107,221 research outputs found
An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems
In the context of analyzing a new model for nonlinear diffusion in polymers, an
unusual condition appears at the moving interface between the glassy and rubbery phases of the
polymer. This condition, which arises from the inclusion of a viscoelastic memory term in our
equations, has received very little attention in the mathematical literature. Due to the unusual form
of the moving-boundary condition, further study is needed as to the existence and uniqueness of
solutions satisfying such a condition. The moving boundary condition which results is not solvable
by similarity solutions, but can be solved by integral equation techniques. A solution process is
outlined to illustrate the unusual nature of the condition; the profiles which result are characteristic
of a dissolving polymer
Non-equilibrium steady state of sparse systems
A resistor-network picture of transitions is appropriate for the study of
energy absorption by weakly chaotic or weakly interacting driven systems. Such
"sparse" systems reach a novel non-equilibrium steady state (NESS) once coupled
to a bath. In the stochastic case there is an analogy to the physics of
percolating glassy systems, and an extension of the fluctuation-dissipation
phenomenology is proposed. In the mesoscopic case the quantum NESS might differ
enormously from the stochastic NESS, with saturation temperature determined by
the sparsity. A toy model where the sparsity of the system is modeled using a
log-normal random ensemble is analyzed.Comment: 6 pages, 6 figures, EPL accepted versio
New Relations for Excited Baryons in Large N_c QCD
We show that excited baryons in large N_c QCD form multiplets, within which
masses are first split at O(1/N_c). The dominant couplings of resonances to
various mesons are highly constrained: The N(1535) decays at leading 1/N_c
order exclusively to eta-N rather than pi-N, and vice versa for the N(1650).
This multiplet structure is reproduced by a simple large N_c quark model, well
studied in the literature, that describes resonances as single-quark
excitations.Comment: 4 pages, no figures, ReVTeX 4. Includes new discussion of previous
work on excited baryon tower
A Poset Connected to Artin Monoids of Simply Laced Type
Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several
W-orbits of sets of mutually commuting reflections, a poset is described which
plays a role in linear representatons of the corresponding Artin group A. The
poset generalizes many properties of the usual order on positive roots of W
given by height. In this paper, a linear representation of the positive monoid
of A is defined by use of the poset
BMW algebras of simply laced type
It is known that the recently discovered representations of the Artin groups
of type A_n, the braid groups, can be constructed via BMW algebras. We
introduce similar algebras of type D_n and E_n which also lead to the newly
found faithful representations of the Artin groups of the corresponding types.
We establish finite dimensionality of these algebras. Moreover, they have
ideals I_1 and I_2 with I_2 contained in I_1 such that the quotient with
respect to I_1 is the Hecke algebra and I_1/I_2 is a module for the
corresponding Artin group generalizing the Lawrence-Krammer representation.
Finally we give conjectures on the structure, the dimension and parabolic
subalgebras of the BMW algebra, as well as on a generalization of deformations
to Brauer algebras for simply laced spherical type other than A_n.Comment: 39 page
Nonresonance conditions for arrangements
We prove a vanishing theorem for the cohomology of the complement of a
complex hyperplane arrangement with coefficients in a complex local system.
This result is compared with other vanishing theorems, and used to study Milnor
fibers of line arrangements, and hypersurface arrangements.Comment: LaTeX, 10 page
Proof of some asymptotic results for a model equation for low Reynolds number flow
A two-point boundary value problem in the interval [ε, ∞], ε > 0 is studied. The problem contains additional parameters α ≥ 0, β ≥ 0, 0 ≤ U 0; for α = 0 an explicit construction shows that no solution exists unless k > 1. A special method is used to show uniqueness. For ε ↓ 0, k ≥ 1, various results had previously been obtained by the method of matched asymptotic expansions. Examples of these results are verified rigorously using the integral representation. For k < 1, the problem is shown not to be a layer-type problem, a fact previously demonstrated explicitly for k = 0. If k is an integer ≥ 0 the intuitive understanding of the problem is aided by regarding it as spherically symmetric in k + 1 dimensions. In the present study, however, k may be any real number, even negative
Progress in Electroweak Baryogenesis
Recent work on generating the excess of matter over antimatter in the early
universe during the electroweak phase transition is reviewed.Comment: 50 pages (figures on request), uses harvmac (table of contents
correct for "l" format), UCSD-93-2,BU-HEP-93-
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