Invasive weed optimization for model order reduction of linear MIMO systems

In this work, a model order reduction (MOR) technique for a linear multivariable system is proposed using invasive weed optimization (IWO). This technique is applied with the combined advantages of retaining the dominant poles and the error minimization. The state space matrices of the reduced order system are chosen such that the dominant eigenvalues of the full order system are unchanged. The other system parameters are chosen using the invasive weed optimization with objective function to minimize the mean squared errors between the outputs of the full order system and the outputs of the reduced order model when the inputs are unit step. The proposed algorithm has been applied successfully, a 10th order Multiple-Input–Multiple-Output (MIMO) linear model for a practical power system was reduced to a 3rd order and compared with recently published work.     

Tailored coordination nanoparticles: assessing the magnetic single-domain critical size

Negatively charged nanocrystals of the magnetic coordination network CsNiCr(CN)(6) were prepared in water through a seed-mediated growth with a few atomic layers accuracy and final sizes tailored from 6 to 30 nm. A lower limit of the magnetic single-domain critical size was determined to be around 15 nm possessing a blocking temperature above 20 K.     

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.     

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.     

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.