On a Heat Exchange Problem under Sharply Changing External Conditions

The heat exchange problem between carbon particles and an external environment (water) is stated and investigated based on the equations of heat conducting compressible fluid. The environment parameters are supposed to undergo large and fast variations. In the time of about 100 μs, the temperature of the environment first increases from the normal one to 2400 K, is preserved at this level for about 60 μs, and then decreases to 300 K during approximately 50 μs. At the same periods of time, the pressure of the external environment increases from the normal one to 67 GPa, is preserved at this level, and then decreases to zero. Under such external conditions, the heating of graphite particles of various sizes, their phase transition to the diamond phase, and the subsequent unloading and cooling almost to the initial values of the pressure and temperature without the reverse transition from the diamond to the graphite phase are investigated. Conclusions about the maximal size of diamond particles that can be obtained in experiments on the shock compression of the mixture of graphite with water are drawn.     

Numerical analysis of diamond buckles

The “diamond” modes of collapse are studied with finite element methods. Both linear and nonlinear analyses are performed on the buckling of a cylindrical shell under axial compression. Among the postbuckling shapes of the cylindrical shell, a number of diamond modes (cost nθ; N = 0, 14, 18, 10, 24 and 28) are found to be possible. The analysis is compared to those conducted by Maewal and Nachbar, Crisfield, and Yoshida et al. Agreement is established in conceiving the deformed shape with circumferential number of 14 as the stable postbuckling mode of the cylindrical shell.

The transition from the axisymmetric mode to a diamond mode of collapse is shown to be an instantaneous process triggered in the proximity of the critical state by a small perturbation of the load increment.     

Simulating resistance switching in amorphous carbon

The resistance switching in amorphous carbon (a-C) is mathematically simulated on the basis of quantum molecular dynamics. The electric conductivity in thin a-C films is related to a phase transition due to an electric field and corresponding Joule heating and cooling. Simulations show that the transition mechanism is related to the clusterization of existing conducting regions of graphite (sp ²) in a nonconducting diamond (sp ³) matrix. Simulations yield the conditions for the phase transition in a-C from one state to another. Excited molecular orbitals and the energy gap at different temperatures are also calculated.     

Nanocrystalline Diamond Coatings

Carbon—in the form of diamond coatings (nanocrystalline diamond—NCD) on suitable substrates—has attractive properties for biomedical applications. The excellent chemical inertness of NCD films makes them a promising material for medical implants, cardiovascular surgery and for coating of certain components of artificial heart valves.

The medical applications of carbon films impose some special requirements on their quality, purity, phase content and the state of the surface. Of particular importance is the smoothness of the surface and good adhesion of the coatings to the substrate. We have investigated carbon films which were synthesized by Radio Frequency Plasma Chemical Vapour Deposition (RF–PCVD).

The specimens obtained have been tested to show their structure and their biological, mechanical and chemical resistance. Additional investigations of the NCD films were carried out by micro-X-ray spectroscopy, Raman spectroscopy, AFM, Auger spectroscopy, corrosion tests, breakdown tests and clinical investigations. Nanocrystalline diamond (NCD) layers obtained by a new method of RF dense plasma CVD onto AISI-316L steel used in surgery were investigated to determine their suitability as biomaterials.     

A Simple Cluster Model for the Liquid–Glass Transition

Using the classical distribution-function approach to simple liquids, we estimate the orientational interaction between clusters consisting of a particle and its nearest neighbors. We show that there are density and temperature ranges where the interaction changes sign as a function of the cluster radius. On this basis, the corresponding model of interacting cubic and icosahedral clusters (of the type of a spin glass model) is proposed and solved in the replica-symmetric approximation. We show that the glass order parameter grows continuously on cooling and the replica-symmetry-breaking temperature can be identified with the glass transition temperature. We also show that on cooling a system of particles with a Lennard-Jones interaction, cubic clusters freeze first. The transition temperature for icosahedral clusters is somewhat lower; therefore, the cubic structure of the short-range order is more likely in a Lennard-Jones glass near transition.     

Silica fractal atomic clusters saturated with OH

We constructed regular fractal SiOH atomic clusters which pending bonds are saturated with OH molecules. We calculated the binding energies of these clusters as well as for sp² hybridization as for sp³ hybridizations. The result are the following: for the two hybridizations, the total binding energies have a linear dependence on the size of the fractal cluster, which comes directly from the scaling law of the fractal characteristic of the building of the cluster. We related by a scaling law, the number of electronic bonds and the total bonding energy.     

Description of the Structure of the Polymer Matrix of Particulate-Filled Polymer Composites as a Thermal Cluster: the Critical Indices

The adequacy of the model of a thermal cluster for describing the structure of the polymer matrix of particulate-filled composites is shown. The equality of the critical indices _T = of thermal and percolation clusters is realized in the composites at a nonzero molecular mobility, which is characterized by the fractal dimension D of the chain fragment between entanglements. The variation interval of D for the polymer matrix of a composite is smaller than for the initial polymer because of the influence of the filler on its structure.     

Stability and Noise-induced Transitions in an Ensemble of Nonlocally Coupled Chaotic Maps

The influence of noise on chimera states arising in ensembles of nonlocally coupled chaotic maps is studied. There are two types of chimera structures that can be obtained in such ensembles: phase and amplitude chimera states. In this work, a series of numerical experiments is carried out to uncover the impact of noise on both types of chimeras. The noise influence on a chimera state in the regime of periodic dynamics results in the transition to chaotic dynamics. At the same time, the transformation of incoherence clusters of the phase chimera to incoherence clusters of the amplitude chimera occurs. Moreover, it is established that the noise impact may result in the appearance of a cluster with incoherent behavior in the middle of a coherence cluster.     

Thermodynamic Potential of a System of Electrons and Phonons in a Disordered Alloy

We obtain a cluster expansion for the two-time retarded Green's functions and the thermodynamic potential of a disordered crystal taking the electron–phonon and electron–electron interactions into account. The electron states of the system are described in the framework of a multiband tight-binding model. The calculations are based on the diagram techniques for the temperature Green's functions. The coherent potential approximation is chosen as a zeroth-order one-site approximation in this cluster expansion method. We show that the contributions from the processes of scattering of elementary excitations on clusters decrease as the number of sites in the cluster increases in accordance with certain small parameters. Analytic estimates of the influence of the electron–phonon interaction on the energy spectrum of electrons of an alloy being ordered are obtained in a one-band model. The applicability of these results to describing the influence of strong electron correlations on the electron structure and properties of alloys of transition metals with narrow energy bands is illustrated with the example of the Fe–Ti alloy.     

Interaction of a granular flow with a rectangular obstacle

In this work we studied the cluster formation of particles flowing between two parallel plates hitting a rectangular obstacle. After a short time a cluster is formed on top of the obstacle. Quantification of the cluster formation, shows that the number of clusters decrease with time, whereas the mean and maximum cluster size grow during the simulation. Our results indicate that for the development of clusters the value of the restitution coefficient for particle–particle collisions is most important parameter for this formation process. We found that changes in the value of the restitution parameters for particle–obstacle and particle–wall did not show significant changes in the cluster development.     

El Naschie’s structures in the electrodynamics of polarizable media

Using the concept of ‘combined field’, an electrodynamics of polarizable media on a fractal space–time is constructed. In this context, using the scale relativity theory, the permanent electric moment, the induced electric moment, the vacuum fluctuations, the paraelectrics, the diaelectrics, the electric Zeeman-type effect, the electric Einstein–de Haas-type effect, the electric Aharonov–Bohm-type effect, the superconductors in the ‘combined field’, the double layers as coherent structures, the magnetic Aharonov–Casher-type effect, are analyzed. Correspondence with the ε^(∞) space–time is accomplished either by admitting an anomal electric Zeeman-type effect, or through a fractal string as in the case of a superconductor in ‘combined field’, or, by phase coherence of the electron–ion pairs from the electric double layers (El Naschie’s coherence). Moreover, the electric double layer or multiple layer may be considered as two-dimensional projections of the same El Naschie’s fractal strings (higher-dimensional strings in ε^(∞) space–time).     

铜基复合材料组织形态分形特征的统计分析与研究

通过对铜基复合材料显微组织结构相图的分析和研究,根据分形理论,计算了不同实验条件下铜基复合材料横截面和平行压制力面的显微组织结构相图的分形维数,同时结合统计方法分析了铜基复合材料分形维数的一些统计特性,结果表明,分形维数反映了石墨在样品中的分布规律,分形维数越大,组织结构相图越复杂,石墨分布越不规则,故石墨分布的不规则性可用分形维数来刻画,分形维数可作为材料组织形态分析的一个表征参数,通过统计分析可知,铜基复合材料横截面和平行压制力面的组织结构相图的分形维数服从正态分布,且横截面和平行压制力面的分形维数随石墨含量变化的情况互不影响。     

The nature of the β transition in the temperature dependence of polyamide mechanical loss

The mechanical loss maximum in polycaprolactam in the vicinity of –50°C at a frequency of 10 Hz ( transition) was shown not to be related directly to the presence of moisture in the polymer. This transition is also observed in dried caprone (vacuum drying at 10^–4 torr and 180°C for 30 h) after a few days following annealing. The maximum was shown by IR spectroscopy to decrease and shift towards lower temperatures when hydrogen bonding is weakened as a result of prior heating or compression strain. A conclusion is drawn concerning the relationship between the transition and hydrogen bonding which fixes the amide groups in the amorphous polymer phase.M. I. Kalinin Leningrad Polytechnic Institute. A. F. Ioffe Physical Technical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 5, pp. 919–922, September–October, 1972.     

Effect of crystallization on the adhesion of polycaprolactam to metal

The effect of the melt cooling and annealing conditions on the supermolecular structure of polycaprolactam and its adhesion to aluminum has been studied. It is shown that the transition from amorphous-mesomorphous to crystalline structure leads to a decrease in adhesion.Institute of Mechanics of Metal-Polymer Systems, Academy of Sciences of the Belorussian SSR, Gomel'. Translated from Mekhanika Polimerov, No. 1, pp. 170–172, January–February, 1976.     

El Naschie’s ε theory and effects of nanoparticle clustering on the heat transport in nanofluids

Effects of nanoparticle clustering on the heat transfer in nanofluids using the scale relativity theory in the topological dimension D_T = 3 are analyzed. In the one-dimensional differentiable case, the clustering morphogenesis process is achieved by cnoidal oscillation modes of the speed field. In such conjecture, a non-autonomous regime implies a relation between the radius and growth speed of the cluster while, a quasi-autonomous regime requires El Naschie’s ε^(∞) theory through the cluster–cluster coherence (El Naschie global coherence). Moreover, these two regimes are separated by the golden mean. In the one-dimensional non-differentiable case, the fractal kink spontaneously breaks the ‘vacuum symmetry’ of the fluid by tunneling and generates coherent structures. This mechanism is similar to the one of superconductivity. Thus, the fractal potential acts as an energy accumulator while, the fractal soliton, implies El Naschie’s ε^(∞) theory (El Naschie local coherence). Since all the properties of the speed field are transferred to the thermal one, for a certain conditions of an external load (e.g. for a certain value of thermal gradient) the soliton and fractal one breaks down (blows up) and release energy. As result, the thermal conductibility in nanofluids unexpectedly increases. Here, El Naschie’s ε^(∞) theory interferes through El Naschie global and local coherences.     

Strength vs. toughness optimization of microstructured composites

Aim of this paper is to present a new fractal approach linking the macroscopic mechanical properties of micro- and nano-structured materials with the main parameters: composition, grain size and structural dimension, as well as contiguity and mean free path. Assuming the key role played by the interfaces, the proposed fractal energy approach unifies the influences of all the above parameters, through the introduction of a fractal structural parameter (FSP), which represents an extension of the Gurland’s structural parameter. This modeling approach is assessed through an extensive comparison with experimental data on poly crystalline diamond (PCD) and WC–Co alloys. The results clearly show that the theoretical fractal predictions are in a fairly good agreement with the experiments on both hardness and toughness. This new synthetic parameter is thus proposed to investigate, design and optimize new micro- and nano-grained materials. Eventually, FSP-based optimization maps are developed, that allow to design new materials with high hardness and toughness.     

On the spectrum of semi-classical Witten-Laplacians and Schrödinger operators in large dimension

We investigate the low-lying spectrum of Witten–Laplacians on forms of arbitrary degree in the semi-classical limit and uniformly in the space dimension. We show that under suitable assumptions implying that the phase function has a unique local minimum one obtains a number of clusters of discrete eigenvalues at the bottom of the spectrum. Moreover, we are able to count the number of eigenvalues in each cluster. We apply our results to certain sequences of Schrödinger operators having strictly convex potentials and show that some well-known results of semi-classical analysis hold also uniformly in the dimension.     

Approximation algorithm for the problem of partitioning a sequence into clusters

We consider the problem of partitioning a finite sequence of Euclidean points into a given number of clusters (subsequences) using the criterion of the minimal sum (over all clusters) of intercluster sums of squared distances from the elements of the clusters to their centers. It is assumed that the center of one of the desired clusters is at the origin, while the center of each of the other clusters is unknown and determined as the mean value over all elements in this cluster. Additionally, the partition obeys two structural constraints on the indices of sequence elements contained in the clusters with unknown centers: (1) the concatenation of the indices of elements in these clusters is an increasing sequence, and (2) the difference between an index and the preceding one is bounded above and below by prescribed constants. It is shown that this problem is strongly NP-hard. A 2-approximation algorithm is constructed that is polynomial-time for a fixed number of clusters.     

Glass transition and crystallization process of hard magnetic bulk Nd60Al10Fe20Co10 metallic glass

Glass transition and crystallization process of bulk Nd60Al10Fe20Co10 metallic glass were investigated by means of dynamic mechanical thermal analysis (DMTA), differential scanning calorimetry (DSC), X-ray diffraction (XRD) and scanning electronic microscopy (SEM). It is shown that the glass transition and onset crystallization temperature determined by DMTA at a heating rate of 0.167 K/s are 480 and 588 K respectively. The crystallization process of the metallic glass is concluded as follows: amorphous α→α′＋metastable FeNdAl novel phase →α′＋primary δ phase→primary δ phase＋eutectic δ phase Nd3Al phase＋Nd3Co phase. The appearance of hard magnetism in this alloy is ascribed to the presence of amorphous phase with highly relaxed structure. The hard magnetism disappeared after the eutectic crystallization of amorphous phase.     

Fractal properties of percolation clusters in Euclidian neural networks

The process of spike packet propagation is observed in two-dimensional recurrent networks, consisting of locally coupled neuron pools. Local population dynamics is characterized by three key parameters – probability for pool connectedness, synaptic strength and neuron refractoriness. The formation of dynamic attractors in our model, synfire chains, exhibits critical behavior, corresponding to percolation phase transition, with probability for non-zero synaptic strength values representing the critical parameter. Applying the finite-size scaling method, we infer a family of critical lines for various synaptic strengths and refractoriness values, and determine the Hausdorff–Besicovitch fractal dimension of the percolation clusters.