4,365 research outputs found
Normal subgroups of diffeomorphism and homeomorphism groups of R^n and other open manifolds
We determine all the normal subgroups of the group of C^r diffeomorphisms of
R^n, r = 1,2,...,infinity, except when r=n+1 or n=4, and also of the group of
homeomorphisms of R^n (r=0). We also study the group A_0 of diffeomorphisms of
an open manifold M that are isotopic to the identity. If M is the interior of a
compact manifold with nonempty boundary, then the quotient of A_0 by the normal
subgroup of diffeomorphisms that coincide with the identity near to a given end
e of M is simple.Comment: This version corrects an error regarding the diffeomorphism groups of
R^1, since the line has two ends, in contrast to higher dimension
Critical regime of two dimensional Ando model: relation between critical conductance and fractal dimension of electronic eigenstates
The critical two-terminal conductance and the spatial fluctuations of
critical eigenstates are investigated for a disordered two dimensional model of
non-interacting electrons subject to spin-orbit scattering (Ando model). For
square samples, we verify numerically the relation between critical conductivity and
the fractal information dimension of the electron wave function, . Through a detailed numerical scaling analysis of the two-terminal
conductance we also estimate the critical exponent that
governs the quantum phase transition.Comment: IOP Latex, 7 figure
XYZ-polarisation analysis of diffuse magnetic neutron scattering from single crystals
Studies of diffuse magnetic scattering largely benefit from the use of a
multi-detector covering wide scattering angles. Therefore, the different
contributions to the diffuse scattering that originate from magnetic, nuclear
coherent, and nuclear spin-incoherent scattering can be separated by the
so-called XYZ-polarization analysis. In the past this method has been
successfully applied to the analysis of diffuse scattering by polycrystalline
samples of magnetic disordered materials. Single crystal studies that exploit
the vector properties of spin correlations are of particular interest for
furthering our understanding of frustration effects in magnetism. Based on the
symmetry properties of polarised scattering a suitable extension of the
conventional XYZ method has been derived, which allows for the complete
separation and the analysis of features of diffuse magnetic scattering from
single crystals.Comment: 6 pages 2 figures, revised as published, one Eq. removed, minor
corrections, typos correcte
Systemic risk in a unifying framework for cascading processes on networks
We introduce a general framework for models of cascade and contagion processes on networks, to identify their commonalities and differences. In particular, models of social and financial cascades, as well as the fiber bundle model, the voter model, and models of epidemic spreading are recovered as special cases. To unify their description, we define the net fragility of a node, which is the difference between its fragility and the threshold that determines its failure. Nodes fail if their net fragility grows above zero and their failure increases the fragility of neighbouring nodes, thus possibly triggering a cascade. In this framework, we identify three classes depending on the way the fragility of a node is increased by the failure of a neighbour. At the microscopic level, we illustrate with specific examples how the failure spreading pattern varies with the node triggering the cascade, depending on its position in the network and its degree. At the macroscopic level, systemic risk is measured as the final fraction of failed nodes, X*, and for each of the three classes we derive a recursive equation to compute its value. The phase diagram of X* as a function of the initial conditions, thus allows for a prediction of the systemic risk as well as a comparison of the three different model classes. We could identify which model class leads to a first-order phase transition in systemic risk, i.e. situations where small changes in the initial conditions determine a global failure. Eventually, we generalize our framework to encompass stochastic contagion models. This indicates the potential for further generalization
Decelerating microdynamics can accelerate macrodynamics in the voter model
For the voter model, we study the effect of a memory-dependent transition
rate. We assume that the transition of a spin into the opposite state decreases
with the time it has been in its current state. Counter-intuitively, we find
that the time to reach a macroscopically ordered state can be accelerated by
slowing-down the microscopic dynamics in this way. This holds for different
network topologies, including fully-connected ones. We find that the ordering
dynamics is governed by two competing processes which either stabilize the
majority or the minority state. If the first one dominates, it accelerates the
ordering of the system. The conclusions of this Letter are not restricted to
the voter model, but remain valid to many other spin systems as well.Comment: See http://www.sg.ethz.ch for related publication
Ferroelectric properties of charge-ordered alpha-(BEDT-TTF)2I3
A detailed investigation of the out-of-plane electrical properties of
charge-ordered alpha-(BEDT-TTF)2I3 provides clear evidence for
ferroelectricity. Similar to multiferroic alpha-(BEDT-TTF)2Cu[N(CN)2]Cl, the
polar order in this material is ascribed to the occurrence of bond- and
site-centered charge order. Dielectric response typical for relaxor
ferroelectricity is found deep in the charge-ordered state. We suggest an
explanation in terms of the existence of polar and nonpolar stacks of the
organic molecules in this material, preventing long-range ferroelectricity. The
results are discussed in relation to the formation or absence of electronic
polar order in related charge-transfer salts.Comment: 8 pages, 4 figures. Revised version as accepted for publication in
Phys. Rev.
Strategy discourse as collaborative design practice: Can design thinking benefit strategy development?
This paper provides an investigation into strategic processes, focusing on identifying the processes, practices and capabilities characterising intra- and inter-organisational collaboration that foster strategy development and innovation through creativity in thinking and problem solving. To do so we build our research framework at the intersection of four theoretical foundations: integrative design practice (or design thinking), inter-organizational collaboration, dynamic capabilities and practice theory
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