Tighter αBB relaxations through a refi nement scheme for the scaled Gerschgorin theorem

Of central importance to the αBB algorithm is the calculation of the α values that guarantee the convexity of the underestimator. Improvement (reduction) of these values can result in tighter underestimators and thus increase the performance of the algorithm. For instance, it was shown by Wechsung et al. (J Glob Optim 58(3):429-438, 2014) that the emergence of the cluster effect can depend on the magnitude of the α values. Motivated by this, we present a refinement method that can improve (reduce) the magnitude of α values given by the scaled Gerschgorin method and thus create tighter convex underestimators for the αBB algorithm. We apply the new method and compare it with the scaled Gerschgorin on randomly generated interval symmetric matrices as well as interval Hessians taken from test functions. As a measure of comparison, we use the maximal separation distance between the original function and the underestimator. Based on the results obtained, we conclude that the proposed refinement method can significantly reduce the maximal separation distance when compared to the scaled Gerschgorin method. This approach therefore has the potential to improve the performance of the αBB algorithm

Distributed Reasoning in a Peer-to-Peer Setting: Application to the Semantic Web

In a peer-to-peer inference system, each peer can reason locally but can also solicit some of its acquaintances, which are peers sharing part of its vocabulary. In this paper, we consider peer-to-peer inference systems in which the local theory of each peer is a set of propositional clauses defined upon a local vocabulary. An important characteristic of peer-to-peer inference systems is that the global theory (the union of all peer theories) is not known (as opposed to partition-based reasoning systems). The main contribution of this paper is to provide the first consequence finding algorithm in a peer-to-peer setting: DeCA. It is anytime and computes consequences gradually from the solicited peer to peers that are more and more distant. We exhibit a sufficient condition on the acquaintance graph of the peer-to-peer inference system for guaranteeing the completeness of this algorithm. Another important contribution is to apply this general distributed reasoning setting to the setting of the Semantic Web through the Somewhere semantic peer-to-peer data management system. The last contribution of this paper is to provide an experimental analysis of the scalability of the peer-to-peer infrastructure that we propose, on large networks of 1000 peers

Accurate and efficient representation of intra­molecular energy in ab initio generation of crystal structures. II. Smoothed intramolecular potentials

The application of Crystal Structure Prediction (CSP) to industrially-relevant molecules requires the handling of increasingly large and flexible compounds. We present a revised model for the effect of molecular flexibility on the lattice energy that removes the discontinuities and non-differentiabilities present in earlier models (Sugden et al., 2016), with a view to improving the performance of CSP. The approach is based on the concept of computing a weighted average of local models, and has been implemented within the CrystalPredictor code. Through the comparative investigation of several compounds studied in earlier literature, we show that this new model results in large reductions in computational effort (of up to 65%) and in significant increases in reliability. The approach is further applied to investigate, for the first time, the computational polymorphic landscape of flufenamic acid for Z’=1 structures, resulting in the successful identification of all three experimentally resolved polymorphs within reasonable computational time

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

Predictive models for the phase behaviour and solution properties of weak electrolytes: nitric, sulfuric and carbonic acid

The distribution of ionic species in electrolyte systems is important in many fields of science and engineering, ranging from the study of degradation mechanisms to the design of systems for electrochemical energy storage. Often, other phenomena closely related to the ionic speciation, such as ion pairing, clustering and hydrogen bonding, which are difficult to investigate experimentally, are also of interest. Here, we develop an accurate molecular approach, accounting for reactions as well as association and ion pairing, to deliver a predictive framework that helps validate experiment and guides future modelling of speciation phenomena of weak electrolytes. We extend the SAFT-VRE Mie equation of state [D. K. Eriksen et al., Mol. Phys., 2016, 114, 2724–2749] to study aqueous solutions of nitric, sulphuric and carbonic acid, considering complete and partially dissociated models. In order to incorporate the dissociation equilibria, correlations to experimental data for the relevant thermodynamic equilibrium constants of the dissociation reactions are taken from the literature and are imposed as a boundary condition in the calculations. The models for water, the hydronium ion, and carbon dioxide are treated as transferable and are taken from our previous work. Here we present new molecular models for nitric acid, and the nitrate, bisulfate, sulfate, and bicarbonate anions. The resulting framework is used to predict a range of phase behaviour and solution properties of the aqueous acids over wide ranges of concentration and temperature, including the degree of dissociation, as well as the activity coefficients of the ionic species, and the activity of water and osmotic coefficient, density, and vapour pressure of the solutions. The SAFT-VRE Mie models obtained in this manner provide a means of elucidating the mechanisms of association and ion pairing in the systems studied, complementing the experimental observations reported in the literature

Systems thinking for the transition to zero pollution

Systems approaches are vital for coordinating decision-making in the face of complex issues because they provide the whole picture view needed to avoid negative unintended consequences and to generate genuine benefits. This paper explains how systems thinking can be used to address environmental pollution and support decision-makers in finding solutions

Toward a simulation approach for alkene ring-closing metathesis : scope and limitations of a model for RCM

A published model for revealing solvent effects on the ring-closing metathesis (RCM) reaction of di-Et diallylmalonate 7 has been evaluated over a wider range of conditions, to assess its suitability for new applications. Unfortunately, the model is too flexible and the published rate consts. do not agree with exptl. studies in the literature. However, by fixing the values of important rate consts. and restricting the concn. ranges studied, useful conclusions can be drawn about the relative rates of RCM of different substrates, precatalyst concn. can be simulated accurately and the effect of precatalyst loading can be anticipated. Progress has also been made toward applying the model to precatalyst evaluation, but further modifications to the model are necessary to achieve much broader aims

Compact relaxations for polynomial programming problems

Reduced RLT constraints are a special class of Reformulation- Linearization Technique (RLT) constraints. They apply to nonconvex (both continuous and mixed-integer) quadratic programming problems subject to systems of linear equality constraints. We present an extension to the general case of polynomial programming problems and discuss the derived convex relaxation. We then show how to perform rRLT constraint generation so as to reduce the number of inequality constraints in the relaxation, thereby making it more compact and faster to solve. We present some computational results validating our approach