Stress of a Spatially Uniform Dislocation Density Field

A new approach to the fundamental theorem of surface theory, by means of the Darboux–Vallée–Fortuné compatibility relation

Existing uniform fields are usually based on the special arrangement of the array antenna. The uniform fields generated by flat-top beam shaping in angular far-field area or by point focusing in near-field area are directly subject to the array configuration and cannot be flexibly controlled. This paper presents a method of generating uniform field based on the combination of angular spectral domain and improved time reversal technique. This method is not limited by the array arrangement. It can generate a uniform field of specified size, shape and deflection angle in the same array arrangement at any position, including the near-field region. In this work, the reason why this method is not limited by array arrangement is explained theoretically. Secondly, the ability of the fixed array configuration to generate multiple uniform fields is validated numerically. Finally, the time-reversal technique of reversal signal amplitude reciprocal weighting is introduced. The problem of deterioration of uniform field flatness, caused by amplitude decay and phase delay during the generation of uniform field, is solved through this technology. The results show that the quality of the synthesized field is related to the main lobe and sidelobe information of its corresponding angular spectrum domain envelope, and the generated any uniform field must contain at least half of the angular spectrum domain main lobe information and half of the sidelobe information. This method can flexibly control the position, size, shape and deflection angle of one-dimensional and two-dimensional uniform field, which provides a new way to flexibly generating uniform fields.

The atomic structure of crystal defects such as dislocations, grain or phase boundaries, control these defects’ properties: their mobility, ability to cross-slip, or solute segregation. These crystal defects can be conveniently studied by atomistic simulations and one then needs to transfer relevant information at the upper scale to model microstructures containing a large number of defects, e.g., a polycrystal. Here, we propose an atomistic to continuum mechanics crossover method that (i) represents the atomic structure of dislocations cores by an appropriate Nye dislocation density tensor field and (ii), captures quantitatively the short and long range mechanical fields of defects. For (i), we propose a modified and improved interpolation method based on the original work by Hartley and Mishin. For (ii), we use a field dislocation mechanics framework that rigorously calculates/evaluates the mechanical fields associated with any Nye dislocation density distribution. The transfer method relies on molecular static calculations using two energetic models — ab-initio for screw dislocation core simulations in tungsten, and EAM potential for low and large angle grain boundaries in copper. Our findings demonstrate the effectiveness of the proposed approach in reconstructing the Burgers vector, and continuous strain and rotation fields. The framework is further applied to analyze the elastic interactions between extrinsic edge dislocations and a low angle grain boundary in copper.

Director structures in an infinite slab in the presence of a magnetic field are considered. The director is pinned parallel to the slab faces on one of the faces and is free on the other face. It is shown that when the field is parallel to the direction of pinning, the only stable state is that of a uniform director field. It follows that in ferromagnetic slabs pinned by exchange anisotropy on one side, it is impossible to introduce a multiturn helix by rotation in a uniform magnetic field. A similar result follows for a nematic liquid crystal pinned by the Chatelain method.

A crystal plasticity analysis of length-scale dependent internal stresses with image effects

Magnetorheological properties significantly depend on the regime of aggregate structures. In the case of cubic particles, closely-packed clusters that are significantly different from those for the case of spherical or rod-like particles are formed in the system since magnetic cube-like particles prefer a face-to-face contact with the neighboring particles. Therefore, a cubic particle suspension is expected to exhibit a sufficiently strong magnetorheological effect, which may be investigated by means of Brownian dynamics simulations. However, the translational and rotational diffusion (or friction) coefficients of a cube are not known and indispensable in order to develop this simulation technique. From this background, in the present study, we have analyzed the flow field around a cube in a Stokes flow regime in order to estimate the diffusion (or friction) coefficients of cube-like particles that are required for performing Brownian dynamics simulations of a cubic particle suspension. In the situation of a uniform flow field with a Reynolds number sufficiently smaller than unity, the force acts on the cube only in the flow field direction, and the torque acting on the cube may be regarded as negligible. In the situation of a rotational flow field with a sufficiently low Reynolds number, the torque acts on the cube only in the direction of angular velocity of the rotational flow field, and the force negligibly act on the cube. These characteristics are in significantly similar to those for the case of spheres in a Stokes flow situation. From these results, we may conclude that the diffusion coefficients of cube-like particles can be expressed by introducing a correction factor to those of the spherical particles.

Snake states are open trajectories for charged particles propagating in two\ndimensions under the influence of a spatially varying perpendicular magnetic\nfield. In the quantum limit they are protected edge modes that separate\ntopologically inequivalent ground states and can also occur when the particle\ndensity rather than the field is made nonuniform. We examine the correspondence\nof snake trajectories in single-layer graphene in the quantum limit for two\nfamilies of domain walls: (a) a uniform doped carrier density in an\nantisymmetric field profile and (b) antisymmetric carrier distribution in a\nuniform field. These families support different internal symmetries but the\nsame pattern of boundary and interface currents. We demonstrate that these\nphysically different situations are gauge equivalent when rewritten in a Nambu\ndoubled formulation of the two limiting problems. Using gauge transformations\nin particle-hole space to connect these problems, we map the protected\ninterfacial modes to the Bogoliubov quasiparticles of an interfacial\none-dimensional p-wave paired state. A variational model is introduced to\ninterpret the interfacial solutions of both domain wall problems.\n

In this work, we study the relation between the noncommutative topological entropy of the canonical map for Exel-Laca algebra A : O A O A and the Gurevich entropy of the respective Markov shift map A : A A .We prove that these two entropies coincide for the Renewal shift.In fact, one inequality holds for a more general situation whose proof follows from a series of classical entropy results and an equality that relates the maps A and A ; the proof of the other inequality is more technical and requires some specific properties of the Renewal shift.

We present a small flux rope (SFR) with smooth magnetic field rotations entrained by rolling back magnetic field lines around 1 AU. Such SFRs have only been seldom reported in the literature. This SFR was adjacent to a heliospheric plasma sheet (HPS), which is defined as a high plasma beta region in the vicinity of a heliospheric current sheet. Even though the SFR and HPS have different plasma beta, they possess similar plasma signatures (such as temperature, density, and bulk speed), density ratio of alpha particle‐to‐proton (Nα/Np), and heavy ion ionization states, which imply that they may have a similar origin in the corona. The composition and the configuration of the rolling back magnetic field lines suggested that the SFR originated from the streamer belt through interchange reconnection. The origin processes of the SFR are presented here. Combining the observations of STEREO and ACE, the SFR was shown to have an axis tilted to the ecliptic plane and the radius may vary with different spatial positions. In this study, we suggest that interchange reconnection can play an important role for the origin of, at least, some SFRs and slow solar wind.

Continuum theory for ionic field charging of spheroidal aerosols in nonuniform electric field

The high strain deformation of an aluminium-4% copper alloy in the supersaturated and aged conditions

The g-function is a measure of degrees of freedom associated to a boundary of two-dimensional quantum field theories. In integrable theories, it can be computed exactly in a form of the Fredholm determinant, but it is often hard to evaluate numerically. In this paper, we derive functional equations — or equivalently integral equations of the thermodynamic Bethe ansatz (TBA) type — which directly compute the g-function in the simplest integrable theory; the sinh-Gordon theory at the self-dual point. The derivation is based on the classic result by Tracy and Widom on the relation between Fredholm determinants and TBA, which was used also in the context of topological string. We demonstrate the efficiency of our formulation through the numerical computation and compare the results in the UV limit with the Liouville CFT. As a side result, we present multiple integrals of Q-functions which we conjecture to describe a universal part of the g-function, and discuss its implication to integrable spin chains.

A hole in a common wall is used to provide coupling between two resonant cavities (k=coefficient of coupling) or between two waveguides (x or b=normalized reactance or susceptance) or between cavity and waveguide (p=loading power factor of cavity). Referring to either side of a thin common wall, the field intensity in the center of a small hole is 1/2 what it would have been at that location on the wall. Between two equal regions, the coupling (k, x or b) by magnetic or electric field is expressed as 1/4 the ratio of the effective volume of the hole over the effective volume of each region, by duality (Booker's principle), the effective volume (related to the polarizability) of an aperture in a thin wall is identified with that of an analogous thin body in a uniform field. For a resonant cavity loaded by coupling to a waveguide, the loading power factor is p=kx; this theorem is proved by reference to an equivalent network. Various cases of coupling by two-dimensional and three-dimensional fields are formulated in terms of area or volume ratios, especially between pillbox resonators (rectangular, circular, or coaxial-circular) and between rectangular waveguides with common side walls or top and bottom walls. The effective area or volume of a small hole in a thin conducting wall is given for various symmetrical shapes, in a magnetic or electric field.

Ring–shaped homogeneous YBCO and DyBCO bulks were successfully fabricated using the Single–Direction Melt Growth (SDMG) method. The bulks were directly grown from ring–shaped compacted powder using ring–shaped molds with an outer diameter of 50 mm and inner diameters of 15, 20, and 25 mm. The ring–shaped bulks exhibited high trapped fields inside the rings up to 1.2 T at 77 K. Analyses of trapped field distributions revealed uniform current density distributions along the orbital direction. Stacked ring bulks demonstrated even higher trapped fields, reaching 2.0 T at 77 K. It was confirmed for the stacked bulks that time–independent uniform trapped fields can be achieved by magnetizing at lower fields than fully magnetizing conditions. Observed paramagnetic magnetization of the SDMG–processed YBCO bulk was negligibly small below the detection limit, which is considered to be more suitable for bulk NMR/MRI applications than DyBCO. Additionally, we proposed a method to quantitatively evaluate trapped fields of superconducting bulks with various diameters and thicknesses, where the estimated average current densities from the maximum trapped fields for all the obtained ring–shaped bulks were above 104 A cm–2 at 77 K. These results indicate that SDMG is an effective method for fabricating high–quality, large–scale ring–shaped bulks with superior field–trapping properties.

Superconducting, saddle-coil dipole magnets are used for bending and magnetohydrodynamic generator magnets. The uniform transverse fields may be produced by coils of tubular form with a sin θ current distribution or by uniform current density coils with cross sections of overlapping circles or ellipses. It is shown that overlapping circles and ellipses use less conductor. A simple new approximation to the overlapping circle or ellipse form is shown, in which pancake windings are used rather than the layer-type windings used previously. Pancake windings have an advantage in that the large transverse mechanical forces are transmitted through the pancakes without passing through the cooling channels as in layer-wound dipole coils. Pancake coils are simple to wind and permit an additional important innovation in that bell-shaped ends can prevent the field at the windings exceeding the uniform central field anywhere, thus allowing conductors to be optimized for actual working field rather than a higher peak field. Reduced end effects and high homogeneity are obtainable with these techniques. Models and tests are described.