scholarly journals Kullback-Leibler Divergence of a Freely Cooling Granular Gas of Inelastic Hard Disks and Spheres

2021 ◽  
Author(s):  
Andrés Santos ◽  
Alberto Megías
Keyword(s):  
Hard Disks ◽  
Granular Gas ◽  
Leibler Divergence

scholarly journals Kullback–Leibler Divergence of a Freely Cooling Granular Gas

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1308
Author(s):  
Alberto Megías ◽  
Andrés Santos
Keyword(s):  
Lyapunov Functional ◽  
Initial Conditions ◽  
Hard Disks ◽  
Potential Candidate ◽  
Reference Distribution ◽  
Additional Measure ◽  
Actual Distribution ◽  
Granular Gas ◽  
Wide Range ◽  
Leibler Divergence

Finding the proper entropy-like Lyapunov functional associated with the inelastic Boltzmann equation for an isolated freely cooling granular gas is a still unsolved challenge. The original H-theorem hypotheses do not fit here and the H-functional presents some additional measure problems that are solved by the Kullback–Leibler divergence (KLD) of a reference velocity distribution function from the actual distribution. The right choice of the reference distribution in the KLD is crucial for the latter to qualify or not as a Lyapunov functional, the asymptotic “homogeneous cooling state” (HCS) distribution being a potential candidate. Due to the lack of a formal proof far from the quasielastic limit, the aim of this work is to support this conjecture aided by molecular dynamics simulations of inelastic hard disks and spheres in a wide range of values for the coefficient of restitution (α) and for different initial conditions. Our results reject the Maxwellian distribution as a possible reference, whereas they reinforce the HCS one. Moreover, the KLD is used to measure the amount of information lost on using the former rather than the latter, revealing a non-monotonic dependence with α.

On Knudsen-minimum effect and temperature bimodality in a dilute granular Poiseuille flow

2015 ◽  
Vol 782 ◽  
pp. 99-126 ◽  
Author(s):  
Meheboob Alam ◽  
Achal Mahajan ◽  
Deepthi Shivanna
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Poiseuille Flow ◽  
Molecular Gas ◽  
Hard Disks ◽  
Restitution Coefficient ◽  
Excess Temperature ◽  
Granular Gas ◽  
Gravity Driven Flow

The numerical simulation of gravity-driven flow of smooth inelastic hard disks through a channel, dubbed ‘granular’ Poiseuille flow, is conducted using event-driven techniques. We find that the variation of the mass-flow rate ($Q$) with Knudsen number ($Kn$) can be non-monotonic in the elastic limit (i.e. the restitution coefficient $e_{n}\rightarrow 1$) in channels with very smooth walls. The Knudsen-minimum effect (i.e. the minimum flow rate occurring at $Kn\sim O(1)$ for the Poiseuille flow of a molecular gas) is found to be absent in a granular gas with $e_{n}<0.99$, irrespective of the value of the wall roughness. Another rarefaction phenomenon, the bimodality of the temperature profile, with a local minimum ($T_{\mathit{min}}$) at the channel centerline and two symmetric maxima ($T_{\mathit{max}}$) away from the centerline, is also studied. We show that the inelastic dissipation is responsible for the onset of temperature bimodality (i.e. the ‘excess’ temperature, ${\rm\Delta}T=(T_{\mathit{max}}/T_{\mathit{min}}-1)\neq 0$) near the continuum limit ($Kn\sim 0$), but the rarefaction being its origin (as in the molecular gas) holds beyond $Kn\sim O(0.1)$. The dependence of the excess temperature ${\rm\Delta}T$ on the restitution coefficient is compared with the predictions of a kinetic model, with reasonable agreement in the appropriate limit. The competition between dissipation and rarefaction seems to be responsible for the observed dependence of both the mass-flow rate and the temperature bimodality on $Kn$ and $e_{n}$ in this flow. The validity of the Navier–Stokes-order hydrodynamics for granular Poiseuille flow is discussed with reference to the prediction of bimodal temperature profiles and related surrogates.

scholarly journals Inherent thermal convection in a granular gas inside a box under a gravity field

2018 ◽  
Vol 859 ◽  
pp. 160-173
Author(s):  
Francisco Vega Reyes ◽  
Andrea Puglisi ◽  
Giorgio Pontuale ◽  
Andrea Gnoli
Keyword(s):  
Gravity Field ◽  
Thermal Convection ◽  
Numerical Solutions ◽  
Boussinesq Approximation ◽  
Hard Disks ◽  
Particle Collisions ◽  
Granular Gas ◽  
Combined Action ◽  
Vertical Walls ◽  
Lateral Walls

We theoretically prove the existence in granular fluids of a thermal convection that is inherent in the sense that it is always present and has no thermal gradient threshold (convection occurs for all finite values of the Rayleigh number). More specifically, we study a gas of inelastic smooth hard disks enclosed in a rectangular region under a constant gravity field. The vertical walls act as energy sinks (i.e. inelastic walls that are parallel to gravity), whereas the other two walls are perpendicular to gravity and act as energy sources. We show that this convection is due to the combined action of dissipative lateral walls and a volume force (in this case, gravitation). Hence, we call it dissipative lateral walls convection (DLWC). Our theory, which also describes the limit case of elastic collisions, shows that inelastic particle collisions enhance the DLWC. We perform our study via numerical solutions (volume-element method) of the corresponding hydrodynamic equations in an extended Boussinesq approximation. We show that our theory describes the essentials of the results for similar (but more complex) laboratory experiments.

Routine Digital Processing of Microscope Images

1990 ◽  
Vol 48 (1) ◽  
pp. 550-551
Author(s):  
E. Wisse ◽  
A. Geerts ◽  
R.B. De Zanger
Keyword(s):  
Operating System ◽  
Digital Processing ◽  
Hard Disks ◽  
The Sun ◽  
Tape Drive ◽  
High Definition ◽  
Fluorescent Microscope ◽  
Microscope Images ◽  
Helical Scan ◽  
Ethernet Connection

The slowscan and TV signal of the Philips SEM 505 and the signal of a TV camera attached to a Leitz fluorescent microscope, were digitized by the data acquisition processor of a Masscomp 5520S computer, which is based on a 16.7 MHz 68020 CPU with 10 Mb RAM memory, a graphics processor with two frame buffers for images with 8 bit / 256 grey values, a high definition (HD) monitor (910 × 1150), two hard disks (70 and 663 Mb) and a 60 Mb tape drive. The system is equipped with Imaging Technology video digitizing boards: analog I/O, an ALU, and two memory mapped frame buffers for TV images of the IP 512 series. The Masscomp computer has an ethernet connection to other computers, such as a Vax PDP 11/785, and a Sun 368i with a 327 Mb hard disk and a SCSI interface to an Exabyte 2.3 Gb helical scan tape drive. The operating system for these computers is based on different versions of Unix, such as RTU 4.1 (including NFS) on the acquisition computer, bsd 4.3 for the Vax, and Sun OS 4.0.1 for the Sun (with NFS).

Large-sample confidence intervals of information-theoretic measures in linguistics

2020 ◽  
Vol 6 (1) ◽  
pp. 19-54
Author(s):  
Ryan Ka Yau Lai ◽  
Youngah Do
Keyword(s):  
Maximum Likelihood ◽  
Corpus Linguistics ◽  
Delta Method ◽  
Confidence Bounds ◽  
Likelihood Estimator ◽  
Information Theoretic ◽  
Leibler Divergence ◽  
Information Theoretic Measures ◽  
Data Points ◽  
Measure Of Uncertainty

This article explores a method of creating confidence bounds for information-theoretic measures in linguistics, such as entropy, Kullback-Leibler Divergence (KLD), and mutual information. We show that a useful measure of uncertainty can be derived from simple statistical principles, namely the asymptotic distribution of the maximum likelihood estimator (MLE) and the delta method. Three case studies from phonology and corpus linguistics are used to demonstrate how to apply it and examine its robustness against common violations of its assumptions in linguistics, such as insufficient sample size and non-independence of data points.

Integrating Second-order Moving Average and Over-sampling Algorithm to Predict Apoptosis Protein Subcellular Localization

2020 ◽  
Vol 15 (6) ◽  
pp. 517-527
Author(s):  
Yunyun Liang ◽  
Shengli Zhang
Keyword(s):  
Subcellular Localization ◽  
Moving Average ◽  
Subcellular Location ◽  
Second Order ◽  
Test Method ◽  
Support Vector ◽  
Protein Subcellular Localization ◽  
Protein Subcellular Location ◽  
Apoptosis Protein ◽  
Leibler Divergence

Background: Apoptosis proteins have a key role in the development and the homeostasis of the organism, and are very important to understand the mechanism of cell proliferation and death. The function of apoptosis protein is closely related to its subcellular location. Objective: Prediction of apoptosis protein subcellular localization is a meaningful task. Methods: In this study, we predict the apoptosis protein subcellular location by using the PSSMbased second-order moving average descriptor, nonnegative matrix factorization based on Kullback-Leibler divergence and over-sampling algorithms. This model is named by SOMAPKLNMF- OS and constructed on the ZD98, ZW225 and CL317 benchmark datasets. Then, the support vector machine is adopted as the classifier, and the bias-free jackknife test method is used to evaluate the accuracy. Results: Our prediction system achieves the favorable and promising performance of the overall accuracy on the three datasets and also outperforms the other listed models. Conclusion: The results show that our model offers a high throughput tool for the identification of apoptosis protein subcellular localization.

Structure of nitrogenated carbon overcoats on thin-film hard disks

1997 ◽  
Vol 33 (6) ◽  
pp. 4551-4559 ◽  
Author(s):  
L. Huang ◽  
Y. Hung ◽  
S. Chang
Keyword(s):  
Thin Film ◽  
Hard Disks ◽  
Carbon Overcoats ◽  
Nitrogenated Carbon
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