9,244 research outputs found
On O(1) contributions to the free energy in Bethe Ansatz systems: the exact g-function
We investigate the sub-leading contributions to the free energy of Bethe
Ansatz solvable (continuum) models with different boundary conditions. We show
that the Thermodynamic Bethe Ansatz approach is capable of providing the O(1)
pieces if both the density of states in rapidity space and the quadratic
fluctuations around the saddle point solution to the TBA are properly taken
into account. In relativistic boundary QFT the O(1) contributions are directly
related to the exact g-function. In this paper we provide an all-orders proof
of the previous results of P. Dorey et al. on the g-function in both massive
and massless models. In addition, we derive a new result for the g-function
which applies to massless theories with arbitrary diagonal scattering in the
bulk.Comment: 28 pages, 2 figures, v2: minor corrections, v3: minor corrections and
references adde
Numerical instability of the Akhmediev breather and a finite-gap model of it
In this paper we study the numerical instabilities of the NLS Akhmediev
breather, the simplest space periodic, one-mode perturbation of the unstable
background, limiting our considerations to the simplest case of one unstable
mode. In agreement with recent theoretical findings of the authors, in the
situation in which the round-off errors are negligible with respect to the
perturbations due to the discrete scheme used in the numerical experiments, the
split-step Fourier method (SSFM), the numerical output is well-described by a
suitable genus 2 finite-gap solution of NLS. This solution can be written in
terms of different elementary functions in different time regions and,
ultimately, it shows an exact recurrence of rogue waves described, at each
appearance, by the Akhmediev breather. We discover a remarkable empirical
formula connecting the recurrence time with the number of time steps used in
the SSFM and, via our recent theoretical findings, we establish that the SSFM
opens up a vertical unstable gap whose length can be computed with high
accuracy, and is proportional to the inverse of the square of the number of
time steps used in the SSFM. This neat picture essentially changes when the
round-off error is sufficiently large. Indeed experiments in standard double
precision show serious instabilities in both the periods and phases of the
recurrence. In contrast with it, as predicted by the theory, replacing the
exact Akhmediev Cauchy datum by its first harmonic approximation, we only
slightly modify the numerical output. Let us also remark, that the first rogue
wave appearance is completely stable in all experiments and is in perfect
agreement with the Akhmediev formula and with the theoretical prediction in
terms of the Cauchy data.Comment: 27 pages, 8 figures, Formula (30) at page 11 was corrected, arXiv
admin note: text overlap with arXiv:1707.0565
Universality in Systems with Power-Law Memory and Fractional Dynamics
There are a few different ways to extend regular nonlinear dynamical systems
by introducing power-law memory or considering fractional
differential/difference equations instead of integer ones. This extension
allows the introduction of families of nonlinear dynamical systems converging
to regular systems in the case of an integer power-law memory or an integer
order of derivatives/differences. The examples considered in this review
include the logistic family of maps (converging in the case of the first order
difference to the regular logistic map), the universal family of maps, and the
standard family of maps (the latter two converging, in the case of the second
difference, to the regular universal and standard maps). Correspondingly, the
phenomenon of transition to chaos through a period doubling cascade of
bifurcations in regular nonlinear systems, known as "universality", can be
extended to fractional maps, which are maps with power-/asymptotically
power-law memory. The new features of universality, including cascades of
bifurcations on single trajectories, which appear in fractional (with memory)
nonlinear dynamical systems are the main subject of this review.Comment: 23 pages 7 Figures, to appear Oct 28 201
The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions
We show how a proper use of the Lippmann–Schwinger equation simplifies the calculations to obtain scattering states for one dimensional systems perturbed by N Dirac delta equations. Here, we consider two situations. In the former, attractive Dirac deltas perturbed the free one dimensional Schrödinger Hamiltonian. We obtain explicit expressions for scattering and Gamow states. For completeness, we show that the method to obtain bound states use comparable formulas, although not based on the Lippmann–Schwinger equation. Then, the attractive N deltas perturbed the one dimensional Salpeter equation. We also obtain explicit expressions for the scattering wave functions. Here, we need regularisation techniques that we implement via heat kernel regularisation
Solubilities of sub- and supercritical carbon dioxide in polyester resins
In supercritical carbon dioxide (CO2) assisted polymer processes the solubility of CO2 in a polymer plays a vital role. The higher the amount of CO2 dissolved in a polymer the higher is the viscosity reduction of the polymer. Solubilities Of CO2 in polyester resins based on propoxylated bisphenol (PPB) and ethoxylated bisphenol (PEB) have been measured using a magnetic suspension balance at temperatures ranging from 333 to 420 K and pressures up to 30 MPa. An optical cell has been used to independently determine the swelling of the polymers, which has been incorporated in the buoyancy correction. In both polyester resins, the solubility of CO, increases with increasing pressure and decreasing temperature as a result of variations in CO, density. The experimental solubility has been correlated to the Sanchez-Lacombe equation of state.</p
Joining the conspiracy? Negotiating ethics and emotions in researching (around) AIDS in southern Africa
AIDS is an emotive subject, particularly in southern Africa. Among those who have been directly affected by the disease, or who perceive themselves to be personally at risk, talking about AIDS inevitably arouses strong emotions - amongst them fear, distress, loss and anger. Conventionally, human geography research has avoided engagement with such emotions. Although the ideal of the detached observer has been roundly critiqued, the emphasis in methodological literature on 'doing no harm' has led even qualitative researchers to avoid difficult emotional encounters. Nonetheless, research is inevitably shaped by emotions, not least those of the researchers themselves. In this paper, we examine the role of emotions in the research process through our experiences of researching the lives of 'Young AIDS migrants' in Malawi and Lesotho. We explore how the context of the research gave rise to the production of particular emotions, and how, in response, we shaped the research, presenting a research agenda focused more on migration than AIDS. This example reveals a tension between universalised ethics expressed through ethical research guidelines that demand informed consent, and ethics of care, sensitive to emotional context. It also demonstrates how dualistic distinctions between reason and emotion, justice and care, global and local are unhelpful in interpreting the ethics of research practice
A soliton menagerie in AdS
We explore the behaviour of charged scalar solitons in asymptotically global
AdS4 spacetimes. This is motivated in part by attempting to identify under what
circumstances such objects can become large relative to the AdS length scale.
We demonstrate that such solitons generically do get large and in fact in the
planar limit smoothly connect up with the zero temperature limit of planar
scalar hair black holes. In particular, for given Lagrangian parameters we
encounter multiple branches of solitons: some which are perturbatively
connected to the AdS vacuum and surprisingly, some which are not. We explore
the phase space of solutions by tuning the charge of the scalar field and
changing scalar boundary conditions at AdS asymptopia, finding intriguing
critical behaviour as a function of these parameters. We demonstrate these
features not only for phenomenologically motivated gravitational Abelian-Higgs
models, but also for models that can be consistently embedded into eleven
dimensional supergravity.Comment: 62 pages, 21 figures. v2: added refs and comments and updated
appendice
Lifshitz spacetimes from AdS null and cosmological solutions
We describe solutions of 10-dimensional supergravity comprising null
deformations of with a scalar field, which have
Lifshitz symmetries. The bulk Lifshitz geometry in 3+1-dimensions arises by
dimensional reduction of these solutions. The dual field theory in this case is
a deformation of the N=4 super Yang-Mills theory. We discuss the holographic
2-point function of operators dual to bulk scalars. We further describe
time-dependent (cosmological) solutions which have anisotropic Lifshitz scaling
symmetries. We also discuss deformations of in 11-dimensional
supergravity, which are somewhat similar to the solutions above. In some cases
here, we expect the field theory duals to be deformations of the Chern-Simons
theories on M2-branes stacked at singularities.Comment: Latex, 29pgs, v3. references, minor clarifications (subsection on
Lifshitz geometry seen by scalar probes) added, to appear in JHE
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