125 research outputs found
Coexistence of double alternating antiferromagnetic chains in (VO)_2P_2O_7 : NMR study
Nuclear magnetic resonance (NMR) of 31P and 51V nuclei has been measured in a
spin-1/2 alternating-chain compound (VO)_2P_2O_7. By analyzing the temperature
variation of the 31P NMR spectra, we have found that (VO)_2P_2O_7 has two
independent spin components with different spin-gap energies. The spin gaps are
determined from the temperature dependence of the shifts at 31P and 51V sites
to be 35 K and 68 K, which are in excellent agreement with those observed in
the recent inelastic neutron scattering experiments [A.W. Garrett et al., Phys.
Rev. Lett. 79, 745 (1997)]. This suggests that (VO)_2P_2O_7 is composed of two
magnetic subsystems showing distinct magnetic excitations, which are associated
with the two crystallographically-inequivalent V chains running along the b
axis. The difference of the spin-gap energies between the chains is attributed
to the small differences in the V-V distances, which may result in the
different exchange alternation in each magnetic chain. The exchange
interactions in each alternating chain are estimated and are discussed based on
the empirical relation between the exchange interaction and the interatomic
distance.Comment: 10 pages, 11 embedded eps figures, REVTeX, Submitted to Phys. Rev.
Nonlinear Differential Equations Satisfied by Certain Classical Modular Forms
A unified treatment is given of low-weight modular forms on \Gamma_0(N),
N=2,3,4, that have Eisenstein series representations. For each N, certain
weight-1 forms are shown to satisfy a coupled system of nonlinear differential
equations, which yields a single nonlinear third-order equation, called a
generalized Chazy equation. As byproducts, a table of divisor function and
theta identities is generated by means of q-expansions, and a transformation
law under \Gamma_0(4) for the second complete elliptic integral is derived.
More generally, it is shown how Picard-Fuchs equations of triangle subgroups of
PSL(2,R) which are hypergeometric equations, yield systems of nonlinear
equations for weight-1 forms, and generalized Chazy equations. Each triangle
group commensurable with \Gamma(1) is treated.Comment: 40 pages, final version, accepted by Manuscripta Mathematic
Red Queen Coevolution on Fitness Landscapes
Species do not merely evolve, they also coevolve with other organisms.
Coevolution is a major force driving interacting species to continuously evolve
ex- ploring their fitness landscapes. Coevolution involves the coupling of
species fit- ness landscapes, linking species genetic changes with their
inter-specific ecological interactions. Here we first introduce the Red Queen
hypothesis of evolution com- menting on some theoretical aspects and empirical
evidences. As an introduction to the fitness landscape concept, we review key
issues on evolution on simple and rugged fitness landscapes. Then we present
key modeling examples of coevolution on different fitness landscapes at
different scales, from RNA viruses to complex ecosystems and macroevolution.Comment: 40 pages, 12 figures. To appear in "Recent Advances in the Theory and
Application of Fitness Landscapes" (H. Richter and A. Engelbrecht, eds.).
Springer Series in Emergence, Complexity, and Computation, 201
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