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

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.

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.

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