Wavenumber-explicit analysis for the Helmholtz h-BEM: error estimates and iteration counts for the Dirichlet problem

We consider solving the exterior Dirichlet problem for the Helmholtz equation with the h-version of the boundary element method (BEM) using the standard second-kind combined-field integral equations. We prove a new, sharp bound on how the number of GMRES iterations must grow with the wavenumber k to have the error in the iterative solution bounded independently of k as k→∞ when the boundary of the obstacle is analytic and has strictly positive curvature. To our knowledge, this result is the first-ever sharp bound on how the number of GMRES iterations depends on the wavenumber for an integral equation used to solve a scattering problem. We also prove new bounds on how h must decrease with k to maintain k-independent quasi-optimality of the Galerkin solutions as k→∞ when the obstacle is nontrapping

A corresponding-states framework for the description of the Mie family of intermolecular potentials

The Mie (λr, λa) intermolecular pair potential has been suggested as an alternative to the traditional Lennard–Jones (12–6) potential for modelling real systems both via simulation and theory as its implementation leads to an accuracy and flexibility in the determination of thermophysical properties that cannot be obtained when potentials of fixed range are considered. An additional advantage of using variable-range potentials is noted in the development of coarse-grained models where, as the superatoms become larger, the effective potentials are seen to become softer. However, the larger number of parameters that characterise the Mie potential (λr, λa, σ, ϵ) can hinder a rational study of the particular effects that each individual parameter have on the observed thermodynamic properties and phase equilibria, and higher degeneracy of models is observed. Here a three-parameter corresponding states model is presented in which a cohesive third parameter α is proposed following a perturbation expansion and assuming a mean-field limit. It is shown that in this approximation the free energy of any two Mie systems sharing the same value of α will be the same. The parameter α is an explicit function of the repulsive and attractive exponents and consequently dictates the form of the intermolecular pair potential. Molecular dynamics simulations of a variety of Mie systems over a range of values of α are carried out and the solid–liquid, liquid–vapour and vapour–solid phase boundaries for the systems considered are presented. Using the simulation data, we confirm that systems of the same α exhibit conformal phase behaviour for the fluid-phase properties as well as for the solid–fluid boundary, although larger differences are noted in the solid region; these can be related to the approximations in the definition of the parameter. Furthermore, it is found that the temperature range over which the vapour–liquid envelope of a given Mie system is stable follows a linear dependency with α when expressed as the ratio of the critical–point temperature to the triple–point temperature. The limit where potentials of the Mie family will not present a stable fluid envelope is predicted in terms of the parameter α and the result is found to be in excellent agreement with previous studies. This unique relation between the fluid range and the cohesive parameter α is shown to be useful to limit the pairs of Mie exponents that can be used in coarse-grained potentials to treat real systems in order to obtain temperature ranges of stability for the fluid envelope consistent with experiment

Group contribution methodology based on the statistical associating fluid theory for heteronuclear molecules formed from Mie segments

A generalization of the recent version of the statistical associating fluid theory for variable range Mie potentials [Lafitte et al., J. Chem. Phys. 139, 154504 (2013)] is formulated within the framework of a group contribution approach (SAFT-γ Mie). Molecules are represented as comprising distinct functional (chemical) groups based on a fused heteronuclear molecular model, where the interactions between segments are described with the Mie (generalized Lennard-Jonesium) potential of variable attractive and repulsive range. A key feature of the new theory is the accurate description of the monomeric group-group interactions by application of a high-temperature perturbation expansion up to third order. The capabilities of the SAFT-γ Mie approach are exemplified by studying the thermodynamic properties of two chemical families, the n-alkanes and the n-alkyl esters, by developing parameters for the methyl, methylene, and carboxylate functional groups (CH3, CH2, and COO). The approach is shown to describe accurately the fluid-phase behavior of the compounds considered with absolute average deviations of 1.20% and 0.42% for the vapor pressure and saturated liquid density, respectively, which represents a clear improvement over other existing SAFT-based group contribution approaches. The use of Mie potentials to describe the group-group interaction is shown to allow accurate simultaneous descriptions of the fluid-phase behavior and second-order thermodynamic derivative properties of the pure fluids based on a single set of group parameters. Furthermore, the application of the perturbation expansion to third order for the description of the reference monomeric fluid improves the predictions of the theory for the fluid-phase behavior of pure components in the near-critical region. The predictive capabilities of the approach stem from its formulation within a group-contribution formalism: predictions of the fluid-phase behavior and thermodynamic derivative properties of compounds not included in the development of group parameters are demonstrated. The performance of the theory is also critically assessed with predictions of the fluid-phase behavior (vapor-liquid and liquid-liquid equilibria) and excess thermodynamic properties of a variety of binary mixtures, including polymer solutions, where very good agreement with the experimental data is seen, without the need for adjustable mixture parameters

Aspects of asphaltene aggregation obtained from coarse-grained molecular modeling

We have performed a molecular-simulation-based study to explore some of the underlying mechanisms of asphaltene aggregation. The daunting complexity of the crude oil + asphaltene system precludes any type of meaningful molecular simulation unless some assumptions are made with respect to the key physical and chemical properties that must be explicitly described. In the present work, we focus on molecular simulations of a coarse-grained model of asphaltene molecules in pure solvents, which are based on the assumption that the general size asymmetry and asphaltene morphology play a key role in the aggregation process. We use simple single isotropic Lennard-Jones sites to represent paraffinic and aromatic C₆ segments, which are used as building blocks for the description of continental asphaltene models and solvent moieties. The energy and size parameters for the intermolecular models (ε and σ) for solute and solvent molecules are chosen to reproduce the experimental density of the liquid phase for different mixtures. An explicit pure solvent is considered, and the relationship between the aggregation mechanism and the solvent nature is investigated through direct simulation of the aggregation process. The results reproduce accurately expected trends observed for more-complex models as well as experiments, for example, strong aggregation of asphaltene molecules in <i>n-</i>heptane and high solubility in toluene. Different asphaltene models based on different geometries reveal that even at this level of simplification the topology of the molecules (number and position of aliphatic branches) does affect the way molecules aggregate

Deep Inelastic Scattering in Conformal QCD

We consider the Regge limit of a CFT correlation function of two vector and two scalar operators, as appropriate to study small-x deep inelastic scattering in N=4 SYM or in QCD assuming approximate conformal symmetry. After clarifying the nature of the Regge limit for a CFT correlator, we use its conformal partial wave expansion to obtain an impact parameter representation encoding the exchange of a spin j Reggeon for any value of the coupling constant. The CFT impact parameter space is the three-dimensional hyperbolic space H3, which is the impact parameter space for high energy scattering in the dual AdS space. We determine the small-x structure functions associated to the exchange of a Reggeon. We discuss unitarization from the point of view of scattering in AdS and comment on the validity of the eikonal approximation. We then focus on the weak coupling limit of the theory where the amplitude is dominated by the exchange of the BFKL pomeron. Conformal invariance fixes the form of the vector impact factor and its decomposition in transverse spin 0 and spin 2 components. Our formalism reproduces exactly the general results predict by the Regge theory, both for a scalar target and for gamma*-gamma* scattering. We compute current impact factors for the specific examples of N=4 SYM and QCD, obtaining very simple results. In the case of the R-current of N=4 SYM, we show that the transverse spin 2 component vanishes. We conjecture that the impact factors of all chiral primary operators of N=4 SYM only have components with 0 transverse spin.Comment: 44+16 pages, 7 figures. Some correction

Burden of visceral leishmaniasis in villages of eastern gedaref state, Sudan: an exhaustive cross-sectional survey.

Since December 2009, Médecins Sans Frontières has diagnosed and treated patients with visceral leishmaniasis (VL) in Tabarak Allah Hospital, eastern Gedaref State, one of the main endemic foci of VL in Sudan. A survey was conducted to estimate the VL incidence in villages around Tabarak Allah

The Regge Limit for Green Functions in Conformal Field Theory

We define a Regge limit for off-shell Green functions in quantum field theory, and study it in the particular case of conformal field theories (CFT). Our limit differs from that defined in arXiv:0801.3002, the latter being only a particular corner of the Regge regime. By studying the limit for free CFTs, we are able to reproduce the Low-Nussinov, BFKL approach to the pomeron at weak coupling. The dominance of Feynman graphs where only two high momentum lines are exchanged in the t-channel, follows simply from the free field analysis. We can then define the BFKL kernel in terms of the two point function of a simple light-like bilocal operator. We also include a brief discussion of the gravity dual predictions for the Regge limit at strong coupling.Comment: 23 pages 2 figures, v2: Clarification of relation of the Regge limit defined here and previous work in CFT. Clarification of causal orderings in the limit. References adde