246 research outputs found
Real space first-principles derived semiempirical pseudopotentials applied to tunneling magnetoresistance
In this letter we present a real space density functional theory (DFT)
localized basis set semi-empirical pseudopotential (SEP) approach. The method
is applied to iron and magnesium oxide, where bulk SEP and local spin density
approximation (LSDA) band structure calculations are shown to agree within
approximately 0.1 eV. Subsequently we investigate the qualitative
transferability of bulk derived SEPs to Fe/MgO/Fe tunnel junctions. We find
that the SEP method is particularly well suited to address the tight binding
transferability problem because the transferability error at the interface can
be characterized not only in orbital space (via the interface local density of
states) but also in real space (via the system potential). To achieve a
quantitative parameterization, we introduce the notion of ghost semi-empirical
pseudopotentials extracted from the first-principles calculated Fe/MgO bonding
interface. Such interface corrections are shown to be particularly necessary
for barrier widths in the range of 1 nm, where interface states on opposite
sides of the barrier couple effectively and play a important role in the
transmission characteristics. In general the results underscore the need for
separate tight binding interface and bulk parameter sets when modeling
conduction through thin heterojunctions on the nanoscale.Comment: Submitted to Journal of Applied Physic
A survey on graphs with polynomial growth
AbstractIn this paper we give an overview on connected locally finite transitive graphs with polynomial growth. We present results concerning the following topics: •Automorphism groups of graphs with polynomial growth.•Groups and graphs with linear growth.•S-transitivity.•Covering graphs.•Automorphism groups as topological groups
Infinite primitive directed graphs
A group G of permutations of a set Ω is primitive if it acts transitively on Ω, and the only G-invariant equivalence relations on Ω are the trivial and universal relations.
A digraph Γ is primitive if its automorphism group acts primitively on its vertex set, and is infinite if its vertex set is infinite. It has connectivity one if it is connected and there exists a vertex α of Γ, such that the induced digraph Γ∖{α} is not connected. If Γ has connectivity one, a lobe of Γ is a connected subgraph that is maximal subject to the condition that it does not have connectivity one. Primitive graphs (and thus digraphs) with connectivity one are necessarily infinite.
The primitive graphs with connectivity one have been fully classified by Jung and Watkins: the lobes of such graphs are primitive, pairwise-isomorphic and have at least three vertices. When one considers the general case of a primitive digraph with connectivity one, however, this result no longer holds. In this paper we investigate the structure of these digraphs, and obtain a complete characterisation
On the degree conjecture for separability of multipartite quantum states
We settle the so-called degree conjecture for the separability of
multipartite quantum states, which are normalized graph Laplacians, first given
by Braunstein {\it et al.} [Phys. Rev. A \textbf{73}, 012320 (2006)]. The
conjecture states that a multipartite quantum state is separable if and only if
the degree matrix of the graph associated with the state is equal to the degree
matrix of the partial transpose of this graph. We call this statement to be the
strong form of the conjecture. In its weak version, the conjecture requires
only the necessity, that is, if the state is separable, the corresponding
degree matrices match. We prove the strong form of the conjecture for {\it
pure} multipartite quantum states, using the modified tensor product of graphs
defined in [J. Phys. A: Math. Theor. \textbf{40}, 10251 (2007)], as both
necessary and sufficient condition for separability. Based on this proof, we
give a polynomial-time algorithm for completely factorizing any pure
multipartite quantum state. By polynomial-time algorithm we mean that the
execution time of this algorithm increases as a polynomial in where is
the number of parts of the quantum system. We give a counter-example to show
that the conjecture fails, in general, even in its weak form, for multipartite
mixed states. Finally, we prove this conjecture, in its weak form, for a class
of multipartite mixed states, giving only a necessary condition for
separability.Comment: 17 pages, 3 figures. Comments are welcom
Considerations for the design of an onboard air traffic situation display
The basic concept of remoting information to the cockpit is used to design and develop a computerized airborne traffic situation display device that automatically selects and presents segments of a controller's scope to the aircraft pilot via a narrow band digital data link. These data are integrated with aircraft heading and navigation information to provide a display useful in congested air space. The display can include alphanumerical symbols, air route maps, and controller instructions
Covering Partial Cubes with Zones
A partial cube is a graph having an isometric embedding in a hypercube.
Partial cubes are characterized by a natural equivalence relation on the edges,
whose classes are called zones. The number of zones determines the minimal
dimension of a hypercube in which the graph can be embedded. We consider the
problem of covering the vertices of a partial cube with the minimum number of
zones. The problem admits several special cases, among which are the problem of
covering the cells of a line arrangement with a minimum number of lines, and
the problem of finding a minimum-size fibre in a bipartite poset. For several
such special cases, we give upper and lower bounds on the minimum size of a
covering by zones. We also consider the computational complexity of those
problems, and establish some hardness results
Infinite motion and 2-distinguishability of graphs and groups
A group A acting faithfully on a set X is 2-distinguishable if there is a 2-coloring of X that is not preserved by any nonidentity element of A, equivalently, if there is a proper subset of X with trivial setwise stabilizer. The motion of an element a in A is the number of points of X that are moved by a, and the motion of the group A is the minimal motion of its nonidentity elements. When A is finite, the Motion Lemma says that if the motion of A is large enough (specifically at least 2 log_2 |A|), then the action is 2-distinguishable. For many situations where X has a combinatorial or algebraic structure, the Motion Lemma implies that the action of Aut(X) on X is 2-distinguishable in all but finitely many instances.
We prove an infinitary version of the Motion Lemma for countably infinite permutation groups, which states that infinite motion is large enough to guarantee 2-distinguishability. From this we deduce a number of results, including the fact that every locally finite, connected graph whose automorphism group is countably infinite is 2-distinguishable. One cannot extend the Motion Lemma to uncountable permutation groups, but nonetheless we prove that (under the permutation topology) every closed permutation group with infinite motion has a dense subgroup which is 2-distinguishable. We conjecture an extension of the Motion Lemma which we expect holds for a restricted class of uncountable permutation groups, and we conclude with a list of open questions. The consequences of our results are drawn for orbit equivalence of infinite permutation groups
DWPF MATERIALS EVALUATION SUMMARY REPORT
To better ensure the reliability of the Defense Waste Processing Facility (DWPF) remote canyon process equipment, a materials evaluation program was performed as part of the overall startup test program. Specific test programs included FA-04 ('Process Vessels Erosion/Corrosion Studies') and FA-05 (melter inspection). At the conclusion of field testing, Test Results Reports were issued to cover the various test phases. While these reports completed the startup test requirements, DWPF-Engineering agreed to compile a more detailed report which would include essentially all of the materials testing programs performed at DWPF. The scope of the materials evaouation programs included selected equipment from the Salt Process Cell (SPC), Chemical Process Cell (CPC), Melt Cell, Canister Decon Cell (CDC), and supporting facilities. The program consisted of performing pre-service baseline inspections (work completed in 1992) and follow-up inspections after completion of the DWPF cold chemical runs. Process equipment inspected included: process vessels, pumps, agitators, coils, jumpers, and melter top head components. Various NDE (non-destructive examination) techniques were used during the inspection program, including: ultrasonic testing (UT), visual (direct or video probe), radiography, penetrant testing (PT), and dimensional analyses. Finally, coupon racks were placed in selected tanks in 1992 for subsequent removal and corrosion evaluation after chemical runs
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