In this letter we construct the St\"{u}ckelberg holographic superconductor with Weyl corrections. Under such corrections, coupling parameter $\gamma$ plays an important role in order of phase transitions and critical exponents second transitions. So do model parameters $c_{\alpha}$, $\alpha$ $c_{4}$. Moreover, show that $\alpha$, $c_{4}$ which together control size strength conductivity coherence peak ratio gap frequency over temperature $\omega_{g}/T_{c}$.

The leading-order spin-orbit coupling is included in a post-Newtonian Lagrangian formulation of spinning compact binaries, which consists the Newtonian term, first (1PN) and 2PN non-spin terms spin-spin coupling. This makes 3PN occur derived Hamiltonian. couplings are mainly responsible for chaos Hamiltonians. However, Hamiltonian small has different signs, compared with equivalent to Lagrangian. As result, probability occurrence without larger than that Numerical evidences support claim.

For each object of an n-body problem in planetary dynamics, orbital elements except the mean anomaly are directly determined by five independently slow-varying quantities or quasi-integrals, which include Keplerian energy, three components angular momentum vector, and z-component Laplace vector. The depends on motion specified energy. Decreasing integration errors these quasi-integrals at every step means improving accuracy all to a great extent. Because this, we take reference values terms...

By the Poincare sections, dynamical behaviors of ring string in anti-de Sitter--Gauss-Bonnet black hole are studied. A threshold value Gauss-Bonnet parameter $\ensuremath{\lambda}$ is found by numerical method, below which behavior this system nonchaotic and above becomes gradually chaotic. The chaotic stronger with increases parameter. It different from case Sitter--Schwarzschild hole, weakly Furthermore, we confirm our findings fast Lyapunov indicator.

Recently, our group developed explicit symplectic methods for curved spacetimes that are not split into several explicitly integrable parts, but via appropriate time transformations. Such time-transformed integrators should have employed adaptive steps in principle, they often difficult practical implementations. In fact, work well if transformation functions cause the Hamiltonians to desired splits and approach 1 or constants sufficiently large distances. However, do satisfy requirement of...

Recent observation reveals two interacting Jupiters possibly trapped in a 2:1 mean motion resonance (MMR) around the star HD 155358. For MMR, Beaugé et al. found that as long orbital decay was sufficiently slow, planets should also be apsidal co-rotation. So it is very interesting to explore whether 155358 did undergo such an evolution and presents Based on existing results of spectroscopic determination, global dynamics system shows are co-rotation if eccentricity outer planet (ec) takes...

By fast Lyapunov indicator (FLI), we study the chaotic dynamics of closed string around charged black brane with hyperscaling violation (HV). The Hawking temperature, Lifshitz dynamical exponent and HV together affect this system. temperature plays role driving to escape infinity. There is a threshold value $z_{\ast}=2$, below which captured by no matter where placed at beginning. However, when $z>2$, escapes infinity if it near beginning, but initial position far away from brane, oscillates...

For each celestial body of multi-planet systems, there are two slowly varying quantities or quasi-integrals, Kepler energy and Laplace integral, which closely associated with the orbital semimajor axis eccentricity, respectively. To correct numerical errors quantities, we give an extension Nacozy's approach develop a new manifold correction method, where corresponding reference values at every integration step obtained from integral invariant relations, only velocity corrections used to...

Abstract In this paper, we make a systematical and in-depth study on the chaotic dynamics of string around conformal black hole. Depending characteristic parameter hole initial position string, there are three kinds dynamical behaviors: ordered, being captured, but not captured. A particular interesting observation is that sharp transition in when horizon disappears, which independent string. It provides possible way to probe structure massive body. We also examine generalized MSS...

The dependence of chaos on two parameters the cosmological constant and self-interacting coefficient in imaginary phase space for a closed Friedman–Robertson–Walker (FRW) universe with conformally coupled scalar field, as full understanding real space, is investigated numerically. It found that Poincaré plots less than 1 are almost same those absence terms. For energies below energy threshold 0.5 problem which there no terms, an abrupt transition to occurs when at least one 1. However,...

Lyapunov exponent (LE), fast indicator (FLI), relative finite-time (RLI), smaller alignment index (SALI), and generalized (GALI) are some of the available methods in most conservative systems. This study focuses on effects above indicators dissipative chaotic circuit systems such as Lorenz system a hyperchaotic model. Numerical experiments show that performances chaos almost similar to those system. These clearly provide transition from regular motion. However, FLI, RLI, SALI, GALI cannot...

Newtonian core-shell systems, as limiting cases of relativistic models under the two conditions weak field and slow motion, could account for massive circumstellar dust shells rings around certain types star remnants. Because this kind systems have Hamiltonians that can be split into a main part small perturbing part, good choice numerical tool is pseudo 8th order symplectic integrator Laskar & Robutel, and, to match calculations, chaos indicator fast Lyapunov (FLI) with nearby trajectories...

Recently, Kerr-MOG black hole has attracted widespread research interest and been widely used in fields such as galaxy rotation curves, gravitational lensing clusters, the formation of large-scale structures universe. In this paper, we mainly focus on dynamics charged particle around hole. At first, field equations for under Scalar-Tensor-Vector Gravity (STVG) theory are presented. Then, according to characteristics Hamiltonian system, can be decomposed into five integrable parts, three...

Abstract By means of a canonical generalized momentum and conjugate spin variable, complete Hamiltonian formalism is designed to describe coulomb field with electronic spin–orbit coupling in semi-classical non-relativistic way. After this operation, unlike the existing Lagrange formulation, concepts hidden momentum, angular kinetic energy are not used formalism. Besides, it easy find that there four first integrals involving conserved total vector an 8-dimensional phase space system. In...

Manifold correction methods are not only useful in controlling the growth of energy error, but also easy to operate application. By comparison, we found that velocity scaling method Ma et al. is a one-step method, linear transformation idea discovered by Fukushima two-step algorithm. From numerical examples, it see two have almost same effectiveness preserving integral. Both can improve orbital semi-major axis and mean anomaly similarly. However, since factor latter obtained from integral...

Symplectic integrators are suitable for an autonomous Hamiltonian system which can be split into two integrable parts of kinetic and potential energies. Compared with several existed fourth-order symplectic integrators, the optimal gradient integrator is better in aspect precision relative energy computation, so it used as a basic numerical tool two-dimensional nonlinear oscillator. Based on high accuracy value position velocity provided by integrator, Poincare sections Fast Lyapunov...