abstract

In this paper, lattice simulations are used to propose a potential model for gluonic excited \({\mit \Sigma }^-_u\) states of bottomonium meson. This proposed model is used to calculate radial wave functions, masses and radii of \({\mit \Sigma }_u^-\) bottomonium hybrid mesons. Here, the gluonic field between a quark and an antiquark is treated as in the Born–Oppenheimer approximation, and the Schrödinger equation is numerically solved employing the shooting method.

abstract

The fusion process is the effect of a one-dimensional barrier penetration model that incorporates scattering potential as a combination of Coulomb and proximity potentials. Heavy-ion fusion reactions were performed with coupled-channel (CC) calculations. In heavy-ion fusion reactions, CC formalism is carried through the under-barrier energy. Here, fusion cross sections were calculated and investigated for the O\(^{16}+\)Ge\(^{70,72,74,76}\), O\(^{16}+\)Sm\(^{148,150,152,154}\), Ne\(^{20}+\)Zr\(^{90,92,94,96}\), Ne\(^{20}+\)Sn\(^{112,114,116,118,120}\), Si\(^{28}+ \)Mo\(^{90,96}\), Si\(^{28}+\)Mg\(^{24,26}\), Si\(^{28}+\)Ni\(^{58,64}\), Si\(^{28}+\)Zr\(^{90,94,96}\), S\(^{32}+\)Zr\(^{90,96}\), S\(^{36}+ \)Pb\(^{204,206,208,210}\), Ar\(^{40}+\)Hf\(^{176,178,180}\) in the framework of CC calculations (CCFULL, NRV) and Wong’s formula. Fusion cross sections were analyzed in detail by CC calculations considering \({2^+}\) and \({3^-}\) excitation modes for the projectile and the target. The calculated cross-section results were compared with the experimental data. The calculations were found to produce reliable data compared to experimental data. Fusion barrier distributions \((D_{\mathrm {fus}})\) for all reactions have been investigated below and above the Coulomb barrier using the coupled-channel method with CCFULL, NRV codes and second derivative of Wong’s formula. The harmony among these calculations was examined and it was determined that the models were in harmony with each other.

abstract

In this paper, we study analytically and numerically the solitary wave transition from low to high energy in localization, the relation between energy and velocity, propagation and scattering property in the Fermi–Pasta–Ulam lattice . When the energy of solitary wave increases to the threshold, the properties transform such as the width of solitary wave, the fluctuation of kinetic energy, the scattering effect after the head-on collision of two solitary waves, and the energy fluctuation after the scattering of a solitary wave and a discrete breather. The transition could help to understand the different chaotic dynamics of the Fermi–Pasta–Ulam lattice at low- and high-energy density.

abstract

With the advent of the big data era, the ever-increasing accumulated financial data plays a significant role in people’s daily life. The ensemble methods are the most efficient and accurate methods for analyzing the essential phenomenon of the financial data. In this paper, a novel approach, which incorporates the complementary ensemble empirical mode decomposition (CEEMD) and semi-parametric linear non-Gaussian analysis (Spline-LCA), i.e. , CEEMD-Spline-LCA, is proposed to analyze the nonlinear and non-stationary financial time series. The proposed CEEMD-Spline-LCA method consists of three steps: In the first place, the CEEMD is applied to obtain Intrinsic Mode Functions (IMFs) of the analyzed data. Next, according to the contribution coefficients between the IMFs and the financial time series, IMFs are reorganized to get a new collection of the IMFs (NIMFs) for the subsequent explanation of influence factors of financial time series. Furthermore, Spline-LCA is utilized to separate the NIMFs into independent components (ICs), reflecting the different inner driving factors. Concentrating the established model on the stock price (the Dow Jones Industrial Average, the oldest stock index generally used), by comparing with real economic indicators, we find that the obtained ICs are close approximation of the exchange rate (U.S. Dollar Index), interest rate (Fed funds rate), GDP growth rate, CPI and major events, respectively.