scholarly journals MODEL REPRESENTATIONS OF THE MELTS STRUCTURE DESCRIPTION BY THE MODEL OF HARD SPHERES

2021 ◽  
pp. 72-78
Author(s):  
O. O. Petruk ◽  
O. T. Vavryk ◽  
O. S. Tsareva ◽  
L. M. Hobyr
Keyword(s):  
Structural Factor ◽  
Oil And Gas ◽  
Dynamic Models ◽  
Hard Spheres ◽  
Distribution Functions ◽  
Integrodifferential Equations ◽  
Theoretical Research ◽  
Kinetic Properties ◽  
Rigid Spheres ◽  
Economic Point

In the article the optimization of the oil and gas enterprise, a complex process both from the technological and from the economic point of view is investigated. It is noted that today the development of methods of mathematical modeling of physical processes, for example, in oil fields on the basis of theoretical research and modern computer technology is absolutely relevant One of the ways is to create new or improve existing mathematical models of processes occurring in oil and gas reservoirs, and calculate on their basis the characteristics of the process that optimize production. From this perspective, the study appears particularly relevant liquids in a narrow, purely physical and chemical aspects – namely melt. Various fluid models have been proposed to describe the equilibrium and kinetic properties of liquids (melts), as well as to interpret experimental results. Model representations are also used in solving integrodifferential equations that relate distribution functions to interaction potentials. It is noted that integrodifferential equations are a powerful mathematical algorithm for describing inhomogeneous dynamic models, but they depend directly on the efficiency of software that implements the proposed models. The model of hard spheres as simple fluid model proposed use. The reasons that allow you to choose this model as optimal were defined. Namely: the presence of analytical expression for the structural factor; application to describe the electronic and atomic properties of melts. The optimal methods for obtaining optimal values for the theoretical calculation of the structural factor of the proposed model were determined. As a result of the analysis of existence of correspondence between the calculated and experimental structural factors it is established. This led to the conclusion that the possibility of applying the model of rigid to calculate the equilibrium and kinetic properties of melts exists. It is determined that the model of rigid spheres could be used as an approximation to describe the structure of both one-component and multicomponential melts (liquids).

An approximation for the radial distribution function

1957 ◽  
Vol 239 (1218) ◽  
pp. 373-381 ◽  
Keyword(s):  
Distribution Function ◽  
Radial Distribution Function ◽  
Radial Distribution ◽  
Hard Spheres ◽  
Virial Coefficients ◽  
Distribution Functions ◽  
Rigid Spheres ◽  
Third Order ◽  
Alternative Assumption ◽  
Better Than

The present paper is concerned with a new approximation for the distribution function of third order. This approximation may be regarded as an improved form of the well-known superposition assumption of Kirkwood. The idea is to add to Kirkwood’s expression a linear combination of distribution functions of the same type, the coefficients of which can be easily determined. The new approximation is introduced in the Bom—Green integral equation for the radial distribution function, for which an expansion into powers of the density is used. From this the terms proportional to the first and second power of the density are calculated. The first four virial coefficients can be expressed as functions of these terms, whether the pressure equation or the compressibility equation is used. Numerical evaluation is performed for the ideal case of a gas of rigid spheres. The value obtained for the fourth virial coefficient is compared with the exact one and those given by naing Kirkwood’s assumption by Rushbrooke & Scoins, and Nijboer & van Hove. It is seen to be more nearly exact and internally consistent. The term proportional to the square of the density, in the expansion of the radial distribution function, appears to be very similar to the exact one as calculated by Nijboer & van Hove. It can be seen to be better than the corresponding term when Kirkwood’s assumption or one proposed by Nijboer & van Hove is used. Finally, an alternative assumption is suggested, and applied to the case of hard spheres.

Arctic Europe Between National Interests and Arctic Governance

2019 ◽  
pp. 117-131
Author(s):  
Igor Kochev ◽  
Wim Heijman
Keyword(s):  
Marine Mammals ◽  
Oil And Gas ◽  
Point Of View ◽  
The Arctic ◽  
National Interests ◽  
Economic Point ◽  
Oil And Gas Operations ◽  
Offshore Oil And Gas ◽  
Offshore Oil ◽  
The Eu

From an economic point of view, melting ice is making the Arctic ocean increasingly important for a number of countries – Arctic states as well as non-Arctic states. Also, the EU has clear interests in the area. This chapter provides a brief description of those interests and its implications on the EU's relationship with the Arctic partners. This note takes seven aspects of the EU-relations with the Arctic states into consideration (i.e., the institutional framework, the EU Arctic interests and policies, shipping, fishing, marine mammals, offshore oil and gas operations, and the EU's Arctic partners).

Design and Posture Control of a Wheel-Legged Robot With Actively Passively Transformable Suspension System

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Liwei Ni ◽  
Fangwu Ma ◽  
Linhe Ge ◽  
Liang Wu
Keyword(s):  
Complex Terrain ◽  
Vibration Isolation ◽  
Dynamic Models ◽  
Ride Comfort ◽  
Suspension System ◽  
Posture Control ◽  
Theoretical Research ◽  
Legged Robot ◽  
Passive System ◽  
The Impact

Abstract This paper presents a novel solution for the posture control and ride comfort between the proposed wheel-legged robot (four wheel-legged robot (FWLR)) and the unstructured terrain by means of an actively passively transformable suspension system. Unlike most traditional robots, each leg of FWLR is independent of each other with a spring-damping system (passive system) is connected in series with an actuator (active system), so the posture control and ride comfort in complex terrain can be realized by the combination between active and passive systems. To verify the performance of posture control in complex terrain, a prototype and complex terrain are established first, then a posture control model, algorithm, and controller considering the suspension system are proposed and verified by the comparison between co-simulation and experiment, the results showed that the pitch angle and roll angles in complex terrain can be controlled. To show the impact of the actively passively transformable suspension system on ride comfort (vibration isolation performance), different dynamic models with different degree-of–freedom (DOF) are established, the co-simulation results showed that the passive system and active posture control system can also effectively improve the ride comfort of FWLR in complex terrain. The research results of this paper have important reference significance and practical value for enriching and developing the mechanism design and theoretical research of wheel-legged robot and promoting the engineering application of all-terrain robot.

Scattering by Two Impenetrable Spheres

1973 ◽  
Vol 51 (17) ◽  
pp. 1850-1860
Author(s):  
M. Razavy
Keyword(s):  
Wave Function ◽  
Scattering Amplitude ◽  
Hard Spheres ◽  
Scattering Length ◽  
Separation Of Variables ◽  
Scattered Wave ◽  
Simple Expression ◽  
Rigid Spheres ◽  
Low Energies ◽  
Bispherical Coordinates

The problem of multiple scattering by two rigid spheres is studied in the context of an effective range theory. At low energies, by expanding the total wave function in powers of the momentum of the incident particle, it is observed that the coefficients of different terms of the expansion are solutions of either Laplace or Poisson equations. These equations are separable in bispherical coordinates. Using the method of separation of variables, one can determine the scattering amplitude and its first and second derivatives with respect to momentum, at zero energy. In particular, a simple expression is obtained for the scattering length of two hard spheres. With the help of the Green's function in bispherical coordinates, it is shown that for any wavenumber, the scattered wave satisfies an inhomogeneous integral equation in two variables. Hence, the exact wave function and the scattering amplitude can be found numerically for all energies.

scholarly journals Enhanced production surveillance using probabilistic dynamic models

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Ashutosh Tewari ◽  
Stijn De Waele ◽  
Niranjan Subrahmanya
Keyword(s):  
Oil And Gas ◽  
Dynamic Models ◽  
Gas Production ◽  
Phase Flow ◽  
Flow Measurements ◽  
Oil And Gas Production ◽  
Enhanced Production ◽  
Multi Phase Flow ◽  
Multi Phase ◽  
Water Gas

Production surveillance is the task of monitoring oil and gas production from every well in a hydrocarbon field. A key opportunity in this domain is to improve the accuracy of flow measurements per phase (oil, water, gas) from a multi-phase flow. Multi-phase flow sensors are costly and therefore not instrumented for every production well. Instead, several low fidelity surrogate measurements are performed that capture different aspects of the flow. These measurements are then reconciled to obtain per-phase rate estimates. Current practicesmay not appropriately account for the production dynamics and the sensor issues, thus, fall far short in terms of achieving a desired surveillance accuracy. To improve surveillance accuracy, we pose rate reconciliation as a state estimation problem. We begin with hypothesizing a model that describes the dynamics of production rates and their relationship with thefield measurements. The model appropriately accounts for the uncertainties in field conditions and measurements. We then develop robust probabilistic estimators for reconciliationto yield the production estimates and the uncertainties therein. We highlight recent advancements in the area of probabilistic programming that can go a long way in improving the performance and the portability of such estimators. The exposition of our methods is accompanied by experiments in a simulation environment to illustrate improved surveillance accuracy achieved in different production scenarios.

scholarly journals Spin-Dependent Coupled Altarelli-Parisi Equations in the NLO and the Method of Successive Approximations

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Ranjit Choudhury ◽  
D. K. Choudhury
Keyword(s):  
Gluon Distribution ◽  
Quark Distribution ◽  
Distribution Functions ◽  
Integrodifferential Equations ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Leading Order ◽  
Order Linear ◽  
First Order ◽  
Analytic Expressions

The coupled Altarelli-Parisi (AP) equations for polarized singlet quark distribution and polarized gluon distribution, when considered in the small x limit of the next to leading order (NLO) splitting functions, reduce to a system of two first order linear nonhomogeneous integrodifferential equations. We have applied the method of successive approximations to obtain the solutions of these equations. We have applied the same method to obtain the approximate analytic expressions for spin-dependent quark distribution functions with individual flavour and polarized structure functions for nucleon.

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