3,762 research outputs found
Intracultural diversity in a model of social dynamics
We study the consequences of introducing individual nonconformity in social
interactions, based on Axelrod's model for the dissemination of culture. A
constraint on the number of situations in which interaction may take place is
introduced in order to lift the unavoidable ho mogeneity present in the final
configurations arising in Axelrod's related models. The inclusion of this
constraint leads to the occurrence of complex patterns of intracultural
diversity whose statistical properties and spatial distribution are
characterized by means of the concepts of cultural affinity and cultural cli
ne. It is found that the relevant quantity that determines the properties of
intracultural diversity is given by the fraction of cultural features that
characterizes the cultural nonconformity of individuals.Comment: 7 pages, 2 tables, 6 figure
Holomorphic Anomaly in Gauge Theories and Matrix Models
We use the holomorphic anomaly equation to solve the gravitational
corrections to Seiberg-Witten theory and a two-cut matrix model, which is
related by the Dijkgraaf-Vafa conjecture to the topological B-model on a local
Calabi-Yau manifold. In both cases we construct propagators that give a
recursive solution in the genus modulo a holomorphic ambiguity. In the case of
Seiberg-Witten theory the gravitational corrections can be expressed in closed
form as quasimodular functions of Gamma(2). In the matrix model we fix the
holomorphic ambiguity up to genus two. The latter result establishes the
Dijkgraaf-Vafa conjecture at that genus and yields a new method for solving the
matrix model at fixed genus in closed form in terms of generalized
hypergeometric functions.Comment: 34 pages, 2 eps figures, expansion at the monopole point corrected
and interpreted, and references adde
A Note on ODEs from Mirror Symmetry
We give close formulas for the counting functions of rational curves on
complete intersection Calabi-Yau manifolds in terms of special solutions of
generalized hypergeometric differential systems. For the one modulus cases we
derive a differential equation for the Mirror map, which can be viewed as a
generalization of the Schwarzian equation. We also derive a nonlinear seventh
order differential equation which directly governs the instanton corrected
Yukawa coupling.Comment: 24 pages using harvma
Searching for K3 Fibrations
We present two methods for studying fibrations of Calabi-Yau manifolds
embedded in toric varieties described by single weight systems. We analyse
184,026 such spaces and identify among them 124,701 which are K3 fibrations. As
some of the weights give rise to two or three distinct types of fibrations, the
total number we find is 167,406. With our methods one can also study elliptic
fibrations of 3-folds and K3 surfaces. We also calculate the Hodge numbers of
the 3-folds obtaining more than three times as many as were previously known.Comment: 21 pages, LaTeX2e, 4 eps figures, uses packages
amssymb,latexsym,cite,epi
Vector opinion dynamics in a model for social influence
We present numerical simulations of a model of social influence, where the
opinion of each agent is represented by a binary vector. Agents adjust their
opinions as a result of random encounters, whenever the difference between
opinions is below a given threshold. Evolution leads to a steady state, which
highly depends on the threshold and a convergence parameter of the model. We
analyze the transition between clustered and homogeneous steady states. Results
of the cases of complete mixing and small-world networks are compared.Comment: Latex file, 14 pages and 11 figures, Accepted in Physica
Single-ion and exchange anisotropy effects and multiferroic behavior in high-symmetry tetramer single molecule magnets
We study single-ion and exchange anisotropy effects in equal-spin
tetramer single molecule magnets exhibiting , , ,
, , or ionic point group symmetry. We first write the
group-invariant quadratic single-ion and symmetric anisotropic exchange
Hamiltonians in the appropriate local coordinates. We then rewrite these local
Hamiltonians in the molecular or laboratory representation, along with the
Dzyaloshinskii-Moriay (DM) and isotropic Heisenberg, biquadratic, and
three-center quartic Hamiltonians. Using our exact, compact forms for the
single-ion spin matrix elements, we evaluate the eigenstate energies
analytically to first order in the microscopic anisotropy interactions,
corresponding to the strong exchange limit, and provide tables of simple
formulas for the energies of the lowest four eigenstate manifolds of
ferromagnetic (FM) and anitiferromagnetic (AFM) tetramers with arbitrary .
For AFM tetramers, we illustrate the first-order level-crossing inductions for
, and obtain a preliminary estimate of the microscopic
parameters in a Ni from a fit to magnetization data.
Accurate analytic expressions for the thermodynamics, electron paramagnetic
resonance absorption and inelastic neutron scattering cross-section are given,
allowing for a determination of three of the microscopic anisotropy
interactions from the second excited state manifold of FM tetramers. We also
predict that tetramers with symmetries and should exhibit both
DM interactions and multiferroic states, and illustrate our predictions for
.Comment: 30 pages, 14 figures, submitted to Phys. Rev.
Exact Solutions of Exceptional Gauge Theories from Toric Geometry
We derive four dimensional gauge theories with exceptional groups ,
, , and with matter, by starting from the duality between the
heterotic string on and F-theory on a elliptically fibered Calabi-Yau
3-fold. This configuration is compactified to four dimensions on a torus, and
by employing toric geometry, we compute the type IIB mirrors of the Calabi-Yaus
of the type IIA string theory. We identify the Seiberg-Witten curves describing
the gauge theories as ALE spaces fibered over a base.Comment: 18 pages, 5 figures, uses harvmac and eps
Mirror Maps, Modular Relations and Hypergeometric Series I
Motivated by the recent work of Kachru-Vafa in string theory, we study in
Part A of this paper, certain identities involving modular forms,
hypergeometric series, and more generally series solutions to Fuchsian
equations. The identity which arises in string theory is the simpliest of its
kind. There are nontrivial generalizations of the identity which appear new. We
give many such examples -- all of which arise in mirror symmetry for algebraic
K3 surfaces.
In Part B, we study the integrality property of certain -series, known as
mirror maps, which arise in mirror symmetry.Comment: 24 pages; harvma
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