Mathematical Apparatus for the Synthesis of Composite Materials with Specified Properties

The meaning of the creation and functioning of the system is defined as the achievement of extreme values of goals that unite the individual elements of the system into a single whole. Based on this, the main system attributes of composite materials are indicated. It is assumed that the systemic effect is generated by the systemic properties of quality criteria. The implementation of the technical task is initially determined at the stage of cognitive modeling with the establishment of intensive and extensive properties with the allocation of control parameters. Based on the cognitive map, hierarchical structures of quality criteria are determined, and in accordance with the selected quality criteria, the corresponding structural schemes of the system (for each selected scale level). Further, the system's quality criteria are formalized, and mathematical models are developed in accordance with each of the criteria. The main purpose of using system analysis is to apply the general principles of decomposition of the system into individual elements and establish connections between them, in determining the research goal and stages to achieve this goal (based on solving single-criterion optimization problems using the found optimal values). The formalization of the multicriteria problem and its solution are made based on the required operational values, the type of kinetic processes of the formation of the physical and mechanical characteristics of the material (determine its structure and properties). The problem of materials synthesis is reduced to the choice of the order and type of the differential equation; parametric identification within the chosen model; comparison of experimental and model kinetic processes at a given accuracy; adjusting the model (if necessary). Therefore, it is important to interpolate the kinetic processes of the formation of the main physical and mechanical characteristics of composite materials. The technological process is considered as a complex system consisting of elements of various levels of detail: from atomic to a separate process. Decomposition of the technological process consists in dividing it into basic operations (elements): preparation of materials, mixing of components, molding of a semi-finished product, heat treatment and additional operations. The effectiveness of this approach was confirmed in the development of chemically resistant sulfur composites, epoxy composites for radiation protection, etc. The initial prerequisite was the required operational values of the material and the type of kinetic processes. The results of effective use of interpolation models (including splines) of compressive strength, heat release, and shrinkage of composite epoxy materials are presented.

Approximation of Functions in Multi-criterial Synthesis of Composite Materials

A prerequisite for the synthesis of composite materials as complex systems is the principles of the control paradigm of Peace and the effectiveness of mathematics (for any reality and any given (not absolute) accuracy, there is a mathematical structure that describes this reality with this accuracy; the converse is also true (homomorphism, arbitrarily close to isomorphism between reality and mathematical structures)).The proposed methodology for managing the identification process (design of composites) includes the process of human choice: the probabilistic nature of the control; the main reason for the inadequacy of a purely analytical research procedure. Here, the optimization of the control of the properties of the composite is carried out experimentally on the model as a result of the approximation of the response function: not the generalized functional is approximated, but the particular criteria of which it consists. The development of composite materials is carried out on the basis of evaluating the parameters of the formation of operational properties. The parameters of each of the kinetic processes of the formation of the physical and mechanical characteristics of the material were taken as particular criteria. Kinetic processes are asymptotic for the composites under study and contain extremum and inflection points. A method is used to approximate multidimensional table-defined functions by generalized polynomials of a particular form. In the parametric identification of kinetic processes, their parameters are considered basic. Approximating models of the main properties are presented. Vector optimization of properties (selection of recipes, technologies and methods of material quality control) is carried out by overcoming ambiguities of goals using linear convolution, introducing benchmarks, building Pareto sets, etc. The expediency of using a systematic approach (the hierarchical structure of properties and the hierarchical structure of the composite proper) to the design of building materials as complex systems is shown. The research results are introduced as prototypes of new identification systems in the development of composite materials with adjustable structure and properties, in contrast to the replication of reference applied developments of identification theory in various industries.

The Occurrence and Prevalence of Time Domain Structures in the Kelvin-Helmholtz Instability at Different Positions Along the Earth’s Magnetospheric Flanks

The Kelvin-Helmholtz instability (KHI) is thought to be an important driver for mass, momentum, and energy transfer between the solar wind and magnetosphere. This can occur through global-scale “viscous-like” interactions, as well as through local kinetic processes such as magnetic reconnection and turbulence. An important aspect of these kinetic processes for the dynamics of particles is the electric field parallel to the background magnetic field. Parallel electric field structures that can occur in the KHI include the reconnection electric field of high guide field reconnection, large amplitude ion acoustic waves, as well as time domain structures (TDS) such as double layers and electrostatic solitary waves. In this study, we present a survey of parallel electric field structures observed during three Kelvin Helmholtz events observed by NASA’s Magnetospheric Multiscale (MMS), each at different positions along the magnetosphere’s dusk flank. Using data from MMS’s on-board solitary wave detector (SWD) algorithm, we statistically investigate the occurrence of TDS within the KHI events. We find that early in the KHI development, TDS typically occur in regions with strong field-aligned currents (FACs) on the magnetospheric side of the vortices. Further down the flanks, as the vortices become more rolled up, the prevalence of large electric currents decreases, as well as the prevalence of SWDs. These results suggest that as the instability develops and vortices grow in size along the flanks, kinetic-scale activity becomes less prevalent.