Systems of Interacting Particles

2021 ◽  
pp. 327-356
Author(s):  
Daniel V. Schroeder
Keyword(s):  
Numerical Simulation ◽  
Critical Temperature ◽  
Series Expansion ◽  
Random Sampling ◽  
Nearest Neighbors ◽  
Boltzmann Distribution ◽  
Three Dimensions ◽  
Interacting Particles ◽  
Nonideal Gas ◽  
Quantitative Understanding

This chapter presents two examples of the application of Boltzmann statistics to systems with nontrivial interactions between particles. The first example is a nonideal gas, treated approximately using a series expansion that we can visualize in terms of simple diagrams. The second example is a model of a ferromagnet as a collection of two-state particles interacting with their nearest neighbors. It is easy to solve this model exactly in one dimension, and to gain a semi-quantitative understanding of why the system magnetizes below a critical temperature in two or three dimensions. The most powerful tool for studying this model, however, is numerical simulation on a computer using a random-sampling algorithm based on the Boltzmann distribution.

Hydraulic Characteristics of the New Type Bulb Turbine With Micro-Head

2013 ◽  
Author(s):  
Lingyu Li ◽  
Yuan Zheng ◽  
Daqing Zhou ◽  
Zihao Mi
Keyword(s):  
Numerical Simulation ◽  
Cfd Simulation ◽  
Guide Vane ◽  
Three Dimensional ◽  
Flow Distribution ◽  
Three Dimensions ◽  
Guide Vanes ◽  
Runner Blade ◽  
Cfd Method ◽  
Bulb Turbine

The head of low-head hydropower stations is generally higher than 2.5m in the world, while micro-head hydropower resources which head is less than 2.5m are also very rich. In the paper, three-dimensional CFD method has been used to simulate flow passage of the micro-head bulb turbine. The design head and unit flow of the turbine was 1m and 3m3/s respectively. With the numerical simulation, the bulb turbine is researched by analyzing external characteristics of the bulb turbine, flow distribution before the runner, pressure distribution of the runner blade surface, and flow distribution of the outlet conduit under three different schemes. The turbine in second scheme was test by manufactured into a physical model. According to the results of numerical simulation and model test, bulb turbine with no guide vane in second scheme has simpler structure, lower cost, and better flow capacity than first scheme, which has traditional multi-guide vanes. Meanwhile, efficiency of second scheme has just little decrease. The results of three dimensions CFD simulation and test results agree well in second scheme, and higher efficiency is up to 77% which has a wider area with the head of 1m. The curved supports in third scheme are combined guide vanes to the fixed supports based on 2nd scheme. By the water circulations flowing along the curved supports which improve energy transformation ability of the runner, the efficiency of the turbine in third scheme is up to 82.6%. Third scheme, which has simpler structure and best performance, is appropriate for the development and utilization of micro-head hydropower resources in plains and oceans.

scholarly journals Global ionospheric models in three dimensions from GPS measurements: Numerical simulation

2000 ◽  
Vol 39 (1) ◽  
pp. 21-27
Author(s):  
Amali Meza ◽  
Claudio Brunini ◽  
Alfred Kleusberg
Keyword(s):  
Numerical Simulation ◽  
Three Dimensions ◽  
Gps Measurements ◽  
Atmospheric Research ◽  
Ionospheric Models

Gracias a las observaciones GPS en doble - frecuencia de receptores distribuidos uniformemente sobre la superficie terrestre es posible hacer un análisis de la ionosfera como puede verse en los trabajos de Mannucci A. et al., 1993; Beutler G., 1995 y Brunini C. et al., 1997 entre otros. Este análisis consiste básicamente en el modelado de las variaciones del contenido total de electrones en función de 2 coordenadas que bien pueden ser la latitud y la longitud en un sistema sol fijo. Estos modelos asumen que la ionosfera puede representarse por una capa esférica de espesor despreciable, situada a una determinada altura (entre los 300 y 400 km), donde se concentra la totalidad de los electrones libres. Para modelar la distribución espacial de la concentración total de electrones en la delgada capa, se han utilizado series de Taylor en dos dimensiones o armónicos esféricos entre otros. En abril de 1995, gracias al lanzamiento de la misión GPS-MET, se pudo hacer realidad la obtención de observaciones GPS desde un receptor en el espacio. GPS-MET es un experimento dirigido por el UCAR (University Corporation of Atmospheric Research), cuyo objetivo es el sondeo de la atmósfera terrestre mediante observaciones GPS colectadas por un receptor de alto rendimiento situado a bordo del satélite MicroLab I (MLI). Este satélite describe una órbita circular a 730 km de altura (LEO=Low Elevation Orbit), con una inclinación de 60°. Las observaciones colectadas por este receptor están disponibles vía ftp en una base de datos administrada por el UCAR. Este satélite de baja altura con receptor GPS de doble frecuencia nos brinda la posibilidad de contar con señales GPS que atraviesan la ionosfera a diferentes alturas. Este trabajo no apunta a discutir un modelo ionosférico en sí mismo, sino más bien a analizar las posibilidades de utilizar mediciones GPS para extraer información sobre el comportamiento vertical de la densidad electrónica, basadas en un modelo medio y global. En este trabajo emplearemos simulaciones numéricas con el objetivo de analizar si las observaciones del Microlab I son suficientemente sensibles a las variaciones en altura de la ionosfera. Afortunadamente y pese a la limitación en la geometría del problema, ya que sólo contamos con un satélite de órbita fija, se concluye que el receptor espacial nos brinda información fundamental para el modelado en altura de la densidad de electrones.

Numerical Simulation of Multibody Systems With Time Dependant Structure

1993 ◽  
Author(s):  
Pierre Joli ◽  
Madeleine Pascal ◽  
René Gibert
Keyword(s):  
Numerical Simulation ◽  
Multibody Systems ◽  
Computational Algorithm ◽  
Rigid Bodies ◽  
Three Dimensions ◽  
Integration Step ◽  
General Systems ◽  
Articulated Systems ◽  
Jump Velocity ◽  
Assembly Tasks

Abstract Current dynamic simulation programs are able to calculate the continuous motions of articulated systems or more general systems of rigid bodies in the absence of contact between members of the system or between the system and its environment. Some are able to simulate the effects of isolated contacts and impacts but none are able to simulate the motion with unrestricted multiple concurrent contacts. However, in special robotic programs such as robots performing assembly tasks or walking, it would be very interesting to simulate appropriate commands before implementing them on the robots. This paper develops intrinsic problems of collision to produce an efficient computational algorithm. This algorithm handles the detection of collision in three dimensions, the reduction of the integration step in order to avoid interpenetration between the bodies before impact, the jump velocity caused by a new collision and indicator magnitudes which determine the addition or deletion of constraints.

scholarly journals Modeling debris-flow runout patterns on two alpine fans with different dynamic simulation models

2015 ◽  
Vol 15 (7) ◽  
pp. 1483-1492 ◽  
Author(s):  
K. Schraml ◽  
B. Thomschitz ◽  
B. W. McArdell ◽  
C. Graf ◽  
R. Kaitna
Keyword(s):  
Numerical Simulation ◽  
Debris Flow ◽  
Mass Movement ◽  
Simulation Models ◽  
Realistic Model ◽  
Three Dimensions ◽  
Model Parameters ◽  
Alpine Regions ◽  
Digital Elevation ◽  
Higher Sensitivity

Abstract. Predicting potential deposition areas of future debris-flow events is important for engineering hazard assessment in alpine regions. To this end, numerical simulation models are commonly used tools. However, knowledge of appropriate model parameters is essential but often not available. In this study we use two numerical simulation models, RAMMS–DF (rapid mass movement system–debris-flow) and DAN3D (dynamic analysis of landslides in three dimensions), to back-calculate two well-documented debris-flow events in Austria and to compare the range and sensitivity of input parameters for the Voellmy flow model. All simulations are based on the same digital elevation models and similar boundary conditions. Our results show that observed deposition patterns are best matched with a parameter set of μ [–] and ξ [m s-2], ranging between 0.07 to 0.11 and 200 to 300 m s-2, respectively, for RAMMS–DF, and between 0.07 to 0.08 and 300 to 400 m s-2, respectively, for DAN3D. Sensitivity analysis shows a higher sensitivity of model parameters for the DAN3D model than for the RAMMS–DF model. This contributes to the evaluation of realistic model parameters for simulation of debris-flows in steep mountain catchments and highlights the sensitivity of the models.

Numerical Simulation of Thermocapillary Convection in an Annular Pool of Silicone Oil Heated From Inner Wall

2007 ◽  
Author(s):  
Wanyuan Shi ◽  
Nobuyuki Oshima ◽  
Nobuyuki Imaishi
Keyword(s):  
Numerical Simulation ◽  
Critical Temperature ◽  
Temperature Gradient ◽  
Numerical Simulations ◽  
Temperature Difference ◽  
Significant Influence ◽  
Thermocapillary Convection ◽  
Silicone Oil ◽  
Annular Pool ◽  
Surface Temperature Gradient

Thermocapillary convection in a shallow annular pool (depth d = 1 mm) of silicone oil (0.65 cSt, Pr = 6.7), heated from the inner wall, is investigated by numerical simulations. Under a fixed value of temperature difference between the outer and inner walls, surface temperature gradient in the inner heated pool is about 10% higher than that in the outer heated pool. Accordingly, the critical temperature difference for the incipience of HTW (ΔTc = 4.58K) is smaller than that (ΔTc = 5.0K) in the outer heated pool. Numerical simulations indicate that two groups of HTW, propagating in opposite azimuthal directions to each other, coexist and produce interference patterns in the inner heated pool. Rotation of the pool around its axis gives no significant influence on the behavior of HTW in the inner heated pool. The characteristics of HTW are discussed in contrast with those in the outer heated pool.

Observation and Numerical Simulation of Propagation of ULF Waves From the Ion Foreshock Into the Magnetosphere

2020 ◽  
Author(s):  
Kazue Takahashi ◽  
Turc Turc ◽  
Emilia Kilpua ◽  
Naoko Takahashi ◽  
Andrew Dimmock ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Ion Beam ◽  
Ulf Waves ◽  
Time Interval ◽  
Multiple Sources ◽  
Outer Magnetosphere ◽  
Magnetic Field Magnitude ◽  
Quantitative Understanding ◽  
Pass Through ◽  
The Waves

<p>Observational studies have demonstrated that ULF waves excited in the ion foreshock are a main source of Pc3-4 ULF waves detected in the magnetosphere. However, quantitative understanding of the propagation of the waves is not easy, because the waves are generated through a kinetic process in the foreshock, pass through the turbulent magnetosheath, and propagate as fast mode waves and couple to shear Alfven waves within the magnetosphere.  Recent advancement of hybrid numerical simulations of foreshock dynamics motivated us to analyze observational data from multiple sources and compare the results with simulation results. We have selected the time interval 1000-1200 UT on 20 July 2016, when the THEMIS, GOES, and Van Allen Probe spacecraft covered the solar wind, foreshock, magnetosheath, and magnetosphere. The EMMA magnetometers (L=1.6-6.5) were located near noon. We found that the spectrum of the magnetic field magnitude (Bt) in the foreshock exhibits a peak near 90 mHz, which agrees with the theoretical prediction assuming an ion beam instability in the foreshock.  A similar Bt spectrum is found in the dayside outer magnetosphere but not in the magnetosheath or in the nightside magnetosphere.  On the ground, a 90 mHz spectral peak was detected in the H component only at L=2-3. The numerical simulation using the VLASIATOR code shows that the foreshock is formed on the prenoon sector but that the effect of the upstream waves in the magnetosphere is most pronounced at noon. The Bt spectrum of the simulated waves in the outer magnetosphere exhibits a peak at 90 mHz, which is consistent with the observation.</p>

scholarly journals Modified Sonine approximation for granular binary mixtures

2009 ◽  
Vol 623 ◽  
pp. 387-411 ◽  
Author(s):  
VICENTE GARZÓ ◽  
FRANCISCO VEGA REYES ◽  
JOSÉ MARÍA MONTANERO
Keyword(s):  
Transport Coefficients ◽  
Direct Simulation Monte Carlo ◽  
Boltzmann Distribution ◽  
Three Dimensions ◽  
Navier Stokes ◽  
State Distribution ◽  
New Approach ◽  
Viscosity Coefficients ◽  
Stokes Transport ◽  
Simulation Monte Carlo

We evaluate in this work the hydrodynamic transport coefficients of a granular binary mixture in d dimensions. In order to eliminate the observed disagreement (for strong dissipation) between computer simulations and previously calculated theoretical transport coefficients for a monocomponent gas, we obtain explicit expressions of the seven Navier–Stokes transport coefficients by the use of a new Sonine approach in the Chapman–Enskog (CE) theory. This new approach consists of replacing, where appropriate in the CE procedure, the Maxwell–Boltzmann distribution weight function (used in the standard first Sonine approximation) by the homogeneous cooling state distribution for each species. The rationale for doing this lies in the well-known fact that the non-Maxwellian contributions to the distribution function of the granular mixture are more important in the range of strong dissipation we are interested in. The form of the transport coefficients is quite common in both standard and modified Sonine approximations, the distinction appearing in the explicit form of the different collision frequencies associated with the transport coefficients. Additionally, we numerically solve by the direct simulation Monte Carlo method the inelastic Boltzmann equation to get the diffusion and the shear viscosity coefficients for two and three dimensions. As in the case of a monocomponent gas, the modified Sonine approximation improves the estimates of the standard one, showing again the reliability of this method at strong values of dissipation.

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