Testing copositivity with the help of difference-of-convex optimization

We consider the problem of minimizing an indefinite quadratic form over the nonnegative orthant, or equivalently, the problem of deciding whether a symmetric matrix is copositive. We formulate the problem as a difference of convex functions problem. Using conjugate duality, we show that there is a one-to-one correspondence between their respective critical points and minima. We then apply a subgradient algorithm to approximate those critical points and obtain an efficient heuristic to verify non-copositivity of a matrix.     

A Gurson-type criterion for porous ductile solids containing arbitrary ellipsoidal voids—I: Limit-analysis of some representative cell

Gurson (1977)'s famous model of the behavior of porous ductile solids, initially developed for spherical cavities, was extended by Gologanu et al., 1993, Gologanu et al., 1994, Gologanu et al., 1997 to spheroidal, both prolate and oblate voids. The aim of this work is to further extend it to general (non-spheroidal) ellipsoidal cavities, through approximate homogenization of some representative elementary porous cell. As a first step, we perform in the present Part I a limit-analysis of such a cell, namely an ellipsoidal volume made of some rigid-ideal-plastic von Mises material and containing a confocal ellipsoidal void, loaded arbitrarily under conditions of homogeneous boundary strain rate. This analysis provides an estimate of the overall plastic dissipation based on a family of trial incompressible velocity fields recently discovered by Leblond and Gologanu (2008), satisfying conditions of homogeneous strain rate on all ellipsoids confocal with the void and the outer boundary. The asymptotic behavior of the integrand in the expression of the global plastic dissipation is studied both far from and close to the void. The results obtained suggest approximations leading to explicit approximate expressions of the overall dissipation and yield function. These expressions contain parameters the full determination of which will be the object of Part II.     

Evaluation of Energy Balance in a Batch and Circulating Non-thermal Plasma Reactors During Organic Pollutant Oxidation in Aqueous Solution

Plasma Chemistry and Plasma Processing - This work presents the treatment of an organic waste solution using gliding arc plasma in moist air, which is an excellent source of oxidizing species....     

A new strategy for the numerical modeling of a weld pool

Welding processes involve high temperatures and metallurgical and mechanical consequences that must be controlled. For this purpose, numerical simulations have been developed to study the effects of the process on the final structure. During the welding process, the material undergoes thermal cycles that can generate different physical phenomena, like phase changes, microstructure changes and residual stresses and distortions. But the accurate simulation of transient temperature distributions in the part needs to carefully take account of the fluid flow in the weld pool. The aim of this paper is thus to propose a new approach for such a simulation taking account of surface tension effects (including both the “curvature effect” and the “Marangoni effect”), buoyancy forces and free surface motion.The proposed approach is validated by two numerical tests from the literature: a sloshing test and a plate subjected to a static heat source. Then, the effects of the fluid flow on temperature distributions are discussed in a hybrid laser/arc welding example.     

Content and Isotope Ratios of Noble Gases in Congelation Ice of Lake Vostok

Isotope ratios of noble gases (He, Ne, Ar) were studied in samples collected by degassing of cores of water frozen over a glacier of Lake Vostok. The gases were collected into glass retorts during three days of degassing of cores, which have just been extracted from the borehole. Within the error, the isotope ³He/⁴He ratios of 0.28 ± 0.08 R_A (R_A = 1.38 × 10^–6 is the ratio for air) correspond to those from [1]. The ⁴He/²⁰Ne and ⁴⁰Ar/³⁶Ar ratios (12.4 ± 4.6 R_A and 1.0074 ± 0.0023 R_A, respectively) exceed their contents in air (⁴He/²⁰Ne_A = 0.29; ⁴⁰Ar/³⁶Ar_A = 298.6) and may indicate some contribution of terrigenous gas to the gaseous balance of the lake, as well as the high content of ancient ground waters in the lake. The ³He/⁴He ratio of 0.28 R_A means low mantle ³He flux typical of continental platforms far from active rift zones.     

Comparison of Differing Formulations of the PCM Model by their Application to the Simulation of an Auto-igniting H 2/air Jet

Different combustion models such as PCM (Presumed Conditional Moments) or ADF-PCM (Approximated Diffusion Flames Presumed Conditional Moments) can be used for RANS simulations of non premixed or partially premixed turbulent flames. In this paper, the auto-ignition experiment performed by Mastorakos and co-workers at Cambridge University is used as a validation case for comparing these two approaches. Furthermore, the first order PCM model is introduced to analyze the effects of the progress variable segregation and an improved version of ADF-PCM is developed with a pdf of the scalar dissipation rate. Compared to ADF-PCM models, the first and second order PCM models predict very sharp temperature and progress variable increase after ignition for all simulated cases. The segregation factors of the progress variable reach important values during the ignition for ADF-PCM models whereas for PCM, high values are reached at the beginning of the ignition.     

Electronic structure,physico-chemical,linear and non linear optical properties analysis of coronene, 6B-, 6N-, 3B3N- substituted C24H12 using RHF,B3LYP and wB97XD methods

In this work we have investigated the effects of substituting carbon atoms with B, N and BN on the electronic structure, physico-chemical, linear and non linear optical properties of Coronene (C24H12) using HF and DFT methods. We have calculated total electronic energy E₀, zero point vibrational energy ZPVE, the enthalpy H, entropy S, molar heat capacity at constant volume C_v, ionization potential IP, electron affinity EA, hardness \(\kappa\), softness \(\vartheta\), electronegativity EN, dipole moment µ, average polarizability \(< \alpha >\), anisotropy \(\Delta \alpha\), the first molecular hyperpolarizability β_mol, second order hyperpolarizability \(\gamma_{av}\), HOMO–LUMO Energy gap E_gap, work function E_F, refractive index n, susceptibility χ, dielectric constant ε and molar refractivity MR of coronene (C24H12), the 6B-, 6N- and 3B3N- substitute-doped C24H12 C18B6H12 C18N6H12 and C18B3N3H12. The E_gap values of the molecules are between 0.91 and 2.36 eV. We observed that β_mol changes slightly when C24H12 is doped with either 6B or 6N even though their β_mol values are too small. However, by doping C24H12 with both 3B and 3N, creating a strong donor–acceptor system, a very large increase in µ and β_mol was found for C18B3N3H12. This study was done using RHF, B3LYP and wB97XD methods with the cc-pVDZ basis set. The studies have shown that doping decreases some of the above properties significantly while some increases significantly compared to pure coronene, suggesting that 6B-, 6N-, and 3B3N-doped Coronene as serious candidates for electronics, optoelectronics and photonic devices.