Dynamics of domain walls in pattern formation under traveling-wave forcing

We study dynamics of domain walls in pattern forming systems that are externally forced by a moving space-periodic modulation close to 2:1 spatial resonance. The motion of the forcing induces nongradient dynamics, while the wave number mismatch breaks explicitly the chiral symmetry of the domain walls. The combination of both effects yields an imperfect nonequilibrium Ising-Bloch bifurcation, where all kinks (including the Ising-like one) drift. Kink velocities and interactions are studied within the generic amplitude equation. For nonzero mismatch, a transition to traveling bound kink-antikink pairs and chaotic wave trains occurs.

Perturbations on domain walls and strings: A covariant theory

A covariant formalism is developed for describing perturbations on vacuum domain walls and strings. The treatment applies to arbitrary domain walls in (N+1)-dimensional flat spacetime, including the case of bubbles of a true vacuum nucleating in a false vacuum. Straight strings and planar walls in de Sitter space, as well as closed strings and walls nucleating during inflation, are also considered. Perturbations are represented by a scalar field defined on the unperturbed wall or string world sheet. In a number of interesting cases, this field has a tachyonic mass and a nonminimal coupling to the world-sheet curvature.

Quantum fluctuations on domain walls, strings, and vacuum bubbles

We develop a covariant quantum theory of fluctuations on vacuum domain walls and strings. The fluctuations are described by a scalar field defined on the classical world sheet of the defects. We consider the following cases: straight strings and planar walls in flat space, true vacuum bubbles nucleating in false vacuum, and strings and walls nucleating during inflation. The quantum state for the perturbations is constructed so that it respects the original symmetries of the classical solution. In particular, for the case of vacuum bubbles and nucleating strings and walls, the geometry of the world sheet is that of a lower-dimensional de Sitter space, and the problem reduces to the quantization of a scalar field of tachyonic mass in de Sitter space. In all cases, the root-mean-squared fluctuation is evaluated in detail, and the physical implications are briefly discussed.

Quantum tunneling of domain walls in ferromagnets

We present a theoretical study of the quantum depinning of domain walls. Our approach extends earlier work by Stamp and confirms his suggestion that quantum tunneling of domain walls in ferromagnets may reveal itself at a macroscopic level in a manner similar to the Josephson effect in superconductors. The rate of tunneling of a domain wall through a barrier formed by a planar defect is calculated in terms of macroscopic parameters of the ferromagnet. A universal behavior of the WKB exponent in the limit of small barriers is demonstrated. The effect of dissipation on the tunneling rate is studied. It is argued that quantum diffusion of domain walls apparently explains a nonthermal magnetic relaxation observed in some materials at low temperatures.

Magnetic properties and domain-wall motion in single-crystal BaFe10.2Sn0.74Co0.66O19

The magnetic properties of BaFe12O19 and BaFe10.2Sn0.74Co0.66O19 single crystals have been investigated in the temperature range (1.8 to 320 K) with a varying field from -5 to +5 T applied parallel and perpendicular to the c axis. Low-temperature magnetic relaxation, which is ascribed to the domain-wall motion, was performed between 1.8 and 15 K. The relaxation of magnetization exhibits a linear dependence on logarithmic time. The magnetic viscosity extracted from the relaxation data, decreases linearly as temperature goes down, which may correspond to the thermal depinning of domain walls. Below 2.5 K, the viscosity begins to deviate from the linear dependence on temperature, tending to be temperature independent. The near temperature independence of viscosity suggests the existence of quantum tunneling of antiferromagnetic domain wall in this temperature range.

Transient patterns in nematic liquid crystals: Domain-wall dynamics

We study the dynamics of the late stages of the Fréedericksz transition in which a periodic transient pattern decays to a final homogeneous state. A stability analysis of an unstable stationary pattern is presented, and equations for the evolution of the domain walls are obtained. Using results of previous theories, we analyze the effect that the specific dynamics of the problem, incorporating hydrodynamic couplings, has on the expected logarithmic domain growth law.

Slow Dynamics of Ising Models with Energy Barriers

Using Monte Carlo simulations we study the dynamics of three-dimensional Ising models with nearest-, next-nearest-, and four-spin (plaquette) interactions. During coarsening, such models develop growing energy barriers, which leads to very slow dynamics at low temperature. As already reported, the model with only the plaquette interaction exhibits some of the features characteristic of ordinary glasses: strong metastability of the supercooled liquid, a weak increase of the characteristic length under cooling, stretched-exponential relaxation, and aging. The addition of two-spin interactions, in general, destroys such behavior: the liquid phase loses metastability and the slow-dynamics regime terminates well below the melting transition, which is presumably related with a certain corner-rounding transition. However, for a particular choice of interaction constants, when the ground state is strongly degenerate, our simulations suggest that the slow-dynamics regime extends up to the melting transition. The analysis of these models leads us to the conjecture that in the four-spin Ising model domain walls lose their tension at the glassy transition and that they are basically tensionless in the glassy phase.

Nucleation rates in flat and curved space

Nucleation rates for tunneling processes in Minkowski and de Sitter space are investigated, taking into account one loop prefactors. In particular, we consider the creation of membranes by an antisymmetric tensor field, analogous to Schwinger pair production. This can be viewed as a model for the decay of a false (or true) vacuum at zero temperature in the thin wall limit. Also considered is the spontaneous nucleation of strings, domain walls, and monopoles during inflation. The instantons for these processes are spherical world sheets or world lines embedded in flat or de Sitter backgrounds. We find the contribution of such instantons to the semiclassical partition function, including the one loop corrections due to small fluctuations around the spherical world sheet. We suggest a prescription for obtaining, from the partition function, the distribution of objects nucleated during inflation. This can be seen as an extension of the usual formula, valid in flat space, according to which the nucleation rate is twice the imaginary part of the free energy. For the case of pair production, the results reproduce those that can be obtained using second quantization methods, confirming the validity of instanton techniques in de Sitter space. Throughout the paper, both the gravitational field and the antisymmetric tensor field are assumed external.

Asymmetric reversal in inhomogeneous magnetic heterostructures

Asymmetric magnetization reversal is an unusual phenomenon in antiferromagnet/ferromagnet (AF/FM) exchange biased bilayers. We investigated this phenomenon in a simple model system experimentally and by simulation assuming inhomogeneously distributed interfacial AF moments. The results suggest that the observed asymmetry originates from the intrinsic broken symmetry of the system, which results in local incomplete domain walls parallel to the interface in reversal to negative saturation of the FM. The magneto-optical Kerr effect unambiguously confirms such an asymmetric reversal and a depth-dependent FM domain wall in accord with the magnetometry and simulations.

Chaos in resonant-tunneling superlattices

Spatiotemporal chaos is predicted to occur in n-doped semiconductor superlattices with sequential resonant tunneling as their main charge transport mechanism. Under dc voltage bias, undamped time-dependent oscillations of the current (due to the motion and recycling of electric field domain walls) have been observed in recent experiments. Chaos is the result of forcing this natural oscillation by means of an appropriate external microwave signal.

A maximal domain of preferences for tops-only rules in the division problem

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and Serizawa (1998) extended this result by showing that the set of single-plateaued preferences is the largest domain, for all possible values of M, admitting a rule (the extended uniform rule) satisfying strategy-proofness, efficiency and symmetry. We identify, for each M and n, a maximal domain of preferences under which the extended uniform rule also satisfies the properties of strategy-proofness, efficiency, continuity, and "tops-onlyness". These domains (called weakly single-plateaued) are strictly larger than the set of single-plateaued preferences. However, their intersection, when M varies from zero to infinity, coincides with the set of single-plateaued preferences.

Two necessary conditions for strategy-proofness: on what domains are they also sufficient?

A social choice function may or may not satisfy a desirable property depending on its domain of definition. For the same reason, different conditions may be equivalent for functions defined on some domains, while different in other cases. Understanding the role of domains is therefore a crucial issue in mechanism design. We illustrate this point by analyzing the role of different conditions that are always related, but not always equivalent to strategy-proofness. We define two very natural conditions that are necessary for strategy-proofness: monotonicity and reshuffling invariance. We remark that they are not always sufficient. Then, we identify a domain condition, called intertwinedness, that ensures the equivalence between our two conditions and that of strategy-proofness. We prove that some important domains are intertwined: those of single-peaked preferences, both with public and private goods, and also those arising in simple models of house allocation. We prove that other necessary conditions for strategy-proofness also become equivalent to ours when applied to functions defined on intertwined domains, even if they are not equivalent in general. We also study the relationship between our domain restrictions and others that appear in the literature, proving that we are indeed introducing a novel proposal.

Mining and exploiting domain-specific corpora in the PANACEA platform

The objective of the PANACEA ICT-2007.2.2 EU project is to build a platform that automates the stages involved in the acquisition,production, updating and maintenance of the large language resources required by, among others, MT systems. The development of a Corpus Acquisition Component (CAC) for extracting monolingual and bilingual data from the web is one of the most innovative building blocks of PANACEA. The CAC, which is the first stage in the PANACEA pipeline for building Language Resources, adopts an efficient and distributed methodology to crawl for web documents with rich textual content in specific languages and predefined domains. The CAC includes modules that can acquire parallel data from sites with in-domain content available in more than one language. In order to extrinsically evaluate the CAC methodology, we have conducted several experiments that used crawled parallel corpora for the identification and extraction of parallel sentences using sentence alignment. The corpora were then successfully used for domain adaptation of Machine Translation Systems.

Effects of domain morphology in phase-separation dynamics at low temperature

We present numerical results of the deterministic Ginzburg-Landau equation with a concentration-dependent diffusion coefficient, for different values of the volume fraction phi of the minority component. The morphology of the domains affects the dynamics of phase separation. The effective growth exponents, but not the scaled functions, are found to be temperature dependent.

Monte Carlo Study of the Growth of L12 ordered domains in fcc A3B binary alloys

A Monte Carlo study of the late time growth of L12-ordered domains in a fcc A3B binary alloy is presented. The energy of the alloy has been modeled by a nearest-neighbor interaction Ising Hamiltonian. The system exhibits a fourfold degenerated ground state and two kinds of interfaces separating ordered domains: flat and curved antiphase boundaries. Two different dynamics are used in the simulations: the standard atom-atom exchange mechanism and the more realistic vacancy-atom exchange mechanism. The results obtained by both methods are compared. In particular we study the time evolution of the excess energy, the structure factor and the mean distance between walls. In the case of atom-atom exchange mechanism anisotropic growth has been found: two characteristic lengths are needed in order to describe the evolution. Contrarily, with the vacancyatom exchange mechanism scaling with a single length holds. Results are contrasted with existing experiments in Cu3Au and theories for anisotropic growth.