123 research outputs found
Chaotic motion and spiral structure in self-consistent models of rotating galaxies
Dissipationless N-body models of rotating galaxies, iso-energetic to a
non-rotating model, are examined as regards the mass in regular and in chaotic
motion. The values of their spin parameters are near the value
of our Galaxy.
We obtain the distinction between the sets of particles moving in regular and
in chaotic orbits and we show that the spatial distribution of these two sets
of particles is much different. The rotating models are characterized by larger
fractions of mass in chaotic motion () compared with the
fraction of mass in chaotic motion in the non-rotating iso-energetic model
(). Furthermore, the Lyapunov numbers of the chaotic orbits
in the rotating models become by about one order of magnitude larger than in
the non-rotating model. Chaotic orbits are concentrated preferably in values of
the Jacobi integral around the value of the effective potential at the
corotation radius.
We find that density waves form a central rotating bar embedded in a thin and
a thick disc with exponential surface density profile. A surprising new result
is that long living spiral arms are exited on the disc, composed almost
completely by chaotic orbits.
The bar excites an mode of spiral waves on the surface density of the
disc, emanating from the corotation radius. These spiral waves are deformed,
fade, or disappear temporarily, but they grow again re-forming a well developed
spiral pattern. Spiral arms are discernible up to 20 or 30 rotations of the bar
(lasting for about a Hubble time).Comment: 30 pages, 17 figures (low resolution). Revised version. Accepted for
publication in MNRAS. For high resolution figures please send email to
[email protected]
The production of Tsallis entropy in the limit of weak chaos and a new indicator of chaoticity
We study the connection between the appearance of a `metastable' behavior of
weakly chaotic orbits, characterized by a constant rate of increase of the
Tsallis q-entropy (Tsallis 1988), and the solutions of the variational
equations of motion for the same orbits. We demonstrate that the variational
equations yield transient solutions, lasting for long time intervals, during
which the length of deviation vectors of nearby orbits grows in time almost as
a power-law. The associated power exponent can be simply related to the
entropic exponent for which the q-entropy exhibits a constant rate of increase.
This analysis leads to the definition of a new sensitive indicator
distinguishing regular from weakly chaotic orbits, that we call `Average Power
Law Exponent' (APLE). We compare the APLE with other established indicators of
the literature. In particular, we give examples of application of the APLE in
a) a thin separatrix layer of the standard map, b) the stickiness region around
an island of stability in the same map, and c) the web of resonances of a 4D
symplectic map. In all these cases we identify weakly chaotic orbits exhibiting
the `metastable' behavior associated with the Tsallis q-entropy.Comment: 19 pages, 12 figures, accepted for publication by Physica
Invariant manifolds and the response of spiral arms in barred galaxies
The unstable invariant manifolds of the short-period family of periodic
orbits around the unstable Lagrangian points and of a barred galaxy
define loci in the configuration space which take the form of a trailing spiral
pattern. In the present paper we investigate this association in the case of
the self-consistent models of Kaufmann & Contopoulos (1996) which provide an
approximation of real barred-spiral galaxies. We also examine the relation of
`response' models of barred-spiral galaxies with the theory of the invariant
manifolds. Our main results are the following: The invariant manifolds yield
the correct form of the imposed spiral pattern provided that their calculation
is done with the spiral potential term turned on. We provide a theoretical
model explaining the form of the invariant manifolds that supports the spiral
structure. The azimuthal displacement of the Lagrangian points with respect to
the bar's major axis is a crucial parameter in this modeling. When this is
taken into account, the manifolds necessarily develop in a spiral-like domain
of the configuration space, delimited from below by the boundary of a
banana-like non-permitted domain, and from above either by rotational KAM tori
or by cantori forming a stickiness zone. We construct `spiral response' models
on the basis of the theory of the invariant manifolds and examine the
connection of the latter to the `response' models (Patsis 2006) used to fit
real barred-spiral galaxies, explaining how are the manifolds related to a
number of morphological features seen in such models.Comment: 16 Page
NGC 1300 Dynamics: III. Orbital analysis
We present the orbital analysis of four response models, that succeed in
reproducing morphological features of NGC 1300. Two of them assume a planar
(2D) geometry with =22 and 16 \ksk respectively. The two others
assume a cylindrical (thick) disc and rotate with the same pattern speeds as
the 2D models. These response models reproduce most successfully main
morphological features of NGC 1300 among a large number of models, as became
evident in a previous study. Our main result is the discovery of three new
dynamical mechanisms that can support structures in a barred-spiral grand
design system. These mechanisms are presented in characteristic cases, where
these dynamical phenomena take place. They refer firstly to the support of a
strong bar, of ansae type, almost solely by chaotic orbits, then to the support
of spirals by chaotic orbits that for a certain number of pat tern revolutions
follow an n:1 (n=7,8) morphology, and finally to the support of spiral arms by
a combination of orbits trapped around L and sticky chaotic orbits with
the same Jacobi constant. We have encountered these dynamical phenomena in a
large fraction of the cases we studied as we varied the parameters of our
general models, without forcing in some way their appearance. This suggests
that they could be responsible for the observed morphologies of many
barred-spiral galaxies. Comparing our response models among themselves we find
that the NGC 130 0 morphology is best described by a thick disc model for the
bar region and a 2D disc model for the spirals, with both components rotating
with the same pattern speed =16 \ksk !. In such a case, the whole
structure is included inside the corotation of the system. The bar is supported
mainly by regular orbits, while the spirals are supported by chaotic orbits.Comment: 18 pages, 32 figures, accepted for publication in MNRA
Asymptotic Orbits in Barred Spiral Galaxies
We study the formation of the spiral structure of barred spiral galaxies,
using an -body model. The evolution of this -body model in the adiabatic
approximation maintains a strong spiral pattern for more than 10 bar rotations.
We find that this longevity of the spiral arms is mainly due to the phenomenon
of stickiness of chaotic orbits close to the unstable asymptotic manifolds
originated from the main unstable periodic orbits, both inside and outside
corotation. The stickiness along the manifolds corresponding to different
energy levels supports parts of the spiral structure. The loci of the disc
velocity minima (where the particles spend most of their time, in the
configuration space) reveal the density maxima and therefore the main
morphological structures of the system. We study the relation of these loci
with those of the apocentres and pericentres at different energy levels. The
diffusion of the sticky chaotic orbits outwards is slow and depends on the
initial conditions and the corresponding Jacobi constant.Comment: 17 pages, 24 figure
Gravitational Mesoscopic Constraints in Cosmological Dark Matter Halos
We present an analysis of the behaviour of the `coarse-grained'
(`mesoscopic') rank partitioning of the mean energy of collections of particles
composing virialized dark matter halos in a Lambda-CDM cosmological simulation.
We find evidence that rank preservation depends on halo mass, in the sense that
more massive halos show more rank preservation than less massive ones. We find
that the most massive halos obey Arnold's theorem (on the ordering of the
characteristic frequencies of the system) more frequently than less massive
halos. This method may be useful to evaluate the coarse-graining level (minimum
number of particles per energy cell) necessary to reasonably measure signatures
of `mesoscopic' rank orderings in a gravitational system.Comment: LaTeX, 15 pages, 3 figures. Accepted for publication in Celestial
Mechanics and Dynamical Astronomy Journa
Adaptive Memetic Particle Swarm Optimization with Variable Local Search Pool Size
We propose an adaptive Memetic Particle Swarm Optimization algorithm where local search is selected from a pool of different algorithms. The choice of local search is based on a probabilistic strategy that uses a simple metric to score the efficiency of local search. Our study investigates whether the pool size affects the memetic algorithm’s performance, as well as the possible benefit of using the adaptive strategy against a baseline static one. For this purpose, we employed the memetic algorithms framework provided in the recent MEMPSODE optimization software, and tested the proposed algorithms on the Benchmarking Black Box Optimization (BBOB 2012) test suite. The obtained results lead to a series of useful conclusions
Maximal surgical tumour load reduction in immune-checkpoint inhibitor naïve patients with melanoma brain metastases correlates with prolonged survival
Background: Recent therapeutic advances in metastatic melanoma have led to improved overall survival (OS) rates, with consequently an increased incidence of brain metastases (BM). The role of BM resection in the era of targeted and immunotherapy should be reassessed. In the current study we analysed the role of residual intracranial tumour load in a cohort of melanoma BM patients.
Methods: Retrospective single-centre analysis of a prospective registry of resected melanoma BM from 2013 to 2021. Correlations of residual tumour volume and outcome were determined with respect to patient, tumour and treatment regimens characteristics.
Results: 121 individual patients (66% male, mean age 59.9 years) were identified and included in the study. Pre- and postoperative systemic treatments included BRAF/MEK inhibitors, as well as combination or monotherapy of immune-checkpoint inhibitors (ICIs). Median OS of the entire cohort was 20 months. Cox proportional-hazard analysis revealed postoperative anti-CTLA4+anti-PD-1 therapy (HR 0.07, p = .01) and postoperative residual intracranial tumour burden (HR 1.4, p = .027) as significant predictors for OS. Further analysis revealed that ICI-naïve patients with residual tumour volume ≤3.5 cm3 and postoperative ICI showed significantly prolonged OS compared to patients with residual volume >3.5 cm3 (p < .0001). Subgroup analysis of ICI-naïve patients showed steroid intake postoperatively to be negatively associated with OS, however residual tumour volume ≤3.5 cm3 remained independently correlated with superior OS (HR 0.14, p < .001).
Conclusion: Besides known predictive factors like postoperative ICI, a maximal intracranial tumour burden reduction seems to be beneficial, especially in ICI-naïve patients. This highlights the importance of local CNS control and the need to further investigating the role of initial surgical tumour load reduction in randomised clinical trials.
Keywords: Brain metastases; Extent of resection; Immunotherapy; Melanoma; Tumour residua
Multiple roots of systems of equations by repulsion merit functions
In this paper we address the problem of computing multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function. The search procedure for a global min- imizer of the merit function is carried out by a metaheuristic, known as harmony search, which does not require any derivative information. The multiple roots of the system are sequentially determined along several ite- rations of a single run, where the merit function is accordingly modified by penalty terms that aim to create repulsion areas around previously computed minimizers. A repulsion algorithm based on a multiplicative kind penalty function is proposed. Preliminary numerical experiments with a benchmark set of problems show the effectiveness of the proposed method.Fundação para a Ciência e a Tecnologia (FCT
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