• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.1021-1034
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• 2021

This paper deals with a nonlinear Langevin equation involving two fractional orders with three-point boundary conditions. Our aim is to find the existence of solutions for the proposed Langevin equation by using the Banach contraction mapping principle and the Krasnoselskii's fixed point theorem. Three examples are also given to show the significance of our results.

• Korean Journal of Optics and Photonics
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• v.14 no.1
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• pp.103-106
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• 2003

The microscopic quantum Langevin equations for two-level atom electric dipole systems are derived. starting from the microscopic interaction Hamiltonian of the systems. By averaging those microscopic equations over a macroscopic region, the macroscopic quantum Langevin equations are derived and the effect of local-field corrections on the two-level systems is investigated.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2000.05a
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• pp.163-163
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• 2000

• Proceedings of the Korea Water Resources Association Conference
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• 1996.05a
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• pp.553-558
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• 1996

• Journal of the Optical Society of Korea
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• v.1 no.2
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• pp.94-99
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• 1997

In this paper, we calculate the four coefficients for the quantum theory of multiwave mixing including a local-field correction resulting from dipole-dipole interactions. We make contact with the semiclassical calculations of probe absorption and four-wave-mixing coupling coefficients, and illustrate the effects of local field corrections on resonance-fluorescence and coupled-mode-fluorescence spectra. The method uses the hybrid quantum-Langevin-equation master-equation approach of An and Sargent.

• Bulletin of the Korean Chemical Society
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• v.27 no.10
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• pp.1659-1663
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• 2006

A many-body master equation is constructed by incorporating stochastic terms responsible for chemical reactions into the many-body Smoluchowski equation. Two forms of Langevin-type of memory equations describing the time evolution of dynamical variables under the influence of time-independent perturbation with an arbitrary intensity are derived. One form is convenient in obtaining the dynamics approaching the steady-state attained by the perturbation and the other in describing the fluctuation dynamics at the steady-state and consequently in obtaining the linear response of the system at the steady-state to time-dependent perturbation. In both cases, the kinetics of statistical averages of variables is found to be obtained by analyzing the dynamics of time-correlation functions of the variables.

• Korean Journal of Mathematics
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• v.8 no.2
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• pp.163-172
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• 2000

Let $\mathcal{S}^{\prime}(\mathbb{R})$ be the dual of the Schwartz spaces $\mathcal{S}(\mathbb{R})$), A be a self-adjoint operator in $L^2(\mathbb{R})$ and ${\Gamma}(A)^*$ be the adjoint operator of ${\Gamma}(A)$ which is the second quantization operator of A. It is proven that under a suitable condition on A there exists a nuclear subspace $\mathcal{S}$ of a fundamental space $\mathcal{S}_A$ of Hida's type on $\mathcal{S}^{\prime}(\mathbb{R})$) such that ${\Gamma}(A)\mathcal{S}{\subset}\mathcal{S}$ and $e^{-t{\Gamma}(A)}\mathcal{S}{\subset}\mathcal{S}$, which enables us to show that a stochastic differential equation: $$dX(t)=dW(t)-{\Gamma}(A)^*X(t)dt$$, arising from the central limit theorem for spatially extended neurons has an unique solution on the dual space $\mathcal{S}^{\prime}$ of $\mathcal{S}$.

• Proceedings of the KSME Conference
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• 2001.06d
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• pp.605-611
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• 2001

A numerical technique for simulating the aggregation of charged particles was presented with a Brownian dynamic simulation in the free molecular regime. The Langevin equation was used for tracking each particle making up an aggregate. A periodic boundary condition was used for calculation of the aggregation process in each cell with 500 primary particles of 16 nm in diameter. We considered the thermal force and the electrostatic force for the calculation of the particle motion. The morphological shape of aggregates was described in terms of the fractal dimension. The fractal dimension for the uncharged aggregate was $D_{f}=1.761$. The fractal dimension changed slightly for the various amounts of bipolar charge. However, in case of unipolar charge, the fractal dimension decreased from 1.641 to 1.537 with the increase of the average number of charges on the particles from 0.2 to 0.3 in initial states.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.33 no.10
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• pp.811-819
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• 2009

In the present study, deposition of discrete and small particles on a filter fiber was simulated by stochastic method. Trajectory of each particle was numerically solved by Langevin equation. And Lattice Boltzmann method (LBM) was used to solve flow field around the filter collector for considering complex shape of deposit layer. Interaction between the flow field and the deposit layer was obtained from a converged solution from an inner-loop calculation. Simulation method is properly validated with filtration theory and collection efficiency due to different filtration parameters are examined and discussed. Morphology of deposit layer and its evolution was visualized in terms of the particle size. The particle loaded effect on collection efficiency was also discussed.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1922-1927
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• 2008

In the present study, deposition of discrete and small particles, which diameter is less than $1{\mu}m$, on a filter element was simulated by stochastic method. Trajectory of each particle was numerically solved by Langevin equation and Brownian random motion was treated by Brownian dynamics. Lattice Boltzmann method (LBM) was used to solve flow field around the filter collector and deposit layer. Interaction between flow field and deposit layer was obtained from a converged solution from an inner-loop calculation. Simulation method is properly validated and collection efficiency due to different filtration parameters are examined and discussed. Morphology of deposit layer and its evolution was visualized in terms of the particle size. The particle loaded effect on collection efficiency was also discussed.