Domain Wall Equation Research Articles

Living on the walls of super-QCD

We study BPS domain walls in four-dimensional N=1N=1 massive SQCD with gauge group SU(N)SU(N) and F<NF<N flavors. We propose a class of three-dimensional Chern-Simons-matter theories to describe the effective dynamics on the walls. Our proposal passes several checks, including the exact matching between its vacua and the solutions to the four-dimensional BPS domain wall equations, that we solve in the small mass regime. As the flavor mass is varied, domain walls undergo a second-order phase transition, where multiple vacua coalesce into a single one. For special values of the parameters, the phase transition exhibits supersymmetry enhancement. Our proposal includes and extends previous results in the literature, providing a complete picture of BPS domain walls for F<NF<N massive SQCD. A similar picture holds also for SQCD with gauge group Sp(N)Sp(N) and F < N+1F<N+1 flavors.

Incident Power Influence on Magnetoimpedance Element With Domain-Wall Resonance

Magnetoimpedance(MI) sensor utilizes permeability changes of the material through skin effect and ferromagnetic resonance when the sensor is applied to a magnetic field, and it has a higher sensitivity [1]. The sensors, which are composed of amorphous wires, are currently commercialized as compasses in mobile phones, and researches advance their sensitivity still continue for application of biomedical research [2] and nondestructive testing [3]. On the other hand, thin-film MI elements which has the compatibility with miniaturized integrated electronic devices such as driving and detecting circuits, contributes to the miniaturization of sensor device with higher spatial resolution. However, one problem of using thinfilm elements is higher operating frequency. Typically, operating frequency is above 100 MHz to GHz range for elements with several μm thickness; this is unsuitable for general-purpose driving and detecting circuits, which normally operate below 20–30 MHz. During our investigations about thinfilm MI elements, we found an interesting behavior that the frequency profile of impedance shows double peak depending on the applied bias field, that is, another peak appears at lower frequency region [4]. Then we analyzed this profile based on the domain wall equation and indicated the changes in impedance is attributed to the domain wall resonance (DWR) [5]. We also showed a potential of the phenomenon applied for developing a highly sensitive sensor operated at frequencies around the dozen megahertz region. In such cases, more detailed investigations about incident power is required because the behavior of impedance changes strongly depends on input high frequency power and this behavior is not still clear. Thus, in this study, we evaluated experimentally the impedance profile around frequency where the DWR occurs when the incident ac power modulated, and discussed about the sensitivity of impedance changes.

Analysis of thin-film magnetoimpedance behavior in low MHz regions based on domain wall equation and bias susceptibility theory

An interesting behavior of thin-film magnetoimpedance elements in the relatively low megahertz (MHz) region is found experimentally when the width of the element is narrow and the thickness of elements is several micrometers. The impedance peaks and inductance shows a rapid drop at around 10 MHz when a bias field is applied to such elements. The impedance profiles of the elements were analyzed on the basis of a domain wall motion equation and bias susceptibility theory. Calculation of the domain wall motion equation when accounting for domain resonance explains the impedance behavior in the low MHz region. The rapid drop in inductance and peak in impedance can be attributed to the domain wall resonance. At a relatively higher frequency, above 100 MHz, the calculation of bias susceptibility while considering ferromagnetic resonance thoroughly explains the experimental behavior.

Domain wall equations, Hessian of superpotential, and Bogomol'nyi bounds

An important question concerning the classical solutions of the equations of motion arising in quantum field theories at the BPS critical coupling is whether all finite-energy solutions are necessarily BPS. In this paper we present a study of this basic question in the context of the domain wall equations whose potential is induced from a superpotential so that the ground states are the critical points of the superpotential. We prove that the definiteness of the Hessian of the superpotential suffices to ensure that all finite-energy domain-wall solutions are BPS. We give several examples to show that such a BPS property may fail such that non-BPS solutions exist when the Hessian of the superpotential is indefinite.

Nonintegrability of self-dual Yang–Mills–Higgs system

We examine integrability of self-dual Yang–Mills system in the Higgs phase, with taking simpler cases of vortices and domain walls. We show that the vortex equations and the domain-wall equations do not have Painlevé property. This fact suggests that these equations are not integrable.

Comparative analysis of two methods of calculation of the orientation of domain walls in ferroelastics

Two types of domain-wall equations are analyzed: the equations derived by the Sapriel method and the equations obtained by interface matching of the thermal-expansion tensor. It is shown that, for W-type domain walls, these methods yield the same equations. For W′-type domain walls, the equations obtained by different methods coincide for proper ferroelastics and differ for improper ferroelastics.

Plane symmetric traversable wormholes in an anti–de Sitter background

We construct solutions of plane symmetric wormholes in the presence of a negative cosmological constant by matching an interior spacetime to the exterior anti-de Sitter vacuum solution. The spatial topology of this plane symmetric wormhole can be planar, cylindrical and toroidal. As usual the null energy condition is necessarily violated at the throat. At the junction surface, the surface stresses are determined. By expressing the tangential surface pressure as a function of several parameters, namely, that of the matching radius, the radial derivative of the redshift function and of the surface energy density, the sign of the tangential surface pressure is analyzed. We then study four specific equations of state at the junction: zero surface energy density, constant redshift function, domain wall equation of state, and traceless surface stress-energy tensor. The equation governing the behavior of the radial pressure, in terms of the surface stresses and the extrinsic curvatures, is also displayed. Finally, we construct a model of a plane symmetric traversable wormhole which minimizes the usage of the exotic matter at the throat, i.e., the null energy condition is made arbitrarily small at the wormhole throat, while the surface stresses on the junction surface satisfy the weak energy condition, and consequently the null energy condition. The construction of these wormholes does not alter the topology of the background spacetime (i.e., spacetime is not multiply-connected), so that these solutions can instead be considered domain walls. Thus, in general, these wormhole solutions do not allow time travel.

Exchange stiffness constant and effective gyromagnetic factor of Gd, Tb and Nd containing, amorphous rare earth-transition metal films

The exchange stiffness constant and the effective gyromagnetic factor of amorphous Gd/sub 13.5/Tb/sub 6.2/Fe/sub 80.3/, Gd/sub 21.2/Co/sub 78.8/, Gd/sub 19.4/Nd/sub 6.1/Fe/sub 74.5/ and Gd/sub 19.6/Nd/sub 10.3/Fe/sub 70.1/ alloy films have been determined by Brillouin light scattering and from measurements of the domain wall energy. All samples, which show a constant Curie temperature of 465 K, exhibit the same exchange stiffness constant, as measured by Brillouin light. The obtained values of both methods agree Gd/sub 13.5/Tb/sub 6.2/Fe/sub 80.3/ and Gd/sub 21.2/Co/sub 78.8/ films, but not for the Nd containing films. The latter is attributed to a breakdown of the standard Bloch domain wall equation in Nd containing systems. >

Dynamical behavior of domain walls in quenched quasi-one-dimensional systems

Dynamics of ordering processes in quenched systems with strong spatial anisotropy was investigated on the basis of the domain wall equations reduced from time-dependent Ginzburg-Landau type models. We specifically focus on the long-time scaling behavior and find the two universality classes arising from relevance of the domain wall curvature. Results are compared with the existing experiments on layered Ising antiferromagnets and further experiments with anisotropic systems are suggested, which include systems represented by chiral Potts models.

Morphology dynamics of block copolymer systems

The approach to polymer morphology dynamics developed in our previous paper (Physica 143A (1987) 349) is applied to block copolymer systems. The combination of the reptation idea and the incompressibility requirement introduces correlations among reptative motions, where polymer ends as well as junction points play important roles. Diffusive motion of smooth deformations of the lamellar structure is derived. The domain wall equation of motion is also derived in the strong segregation limit. However, there are some difficulties in the simple reptation model in this limit which are also discussed. Finally, consequences of certain ways of relaxing the strict incompressibility requirement are discussed.

Calculation of magnetic domain wall bowing and eddy current losses in an infinite sheet of bar-like domains

An analytic solution has been obtained for the magnetic field distribution and eddy current losses associated with an infinite array of regularly spaced 180° domain walls which are allowed to bow during their motion. Wall motion was constrained to satisfy a sinusoidal total flux boundary condition. The field solution was solved self-consistently with the domain wall equation of motion. Calculated losses were always lowered relative to the plane wall case. Difficulties were encountered in the numerical iteration scheme as the degree of bowing increased. Using an approximation for the high bowing case, a physical instability occurred before bowing became too severe.

The spin correlation in a ferromagnet with random anisotropy

A computer simulation technique has been used to study the static spin correlation in a ferromagnet with random magnetic anisotropy. An effective anisotropy constant which enables us to express the spin correlation by the domain wall equation was calculated for various values of single-ion anisotropy constant. Allowing the spin tunnelling or not makes a significant difference in the high anisotropy region. The energy of a relaxed domain wall was calculated and it was shown that the domain wall energy approached to zero in the Ising limit, suggesting the instability of the ferromagnetic remanent state. The ground state can be obtained by creating reverse domains in the ferromagnetic state, and should be classified as the spin-glass state. The temperature dependence of the coercivity of the amorphous magnet was explained by the theory developed for highly anisotropic crystalline magnets.