scholarly journals Asymptotic behavior of N-fields Chiral cosmology

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Genly Leon
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Behaviour ◽  
Background Level ◽  
Scalar Fields ◽  
Stationary Points ◽  
Chiral Model ◽  
Conserved Quantities ◽  
New Exact Solutions ◽  
Cosmological Scenario ◽  
The One

AbstractWe perform a detailed analysis for the asymptotic behaviour for the multi-scalar field Chiral cosmological scenario. We present the asymptotic behaviour for the one-field, two-fields and three-fields Chiral models. From these results, and deriving conserved quantities, we present a Theorem for the N-fields model for the Chiral model with N-fields. We find that the maximum number of scalar fields which provide interesting physical results at the background level is two-fields, while for $$N>2$$ N > 2 the new stationary points are only of mathematical interest since they do not describe new exact solutions different from those recovered for $$N=2$$ N = 2 .

scholarly journals Weak cosmic censorship with self-interacting scalar and bound on charge to mass ratio

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Yan Song ◽  
Tong-Tong Hu ◽  
Yong-Qiang Wang
Keyword(s):  
Scalar Field ◽  
Scalar Fields ◽  
Cosmic Censorship ◽  
Mass Ratio ◽  
Quartic Coupling ◽  
Scalar Theory ◽  
Free Scalar ◽  
The One ◽  
Nonzero Scalar ◽  
Large Charge

Abstract We study the model of four-dimensional Einstein-Maxwell-Λ theory minimally coupled to a massive charged self-interacting scalar field, parameterized by the quartic and hexic couplings, labelled by λ and β, respectively. In the absence of scalar field, there is a class of counterexamples to cosmic censorship. Moreover, we investigate the full nonlinear solution with nonzero scalar field included, and argue that these counterexamples can be removed by assuming charged self-interacting scalar field with sufficiently large charge not lower than a certain bound. In particular, this bound on charge required to preserve cosmic censorship is no longer precisely the weak gravity bound for the free scalar theory. For the quartic coupling, for λ < 0 the bound is below the one for the free scalar fields, whereas for λ > 0 it is above. Meanwhile, for the hexic coupling the bound is always above the one for the free scalar fields, irrespective of the sign of β.

scholarly journals Limit of 𝑝-Laplacian obstacle problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Raffaela Capitanelli ◽  
Maria Agostina Vivaldi
Keyword(s):  
Asymptotic Behavior ◽  
Uniform Convergence ◽  
Explicit Expression ◽  
Positive Measure ◽  
Sufficient Conditions ◽  
Obstacle Problems ◽  
Dimensional Case ◽  
Asymptotic Behavior Of Solutions ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we study asymptotic behavior of solutions to obstacle problems for p-Laplacians as {p\to\infty}. For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of the whole family of the solutions of obstacle problems either for data f that change sign in Ω or for data f (that do not change sign in Ω) possibly vanishing in a set of positive measure.

scholarly journals Comparison between the Cauchy problem and the scattering problem for the Landau damping in the Vlasov-HMF equation

2021 ◽  
pp. 1-24
Author(s):  
Dario Benedetto ◽  
Emanuele Caglioti ◽  
Stefano Rossi
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Scattering Problem ◽  
New Method ◽  
Landau Damping ◽  
The Cauchy Problem ◽  
The One ◽  
Perturbative Result

We analyze the analytic Landau damping problem for the Vlasov-HMF equation, by fixing the asymptotic behavior of the solution. We use a new method for this “scattering problem”, closer to the one used for the Cauchy problem. In this way we are able to compare the two results, emphasizing the different influence of the plasma echoes in the two approaches. In particular, we prove a non-perturbative result for the scattering problem.

scholarly journals Asymptotic and transient behaviour for a nonlocal problem arising in population genetics

2018 ◽  
Vol 31 (1) ◽  
pp. 84-110
Author(s):  
J.-B. BURIE ◽  
R. DJIDJOU-DEMASSE ◽  
A. DUCROT
Keyword(s):  
Asymptotic Behaviour ◽  
Large Time ◽  
Nonlocal Problem ◽  
Genetic Adaptation ◽  
System Of Equations ◽  
Pathogen Population ◽  
Transient Behaviour ◽  
Selection Processes ◽  
The One ◽  
Mutation And Selection

This work is devoted to the study of an integro-differential system of equations modelling the genetic adaptation of a pathogen by taking into account both mutation and selection processes. First, we study the asymptotic behaviour of the system and prove that it eventually converges to a stationary state. Next, we more closely investigate the behaviour of the system in the presence of multiple EAs. Under suitable assumptions and based on a small mutation variance asymptotic, we describe the existence of a long transient regime during which the pathogen population remains far from its asymptotic behaviour and highly concentrated around some phenotypic value that is different from the one described by its asymptotic behaviour. In that setting, the time needed for the system to reach its large time configuration is very long and multiple evolutionary attractors may act as a barrier of evolution that can be very long to bypass.

scholarly journals Asymptotic Behaviour of Christoffel–Darboux Kernel Via Three-Term Recurrence Relation I

2020 ◽  
Author(s):  
Grzegorz Świderski ◽  
Bartosz Trojan
Keyword(s):  
Asymptotic Behavior ◽  
Asymptotic Behaviour ◽  
Recurrence Relation ◽  
Scaling Limits ◽  
Christoffel Functions ◽  
Asymptotically Periodic ◽  
Three Term Recurrence Relation

Abstract For Jacobi parameters belonging to one of three classes: asymptotically periodic, periodically modulated, and the blend of these two, we study the asymptotic behavior of the Christoffel functions and the scaling limits of the Christoffel–Darboux kernel. We assume regularity of Jacobi parameters in terms of the Stolz class. We emphasize that the first class only gives rise to measures with compact supports.

On the minimizers of the Ginzburg–Landau energy for high kappa: the one-dimensional case

1997 ◽  
Vol 8 (4) ◽  
pp. 331-345 ◽  
Author(s):  
AMANDINE AFTALION
Keyword(s):  
Magnetic Field ◽  
Asymptotic Behaviour ◽  
Dimensional Case ◽  
Numerical Computations ◽  
Ginzburg Landau ◽  
Landau Model ◽  
One Dimensional ◽  
Landau Parameter ◽  
Convergence Results ◽  
The One

The Ginzburg–Landau model for superconductivity is examined in the one-dimensional case. First, putting the Ginzburg–Landau parameter κ formally equal to infinity, the existence of a minimizer of this reduced Ginzburg–Landau energy is proved. Then asymptotic behaviour for large κ of minimizers of the full Ginzburg–Landau energy is analysed and different convergence results are obtained, according to the exterior magnetic field. Numerical computations illustrate the various behaviours.

scholarly journals Reheating constraints on Kähler moduli inflation

2019 ◽  
Vol 34 (15) ◽  
pp. 1950114 ◽  
Author(s):  
Rakesh Kabir ◽  
Amitabha Mukherjee ◽  
Daksh Lohiya
Keyword(s):  
Equation Of State ◽  
State Parameter ◽  
Index Formula ◽  
Planck Data ◽  
Slow Roll ◽  
Cosmological Scenario ◽  
Hubble Radius ◽  
The One ◽  
Potential Parameters ◽  
The Universe

The end of inflation is connected to the standard cosmological scenario through reheating. During reheating, the inflaton oscillates around the minimum of the potential and thus decays into the daughter particles that populate the Universe at later times. Using cosmological evolution for observable CMB scales from the time of Hubble crossing to the present time, we translate the constraint on the spectral index [Formula: see text] from Planck data to the constraint on the reheating scenario in the context of Kähler moduli inflation. We find that the equation of state parameter plays a crucial role in the reheating analysis, however the details of the one parameter potential are irrelevant if the analysis is done strictly within the slow-roll formalism. In addition, we extend the de facto analysis generally done only for the pivot scale to all the observable scales which crossed the Hubble radius during inflation, where we study how the maximum number of e-folds varies for different scales, and the effect of the equation of state and potential parameters.

ON THE ROTATING SOLITON IN THE CHIRAL MODEL

1992 ◽  
Vol 07 (27) ◽  
pp. 6763-6772 ◽  
Author(s):  
TAKASHI OKAZAKI ◽  
KANJI FUJII ◽  
NAOHISA OGAWA
Keyword(s):  
Asymptotic Behavior ◽  
Trial Function ◽  
Pion Mass ◽  
Rotational Energy ◽  
Chiral Model ◽  
Profile Function ◽  
Physical Pion ◽  
Total Energies

We study the quantum rotating soliton in the nonlinear σ model which is obtained by minimizing the total energies of rotating soliton. Existence of such a soliton is expected from the Derrick’s theorem even when the Skyrme term is absent because the rotational energy prevents the soliton from collapsing. The asymptotic behavior of the profile function is shown to be determined by the physical pion mass which appears in the PCAC relation in the nonlinear σ model. The energies of spin-1/2 and − 3/2 solitons are obtained numerically with the use of a simple trial function.

Sign in / Sign up

Export Citation Format

Share Document