Application of a thermodynamically compatible two‐phase flow model to the high‐resolution simulations of compressible gas–magma flow

This paper reports on the application and development of a fully hyperbolic and fully conservative two‐phase flow model for the simulation of gas and magma flow within volcanic processes. The model solves a set of mixture conservation equations for the gas and magma two‐phase flow with velocity non‐equilibrium. In this model, the effect of the relative velocity is introduced by a kinetic constitutive equation with other equations for volume and mass fractions of the gas phase. The model is examined numerically by the widely used finite volume Godunov methods of centered‐type. Using the Riemann problem, we numerically simulate wave propagation and the development of shocks and rarefactions in volcanic eruptions. These simulations are of magma fragmentation type where the relative velocity continues to dominate. A series of test cases whose solution contains features relevant to gas–magma mixtures are conducted. In particular, numerical results indicate that the model implementation predicts key features of the relative velocity within volcanic processes without any mathematical or physical simplifications. Simulation results are sharply and accurately provided without any spurious oscillations in all of the flow variables. The numerical methods and results are also compared with other numerical methods available in the literature. It is found that the provided resolutions are more accurate for the considered test cases. Copyright © 2014 John Wiley & Sons, Ltd.     

Delta Shock Wave Solution of the Riemann Problem for the Non-homogeneous Modified Chaplygin Gasdynamics

The motivation of the present study is to derive the solution of the Riemann problem for modified Chaplygin gas equations in the presence of constant external force. The analysis leads to the fact that in some special circumstances delta shock appears in the solution of the Riemann problem. Also, the Rankine–Hugoniot relations for delta shock wave which are utilized to determine the strength, position and propagation speed of the delta shocks have been derived. Delta shock wave solution to the Riemann problem for the modified Chaplygin gas equation is obtained. It is found that the external force term, appearing in the governing equations, influences the Riemann solution for the modified Chaplygin gas equation.

     

Critical and Critical Tangent Cones in Optimization Problems

In this paper the notion of critical tangent cone CT(x|Q) to Q at x is introduced for the case when Q is a convex subset of a normed space X. If Q is closed with nonempty interior, and x∈Q, the nonemptiness of the Dubovitskii–Milyutin set of second-order admissible variations, V(x,d|Q), is then characterized by the condition d∈CT(x|Q). Furthermore, the support function of V(x,d|Q) is shown to be evaluated in terms of that support function of Q. For the cases when Q is the set of continuous or L ^∞ selections of a certain set-valued map, the corresponding characterization of the cone CT(x|Q) and the formula for the support function of V(x,d|Q) are obtained in terms of more verifiable conditions.     

Simulation of Aggregation with Applications to Soot Laden Lubricating Fluids

The requirement for heavy duty diesel engines to reduce the level of NOx emissions has resulted in higher soot loading of engine lubricants due to fuel injection retardation and exhaust gas re‐circulation. An improved understanding of the process of soot aggregation and aggregate morphology is therefore required to provide an insight into the consequences of soot‐laden lubricants. These include the effects of dispersant architecture and soot loading rate on aggregate morphology. A 2D and 3D study using a semi‐quantitative random walk based simulation model into the evolution of simulated fractal‐like colloidal aggregates has been carried out and applied to address these issues. The effects of variable soot loading rates, which are engine dependent, are reported. The role of different interaction forces which are, among other things, engine temperature and lubricant formulation dependent is explored. Differences between the simulations run under the same conditions but in different dimensions are highlighted and their implications discussed. The data indicate that a correlation can be established between inter‐particle forces (represented via a sticking probability) and both aggregate morphology (represented by fractal dimension) and aggregate dispersancy and the degree of dispersion of those aggregates (measured by the mean empty space parameter). Significantly, a strong relationship was found between soot‐loading rate and aggregate morphology, with higher loading rates leading to both a much lower fractal dimension and a higher degree of aggregate dispersion, which in turn would lead to a higher lubricant viscosity.     

Exact Solution of the Time Fractional Variant Boussinesq-Burgers Equations

Applications of Mathematics - In the present article, we consider a nonlinear time fractional system of variant Boussinesq-Burgers equations. Using Lie group analysis, we derive the infinitesimal...     

Generalized hessian forC 1,1 functions in infinite dimensional normed spaces

The subject of this paper is the systematic study of second order notions concerning differentiable functions with Lipschitz derivative. The results and notions are motivated by recent papers of Cominetti, Correa and Hiriart-Urruty. The first goal of this paper is the comparison of several known second order directional derivatives. The second goal is the introduction of a generalized Hessian which is a set of certain symmetric bilinear forms. The relation of this generalized Hessian to other existing second order derivatives is also described. The research was supported by a grant from the National Science Foundation NSF-66-2270, which is gratefully acknowledged. Research supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. T-016846 and by the Humboldt Foundation.     

Sufficiency conditions with minimal regularity assumptions

The aim of this article is to provide second-order sufficiency criteria that extend known ones in [6] and [7] to the case where the control candidate and some of the data are merely essentially bounded, and/or the control setU is any convex subset of ^m . In the classical setting, where a restriction on the velocity is imposed , it is shown that whenU is compact the known strengthened Weierstrass condition is equivalent to the Weierstrass condition with strict inequality.The research was supported by an NSERC Grant and by GNAFA of CNR, which are gratefully acknowledged.     

A modified Hamilton-Jacobi approach in the generalized problem of Bolza

We are concerned with developing sufficiency criteria for the generalized problem of Bolza, where the Hamiltonian is neither concave-convex nor differentiable. The core of the approach is the modified Hamilton-Jacobi inequality which leads to a new type of sufficient conditions. This latter is then used to derive new first order and known second order sufficient conditions.The publication of this report has been made possible due to a grant of the Fonds FCAC for the help and support of research.     

Triplet acetylenes as synthetic equivalents of 1,2-bicarbenes, part II: new supramolecular scaffolds from photochemical cycloaddition of diarylacetylenes to 1,4-cyclohexadienes

1,5-Diaryl substituted homoquadricyclanes which are readily available through cascade photocycloaddition of diarylacetylenes to 1,4-cyclohexadienes are useful supramolecular scaffolds with an angle of about 60 degrees formed by the two aromatic rings defining a hydrophobic cavity. These structural features of pyridinyl homoquadricyclanes were applied to the design of composite organic/inorganic materials with topologies depending on the ratio of ligand to metal. The crystal structure of complex 1 (L1/AgNO(3) in a 1:1 ratio) shows an alternating ligand-metal polymer in which each of the silver ions in its linear coordination geometry is shared between two L1 molecules. A small change in the crystallization method yields a supramolecular rhomboid (complex 2, L1/AgNO(3) 3:2 ratio) which has two ligands that occupy opposite corners of the rhomboid and two silver atoms occupy the other two corners. Connection of the rhomboids units through a third molecule forms unique "beads on a string" polymeric chains. In complex 2, the silver ions adopt a distorted tetrahedral geometry with the nitrate anion occupying one of the vertices of the tetrahedron. The crystal packing of the chain of rhomboids generates cavities which are filled with disordered solvent molecules. Non-symmetrical homoquadricyclane L3 coordinates with silver only through the nitrogen of the pyridine ring but not through the nitrogen of the tetrafluoropyridine ring in which the electron density of the nitrogen lone-pair is very low. The substituents on the polycyclic moiety of the homoquadricyclane cause restricted rotation of the pyridine rings which suggests that the flexibility of such systems can be fine-tuned to create a family of supramolecular scaffolds of controlled rigidity.