• Bulletin of the Korean Mathematical Society
• /
• v.58 no.5
• /
• pp.1109-1127
• /
• 2021

We study the long-term dynamics for a family of incompressible three-dimensional Leray-α-like models that employ the spectral fractional Laplacian operators. This family of equations interpolates between incompressible hyperviscous Navier-Stokes equations and the Leray-α model when varying two nonnegative parameters 𝜃₁ and 𝜃₂. We prove the existence of a finite-dimensional global attractor for the continuous semigroup associated to these models. We also show that an operator which projects the weak solution of Leray-α-like models into a finite-dimensional space is determining if it annihilates the difference of two "nearby" weak solutions asymptotically, and if it satisfies an approximation inequality.

• Bulletin of the Korean Chemical Society
• /
• v.17 no.2
• /
• pp.188-192
• /
• 1996

It is shown that the inversion of the undamped Bloch equation for an amplitude-modulated broadband π/2 pulse can be precisely treated as an inverse scattering problem for a Schrodinger equation on the positive semiaxis. The pulse envelope is closely related to the central potential and asymptotically the wave function takes the form of a regular solution of the radial Schrodinger equation for s-wave scattering. An integral equation, which allows the calculation of the pulse amplitude (the potential) from the phase shift of the asymptotic solution, is derived. An exact analytical inversion of the integral equation shows that the detuning-independent π/2 pulse amplitude is given by a delta function. The equation also provides a means to calculate numerically approximate π/2 pulses for broadband excitation.

• Journal of the Korean Mathematical Society
• /
• v.58 no.4
• /
• pp.873-894
• /
• 2021

In this paper, we consider the Gudnason model of 𝒩 = 2 supersymmetric field theory, where the gauge field dynamics is governed by two Chern-Simons terms. Recently, it was shown by Han et al. that for a prescribed configuration of vortex points, there exist at least two distinct solutions for the Gudnason model in a flat two-torus, where a sufficient condition was obtained for the existence. Furthermore, one of these solutions has the asymptotic behavior of topological type. In this paper, we prove that such doubly periodic topological solutions are uniquely determined by the location of their vortex points in a weak-coupling regime.

• Honam Mathematical Journal
• /
• v.45 no.3
• /
• pp.457-470
• /
• 2023

In this study, we set a boundary value problem (BVP) consisting of a discrete Sturm-Liouville equation with transmission condition and boundary conditions depending on generalized eigenvalue parameter. Discussing the Jost and scattering solutions of this BVP, we present scattering function and find some properties of this function. Furthermore, we obtain resolvent operator, continuous and discrete spectrum of this problem and we give an valuable asymptotic equation to get the properties of eigenvalues. Finally, we give an example to compare our results with other studies.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.1
• /
• pp.93-111
• /
• 2023

In this paper we study a nudging continuous data assimilation algorithm for the three-dimensional Leray-α model, where measurement errors are represented by stochastic noise. First, we show that the stochastic data assimilation equations are well-posed. Then we provide explicit conditions on the observation density (resolution) and the relaxation (nudging) parameter which guarantee explicit asymptotic bounds, as the time tends to infinity, on the error between the approximate solution and the actual solution which is corresponding to these measurements, in terms of the variance of the noise in the measurements.

• Journal of the Korean Society for Precision Engineering
• /
• v.14 no.2
• /
• pp.152-159
• /
• 1997

The asymptotic convergence of a coupled dynamic system, which is motivated from infinite dimensional adaptive systems, is investigated. The convergence analysis is formulated in abstract Banch spaces and is shown to applicable to a broad class of infinite dimensional systems including adaptive identification and adaptive control. Particularly it is shown that if a uniquely existing solution is p-th power integrable, then the solution converges to zero asymptotically. The persistence of excitation(PE) of a signal which arises in an infinite dimensional adaptive system is investigated. The PE property is not completely known yet for infinite dimensional adaptive systems, however it should be investigated in relation to spatial variable, boundary conditions as well as time variable.

• Journal of applied mathematics & informatics
• /
• v.40 no.3_4
• /
• pp.603-618
• /
• 2022

In this paper, a numerical solution of the generalized diffusion equation with a delay has been obtained by a numerical technique based on the Galerkin finite element method by applying the cubic B-spline basis functions. The time discretization process is carried out using the forward Euler method. The numerical scheme is required to preserve the delay-independent asymptotic stability with an additional restriction on time and spatial step sizes. Both the theoretical and computational rates of convergence of the numerical method have been examined and found to be in agreement. As it can be observed from the numerical results given in tables and graphs, the proposed method approximates the exact solution very well. The accuracy of the numerical scheme is confirmed by computing L₂ and L_∞ error norms.

• Journal of the Society of Naval Architects of Korea
• /
• v.45 no.5
• /
• pp.477-486
• /
• 2008

Numerical analysis for slamming impact phenomena has been carried out when 2-dimensional wedge shaped structure with finite deadrise angles enter the free surface by using a commertial CFD code, FLUENT. Fluid is assumed incompressible and entry speed of the structure is kept constant. Geo-reconstruct scheme (or PLIC-VOF scheme) is used for the tracking of the deforming free surface. User defined function of 6 degrees of freedom motion and moving dynamic mesh option are used for the expression of the downward motion of the structure and deforming of unstructured meshes adjacent to the structure. The magnitude and the location of impact pressure and the total drag force which is the summation of pressures distributed at the bottom of the structure are analyzed. Results of the analysis show good agreement with the results of similarity solution, asymptotic solution and the solution of BEM.

• Journal of the Korean Chemical Society
• /
• v.18 no.5
• /
• pp.307-319
• /
• 1974

The accuracy of the uniform WKB solution for a two-turning point problem is examined in comparison with the corresponding numerical solution. It is found that the uniform WKB solution is extremely accurate. Various Franck-Condon factors for a model system are calculated as an example of applications of such approximate wavefunction. The accuracy of the factors thus calculated is very good. By using the uniform WKB wavefunctions, we have examined the asymptotic limit of the Frank-Condon factors and derived the condition for the frequencies of the transitions, $E'_{n'J'}-U'_{eff}(r_s)=E"_{n"J"}-U"_{eff}(r_s),$, which was obtained by Mulliken using physical arguments.

• Nuclear Engineering and Technology
• /
• v.24 no.3
• /
• pp.228-235
• /
• 1992

Some soluble species may not be solubility-limited or congruent-released with the matrix species. For example, during the operation of the nuclear reactor, the fission products can be accumulated in the fuel-cladding gap, voids, and grain boundaries of the fuel rods. In the waste package for spent-fuel placed in a geologic repository, the high solubility species of these fission products accumulated in the“gap”, e.g. cesium or iodine are expected to dissolve rapidly when ground water penetrates fuel rods. The time and space dependent mass transport for high solubility nuclides in the gap is analyzed, and its numerical illustrations are demonstrated. The approximate solution that is valid for all times is developed, and validated by comparison with an asymptotic solution and the solution obtained by the numerical inversion of Laplace transform covering the entire time span.