16,260 research outputs found
Hamiltonian structure of peakons as weak solutions for the modified Camassa-Holm equation
The modified Camassa-Holm (mCH) equation is a bi-Hamiltonian system
possessing -peakon weak solutions, for all , in the setting of an
integral formulation which is used in analysis for studying local
well-posedness, global existence, and wave breaking for non-peakon solutions.
Unlike the original Camassa-Holm equation, the two Hamiltonians of the mCH
equation do not reduce to conserved integrals (constants of motion) for
-peakon weak solutions. This perplexing situation is addressed here by
finding an explicit conserved integral for -peakon weak solutions for all
. When is even, the conserved integral is shown to provide a
Hamiltonian structure with the use of a natural Poisson bracket that arises
from reduction of one of the Hamiltonian structures of the mCH equation. But
when is odd, the Hamiltonian equations of motion arising from the conserved
integral using this Poisson bracket are found to differ from the dynamical
equations for the mCH -peakon weak solutions. Moreover, the lack of
conservation of the two Hamiltonians of the mCH equation when they are reduced
to -peakon weak solutions is shown to extend to -peakon weak solutions
for all . The connection between this loss of integrability structure
and related work by Chang and Szmigielski on the Lax pair for the mCH equation
is discussed.Comment: Minor errata in Eqns. (32) to (34) and Lemma 1 have been fixe
Supersymmetric Yang-Mills theories with local coupling: The supersymmetric gauge
Supersymmetric pure Yang-Mills theory is formulated with a local, i.e.
space-time dependent, complex coupling in superspace. Super-Yang-Mills theories
with local coupling have an anomaly, which has been first investigated in the
Wess-Zumino gauge and there identified as an anomaly of supersymmetry. In a
manifest supersymmetric formulation the anomaly appears in two other
identities: The first one describes the non-renormalization of the topological
term, the second relates the renormalization of the gauge coupling to the
renormalization of the complex supercoupling. Only one of the two identities
can be maintained in perturbation theory. We discuss the two versions and
derive the respective beta function of the local supercoupling, which is
non-holomorphic in the first version, but directly related to the coupling
renormalization, and holomorphic in the second version, but has a non-trivial,
i.e.anomalous, relation to the beta function of the gauge coupling.Comment: References correcte
A temperature-dependent phase-field model for phase separation and damage
In this paper we study a model for phase separation and damage in
thermoviscoelastic materials. The main novelty of the paper consists in the
fact that, in contrast with previous works in the literature (cf., e.g., [C.
Heinemann, C. Kraus: Existence results of weak solutions for Cahn-Hilliard
systems coupled with elasticity and damage. Adv. Math. Sci. Appl. 21 (2011),
321--359] and [C. Heinemann, C. Kraus: Existence results for diffuse interface
models describing phase separation and damage. European J. Appl. Math. 24
(2013), 179--211]), we encompass in the model thermal processes, nonlinearly
coupled with the damage, concentration and displacement evolutions. More in
particular, we prove the existence of "entropic weak solutions", resorting to a
solvability concept first introduced in [E. Feireisl: Mathematical theory of
compressible, viscous, and heat conducting fluids. Comput. Math. Appl. 53
(2007), 461--490] in the framework of Fourier-Navier-Stokes systems and then
recently employed in [E. Feireisl, H. Petzeltov\'a, E. Rocca: Existence of
solutions to a phase transition model with microscopic movements. Math. Methods
Appl. Sci. 32 (2009), 1345--1369], [E. Rocca, R. Rossi: "Entropic" solutions to
a thermodynamically consistent PDE system for phase transitions and damage.
SIAM J. Math. Anal., 47 (2015), 2519--2586] for the study of PDE systems for
phase transition and damage. Our global-in-time existence result is obtained by
passing to the limit in a carefully devised time-discretization scheme
Strategies for distributing goals in a team of cooperative agents
This paper addresses the problem of distributing goals to individual agents inside a team of cooperative agents. It shows that several parameters determine the goals of particular agents. The first parameter is the set of goals allocated to the team; the second parameter is the description of the real actual world; the third parameter is the description of the agents' ability and commitments. The last parameter is the strategy the team agrees on: for each precise goal, the team may define several strategies which are orders between agents representing, for instance, their relative competence or their relative cost. This paper also shows how to combine strategies. The method used here assumes an order of priority between strategie
D7-Brane Chaotic Inflation
We analyze string-theoretic large-field inflation in the regime of
spontaneously-broken supergravity with conventional moduli stabilization by
fluxes and non-perturbative effects. The main ingredient is a shift-symmetric
Kahler potential, supplemented by flux-induced shift symmetry breaking in the
superpotential. The central technical observation is that all these features
are present for D7-brane position moduli in Type IIB orientifolds, allowing for
a realization of the axion monodromy proposal in a controlled string theory
compactification. On the one hand, in the large complex structure regime the
D7-brane position moduli inherit a shift symmetry from their mirror-dual Type
IIA Wilson lines. On the other hand, the Type IIB flux superpotential
generically breaks this shift symmetry and allows, by appealing to the large
flux discretuum, to tune the relevant coefficients to be small. The
shift-symmetric direction in D7-brane moduli space can then play the role of
the inflaton: While the D7-brane circles a certain trajectory on the Calabi-Yau
many times, the corresponding F-term energy density grows only very slowly,
thanks to the above-mentioned tuning of the flux. Thus, the large-field
inflationary trajectory can be realized in a regime where Kahler, complex
structure and other brane moduli are stabilized in a conventional manner, as we
demonstrate using the example of the Large Volume Scenario.Comment: 8 pages, 2 figures; v2: references adde
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