13,149 research outputs found
Understanding fragility in supercooled Lennard-Jones mixtures. I. Locally preferred structures
We reveal the existence of systematic variations of isobaric fragility in
different supercooled Lennard-Jones binary mixtures by performing molecular
dynamics simulations. The connection between fragility and local structures in
the bulk is analyzed by means of a Voronoi construction. We find that clusters
of particles belonging to locally preferred structures form slow, long-lived
domains, whose spatial extension increases by decreasing temperature. As a
general rule, a more rapid growth, upon supercooling, of such domains is
associated to a more pronounced super-Arrhenius behavior, hence to a larger
fragility.Comment: 14 pages, 14 figures, minor revisions, one figure adde
Atoms in the p-localization of stable homotopy category
We study p-localizations, where p is an odd prime, of the full subcategories Sⁿ of stable homotopy category formed by CW-complexes with cells in n successive dimensions. Using the technique of triangulated categories and matrix problems, we classify the atoms (indecomposable objects) in Spⁿ for n ≤ 4(p − 1) and show that, for n > 4(p − 1), this classification is wild in a sense of the representation theory.Вивчаються p-локалiзацiї (де p — непарне просте число) повних підкатегорій Sⁿ стабільної гомотопічної категорії, що складається з CW-комплексів із клітинами в n послідовних розмірностях. Застосовуючи техніку триангульованих категорій та матричні задачі, ми наводимо класифікацію атомів (нерозкладних об'єктів) у Spⁿ Для n≤4(p−1) i показуємо, що для n>4(p—1) ця класифікація є дикою у сенсі теорії зображень
Polyhedral units and network connectivity in calcium aluminosilicate glasses from high-energy x-ray diffraction
Structure factors for Cax/2AlxSi1-xO2 glasses (x=0,0.25,0.5,0.67) extended to
a wave vector of magnitude Q= 40 1/A have been obtained by high-energy x-ray
diffraction. For the first time, it is possible to resolve the contributions of
Si-O, Al-O and Ca-O coordination polyhedra to the experimental atomic pair
distribution functions (PDF). It has been found that both Si and Al are
four-fold coordinated and so participate in a continuous tetrahedral network at
low values of x. The number of network breaking defects in the form of
non-bridging oxygens (NBO's) increases slowly with x until x=0.5 (NBO's ~ 10%
at x=0.5). By x=0.67 the network breaking defects become significant as
evidenced by the significant drop in the average coordination number of Si. By
contrast, Al-O tetrahedra remain free of NBO's and fully integrated in the
Al/Si-O network for all values of x. Calcium maintains a rather uniform
coordination sphere of approximately 5 oxygen atoms for all values of x. The
results suggest that not only Si/Al-O tetrahedra but Ca-O polyhedra, too, play
a role in determining the glassy structure
Structural Disorder, Octahedral Coordination, and 2-Dimensional Ferromagnetism in Anhydrous Alums
The crystal structures of the triangular lattice, layered anhydrous alums
KCr(SO4)2, RbCr(SO4)2 and KAl(SO4)2 are characterized by X-ray and neutron
powder diffraction at temperatures between 1.4 and 773 K. The compounds all
crystallize in the space group P-3, with octahedral coordination of the
trivalent cations. In all cases, small amounts of disorder in the stacking of
the triangular layers of corner sharing MO6 octahedra and SO4 tetrahedra is
seen, with the MO6-SO4 network rotated in opposite directions between layers.
The electron diffraction study of KCr(SO4)2 supports this model, which on
average can be taken to imply trigonal prismatic coordination for the M3+ ions;
as was previously reported for the prototype anhydrous alum KAl(SO4)2. The
temperature dependent magnetic susceptibilities for ACr(SO4)2 (A = K,Rb,Cs)
indicate the presence of predominantly ferromagnetic interactions. Low
temperature powder neutron diffraction reveals that the magnetic ordering is
ferromagnetic in-plane, with antiferromagnetic ordering between planes below 3
K.Comment: Accepted to the Journal of Solid State Chemistr
The Structure of Liquid and Amorphous Hafnia.
Understanding the atomic structure of amorphous solids is important in predicting and tuning their macroscopic behavior. Here, we use a combination of high-energy X-ray diffraction, neutron diffraction, and molecular dynamics simulations to benchmark the atomic interactions in the high temperature stable liquid and low-density amorphous solid states of hafnia. The diffraction results reveal an average Hf-O coordination number of ~7 exists in both the liquid and amorphous nanoparticle forms studied. The measured pair distribution functions are compared to those generated from several simulation models in the literature. We have also performed ab initio and classical molecular dynamics simulations that show density has a strong effect on the polyhedral connectivity. The liquid shows a broad distribution of Hf-Hf interactions, while the formation of low-density amorphous nanoclusters can reproduce the sharp split peak in the Hf-Hf partial pair distribution function observed in experiment. The agglomeration of amorphous nanoparticles condensed from the gas phase is associated with the formation of both edge-sharing and corner-sharing HfO6,7 polyhedra resembling that observed in the monoclinic phase
Discrete conformal maps and ideal hyperbolic polyhedra
We establish a connection between two previously unrelated topics: a
particular discrete version of conformal geometry for triangulated surfaces,
and the geometry of ideal polyhedra in hyperbolic three-space. Two triangulated
surfaces are considered discretely conformally equivalent if the edge lengths
are related by scale factors associated with the vertices. This simple
definition leads to a surprisingly rich theory featuring M\"obius invariance,
the definition of discrete conformal maps as circumcircle preserving piecewise
projective maps, and two variational principles. We show how literally the same
theory can be reinterpreted to addresses the problem of constructing an ideal
hyperbolic polyhedron with prescribed intrinsic metric. This synthesis enables
us to derive a companion theory of discrete conformal maps for hyperbolic
triangulations. It also shows how the definitions of discrete conformality
considered here are closely related to the established definition of discrete
conformality in terms of circle packings.Comment: 62 pages, 22 figures. v2: typos corrected, references added and
updated, minor changes in exposition. v3, final version: typos corrected,
improved exposition, some material moved to appendice
Picture Changing Operators in Closed Fermionic String Field Theory
We discuss appropriate arrangement of picture changing operators required to
construct gauge invariant interaction vertices involving Neveu-Schwarz states
in heterotic and closed superstring field theory. The operators required for
this purpose are shown to satisfy a set of descent equations.Comment: 15 page
Geometric entropy, area, and strong subadditivity
The trace over the degrees of freedom located in a subset of the space
transforms the vacuum state into a density matrix with non zero entropy. This
geometric entropy is believed to be deeply related to the entropy of black
holes. Indeed, previous calculations in the context of quantum field theory,
where the result is actually ultraviolet divergent, have shown that the
geometric entropy is proportional to the area for a very special type of
subsets. In this work we show that the area law follows in general from simple
considerations based on quantum mechanics and relativity. An essential
ingredient of our approach is the strong subadditive property of the quantum
mechanical entropy.Comment: Published versio
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