll is transported about 400 km offshore. Modelled particle distributions along a zonal transect at 21°N showed that particles with a sinking velocity of 5 m d**-1 are advected offshore by up to 600 km in subsurface particle clouds generally located between 400 m and 800 m water depth, forming an Intermediate Nepheloid Layer (INL). It corresponds to the depth of the oxygen minimum zone. Heavier particles with a sinking velocity of 30 m d**-1 are transported from the shelf within the Bottom Layer (BL) of more than 1000 m thickness, largely following the topography of the bottom slope. The particles advected within the BL contribute to the enhanced winter-spring mass fluxes collected at the open-ocean mesotrophic sediment trap site CB-13 (200 nm offshore), due to a long distance advection in deeper waters. The lateral contribution to the deep sediment trap in winter-spring is estimated to be 63% and 72% for organic carbon and total mass, respectively, whereas the lateral input for both components on an annual basis is estimated to be in the order of 15%. Biogenic opal increases almost fivefold from the upper to the lower mesotrophic CB-13 trap, also pointing to an additional source for biogenic silica from eutrophic coastal waters. Blooms obviously sink in smaller, probably mesoscale-sized patches with variable settling rates, depending on the type of aggregated particles and their ballast content. Generally, particle sinking rates are exceptionally high off NW Africa. Very high chlorophyll values and a large size of the Cape Blanc filament in 1998-1999 are also documented in enhanced total mass and organic carbon fluxes. An increasing trend in satellite chlorophyll concentrations and the size of the Cape Blanc filament between 1997 and 2008 as observed for other coastal upwelling areas is not documented.

Asymptotic scattering and duality in the one-dimensional three-state quantum Potts model on a lattice

We determine numerically the single-particle and the two-particle spectrum of the three-state quantum Potts model on a lattice by using the density matrix renormalization group method, and extract information on the asymptotic (small momentum) S-matrix of the quasiparticles. The low energy part of the finite size spectrum can be understood in terms of a simple effective model introduced in a previous work, and is consistent with an asymptotic S-matrix of an exchange form below a momentum scale p*. This scale appears to vanish faster than the Compton scale, mc, as one approaches the critical point, suggesting that a dangerously irrelevant operator may be responsible for the behaviour observed on the lattice.

Application of Mixture Models to Survival Data

Survival models are being widely applied to the engineering field to model time-to-event data once censored data is here a common issue. Using parametric models or not, for the case of heterogeneous data, they may not always represent a good fit. The present study relays on critical pumps survival data where traditional parametric regression might be improved in order to obtain better approaches. Considering censored data and using an empiric method to split the data into two subgroups to give the possibility to fit separated models to our censored data, we’ve mixture two distinct distributions according a mixture-models approach. We have concluded that it is a good method to fit data that does not fit to a usual parametric distribution and achieve reliable parameters. A constant cumulative hazard rate policy was used as well to check optimum inspection times using the obtained model from the mixture-model, which could be a plus when comparing with the actual maintenance policies to check whether changes should be introduced or not.

Accurate stratospheric particle size distributions from two separate flat-plate collection surfaces

Over the past two decades, flat-plate particle collections have revealed the presence of a remarkable variety of both terrestrial and extraterrestrial material in the stratosphere [1-6]. The ratio of terrestrial to extraterrestrial material and the nature of material collected may vary over observable time scales. Variations in particle number density can be important since the earth’s atmospheric radiation balance, and therefore the earth’s climate, can be influenced by articulate absorption and scattering of radiation from the sun and earth [7-9]. In order to assess the number density of solid particles in the stratosphere, we have examined a representative fraction of the so1id particles from two flat-plate collection surfaces, whose collection dates are separated in time by 5 years.