Almost overlap-free words and the word problem for the free Burnside semigroup satisfying x^2=x^3

In this paper we investigate the word problem of the free Burnside semigroup satisfying x^2=x^3 and having two generators. Elements of this semigroup are classes of equivalent words. A natural way to solve the word problem is to select a unique "canonical" representative for each equivalence class. We prove that overlap-free words and so-called almost overlap-free words (this notion is some generalization of the notion of overlap-free words) can serve as canonical representatives for corresponding equivalence classes. We show that such a word in a given class, if any, can be efficiently found. As a result, we construct a linear-time algorithm that partially solves the word problem for the semigroup under consideration.Comment: 33 pages, submitted to Internat. J. of Algebra and Compu

Humidity effects on tip-induced polarization switching in lithium niobate

Interest to ferroelectric materials has been increased significantly in last decades due to development of new generation of nonlinear optical and data storage devices. Scanning probe microscopy (SPM) can be used both for study of domain structures with nanoscale spatial resolution and for writing the isolated nanodomains by local application of the electric field. Tip-induced switching in the ambient still needs experimental investigations and theoretical explorations. Here we studied influence of the value of relative humidity in the SPM chamber on the process of tip-induced polarization switching. This phenomenon was attributed to existing of the water meniscus between tip and the sample surface in humid atmosphere. Presented results are important for further complex investigations of the ferroelectric materials and their applications.Comment: 15 pages, 5 figures, Submitted to Applied Physics Letter

Magnetization reversal in spin patterns with complex geometry

We study field-driven dynamics of spins with antiferromagnetic interaction along the links of a complex substrate geometry, which is modeled by graphs of a controlled connectivity distribution. The magnetization reversal occurs in avalanches of spin flips, which are pinned by the topological constraints of the underlying graph. The hysteresis loop and avalanche sizes are analyzed and classified in terms of graph's connectivity and clustering. The results are relevant for magnets with a hierarchical spatial inhomogeneity and for design of nanoscale magnetic devices.Comment: 4 pages, 3 color figures, revtex

The effect of electromechanical coupling on the strain in AlGaN/GaN heterojunction field effect transistors

The strain in AlGaN/GaN heterojunction field-effect transistors (HFETs) is examined theoretically in the context of the fully-coupled equation of state for piezoelectric materials. Using a simple analytical model, it is shown that, in the absence of a two-dimensional electron gas (2DEG), the out-of-plane strain obtained without electromechanical coupling is in error by about 30% for an Al fraction of 0.3. This result has consequences for the calculation of quantities that depend directly on the strain tensor. These quantities include the eigenstates and electrostatic potential in AlGaN/GaN heterostructures. It is shown that for an HFET, the electromechanical coupling is screened by the 2DEG. Results for the electromechanical model, including the 2DEG, indicate that the standard (decoupled) strain model is a reasonable approximation for HFET calculataions. The analytical results are supported by a self-consistent Schr\"odinger-Poisson calculation that includes the fully-coupled equation of state together with the charge-balance equation.Comment: 6 figures, revte

The MRO-accompanied modes of Re-implantation into SiO2-host matrix: XPS and DFT based scenarios

The following scenarios of Re-embedding into SiO2-host by pulsed Re-implantation were derived and discussed after XPS-and-DFT electronic structure qualification: (i) low Re-impurity concentration mode -> the formation of combined substitutional and interstitial impurities with Re2O7-like atomic and electronic structures in the vicinity of oxygen vacancies; (ii) high Re-impurity concentration mode -> the fabrication of interstitial Re-metal clusters with the accompanied formation of ReO2-like atomic structures and (iii) an intermediate transient mode with Re-impurity concentration increase, when the precursors of interstitial defect clusters are appeared and growing in the host-matrix structure occur. An amplification regime of Re-metal contribution majority to the final Valence Band structure was found as one of the sequences of intermediate transient mode. It was shown that most of the qualified and discussed modes were accompanied by the MRO (middle range ordering) distortions in the initial oxygen subnetwork of the a-SiO2 host-matrix because of the appeared mixed defect configurations.Comment: 19 pages, 7 figures, accepted to J. Alloys and Compound

Transition Property For Cube-Free Words

We study cube-free words over arbitrary non-unary finite alphabets and prove the following structural property: for every pair $(u,v)$ of $d$-ary cube-free words, if $u$ can be infinitely extended to the right and $v$ can be infinitely extended to the left respecting the cube-freeness property, then there exists a "transition" word $w$ over the same alphabet such that $uwv$ is cube free. The crucial case is the case of the binary alphabet, analyzed in the central part of the paper. The obtained "transition property", together with the developed technique, allowed us to solve cube-free versions of three old open problems by Restivo and Salemi. Besides, it has some further implications for combinatorics on words; e.g., it implies the existence of infinite cube-free words of very big subword (factor) complexity.Comment: 14 pages, 5 figure

Static conductivity of charged domain wall in uniaxial ferroelectric-semiconductors

Using Landau-Ginzburg-Devonshire theory we calculated numerically the static conductivity of both inclined and counter domain walls in the uniaxial ferroelectrics-semiconductors of n-type. We used the effective mass approximation for the electron and holes density of states, which is valid at arbitrary distance from the domain wall. Due to the electrons accumulation, the static conductivity drastically increases at the inclined head-to-head wall by 1 order of magnitude for small incline angles theta pi/40 by up 3 orders of magnitude for the counter domain wall (theta=pi/2). Two separate regions of the space charge accumulation exist across an inclined tail-to-tail wall: the thin region in the immediate vicinity of the wall with accumulated mobile holes and the much wider region with ionized donors. The conductivity across the tail-to-tail wall is at least an order of magnitude smaller than the one of the head-to-head wall due to the low mobility of holes, which are improper carries. The results are in qualitative agreement with recent experimental data for LiNbO3 doped with MgO.Comment: 20 pages, 6 figures, 1 appendi