Statistical properties of ideal photons in a two-dimensional dye-filled spherical cap cavity

Within the framework of quantum statistical mechanics,we have proposed an exact analytical solution to the problemof Bose-Einstein condensation(BEC)of harmonically trapped two-dimensional(2D)ideal photons.We utilize this analyticalsolution to investigate the statistical properties of ideal photons in a 2D dye-filled spherical cap cavity.The resultsof numerical calculation of the analytical solution agree completely with the foregoing experimental results in the BEC ofharmonically trapped 2D ideal photons.The analytical expressions of the critical temperature and the condensate fractionare derived in the thermodynamic limit.It is found that the 2D critical photon number is larger than the one-dimensional(1D)critical photon number by two orders of magnitude.The spectral radiance of a 2D spherical cap cavity has a sharppeak at the frequency of the cavity cutoff when the photon number exceeds the critical value determined by a temperature.

Swarming Computational Efficiency to Solve a Novel Third-Order Delay Differential Emden-Fowler System

The purpose of this research is to construct an integrated neuro swarming scheme using the procedures of the artificial neural networks(ANNs)with the use of global search particle swarm optimization(PSO)along with the competent local search interior-point programming(IPP)called as ANN-PSOIPP.The proposed computational scheme is implemented for the numerical simulations of the third order nonlinear delay differential Emden-Fowler model(TON-DD-EFM).The TON-DD-EFM is based on two types along with the particulars of shape factor,delayed terms,and singular points.A merit function is performed using the optimization of PSOIPP to find the solutions to the TON-DD-EFM.The effectiveness of the ANN-PSOIPP is certified through the comparison with the exact results for solving four examples of the TON-DD-EFM.The scheme’s efficiency is observed by performing the absolute error in suitable measures found around 10−04 to 10−07.Furthermore,the statistical-based assessments for 100 trials are provided to compute the accuracy,stability,and constancy of the ANNPSOIPP for solving the TON-DD-EFM.

Quantitative Comparison of Predictabilities of Warm and Cold Events Using the Backward Nonlinear Local Lyapunov Exponent Method

The backward nonlinear local Lyapunov exponent method(BNLLE)is applied to quantify the predictability of warm and cold events in the Lorenz model.Results show that the maximum prediction lead times of warm and cold events present obvious layered structures in phase space.The maximum prediction lead times of each warm(cold)event on individual circles concentric with the distribution of warm(cold)regime events are roughly the same,whereas the maximum prediction lead time of events on other circles are different.Statistical results show that warm events are more predictable than cold events.