29,303 research outputs found
Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips
We determine the general structure of the partition function of the -state
Potts model in an external magnetic field, for arbitrary ,
temperature variable , and magnetic field variable , on cyclic, M\"obius,
and free strip graphs of the square (sq), triangular (tri), and honeycomb
(hc) lattices with width and arbitrarily great length . For the
cyclic case we prove that the partition function has the form ,
where denotes the lattice type, are specified
polynomials of degree in , is the corresponding
transfer matrix, and () for ,
respectively. An analogous formula is given for M\"obius strips, while only
appears for free strips. We exhibit a method for
calculating for arbitrary and give illustrative
examples. Explicit results for arbitrary are presented for
with and . We find very simple formulas
for the determinant . We also give results for
self-dual cyclic strips of the square lattice.Comment: Reference added to a relevant paper by F. Y. W
Computational predictive methods for fracture and fatigue
The damage-tolerant design philosophy as used by aircraft industries enables aircraft components and aircraft structures to operate safely with minor damage, small cracks, and flaws. Maintenance and inspection procedures insure that damages developed during service remain below design values. When damage is found, repairs or design modifications are implemented and flight is resumed. Design and redesign guidelines, such as military specifications MIL-A-83444, have successfully reduced the incidence of damage and cracks. However, fatigue cracks continue to appear in aircraft well before the design life has expired. The F16 airplane, for instance, developed small cracks in the engine mount, wing support, bulk heads, the fuselage upper skin, the fuel shelf joints, and along the upper wings. Some cracks were found after 600 hours of the 8000 hour design service life and design modifications were required. Tests on the F16 plane showed that the design loading conditions were close to the predicted loading conditions. Improvements to analytic methods for predicting fatigue crack growth adjacent to holes, when multiple damage sites are present, and in corrosive environments would result in more cost-effective designs, fewer repairs, and fewer redesigns. The overall objective of the research described in this paper is to develop, verify, and extend the computational efficiency of analysis procedures necessary for damage tolerant design. This paper describes an elastic/plastic fracture method and an associated fatigue analysis method for damage tolerant design. Both methods are unique in that material parameters such as fracture toughness, R-curve data, and fatigue constants are not required. The methods are implemented with a general-purpose finite element package. Several proof-of-concept examples are given. With further development, the methods could be extended for analysis of multi-site damage, creep-fatigue, and corrosion fatigue problems
Biochemical characterization of the initial steps of the Kennedy pathway in Trypanosoma brucei:the ethanolamine and choline kinases
Note related output below contains correction of this paper.Ethanolamine and choline are major components of the trypanosome membrane phospholipids, in the form of GPEtn (glycero-phosphoethanolamine) and GPCho (glycerophosphocholine). Ethanolamine is also found as an integral component of the GPI (glycosylpliosphatidylinositol) anchor that is required for membrane attachment of cell-surface proteins, most notably the variant-surface glycoproteins. The de novo synthesis of GPEtn and GPCho starts with the generation of phosphoethanolamine and phosphocholine by ethanolamine and choline kinases via the Kennedy pathway. Database mining revealed two putative C/EKs (choline/ethanolamine kinases) in the Trypanosoma brucei genome, which were cloned, overexpressed, purified and characterized. TbEK 1 (T brucei ethanolamine kinase 1) was shown to be catalytically active as an ethanolamine-specific kinase, i.e. it had no choline kinase activity. The K values for ethanolamine and ATP were found to be 18.4 +/- 0.9 and 219 29 mu M respectively. TbC/EK2 (T brucei choline/ethanolamine kinase 2), on the other hand, was found to be able to phosphorylate both ethanolamine and choline, even though choline was the preferred substrate, with a K-m 80 times lower than that of ethanolamine. The K. values for choline, ethanolamine and ATP were 31.4 +/- 2.6 mu M, 2.56 +/- 0.31 mu M and 20.6 +/- 1.96 mu M respectively. Further substrate specificity analysis revealed that both TbEK1 and TbC/EK2 were able to tolerate various modifications at the amino group, with the exception of a quaternary amine for TbEK1 (choline) and a primary amine for TbC/EK2 (ethanolamine). Both enzymes recognized analogues with substituents oil C-2, but substitutions oil C-1 and elongations of the carbon chain were not well tolerated.Publisher PDFPeer reviewe
Exact Results on Potts Model Partition Functions in a Generalized External Field and Weighted-Set Graph Colorings
We present exact results on the partition function of the -state Potts
model on various families of graphs in a generalized external magnetic
field that favors or disfavors spin values in a subset of
the total set of possible spin values, , where and are
temperature- and field-dependent Boltzmann variables. We remark on differences
in thermodynamic behavior between our model with a generalized external
magnetic field and the Potts model with a conventional magnetic field that
favors or disfavors a single spin value. Exact results are also given for the
interesting special case of the zero-temperature Potts antiferromagnet,
corresponding to a set-weighted chromatic polynomial that counts
the number of colorings of the vertices of subject to the condition that
colors of adjacent vertices are different, with a weighting that favors or
disfavors colors in the interval . We derive powerful new upper and lower
bounds on for the ferromagnetic case in terms of zero-field
Potts partition functions with certain transformed arguments. We also prove
general inequalities for on different families of tree graphs.
As part of our analysis, we elucidate how the field-dependent Potts partition
function and weighted-set chromatic polynomial distinguish, respectively,
between Tutte-equivalent and chromatically equivalent pairs of graphs.Comment: 39 pages, 1 figur
Probing AdS4/CFT3 proposals beyond chiral rings
We calculate the superconformal Witten index for the Chern-Simons-matter
theory which was proposed to describe multiple M2-branes on . We
consider a variant of this model, which exhibits explicit N=3 supersymmetry and
has the advantage of not having an exotic branch of the moduli space. At ,
we compare the index with that from the proposed gravity dual and find a
disagreement.Comment: references added; introduction modifie
Surface electronic structure of a topological Kondo insulator candidate SmB6: insights from high-resolution ARPES
The Kondo insulator SmB6 has long been known to exhibit low temperature (T <
10K) transport anomaly and has recently attracted attention as a new
topological insulator candidate. By combining low-temperature and high
energy-momentum resolution of the laser-based ARPES technique, for the first
time, we probe the surface electronic structure of the anomalous conductivity
regime. We observe that the bulk bands exhibit a Kondo gap of 14 meV and
identify in-gap low-lying states within a 4 meV window of the Fermi level on
the (001)-surface of this material. The low-lying states are found to form
electron-like Fermi surface pockets that enclose the X and the Gamma points of
the surface Brillouin zone. These states disappear as temperature is raised
above 15K in correspondence with the complete disappearance of the 2D
conductivity channels in SmB6. While the topological nature of the in-gap
metallic states cannot be ascertained without spin (spin-texture) measurements
our bulk and surface measurements carried out in the
transport-anomaly-temperature regime (T < 10K) are consistent with the
first-principle predicted Fermi surface behavior of a topological Kondo
insulator phase in this material.Comment: 4 Figures, 6 Page
Bayesian Model Calibration and Sensitivity Analysis for Oscillating Biological Experiments
Understanding the oscillating behaviors that govern organisms' internal
biological processes requires interdisciplinary efforts combining both
biological and computer experiments, as the latter can complement the former by
simulating perturbed conditions with higher resolution. Harmonizing the two
types of experiment, however, poses significant statistical challenges due to
identifiability issues, numerical instability, and ill behavior in high
dimension. This article devises a new Bayesian calibration framework for
oscillating biochemical models. The proposed Bayesian model is estimated
relying on an advanced Markov chain Monte Carlo (MCMC) technique which can
efficiently infer the parameter values that match the simulated and observed
oscillatory processes. Also proposed is an approach to sensitivity analysis
based on the intervention posterior. This approach measures the influence of
individual parameters on the target process by using the obtained MCMC samples
as a computational tool. The proposed framework is illustrated with circadian
oscillations observed in a filamentous fungus, Neurospora crassa.Comment: manuscript 33 pages, appendix 6 page
Spectrum for Heavy Quankonia and Mixture of the Relevant Wave Functions within the Framework of Bethe-Salpeter Equation
Considering the fact that some excited states of the heavy quarkonia
(charmonium and bottomonium) still missing in experimental observations and
potential applications of the relevant wave functions of the bound states, we
re-analyze the spectrum and the relevant wave functions of the heavy quarkonia
within the framework of Bethe-Salpeter (B.S.) equation with a proper
QCD-inspired kernel. Such a kernel for the heavy quarkonia, relating to
potential of non-relativistic quark model, is instantaneous, so we call the
corresponding B.S. equation as BS-In equation throughout the paper.
Particularly, a new way to solve the B.S. equation, which is different from the
traditional ones, is proposed here, and with it not only the known spectrum for
the heavy quarkonia is re-generated, but also an important issue is brought in,
i.e., the obtained solutions of the equation `automatically' include the
'fine', 'hyperfine' splittings and the wave function mixture, such as
wave mixing in states, wave mixing in
states for charmonium and bottomonium etc. It is pointed out that the best
place to test the wave mixture probably is at -factory ( collider
running at -boson pole with extremely high luminosity).Comment: 26 pages, 8 figure
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