Search results for "Linear system"
showing 10 items of 1558 documents
Fully relativistic non-linear cosmological evolution in spherical symmetry using the BSSN formalism
2014
We present a fully relativistic numerical method for the study of cosmological problems using the Baumgarte-Shapiro-Shibata-Nakamura formalism on a dynamical Friedmann-Lema\^itre-Robertson-Walker background. This has many potential applications including the study of the growth of structures beyond the linear regime. We present one such application by reproducing the Lema\^itre-Tolman-Bondi solution for the collapse of pressureless matter with arbitrary lapse function. The regular and smooth numerical solution at the center of coordinates proceeds in a natural way by relying on the Partially Implicit Runge-Kutta algorithm described in Montero and Cordero-Carri\'on [arXiv:1211.5930]. We gene…
Palatini $f(R)$ Black Holes in Nonlinear Electrodynamics
2011
The electrically charged Born-Infeld black holes in the Palatini formalism for $f(R)$ theories are analyzed. Specifically we study those supported by a theory $f(R)=R\pm R^2/R_P$, where $R_P$ is Planck's curvature. These black holes only differ from their General Relativity counterparts very close to the center, but may give rise to different geometrical structures in terms of inner horizons. The nature and strength of the central singularities are also significantly affected. In particular, for the model $f(R)=R - R^2/R_P$ the singularity is shifted to a finite radius, $r_+$, and the Kretschmann scalar diverges only as $1/(r-r_+)^{2}$.
Effect of three-body cluster on the healing properties of the Jastrow Correlation function
1973
A variational equation for the Jastrow Correlation function is derived from the energy functional expanded up to three-body cluster terms. The asymptotic behaviour of this nonlinear equation is studied. The solutions show a healing at least of the type cos(tαr)/r2. The influence of higher cluster contributions is studied. Finally, it is discussed, how one can reduce the many-body cluster contributions to healing conditions to be used in the two-body cluster treatment.
Nonlinear dynamics in three-dimensional QED and nontrivial infrared structure
1999
In this work we consider a coupled system of Schwinger-Dyson equations for self-energy and vertex functions in QED_3. Using the concept of a semi-amputated vertex function, we manage to decouple the vertex equation and transform it in the infrared into a non-linear differential equation of Emden-Fowler type. Its solution suggests the following picture: in the absence of infrared cut-offs there is only a trivial infrared fixed-point structure in the theory. However, the presence of masses, for either fermions or photons, changes the situation drastically, leading to a mass-dependent non-trivial infrared fixed point. In this picture a dynamical mass for the fermions is found to be generated c…
On the gluon spectrum in the glasma
2010
We study the gluon distribution in nucleus-nucleus collisions in the framework of the Color-Glass-Condensate. Approximate analytical solutions are compared to numerical solutions of the non-linear Yang-Mills equations. We find that the full numerical solution can be well approximated by taking the full initial condition of the fields in Coulomb gauge and using a linearized solution for the time evolution. We also compare kt-factorized approximations to the full solution.
Moments of inertia of nuclei in the rare earth region: A relativistic versus nonrelativistic investigation
2000
A parameter free investigation of the moments of inertia of ground state rotational bands in well deformed rare-earth nuclei is carried out using Cranked Relativistic Hartree-Bogoliubov (CRHB) and non-relativistic Cranked Hartree-Fock-Bogoliubov (CHFB) theories. In CRHB theory, the relativistic fields are determined by the non-linear Lagrangian with the NL1 force and the pairing interaction by the central part of finite range Gogny D1S force. In CHFB theory, the properties in particle-hole and particle-particle channels are defined solely by Gogny D1S forces. Using an approximate particle number projection before variation by means of the Lipkin Nogami method improves the agreement with the…
Enhanced charm hadroproduction due to nonlinear corrections to the DGLAP equations
2004
We have studied the effects of nonlinear scale evolution of the parton distribution functions to charm production in $pp$ collisions at center-of-mass energies of 5.5, 8.8 and 14 TeV. We find that the differential charm cross section can be enhanced up to a factor of 4-5 at low $p_T$. The enhancement is quite sensitive to the charm quark mass and the renormalization/factorization scales.
Nonlinear corrections to the DGLAP equations in view of the HERA data
2002
The effects of the first nonlinear corrections to the DGLAP evolution equations are studied by using the recent HERA data for the structure function $F_2(x,Q^2)$ of the free proton and the parton distributions from CTEQ5L and CTEQ6L as a baseline. By requiring a good fit to the H1 data, we determine initial parton distributions at $Q_0^2=1.4$ GeV$^2$ for the nonlinear scale evolution. We show that the nonlinear corrections improve the agreement with the $F_2(x,Q^2)$ data in the region of $x\sim 3\cdot 10^{-5}$ and $Q^2\sim 1.5$ GeV$^2$ without paying the price of obtaining a worse agreement at larger values of $x$ and $Q^2$. For the gluon distribution the nonlinear effects are found to play…
Modulational stability brought by cubic–quartic interactions of the nearest-neighbor in FK model subjected in a parametrized on-site potential
2022
Abstract This work extends to higher-order interactions the results of Ref. Nguetcho (2021), in which we discussed only on modulational instability in one-dimensional chain made of atoms, harmonically coupled to their nearest neighbors and subjected to an external on-site potential. Here we investigate the competition between cubic-quartic nonlinearities interactions of the nearest-neighbor and substrate’s deformability, and mainly discuss its impact on the modulational instability of the system. This makes it possible to adapt the theoretical model to a real physical system such as atomic chains or DNA lattices. The governing equation, derived from the modified Frenkel-Kontorova model, is …
Bifurcations of phase portraits of a Singular Nonlinear Equation of the Second Class
2014
Abstract The soliton dynamics is studied using the Frenkel Kontorova (FK) model with non-convex interparticle interactions immersed in a parameterized on-site substrate potential. The case of a deformable substrate potential allows theoretical adaptation of the model to various physical situations. Non-convex interactions in lattice systems lead to a number of interesting phenomena that cannot be produced with linear coupling alone. In the continuum limit for such a model, the particles are governed by a Singular Nonlinear Equation of the Second Class. The dynamical behavior of traveling wave solutions is studied by using the theory of bifurcations of dynamical systems. Under different para…