Energy function for Ω-stable flows without limit cycles on surfaces

The paper is devoted to the study of the class of Ω-stable flows without limit cycles on surfaces, i.e. flows on surfaces with non-wandering set consisting of a finite number of hyperbolic fixed points. This class is a generalization of the class of gradient-like flows, differing by forbiddance of saddle points connected by separatrices. The results of the work are the proof of the existence of a Morse energy function for any flow from the considered class and the construction of such a function for an arbitrary flow of the class. Since the results are a generalization of the corresponding results of K. Meyer for Morse-Smale flows and, in particular, for gradient-like flows, the methods for constructing the energy function for the case of this article are a further development of the methods used by K. Meyer, taking in sense the specifics of Ω-stable flows having a more complex structure than gradient-like flows due to the presence of the so-called "chains" of saddle points connected by their separatrices.

ON THE HAMILTONIAN REDUCTION OF THE ASSOCIATIVITY EQUATIONS IN THE CASE OF FOUR PRIMARY FIELDS

The associativity equations arose in the papers of Witten (Witten, 1990) and Dijkgraaf, Verlinde, (Dijkgraaf et al., 1991) on two-dimensional topological field theories and subsequently they became to play a key role in many other important domains of mathematics and mathematical physics: in quantum cohomology, Gromov–Witten invariants, enumerative geometry, theory of submanifolds and so on. In Mokhov’s papers (Mokhov, 1984), (Mokhov, 1987) a general fundamental principle stating a canonical Hamiltonian property for the restriction of an arbitrary flow on the set of stationary points of its nondegenerate integral was proposed and proved. In this paper the Hamiltonians of the reductions of the associativity equations with antidiagonal matrix ηij in the case of four primary fields according to Mokhov`s construction is found in an explicit form.

Computational Investigation of Flow Over Geometry Compliant Lattice Structures

With the increasing prevalence of additive manufacturing, geometries that would not have been possible to manufacture just a few years ago are becoming a reality. One example is the ability to create pipes with integral, geometry compliant lattice structures. These compliant lattice structures offer the potential to greatly enhance heat transfer in arbitrary flow passages. This preliminary paper will focus on the development of an isothermal simulation model in OpenFOAM, to model the nature of the flow for a single unit cell, a unit cell screen, and a series of unit cell screens. Honeywell FM&T is a contractor of the U.S. Government under Contract No. DE-NA0002839.

ANALYTICALLY APPROACH OF A COST FUNCTION TO OPTIMIZE AND ESTIMATE OF EFFICIENCE FOR RADIO- AND ELECTRONIC SYSTEMS

The problem of extending the scope of practical application of the methods of the theory of statistical solutions to problems arising in the design and operation of radio electronic systems is reviewed. Existing methods are applied in advanced systems in a very limited scope. Among the variety of problems causing such limitations the most significant one is a lack of loss functions that could be adequate for practical tasks and the same time, suitable for analytical calculations. Using the example of information-control systems designed for defense purposes and with allowance for the physical specifics of their operation, the structure of the loss function suitable for use in analytical constructions of the theory of statistical solutions and reflecting the physical specifics of the most important applications is proposed. An analytical model of damage in a single-purpose and multi-purpose situation is proposed. A multiplicative model and resulting additive model of damage from many targets are reviewed. A generalization was made for a environment featured by random number and values of target parameters-a random flow of targets. A simple analytical expression for a posteriori average risk is obtained, such risk been defined as a measure of the average expected damage from an arbitrary flow of targets. A model of counteraction with the aim of reducing damage is reviewed. Analytical expressions for the average risk and the value of prevented damage and their dependence on the parameters of counteraction have been obtained, and inter alia, in the presence of a flow of targets. A number of examples have been reviewed that show a possibility for splitting a complex multidimensional problem into parallel problems of a limited dimension, for simultaneous resolution of the problem of optimal detection, measurement and counteraction. Also, additional possibilities are opened for optimizing requirements to characteristics of the subsystems components. The proposed method makes it possible to significantly expand the scope of the theory of statistical solutions and to resolve a number of urgent problems that were previously irresolvable analytically. The proposed method can be applied in other areas as well.

Design protocol of microjet mixers for achieving desirable mixing times with arbitrary flow rate ratios

We extensively examined the performance of microjet mixers.