625 research outputs found
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
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 of -ary cube-free
words, if can be infinitely extended to the right and can be infinitely
extended to the left respecting the cube-freeness property, then there exists a
"transition" word over the same alphabet such that 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
Engineering Logical Inflammation Sensing Circuit for Modulating Gut Conditions
The mammalian gut contains trillions of microbes that interact with host cells and monitor changes in the environment. Opportunistic pathogens exploit environmental conditions to stimulate their growth and virulence, leading to a resurgence of chronic disorders such as inflammatory bowel disease (IBD). Current therapies are effective in less than 30% of patients due to the lack of adherence to prescription schedules and overall, off-target effects. Smart microbial therapeutics can be engineered to colonize the gut, providing in situ surveillance and conditional disease modulation. However, many current engineered microbes can only respond to single gut environmental factors, limiting their effectiveness. In this work, we implement the previously characterized split activator AND logic gate in the probiotic E. coli strain Nissle 1917. Our system can respond to two input signals: the inflammatory biomarker tetrathionate and a second input signal, IPTG. We report 4-6 fold induction with minimal leak when both signals are present. We model the dynamics of the AND gate using chemical reaction networks, and by tuning parameters in silico, we identified perturbations that affect our circuit's selectivity. We anticipate that our results will prove useful for designing living therapeutics for spatial targeting and signal processing in complex environments
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