Micropolar theory from the viewpoint of mesoscopic and mixture theories

This paper takes a nontraditional look at micropolar media. It emphasizes the idea that it may become necessary to abandon the concept of material particles if one wishes to describe micropolar matter in which structural changes or chemical reactions occur. Based on recent results presented by Ivanova and Vilchevskaya (2016) we will proceed as follows. First we shall summarize the theory required for handling such situations in terms of a single macroscopic continuum. Mne of its main features are new balance equations for the local tensors of inertia containing production terms. The new balances and in particular the productions will then be interpreted mesoscopically by taking the inner structure of micropolar matter into account. As an alternative way of understanding the new relations we shall also attempt to use the concepts of the theory of mixtures. However, we shall see by example that this line of reasoning has its limitations: A binary mixture of electrically charged species subjected to gravity will segregate. Hence it is impossible to use a single continuum for modeling this kind of motion. However, in this context it will also become clear that the traditional Lagrangian way of describing motion of structurally transforming materials is no longer adequate and should be superseded by the Eulerian approach.     

Dynamical theory of topological defects

A method is presented to obtain stochastic equations of motion for topological defects from the underlying TDGL-like stochastic dissipative field equations. The method makes use of virtual displacements of the Goldstone coordinates of topological defects. Effects of kinematical constraints among Goldstone coordinates are studied. The method is applied to modulated systems and we obtain stochastic equations of motion for interfaces (domain walls) and vortex lines (dislocation or defect lines). The driving force for a vortex line is found to include besides the usual surface tension force a new force due to misfit, which is an analogue of the Magnus force on a quantized vortex line and the Peach-Kochler force on a dislocation. A general expression for interactions between parts of interfaces is obtained in terms of asymptotic forms of field variables far from interfaces.     

Metric-torsion gauge theory of continuum line defects

Basic points underlying the geometrization of continuum defects are discussed. Following an analogy with gravitational gauge theories, a metric-torsion gauge theory of continuum line defects is developed. Gauge-invariant action integrals are constructed and their equations of motion are obtained. A Lagrangian containing curvature terms up to second power has constant-curvature solutions. In linear approximation these solutions correspond to line defects which form closed loops separately.     

On the isotropy of continuized dislocated crystals. I. The isotropic lattice distortion

The geometrical theory of continuous distributions of dislocations traditionally neglects the dependence of a distribution of dislocations on the existence of point defects created by this distribution (e.g., due to intersections of dislocation lines). In this paper the influence of such point defects on metric properties of the continuized dislocated Bravais crystalline structure is assumed to be isotropic. The influence of the point defects on the distribution of dislocations is then modeled by treating dislocations as those located in a conformally flat space. This approach leads (among others) to new results concerning the geometry of glide surfaces.     

Pinning in superconductors with attractive and repulsive interaction defect-flux line

We illustrate some results of the statistical theory of pinning as well as the processes which lead to the existence of volume pinning force, and calculate some quantities determining the pinning and other effects in type II superconductors by means of a model potential for both attractive and repulsive interactions between individual defects and individual flux lines. For some of these quantities (e.g. the volume pinning force) in superconductors with line defects perpendicular to the flux lines, we find large differences with respect to the shape and character (attractive, repulsive) of the interaction potential, whereas other quantities (e.g. the maximum reversible displacement of the flux line lattice, the force on the flux line lattice in the reversible regime) are rather little dependent on the shape and the character of the interaction potential.     

Second order non-linear equations of motion for spinning highly flexible line elements

The second order non-linear equations of motion are formulated for spinning line elements having little or no intrinsic structural stiffness. The derivation is based on the extended Hamilton's principle and includes the effect of initial geometric imperfections (axial, curvature, and twist) on the line element dynamics. For comparison with previous work, the non-linear equations are reduced to a linearized form frequently found in the literature. The comparison revealed several new spin-stiffening terms that have not been previously identified and/or retained. They combine geometric imperfections, rotary inertia, Coriolis, and gyroscopic terms.     

Structural, electronic, and chemical properties of nanoporous carbon

Nanoporous carbon (NPC) exhibits unexplained chemical properties, making it distinct from other graphenelike materials, such as graphite, fullerenes, or nanotubes. In this Letter, we analyze the properties of NPC in terms of its structural motifs, which are derived from defects in distorted graphene sheets. Our density-functional theory calculations show that these motifs can be present in high concentration (up to 1%). Some of them induce localized levels close to the Fermi level, therefore leading to local charging and controlling the material's chemical function, for example, as a catalyst.     

Charged shells in general relativity and their gravitational collapse

The boundary conditions for the gravitational and electromagnetic fields on charged shells are formulated. The shells are characterized in geometrical terms and the boundary conditions are manifestly covariant. The formalism is applied to the study of the gravitational collapse of homogeneous charged spherical shells. The law of conservation of energy, obtained by integrating the equations of motion of the shell and interpreted in full analogy with the special theory of relativity, is the starting point in analyzing the equilibrium states and the motion of the shells. It is concluded that no charge, however high it may be, can stop the gravitational collapse of the shell below the upper Nordström radius.     

Slow crack propagation in heterogeneous materials

Statistics and thermally activated dynamics of crack nucleation and propagation in a two-dimensional heterogeneous material containing quenched randomly distributed defects are studied theoretically. Using the generalized Griffith criterion we derive the equation of motion for the crack tip position accounting for dissipation, thermal noise, and the random forces arising from the defects. We find that aggregations of defects generating long-range interaction forces (e.g., clouds of dislocations) lead to anomalously slow creep of the crack tip or even to its complete arrest. We demonstrate that heterogeneous materials with frozen defects contain a large number of arrested microcracks and that their fracture toughness is enhanced to the experimentally accessible time scales.     

Fluid molecule oscillations and the continuous spectrum near the rayleigh line

Of late there have been considerable developments in the theoretical study of the contour of spectral lines and the Rayleigh line by general statistical methods in the theory of random processes. On the basis of the general equations describing the rotational motion of molecules [1,2], and also of the equation which describes the change in the projection of the dipole moment onto the laboratory coordinate axes [3], we seek a correlation function whose Fourier transform leads finally to the required spectral distribution. In the present article we solve the problem of the spectral distribution by a direct analysis of the change in the projection onto the laboratory coordinate axes of the dipole moment induced in a molecule by an incident light wave. We consider a specific model for the rotational motion of fluid molecules.     

A geometrical description of local and global anomalies

The general topological framework for testing the possible occurrence of anomalies in gauge theories can be constructed in terms of the theory of group actions on line bundles through the introduction of a suitable group cohomology. In this Letter, we generalize this construction in such a way that it can be applied to a larger class of theories, allowing for a noncontractible configuration space and a nonconnected ‘gauge’ group. This construction find applications to the problem of the lifts of principal group actions. As a physical application, we compare the mechanisms of the anomalies cancelation in gauge and string theories, through a geometrical splitting of local and global anomalies.     

Geometric model of a fullerene molecule in the presence of Aharonov–Bohm flux

In this study, we describe a geometric model of a fullerene molecule with Ih symmetry. We combine the well known non-Abelian monopole approach and the geometric theory of defects, where every topological defect is associated with curvature and torsion, to describe a fullerene molecule. The geometric theory of defects in solids is used to consider the topological defects that allow this molecule to form and we apply a continuum formulation to describe this spherical geometry in the presence of an external Aharonov–Bohm flux. We solve a Dirac equation for this model and obtain the eigenvalues and eigenfunction of the Hamiltonian, and we obtain the persistent current for this model and show that it depends on the geometrical and topological properties of the fullerene.     

四种磁绝缘传输线的横向空间电荷流

 根据电磁场基本理论及电子运动守恒方程，导出平板、圆柱、圆锥和圆盘这4种常用传输线的横向空间电荷流的数值模型和磁绝缘临界条件。通过数值模拟得到:传输线的电压越高，无磁场的横向空间电荷流越大，但是磁缘性能却越显著；若分别增大圆柱、圆锥的几何结构因子，既有助于减小它们的无磁场横向空间电荷流又有助于增强它们的磁绝缘性能；对于圆锥，若电极夹角较大，内电极的极角较小，则对减小无磁场空间电荷流和增强磁绝缘性也有一定好处。     

圆锥磁绝缘传输线的横向空间电荷流

 根据电磁场基本理论及电子运动守恒方程，导出圆锥传输线横向空间电荷流的数值模型和磁绝缘临界条件。通过数值计算，讨论了电压及圆锥几何结构参数等对横向空间电荷流和磁绝缘性能的影响。电压较高时,无磁场的空间电荷流较大，而磁绝缘性能更好。在传输线的三个几何参数中，几何因子对传输性能影响最大。     

Symmetry characterization of Pimenov's spacetime: A reformulation of causality axioms

In modern physics, many theories are formulated in terms of symmetries; therefore, if we want to incorporate, e.g., space-time physics into modern physics, it is desirable to reformulate space-time physical theories in terms of symmetries. In this paper, we provide such a reformulation for an axiomatic theory of kinematic causality.     

Vortex lines in a ferromagnetic spin-triplet superconductor

Based on Duan's topological current theory, we show that in a ferromagnetic spin-triplet superconductor there is a topological defect of string structures which can be interpreted as vortex lines. Such defects are different from the Abrikosov vortices in one-component condensate systems. We investigate the inner topological structure of the vortex lines. The topological charge density, velocity, and topological current of the vortex lines can all be expressed in terms of δ function, which indicates that the vortices can only arise from the zero points of an order parameter field. The topological charges of vortex lines are quantized in terms of the Hopf indices and Brouwer degrees of φ-mapping. The divergence of the self-induced magnetic field can be rigorously determined by the corresponding order parameter fields and its expression also takes the form of a δ-like function. Finally, based on the implicit function theorem and the Taylor expansion, we conduct detailed studies on the bifurcation of vortex topological current and find different directions of the bifurcation.     

Disconnections in simple and complex structures

Disconnections are interfacial defects with dislocation and step character; for example, twinning dislocations in homo-phase and transformation dislocations in hetero-phase materials. They play important structural roles and are classified as either ‘perfect’, separating energetically degenerate regions of interface, or ‘partial’, bounding a faulted region. In kinetic mechanisms, disconnection motion can be glissile, by conservative climb or climb. In the present paper, disconnection mobility is analyzed in terms of shear and shuffle-type atomic displacements and diffusional flux. This is applied to a sequence of hetero-phase materials with increasing structural complexity, namely the β to α transformation in Ti, θ′ precipitation in Al(Cu) and the orthorhombic to monoclinic martensitic transformation in ZrO₂. A disconnection source mechanism in Ti, involving conservative climb, is also described.     

The volume pinning force for different shapes of the interaction potential between defects and flux lines

The volume pinning force in superconductors with randomly distributed line defects nearly perpendicular to the flux lines is calculated for model as well as realistic interaction potentials between single defects and single flux lines. Both attractive and repulsive interactions defect — flux line were considered. The line defects were constructed from point defects distributed with constant density on straight lines. The deviations of the results from the theory of Labusch are considerable for small elementary interaction forces between defects and flux lines. The deviations (as well as the differences between repulsive and attractive interaction potentials) are larger for the realistic interaction potential than those for the different model potentials. The threshold values for the flux line distortion (under which no net volume pinning can exist) is also given.