scholarly journals Analytical halo models of cosmic tidal fields

2021 ◽  
Vol 502 (4) ◽  
pp. 5210-5226
Author(s):  
Aseem Paranjape
Keyword(s):  
Dark Matter ◽  
Mass Loss ◽  
Gaussian Mixture ◽  
Dynamical Mass ◽  
Host Environment ◽  
Density Distributions ◽  
Web Environment ◽  
Non Linear ◽  
Analytical Expressions ◽  
Model Formalism

ABSTRACT The non-linear cosmic web environment of dark matter haloes plays a major role in shaping their growth and evolution, and potentially also affects the galaxies that reside in them. We develop an analytical (halo model) formalism to describe the tidal field of anisotropic halocentric density distributions, as characterized by the halocentric tidal tensor $\left\langle \, T_{ij}\, \right\rangle (\lt R)$ spherically averaged on scale R ∼ 4Rvir for haloes of virial radius Rvir. We focus on axisymmetric anisotropies, which allows us to explore simple and intuitive toy models of (sub)halo configurations that exemplify some of the most interesting anisotropies in the cosmic web. We build our models around the spherical Navarro–Frenk–White profile after describing it as a Gaussian mixture, which leads to almost fully analytical expressions for the ‘tidal anisotropy’ scalar α(< 4Rvir) extracted from the tidal tensor. Our axisymmetric examples include (i) a spherical halo at the axis of a cylindrical filament, (ii) an off-centred satellite in a spherical host halo, and (iii) an axisymmetric halo. Using these, we demonstrate several interesting results. For example, the tidal tensor at the axis of a pure cylindrical filament gives α(fil)(< R) = 1/2 exactly, for any R. Also, α(< 4Rvir,sat) for a satellite of radius Rvir,sat as a function of its hostcentric distance is a sensitive probe of dynamical mass-loss of the satellite in its host environment. Finally, we discuss a number of potentially interesting extensions and applications of our formalism that can deepen our understanding of the multiscale phenomenology of the cosmic web.

Distributed track‐to‐track fusion for non‐linear systems with Gaussian mixture noise

2019 ◽  
Vol 13 (5) ◽  
pp. 740-749 ◽  
Author(s):  
Kelin Lu ◽  
Changyin Sun ◽  
Qien Fu ◽  
Qian Zhu
Keyword(s):  
Linear Systems ◽  
Gaussian Mixture ◽  
Track Fusion ◽  
Non Linear ◽  
Non Linear Systems

scholarly journals Separate Universe calibration of the dependence of halo bias on cosmic web anisotropy

2020 ◽  
Vol 499 (3) ◽  
pp. 4418-4431 ◽  
Author(s):  
Sujatha Ramakrishnan ◽  
Aseem Paranjape
Keyword(s):  
Dark Matter ◽  
High Precision ◽  
Gaussian Distribution ◽  
Initial Perturbation ◽  
Analytical Framework ◽  
Web Environment ◽  
Wide Range ◽  
Galaxy Assembly ◽  
Very High ◽  
Good Agreement

ABSTRACT We use the Separate Universe technique to calibrate the dependence of linear and quadratic halo bias b1 and b2 on the local cosmic web environment of dark matter haloes. We do this by measuring the response of halo abundances at fixed mass and cosmic web tidal anisotropy α to an infinite wavelength initial perturbation. We augment our measurements with an analytical framework developed in earlier work that exploits the near-lognormal shape of the distribution of α and results in very high precision calibrations. We present convenient fitting functions for the dependence of b1 and b2 on α over a wide range of halo mass for redshifts 0 ≤ z ≤ 1. Our calibration of b2(α) is the first demonstration to date of the dependence of non-linear bias on the local web environment. Motivated by previous results that showed that α is the primary indicator of halo assembly bias for a number of halo properties beyond halo mass, we then extend our analytical framework to accommodate the dependence of b1 and b2 on any such secondary property that has, or can be monotonically transformed to have, a Gaussian distribution. We demonstrate this technique for the specific case of halo concentration, finding good agreement with previous results. Our calibrations will be useful for a variety of halo model analyses focusing on galaxy assembly bias, as well as analytical forecasts of the potential for using α as a segregating variable in multitracer analyses.

scholarly journals Two-component galaxy models with a central BH – II. The ellipsoidal case

2020 ◽  
Vol 500 (1) ◽  
pp. 1054-1070
Author(s):  
Luca Ciotti ◽  
Antonio Mancino ◽  
Silvia Pellegrini ◽  
Azadeh Ziaee Lorzad
Keyword(s):  
Dark Matter ◽  
Stellar Dynamics ◽  
Azimuthal Velocity ◽  
Dark Matter Halo ◽  
Gas Flows ◽  
Total Density ◽  
Density Distributions ◽  
Stellar Component ◽  
Two Component ◽  
Analytical Formulae

ABSTRACT Recently, two-component spherical galaxy models have been presented, where the stellar profile is described by a Jaffe law, and the total density by another Jaffe law, or by an r−3 law at large radii. We extend these two families to their ellipsoidal axisymmetric counterparts: the JJe and J3e models. The total and stellar density distributions can have different flattenings and scale lengths, and the dark matter halo is defined by difference. First, the analytical conditions required to have a nowhere negative dark matter halo density are derived. The Jeans equations for the stellar component are then solved analytically, in the limit of small flattenings, also in the presence of a central BH. The azimuthal velocity dispersion anisotropy is described by the Satoh k-decomposition. Finally, we present the analytical formulae for velocity fields near the centre and at large radii, together with the various terms entering the virial theorem. The JJe and J3e models can be useful in a number of theoretical applications, e.g. to explore the role of the various parameters (flattening, relative scale lengths, mass ratios, rotational support) in determining the behaviour of the stellar kinematical fields before performing more time-expensive integrations with specific galaxy models, to test codes of stellar dynamics and in numerical simulations of gas flows in galaxies.

scholarly journals A Hybrid Hidden Markov Model for Pipeline Leakage Detection

2021 ◽  
Vol 11 (7) ◽  
pp. 3138
Author(s):  
Mingchi Zhang ◽  
Xuemin Chen ◽  
Wei Li
Keyword(s):  
Neural Network ◽  
Markov Model ◽  
Hidden Markov Model ◽  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Deep Neural Network ◽  
Hidden Markov ◽  
Gaussian Mixture ◽  
State Sequence ◽  
Non Linear

In this paper, a deep neural network hidden Markov model (DNN-HMM) is proposed to detect pipeline leakage location. A long pipeline is divided into several sections and the leakage occurs in different section that is defined as different state of hidden Markov model (HMM). The hybrid HMM, i.e., DNN-HMM, consists of a deep neural network (DNN) with multiple layers to exploit the non-linear data. The DNN is initialized by using a deep belief network (DBN). The DBN is a pre-trained model built by stacking top-down restricted Boltzmann machines (RBM) that compute the emission probabilities for the HMM instead of Gaussian mixture model (GMM). Two comparative studies based on different numbers of states using Gaussian mixture model-hidden Markov model (GMM-HMM) and DNN-HMM are performed. The accuracy of the testing performance between detected state sequence and actual state sequence is measured by micro F1 score. The micro F1 score approaches 0.94 for GMM-HMM method and it is close to 0.95 for DNN-HMM method when the pipeline is divided into three sections. In the experiment that divides the pipeline as five sections, the micro F1 score for GMM-HMM is 0.69, while it approaches 0.96 with DNN-HMM method. The results demonstrate that the DNN-HMM can learn a better model of non-linear data and achieve better performance compared to GMM-HMM method.

scholarly journals APPLICATIONS OF DENSITY MATRICES IN A TRAPPED BOSE GAS

2006 ◽  
Vol 20 (15) ◽  
pp. 2189-2221 ◽  
Author(s):  
K. CH. CHATZISAVVAS ◽  
S. E. MASSEN ◽  
CH. C. MOUSTAKIDIS ◽  
C. P. PANOS
Keyword(s):  
Quantum Information ◽  
Bose Gas ◽  
Einstein Condensation ◽  
Density Distributions ◽  
Occupation Numbers ◽  
The One ◽  
Bose Einstein ◽  
Jensen Shannon Divergence ◽  
Analytical Expressions ◽  
Short Range Correlations

An overview of the Bose–Einstein condensation of correlated atoms in a trap is presented by examining the effect of interparticle correlations to one- and two-body properties of the above systems at zero temperature in the framework of the lowest order cluster expansion. Analytical expressions for the one- and two-body properties of the Bose gas are derived using Jastrow-type correlation function. In addition numerical calculations of the natural orbitals and natural occupation numbers are also carried out. Special effort is devoted for the calculation of various quantum information properties including Shannon entropy, Onicescu informational energy, Kullback–Leibler relative entropy and the recently proposed Jensen–Shannon divergence entropy. The above quantities are calculated for the trapped Bose gases by comparing the correlated and uncorrelated cases as a function of the strength of the short-range correlations. The Gross–Piatevskii equation is solved, giving the density distributions in position and momentum space, which are employed to calculate quantum information properties of the Bose gas.

scholarly journals Non-Gaussian inference from non-linear and non-Poisson biased distributed data

2014 ◽  
Vol 10 (S306) ◽  
pp. 258-261
Author(s):  
Metin Ata ◽  
Francisco-Shu Kitaura ◽  
Volker Müller
Keyword(s):  
Dark Matter ◽  
Statistical Inference ◽  
Computer Code ◽  
Matter Density ◽  
Density Field ◽  
Distributed Data ◽  
Dark Matter Density ◽  
Posterior Sampling ◽  
Non Linear ◽  
Non Gaussian

AbstractWe study the statistical inference of the cosmological dark matter density field from non-Gaussian, non-linear and non-Poisson biased distributed tracers. We have implemented a Bayesian posterior sampling computer-code solving this problem and tested it with mock data based onN-body simulations.

scholarly journals Recoiling black holes in static and evolving dark matter halo potential

2015 ◽  
pp. 17-28 ◽  
Author(s):  
M. Smole
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Dark Matter ◽  
Critical Velocity ◽  
Complete Removal ◽  
Matter Density ◽  
Dark Matter Halo ◽  
Dark Matter Halos ◽  
Critical Amplitude ◽  
Density Distributions

We follow trajectories of kicked black holes in static and evolving dark matter halo potential. We explore both NFW and Einasto dark matter density distributions. Considered dark matter halos represent hosts of massive spiral and elliptical field galaxies. We study critical amplitude of kick velocity necessary for complete black hole ejection at various redshifts and find that ~40% lower kick velocities can remove black holes from their host haloes at z = 7 compared to z = 1. The greatest difference between static and evolving potential occurs near the critical velocity for black hole ejection and at high redshifts. When NFW and Einasto density distributions are compared ~30% higher kick velocities are needed for complete removal of BHs from dark matter halo described by NFW profile.

scholarly journals Holographic cosmology with two coupled fluids in the presence of viscosity

2021 ◽  
pp. 2150149
Author(s):  
I. Brevik ◽  
A. V. Timoshkin
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Holographic Dark Energy ◽  
Exponential Model ◽  
Point Of View ◽  
Accelerating Universe ◽  
Late Time ◽  
Conservation Of Energy ◽  
Analytical Expressions ◽  
Friedmann Robertson Walker

We explore the cosmological models of the late-time universe based on the holographic principle, taking into account the properties of the viscosity of the dark fluid. We use the mathematical formalism of generalized infrared cutoff holographic dark energy, as presented by Nojiri and Odintsov [Covariant generalized holographic dark energy and accelerating universe, Eur. Phys. J. C 77 (2017) 528]. We consider the Little Rip, the Pseudo Rip, and a bounce exponential model, with two interacting fluids, namely dark energy and dark matter in a spatially-flat Friedmann–Robertson–Walker universe. Within these models, analytical expressions are obtained for infrared cutoffs in terms of the particle horizons. The law of conservation of energy is presented, from a holographic point of view.

scholarly journals Non-linear analysis of laminated composite doubly curved shallow shells

2006 ◽  
Vol 28 (1) ◽  
pp. 43-55
Author(s):  
Dao Huy Bich
Keyword(s):  
Laminated Composite ◽  
Governing Equations ◽  
Shallow Shells ◽  
Approximate Analytical Solutions ◽  
Linear Buckling ◽  
Non Linear ◽  
Vibration Problems ◽  
Doubly Curved ◽  
Analytical Expressions ◽  
Load Deflection Curve

This paper deals with governing equations and approximate analytical solutions based on some wellknown assumptions to the non-linear buckling and vibration problems of laminated composite doubly curved shallow shells. Obtained results will be presented by analytical expressions of the lower critical load, the postbuckling load-deflection curve and the fundamental frequency of non-linear free vibration of the shell.

Non-linear automatic target tracking in clutter using dynamic Gaussian mixture

2012 ◽  
Vol 6 (9) ◽  
pp. 937-944 ◽  
Author(s):  
D. Mušicki ◽  
T.L. Song ◽  
W.C. Kim ◽  
D. Nešić
Keyword(s):  
Target Tracking ◽  
Gaussian Mixture ◽  
Non Linear
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