Modeling of the Process of Drying and Coalescing Nanodispersion Spreading

2021 ◽  
Vol 887 ◽  
pp. 557-563
Author(s):  
D.M. Mordasov ◽  
M.D. Mordasov
Keyword(s):  
Contact Angle ◽  
Differential Equations ◽  
Mathematical Description ◽  
Transition Function ◽  
System Of Differential Equations ◽  
Theoretical Justification ◽  
Spreading Process ◽  
Optimal Amount ◽  
First Order ◽  
Energy Processes

The spreading process of drying and coalescing nanodispersion was simulated using the method of analogies. A mathematical description of the energy processes in the proposed physical model was obtained in the form of a system of differential equations of the first order. A transition function that describes the dynamics of the change in the contact angle when the nanodispersion drop spreads was obtained as a result of solving the system of differential equations. The physical meaning of the transition function coefficients was established. Based on the analysis of the ratio of the transition function coefficients, a theoretical justification for the results of experiments on choosing the optimal amount of desiccant introduced into styrene-acrylic nanodispersion was given.

A first order system of differential equations for covariant σ models

1979 ◽  
Vol 20 (12) ◽  
pp. 2619-2620
Author(s):  
C. Reina ◽  
M. Martellini ◽  
P. Sodano
Keyword(s):  
Differential Equations ◽  
Order System ◽  
System Of Differential Equations ◽  
First Order

scholarly journals On conditions of solvability of three-dimensional integralsystem in quadratures

2017 ◽  
Vol 21 (10) ◽  
pp. 40-46
Author(s):  
E.A. Sozontova
Keyword(s):  
Differential Equations ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Original System ◽  
Goursat Problem ◽  
System Of Differential Equations ◽  
Third Order ◽  
First Order ◽  
Three Dimensional Space

In this paper we consider the system of equations with partial integrals in three-dimensional space. The purpose is to find sufficient conditions of solvability of this system in quadratures. The proposed method is based on the reduction of the original system, first, to the Goursat problem for a system of differential equations of the first order, and after that to the three Goursat problems for differential equations of the third order. As a result, the sufficient conditions of solvability of the considering system in explicit form were obtained. The total number of cases discussing solvability is 16.

scholarly journals MHV graviton scattering amplitudes and current algebra on the celestial sphere

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Shamik Banerjee ◽  
Sudip Ghosh ◽  
Partha Paul
Keyword(s):  
Scattering Amplitudes ◽  
Differential Equations ◽  
Current Algebra ◽  
Minimal Model ◽  
Symmetry Algebra ◽  
Local Symmetry ◽  
The Other ◽  
System Of Differential Equations ◽  
First Order ◽  
Celestial Sphere

Abstract The Cachazo-Strominger subleading soft graviton theorem for a positive helicity soft graviton is equivalent to the Ward identities for $$ \overline{\mathrm{SL}\left(2,\mathrm{\mathbb{C}}\right)} $$ SL 2 ℂ ¯ currents. This naturally gives rise to a $$ \overline{\mathrm{SL}\left(2,\mathrm{\mathbb{C}}\right)} $$ SL 2 ℂ ¯ current algebra living on the celestial sphere. The generators of the $$ \overline{\mathrm{SL}\left(2,\mathrm{\mathbb{C}}\right)} $$ SL 2 ℂ ¯ current algebra and the supertranslations, coming from a positive helicity leading soft graviton, form a closed algebra. We find that the OPE of two graviton primaries in the Celestial CFT, extracted from MHV amplitudes, is completely determined in terms of this algebra. To be more precise, 1) The subleading terms in the OPE are determined in terms of the leading OPE coefficient if we demand that both sides of the OPE transform in the same way under this local symmetry algebra. 2) Positive helicity gravitons have null states under this local algebra whose decoupling leads to differential equations for MHV amplitudes. An n point MHV amplitude satisfies two systems of (n − 2) linear first order PDEs corresponding to (n − 2) positive helicity gravitons. We have checked, using Hodges’ formula, that one system of differential equations is satisfied by any MHV amplitude, whereas the other system has been checked up to six graviton MHV amplitude. 3) One can determine the leading OPE coefficients from these differential equations.This points to the existence of an autonomous sector of the Celestial CFT which holographically computes the MHV graviton scattering amplitudes and is completely defined by this local symmetry algebra. The MHV-sector of the Celestial CFT is like a minimal model of 2-D CFT.

Numerical solution of the system of Marchenko integral equations

2021 ◽  
Vol 65 (3) ◽  
pp. 159-165
Keyword(s):  
Differential Equations ◽  
Integral Equations ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Algebraic Equations ◽  
System Of Differential Equations ◽  
Scattering Problems ◽  
First Order ◽  
First Order Differential Equations

In this paper, inverse scattering problems for a system of differential equations of the first order are considered. The Marchenko approach is used to solve the inverse scattering problem. The system of Marchenko integral equations is reduced to a linear system of algebraic equations such that the solution of the resulting system yields to the unknown coefficients of the system of first-order differential equations. Illustrative examples are provided to demonstrate the preciseness and effectiveness of the proposed technique. The results are compared with the exact solution by using computer simulations.

Numerical Kinematical Analysis of the Articulated Quadrilateral Mechanism

2019 ◽  
Vol 17 (17) ◽  
pp. 52-62
Author(s):  
Mircea Bogdan Tătaru ◽  
Vladimir Dragoş Tătaru
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Reference System ◽  
Electronic Computer ◽  
System Of Differential Equations ◽  
First Order ◽  
Kinematical Analysis ◽  
Fixed Reference ◽  
Numerical Integration Methods ◽  
Kinematical Parameters

AbstractThe paper presents a numerical method of kinematical analysis of the articulated quadrilateral mechanism. Starting from Euler’s relation concerning the distribution of speeds written in projections on the fixed reference system axes, a system of differential equations describing the movement of the mechanism was obtained. This system of differential equations was then solved using numerical integration methods and the variation with respect to time of the position kinematical parameters, of the velocities (the first order kinematical parameters), and of the accelerations (the second order kinematical parameters), was obtained. Matrix writing of the differential equations was used in order to make the differential equations set out in the paper easier to solve using the electronic computer.

scholarly journals ON STABILITY OF STATIONARY STATES OF REVERSIBLE REACTIONS OF THE FIRST ORDER

2022 ◽  
Vol 1 (15) ◽  
pp. 119-122
Author(s):  
Svetlana Senotova
Keyword(s):  
Differential Equations ◽  
Stationary State ◽  
Direct Method ◽  
First Integral ◽  
Stationary States ◽  
System Of Differential Equations ◽  
First Order ◽  
Lyapunov’S Direct Method ◽  
Reversible Reactions

The article discusses reversible first-order reactions. A system of differential equations is written. First integral and stationary state found. Using Lyapunov's direct method, stationary stability was investigated

scholarly journals ON SOME ALGORITHMS FOR THE NUMERICAL SOLUTION OF THE CAUCHY PROBLEM FOR A SYSTEM OF DIFFERENTIAL EQUATIONS OF THE FIRST ORDER RUNGE - KUTT METHOD IN DELPHI

2014 ◽  
Vol 12 (04) ◽  
pp. 26-31
Author(s):  
Erik Nurlanovich Bayandiyev ◽  
◽  
Lyazat Rysbekovna Seytbekova ◽  
Aynur Tursynkhanovna Tolkynbayeva ◽  
◽  
...  
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Numerical Solution ◽  
System Of Differential Equations ◽  
First Order ◽  
The Cauchy Problem

scholarly journals Study of stiff differential equations of mathematical description of izomerization of pentane-hexane cut process

2021 ◽  
Vol 2131 (2) ◽  
pp. 022003
Author(s):  
R I Faskhutdinova ◽  
A G Faskhutdinov ◽  
L V Enikeeva ◽  
I M Gubaydullin
Keyword(s):  
Differential Equations ◽  
Chemical Kinetics ◽  
Mathematical Description ◽  
Hexane Fraction ◽  
Chemical Transformations ◽  
System Of Differential Equations ◽  
Stiff Differential Equations ◽  
Stiff System ◽  
Catalytic Isomerization ◽  
The Given

Abstract This paper provides a brief overview of the existing definitions of a stiff system of differential equations. Further, on the example of the accepted scheme of chemical transformations of the catalytic isomerization process of the pentane-hexane fraction, the stiffness of the system of differential equations was studied. In the course of the work, a method for studying the direct kinetic problem for stiffness is presented. In the Matlab software, the results of solving a system of differential equations by five methods (solvers) were compared. The given method can be tried for solving other problems of chemical kinetics.

scholarly journals On a curve and a system

2020 ◽  
Vol 5 (3) ◽  
pp. 030-052
Author(s):  
Tuba Ağırman Aydın ◽  
Seda Çayan ◽  
Mehmet Sezer ◽  
Abdullah Mağden
Keyword(s):  
Differential Equations ◽  
Constant Width ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
System Of Differential Equations ◽  
Similar System ◽  
First Order ◽  
Cam Design ◽  
Different Types ◽  
Curves Of Constant Width

Curves of constant width, which have a very special place in many fields such as kinematics, engineering, art, cam design and geometry, are specially discussed under this title. In this study, a system of differential equations characterizing the curves of constant width is examined. This is the system of the first order homogenous differential equations with variable coefficients in the normal form. Approximate solutions of the system, by means of two different polynomial approaches, are calculated and error analysis is made. The obtained results are analyzed on a numerical sample and the best method of approach is determined. This system can also constitute a characterization for different types of curves according to different frames in different spaces. Therefore, this study is important not only for this curve type but also for the geometry of all curves that can be expressed in a similar system.

scholarly journals The analysis of gas dynamics equations with initial and boundary conditions and the construction of the corresponding averaged system

2013 ◽  
Vol 54 ◽  
Author(s):  
Aleksandras Krylovas ◽  
Rima Kriauzienė
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Hyperbolic System ◽  
Gas Dynamics ◽  
System Of Differential Equations ◽  
Gas Dynamics Equations ◽  
Large Domain ◽  
First Order ◽  
Initial And Boundary Conditions ◽  
Asymptotical Analysis

In this paper hyperbolic system of the first order gas dynamics PDE with initial and boundary conditions is studied. The aim of the paper is to construct the averaged system of differential equations in order to find the uniformly valid in a large domain asymptotical solution. The averaged system is a new object of asymptotical analysis.

Sign in / Sign up

Export Citation Format

Share Document