ARTICLE | doi:10.20944/preprints201611.0146.v1
Subject: Mathematics & Computer Science, Analysis Keywords: explicit form; inhomogeneous linear ordinary differential equation; derivative; Lerch transcendent; absolute monotonicity; complete monotonicity; Bernstein function; inequality; diagonal recurrence relation; Stirling numbers of the first kind; logarithmic function
Online: 29 November 2016 (08:00:53 CET)
In the paper, the authors present an explicit form for a family of inhomogeneous linear ordinary differential equations, find a more significant expression for all derivatives of a function related to the solution to the family of inhomogeneous linear ordinary differential equations in terms of the Lerch transcendent, establish an explicit formula for computing all derivatives of the solution to the family of inhomogeneous linear ordinary differential equations, acquire the absolute monotonicity, complete monotonicity, the Bernstein function property of several functions related to the solution to the family of inhomogeneous linear ordinary differential equations, discover a diagonal recurrence relation of the Stirling numbers of the first kind, and derive an inequality for bounding the logarithmic function.
ARTICLE | doi:10.20944/preprints202209.0478.v1
Subject: Physical Sciences, Optics Keywords: gain-switching; semiconductor laser; quantum-dot; homogeneous-broadening; inhomogeneous-broadening; pulse generation
Online: 30 September 2022 (08:02:06 CEST)
For the first time the gain switching properties of an InAs-InP (113)B quantum dot laser are examined theoretically in detail to generate shorter pulses with the application of a Gaussian pulse beam to the laser excited state. The multi population rate equations considering nonlinear gain are solved by the Runge –Kutta method. The numerical results demonstrated that as the homogeneous and the inhomogeneous broadening increase, the differential gain, the gain compression factor and the threshold current of excited state decrease, while threshold current of ground state increases. It was also observed that the contribution of the excited state to gain-switched output pulses depends on not only the value of the inhomogeneous broadening but also the magnitude of the applied current. Finally it was shown that without an optical beam, output pulse has long pulse width due to ground state emission, whereas with an optical beam, narrow pulses having high peak power owing to the excited state emission are generated even though at low currents.
Subject: Materials Science, Biomaterials Keywords: Local polymer structure; Monte Carlo bond fluctuation; time scales; inhomogeneous dynamics; complexity
Online: 22 June 2021 (09:26:19 CEST)
We report the results of the characterization of local Monte Carlo (MC) dynamics of an equilibrium bond fluctuation model polymer matrix (BFM), in time interval typical for MC simulations of non-linear optical phenomena in host-guest systems. The study contributes to the physical picture of the dynamical aspects of quasi-binary mosaic states characterized previously in the static regime. The polymer dynamics was studied at three temperatures (below, above and close to the glass transition), using time-dependent generalization of the static parameters which characterize local free volume and local mobility of the matrix. Those parameters play the central role in the kinetic MC model of host-guest systems. The analysis was done in terms of the probability distributions of instantaneous and time-averaged local parameters. The main result is the characterization of time scales characteristic of various local structural processes. Slowing down effects close to the glass transition are clearly marked. The approach yields an elegant geometric criterion for the glass transition temperature. A simplified quantitative physical picture of the dynamics of guest molecules dispersed in BFM matrix at low temperatures offers a starting point for stochastic modeling of host-guest systems.
ARTICLE | doi:10.20944/preprints202112.0369.v1
Subject: Physical Sciences, Nuclear & High Energy Physics Keywords: inhomogeneous phases; chiral imbalance; isospin imbalance; 2+1 dimensional field theories; Gross-Neveu model; mean-field
Online: 22 December 2021 (13:15:54 CET)
We study the μ-μ45-T phase diagram of the 2+1-dimensional Gross-Neveu model, where μ denotes the ordinary chemical potential, μ45 the chiral chemical potential and T the temperature. We use the mean-field approximation and two different lattice regularizations with naive chiral fermions. An inhomogeneous phase at finite lattice spacing is found for one of the two regularizations. Our results suggest that there is no inhomogeneous phase in the continuum limit. We show that a chiral chemical potential is equivalent to an isospin chemical potential. Thus, all results presented in this work can also be interpreted in the context of isospin imbalance.