769,898 research outputs found
On the weak order of Coxeter groups
This paper provides some evidence for conjectural relations between
extensions of (right) weak order on Coxeter groups, closure operators on root
systems, and Bruhat order. The conjecture focused upon here refines an earlier
question as to whether the set of initial sections of reflection orders,
ordered by inclusion, forms a complete lattice. Meet and join in weak order are
described in terms of a suitable closure operator. Galois connections are
defined from the power set of W to itself, under which maximal subgroups of
certain groupoids correspond to certain complete meet subsemilattices of weak
order. An analogue of weak order for standard parabolic subsets of any rank of
the root system is defined, reducing to the usual weak order in rank zero, and
having some analogous properties in rank one (and conjecturally in general).Comment: 37 pages, submitte
Culture, Utility or Social Systems?:Explaining the Cross-National Ties of Emigrants from Borsa, Romania
Emigrants from BorĆa, Romania, display two quite distinct patterns of ties with their community of origin: migration to Italy is discernibly transnational, with a strong reliance on migrant networks; while migration to the UK is more individualistic, with emigrants shunning interaction with compatriots and retaining only weak ties to BorĆa. We argue that prevalent theories of cross-national ties fail adequately to explain this divergence. Instead, we draw on systems theory to explain the discrepancy in terms of divergent conditions for societal inclusion. In Italy, incorporation into parallel, unofficial structures of work, welfare and accommodation encouraged a reliance on cultural criteria for maintaining social ties. In the UK, migrants were obliged to integrate into state-sponsored systems, encouraging the relinquishing of ethnic ties in favour of more strategic networking to facilitate societal inclusion
Molecular Biology at the Quantum Level: Can Modern Density Functional Theory Forge the Path?
Recent years have seen vast improvements in the ability of rigorous
quantum-mechanical methods to treat systems of interest to molecular biology.
In this review article, we survey common computational methods used to study
such large, weakly bound systems, starting from classical simulations and
reaching to quantum chemistry and density functional theory. We sketch their
underlying frameworks and investigate their strengths and weaknesses when
applied to potentially large biomolecules. In particular, density functional
theory---a framework that can treat thousands of atoms on firm theoretical
ground---can now accurately describe systems dominated by weak van der Waals
interactions. This newfound ability has rekindled interest in using this
tried-and-true approach to investigate biological systems of real importance.
In this review, we focus on some new methods within density functional theory
that allow for accurate inclusion of the weak interactions that dominate
binding in biological macromolecules. Recent work utilizing these methods to
study biologically-relevant systems will be highlighted, and a vision for the
future of density functional theory within molecular biology will be discussed
Stationary distributions and condensation in autocatalytic CRN
We investigate a broad family of non weakly reversible stochastically modeled
reaction networks (CRN), by looking at their steady-state distributions. Most
known results on stationary distributions assume weak reversibility and zero
deficiency. We first give explicitly product-form steady-state distributions
for a class of non weakly reversible autocatalytic CRN of arbitrary deficiency.
Examples of interest in statistical mechanics (inclusion process), life
sciences and robotics (collective decision making in ant and robot swarms) are
provided. The product-form nature of the steady-state then enables the study of
condensation in particle systems that are generalizations of the inclusion
process.Comment: 25 pages. Some typos corrected, shortened some part
Modeling and analysis of a phase field system for damage and phase separation processes in solids
In this work, we analytically investigate a multi-component system for
describing phase separation and damage processes in solids. The model consists
of a parabolic diffusion equation of fourth order for the concentration coupled
with an elliptic system with material dependent coefficients for the strain
tensor and a doubly nonlinear differential inclusion for the damage function.
The main aim of this paper is to show existence of weak solutions for the
introduced model, where, in contrast to existing damage models in the
literature, different elastic properties of damaged and undamaged material are
regarded. To prove existence of weak solutions for the introduced model, we
start with an approximation system. Then, by passing to the limit, existence
results of weak solutions for the proposed model are obtained via suitable
variational techniques.Comment: Keywords: Cahn-Hilliard system, phase separation, elliptic-parabolic
systems, doubly nonlinear differential inclusions, complete damage, existence
results, energetic solutions, weak solutions, linear elasticity,
rate-dependent system
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