scholarly journals Gravothermal Oscillations

1996 ◽  
Vol 174 ◽  
pp. 151-160 ◽  
Author(s):  
Junichiro Makino
Keyword(s):  
Temperature Inversion ◽  
Point Mass ◽  
Central Density ◽  
Expansion Phase ◽  
One Dimensional ◽  
Maximum Expansion ◽  
The Core ◽  
Approximate Models ◽  
Number Of Particles ◽  
Fokker Planck

We present the first clear evidence that the gravothermal oscillation takes place in N-body systems. We performed direct N-body simulations of systems of point-mass particles with particle numbers from 2,048 to 32,768. In the simulation with 32,768 particles, the central density shows an oscillation with an amplitude of ∼ 103, which is similar to what was observed in more approximate models such as a conducting gas sphere and one-dimensional Fokker-Planck calculations. The amplitude is smaller for a smaller number of particles. The number of particles in the core at the maximum contraction is ∼ 10 for all runs, while the number of particles at the maximum expansion is about 0.01N. For 16,384- and 32,768-body runs, the temperature inversion during the expansion phase is clearly visible.

scholarly journals Probing the edge between integrability and quantum chaos in interacting few-atom systems

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 486
Author(s):  
Thomás Fogarty ◽  
Miguel Ángel García-March ◽  
Lea F. Santos ◽  
Nathan L. Harshman
Keyword(s):  
Quantum Chaos ◽  
Cold Atoms ◽  
Quantum Systems ◽  
Particle Interactions ◽  
Body System ◽  
Many Body ◽  
One Dimensional ◽  
The Core ◽  
Emergence Of Chaos ◽  
Number Of Particles

Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary between integrability and chaos in a highly tunable few-body system. We show that the competition between the particle interactions and the periodic structure of the confining potential reveals subtle indications of quantum chaos for 3 particles, while for 4 particles stronger signatures are seen. The analysis is performed for bosonic particles and could also be extended to distinguishable fermions.

scholarly journals Dynamical Evolution of Globular Clusters After Core Collapse

1985 ◽  
Vol 113 ◽  
pp. 139-160 ◽  
Author(s):  
Douglas C. Heggie
Keyword(s):  
Surface Density ◽  
Globular Clusters ◽  
Stellar System ◽  
Dynamical Evolution ◽  
Theoretical Models ◽  
Numerical Calculations ◽  
Core Collapse ◽  
Density Profiles ◽  
The Core ◽  
Fokker Planck

This review describes work on the evolution of a stellar system during the phase which starts at the end of core collapse. It begins with an account of the models of Hénon, Goodman, and Inagaki and Lynden-Bell, as well as evaporative models, and modifications to these models which are needed in the core. Next, these models are related to more detailed numerical calculations of gaseous models, Fokker-Planck models, N-body calculations, etc., and some problems for further work in these directions are outlined. The review concludes with a discussion of the relation between theoretical models and observations of the surface density profiles and statistics of actual globular clusters.

Experimental assessment of the rotor outlet flow in a twin-entry radial turbine by means of Laser Doppler Anemometry

2021 ◽  
pp. 146808742110344
Author(s):  
José Galindo ◽  
Andrés Omar Tiseira ◽  
Luis Miguel García-Cuevas ◽  
Nicolás Medina
Keyword(s):  
Laser Doppler Anemometry ◽  
Effective Area ◽  
Laser Doppler ◽  
Flow Ratio ◽  
One Dimensional ◽  
Radial Turbine ◽  
Single Entry ◽  
Outlet Flow ◽  
Dimensional Models ◽  
Number Of Particles

The current paper presents the validation of some hypotheses used for developing a one-dimensional twin-entry turbine model with experimental measurements. A Laser Doppler Anemometry (LDA) technique has been used for measuring the axial Mach number and for counting the number of particles downstream of the rotor outlet. These measurements have been done for different mass flow ratio (MFR) and reduced turbocharger speed conditions. The flow coming from each turbine entry does not fully mix with the other within the rotor since, downstream of the rotor, they can still be differentiated. Thus, the hypothesis of studying twin-entry turbines as two separated single-entry turbines in one-dimensional models is corroborated. Moreover, the rotor outlet area corresponding to each flow branch has linear trends with the MFR value. Therefore, the rotor outlet effective area used for one-dimensional models should vary linearly with the MFR value.

A One Dimensional Crystal With Nearest Neighbors Coupled Through Their Velocities

1981 ◽  
Vol 103 (3) ◽  
pp. 293-296 ◽  
Author(s):  
J. N. Boyd ◽  
P. N. Raychowdhury
Keyword(s):  
Natural Frequencies ◽  
Nearest Neighbors ◽  
Projection Operators ◽  
Circular Array ◽  
One Dimensional ◽  
Neighboring Point ◽  
Large Numbers ◽  
Kinetic And Potential Energies ◽  
Dimensional Crystal ◽  
Number Of Particles

We consider a circular array of point masses connected by springs of non-negligible mass. In the Lagrangian for the harmonic motions of this system, the movements of neighboring point masses are coupled through both the kinetic and potential energies. By use of transformations derived from the theory of projection operators, we simplify the Lagrangian and obtain the natural frequencies of the motions of the system as functions of the number of particles present. We note that for large numbers of particles, the results for our circular array will yield the frequencies of a one dimensional crystal.

Non-Maxwellian kinetic equations modeling the dynamics of wealth distribution

2020 ◽  
Vol 30 (04) ◽  
pp. 685-725 ◽  
Author(s):  
Giulia Furioli ◽  
Ada Pulvirenti ◽  
Elide Terraneo ◽  
Giuseppe Toscani
Keyword(s):  
Steady State ◽  
Wealth Distribution ◽  
Kinetic Equations ◽  
Planck Equation ◽  
Logarithmic Sobolev Inequality ◽  
One Dimensional ◽  
Distribution Of Wealth ◽  
Multi Agent ◽  
Fokker Planck Equations ◽  
Fokker Planck

We introduce a class of new one-dimensional linear Fokker–Planck-type equations describing the dynamics of the distribution of wealth in a multi-agent society. The equations are obtained, via a standard limiting procedure, by introducing an economically relevant variant to the kinetic model introduced in 2005 by Cordier, Pareschi and Toscani according to previous studies by Bouchaud and Mézard. The steady state of wealth predicted by these new Fokker–Planck equations remains unchanged with respect to the steady state of the original Fokker–Planck equation. However, unlike the original equation, it is proven by a new logarithmic Sobolev inequality with weight and classical entropy methods that the solution converges exponentially fast to equilibrium.

scholarly journals Some Improvements in a Gas Turbine Stator-Rotor Systems Core-Swirl Ratio Correlation

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
R. Da Soghe ◽  
B. Facchini ◽  
L. Innocenti ◽  
M. Micio
Keyword(s):  
Swirl Ratio ◽  
Rotating Fluid ◽  
One Dimensional ◽  
Rotor Systems ◽  
Solid Body Rotation ◽  
The Core ◽  
Turbine Stator ◽  
Experimental Correlation ◽  
Ratio Correlation ◽  
Good Agreement

The present work concerns the turbulent flow inside a rotor-stator cavity with superimposed throughflow. The authors focused their analysis on a simple two-faced disk cavity, without shrouds, with interdisk-spacing sufficiently large so that the boundary layers developed on each disk are separated and the flow is turbulent. In such a system, the solid body rotation of the core predicted by Batchelor can develop. The evolution of the core-swirl ratio of the rotating fluid with an outward throughflow is studied by applying a classical experimental correlation, inserted in a one-dimensional (1D) in-house developed code. Results are compared to those predicted by CFD computations. Due to the discrepancies revealed, the authors provided a correction of the experimental correlation, based on CFD computation. Results thus obtained are finally in good agreement with CFD predictions.

Differences in the Heat Transfer at the Core-Reflector Boundary of the PBMR Due to the Use of Different Numerical Methods

2009 ◽  
Author(s):  
Pieter S. du Toit ◽  
Onno Ubbink
Keyword(s):  
Two Dimensions ◽  
Heat Sources ◽  
Coarse Mesh ◽  
One Dimensional ◽  
Root Cause ◽  
The Core ◽  
Modified Method ◽  
The Difference ◽  
Horizontal Slice ◽  
Mesh Cell

The PBMR (Pebble Bed Modular Reactor) is a High-Temperature Gas-cooled Reactor (HTGR) concept. One of the exercises of the PBMR benchmark of the Organization for Economic Cooperation and Development (OECD) is a steady state two-dimensional (2D) thermal-hydraulics simulation of a simplified PBMR with prescribed heat sources. Two different programs were used to model this exercise. They predicted similar core temperatures but the side reflector temperatures next to the core differed by more than 30 °C (when using a relatively coarse mesh). The underlying methods define temperatures at either vertices (VC) or at mesh cell centres (CC). A study was undertaken using one-dimensional (1D) implementations of the VC and CC methods to model a horizontal slice through the core. This study revealed the root cause of the different predictions. A modified version of the 1D CC method was developed that essentially predicts the same temperatures as the VC method. The extension of the modified method to two dimensions is under investigation. If the difference in predicted temperatures next to the core can be eliminated or reduced, then the focus can shift to other differences between the results of the two programs.

Numerical Investigation of Heat Transfer Characteristics of Debris Bed After Severe Accident of SFR Based on 1-D Heat Conduction Model

2018 ◽  
Author(s):  
Mengwei Zhang ◽  
Bin Zhang ◽  
Jianqiang Shan
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Transfer Process ◽  
Severe Accident ◽  
Heat Transfer Characteristics ◽  
Conduction Model ◽  
One Dimensional ◽  
The Core ◽  
Transfer Characteristics ◽  
Core Catcher

Nuclear reactor severe accidents can lead to the release of a large amount of radioactive material and cause immense disaster to the environment. Since the Fukushima nuclear accident in Japan, the severe accident research has drawn worldwide attention. Based on the one-dimensional heat conduction model, a DEBRIS-HT program for analyzing the heat transfer characteristics of a debris bed after a severe accident of a sodium-cooled fast reactor was developed. The basic idea of the DEBRIS-HT program is to simplify the complex energy transfer process in the debris bed to a simple one-dimensional heat transfer problem by solving the equivalent thermal conductivity in different situations. In this paper, the DEBRIS-HT program code is prepared by using the existing model and compared with the experimental results. The results show that the DEBRIS-HT program can correctly predict the heat transfer process in the fragment bed. In addition, the heat transfer characteristics analysis program is also used to model the core catcher of the China fast reactor. Firstly, the dryout heat flux when all of molten core dropped on the core catcher was calculated, which was compared with the result of Lipinski’s zero dimensional model, and the error between two values is only 11.2%. Then, the temperature distribution was calculated with the heat power of 15MW.

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