17,425 research outputs found
Nivat's conjecture holds for sums of two periodic configurations
Nivat's conjecture is a long-standing open combinatorial problem. It concerns
two-dimensional configurations, that is, maps where is a finite set of symbols. Such configurations are often
understood as colorings of a two-dimensional square grid. Let denote
the number of distinct block patterns occurring in a configuration
. Configurations satisfying for some
are said to have low rectangular complexity. Nivat conjectured that such
configurations are necessarily periodic.
Recently, Kari and the author showed that low complexity configurations can
be decomposed into a sum of periodic configurations. In this paper we show that
if there are at most two components, Nivat's conjecture holds. As a corollary
we obtain an alternative proof of a result of Cyr and Kra: If there exist such that , then is periodic. The
technique used in this paper combines the algebraic approach of Kari and the
author with balanced sets of Cyr and Kra.Comment: Accepted for SOFSEM 2018. This version includes an appendix with
proofs. 12 pages + references + appendi
Ab-initio simulation and experimental validation of beta-titanium alloys
In this progress report we present a new approach to the ab-initio guided
bottom up design of beta-Ti alloys for biomedical applications using a quantum
mechanical simulation method in conjunction with experiments. Parameter-free
density functional theory calculations are used to provide theoretical guidance
in selecting and optimizing Ti-based alloys with respect to three constraints:
(i) the use of non-toxic alloy elements; (ii) the stabilization of the body
centered cubic beta phase at room temperature; (iii) the reduction of the
elastic stiffness compared to existing Ti-based alloys. Following the
theoretical predictions, the alloys of interest are cast and characterized with
respect to their crystallographic structure, microstructure, texture, and
elastic stiffness. Due to the complexity of the ab initio calculations, the
simulations have been focused on a set of binary systems of Ti with two
different high melting bcc metals, namely, Nb and Mo. Various levels of model
approximations to describe mechanical and thermodynamic properties are tested
and critically evaluated. The experiments are conducted both, on some of the
binary alloys and on two more complex engineering alloy variants, namely,
Ti-35wt.%Nb-7wt.%Zr-5wt.%Ta and a Ti-20wt.%Mo-7wt.%Zr-5wt.%Ta.Comment: 23 pages, progress report on ab initio alloy desig
Surface stress of Ni adlayers on W(110): the critical role of the surface atomic structure
Puzzling trends in surface stress were reported experimentally for Ni/W(110)
as a function of Ni coverage. In order to explain this behavior, we have
performed a density-functional-theory study of the surface stress and atomic
structure of the pseudomorphic and of several different possible 1x7
configurations for this system. For the 1x7 phase, we predict a different, more
regular atomic structure than previously proposed based on surface x-ray
diffraction. At the same time, we reproduce the unexpected experimental change
of surface stress between the pseudomorphic and 1x7 configuration along the
crystallographic surface direction which does not undergo density changes. We
show that the observed behavior in the surface stress is dominated by the
effect of a change in Ni adsorption/coordination sites on the W(110) surface.Comment: 14 pages, 3 figures Published in J. Phys.: Condens. Matter 24 (2012)
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First principles calculation of structural and magnetic properties for Fe monolayers and bilayers on W(110)
Structure optimizations were performed for 1 and 2 monolayers (ML) of Fe on a
5 ML W(110) substrate employing the all-electron full-potential linearized
augmented plane-wave (FP-LAPW) method. The magnetic moments were also obtained
for the converged and optimized structures. We find significant contractions
( 10 %) for both the Fe-W and the neighboring Fe-Fe interlayer spacings
compared to the corresponding bulk W-W and Fe-Fe interlayer spacings. Compared
to the Fe bcc bulk moment of 2.2 , the magnetic moment for the surface
layer of Fe is enhanced (i) by 15% to 2.54 for 1 ML Fe/5 ML W(110), and
(ii) by 29% to 2.84 for 2 ML Fe/5 ML W(110). The inner Fe layer for 2
ML Fe/5 ML W(110) has a bulk-like moment of 2.3 . These results agree
well with previous experimental data
Near-Infrared Kinetic Spectroscopy of the HO_2 and C_2H_5O_2 Self-Reactions and Cross Reactions
The self-reactions and cross reactions of the peroxy radicals HO_2 and C_2H_5O_2 and HO_2 were monitored using simultaneous independent spectroscopic probes to observe each radical species. Wavelength modulation (WM) near-infrared (NIR) spectroscopy was used to detect HO_2, and UV absorption monitored HO_2 and C_2H_5O_2. The temperature dependences of these reactions were investigated over a range of interest to tropospheric chemistry, 221−296 K. The Arrhenius expression determined for the cross reaction, k_2(T) = (6.01^(+1.95)_(−1.47)) × 10^(−13) exp((638 ± 73)/T) cm^3 molecules^(−1) s^(−1) is in agreement with other work from the literature. The measurements of the HO_2 self-reaction agreed with previous work from this lab and were not further refined.(1) The C_2H_5O_2 self-reaction is complicated by secondary production of HO_2. This experiment performed the first direct measurement of the self-reaction rate constant, as well as the branching fraction to the radical channel, in part by measurement of the secondary HO_2. The Arrhenius expression for the self-reaction rate constant is k_3(T) = (1.29^(+0.34)_(−0.27)) × 10^(−13)exp((−23 ± 61)/T) cm^3 molecules^(−1) s^(−1), and the branching fraction value is α = 0.28 ± 0.06, independent of temperature. These values are in disagreement with previous measurements based on end product studies of the branching fraction. The results suggest that better characterization of the products from RO_2 self-reactions are required
Evidence for a Low Bulk Crustal Density for Mars from Gravity and Topography
Knowledge of the average density of the crust of a planet is important in determining its interior structure. The combination of high-resolution gravity and topography data has yielded a low density for the Moons crust, yet for other terrestrial planets the resolution of the gravity field models has hampered reasonable estimates. By using well-chosen constraints derived from topography during gravity field model determination using satellite tracking data, we show that we can robustly and independently determine the average bulk crustal density directly from the tracking data, using the admittance between topography and imperfect gravity. We find a low average bulk crustal density for Mars, 2582 209 kgm3. This bulk crustal density is lower than that assumed until now. Densities for volcanic complexes are higher, consistent with earlier estimates, implying large lateral variations in crustal density. In addition, we find indications that the crustal density increases with depth
The Barrier Method: A Technique for Calculating Very Long Transition Times
In many dynamical systems there is a large separation of time scales between
typical events and "rare" events which can be the cases of interest. Rare-event
rates are quite difficult to compute numerically, but they are of considerable
practical importance in many fields: for example transition times in chemical
physics and extinction times in epidemiology can be very long, but are quite
important. We present a very fast numerical technique that can be used to find
long transition times (very small rates) in low-dimensional systems, even if
they lack detailed balance. We illustrate the method for a bistable
non-equilibrium system introduced by Maier and Stein and a two-dimensional (in
parameter space) epidemiology model.Comment: 20 pages, 8 figure
Computation of nucleation of a non-equilibrium first-order phase transition using a rare-event algorithm
We introduce a new Forward-Flux Sampling in Time (FFST) algorithm to
efficiently measure transition times in rare-event processes in non-equilibrium
systems, and apply it to study the first-order (discontinuous) kinetic
transition in the Ziff-Gulari-Barshad model of catalytic surface reaction. The
average time for the transition to take place, as well as both the spinodal and
transition points, are clearly found by this method.Comment: 12 pages, 10 figure
Development of a Plasma Solver for Surge Protective Devices using Spark Gap Technology
In this article we present the development of a single-fluid plasma model using the open-source CFD-based modelling framework OpenFOAM for the simulation of surge protective devices. The model uses a pressure based flow solver and supports the use of common radiation models such as the P1 model. Empirical models for electrode sheaths can be used and coupling the simulation to external circuits is possible. Some initial results are presented and compared with high-speed camera recordings
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