scholarly journals A medieval multiverse?: Mathematical modelling of the thirteenth century universe of Robert Grosseteste

2014 ◽  
Vol 470 (2167) ◽  
pp. 20140025 ◽  
Author(s):  
Richard G. Bower ◽  
Tom C. B. McLeish ◽  
Brian K. Tanner ◽  
Hannah E. Smithson ◽  
Cecilia Panti ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Initial Density ◽  
Outer Region ◽  
Big Bang ◽  
Small Range ◽  
Density Profiles ◽  
Material Body ◽  
Fundamental Parameters ◽  
Entire Cosmos ◽  
Text Formation

In his treatise on light, written about 1225, Robert Grosseteste describes a cosmological model in which the universe is created in a big-bang-like explosion and subsequent condensation. He postulates that the fundamental coupling of light and matter gives rises to the material body of the entire cosmos. Expansion is arrested when matter reaches a minimum density and subsequent emission of light from the outer region leads to compression and rarefaction of the inner bodily mass so as to create nine celestial spheres, with an imperfect residual core. In this paper, we reformulate the Latin description in terms of a modern mathematical model, teasing out consequences implicit in the text, but which the author would not have had the tools to explore. The equations which describe the coupling of light and matter are solved numerically, subjected to initial conditions and critical criteria consistent with the text. Formation of a universe with a non-infinite number of perfected spheres is extremely sensitive to the initial conditions, the intensity of the light and the transparency of these spheres. In this ‘medieval multiverse’, only a small range of opacity and initial density profiles leads to a stable universe with nine perfected spheres. As in current cosmological thinking, the existence of Grosseteste’s universe relies on a very special combination of fundamental parameters.

scholarly journals Effects of initial density profiles on massive star cluster formation in giant molecular clouds

2021 ◽  
Author(s):  
Yingtian Chen ◽  
Hui Li ◽  
Mark Vogelsberger
Keyword(s):  
Angular Momentum ◽  
Star Formation ◽  
Molecular Clouds ◽  
Globular Clusters ◽  
Cluster Formation ◽  
Initial Density ◽  
Giant Molecular Clouds ◽  
Density Profiles ◽  
Stellar Feedback ◽  
Gas Accretion

Abstract We perform a suite of hydrodynamic simulations to investigate how initial density profiles of giant molecular clouds (GMCs) affect their subsequent evolution. We find that the star formation duration and integrated star formation efficiency of the whole clouds are not sensitive to the choice of different profiles but are mainly controlled by the interplay between gravitational collapse and stellar feedback. Despite this similarity, GMCs with different profiles show dramatically different modes of star formation. For shallower profiles, GMCs first fragment into many self-gravitation cores and form sub-clusters that distributed throughout the entire clouds. These sub-clusters are later assembled ‘hierarchically’ to central clusters. In contrast, for steeper profiles, a massive cluster is quickly formed at the center of the cloud and then gradually grows its mass via gas accretion. Consequently, central clusters that emerged from clouds with shallower profiles are less massive and show less rotation than those with the steeper profiles. This is because 1) a significant fraction of mass and angular momentum in shallower profiles is stored in the orbital motion of the sub-clusters that are not able to merge into the central clusters 2) frequent hierarchical mergers in the shallower profiles lead to further losses of mass and angular momentum via violent relaxation and tidal disruption. Encouragingly, the degree of cluster rotations in steeper profiles is consistent with recent observations of young and intermediate-age clusters. We speculate that rotating globular clusters are likely formed via an ‘accretion’ mode from centrally-concentrated clouds in the early Universe.

scholarly journals Relativistic Cosmology with an Introduction to Inflation

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 276
Author(s):  
Muhammad Zahid Mughal ◽  
Iftikhar Ahmad ◽  
Juan Luis García Guirao
Keyword(s):  
Standard Model ◽  
Early Universe ◽  
Large Scale ◽  
Initial Conditions ◽  
Big Bang ◽  
Relativistic Cosmology ◽  
The Standard Model ◽  
Big Bang Model ◽  
The Big Bang ◽  
The Universe

In this review article, the study of the development of relativistic cosmology and the introduction of inflation in it as an exponentially expanding early phase of the universe is carried out. We study the properties of the standard cosmological model developed in the framework of relativistic cosmology and the geometric structure of spacetime connected coherently with it. The geometric properties of space and spacetime ingrained into the standard model of cosmology are investigated in addition. The big bang model of the beginning of the universe is based on the standard model which succumbed to failure in explaining the flatness and the large-scale homogeneity of the universe as demonstrated by observational evidence. These cosmological problems were resolved by introducing a brief acceleratedly expanding phase in the very early universe known as inflation. The cosmic inflation by setting the initial conditions of the standard big bang model resolves these problems of the theory. We discuss how the inflationary paradigm solves these problems by proposing the fast expansion period in the early universe. Further inflation and dark energy in fR modified gravity are also reviewed.

scholarly journals Fokker-Planck Models for Rotating Stellar Systems

1996 ◽  
Vol 174 ◽  
pp. 363-364 ◽  
Author(s):  
Christian Einsel ◽  
Rainer Spurzem
Keyword(s):  
Initial Conditions ◽  
Planck Equation ◽  
Rotational Energy ◽  
Momentum Transport ◽  
Core Collapse ◽  
Initial Model ◽  
Fundamental Parameters ◽  
Angular Momentum Transport ◽  
Collapse Phase ◽  
Fokker Planck

Observations of Globular Cluster ellipticity distributions related to some fundamental parameters give strong evidence for a decay of rotational energy in these systems with time. In order to study the effectiveness of angular momentum transport (or loss, resp.) a code has been written which solves the Fokker-Planck equation in (E, Jz)-space and follows the evolution from some initial conditions through core collapse (and possibly gravothermal oscillations) up to the post-collapse phase. For the purpose of comparability with N-body simulations rotating initial model configurations according to the prescriptions of Lupton & Gunn (1987) have been constructed. These models are intended to continue previous work by Goodman (1983, Fokker-Planck) and Akiyama & Sugimoto (1989, N-Body). In this contribution the derivation of the flux coefficients is given.

Spectral analysis of forced turbulence in a non-neutral plasma

2017 ◽  
Vol 83 (3) ◽  
Author(s):  
S. Chen ◽  
G. Maero ◽  
M. Romé
Keyword(s):  
Initial Conditions ◽  
Initial Density ◽  
Final States ◽  
Self Similarity ◽  
Subsequent Formation ◽  
Electron Plasmas ◽  
Particle In Cell ◽  
Fluid Turbulence ◽  
Inviscid Incompressible Fluid ◽  
Forced Turbulence

The paper investigates the dynamics of magnetized non-neutral (electron) plasmas subjected to external electric field perturbations. A two-dimensional (2-D) particle-in-cell code is effectively exploited to model this system with a special attention to the role that non-axisymmetric, multipolar radio frequency (RF) drives applied to the cylindrical (circular) boundary play on the insurgence of azimuthal instabilities and the subsequent formation of coherent structures preventing the relaxation to a fully developed turbulent state, when the RF fields are chosen in the frequency range of the low-order fluid modes themselves. The isomorphism of such system with a 2-D inviscid incompressible fluid offers an insight into the details of forced 2-D fluid turbulence. The choice of different initial density (i.e. fluid vorticity) distributions allows for a selection of conditions where different levels of turbulence and intermittency are expected and a range of final states is achieved. Integral and spectral quantities of interest are computed along the flow using a multiresolution analysis based on a wavelet decomposition of both enstrophy and energy 2-D maps. The analysis of a variety of cases shows that the qualitative features of turbulent relaxation are similar in conditions of both free and forced evolution; at the same time, fine details of the flow beyond the self-similarity turbulence properties are highlighted in particular in the formation of structures and their timing, where the influence of the initial conditions and the effect of the external forcing can be distinguished.

scholarly journals The Influence of Particle Concentration on the Formation of Settling-Driven Gravitational Instabilities at the Base of Volcanic Clouds

2021 ◽  
Vol 9 ◽  
Author(s):  
Allan Fries ◽  
Jonathan Lemus ◽  
Paul A. Jarvis ◽  
Amanda B. Clarke ◽  
Jeremy C. Phillips ◽  
...  
Keyword(s):  
Volcanic Ash ◽  
Particle Concentration ◽  
Initial Conditions ◽  
Initial Density ◽  
Fluid Phase ◽  
Dimensionless Number ◽  
Narrow Region ◽  
Gravitational Instabilities ◽  
Volcanic Clouds ◽  
Particle Imaging

Settling-driven gravitational instabilities observed at the base of volcanic ash clouds have the potential to play a substantial role in volcanic ash sedimentation. They originate from a narrow, gravitationally unstable region called a Particle Boundary Layer (PBL) that forms at the lower cloud-atmosphere interface and generates downward-moving ash fingers that enhance the ash sedimentation rate. We use scaled laboratory experiments in combination with particle imaging and Planar Laser Induced Fluorescence (PLIF) techniques to investigate the effect of particle concentration on PBL and finger formation. Results show that, as particles settle across an initial density interface and are incorporated within the dense underlying fluid, the PBL grows below the interface as a narrow region of small excess density. This detaches upon reaching a critical thickness, that scales with (ν2/g′)1/3, where ν is the kinematic viscosity and g′ is the reduced gravity of the PBL, leading to the formation of fingers. During this process, the fluid above and below the interface remains poorly mixed, with only small quantities of the upper fluid phase being injected through fingers. In addition, our measurements confirm previous findings over a wider set of initial conditions that show that both the number of fingers and their velocity increase with particle concentration. We also quantify how the vertical particle mass flux below the particle suspension evolves with time and with the particle concentration. Finally, we identify a dimensionless number that depends on the measurable cloud mass-loading and thickness, which can be used to assess the potential for settling-driven gravitational instabilities to form. Our results suggest that fingers from volcanic clouds characterised by high ash concentrations not only are more likely to develop, but they are also expected to form more quickly and propagate at higher velocities than fingers associated with ash-poor clouds.

scholarly journals Phenomenological Implications of Modified Loop Cosmologies: An Overview

2021 ◽  
Vol 8 ◽  
Author(s):  
Bao-Fei Li ◽  
Parampreet Singh ◽  
Anzhong Wang
Keyword(s):  
Initial Conditions ◽  
Scale Effects ◽  
Hybrid Approach ◽  
Planck Scale ◽  
Power Spectra ◽  
Big Bang ◽  
Hamiltonian Constraint ◽  
Hybrid Approaches ◽  
Effective Dynamics ◽  
The Big Bang

In this paper, we first provide a brief review of the effective dynamics of two recently well-studied models of modified loop quantum cosmologies (mLQCs), which arise from different regularizations of the Hamiltonian constraint and show the robustness of a generic resolution of the big bang singularity, replaced by a quantum bounce due to non-perturbative Planck scale effects. As in loop quantum cosmology (LQC), in these modified models the slow-roll inflation happens generically. We consider the cosmological perturbations following the dressed and hybrid approaches and clarify some subtle issues regarding the ambiguity of the extension of the effective potential of the scalar perturbations across the quantum bounce, and the choice of initial conditions. Both of the modified regularizations yield primordial power spectra that are consistent with current observations for the Starobinsky potential within the framework of either the dressed or the hybrid approach. But differences in primordial power spectra are identified among the mLQCs and LQC. In addition, for mLQC-I, striking differences arise between the dressed and hybrid approaches in the infrared and oscillatory regimes. While the differences between the two modified models can be attributed to differences in the Planck scale physics, the permissible choices of the initial conditions and the differences between the two perturbation approaches have been reported for the first time. All these differences, due to either the different regularizations or the different perturbation approaches in principle can be observed in terms of non-Gaussianities.

Statistical Theory of the SASE Fel Based on the Two-Particle Correlation Function Equation

2013 ◽  
Vol 8 (4) ◽  
pp. 25-34
Author(s):  
Oleg Shevchenko ◽  
Nikolay Vinokurov
Keyword(s):  
Correlation Function ◽  
Initial Conditions ◽  
Initial Density ◽  
Bbgky Hierarchy ◽  
Density Fluctuations ◽  
Distribution Functions ◽  
Time Coordinate ◽  
Particle Correlation ◽  
Sase Fel ◽  
Special Time

The startup from noise problem in SASE FELs is usually treated in linear approximation. In this case amplification of initial density fluctuations may be calculated, and averaging over initial conditions may be fulfilled explicitly. In general nonlinear case the direct averaging is not applicable. During last years we developed the approach based on the BBGKY hierarchy for the n-particle distribution functions. The interaction of particles in FEL is retarded. Nevertheless, using special time-coordinate transformation, it is possible to eliminate the interaction lag and then to write down the BBGKY equations. Similar to plasma physics, the equations may be truncated after the second one (for the two-particle correlation function). Using this approach we consider several particular cases which illustrate some peculiar features of the SASE FEL operation

Problems with the “Old” Big Bang Theory⋆⋆

2018 ◽  
pp. 152-154
Author(s):  
Alvaro De Rújula
Keyword(s):  
Initial Conditions ◽  
Big Bang ◽  
Anthropic Principle ◽  
Big Bang Theory ◽  
The Universe

The problems of “criticality” and causality: Why is the Universe so flat and incomprehensibly homogeneous or uniform? The analogy of the surface of an inflating balloon. Fixed angular distances and varying physical distances. Possible but unpalatable initial conditions. The fate of open or close universes. The visible Universe, for us or for a diStant E.T. In passing, the “anthropic principle.”

scholarly journals On the apparent power law in CDM halo pseudo-phase space density profiles

2017 ◽  
Vol 470 (1) ◽  
pp. 500-511 ◽  
Author(s):  
Ethan O. Nadler ◽  
S. Peng Oh ◽  
Suoqing Ji
Keyword(s):  
Phase Space ◽  
Power Law ◽  
Cold Dark Matter ◽  
Initial Conditions ◽  
Phase Space Density ◽  
Fluid Approximation ◽  
Density Profiles ◽  
Space Density ◽  
Scale Free ◽  
Hydrodynamic Calculations

Abstract We investigate the apparent power-law scaling of the pseudo-phase space density (PPSD) in cold dark matter (CDM) haloes. We study fluid collapse, using the close analogy between the gas entropy and the PPSD in the fluid approximation. Our hydrodynamic calculations allow for a precise evaluation of logarithmic derivatives. For scale-free initial conditions, entropy is a power law in Lagrangian (mass) coordinates, but not in Eulerian (radial) coordinates. The deviation from a radial power law arises from incomplete hydrostatic equilibrium (HSE), linked to bulk inflow and mass accretion, and the convergence to the asymptotic central power-law slope is very slow. For more realistic collapse, entropy is not a power law with either radius or mass due to deviations from HSE and scale-dependent initial conditions. Instead, it is a slowly rolling power law that appears approximately linear on a log–log plot. Our fluid calculations recover PPSD power-law slopes and residual amplitudes similar to N-body simulations, indicating that deviations from a power law are not numerical artefacts. In addition, we find that realistic collapse is not self-similar; scalelengths such as the shock radius and the turnaround radius are not power-law functions of time. We therefore argue that the apparent power-law PPSD cannot be used to make detailed dynamical inferences or extrapolate halo profiles inwards, and that it does not indicate any hidden integrals of motion. We also suggest that the apparent agreement between the PPSD and the asymptotic Bertschinger slope is purely coincidental.

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