ON THE STATISTICAL PROPERTIES OF SOME TRANSPORT EQUATIONS

1961 ◽  
Vol 39 (11) ◽  
pp. 1573-1582 ◽  
Author(s):  
Adrian E. Scheidegger
Keyword(s):  
Suspended Sediment Transport ◽  
Frequency Range ◽  
General Statement ◽  
Microscopic Reversibility ◽  
Equilibrium Conditions ◽  
System A ◽  
Component Systems ◽  
Diffusivity Equation ◽  
Diffusivity Tensor ◽  
Statistical Theory Of Turbulence

It is shown that, whenever a system is a linear combination of a large number of fluctuating component systems and in the "large" system a certain quantity is a constant of the motion, under equilibrium conditions that quantity is canonically distributed in the component systems and, under non-equilibrium conditions (assuming linear regression of the fluctuations and microscopic reversibility), the quantity in question is subject to a diffusivity equation with a symmetric diffusivity tensor. Application of the above to porous media hydrodynamics immediately yields the equations for miscible displacement which were laboriously obtained earlier from a special statistical model. Similarly, the corresponding equations for suspended sediment transport in rivers and for the mixing of a pollutant in air are shown to be the result of an application of the above general statement. Finally, the theory is also applied to the inertial frequency range in the statistical theory of turbulence.

scholarly journals Covariant Relativistic Non-Equilibrium Thermodynamics of Multi-Component Systems

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1034
Author(s):  
Wolfgang Muschik
Keyword(s):  
Momentum Flux ◽  
Equilibrium Thermodynamics ◽  
Equilibrium Conditions ◽  
Component Mixture ◽  
Component Systems ◽  
General Relativistic ◽  
Entropy Flux ◽  
Special Case ◽  
Multi Component System ◽  
Non Equilibrium

Non-equilibrium and equilibrium thermodynamics of an interacting component in a relativistic multi-component system is discussed covariantly by exploiting an entropy identity. The special case of the corresponding free component is considered. Equilibrium conditions and especially the multi-component Killing relation of the 4-temperature are discussed. Two axioms characterize the mixture: additivity of the energy momentum tensors and additivity of the 4-entropies of the components generating those of the mixture. The resulting quantities of a single component and of the mixture as a whole, energy, energy flux, momentum flux, stress tensor, entropy, entropy flux, supply and production are derived. Finally, a general relativistic 2-component mixture is discussed with respect to their gravitation generating energy–momentum tensors.

scholarly journals Thermodynamic modelling of the binary indium-lithium system, a promising li-ion battery material

2021 ◽  
pp. 41-41
Author(s):  
Wojciech Gierlotka ◽  
Władysław Gąsior ◽  
Adam Dębski ◽  
Miłosz Zabrocki
Keyword(s):  
Experimental Data ◽  
Ternary Systems ◽  
Calphad Approach ◽  
Li Ion Battery ◽  
System A ◽  
Proposed Model ◽  
Component Systems ◽  
Li Ion ◽  
Battery Material ◽  
Good Agreement

The binary In - Li system is a promising Li-ion battery anode material as well as a part of the important ternary Ge - In - Li system. The thermodynamic descriptions of metallic systems are widely used to retrieve information necessary for alloy applications. In this work, a thermodynamic model of a binary indium - lithium system prepared by the Calphad approach is proposed. The liquid phase was described by an associate model, and the solid phases determined by the ab-initio calculation were included in thermodynamic modeling. The obtained set of self-consistent thermodynamic parameters well reproduces the available experimental data and enables further calculations of multi-component systems. A good agreement between the calculations and the available experimental data was found. The proposed model can be used for further descriptions of ternary systems.

scholarly journals EnKF and Hybrid Gain Ensemble Data Assimilation. Part II: EnKF and Hybrid Gain Results

2015 ◽  
Vol 143 (12) ◽  
pp. 4865-4882 ◽  
Author(s):  
Massimo Bonavita ◽  
Mats Hamrud ◽  
Lars Isaksen
Keyword(s):  
Data Assimilation ◽  
Hybrid Data Assimilation ◽  
Ensemble Data Assimilation ◽  
System A ◽  
Ensemble Data ◽  
Study Results ◽  
Numerical Experimentation ◽  
Component Systems ◽  
Hybrid Data ◽  
Data Assimilation System

Abstract The desire to do detailed comparisons between variational and more scalable ensemble-based data assimilation systems in a semioperational environment has led to the development of a state-of-the-art EnKF system at ECMWF, which has been described in Part I of this two-part study. In this part the performance of the EnKF system is evaluated compared to a 4DVar of similar resolution. It is found that there is not a major difference between the forecast skill of the two systems. However, similarly to the operational hybrid 4DVar–EDA, a hybrid EnKF–variational system [which we refer to as the hybrid gain ensemble data assimilation (HG-EnDA)] is capable of significantly outperforming both component systems. The HG-EnDA has been implemented with relatively little effort following Penny’s recent study. Results of numerical experimentation comparing the HG-EnDA with the hybrid 4DVar–EDA used operationally at ECMWF are presented, together with diagnostic results, which help characterize the behavior of the proposed ensemble data assimilation system. A discussion of these results in the context of hybrid data assimilation in global NWP is also provided.

On the Addition of the Primary Aberrations

1927 ◽  
Vol 23 (5) ◽  
pp. 584-587
Author(s):  
G. C. Steward
Keyword(s):  
Characteristic Function ◽  
Composite System ◽  
Present Note ◽  
Complete System ◽  
General Will ◽  
Simple Derivation ◽  
First Order ◽  
System A ◽  
Component Systems ◽  
General Investigation

In the application of the Characteristic Function of Hamilton, or of any allied function, to the computation of a symmetrical optical system three steps are necessary. The performance of the system as a whole must be considered, and from this it appears that the aberrations may be derived from certain ‘aberration coefficients’ which occur in the expansion of an ‘aberration function’. In the second place, relations must be obtained giving the properties of the complete system in terms of the properties of the component systems, which, in general, will be single refracting surfaces; and finally, an evaluation of the coefficients must be made for the simple system—a single surface. For the first and third of these steps reference may be made elsewhere, and also for a general investigation of the second; a simple derivation is given, in the present note, of the necessary relations between a composite system and its components in the case where first order aberrations only are considered.

Validation of Clicking-type Noise and Vibration in Automotive HVAC System

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
M.H.A. Satar ◽  
A. Z. A. Mazlan ◽  
M.H. Hamdan ◽  
M.S. Md. Isa ◽  
M.A.R. Paiman ◽  
...  
Keyword(s):  
Scale Model ◽  
Hvac System ◽  
Frequency Range ◽  
Similar Frequency ◽  
Noise And Vibration ◽  
System A ◽  
Vehicle System ◽  
Operating Frequency Range ◽  
Expansion Valve ◽  
Good Agreement

In this study, the characteristics of clicking-type noise and vibration occurring in the automotive heating, ventilation and air conditional (HVAC) systems are investigated. A lab-scale model of HVAC system is developed, and validation is carried out with a vehicle system. A fixed blower speed of 1 (at an airflow of 2.53 m/s) with alternated air conditional (AC) was implied in this study. Three different sensors namely as tachometer, accelerometer, and microphone were used to measure and prove the existing noise in the HVAC system. The study inferred that the compressor contributed significantly to the total vibration and noise in the HVAC system. Other components such as AC pipe, evaporator, and thermal expansion valve (TXV) also contributed to a slight extent. The clicking noise was observed in the operating frequency range of 200 ~ 300 Hz. This noise and vibration issues are partly influenced by the running conditions of the AC and the effect was significant when the AC was turned on. The validation of the findings in the model shows a good agreement with the results obtained in the vehicle system, whereby the clicking noise and vibration can be observed at a similar frequency range.

Phase transitions in two-component systems

1959 ◽  
Vol 249 (1258) ◽  
pp. 335-345
Keyword(s):  
Phase Transitions ◽  
Binary Mixtures ◽  
Fourier Transforms ◽  
Two Component System ◽  
Component System ◽  
System A ◽  
Component Systems ◽  
Two Component ◽  
Two Component Systems

The Born-Green equations have been generalized to binary mixtures, and solutions in terms of Fourier transforms have been found. The singularities of the solution are believed to correspond to the point at which condensation first occurs in the two component system. A plot of this temperature against density for three mole fractions is shown.

scholarly journals TO THE QUESTION OF OPTIMISING THE DYNAMIC CHARACTERISTICS OF A VIBRATIONAL TREE UPROOTING MACHINE

2018 ◽  
Vol 45 (2) ◽  
pp. 149-157
Author(s):  
A. R. Mikhitarov ◽  
V. L. Savich ◽  
V. K. Khegai
Keyword(s):  
Mathematical Model ◽  
Root System ◽  
Dynamic Characteristics ◽  
Mutual Influence ◽  
Frequency Characteristics ◽  
Frequency Range ◽  
System A ◽  
Forest Sites ◽  
Tree Uprooting ◽  
The Mathematical Model

Objectives Following logging operations, tree stumps remain in the site of the former forest.While these may be uprooted by special machines in the course of forestry operations, the use of heavy forestry machines operated repeatedly on the forest sites not only lead to soil erosion, but also to considerable financial expense. Consequently, the development of machines combining cutting (logging) and uprooting operations – that is, uprooting the trees along with their roots – are of a great interest. As research has shown, the main disadvantages of the use of such technology by “conventional” logging or forestry machines are their excessive loading and energy intensity. The aim of the research is to investigate means of eliminating these drawbacks by using vibration.Methods The article deals with theproblem of ensuring the effectiveness of the vibration application – in particular, torsional vibrations, used to stub trees together with their roots. To solve this problem, a mathematical model of the “machine-tree-soil-root system” system was developed, which takes into account the mutual influence of the dynamic characteristics of the machine’s technological equipment and tree and soil-root system, which allows a rational (optimal) frequency range of vibration equipment to be selected by analysing the amplitude-frequency characteristics of a given system. To analyse the amplitude-frequency characteristics of a mechanical system, the Euler-Lagrange equationswere used.Results Based on the mathematical model of the “machine-tree-soil-root system (SRS)” system and an analysis of the amplitude-frequency characteristics of a given system, a rational range of vibration frequencies was determined. As shown by analysis, the work of vibrational equipment in a given frequency range can significantly reduce the dynamic loading of the machine and at the same time create appropriate conditions for the effective destruction of the soil-root system.Conclusion The proposed method allows the rational values of the frequency characteristic of vibration equipment for each calculated tree to be found depending on the soil type and the basic machine.

Microstructural Characterization of Multi-Component Systems Produced by Mechanical Alloying

2009 ◽  
Vol 1243 ◽  
Author(s):  
R. Pérez-Bustamante ◽  
C.D. Gómez-Esparza ◽  
F. Pérez-Bustamante ◽  
I. Estrada-Guel ◽  
J.G. Cabañas-Moreno ◽  
...  
Keyword(s):  
Solid Solution ◽  
Binary System ◽  
Mechanical Alloying ◽  
Microstructural Characterization ◽  
Lattice Parameter ◽  
System A ◽  
Limited Solid Solubility ◽  
Component Systems ◽  
Small Change

ABSTRACTA series of binary to hexanary alloys (Ni, Co, Mo, Al, Fe, Cu) are produced by mechanical alloying. Formation of an FCC solid solution is observed in the binary system. For ternary to quinary systems the presence of an amorphous phase and a BCC solid solution is identified, and for the hexanary system a combination of BCC and FCC solid solutions is detected. There is a very small change in the lattice parameter of Mo, reflecting the limited solid solubility of other element in this structure. However, Mo induces the fast amorphization of other elements and the reduction of crystallite size.

A new study on dynamic adjustment of vibration direction angle for dual-motor-driven vibrating screen

2020 ◽  
pp. 095440892095260 ◽  
Author(s):  
Bing Chen ◽  
Jiwei Yan ◽  
Zhongjun Yin ◽  
Kumar K Tamma
Keyword(s):  
Driving Frequency ◽  
Frequency Range ◽  
Dynamic Adjustment ◽  
Vibration Direction ◽  
Vibrating Screen ◽  
Synchronous System ◽  
Direction Angle ◽  
System A ◽  
New Concepts ◽  
Important Significance

For a dual-motor-driven elliptical vibrating screen, the driving frequencies of the two motors are studied in this paper and it exposes the significant influences of different driving frequencies on the vibration direction angle of the self-synchronous system. A dynamic model is established to demonstrate the new concepts and innovative ideas put forth in this paper. Simulink and prototype experiments are implemented to further study the influences of different driving frequencies on the phase angle and the vibration direction angle. The results of simulation and experiments shows that vibrating screen driven by the two motors can not only achieve a stable synchronization within a certain frequency range by changing the driving frequency of either of the two motors, but also the vibration direction angle significantly changes at similar but different driving frequencies. This is an important finding that has important significance for the future operations of dual-motor-driven vibrating screen in industry. The method developed in this study would be a valuable engineering tool which can be used in design and application of the screens and the screening operations.

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