629 research outputs found
Recent software developments for special functions in the Santander–Amsterdam project
We give an overview of published algorithms by our group and of current activities and future plans. In particular, we give details on methods for computing special functions and discuss in detail two current lines of research. Firstly, we describe the recent developments for the computation of central and non-central ÷-square cumulative distributions (also called Marcum Q.functions), and we present a new quadrature method for computing them. Secondly, we describe the fourth-order methods for computing zeros of special functions recently developed, and we provide an explicit example for the computation of complex zeros of Bessel functions. We end with an overview of published software by our group for computing special functions
A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
These notes are based on lectures delivered by the authors at a Langeoog
seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a
mixed audience of mathematicians and theoretical physicists. After a brief
outline of the basic physical concepts of equilibrium and nonequilibrium
states, the one-dimensional simple exclusion process is introduced as a
paradigmatic nonequilibrium interacting particle system. The stationary measure
on the ring is derived and the idea of the hydrodynamic limit is sketched. We
then introduce the phenomenological Kardar-Parisi-Zhang (KPZ) equation and
explain the associated universality conjecture for surface fluctuations in
growth models. This is followed by a detailed exposition of a seminal paper of
Johansson that relates the current fluctuations of the totally asymmetric
simple exclusion process (TASEP) to the Tracy-Widom distribution of random
matrix theory. The implications of this result are discussed within the
framework of the KPZ conjecture.Comment: 52 pages, 4 figures; to appear in J. Phys. A: Math. Theo
Computation of Asymptotic Expansions of Turning Point Problems via Cauchy's Integral Formula: Bessel Functions
Linear second-order differential equations having a large real parameter and turning point in the complex plane are considered. Classical asymptotic expansions for solutions involve the Airy function and its derivative, along with two infinite series, the coefficients of which are usually difficult to compute. By considering the series as
asymptotic expansions for two explicitly defined analytic functions, Cauchy's integral formula is employed to compute the coefficient functions to a high order of accuracy. The method employs a certain exponential form of Liouville´Green expansions for solutions of the differential equation, as well as for the Airy function. We illustrate the use of the method with the high accuracy computation of Airy-type expansions of Bessel functions of complex argument.The authors acknowledge support from Ministerio de Economía y Competitividad, project MTM2015-67142-P (MINECO/FEDER, UE). A.G. and J.S. acknowledge support from Ministerio de Economía y Competitividad, project MTM2012-34787. A.G. acknowledges the Fulbright/MEC Program for support during her stay at SDSU. J.S. acknowledges the Salvador de Madariaga Program for support during his stay at SDSU
Unruh detectors and quantum chaos in JT gravity
We identify the spectral properties of Hawking-Unruh radiation in the eternal
black hole at ultra low energies as a probe for the chaotic level statistics of
quantum black holes. Level repulsion implies that there are barely Hawking
particles with an energy smaller than the level separation. This effect is
experimentally accessible by probing the Unruh heat bath with a linear
detector. We provide evidence for this effect via explicit and exact
calculations in JT gravity building on a radar definition of bulk observables
in the model. Similar results are observed for the bath energy density. This
universal feature of eternal Hawking radiation should resonate into the
evaporating setup.Comment: 41 pages, v2: added references, fixed some typo
Basic Methods for Computing Special Functions
This paper gives an overview of methods for the numerical evaluation of special functions, that is, the functions that arise in many problems from mathematical physics, engineering, probability theory, and other applied sciences. We consider in detail a selection of basic methods which are
frequently used in the numerical evaluation of special functions: converging and asymptotic series, including Chebyshev expansions, linear recurrence relations, and numerical quadrature. Several other methods are available and some of these will be discussed in less detail. We give examples of recent software for special functions where these methods are used. We mention a list of new publications on computational aspects of special functions available on our website
The evolution of Kerr discs and late-time tidal disruption event light curves
An encounter between a passing star and a massive black hole at the centre of
a galaxy, a so-called tidal disruption event or TDE, may leave a debris disc
that subsequently accretes onto the hole. We solve for the time evolution of
such a TDE disc, making use of an evolutionary equation valid for both the
Newtonian and Kerr regimes. The late time luminosity emergent from such a disc
is of interest as a model diagnostic, as it tends to follow a power law
decline. The original simple ballistic fallback model, with equal mass in equal
energy intervals, produces a -5/3 power law, while standard viscous disc
descriptions yield a somewhat more shallow decline, with an index closer to
-1.2. Of four recent, well-observed tidal disruption event candidates however,
all had fall-off power law indices smaller than 1 in magnitude. In this work,
we revisit the problem of thin disc evolution, solving this reduced problem in
full general relativity. Our solutions produce power law indices that are in
much better accord with observations. The late time observational data from
many TDEs are generally supportive, not only of disc accretion models, but of
finite stress persisting down to the innermost stable circular orbit.Comment: 9 pages, 4 figures. Accepted for publication in MNRA
Deconvolution of JWST/MIRI Images: Applications to an Active Galactic Nucleus Model and GATOS Observations of NGC 5728
The superb image quality, stability, and sensitivity of JWST permit deconvolution techniques to be pursued with a fidelity unavailable to ground-based observations. We present an assessment of several deconvolution approaches to improve image quality and mitigate the effects of the complex JWST point-spread function (PSF). The optimal deconvolution method is determined by using WebbPSF to simulate JWST’s complex PSF and MIRISim to simulate multiband JWST/Mid-Infrared Imager Module (MIRIM) observations of a toy model of an active galactic nucleus (AGN). Five different deconvolution algorithms are tested: (1) Kraken deconvolution, (2) Richardson–Lucy, (3) the adaptive imaging deconvolution algorithm, (4) sparse regularization with the Condat–Vũ algorithm, and (5) iterative Wiener filtering and thresholding. We find that Kraken affords the greatest FWHM reduction of the nuclear source of our MIRISim observations for the toy AGN model while retaining good photometric integrity across all simulated wave bands. Applying Kraken to Galactic Activity, Torus, and Outflow Survey (GATOS) multiband JWST/MIRIM observations of the Seyfert 2 galaxy NGC 5728, we find that the algorithm reduces the FWHM of the nuclear source by a factor of 1.6–2.2 across all five filters. Kraken images facilitate detection of extended nuclear emission ∼2.″5 (∼470 pc, position angle ≃ 115°) in the SE–NW direction, especially at the longest wavelengths. We demonstrate that Kraken is a powerful tool to enhance faint features otherwise hidden in the complex JWST PSF
Representing capabilities of novel semi-analytical triangular plate elements
Two novel plate-bending elements are developed and investigated in this study. Elements with 13 and 15 degree-of-freedoms are named AT13 and AT15, respectively. These triangular elements are formulated in a semi-analytic way. For this aim, the basic elasticity function is employed with unknown parameters. Subsequently, the trial-and-error procedure is used to determine the unidentified constants. Besides, the achieved results are compared with those obtained by displacement-based triangular elements with the same degrees-of-freedom (TUBA13 and TUBA15). In this research, both stress and displacement responses of diverse structures are assessed. After performing extensive numerical studies, the findings clearly demonstrate the superiorities of the proposed elements
Stokes Phenomena and Non-perturbative Completion in the Multi-cut Two-matrix Models
The Stokes multipliers in the matrix models are invariants in the
string-theory moduli space and related to the D-instanton chemical potentials.
They not only represent non-perturbative information but also play an important
role in connecting various perturbative string theories in the moduli space.
They are a key concept to the non-perturbative completion of string theory and
also expected to imply some remnant of strong coupling dynamics in M theory. In
this paper, we investigate the non-perturbative completion problem consisting
of two constraints on the Stokes multipliers. As the first constraint, Stokes
phenomena which realize the multi-cut geometry are studied in the Z_k symmetric
critical points of the multi-cut two-matrix models. Sequence of solutions to
the constraints are obtained in general k-cut critical points. A discrete set
of solutions and a continuum set of solutions are explicitly shown, and they
can be classified by several constrained configurations of the Young diagram.
As the second constraint, we discuss non-perturbative stability of backgrounds
in terms of the Riemann-Hilbert problem. In particular, our procedure in the
2-cut (1,2) case (pure-supergravity case) completely fixes the D-instanton
chemical potentials and results in the Hastings-McLeod solution to the
Painlev\'e II equation. It is also stressed that the Riemann-Hilbert approach
realizes an off-shell background independent formulation of non-critical string
theory.Comment: 71 pages, v3: organization of Sec. 3, Sec. 4, App. C and App. D
improved, final version to be published in Nucl. Phys.
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