Validation analysis of mirror descent stochastic approximation method

The main goal of this paper is to develop accuracy estimates for stochastic programming problems by employing stochastic approximation (SA) type algorithms. To this end we show that while running a Mirror Descent Stochastic Approximation procedure one can compute, with a small additional effort, lower and upper statistical bounds for the optimal objective value. We demonstrate that for a certain class of convex stochastic programs these bounds are comparable in quality with similar bounds computed by the sample average approximation method, while their computational cost is considerably smaller.     

The influence of tributyl phosphate on molybdenum extraction with solutions of dibutyl phosphoric acid

Comparative investigations were carried out to study the influence of TBP on Mo extraction by HDBP solutions in xylene and TBP in xylene. The dependences of D_Mo on HNO₃ concentration for both HDBP and D2EHPA have minima at about 3 mol/L HNO₃. This shows similar extraction properties of HDBP and D2EHPA. The presence of TBP in the solvent results in the reduction of Mo extraction and in an increase in the formal slopes of the falling and rising parts of the logD_Mo — log[HNO₃] curve from −0.5 and +2 up to −2 and +4. Solvent loading curves with Mo show that in the absence of TBP a molybdenum solvate with two molecules of HDBP is formed at low acidity. Anomalous increase in the maximum solvent loading in the presence of TBP is caused by the ability of TBP to extract Mo from oversaturated low acidity solutions following the acidic mechanism. A molybdenum solvate with two HDBP molecules and one HNO₃ molecule is possibly formed at high acidity. A flowsheet for Mo recovery from HLW with HDBP-TBP solvent was tested in centrifugal contactors.     

Preparation of thorium concentrate from concentrated calcium chloride solutions

Extraction, washing, back extraction, and precipitation of Th(IV) from the backwash in the hydrochloric acid processing of perovskite are studied. Process conditions are optimized to obtain a concentrate with a ThO₂ content of about 85 wt %.     

A Study of Nanoparticle Aerosol Charging by Monte Carlo Simulations

A Direct Simulation Monte Carlo (DSMC) technique is applied for describing the dynamics of aerosol charging. The method is based on the transformation of known combination coefficients into charging probabilities. Changes in the particle charge distribution are computed as a stochastic game, calculating the time-step after each event. The simulations are validated by comparison with analytical solutions for unipolar aerosol diffusion charging and aerosol photocharging. The advantage of the DSMC method lies in the uncomplicated simulation of multi-dimensional systems that would result in very elaborate population balances. The DSMC method is used for simulation of the photocharging of moderately concentrated bicomponent polydisperse aerosols. By means of this method, the influence of the particle parameters (size, material) on the dynamics of the charge distribution in different size and material fractions has been studied. It is shown that charge separation between size or material fractions can be achieved for aerosol components with dissimilar work functions, while the total aerosol charge is zero.     

Generalized thermomechanics with dual internal variables

The formal structure of generalized continuum theories is recovered by means of the extension of canonical thermomechanics with dual weakly non-local internal variables. The canonical thermomechanics provides the best framework for such generalization. The Cosserat, micromorphic, and second gradient elasticity theory are considered as examples of the obtained formalization.     

Rippled area formed by surface plasmon polaritons upon femtosecond laser double-pulse irradiation of silicon: the role of carrier generation and relaxation processes

The formation of laser-induced periodic surface structures (LIPSS, ripples) upon irradiation of silicon with multiple irradiation sequences consisting of femtosecond laser pulse pairs (pulse duration 150 fs, central wavelength 800 nm) is studied numerically using a rate equation system along with a two-temperature model accounting for one- and two-photon absorption and subsequent carrier diffusion and Auger recombination processes. The temporal delay between the individual equal-energy fs-laser pulses was varied between 0 and ～4 ps for quantification of the transient carrier densities in the conduction band of the laser-excited silicon. The results of the numerical analysis reveal the importance of carrier generation and relaxation processes in fs-LIPSS formation on silicon and quantitatively explain the two time constants of the delay-dependent decrease of the low spatial frequency LIPSS (LSFL) area observed experimentally. The role of carrier generation, diffusion and recombination is quantified individually.     

Effect of current on magnetization oscillations in the ferromagnet-antiferromagnet junction

The effect of spin-polarized current on the steady-state magnetization and oscillations of antiferromagnet magnetization in a ferromagnetic-antiferromagnetic magnetic junction is analyzed. The macrospin approximation is generalized to describe antiferromagnets. The canted configuration of the antiferromagnet and the resultant magnetic moment are produced by the application of an external magnetic field. The resonance frequency, damping, and threshold current density corresponding to the emergence of instability are calculated. The possibility of generating weakly damped magnetization oscillations in the terahertz range is demonstrated. The effect of fluctuations on the canted configuration of the antiferromagnet is discussed.     

Thermodynamic approach to generalized continua

Governing equations of dissipative generalized solid mechanics are derived by thermodynamic methods in the Piola–Kirchhoff framework using the Liu procedure. The isotropic small-strain case is investigated in more detail. The connection to the Ginzburg–Landau type evolution, dual internal variables, and a thermodynamic generalization of the standard linear solid model of rheology is demonstrated. Specific examples are chosen to emphasize experimental confirmations and predictions beyond less general approaches.     

Decomposition Techniques for Bilinear Saddle Point Problems and Variational Inequalities with Affine Monotone Operators

The majority of first-order methods for large-scale convex–concave saddle point problems and variational inequalities with monotone operators are proximal algorithms. To make such an algorithm practical, the problem’s domain should be proximal-friendly—admit a strongly convex function with easy to minimize linear perturbations. As a by-product, this domain admits a computationally cheap linear minimization oracle (LMO) capable to minimize linear forms. There are, however, important situations where a cheap LMO indeed is available, but the problem domain is not proximal-friendly, which motivates search for algorithms based solely on LMO. For smooth convex minimization, there exists a classical algorithm using LMO—conditional gradient. In contrast, known to us similar techniques for other problems with convex structure (nonsmooth convex minimization, convex–concave saddle point problems, even as simple as bilinear ones, and variational inequalities with monotone operators, even as simple as affine) are quite recent and utilize common approach based on Fenchel-type representations of the associated objectives/vector fields. The goal of this paper was to develop alternative (and seemingly much simpler) decomposition techniques based on LMO for bilinear saddle point problems and for variational inequalities with affine monotone operators.