An adaptive truncation criterion,for linesearch-based truncated Newton methods in large scale nonconvex optimization

Starting from the paper by Nash and Sofer (1990), we propose a heuristic adaptive truncation criterion for the inner iterations within linesearch-based truncated Newton methods. Our aim is to possibly avoid “over-solving” of the Newton equation, based on a comparison between the predicted reduction of the objective function and the actual reduction obtained. A numerical experience on unconstrained optimization problems highlights a satisfactory effectiveness and robustness of the adaptive criterion proposed, when a residual-based truncation criterion is selected.     

Completing orientations of partially oriented graphs

We initiate a general study of what we call orientation completion problems. For a fixed class of oriented graphs, the orientation completion problem asks whether a given partially oriented graph P can be completed to an oriented graph in by orienting the (nonoriented) edges in P. Orientation completion problems commonly generalize several existing problems including recognition of certain classes of graphs and digraphs as well as extending representations of certain geometrically representable graphs. We study orientation completion problems for various classes of oriented graphs, including k‐arc‐strong oriented graphs, k‐strong oriented graphs, quasi‐transitive‐oriented graphs, local tournaments, acyclic local tournaments, locally transitive tournaments, locally transitive local tournaments, in‐tournaments, and oriented graphs that have directed cycle factors. We show that the orientation completion problem for each of these classes is either polynomial time solvable or NP‐complete. We also show that some of the NP‐complete problems become polynomial time solvable when the input‐oriented graphs satisfy certain extra conditions. Our results imply that the representation extension problems for proper interval graphs and for proper circular arc graphs are polynomial time solvable. The latter generalizes a previous result.     

Wave diffraction from the Biconical Section in the semi-infinite conical region

The electromagnetic problem by the finite bicone, which is formed with the perfectly conducting semi-infinite cone and the finite cone with truncated vertex, is studied. Bicone is excited axial-symmetrically by the ring magnetic source. The diffracted field is represented through the series of the transversal magnetic (TM) modes; the lower mode among them is called the transversal electromagnetic wave (TEM). On the basis of this representation and using the mode matching technique, we derive the series equations to determine the unknown complex modes magnitudes. In view of the electric field singularities at the conical edges, these equations are represented in the form of the limiting transition from the finite sums to the series. We derive the rule of this transition, as well as the procedure for reducing them to the infinite system of linear algebraic equations (ISLAE) of the first kind. We study asymptotic properties of the matrix elements and find that the main part of their static limit and their behavior for large indexes form the matrix operator of the convolution type; the corresponding inverted operator in the analytical form is obtained. Both these operators, which we call the regularization operators, are used for the transition from the ISLAE of the first kind to the ISLAE of the second kind. The ISLAE thus obtained allow for the solution of any geometrical parameters and frequency with the given accuracy. The asymptotic properties of their solutions are analyzed, and the numerical examinations of the far field patterns are provided.     

Bayesian estimation of incompletely observed diffusions

We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete. We assume the drift and diffusion coefficient depend on an unknown parameter. A data-augmentation algorithm for drawing from the posterior distribution is presented which is based on simulating diffusion bridges conditional on a noisy incomplete observation at an intermediate time. The dynamics of such filtered bridges are derived and it is shown how these can be simulated using a generalised version of the guided proposals introduced in Schauer, Van der Meulen and Van Zanten (2017, Bernoulli 23(4A)).     

Sensitive Parameter Predicting Steady-State Pressure Difference of Partially Crosslinked Polyacrylamide Suspension in Core Flow Experiments

Using artificial cores, six different partially crosslinked polyacrylamide (PCPAM) suspensions were used for sandpacked core flow experiments; the results indicated that the migration of the PCPAM particles through porous media was a process of plugging and flooding at the same time. A theoretical model was proposed and the sensitive parameter, G′, was determined by rheological oscillation measurements with a 200 μm plate gap. In addition, the validity of the proposed theoretical model was verified by the results of the core flow experiments and a fitting equation of ΔP ₁ with G′ was obtained which can be used for quantifying the steady-state pressure of PCPAM suspensions flowing through porous media in the core flow experiments.     

Homogenisation and spectral convergence of a periodic elastic composite with weakly compressible inclusions

A two-phase elastic composite with weakly compressible elastic inclusions is considered. The homogenised two-scale limit problem is found, via a version of the method of two-scale convergence, and analysed. The microscopic part of the two-scale limit is found to solve a Stokes type problem and shown to have no microscopic oscillations when the composite is subjected to body forces that are microscopically irrotational. The composites spectrum is analysed and shown to converge, in an appropriate sense, to the spectrum of the two-scale limit problem. A characterisation of the two-scale limit spectrum is given in terms of the limit macroscopic and microscopic behaviours.     

Triple flame: Inherent asymmetries and pentasectional character

A two-dimensional triple-flame numerical model of a laminar combustion process reflects flame asymmetric structural features that other analytical models do not generate. It reveals the pentasectional character of the triple flame, composed of the central pure diffusion-flame branch and the fuel-rich and fuel-lean branches, each of which is divided into two sections: a near-stoichiometric section and a previously unreported near-flammability-limits section with combined diffusion and premixed character. Results include propagation velocity, fuel and oxidiser mass fractions, temperature and reaction rates. Realistic stoichiometric ratios and reaction orders match experimental planar flame characteristics. Constant density, a one-step reaction, and a mixture fraction gradient at the inlet as the simulation parameter are imposed. The upstream equivalence ratio or the upstream reactant mass fractions are linear or hyperbolic functions of the transverse coordinate. The use here of experimental kinetics data differs from previous analytical works and results in flame asymmetry and different flammability limits. Upstream mixture composition gradient affects propagation velocity, flame curvature, diffusion flame reaction rate, and flammability limits. Flammability limits extend beyond those of a planar flame due to transverse heat and mass diffusion causing the pentasectional character.     

Multidimensional chemistry coordinate mapping approach for combustion modelling with finite-rate chemistry

A multidimensional chemistry coordinate mapping (CCM) approach is presented for efficient integration of chemical kinetics in numerical simulations of turbulent reactive flows. In CCM the flow transport is integrated in the computational cells in physical space, whereas the integration chemical reactions are carried out in a phase space made up of a few principal variables. Each cell in the phase space corresponds to several computational cells in the physical space, resulting in a speedup of the numerical integration. In reactive flows with small hydrocarbon fuels two principal variables have been shown to be satisfactory to construct the phase space. The two principal variables are the temperature (T) and the specific element mass ratio of the H atom (J _H). A third principal variable, σ=?J _H·?J _H, which is related to the dissipation rate of J _H, is required to construct the phase space for combustion processes with an initially non-premixed mixture. For complex higher hydrocarbon fuels, e.g. n-heptane, care has to be taken in selecting the phase space in order to model the low-temperature chemistry and ignition process. In this article, a multidimensional CCM algorithm is described for a systematic selection of the principal variables. The method is evaluated by simulating a laminar partially remixed pre-vaporised n-heptane jet ignition process. The CCM approach is then extended to simulate n-heptane spray combustion by coupling the CCM and Reynolds averaged Navier–Stokes (RANS) code. It is shown that the computational time for the integration of chemical reactions can be reduced to only 3–7%, while the result from the CCM method is identical to that of direct integration of the chemistry in the computational cells.