Nonlinear effects in resonant layers in solar and space plasmas

The present paper reviews recent advances in the theory of nonlinear driven magnetohydrodynamic (MHD) waves in slow and Alfven resonant layers. Simple estimations show that in the vicinity of resonant positions the amplitude of variables can grow over the threshold where linear descriptions are valid. Using the method of matched asymptotic expansions, governing equations of dynamics inside the dissipative layer and jump conditions across the dissipative layers are derived. These relations are essential when studying the efficiency of resonant absorption. Nonlinearity in dissipative layers can generate new effects, such as mean flows, which can have serious implications on the stability and efficiency of the resonance

Domain Walls and Matter-Antimatter Domains in the Early Universe

We suggest a scenario of spontaneous (or dynamical) C and CP violation according to which it is possible to generate domains of matter and antimatter separated by cosmologically large distances. Such C(CP) violation existed only in the early universe and later it disappeared with the only trace of generated matter and antimatter domains. So this scenario does not suffer from the problem of domain walls. According to this scenario the width of the domain wall should grow exponentially to prevent annihilation at the domain boundaries. Though there is a classical result obtained by Basu and Vilenkin that the width of the wall tends to the one of the stationary solution (constant physical width). That is why we considered thick domain walls in a de Sitter universe following paper by Basu and Vilenkin. However, we were interested not only in stationary solutions found therein, but also investigated the general case of domain wall evolution with time. When the wall thickness parameter, δ0 , is smaller than H−1/2 where H is the Hubble parameter in de Sitter space-time, then the stationary solutions exist, and initial field configurations tend with time to the stationary ones. However, there are no stationary solutions for δ0>H−1/2 We have calculated numerically the rate of the wall expansion in this case and have found that the width of the wall grows exponentially fast for δ0≫H−1 An explanation for the critical value δ0c=H−1/2 is also proposed

Domain Walls and Matter-Antimatter Domains in the Early Universe

We suggest a scenario of spontaneous (or dynamical) C and CP violation according to which it is possible to generate domains of matter and antimatter separated by cosmologically large distances. Such C(CP) violation existed only in the early universe and later it disappeared with the only trace of generated matter and antimatter domains. So this scenario does not suffer from the problem of domain walls. According to this scenario the width of the domain wall should grow exponentially to prevent annihilation at the domain boundaries. Though there is a classical result obtained by Basu and Vilenkin that the width of the wall tends to the one of the stationary solution (constant physical width). That is why we considered thick domain walls in a de Sitter universe following paper by Basu and Vilenkin. However, we were interested not only in stationary solutions found therein, but also investigated the general case of domain wall evolution with time. When the wall thickness parameter, δ0 , is smaller than H−1/2 where H is the Hubble parameter in de Sitter space-time, then the stationary solutions exist, and initial field configurations tend with time to the stationary ones. However, there are no stationary solutions for δ0>H−1/2 We have calculated numerically the rate of the wall expansion in this case and have found that the width of the wall grows exponentially fast for δ0≫H−1 An explanation for the critical value δ0c=H−1/2 is also proposed

Domain Walls in the Early Universe and Generation of Matter and Antimatter Domains

We present a model where it is possible to generate cosmologically large domains of matter and antimatter separated by cosmologically large distances. Domain walls existed only in the early universe and later they disappeared. So the problem of domain walls in this model does not exist. These features are achieved through a postulated form of interaction between inflaton and a new scalar field. This scenario inspired a study of the related problem - evolution of the domain wall width in expanding universe. According to classical results there is a region of parameter space where the solutions with constant physical width exist. Numerical study of the problem demonstrates that initial configurations tend to these solutions with time. However, we have found that the wall width can grow exponentially outside of that parameter region

Evolution of a domain wall in expanding universe: inflation and after it

We study the evolution of thick domain walls in the expanding universe. We have found that the domain wall evolution crucially depends on the time-dependent parameter C(t) = 1/(H(t)δ0)2, where H(t) is the Hubble parameter and δ0 is the width of the wall in flat space-time. For C(t) > 2 the physical width of the wall, a(t)δ(t), tends with time to constant value δ0, which is microscopically small. Otherwise, when C(t) ≤ 2, the wall steadily expands and can grow up to a cosmologically large size

Domain Walls in the Early Universe and Generation of Matter and Antimatter Domains

We present a model where it is possible to generate cosmologically large domains of matter and antimatter separated by cosmologically large distances. Domain walls existed only in the early universe and later they disappeared. So the problem of domain walls in this model does not exist. These features are achieved through a postulated form of interaction between inflaton and a new scalar field. This scenario inspired a study of the related problem - evolution of the domain wall width in expanding universe. According to classical results there is a region of parameter space where the solutions with constant physical width exist. Numerical study of the problem demonstrates that initial configurations tend to these solutions with time. However, we have found that the wall width can grow exponentially outside of that parameter region

Evolution of a domain wall in expanding universe: inflation and after it

We study the evolution of thick domain walls in the expanding universe. We have found that the domain wall evolution crucially depends on the time-dependent parameter C(t) = 1/(H(t)δ0)2, where H(t) is the Hubble parameter and δ0 is the width of the wall in flat space-time. For C(t) > 2 the physical width of the wall, a(t)δ(t), tends with time to constant value δ0, which is microscopically small. Otherwise, when C(t) ≤ 2, the wall steadily expands and can grow up to a cosmologically large size