The thermophysical properties of molten salts promising for the nuclear industry are crucial, but the available data are limited and contradictory. The thermal diffusivity of the molten mixtures (NaF-KF)eut–UF4 containing 30, 40, and 50 mol

In the paper, modifications of visualization algorithms for real-valued functions of two and three arguments given on a rectangular or parallelepipedal grid are considered. In the case of two arguments, the graph of the function is a surface embedded into the three-dimensional space. The majority of scientific visualization systems offer visualization procedures for such surfaces, but they construct them under the assumption that the functions are continuous. In the paper, for the case of a discontinuous function, a modification of this algorithm is proposed. In addition, the algorithm removes “plateaus” that occur after cutting the function at some level (in order to remove too large values). Visualization of a function of three arguments implies showing its level sets, that is, regions of the space of arguments where the magnitudes of the function do not exceed a certain value. In the case of a grid function, such sets are “voxel” sets, that is, they are composed of grid cells. With that, some smoothing of the surface of such sets is required, which is carried out by the Marching Cubes algorithm and algorithms of the Laplacian family. A modification of the Marching Cubes algorithm is proposed, which preserves the symmetry of the set surface with respect to the coordinate planes, axes, or some point, if the rendered set has such a symmetry.

The isobaric heat capacity of solid eutectic mixtures LiCl-KCl-CsCl, LiBr-CsBr and LiBr-KBr-CsBr was investigated from room temperature up to melting point. The molar heat capacity of all mixtures under study was found to be close to the additive sum of that of pure salts. The heat accumulated up to melting temperature is directly dependent on the melting point.

Although the thermal conductivity of molten salt mixtures is of interest for many potential technological applications, precise values are often hard to obtain. In this study, the thermal diffusivity of FliNaK was studied in a molten state using the laser flash method and found to be very slightly dependent on temperature. The heat capacity of FliNaK was measured using the DSC method. There was a minor difference between our results and data from the literature. From calculations based on thermal diffusivity, density and heat capacity values, thermal conductivity was shown to decrease with temperature.

The problem of creating a non-conflict aircraft queue from several incoming flows is considered in the situation of a cascade merge. In this case, groups of flows merge at their joining points, and further the resultant flows merge at some other points. Such a consideration covers, for example, an entire scheme of incoming aircraft flows of an airport zone, as well as taking into account the arriving and departing aircraft. This problem is formalized in the framework of mixed integer linear programming and is solved using the optimization library Gurobi. An approach is proposed to control the permutations of aircraft of the same type within one flow. A series of numerical simulations is carried out. They include both some model examples illustrating the ideas of the algorithm and statistical modeling to estimate the performance of the proposed procedure.

Nowadays, the problem of creating an optimal safe schedule for arrival of aircraft coming in several flows to a checkpoint, where these flows join into one, is very important for air-traffic management. Safety of the resultant queue is present if there is a safe interval between neighbor arrivals to the merge point. Change of an arrival instant of an aircraft is provided by changing its velocity and/or usage of fragments of the air-routes scheme, which elongate or shorten the aircraft path. Optimality of the resultant queue is considered from the point of some additional demands: minimization of the deviation of the actual aircraft arrival instant from the nominal one, minimization of order changes in the resultant queue in comparison with the original one, minimization of fuel expenditures, etc. The optimality criterion to be minimized, which reflects these demands, is often taken as a sum of penalties for deviations of the assigned arrival instants from the nominal ones. Each individual penalty is considered in almost all papers as either the absolute value of the difference between the assigned and nominal arrival instants or a similar function with asymmetric branches (which punishes delays and accelerations of an aircraft in different ways). The problem can be divided into two subproblems: one is a search for an optimal order of aircraft in the resultant queue, and the other is a search for optimal arrival instants for a given order. The second problem is quite simple since it can be formalized in the framework of linear programming and solved quite efficiently. However, the first one is very difficult and now is solved by various methods. The paper suggests sufficient conditions for the problem, which guarantee that the order of the optimal assigned instants is the same as the order of the nominal ones and, therefore, exclude the first subproblem.

The paper discusses the existence of the value function of a time-optimal differential game with lifeline in a quite general formulation. In such a game, the first player tries to lead the trajectory of the system to a terminal set as soon as possible avoiding the lifeline. The aim of the second player is to lead the trajectory to the lifeline or, if it is not possible, to keep it outside the terminal set, or, if the latter is impossible too, to postpone maximally reaching the terminal set.

The paper discusses a numerical grid method for solving time-optimal zero-sum differential games with lifeline. The dynamics of the considered games are supposed to be of a generic non-linear kind. The players’ controls are taken from given compact sets of finite-dimensional Euclidean spaces. The objective of the first player is to reach the target set as fast as possible, with that, avoiding the set called lifeline. The second player counteracts to that: it tries either to guide the system to the lifeline avoiding the target set of the first player, or if it is impossible, to keep the system away from the target set infinitely, or if it is impossible too, to postpone maximally reaching the target set. In the text, we reference out work about theoretical constructions on existence of the value function of such a game. Also, we set forth the idea of the numerical method. Results of solving some model and practical examples are given.

A characteristic of obtaining metal powders by direct current electrolysis is changes in the morphology of particles over the loose deposit layer thickness up to the formation of large spherulites. Deposits should be periodically removed from the cathode in order to obtain a powder with homogeneous composition. This paper justifies the choice of the parameter describing the change in loose deposit properties and proposes a method for determining the periodicity of its removal from the cathode. Loose zinc deposits were obtained at 25°C from zincate electrolyte containing 0.3 mol L–1 of ZnO and 4 mol L–1 of NaOH at a current setpoint exceeding six times the limiting diffusion current calculated using the smooth electrode. Electrode potential, deposit thickness and evolved hydrogen volume were measured directly in the process of electrolysis. Current redistribution between the metal reduction and hydrogen evolution leads to a change in the structure of loose deposit particles. It is shown that the differential current efficiency of zinc is the parameter describing the change in the loose zinc deposit density. Its value should not exceed 0.96, in order to ensure deposition of loose deposit with homogeneous properties. A further increase in current efficiency will lead to the formation of aggregates at the deposit growth front. It is proposed to determine the periodicity of loose deposit removal from the cathode using the empirical equation for the time dependency of differential current efficiency of zinc. The mathematical and statistical analysis of the data obtained in six replicates was carried out. The interval approach made it possible to significantly narrow the range of permissible differential current efficiency values and, as a consequence, to determine empirical equation coefficients with acceptable accuracy and calculate the growth time period of a deposit with homogeneous structure. The obtained approach can be used to estimate the time period of loose metal deposition accompanied by hydrogen evolution.

The paper deals with investigation of the important problem of processing the ophthalmic data on the post-operation status of patients. The groups of patients differ by the type (technology) of fixing the intraocular lenses (IOL). Validity of each type of technology is estimated by computation of criteria for distinction of data between groups. The initial information comprises measurements of several ophthalmic indices. The samples on each index are very short; in each index, as a rule, the samples of patients’ groups overlap each other; any probabilistic characteristics of the measuring indices are unknown; any probabilistic characteristics of the measuring errors are also unknown. So, the standard methods of mathematical statistics can be applied only in the formal way and have shown to be inefficient. In contrast, the Hausdorff distance (from the set theory) as the criterion of distinction between two samples (both for one- and, especially, for two-dimensional indices) demonstrated to be reliable to distinct the patient’s status. Computations of the Hausdorff distance are valid for any relative location of point sets under comparison.

Nowadays, aircraft move along routes consisting of horizontal tunnels and vertical flight levels. With that, the routes can split or join. At the point of route joining, a problem of aircraft flows merging appears. Such a problem is highly important near airports, where the air traffic is very dense. The main demand for aircraft flows merge is the presence of the minimal safe time interval between arrival instants at the merge point. There are two main tools for changing arrival instant of an aircraft to a checkpoint. The first of them is control of the aircraft velocity, which allows to obtain relatively small changes of the arrival instant both to earlier or later times. To get larger delays one uses the second tool, delay schemes. As a result of designing system of delay schemes for a certain airport, one has information about possible acceleration and deceleration of aircraft moving along each route. Further on the basis of this information, it is necessary to study capabilities of the constructed system for formation of safe aircraft flows merge. In the paper, a formalization is set forth for the problem of optimal formation of aircraft arrival schedule under the present delay scheme system as a finite-dimensional optimization problem. Also, the authors consider applicability of different methods for search of multivariable function extrema to this problem. Results of numerical computations are discussed.

The paper deals with application of numerical methods to processing the experimental data on the thermophysical properties of several chemical substances and their compounds (cryolites, rare earth compounds, and alkali halides). The main aim of investigations is in estimating the parameters of dependencies between the heat of fusion and the melting temperature of these chemical substances. The data are corrupted by the measuring errors. Procession is implemented under conditions of uncertainty: there is no any information on probabilistic properties of the corrupting factors, samples of measurements are short, and only approximate functions are known that describes mentioned dependencies. Under such conditions, the standard statistical methods can be applied formally. To obtain guarantied results in parameters estimation, the interval analysis methods and procedures are used.

Time-optimal differential games with a lifeline are considered. In such games, there are two sets of interest: the first player tries to guide the system into a target set as soon as possible, while the second player counteracts him and wins if the system reaches another set (called the lifeline). A numerical method for solving time-optimal games with a lifeline is suggested. With this method, the value function is designed as a viscosity solution to the corresponding boundary-value problem for the Hamilton–Jacobi equation. The convergence of the method is established.

Currently, methods for solving antagonistic differential games with geometric constraints for players’ controls are well developed. In the paper, these methods are used to construct a feedback robust control in situations when a geometric constraint is given a priori for the minimizing player’s control (the useful control) only and there is no any constraint for the disturbance. The suggested method of robust control is applied to a problem of aircraft landing under wind disturbances. Copyright c ©2006 IFAC

We consider time-optimal differential games with a lifeline. In such games, as usual, there is a terminal set to which the first player tries to guide the system as fast as possible, and there is also a set, called a lifeline, such that the second player wins when the system attains this set. The payoff is the result of applying Kruzhkov’s variable change to the time when the system reaches the terminal set. We also consider Hamilton-Jacobi equations corresponding to such games. The existence of a minimax solution of a boundary value problem for a Hamilton-Jacobi type equation is proved. For this, we introduce certain strong assumptions on the dynamics of the game near the boundary of the game domain. More exactly, the first and second players can direct the motion of the system to the terminal set and the lifeline, respectively, if the system is near the corresponding set. Under these assumptions, the value function is continuous in the game domain. The coincidence of the value function and the minimax solution of the boundary value problem is proved under the same assumptions.

Interval analysis procedures are used to estimate the parameters of an experimental chemical process under conditions of noise and uncertainty in the probabilistic characteristics of the measurement errors for a small measurement sample. Interval analysis makes it possible to describe exactly the set of admissible values of the estimated parameters needed for correct organization of the technological process through a correct choice of its parameters. Approximate estimates of the parameters are obtained by formal application of a statistical approach and it is shown that in this case the standard statistical approach yields essentially meaningless estimates for the parameters of the process studied here.

In practice, experimentalist obtains information on the investigated process under conditions of uncertainty of probabilistic characteristics of errors in measurements, the measurement sample is short, errors are supposed to be bounded (on modulus) by some approximate magnitude. So, the experimentalist is hampered in the choice of appropriate type of function for describing the process. Under such conditions, formal application of standard statistical methods (for example, the least squares mean) can give, as a rule, only point-wise estimates of the describing function. In contrast, approach on the basis of Interval Analysis allows one to estimate reliably the type of the process describing function on the basis of its information set of parameters.

This paper discusses time-optimal games with lifeline and corresponding boundary value problems for Hamilton–Jacobi equation as well. Existence of the value function for the time-optimal games with lifeline is proved. Existence of a minimax solution and its coincidence with the value function are shown.