Three-dimensional phase field microelasticity theory of a multivoid multicrack system in an elastically anisotropic body: Model and computer simulations

The phase field microelasticity theory of a three-dimensional, elastically anisotropic system of voids and cracks is proposed. The theory is based on the equation for the strain energy of the continuous elastically homogeneous body presented as a functional of the phase field, which is the effective stress-free strain. It is proved that the stress-free strain minimizing the strain energy of this homogeneous modulus body fully determines the elastic strain and displacement of the body with voids and/or cracks. The proposed phase field integral equation describing the elasticity of an arbitrary system of voids and cracks is exact. The geometry and evolution of multiple voids and/or cracks are described by the phase field, which is the solution of the time-dependent Ginzburg-Landau equation. Other defects, such as dislocations and precipitates, are trivially integrated into this theory. The proposed model does not impose a priori constraints on possible void and crack configurations or their evolution paths. Examples of computations of elastic equilibrium of systems with voids and/or cracks and the evolution of cracks under applied stress are considered.     

Effect of microcracking on electric-field-induced stress intensity factors in dielectric ceramics

This paper gives a quantitative analysis of the effect of near-tip microcracks on electric-field-induced stress intensity factors in isotropic elastic dielectrics. Nucleation of the microcracks is assumed to be governed by the electric-field-induced mean stress or the maximum normal stress. Based on the solutions for the effect of a single microcrack on the local electric field at the main crack, simple formulae are derived for the electric-field-induced stress intensity factors in the presence of the microcracks. It is found that the relative change in the stress intensity factor due to the microcracks for a conducting crack is equal and opposite to that for an insulating crack provided that the distribution of microcrack orientations is random. In particular, the microcracking zone is found to amplify the electric-field-induced stress intensity factor in some cases, especially for stationary insulating cracks, while the microcracking zone wake has an antishielding effect for sufficiently grown conducting cracks. These results are in sharp contrast with the well-known toughening effects of microcracks in elastic media under pure mechanical loads. This is attributed to the fact that the interaction between the microcracks and the main crack in elastic dielectrics under electrical loading is governed essentially by electrostatics, while the shape of the microcracking zone is determined by the electric field induced elastic stress field.     

Packing of molecules and hole formation in lyotropic systems

A vector field q (the order parameter of the molecular packing) describing the packing (specifically, the orientation) of membrane-forming amphiphilic molecules is introduced to describe the structures of lyotropic phases constructed from membranes. In the general case q·n≠0 (where n is the unit normal vector) and therefore the singularities of the vector field q are not determined uniquely by the topology of the surface. The condition q·n=0 signifies disruption of the packing of the molecules. This corresponds to holes, which can form in membranes when lyotropic systems are diluted. As an illustration, the simplest type of such singularities, in which the distribution of the field q around a hole is described by a part of an instanton with unit topological charge, is studied. It is shown that such a distribution guarantees the existence of a local minimum under the condition that the tension per unit length λ of the hole boundary is small compared with the deformation energy of the field q: λh/K≪l (K is the modulus of the orientational elasticity of the field q and h is the thickness of the membrane). The radius of the hole which is formed equals L≈2.52(K/λh)^1/3 and the energy E≈59.79K(λh/K)^1/3. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 575–580 (25 October 1996)     

Scattering of atoms in the field of counterpropagating light waves. Effect of initial conditions

The scattering of an atom in the field of counterpropagating light waves is studied under conditions such that the state of the atom is a superposition of the ground and excited states. For the case in which this superposition is created by the field of a traveling wave, the momentum distribution function of the atom after scattering by a standing wave is found analytically in the approximation of a short interaction time, when the atom’s motion can be neglected. Longer interactions of the atom with the field are studied numerically. We also consider the case of counterpropagating light waves consisting of Gaussian or supergaussian pulses. Zh. éksp. Teor. Fiz. 113, 563–572 (February 1998)     

Solution of collinear cracks in an electrostrictive solid

A general treatment is presented of the two-dimensional problem of N collinear cracks in an infinite electrostrictive material subjected to remote electric loads based on the complex variable method combined with analytical extension of the complex variable functions. First, for the case of permeable cracks, general solutions for the electric potentials, Maxwell stresses, electroelastic stresses and stress intensity factors are derived. As specific examples, explicit and concise results are obtained for the cases of one crack and two collinear cracks. Then, these results are extended to the cases of impermeable and conducting collinear cracks, respectively. It is found that, in general, the total stresses always have the classical singularity of the r ^{- 1/2} type at the crack tips, whereas the Maxwell stresses have an r ^{- 1} singularity for the above three crack models. Finally, it is concluded that the applied electric field may either enhance or retard crack growth depending on the electric boundary conditions adopted on the crack faces, and the Maxwell stresses on the crack faces and at infinity.     

Fracture mechanics of propagating 3-D fatigue cracks with parametric dislocations

Abstract

Propagation of 3-D fatigue cracks is analyzed using a discrete dislocation representation of the crack opening displacement. Three dimensional cracks are represented with Volterra dislocation loops in equilibrium with the applied external load. The stress intensity factor (SIF) is calculated using the Peach–Koehler (PK) force acting on the crack tip dislocation loop. Loading mode decomposition of the SIF is achieved by selection of Burgers vector components to correspond to each fracture mode in the PK force calculations. The interaction between 3-D cracks and free surfaces is taken into account through application of the superposition principle. A boundary integral solution of an elasticity problem in a finite domain is superposed onto the elastic field solution of the discrete dislocation method in an infinite medium. The numerical accuracy of the SIF is ascertained by comparison with known analytical solution of a 3-D crack problem in pure mode I, and for mixed-mode loading. Finally, fatigue crack growth simulations are performed with the Paris law, showing that 3-D cracks do not propagate in a self-similar shape, but they re-configure as a result of their interaction with external boundaries. A specific numerical example of fatigue crack growth is presented to demonstrate the utility of the developed method for studies of 3-D crack growth during fatigue.     

Extension of the Sommerfeld diffraction integral to the case of extremely short optical pulses

The Sommerfeld diffraction theory is extended to the case of extremely short pulses. It is shown that a simple qualitative analysis and a quantitative solution of a wide class of diffraction problems are possible for pulses with durations of the order of the period of the light oscillations and an arbitrary initial distribution of the light field. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 5, 323–326 (10 September 1997) Deceased     

Conduction degradation in anisotropic multi-cracked materials

The electrical and thermal conduction properties of disordered solids and the possible degradation processes induced by the generation of cracks are central issues in the field of the heterogeneous materials. However, most of the existing theories are unable to consider an arbitrary density of cracks. We obtained an exact result for the fields induced within an elliptic anisotropic inhomogeneity embedded in a different anisotropic (two-dimensional) conductor. Then, we applied it to show that the degradation process strongly depends on the statistical orientational distribution of defects: in particular we theoretically prove that parallel cracks lead to the power law decay log σ ∼ − log N while random oriented cracks lead to the exponential law decay log σ ∼ −N (where σ is the effective conductivity of a region with a large number N of defects), as recently predicted by numerical findings.     

The onset of thermomagnetic convection in stratified ferrofluids

A non-uniform magnetic field causes an inhomogeneous distribution of magnetic grains in colloidal magnetics (so-called ferrofluids). The rate of concentration equilibrium settling is very low owing to the smallness of the particle diffusion coefficient. Therefore, if the equilibrium does not have enough time to settle, a ferrofluid behaves like a pure fluid, so that stationary convection occurs and no other. In the opposite case, that is when some non-uniform concentration profile has been formed, an oscillatory instability arises. The latter can be effectively excited under the action of a low-amplitude time-periodic magnetic field of an appropriate frequency.     

Force-sampling methods for density distributions as instances of mapped averaging

ABSTRACT

We show that two recently proposed methods for computing singlet and pair density distributions without histograms are particular implementations of the general mapped-averaging framework for deriving alternative ensemble averages for physical properties.     

Acoustic excitation of nuclear spin waves in the easy-plane antiferromagnetic material KMnF3

Ultrasound damping at T=4.2 K in single crystal easy-plane antiferromagnetic KMnF₃ is studied experimentally as a function of the magnitude and direction of a constant magnetic field H at frequencies of 640–670 MHz, corresponding to the frequencies of nuclear spin waves. Two experimental situations are examined: in the first, the vector H lies in the easy magnetization plane (001), and in the second, H forms an angle with (001). For longitudinal ultrasound waves propagating along the hard magnetization axis [001], it is found that the damping depends resonantly on the magnitude of the field H. In the first case a single damping maximum is observed, and in the second, two damping peaks that are well resolved with respect to the field. The angular dependence of the resonance damping signals on the direction of the constant magnetic field is found to have a 90° periodicity in all cases. The observed effects are explained by resonant ultrasonic excitation of nuclear spin waves. On the basis of an analysis of the magnetoacoustic interaction energy, it is shown that in the first case, nonzero oscillations of the antiferromagnetism vector L occur only in the basal plane, while in the second, oscillations of L occur both in the basal and a vertical plane, which are associated, respectively, with two branches of the nuclear spin waves. It is also shown that the 90° periodicity in the angular dependence of the damping signals is associated with a fourth order [001] axis. Zh. éksp. Teor. Fiz. 112, 1830–1840 (November 1997)     

Nonuniform quasistatic electric field in a weakly conducting anisotropic medium

The intensity distribution of a nonuniform electric field in a quadrupole electrooptic deflector, the properties of the medium in which are described simultaneously by permittivity and conductivity tensors which are not proportional to each other, is calculated as a function of the phase of the ac control voltage. It is shown that the space charge arising in this case is phase-shifted relative to the control voltage. The computational results are compared with experimental data. Zh. Tekh. Fiz. 67, 51–54 (October 1997)     

Statistical analysis of shear cracks on rock surfaces

A set of 3873 cracks on exposed granite rock surfaces are analyzed in order to investigate possible fracture mechanisms. The fracture patterns are compared with the Mohr-Coulomb and the Roscoe fracture models, which can be combined into a single fracture scheme. A third model for comparison is based on interacting `penny-shaped' micro cracks introduced by Healy et al. [Nature 439, 64 (2006)]. The former models predict a bimodal fracture angle distribution, with two narrow peaks separated by 60^○-90^○ symmetrically on both sides of the direction of the largest principal stress, while the latter predicts a single broader peak in the same direction with standard deviation in the range 15^○-20^○. The crack length distributions seem consistent with numerical simulation, whereas the fracture patterns are Euclidean rather than fractal. The statistical analyses indicate that none of the models fully describe the fracture patterns. It seems that natural shear fractures easily become a complex combination of different fracture mechanisms.     

Einstein-Maxwell space-times with symmetries and with non-null electromagnetic fields

General properties of solutions (g, F) of the Einstein-Maxwell field equations are discussed, whereg is a metric tensor andF is a non-null Maxwell field. In particular the case is discussed whereg admits a Killing vector fieldv with special emphasis on the case wherev is not admitted byF, i.e., the electromagnetic field does not have a symmetry of the metric tensor. An example is given of a solution (g, F) in whichg admits a hypersurface orthogonal Killing vector not admitted byF.     

Magnetic field effects on total and partial conductance histograms in Cu and Ni nanowires

Conductance histograms have become a powerful tool for studying transport properties of metallic nanowires. However, the individual conductance curves display a very rich structure that might be concealed by the statistical procedure of finding preferred conductance values by building conductance occurrence histograms using consecutive nanocontact breakage experiments. This is particularly true when it comes to discerning 1/2G₀=e²/hquantization in magnetic nanowires. The effect of disorder, added to possible magnetic sources of scattering, and different magnetic states of different nanowires, might hide its appearance as histogram peaks. This work analyzes and compares Ni and Cu nanowire experimental histograms at room temperature (RT). Those obtained with no curve selection criteria are basically unaffected by the presence of a magnetic field. A selection of particular sets of conductance curves shows that conductance quantization could occur in steps of e²/h and 2e²/h in Ni as well as in Cu in the presence or absence of a magnetic field. Sorting out curves in sets that present conductance plateaus at half integer and integer values, and compiling statistics on the number of such curves that appear, depending on the applied magnetic field, results in differences between the behaviour of Cu and Ni. While for Cu, the magnetic field keeps the ratio of curves that present plateaus at 1/2G₀with respect those presenting G₀ plateaus unchanged; for Ni, the number of curves which exhibit plateaus at just G₀ almost disappears with the applied field. This experimental fact might indicate that the magnetic field removes spin degeneracy in these magnetic nanowires. PACS 72.25.Ba; 73.40.Jn; 73.63.Rt; 75.75.+a     

On a Mathematical Framework for the Constitutive Equations of Anisotropic Dielectric Relaxation

Three classes of time-domain non-relativistic anisotropic dielectric constitutive equations of increasing generality are discussed. In each class dissipativity is ensured by the choice of a class of convolution kernels in the D-to-E constitutive equation expressing the electric field E in terms of the electric displacement field D. Defining properties of the inverse (E-to-D) kernels and their Fourier-Laplace transforms (complex dielectric functions) are determined by inversion of the D-to-E constitutive equation. By this procedure it is shown that dielectric functions of the dipolar dielectrics are tensor-valued Bernstein functions while the dielectric functions of the Drude-Lorentz type are tensor-valued negative definite functions. The properties of the complex dielectric permittivities are also determined for either class. The theory is applied to an exhaustive review of empirical response functions of real dielectric materials encountered in the literature. Each class of convolution kernels is consistent with existence of a conserved energy, but in one case a strictly dissipative energy can be constructed.     

Effect of the state of a quantized electromagnetic field on the interaction with an atom with allowance for the continuum

This paper studies the effect of a transition into the continuous spectrum on the “collapse” and “revival” of population oscillations in an atom. It is shown that at large values of the mean number of photons in a radiation field and in conditions of weak ionization the phenomena of collapse and revival can still be observed, but the amplitude of population oscillations decreases exponentially because of the damping of the level. The interaction of a quantized electromagnetic field with a Λ system of an atom when one state is continuous is examined. Expressions are derived for the probability of “survival” of the atom when the quantized field was initially in a state with a given number of photons and when it was in a coherent state. An approximate calculation of the sum in averaging over the photon number distribution in the case of a coherent field leads to expressions for the probabilities of survival of the atom that transform into expressions, as the mean number of photons tends to infinity, corresponding to the case of a field in the representation of a fixed number of photons. The possibility of a stable state existing in a coherent quantized field is examined. It is found that for a Λ system the condition for the existence of a stable state remains valid in the case of a coherent state of the field when the photon number is large. Zh. éksp. Teor. Fiz. 113, 1193–1205 (April 1998)     

Ground states of the hydrogen molecule and its molecular ion in the presence of a magnetic field using the variational Monte Carlo method

ABSTRACT

By using the variational Monte Carlo (VMC) method, we calculated the 1sσ_g-state energies, the dissociation energies, and the binding energies of the hydrogen molecule and its molecular ion in the presence of an aligned magnetic field regime between 0 and 10?a.u. The present calculations are based on using two types of compact and accurate trial wave functions, which are put forward for consideration in calculating energies in the absence of a magnetic field. The obtained results are compared with the most recent accurate values. We conclude that the applications of the VMC method can be successfully extended to cover the case of molecules under the effect of a magnetic field.