arXiv subjects

Jose Gaite

Publications and source records attributed to Jose Gaite.

At least 37 records · Page 2Linked to original sources

arXiv2009

Statistics and geometry of cosmic voids

We introduce new statistical methods for the study of cosmic voids, focusing on the statistics of largest size voids. We distinguish three different types of distributions of voids, namely, Poisson-like, lognormal-like and Pareto-like distributions. The last two distributions are connected with two types of fractal geometry of the matter distribution. Scaling voids with Pareto distribution appear in fractal distributions with box-counting dimension smaller than three (its maximum value), whereas the lognormal void distribution corresponds to multifractals with box-counting dimension equal to three. Moreover, voids of the former type persist in the continuum limit, namely, as the number density of observable objects grows, giving rise to lacunar fractals, whereas voids of the latter type disappear in the continuum limit, giving rise to non-lacunar (multi)fractals. We propose both lacunar and non-lacunar multifractal models of the cosmic web structure of the Universe. A non-lacunar multifractal model is supported by current galaxy surveys as well as cosmological $N$-body simulations. This model suggests, in particular, that small dark matter halos and, arguably, faint galaxies are present in cosmic voids.

astro-ph.CO↗

arXiv2008

Zipf's law for fractal voids and a new void-finder

Voids are a prominent feature of fractal point distributions but there is no precise definition of what is a void (except in one dimension). Here we propose a definition of voids that uses methods of discrete stochastic geometry, in particular, Delaunay and Voronoi tessellations, and we construct a new algorithm to search for voids in a point set. We find and rank-order the voids of suitable examples of fractal point sets in one and two dimensions to test whether Zipf's power-law holds. We conclude affirmatively and, furthermore, that the rank-ordering of voids conveys similar information to the number-radius function, as regards the scaling regime and the transition to homogeneity. So it is an alternative tool in the analysis of fractal point distributions with crossover to homogeneity and, in particular, of the distribution of galaxies.

astro-ph↗

arXiv2008

Geometry and scaling of cosmic voids

CONTEXT: Cosmic voids are observed in the distribution of galaxies and, to some extent, in the dark matter distribution. If these distributions have fractal geometry, it must be reflected in the geometry of voids; in particular, we expect scaling sizes of voids. However, this scaling is not well demonstrated in galaxy surveys yet. AIMS: Our objective is to understand the geometry of cosmic voids in relation to a fractal structure of matter. We intend to distinguish monofractal voids from multifractal voids, regarding their scaling properties. We plan to analyse voids in the distributions of mass concentrations (halos) in a multifractal and their relation to galaxy voids. METHODS: We make a statistical analysis of point distributions based on the void probability function and correlation functions. We assume that voids are spherical and devise a simple spherical void finder. For continuous mass distributions, we employ the methods of fractal geometry. We confirm the analytical predictions with numerical simulations. Smoothed mass distributions are suitable for the method of excursion sets. RESULTS: Voids are very nonlinear and non-perturbative structures. Voids reflect the fractal geometry of the matter distribution but not always directly: scaling sizes of voids imply fractal geometry, but fractal voids may have a complicated geometry and may not have scaling sizes. Proper multifractal voids are of this type. A natural multifractal biasing model implies that the voids in the galaxy distribution inherit the same complicated geometry. CONCLUSIONS: Current galaxy surveys as well as cosmological N-body simulations indicate that cosmic voids are proper multifractal voids. This implies the presence in the voids of galaxies or, at least, small dark matter halos.

astro-ph↗

arXiv2007

Nonlinear analysis of a simple model of temperature evolution in a satellite

We analyse a simple model of the heat transfer to and from a small satellite orbiting round a solar system planet. Our approach considers the satellite isothermal, with external heat input from the environment and from internal energy dissipation, and output to the environment as black-body radiation. The resulting nonlinear ordinary differential equation for the satellite's temperature is analysed by qualitative, perturbation and numerical methods, which show that the temperature approaches a periodic pattern (attracting limit cycle). This approach can occur in two ways, according to the values of the parameters: (i) a slow decay towards the limit cycle over a time longer than the period, or (ii) a fast decay towards the limit cycle over a time shorter than the period. In the first case, an exactly soluble average equation is valid. We discuss the consequences of our model for the thermal stability of satellites.

physics.space-ph↗

arXiv2006

Halos and voids in a multifractal model of cosmic structure

On the one hand, the large scale structure of matter is arguably scale invariant, and, on the other hand, halos and voids are recognized as prominent features of that structure. To unify both approaches, we propose to model the dark matter distribution as a set of fractal distributions of halos of different kinds. This model relies on the concept of multifractal as the most general scaling distribution and on a plausible notion of halo as a singular mass concentration in a multifractal. Voids arise as complementary to halos, namely, as formed by regular mass depletions. To provide halos with definite size and masses, we coarse-grain the dark matter distribution, using the length given by the lower cutoff to scaling. This allows us to relate the halo mass function to the multifractal spectrum. Hence, we find that a log-normal model of the mass distribution nicely fits in this picture and, moreover, the Press-Schechter mass function can be recovered as a bifractal limit. To support our model of fractal distributions of halos, we perform a numerical study of the distribution produced in cosmological N-body simulations. In the Virgo L-CDM GIF2 simulation, we indeed find fractal distributions of halos with various dimensions and a halo mass function of bifractal type. However, this mass function is not of Press-Schechter's type, and we interprete it instead as caused by the undersampling of the distribution at the scale of halos, due to discretization.

astro-ph↗

arXiv2006

Scaling Laws in the Cosmic Structure and Renormalization Group

There is evidence of a scale-invariant matter distribution up to scales over 10 Megaparsecs. We review scaling (fractal or multifractal) models of large scale structure and their observational evidence. We conclude that the dynamics of cosmological structure formation seems to be driven to a multifractal attractor. This supports previous studies, which we review, of structure formation by means of the renormalization group within a hydrodynamic formulation.

astro-ph↗

arXiv2006

Renormalization Group and Quantum Information

The renormalization group is a tool that allows one to obtain a reduced description of systems with many degrees of freedom while preserving the relevant features. In the case of quantum systems, in particular, one-dimensional systems defined on a chain, an optimal formulation is given by White's "density matrix renormalization group". This formulation can be shown to rely on concepts of the developing theory of quantum information. Furthermore, White's algorithm can be connected with a peculiar type of quantization, namely, angular quantization. This type of quantization arose in connection with quantum gravity problems, in particular, the Unruh effect in the problem of black-hole entropy and Hawking radiation. This connection highlights the importance of quantum system boundaries, regarding the concentration of quantum states on them, and helps us to understand the optimal nature of White's algorithm.

quant-ph↗

arXiv2006

Cut-out sets, fractal voids and cosmic structure

"Cut-out sets" are fractals that can be obtained by removing a sequence of disjoint regions from an initial region of d-dimensional euclidean space. Conversely, a description of some fractals in terms of their void complementary set is possible. The essential property of a sequence of fractal voids is that their sizes decrease as a power law, that is, they follow Zipf's law. We prove the relation between the box dimension of the fractal set (in d <= 3) and the exponent of the Zipf law for convex voids; namely, if the Zipf law exponent e is such that 1 < e < d/(d-1) and, in addition, we forbid the appearance of degenerate void shapes, we prove that the corresponding cut-out set has box dimension d/e (d-1 < d/e < d). We explore the application of this result to the large scale distribution of matter in cosmology, in connection with ``cosmic foam'' models.

astro-ph↗

arXiv2005

Stability of Self-Similar Spherical Accretion

Spherical accretion flows are simple enough for analytical study, by solution of the corresponding fluid dynamic equations. The solutions of stationary spherical flow are due to Bondi. The questions of the choice of a physical solution and of stability have been widely discussed. The answer to these questions is very dependent on the problem of boundary conditions, which vary according to whether the accretor is a compact object or a black hole. We introduce a particular, simple form of stationary spherical flow, namely, self-similar Bondi flow, as a case with physical interest in which analytic solutions for perturbations can be found. With suitable no matter-flux-perturbation boundary conditions, we will show that acoustic modes are stable in time and have no spatial instability at r=0. Furthermore, their evolution eventually becomes ergodic-like and shows no trace of instability or of acquiring any remarkable pattern.

gr-qc↗

arXiv2005

Perturbations of self-similar Bondi accretion

The question of stability of steady spherical accretion has been studied for many years and, recently, the concept of spatial instability has been introduced. Here we study perturbations of steady spherical accretion flows (Bondi solutions), restricting ourselves to the case of self-similar flow, as a case amenable to analytic treatment and with physical interest. We further restrict ourselves to its acoustic perturbations. The radial perturbation equation can be solved in terms of Bessel functions. We study the formulation of adequate boundary conditions and decide for no matter-flux-perturbation conditions (at the Bondi radius and at r=0). We also consider the problem of initial conditions and time evolution, in particular, of radial perturbations. No spatial instability at r=0 is found. The time evolution is such that perturbations eventually become ergodic-like and show no trace of instability or of acquiring any remarkable pattern.

astro-ph↗

arXiv2005

Scaling of voids in the large scale distribution of matter

Voids are a prominent feature of the galaxy distribution but their quantitative study is hindered by the lack of a precise definition of what constitutes a void. Here we propose a definition of voids in point distributions that uses methods of discrete stochastic geometry, in particular, Delaunay and Voronoi tessellations, and we construct a new void-finder. We then apply the void-finder to scaling point distributions. First, we find the voids of pure fractals with a transition to homogeneity and show that the rank ordering of the voids also scales (Zipf's law) and, in addition, shows the transition to homogeneity. However, a pure fractal is arguably not a good model of the galaxy distribution, so we construct from a cosmological $N$-body simulation a bifractal mock galaxy sample representing two galaxy populations, which we identify as "wall" and "field" galaxies. The wall galaxy distribution fits a pure fractal with a transition to homogeneity and, furthermore, the rank ordering of its voids shows a scaling range with the right slope plus a transition to homogeneity.

astro-ph↗

arXiv2005

The fractal distribution of haloes

We examine the proposal that a model of the large-scale matter distribution consisting of randomly placed haloes with power-law profile, as opposed to a fractal model, can account for the observed power-law galaxy-galaxy correlations. We conclude that such model, which can actually be considered as a degenerate multifractal model, is not realistic but suggests a new picture of multifractal models, namely, as sets of fractal distributions of haloes. We analyse, according to this picture, the properties of the matter distribution produced in cosmological N-body simulations, with affirmative results; namely, haloes of similar mass have a fractal distribution with a given dimension, which grows as the mass diminishes.

astro-ph↗

arXiv2004

Stochastic formulation of the renormalization group: supersymmetric structure and topology of the space of couplings

The exact or Wilson renormalization group equations can be formulated as a functional Fokker-Planck equation in the infinite-dimensional configuration space of a field theory, suggesting a stochastic process in the space of couplings. Indeed, the ordinary renormalization group differential equations can be supplemented with noise, making them into stochastic Langevin equations. Furthermore, if the renormalization group is a gradient flow, the space of couplings can be endowed with a supersymmetric structure a la Parisi-Sourlas. The formulation of the renormalization group as supersymmetric quantum mechanics is useful for analysing the topology of the space of couplings by means of Morse theory. We present simple examples with one or two couplings.

hep-th↗

arXiv2003

Nonlinear spherical gravitational downfall of gas onto a solid ball: analytic and numerical results

The process of downfall of initially homogeneous gas onto a solid ball due to the ball's gravity (relevant in astrophysical situations) is studied with a combination of analytic and numerical methods. The initial explicit solution soon becomes discontinuous and gives rise to a shock wave. Afterwards, there is a crossover between two intermediate asymptotic similarity regimes, where the shock wave propagates outwards according to two self-similar laws, initially accelerating and eventually decelerating and vanishing, leading to a static state. The numerical study allows one to investigate in detail this dynamical problem and its time evolution, verifying and complementing the analytic results on the initial solution, intermediate self-similar laws and static long-term solution.

nlin.SI↗

arXiv2003

Analytic solutions for spherical gravitational gas accretion on to a solid body

The process of gravitational accretion of initially homogeneous gas onto a solid ball is studied with methods of fluid dynamics. The fluid partial differential equations for polytropic flow can be solved exactly in an early stage, but this solution soon becomes discontinuous and gives rise to a shock wave. Afterwards, there is a crossover between two intermediate asymptotic self-similar regimes, where the shock wave propagates outwards according to two similarity laws, initially accelerating, then decelerating (and eventually vanishing). Lastly, we study the final static state. Our purpose is to attain a global picture of the process.

astro-ph↗

arXiv2003

Large Scale Features of Rotating Forced Turbulence

Large scale features of a randomly isotropically forced incompressible and unbounded rotating fluid are examined in perturbation theory. At first order in both the random force amplitude and the angular velocity we find two types of modifications to the fluid equation of motion. The first correction transforms the molecular shear viscosity into a (rotation independent) effective viscosity. The second perturbative correction leads to a new large scale non-dissipative force proportional to the fluid angular velocity in the slow rotation regime. This effective force does no net work and alters the dispersion relation of inertial waves propagating in the fluid. Both dynamically generated corrections can be identified with certain components of the most general axisymmetric ``viscosity tensor'' for a Newtonian fluid.

physics.flu-dyn↗

arXiv2003

Entanglement Entropy and The Density Matrix Renormalization Group

Quantum entanglement entropy has a geometric character. This is illustrated by the interpretation of Rindler space or black hole entropy as entanglement entropy. In general, one can define a "geometric entropy", associated with an event horizon as a boundary that concentrates a large number of quantum states. This allows one to connect with the "density matrix renormalization group" and to unveil its connection with the theory of quantum information. This renormalization group has been introduced in condensed matter physics in a heuristic manner, but it can be conceived as a method of compression of quantum information in the presence of a horizon. We propose generalizations to problems of interest in cosmology.

quant-ph↗

arXiv2002

Scaling of voids and fractality in the galaxy distribution

We study here, from first principles, what properties of voids are to be expected in a fractal point distribution and how the void distribution is related to its morphology. We show this relation in various examples and apply our results to the distribution of galaxies. If the distribution of galaxies forms a fractal set, then this property results in a number of scaling laws to be fulfilled by voids. Consider a fractal set of dimension $D$ and its set of voids. If voids are ordered according to decreasing sizes (largest void has rank R=1, second largest R=2 and so on), then a relation between size $Λ$ and rank of the form $Λ(R) \propto R^{-z}$ must hold, with $z = d/D$, and where $d$ is the euclidean dimension of the space where the fractal is embedded. The physical restriction $D < d$ means that $z > 1$ in a fractal set. The average size $\bar Λ$ of voids depends on the upper ($Λ_u$) and the lower ($Λ_l$) cut-off as ${\bar Λ} \propto Λ_u^{1-D/d} Λ_l^{D/d}$. Current analysis of void sizes in the galaxy distribution do not show evidence of a fractal distribution, but are insufficient to rule it out. We identify possible shortcomings of current void searching algorithms, such as changes of shape in voids at different scales or merging of voids, and propose modifications useful to test fractality in the galaxy distribution.

astro-ph↗