Step-size selection for split-step based nonlinear compensation with coherent detection in 112-Gb/s 16-QAM transmission

Non-uniform step-size distribution is implemented for split-step based nonlinear compensation in single- channel 112-Gb/s 16 quadrature amplitude modulation (QAM) transmission. Numerical simulations of the system including a 20×80 km uncompensated link are performed using logarithmic step size distribution to compensate signal distortions. 50% of reduction in number of steps with respect to using constant step sizes is observed. The performance is further improved by optimizing nonlinear calculating position (NLCP) in case of using constant step sizes while NLCP optimization becomes unnecessary when using logarithmic step sizes, which reduces the computational effort due to uniformly distributed nonlinear phase for all successive steps.     

A FINITE DIFFERENCE SCHEME FOR THE GENERALIZED NONLINEAR SCHRDINGER EQUATION WITH VARIABLE COEFFICIENTS

1. Generalized Nonlinear Schrsdinger EquationThe Schr6dinger equation has been extensively used in physics research, particularlyin the modeling of nonlinear dispersion waves [8]. Numerical methods for solving theSchr6dinger equation have been discussed in the literature. In this article, we considera generalized nonlinear Schr6dinger equation with variable coefficientsi: ~ g(A(x)Z) iF(t)u B(x) lulp~' u = 0, iZ ~ ~l, P > 1, (1)where u(x, 0) ~ of (x). The coefficients A(x), F(t) and, …     

A finite difference scheme for solving the heat transport equation at the microscale

Heat transport at the microscale is of vital importance in microtechnology applications. In this study, we develop a finite difference scheme of the Crank‐Nicholson type by introducing an intermediate function for the heat transport equation at the microscale. It is shown by the discrete energy method that the scheme is unconditionally stable. Numerical results show that the solution is accurate. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 697–708, 1999     

Leveraging Torsional and Steric Strains: A Pre-macrocyclization Strategy Enables Conformation-Specific Fullerene Binding in m-Cyclophanes

Though the chemistry of resorcinarenes is half a century old, the conformationally-locked resorcinarene crowns are generally constructed using hydrogen bonds or covalent tethers. Often, covalent tethering involves extra post-macrocyclization steps involving upper-rim functionalities. We have leveraged the torsional and steric strains through α-substituents of the lower-rim C-alkyl chains and accomplished conformationally-rigid fluorescent m-cyclophane deep-crowns in a predetermined way. The strategy offers a pre-macrocyclization route conserving upper-rim functionalities, an aspect overlooked in resorcinarene chemistry. X-ray structural and computational analyses unveil the cause for conformational rigidity in m-cyclophanes due to α-branching in C-alkyls (linear vs. α-/β-branched). The conformationally-locked fluorescent deep-crown with a preorganized cavity captures hydrophobic spherical guest C₆₀ in both solution and solid states specifically, when compared to conformationally-dynamic boats, enabling conformation-specific binding.     

Solution to the Riemann problem for drift-flux model with modified Chaplygin two-phase flows

In this paper, we concern about the Riemann problem for compressible no-slip drift-flux model which represents a system of quasi-linear partial differential equations derived by averaging the mass and momentum conservation laws with modified Chaplygin two-phase flows. We obtain the exact solution of Riemann problem by elaborately analyzing characteristic fields and discuss the elementary waves namely, shock wave, rarefaction wave and contact discontinuity wave. By employing the equality of pressure and velocity across the middle characteristic field, two nonlinear algebraic equations with two unknowns as gas density ahead and behind the middle wave are formed. The Newton–Raphson method of two variables is applied to find the unknowns with a series of initial data from the literature. Finally, the exact solution for the physical quantities such as gas density, liquid density, velocity, and pressure are illustrated graphically.