760 research outputs found
Hybrid expansions for local structural relaxations
A model is constructed in which pair potentials are combined with the cluster
expansion method in order to better describe the energetics of structurally
relaxed substitutional alloys. The effect of structural relaxations away from
the ideal crystal positions, and the effect of ordering is described by
interatomic-distance dependent pair potentials, while more subtle
configurational aspects associated with correlations of three- and more sites
are described purely within the cluster expansion formalism. Implementation of
such a hybrid expansion in the context of the cluster variation method or Monte
Carlo method gives improved ability to model phase stability in alloys from
first-principles.Comment: 8 pages, 1 figur
Seiberg-Witten prepotential for E-string theory and random partitions
We find a Nekrasov-type expression for the Seiberg-Witten prepotential for
the six-dimensional non-critical E_8 string theory toroidally compactified down
to four dimensions. The prepotential represents the BPS partition function of
the E_8 strings wound around one of the circles of the toroidal
compactification with general winding numbers and momenta. We show that our
expression exhibits expected modular properties. In particular, we prove that
it obeys the modular anomaly equation known to be satisfied by the
prepotential.Comment: 14 page
Finite Automata for the Sub- and Superword Closure of CFLs: Descriptional and Computational Complexity
We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the
state-complexity of representing sub- or superword closures of context-free
grammars (CFGs): (1) We prove a (tight) upper bound of on
the size of nondeterministic finite automata (NFAs) representing the subword
closure of a CFG of size . (2) We present a family of CFGs for which the
minimal deterministic finite automata representing their subword closure
matches the upper-bound of following from (1).
Furthermore, we prove that the inequivalence problem for NFAs representing sub-
or superword-closed languages is only NP-complete as opposed to PSPACE-complete
for general NFAs. Finally, we extend our results into an approximation method
to attack inequivalence problems for CFGs
Seiberg-Witten prepotential for E-string theory and global symmetries
We obtain Nekrasov-type expressions for the Seiberg-Witten prepotential for
the six-dimensional (1,0) supersymmetric E-string theory compactified on T^2
with nontrivial Wilson lines. We consider compactification with four general
Wilson line parameters, which partially break the E_8 global symmetry. In
particular, we investigate in detail the cases where the Lie algebra of the
unbroken global symmetry is E_n + A_{8-n} with n=8,7,6,5 or D_8. All our
Nekrasov-type expressions can be viewed as special cases of the elliptic
analogue of the Nekrasov partition function for the SU(N) gauge theory with
N_f=2N flavors. We also present a new expression for the Seiberg-Witten curve
for the E-string theory with four Wilson line parameters, clarifying the
connection between the E-string theory and the SU(2) Seiberg-Witten theory with
N_f=4 flavors.Comment: 22 pages. v2: comments and a reference added, version to appear in
JHE
A new path to measure antimatter free fall
We propose an experiment to measure the free fall acceleration of neutral antihydrogen atoms. The originality of this path is to first produce the Hbar+ ion
Vibration and buckling of thin-walled composite I-beams with arbitrary lay-ups under axial loads and end moments
A finite element model with seven degrees of freedom per node is developed to study vibration and buckling of thin-walled composite I-beams with arbitrary lay-ups under constant axial loads and equal end moments. This model is based on the classical lamination theory, and accounts for all the structural coupling coming from material anisotropy. The governing differential equations are derived from the Hamiltonâs principle. Numerical results are obtained for thin-walled composite I-beams to investigate the effects of axial force, bending moment and fiber orientation on the buckling moments, natural frequencies, and corresponding vibration mode shapes as well as axial-moment-frequency interaction curves
Fatigue strengthening of damaged steel members using wire arc additive manufacturing
In this study, a directed energy deposition (DED) process called wire arc additive manufacturing (WAAM) is employed for the fatigue strengthening of damaged steel members. Three steel specimens with central cracks were tested under a high-cycle fatigue loading (HCF) regime: (1) the reference specimen; (2) the WAAM-repaired specimen with an as-deposited profile, and (3) the WAAM-repaired specimen machined to reduce stress concentration factors (SCF). The corresponding finite element (FE) simulation of the WAAM process was calibrated using static experimental results, which revealed the main mechanism. The process was found to introduce compressive residual stresses at the crack tip owing to the thermal contraction of the repair. The FE results also revealed that stress concentration exists at the root of the as-deposited WAAM; this stress concentration can be mitigated by machining the WAAM to a pyramid-like shape. The fractography analysis indicated that the cracks were initiated at the WAAM-steel interface, and microscopic observations revealed that the microcracks were arrested by the porosities in the melted interface. The results of this pioneering study suggest that WAAM repair is a promising technique for combating fatigue damage in steel structures
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