A stochastic programming approach for planning horizons of infinite horizon capacity planning problems

Planning horizon is a key issue in production planning. Different from previous approaches based on Markov Decision Processes, we study the planning horizon of capacity planning problems within the framework of stochastic programming. We first consider an infinite horizon stochastic capacity planning model involving a single resource, linear cost structure, and discrete distributions for general stochastic cost and demand data (non-Markovian and non-stationary). We give sufficient conditions for the existence of an optimal solution. Furthermore, we study the monotonicity property of the finite horizon approximation of the original problem. We show that, the optimal objective value and solution of the finite horizon approximation problem will converge to the optimal objective value and solution of the infinite horizon problem, when the time horizon goes to infinity. These convergence results, together with the integrality of decision variables, imply the existence of a planning horizon. We also develop a useful formula to calculate an upper bound on the planning horizon. Then by decomposition, we show the existence of a planning horizon for a class of very general stochastic capacity planning problems, which have complicated decision structure.     

Band structures of symmetrical graphene superlattice with cells of three regions

We study the electronic band structures of massless Dirac fermions in symmetrical graphene superlattice with cells of three regions. opening gaps and additional Dirac points. Finally, we inspect the potential effect on minibands, the anisotropy of group velocity and the energy bands contours near Dirac points. We also discuss the evolution of gap edges and cutoff region near the vertical Dirac points.     

Ab-initio calculations of structural,electronic,and optical properties of Zn_3(VO_4)_2

The structural, electronic, and optical properties of Zn_3(VO_4)_2 are investigated using full potential linearized augmented plane wave(FP-LAPW) method within the framework of density functional theory(DFT). Various approaches are adopted to treat the exchange and correlation potential energy such as generalized gradient approximation(GGA),GGA+U, and the Tran–Blaha modified Becke–Johnson(TB-mBJ) potential. The calculated band gap of 3.424 eV by TB-mBJ is found to be close to the experimental result(3.3 eV). The optical anisotropy is analyzed through optical constants,such as dielectric function and absorption coefficient along parallel and perpendicular crystal orientations. The absorption coefficient reveals high absorption(1.5 × 10~(6) cm~(-1)) of photons in the ultraviolet region.     

Statistics of reaction progress variable and mixture fraction gradients of a pulverised coal jet flame using Direct Numerical Simulation data

The statistical behaviour of the variances, covariance and gradients of the reaction progress variable (c), and the mixture fraction (ξ) have been analysed in a pulverised coal jet flame using a three-dimensional carrier phase direct numerical simulation (DNS) dataset. It has been observed that the Favre-probability density functions (PDFs) of c and ξ can be parametrised by the standard β function. Furthermore, the log-normal distribution has been found to accurately represent |?c| and |?ξ|. It is also found that ?c and ?ξ remain aligned throughout the flame brush. Finally the joint PDF of |?c| and |?ξ| has been compared with the product of the PDF of |?c| and PDF of |?ξ| extracted from carrier phase DNS, and it has been found that |?c| and |?ξ| are not statistically independent in the case investigated.The bivariate log-normal distributions with and without correlation have also been considered, and the former is found to be in better agreement with the carrier phase DNS data.     

Reduced-Order Modeling of Subsurface Multi-phase Flow Models Using Deep Residual Recurrent Neural Networks

Transport in Porous Media - We present a reduced-order modeling technique for subsurface multi-phase flow problems building on the recently introduced deep residual recurrent neural network...     

External Classical Field and Damping Effects on a Moving two Level atom in a Cavity Field Interaction with Kerr-like Medium

International Journal of Theoretical Physics - The interaction between a moving two-level atom and squeezed coherent states in the presence of Kerr like medium and an external classical field is...     

Ab initio and Monte Carlo studies of phase transitions and magnetic properties of YCrO3: Heisenberg model

By using the density functional theory (DFT) and Monte Carlo simulations (MCS) with the Heisenberg model, we have studied magnetic properties of the bulk perovskite YCrO₃. The exchange couplings of the Heisenberg model and the magnetic anisotropy are investigated. The 110 direction in the crystalline structure of the compound has shown the minimum energy, it is the easy magnetic direction. Using Monte Carlo simulations, the magnetizations behavior, the effects of system parameters and the critical exponents of the compound YCrO₃ are implemented. It is shown that the bulk perovskite YCrO₃ belongs to the 3D Heisenberg universality class.     

Synthesis,structural, spectroscopic,and thermal studies of some transition-metal complexes of a ligand containing the amino mercapto triazole moiety

A new series of transition-metal complexes of Schiff base ligand containing the amino mercapto triazole moiety ( HL ) was prepared. The Schiff base and its metal complexes were elucidated by different spectroscopic techniques (infrared [IR], ¹H nuclear magnetic resonance, UV–Visible, mass, and electron spin resonance [ESR]), and magnetic moment and thermal studies. Quantum chemical calculations have been carried out to study the structure of the ligand and some of its complexes. The IR spectra showed that the ligand is chelated with the metal ion in a neutral, tridentate, and bidentate manner using NOS and NO donors in complexes 1 – 6 , 10–12 , and 7 and 8 , respectively, whereas it behaves in a monobasic tridentate fashion using NOS donor sites in copper(II) nitrate complex ( 9 ). The magnetic moment and electronic spectra data revealed octahedral and square pyramidal geometries for complexes 2 , 11 , 12 , and 5 – 8 and 10 , respectively. However, the other complexes were found to have tetrahedral ( 4 ), trigonal bipyramidal ( 1 and 3 ), and square planar ( 9 ) structures. Thermal studies revealed that the chelates with different crystallized solvents undergo different types of interactions and the decomposition pathway ended with the formation of metal oxygen (MO) and metal sulfur (MS) as final products. The ESR spectrum of copper(II) complex 10 is axial in nature with hyperfine splitting with ²B_1g as a ground state. By contrast, complexes 7 and 8 undergo distortion around the Cu(II) center, affording rhombic ESR spectra. The HL ligand and some of its complexes were screened against two bacterial species. Data showed that complex 12 demonstrated a better antibacterial activity than HL ligand and other chelates.