scholarly journals Reduction of static field equation of Faddeev model to first order PDE

2007 ◽  
Vol 652 (5-6) ◽  
pp. 384-387 ◽  
Author(s):  
Minoru Hirayama ◽  
Chang-Guang Shi
Keyword(s):  
Field Equation ◽  
Static Field ◽  
First Order ◽  
First Order Pde ◽  
Faddeev Model

scholarly journals APPROXIMATE VORTEX SOLUTION OF FADDEEV MODEL

2008 ◽  
Vol 23 (09) ◽  
pp. 1361-1369 ◽  
Author(s):  
CHANG-GUANG SHI ◽  
MINORU HIRAYAMA
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Minimum Energy ◽  
Azimuthal Angle ◽  
Static Field ◽  
Angle Dependence ◽  
Approximate Analytic Expression ◽  
Vortex Solution ◽  
Analytic Expression ◽  
Faddeev Model

Through an ansatz specifying the azimuthal-angle dependence of the solution, the static field equation for vortex of the Faddeev model is converted to an algebraic ordinary differential equation. An approximate analytic expression of the vortex solution is explored so that the energy per unit vortex length becomes as small as possible. It is observed that the minimum energy of vortex is approximately proportional to the integer which specifies the solution.

scholarly journals Mathematical analysis of nonlocal PDEs for network generation

2019 ◽  
Vol 14 (5) ◽  
pp. 506
Author(s):  
Tobias Böhle ◽  
Christian Kuehn
Keyword(s):  
Partial Differential Equations ◽  
Numerical Simulations ◽  
Mathematical Analysis ◽  
Degree Distribution ◽  
Network Science ◽  
Steady States ◽  
Network Generation ◽  
First Order ◽  
First Order Pde ◽  
Implicit Ode

In this paper, we study a certain class of nonlocal partial differential equations (PDEs). The equations arise from a key problem in network science, i.e., network generation from local interaction rules, which result in a change of the degree distribution as time progresses. The evolution of the generating function of this degree distribution can be described by a nonlocal PDE. To address this equation we will rigorously convert it into a local first order PDE. Then, we use theory of characteristics to prove solvability and regularity of the solution. Next, we investigate the existence of steady states of the PDE. We show that this problem reduces to an implicit ODE, which we subsequently analyze. Finally, we perform numerical simulations, which show stability of the steady states.

scholarly journals Modeling Dark Sector in Horndeski Gravity at First-Order Formalism

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
F. F. Santos ◽  
R. M. P. Neves ◽  
F. A. Brito
Keyword(s):  
Dark Energy ◽  
Field Equation ◽  
Scalar Field ◽  
Free Choice ◽  
Scalar Potential ◽  
Late Time ◽  
De Sitter ◽  
Dark Sector ◽  
First Order ◽  
Cosmological Scenario

We investigate a cosmological scenario by finding solutions using first-order formalism in the Horndeski gravity that constrains the superpotential and implies that no free choice of scalar potential is allowed. Despite this, we show that a de Sitter phase at late-time cosmology can be realized, where the dark energy sector can be identified. The scalar field equation of state tends to the cosmological scenario at present time and allows us to conclude that it can simulate the dark energy in the Horndeski gravity.

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