A Diffusion-Based Analysis of a Multiclass Road Traffic Network

This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows based on conservation laws that incorporate the macroscopic fundamental diagram (a functional relationship between vehicle density and flow). Our setup is capable of handling multiple types of vehicle densities, with general macroscopic fundamental diagrams, on a network with arbitrary topology. Interpreting our system as a spatial population process, we derive, under natural scaling, fluid, and diffusion limits. More specifically, the vehicle density process can be approximated with a suitable Gaussian process, which yield accurate normal approximations to the joint (in the spatial and temporal sense) vehicle density process. The corresponding means and variances can be computed efficiently. Along the same lines, we develop an approximation to the vehicles’ travel time distribution between any given origin and destination pair. Finally, we present a series of numerical experiments that demonstrate the accuracy of the approximations and illustrate the usefulness of the results.

Neutralization of Industrial Water by Electrodialysis

The process of non-reagent adjustment of the pH of a NaCl solution (0.5 g/L) of different acidity was investigated by the method of bipolar electrodialysis on a device operating according to the K-system (concentration). The experiments were carried out in the range pH = 2.0–12.0 with monopolar cation-exchange MK-40 (for alkaline solutions) or anion-exchange MA-40 (for acidic solutions) and bipolar MB-2 membranes. The regularities of the change in the pH of the solution on the current density, process productivity and energy consumption for the neutralization process have been investigated. Revealed: with different productivity of the apparatus (Q = 0.5–1.5 m3/h), in the range of pH 3.0–11.0, with an increase in the current density, a neutral pH value is achieved. It has been shown that at pH above 11.0 and below 3.0, even at high current densities (i > 20 A/m2), its value cannot be changed. This is due to the neutralization of the H+ or OH− ions generated by the bipolar membrane by water ions, which are formed as a result of the dissociation of water molecules at the border of the monopolar membrane and the solution under conditions when the value of current exceeds the limiting value.

THE PROCESS OF SEDIMENTATION OF SOLID PARTICLES OF THE GRINDING SLUDGE

Thousands of tons of grinding slimes are formed every month at the mechanical engineering enterprises (especially at bearing plants) and metallurgy ones, which are processing metals. Slimes are practically not processed at present, but exported to special landfills or dumps, worsening the environment. Slimes of abrasive metal processing can be a raw material base for powder metallurgy, as they contain 60-80% of metal particles. It is necessary to carry out the solid particles separation by density process at the slimes washing stage to increase the homogeneity of metal powder, which is extracted from grinding slimes of abrasive metal processing. The fluid flow consumption through the vertical nozzles, which allow keeping solid particles in a suspended state, is determined in this work on the basis of theoretical studies of the solid particles deposition process of grinding slimes.

The study of dynamics for credit default risk by backward stochastic differential equation method

In this paper, we discuss the dynamics of credit default risk for bilateral collateralized credit valuation adjusted (BCCVA) for counterparty credit risk with two positive collateral accounts by assuming default times for both investor and counterparty satisfying the density hypothesis, and the contagion risk between them being reflected by the density process. We first split the price process into three key parts, and then describe the dynamics of each part by using backward stochastic differential equations (BSDEs). As applications, we introduce the “double” Cox model, in which the BSDEs have their specific forms and thus results in this paper generalize and improve corresponding theoretic results in the existing literature. We also would like to point out that, in this paper, we do not pay attention to explore how the introduction of default contagion impacts with true market data for the BCCVA predicted by for a model without contagion versus a model with contagion, but will plan to conduct the study on the impact for BCCVA with or without contagion in a separate research project.

Optimization and modelling using the response surface methodology (RSM) for ciprofloxacin removal by electrocoagulation

In this study, response surface methodology (RSM) was used to investigate the effects of different operating conditions on the removal of ciprofloxacin (CIP) by the electrocoagulation (EC) with pure iron electrodes. Box-Behnken design was used for the optimization of the EC process and to evaluate the effects and interactions of process variables such as applied current density, process time, initial CIP concentration and pH on the removal of CIP by the EC process. The optimum conditions for maximum CIP removal (86.6%) were found as pH = 4; Co = 5 mg.L1−; Id = 4.325 mA.cm2−; tprocess = 10 min. The model adequacy and the validity of the optimization step were confirmed with additional experiments which were performed under the proposed optimum conditions. The predicted CIP removal as 86.6% was achieved at each experiment by using the optimum conditions. These results specify that the RSM is a useful tool for optimizing the operational conditions for CIP removal by the EC process.

How did we get here?

Looking at a large branching population we determine along which path the population that started at 1 at time 0 ended up in B at time N. The result describes the density process, that is, population numbers divided by the initial number K (where K is assumed to be large). The model considered is that of a Galton-Watson process. It is found that in some cases population paths exhibit the strange feature that population numbers go down and then increase. This phenomenon requires further investigation. The technique uses large deviations, and the rate function based on Cramer's theorem is given. It also involves analysis of existence of solutions of a certain algebraic equation.

How did we get here?

Looking at a large branching population we determine along which path the population that started at 1 at time 0 ended up inBat timeN. The result describes the density process, that is, population numbers divided by the initial numberK(whereKis assumed to be large). The model considered is that of a Galton-Watson process. It is found that in some cases population paths exhibit the strange feature that population numbers go down and then increase. This phenomenon requires further investigation. The technique uses large deviations, and the rate function based on Cramer's theorem is given. It also involves analysis of existence of solutions of a certain algebraic equation.