2,077 research outputs found
Bifurcation of gap solitons through catastrophe theory
In the theory of optical gap solitons, slowly-moving finite-amplitude
Lorentzian solutions are found to mediate the transition from bright to
coexistent dark-antidark solitary wave pairs when the laser frequency is
detuned out of the proper edge of a dynamical photonic bandgap. Catastrophe
theory is applied to give a geometrical description of this strongly
asymmetrical 'morphing' process.Comment: 6 pages, 3 figures, submitted to Phys. Rev.
Dimensions of design space: a decision-theoretic approach to optimal research design
Bayesian decision theory can be used not only to establish the optimal sample size and its allocation in a single clinical study, but also to identify an optimal portfolio of research combining different types of study design. Within a single study, the highest societal pay-off to proposed research is achieved when its sample sizes, and allocation between available treatment options, are chosen to maximise the Expected Net Benefit of Sampling (ENBS). Where a number of different types of study informing different parameters in the decision problem could be conducted, the simultaneous estimation of ENBS across all dimensions of the design space is required to identify the optimal sample sizes and allocations within such a research portfolio. This is illustrated through a simple example of a decision model of zanamivir for the treatment of influenza. The possible study designs include: i) a single trial of all the parameters; ii) a clinical trial providing evidence only on clinical endpoints; iii) an epidemiological study of natural history of disease and iv) a survey of quality of life. The possible combinations, samples sizes and allocation between trial arms are evaluated over a range of costeffectiveness thresholds. The computational challenges are addressed by implementing optimisation algorithms to search the ENBS surface more efficiently over such large dimensions.Bayesian decision theory; expected value of information; research design; costeffectiveness analysis
The perturbation and its geometric interpretation
Starting from the recently-discovered -perturbed
Lagrangians, we prove that the deformed solutions to the classical EoMs for
bosonic field theories are equivalent to the unperturbed ones but for a
specific field-dependent local change of coordinates. This surprising geometric
outcome is fully consistent with the identification of
-deformed 2D quantum field theories as topological
JT gravity coupled to generic matter fields. Although our conclusion is valid
for generic interacting potentials, it first emerged from a detailed study of
the sine-Gordon model and in particular from the fact that solitonic
pseudo-spherical surfaces embedded in are left invariant by the
deformation. Analytic and numerical results concerning the perturbation of
specific sine-Gordon soliton solutions are presented.Comment: v2 : Expanded version with new comments, numerical results and 16
figures added. Minor typos corrected. Extra references added. 25 pages. 4
figures v3 : JHEP version. Section 6 added. Minor typos corrected. Extra
reference added. 30 pages. 5 figure
A look at the inner structure of the 2-adic ring C*-algebra and its automorphism groups
We undertake a systematic study of the so-called 2-adic ring C\u87-algebra Q2. This is the
universal C\u87-algebra generated by a unitary U and an isometry S2 such that S2U = U2S2
and S2S\u87
2+US2S\u87
2U\u87 = 1. Notably, it contains a copy of the Cuntz algebra O2 = C\u87(S1;S2)
through the injective homomorphism mapping S1 to US2. Among the main results, the
relative commutant C\u87(S2)\u9c 9 Q2 is shown to be trivial. This in turn leads to a rigidity
property enjoyed by the inclusion O2 ` Q2, namely the endomorphisms of Q2 that restrict
to the identity on O2 are actually the identity on the whole Q2. Moreover, there is no
conditional expectation from Q2 onto O2. As for the inner structure of Q2, the diagonal
subalgebra D2 and C\u87(U) are both proved to be maximal abelian in Q2. The maximality
of the latter allows a thorough investigation of several classes of endomorphisms and
automorphisms of Q2. In particular, the semigroup of the endomorphisms xing U turns
out to be a maximal abelian subgroup of Aut(Q2) topologically isomorphic with C(T;T).
Finally, it is shown by an explicit construction that Out(Q2) is uncountable and non-
abelian
Diagonal automorphisms of the -adic ring -algebra
The -adic ring -algebra naturally contains a copy of
the Cuntz algebra and, a fortiori, also of its diagonal
subalgebra with Cantor spectrum. This paper is aimed at
studying the group of the
automorphisms of fixing pointwise. It turns out
that any such automorphism leaves globally invariant.
Furthermore, the subgroup is shown
to be maximal abelian in . Saying exactly what the
group is amounts to understanding when an automorphism of that
fixes pointwise extends to . A complete answer
is given for all localized automorphisms: these will extend if and only if they
are the composition of a localized inner automorphism with a gauge
automorphism.Comment: Improved exposition and corrected some typos and inaccuracie
Conserved currents and irrelevant deformations of 2D integrable field theories
It has been recently discovered that the deformation
is closely-related to Jackiw-Teitelboim gravity. At classical level, the
introduction of this perturbation induces an interaction between the
stress-energy tensor and space-time and the deformed EoMs can be mapped,
through a field-dependent change of coordinates, onto the corresponding
undeformed ones. The effect of this perturbation on the quantum spectrum is
non-perturbatively described by an inhomogeneous Burgers equation. In this
paper, we point out that there exist infinite families of models where the
geometry couples instead to generic combinations of local conserved currents
labelled by the Lorentz spin. In spirit, these generalisations are similar to
the model as the resulting theories and the
corresponding scattering phase factors are not Lorentz invariant. The link with
the model is discussed in detail. While the classical
setup described here is very general, we shall use the sine-Gordon model and
its CFT limit as explanatory quantum examples. Most of the final equations and
considerations are, however, of broader validity or easily generalisable to
more complicated systems.Comment: 39 pages, 3 figures. v2: typos corrected, extended version with more
results on the link between the classical and the quantum analysi
On the Cahn-Hilliard-Brinkman system
We consider a diffuse interface model for phase separation of an isothermal
incompressible binary fluid in a Brinkman porous medium. The coupled system
consists of a convective Cahn-Hilliard equation for the phase field ,
i.e., the difference of the (relative) concentrations of the two phases,
coupled with a modified Darcy equation proposed by H.C. Brinkman in 1947 for
the fluid velocity . This equation incorporates a diffuse interface
surface force proportional to , where is the so-called
chemical potential. We analyze the well-posedness of the resulting
Cahn-Hilliard-Brinkman (CHB) system for . Then we establish
the existence of a global attractor and the convergence of a given (weak)
solution to a single equilibrium via {\L}ojasiewicz-Simon inequality.
Furthermore, we study the behavior of the solutions as the viscosity goes to
zero, that is, when the CHB system approaches the Cahn-Hilliard-Hele-Shaw
(CHHS) system. We first prove the existence of a weak solution to the CHHS
system as limit of CHB solutions. Then, in dimension two, we estimate the
difference of the solutions to CHB and CHHS systems in terms of the viscosity
constant appearing in CHB
Shocks in nonlocal media
We investigate the formation of collisionless shocks along the spatial
profile of a gaussian laser beam propagating in nonlocal nonlinear media. For
defocusing nonlinearity the shock survives the smoothing effect of the nonlocal
response, though its dynamics is qualitatively affected by the latter, whereas
for focusing nonlinearity it dominates over filamentation. The patterns
observed in a thermal defocusing medium are interpreted in the framework of our
theory.Comment: 5 pages, 5 figure
Generalised Born-Infeld models, Lax operators and the perturbation
Surprising links between the deformation of 2D quantum field theories induced
by the composite operator, effective string
models and the CFT correspondence, have recently emerged. The purpose of
this article is to discuss various classical aspects related to the deformation
of 2D interacting field theories. Special attention is given to the
sin(h)-Gordon model, for which we were able to construct the -deformed Lax pair. We consider the Lax pair formulation to be
the first essential step toward a more satisfactory geometrical interpretation
of this deformation within the integrable model framework.
Furthermore, it is shown that the 4D Maxwell-Born-Infeld theory, possibly
with the addition of a mass term or a derivative-independent potential,
corresponds to a natural extension of the 2D examples. Finally, we briefly
comment on 2D Yang-Mills theory and propose a modification of the heat kernel,
for a generic surface with genus and boundaries, which fully accounts
for the contribution.Comment: 22 pages, 2 figures, v2: new comments, hyperlinks and minor typos
correcte
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