In the work, a modified effective medium theory is constructed for calculating the effective properties of thermoelectric composites with different values of percolation thresholds. It is shown that ...even at concentrations beyond the critical region, the threshold value is essential for determining the effective properties. Two fundamentally different cases of a set of local properties of the composite are considered. In one of these cases, the conductivity and thermal conductivity of one of the phases is simultaneously greater than the conductivity and thermal conductivity of the other phase. The second, anomalous case, when the electrical conductivity of the first phase is greater than that of the second, but the thermal conductivity of the first phase is less than that of the second, shows unusual concentration behavior of effective conductivity, i.e. with an increase in the well-conducting phase, the effective conductivity shows a decrease (rather than growth as in the standard case), which at goes over to growth.
We propose an algorithm for computing the influence matrix and rank distribution of nodes of a weighted directed graph by calculating the nodes’ mutual impact. The algorithm of accumulative impact ...solves problems of dimension and computational complexity arising in the analysis of large complex systems. The algorithm calculates the mutual impact of each pair of vertices, making it possible to rank the nodes according to their importance within the system and to determine the most influential components. It produces results similar to those of the commonly used impulse method when applied to graphs that are impulse-stable in an impulse process, while overcoming the disadvantages of the impulse method in other situations. Results are always obtained regardless of impulse stability; they do not depend on the initial impulse, so that the initial values of the weights affect the calculation results. When elements in the adjacency matrix of the weighted directed graph are multiplied by a constant factor, scale invariance is not violated, and the full affect for each of the nodes scales proportionally. Several examples of analyses of weighted directed graphs, including one related to the practical problem of urban solid waste removal, are provided to demonstrate the advantages of the proposed algorithm.
It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical ...conductivity. In particular, when describing the elastic and electro-conductive properties of a strongly inhomogeneous two-phase composite material, the steep rise of effective parameters occurs at different concentrations. To achieve the logical concordance between the cross-property relations, a modification of the effective medium theory of the elastic properties is introduced. It is shown that the qualitative conclusions of the theory do not change, while a possibility of describing a broader class of composite materials with various percolation thresholds arises. It is determined under what conditions there is an elastic analogue of the Dykhne formula (for the effective conductivity). The introduction of the theory with the variable percolation threshold paves the way for describing the magneto-elastic properties of magnetorheological elastomers, as it has been achieved for magneto-dielectric and magnetic properties recently.
This paper discusses the dynamics of oxygen partial pressure in intercellular fluid upon a limited load and a subsequent post-ischemic hyperemia in healthy individuals and individuals with vascular ...pathologies of the lower limbs. Within the framework of the phenomenological approach, which takes into consideration the qualitative peculiarities of the gas exchange processes in the body, a formal theory describing the dynamics of oxygen (Formula: see text) concentration dependently on the conditions of blood supply to the tissues has been developed. It was shown that certain parameters, for instance the relaxation time upon the conditions of artificial ischemia and the characteristic time of return of spontaneous blood circulation in the post-ischemic period, depend on the degree of pathology of the vascular system and may be used for assessing the functional status of a biological body.
Composite materials where magnetic micrometer-sized particles are embedded into a compliant polymer matrix are known as magnetorheological or magnetoactive elastomers (MAEs). They are distinguished ...by huge variations of their physical properties in a magnetic field, which is commonly attributed to the restructuring of the filler. The process of the magnetic-field-induced restructuring in a magnetorheological elastomer is interpreted as progression towards percolation. Such a physical model was previously used to explain the dependence of the magnetic permeability and dielectric permittivity of MAEs on the magnetic field strength. Based on this hypothesis, the magnetorheological effect in MAEs is considered theoretically. The theoretical approach is built upon a self-consistent effective-medium theory for the elastic properties, extended to the variable (field dependent) percolation threshold. The proposed model allows one to describe the large variations (over several orders of magnitude) of the effective elastic moduli of these composite materials, known as the giant magnetorheological (MR) and field-stiffening effects. An existence of a giant magnetic Poisson effect is predicted. The relation of the proposed model to the existing theories of the MR effect in MAEs is discussed. The results can be useful for applications of MAEs in magnetic-field controlled vibration dampers and isolators.
A new characteristic of paired nodes in a directed weight complex network is considered. A method (named as K-method) of the characteristics calculation for complex networks is proposed. The method ...is based on transforming the initial network with the subsequent application of the Kirchhoff rules. The scope of the method for sparse complex networks is proposed. The nodes of these complex networks are concepts of the real world, and the connections have a cause-effect character of the so-called "cognitive maps". Two new characteristics of concept nodes having a semantic interpretation are proposed, namely "pressure" and "influence" taking into account the influence of all nodes on each other.
We propose a theoretical approach for calculating effective electric and magnetic properties of composites with field-dependent restructuring of the filler. The theory combines the Bruggeman-Landauer ...approximation extended to a field-dependent (variable) percolation threshold with the approximate treatment of nonlinearity of material properties. Theoretical results are compared with experiments on magnetorheological elastomers, which in the context of investigated phenomena are often called magnetoactive elastomers (MAEs). In MAEs with soft polymer matrices, the mutual arrangement of inclusions changes in an applied magnetic field. This reorganization of the microstructure leads to unconventionally large changes of electrical and magnetic properties. Obtained theoretical results describe observed phenomena in MAEs well. Qualitative agreement between theory and experiment is demonstrated for the magnetodielectric effect. In the case of magnetic permeability, quantitative agreement is achieved. The theoretical approach presented can be useful for development of field-controlled smart materials and design of smart structures on their basis, because the field dependence of physical properties can be predicted.
It is shown that in external magnetic fields, a uniaxial magnetic anisotropy comes into being in a magnetoactive elastomer (MAE). The magnitude of the induced uniaxial anisotropy grows with the ...increasing external magnetic field. The filler particles are immobilized in the matrix if the MAE sample is cooled below 220 K, where the anisotropy can be read out. The cooling of the sample is considered as an alternative methodological approach to the experimental investigation of the magnetized state of MAEs. The appearance of magnetic anisotropy in MAE is associated with restructuring of the filler during magnetization, which leads to an additional effective field felt by the magnetization. It is found that the magnitude of the effective magnetic anisotropy constant of the MAE is approximately two times larger than its effective shear modulus in the absence of magnetic field. It is proposed that the experimentally observed large (about 40) ratio of the magnetic anisotropy constant of the filler to the shear modulus of the matrix deserves attention for the explanation of magnetic and magnetoelastic properties of MAEs. It may lead to additional rigidity of the elastic subsystem increasing the shear modulus of the composite material through the magnetomechanical coupling.
Magnetic properties of a magnetoactive elastomer (MAE) filled with {\mu}m-sized soft-magnetic iron particles have been experimentally studied in the temperature range between 150 K and 310 K. By ...changing the temperature, the elastic modulus of the elastomer matrix was modified and it was possible to obtain magnetization curves for an invariable arrangement of particles in the sample as well as in the case when the particles were able to change their position within the MAE under the influence of magnetic forces. At low (less than 220 K) temperatures, when the matrix becomes rigid, the magnetization of the MAE does not show a hysteresis behavior and it is characterized by a negative value of the Rayleigh constant. At room temperature, when the polymer matrix is compliant, a magnetic hysteresis exists and exhibits local maxima of the field dependence of the differential magnetic susceptibility. The appearance of these maxima is explained by the elastic resistance of the matrix to the displacement of particles under the action of magnetic forces.
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