Stochastic decomposition in production inventory with service time

We study an (s, S) production inventory system where the processing of inventory requires a positive random amount of time. As a consequence a queue of demands is formed. Demand process is assumed to be Poisson, duration of each service and time required to add an item to the inventory when the production is on, are independent, non-identically distributed exponential random variables. We assume that no customer joins the queue when the inventory level is zero. This assumption leads to an explicit product form solution for the steady state probability vector, using a simple approach. This is despite the fact that there is a strong correlation between the lead-time (the time required to add an item into the inventory) and the number of customers waiting in the system. The technique is: combine the steady state vector of the classical M/M/1 queue and the steady state vector of a production inventory system where the service is instantaneous and no backlogs are allowed. Using a similar technique, the expected length of a production cycle is also obtained explicitly. The optimal values of S and the production switching on level s have been studied for a cost function involving the steady state system performance measures. Since we have obtained explicit expressions for the performance measures, analytic expressions have been derived for calculating the optimal values of S and s.     

Approximating max-cut under graph-MSO constraints

We consider the max-cut and max-$k$-cut problems under graph-based constraints. Our approach can handle any constraint specified using monadic second-order (MSO) logic on graphs of constant treewidth. We give a $\frac{1}{2}$-approximation algorithm for this class of problems.     

Simpler analysis of LP extreme points for traveling salesman and survivable network design problems

We consider the Survivable Network Design Problem (SNDP) and the Symmetric Traveling Salesman Problem (STSP). We give simpler proofs of the existence of a -edge and 1-edge in any extreme point of the natural LP relaxations for the SNDP and STSP, respectively. We formulate a common generalization of both problems and show our results by a new counting argument. We also obtain a simpler proof of the existence of a -edge in any extreme point of the set-pair LP relaxation for the element connectivitySurvivable Network Design Problem ().     

Transient interactions between a premixed double flame and a vortex

The interaction between a laminar flame and a vortex is an important study for understanding the fundamentals of turbulent combustion. In the past, however, flame-vortex interactions have been investigated only for high-temperature flames. In this study, the impact of a vortex on a premixed double flame, which consists of a coupled cool flame and a hot flame, is examined experimentally and computationally using dimethyl ether/oxygen/ozone mixtures. The double flame is first shown to occur near the extinction limit of the hot flame. The differences between steady-state cool flames, double flames, and hot flames are explored in a one-dimensional counterflow configuration. The transient interactions between double flames and impinging vortices are then investigated experimentally using a micro-jet and numerically in two-dimensional transient modeling. It is seen that the vortex can extinguish the near-limit hot flame locally, resulting in a lone cool flame. At higher vortex intensities, the cool flame may also be extinguished after the extinction of the hot flame. It is found that there can be three different transient flame structures coexisting at the same time: an extinguished flame hole, a cool flame, and a double flame. Moreover, flame curvature is shown to play an important role in determining whether the vortex weakens or strengthens the cool flame and double flame.     

Multiscale modelling strategies and experimental insights for the solvation of cellulose and hemicellulose in ionic liquids

ABSTRACT

The present study investigates the dissolution behaviour of cellulose and hemicellulose in potential ionic liquids (ILs) using both the quantum chemical and experimental validation. For converging upon the recommended IL, 1428 ILs consisting of 42 cations and 34 anions were studied with the conductor like screening model for real solvents (COSMO-RS) model. Based on the infinite dilution activity coefficient of the components in IL, the selected anions and cations were visualised by observing their interactions with cellulose and hemicellulose using interaction energies, natural bonding orbital analysis and molecular dynamics simulations. The dissolution order of cellulose and hemicellulose in ILs was primarily determined by the evaluation of hydrogen bonds between the oxygen atom of anion and hydroxyl proton of cellulose/hemicellulose. From this discernible fact, the anion of the IL was observed to play a leading role in the solvation process as compared to the cation. Eventually, acetate [OAc]^– anion and 1-ethyl-3-methylimidazolium [EMIM]⁺ cation were found to be good candidates for the dissolution of cellulose and hemicellulose. This was further confirmed by the measurement of solid-liquid equilibria with cellulose and hemicellulose. The regenerated cellulose powder was then characterised by Fourier transform spectroscopy(FTIR), X-ray diffraction (XRD) and Thermal gravimetric analysis (TGA).     

Laser-excited luminescence and absorption study of mixed valence for K2Pt(CN)4—K2Pt(CN)6 crystals

Crystals of K₂Pt(CN)₆ doped with Pt(CN)^2?₄ show an absorption band at 337 nm which is assigned as a mixed-valence (MV) transition from Pt (II) to Pt(IV). From a Hush model analysis, the absorption band is interpreted to be class II in the Day—Robin scheme. When the MV band is laser excited at 337 nm, emmision is observed from Pt(CN)^2?₄ clusters.     

EPR studies of the hydroperoxy radical in x-irradiated single crystals of BaCl2·2H2O

Electron paramagnetic resonance studies of X-irradiated single crystals of BaCl₂-2H₂O have been made at room temperature. Four resonance lines are observed which can be grouped into two hyperfine doublets. Angular variation studies were made in the crystallographic ab, bc and ac planes. There are two magnetically equivalent but physically inequivalent magnetic complexes in the crystal lattice which are mutually perpendicular to each other. The paramagnetic species is identified as the hydroperoxy radical and a detailed discussion is made at the end.     

Specific ion adsorption and short-range interactions at the air aqueous solution interface

We have investigated the surface composition of alkali-halide aqueous solutions using grazing incidence x-ray fluorescence. Using mixtures of salts as a means to enhance the short-range effects, small differences in concentration over a few angstrom could be resolved, with, for example I- or Br- > Cl-. In order to explain our data, we need to include an effective potential accounting for the short-range (A) solvent mediated couplings, responsible for specific effects together with dispersion forces. This attractive potential (few k{B}T for halides) leads to concentration profiles which are in good agreement with recent numerical simulations.