arXiv subjects

Jae-Hun Jung

Publications and source records attributed to Jae-Hun Jung.

42 records · Page 3Linked to original sources

arXiv2013

Stable long-distance propagation and on-off switching of colliding soliton sequences with dissipative interaction

We study propagation and on-off switching of two colliding soliton sequences in the presence of second-order dispersion, Kerr nonlinearity, linear loss, cubic gain, and quintic loss. Employing a Lotka-Volterra (LV) model for dynamics of soliton amplitudes along with simulations with two perturbed coupled nonlinear Schrödinger (NLS) equations, we show that stable long-distance propagation can be achieved for a wide range of the gain-loss coefficients, including values that are outside of the perturbative regime. Furthermore, we demonstrate robust on-off and off-on switching of one of the sequences by an abrupt change in the ratio of cubic gain and quintic loss coefficients, and extend the results to pulse sequences with periodically alternating phases. Our study significantly strengthens the recently found relation between collision dynamics of sequences of NLS solitons and population dynamics in LV models, and indicates that the relation might be further extended to solitary waves of the cubic-quintic Ginzburg-Landau equation.

nlin.PS↗

arXiv2011

Efficient determination of critical parameters of nonlinear Schrödinger equation with point-like potential using generalized polynomial chaos methods

We consider the nonlinear Schrödinger equation with a point-like source term. The soliton interaction with such a singular potential yields a critical solution behavior. That is, for the given value of the potential strength and the soliton amplitude, there exists a critical velocity of the initial soliton solution, around which the solution is either trapped by or transmitted through the potential. In this paper, we propose an efficient method for finding such a critical velocity by using the generalized polynomial chaos method. For the proposed method, we assume that the soliton velocity is a random variable and expand the solution in the random space using the orthogonal polynomials. The proposed method finds the critical velocity accurately with spectral convergence. Thus the computational complexity is much reduced. Numerical results for the smaller and higher values of the potential strength confirm the spectral convergence of the proposed method.

math.NA↗

arXiv2011

Efficient determination of the critical parameters and the statistical quantities for Klein-Gordon and sine-Gordon equations with a singular potential using generalized polynomial chaos methods

We consider the Klein-Gordon and sine-Gordon type equations with a point-like potential, which describes the wave phenomenon in disordered media with a defect. The singular potential term yields a critical phenomenon--that is, the solution behavior around the critical parameter value bifurcates into two extreme cases. Pinpointing the critical value with arbitrary accuracy is even more challenging. In this work, we adopt the generalized polynomial chaos (gPC) method to determine the critical values and the mean solutions around such values. First, we consider the critical value associated with the strength of the singular potential for the Klein-Gordon equation. We expand the solution in the random variable associated with the parameter. The obtained partial differential equations are solved using the Chebyshev collocation method. Due to the existence of the singularity, the Gibbs phenomenon appears in the solution, yielding a slow convergence of the numerically computed critical value. To deal with the singularity, we adopt the consistent spectral collocation method. The gPC method, along with the consistent Chebyshev method, determines the critical value and the mean solution highly efficiently. We then consider the sine-Gordon equation, for which the critical value is associated with the initial velocity of the kink soliton solution. The critical behavior in this case is that the solution passes through (particle-pass), is trapped by (particle-capture), or is reflected by (particle-reflection) the singular potential if the initial velocity of the soliton solution is greater than, equal to, or less than the critical value, respectively. We use the gPC mean value rather than reconstructing the solution to find the critical parameter. Numerical results show that the critical value can be determined efficiently and accurately by using the proposed method.

math.NA↗

arXiv2011

A multi-domain hybrid method for head-on collision of black holes in particle limit

A hybrid method is developed based on the spectral and finite-difference methods for solving the inhomogeneous Zerilli equation in time-domain. The developed hybrid method decomposes the domain into the spectral and finite-difference domains. The singular source term is located in the spectral domain while the solution in the region without the singular term is approximated by the higher-order finite-difference method. The spectral domain is also split into multi-domains and the finite-difference domain is placed as the boundary domain. Due to the global nature of the spectral method, a multi-domain method composed of the spectral domains only does not yield the proper power-law decay unless the range of the computational domain is large. The finite-difference domain helps reduce boundary effects due to the truncation of the computational domain. The multi-domain approach with the finite-difference boundary domain method reduces the computational costs significantly and also yields the proper power-law decay. Stable and accurate interface conditions between the finite-difference and spectral domains and the spectral and spectral domains are derived. For the singular source term, we use both the Gaussian model with various values of full width at half maximum and a localized discrete $δ$-function. The discrete $δ$-function was generalized to adopt the Gauss-Lobatto collocation points of the spectral domain. The gravitational waveforms are measured. Numerical results show that the developed hybrid method accurately yields the quasi-normal modes and the power-law decay profile. The numerical results also show that the power-law decay profile is less sensitive to the shape of the regularized $δ$-function for the Gaussian model than expected. The Gaussian model also yields better results than the localized discrete $δ$-function.

physics.comp-ph↗

arXiv2009

A spectral collocation approximation for the radial-infall of a compact object into a Schwarzschild black hole

The inhomogeneous Zerilli equation is solved in time-domain numerically with the Chebyshev spectral collocation method to investigate a radial-infall of the point particle towards a Schwarzschild black hole. Singular source terms due to the point particle appear in the equation in the form of the Dirac $δ$-function and its derivative. For the approximation of singular source terms, we use the direct derivative projection method without any regularization. The gravitational waveforms are evaluated as a function of time. We compare the results of the spectral collocation method with those of the explicit second-order central-difference method. The numerical results show that the spectral collocation approximation with the direct projection method is accurate and converges rapidly when compared with the finite-difference method.

physics.comp-ph↗

arXiv2006

Instabilities in numerical loop quantum cosmology

In this article we perform von Neumann analysis of the difference equations that arise as a result of loop quantum gravity being applied to models of cosmology and black holes. In particular, we study the numerical stability of Bianchi I LRS (symmetric and non-symmetric constraint) and Schwarzschild interior (symmetric constraint) models, and find that there exist domains over which there are instabilities, generically. We also present explicit evolutions of wave-packets in these models and clearly demonstrate the presence of these instabilities.

gr-qc↗