256 research outputs found
Dilogarithm Identities in Conformal Field Theory and Group Homology
Recently, Rogers' dilogarithm identities have attracted much attention in the
setting of conformal field theory as well as lattice model calculations. One of
the connecting threads is an identity of Richmond-Szekeres that appeared in the
computation of central charges in conformal field theory. We show that the
Richmond-Szekeres identity and its extension by Kirillov-Reshetikhin can be
interpreted as a lift of a generator of the third integral homology of a finite
cyclic subgroup sitting inside the projective special linear group of all real matrices viewed as a {\it discrete} group. This connection
allows us to clarify a few of the assertions and conjectures stated in the work
of Nahm-Recknagel-Terhoven concerning the role of algebraic -theory and
Thurston's program on hyperbolic 3-manifolds. Specifically, it is not related
to hyperbolic 3-manifolds as suggested but is more appropriately related to the
group manifold of the universal covering group of the projective special linear
group of all real matrices viewed as a topological group. This
also resolves the weaker version of the conjecture as formulated by Kirillov.
We end with the summary of a number of open conjectures on the mathematical
side.Comment: 20 pages, 2 figures not include
The low-lying excitations of polydiacetylene
The Pariser-Parr-Pople Hamiltonian is used to calculate and identify the
nature of the low-lying vertical transition energies of polydiacetylene. The
model is solved using the density matrix renormalisation group method for a
fixed acetylenic geometry for chains of up to 102 atoms. The non-linear optical
properties of polydiacetylene are considered, which are determined by the
third-order susceptibility. The experimental 1Bu data of Giesa and Schultz are
used as the geometric model for the calculation. For short chains, the
calculated E(1Bu) agrees with the experimental value, within solvation effects
(ca. 0.3 eV). The charge gap is used to characterise bound and unbound states.
The nBu is above the charge gap and hence a continuum state; the 1Bu, 2Ag and
mAg are not and hence are bound excitons. For large chain lengths, the nBu
tends towards the charge gap as expected, strongly suggesting that the nBu is
the conduction band edge. The conduction band edge for PDA is agreed in the
literature to be ca. 3.0 eV. Accounting for the strong polarisation effects of
the medium and polaron formation gives our calculated E(nBu) ca. 3.6 eV, with
an exciton binding energy of ca. 1.0 eV. The 2Ag state is found to be above the
1Bu, which does not agree with relaxed transition experimental data. However,
this could be resolved by including explicit lattice relaxation in the Pariser-
Parr-Pople-Peierls model. Particle-hole separation data further suggest that
the 1Bu, 2Ag and mAg are bound excitons, and that the nBu is an unbound
exciton.Comment: LaTeX, 23 pages, 4 postscript tables and 8 postscript figure
Confinement Effects in Antiferromagnets
Phase equilibrium in confined Ising antiferromagnets was studied as a
function of the coupling (v) and a magnetic field (h) at the surfaces, in the
presence of an external field H. The ground state properties were calculated
exactly for symmetric boundary conditions and nearest-neighbor interactions,
and a full zero-temperature phase diagram in the plane v-h was obtained for
films with symmetry-preserving surface orientations. The ground-state analysis
was extended to the H-T plane using a cluster-variation free energy. The study
of the finite-T properties (as a function of v and h) reveals the close
interdependence between the surface and finite-size effects and, together with
the ground-state phase diagram, provides an integral picture of the confinement
in anisotropic antiferromagnets with surfaces that preserve the symmetry of the
order parameter.Comment: 10 pages, 8 figures, Accepted in Phys. Rev.
The long-term fate of permafrost peatlands under rapid climate warming
Permafrost peatlands contain globally important amounts of soil organic carbon, owing to cold conditions which suppress anaerobic decomposition. However, climate warming and permafrost thaw threaten the stability of this carbon store. The ultimate fate of permafrost peatlands and their carbon stores is unclear because of complex feedbacks between peat accumulation, hydrology and vegetation. Field monitoring campaigns only span the last few decades and therefore provide an incomplete picture of permafrost peatland response to recent rapid warming. Here we use a high-resolution palaeoecological approach to understand the longer-term response of peatlands in contrasting states of permafrost degradation to recent rapid warming. At all sites we identify a drying trend until the late-twentieth century; however, two sites subsequently experienced a rapid shift to wetter conditions as permafrost thawed in response to climatic warming, culminating in collapse of the peat domes. Commonalities between study sites lead us to propose a five-phase model for permafrost peatland response to climatic warming. This model suggests a shared ecohydrological trajectory towards a common end point: inundated Arctic fen. Although carbon accumulation is rapid in such sites, saturated soil conditions are likely to cause elevated methane emissions that have implications for climate-feedback mechanisms
The Steady State Fluctuation Relation for the Dissipation Function
We give a proof of transient fluctuation relations for the entropy production
(dissipation function) in nonequilibrium systems, which is valid for most time
reversible dynamics. We then consider the conditions under which a transient
fluctuation relation yields a steady state fluctuation relation for driven
nonequilibrium systems whose transients relax, producing a unique
nonequilibrium steady state. Although the necessary and sufficient conditions
for the production of a unique nonequilibrium steady state are unknown, if such
a steady state exists, the generation of the steady state fluctuation relation
from the transient relation is shown to be very general. It is essentially a
consequence of time reversibility and of a form of decay of correlations in the
dissipation, which is needed also for, e.g., the existence of transport
coefficients. Because of this generality the resulting steady state fluctuation
relation has the same degree of robustness as do equilibrium thermodynamic
equalities. The steady state fluctuation relation for the dissipation stands in
contrast with the one for the phase space compression factor, whose convergence
is problematic, for systems close to equilibrium. We examine some model
dynamics that have been considered previously, and show how they are described
in the context of this work.Comment: 30 pages, 1 figur
Wetting films on chemically heterogeneous substrates
Based on a microscopic density functional theory we investigate the
morphology of thin liquidlike wetting films adsorbed on substrates endowed with
well-defined chemical heterogeneities. As paradigmatic cases we focus on a
single chemical step and on a single stripe. In view of applications in
microfluidics the accuracy of guiding liquids by chemical microchannels is
discussed. Finally we give a general prescription of how to investigate
theoretically the wetting properties of substrates with arbitrary chemical
structures.Comment: 56 pages, RevTeX, 20 Figure
Proton-proton scattering above 3 GeV/c
A large set of data on proton-proton differential cross sections, analyzing
powers and the double polarization parameter A_NN is analyzed employing the
Regge formalism. We find that the data available at proton beam momenta from 3
GeV/c to 50 GeV/c exhibit features that are very well in line with the general
characteristics of Regge phenomenology and can be described with a model that
includes the rho, omega, f_2, and a_2 trajectories and single Pomeron exchange.
Additional data, specifically for spin-dependent observables at forward angles,
would be very helpful for testing and refining our Regge model.Comment: 16 pages, 19 figures; revised version accepted for publication in
EPJ
Can forest management based on natural disturbances maintain ecological resilience?
Given the increasingly global stresses on forests, many ecologists argue that managers must maintain ecological resilience: the capacity of ecosystems to absorb disturbances without undergoing fundamental change. In this review we ask: Can the emerging paradigm of natural-disturbance-based management (NDBM) maintain ecological resilience in managed forests? Applying resilience theory requires careful articulation of the ecosystem state under consideration, the disturbances and stresses that affect the persistence of possible alternative states, and the spatial and temporal scales of management relevance. Implementing NDBM while maintaining resilience means recognizing that (i) biodiversity is important for long-term ecosystem persistence, (ii) natural disturbances play a critical role as a generator of structural and compositional heterogeneity at multiple scales, and (iii) traditional management tends to produce forests more homogeneous than those disturbed naturally and increases the likelihood of unexpected catastrophic change by constraining variation of key environmental processes. NDBM may maintain resilience if silvicultural strategies retain the structures and processes that perpetuate desired states while reducing those that enhance resilience of undesirable states. Such strategies require an understanding of harvesting impacts on slow ecosystem processes, such as seed-bank or nutrient dynamics, which in the long term can lead to ecological surprises by altering the forest's capacity to reorganize after disturbance
Current status of the multinational Arabidopsis community
The multinational Arabidopsis research community is highly collaborative and over the past thirty years these activities have been documented by the Multinational Arabidopsis Steering Committee (MASC). Here, we (a) highlight recent research advances made with the reference plant Arabidopsis thaliana; (b) provide summaries from recent reports submitted by MASC subcommittees, projects and resources associated with MASC and from MASC country representatives; and (c) initiate a call for ideas and foci for the “fourth decadal roadmap,” which will advise and coordinate the global activities of the Arabidopsis research community
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