• Nuclear Engineering and Technology
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• v.55 no.6
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• pp.2305-2314
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• 2023

The governing equations of atmospheric dispersion most often taking the form of a second-order partial differential equation (PDE). Currently, typical computational codes for predicting atmospheric dispersion use the Gaussian plume model that is an analytic solution. A Gaussian model is simple and enables rapid simulations, but it can be difficult to apply to situations with complex model parameters. Recently, a method of solving PDEs using artificial neural networks called physics-informed neural network (PINN) has been proposed. The PINN assumes the latent (hidden) solution of a PDE as an arbitrary neural network model and approximates the solution by optimizing the model. Unlike a Gaussian model, the PINN is intuitive in that it does not require special assumptions and uses the original equation without modifications. In this paper, we describe an approach to atmospheric dispersion modeling using the PINN and show its applicability through simple case studies. The results are compared with analytic and fundamental numerical methods to assess the accuracy and other features. The proposed PINN approximates the solution with reasonable accuracy. Considering that its procedure is divided into training and prediction steps, the PINN also offers the advantage of rapid simulations once the training is over.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.3
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• pp.201-222
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• 2011

In the present work, the mathematical model of wire coating in a straight annular die is developed for unsteady second grade fluid in the form of partial differential equation. The Optimal Homotopy Asymptotic Method (OHAM) is applied for obtaining the solution of the model problem. This method provides us a suitable way to control the convergence of the series solution using the auxiliary constants which are optimally determined.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.899-911
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• 2018

In this paper, we consider the second-order nonlinear differential equation with the nonlocal boundary conditions. We first reformulate this boundary value problem as a fixed point problem for a Fredholm integral equation operator, and then present a result on the existence and uniqueness of the solution by using the contraction mapping theorem. Furthermore, we establish a sufficient condition on the functions ${\mu}$ and $h_i$, i = 1, 2 that guarantee a unique solution for this nonlocal problem in a Hilbert space. Also, accurate analytic solutions in series forms for this boundary value problems are obtained by the Adomian decomposition method (ADM).

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.223-240
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• 2020

The paper is concerned with periodic linear evolution equations of the form x"(t) = A(t)x(t)+f(t), where A(t) is a family of (unbounded) linear operators in a Banach space X, strongly and periodically depending on t, f is an almost (or asymptotic) almost periodic function. We study conditions for this equation to have almost periodic solutions on ℝ as well as to have asymptotic almost periodic solutions on ℝ⁺. We convert the second order equation under consideration into a first order equation to use the spectral theory of functions as well as recent methods of study. We obtain new conditions that are stated in terms of the spectrum of the monodromy operator associated with the first order equation and the frequencies of the forcing term f.

• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.175-190
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• 2007

By employing the Riccati transformation technique some new oscillation criteria for the second-order neutral delay dynamic equation $$(y(t)+r(t)y({\tau}(t)))^{{\Delta}{\Delta}}+p(t)y(\delta(t))=0$$, on a time scale $\mathbb{T}$ are established. Our results as a special case when $\mathbb{T}=\mathbb{R}$ and $\mathbb{T}=\mathbb{N}$ improve some well known oscillation criteria for second order neutral delay differential and difference equations, and when $\mathbb{T}=q^{\mathbb{N}}$, i.e., for second-order $q$-neutral difference equations our results are essentially new and can be applied on different types of time scales. Some examples are considered to illustrate the main results.

• The Korean Journal of Zoology
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• v.24 no.1
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• pp.1-7
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• 1981

1. A total of 969 flies were tested and 19 different inversions were found from the present samples collected three times at yearly intervals in an area. 2. Of the 19 polymorphisms, except for the six common paracentric types of cosmopolitan inversions, 13 were endemic. Among this latter group, one was X-chromosomal, 4 were on second chromosome and 8 on third chromosome. 3. Beside two overlapping inversions all the others were identified as single ones. And the inversion frequency on an average in every three samples tested was 38.9%. 4. The high distribution of the inversions apeared to the second chromosome suggests that a differential adaptive force may be present between the second and third chromosome.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.12
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• pp.3196-3207
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• 1993

A second moment turbulent closure for the turbulent heat flux near a wall is developed by modification of model constants in pressure interaction term as the variables of the turbulent Reynolds number using the universal properties of turbulent heat flux near the wall. The present model shows that model constant for the wall reflection term in pressure interaction is most important in modelling of the near wall heat flux. Fully developed pipe flows with constant wall heat flux are tested to validate the proposed model. In most of calculation region, the predicted turbulent properties agree better with the experimetal data than the results from standard algebraic heat flux model which use the uniform model constants.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.289-298
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• 2010

In this paper, we propose a second-order prediction/correction (SPC) domain decomposition method for solving one dimensional linear hyperbolic partial differential equation $u_{tt}+a(x,t)u_t+b(x,t)u=c(x,t)u_{xx}+{\int}(x,t)$. The method can be applied to variable coefficients problems and singular problems. Unconditional stability and error analysis of the method have been carried out. Numerical results support stability and efficiency of the method.

• The Korean Journal of Physiology and Pharmacology
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• v.14 no.3
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• pp.145-150
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• 2010

Adenosine (Ado) is an important mediator of the endogenous defense against ischemia-induced injury in the heart. The action of Ado is mediated by activation of G protein-gated inwardly rectifying $K^+$ (GIRK) channels. In turn, GIRK channels are inhibited by reducing phosphatidylinositol 4,5-bisphosphate ($PIP_2$) through Gq protein-coupled receptors (GqPCRs). We previously found that GIRK channels activated by acetylcholine, a muscarinic M2 acetylcholine receptor agonist, are inhibited by GqPCRs in a receptor-specific manner. However, it is not known whether GIRK channels activated by Ado signaling are also regulated by GqPCRs. Presently, this was investigated in mouse atrial myocytes using the patch clamp technique. GIRK channels were activated by $100\;{\mu}M$ Ado. When Ado was repetitively applied at intervals of 5~6 min, the amplitude of second Ado-activated GIRK currents ($I_{K(Ado)}$) was $88.3{\pm}3.7%$ of the first $I_{K(Ado)}$ in the control. Pretreatment of atrial myocytes with phenylephrine, endothelin-1, or bradykinin prior to a second application of Ado reduced the amplitude of the second $I_{K(Ado)}$ to $25.5{\pm}11.6%$, $30.5{\pm}5.6%$, and $96.0{\pm}2.7%$, respectively. The potency of $I_{K(Ado)}$ inhibition by GqPCRs was different with that observed in acetylcholine-activated GIRK currents ($I_{K(ACh)}$) (endothelin-1>phenylephrine>bradykinin). $I_{K(Ado)}$ was almost completely inhibited by $500\;{\mu}M$ of the $PIP_2$ scavenger neomycin, suggesting low $PIP_2$ affinity of $I_{K(Ado)}$. Taken together, these results suggest that the crosstalk between GqPCRs and the Ado-induced signaling pathway is receptor-specific. The differential change in $PIP_2$ affinity of GIRK channels activated by Ado and ACh may underlie, at least in part, their differential responses to GqPCR agonists.

• Bulletin of the Korean Chemical Society
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• v.30 no.3
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• pp.661-666
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• 2009

1-{2,4-Di-(2-hydroxyethoxy)phenyl}-2-(2-thienyl)ethene (5) was prepared and condensed with terephthaloyl chloride to yield polyester (6). Polymer 6 was reacted with tetracyanoethylene to give novel Y-type polyester (7) containing 1-(2,4-dioxyethoxy)phenyl-2-{5-(2,2,3-tricyanovinyl)-2-thienyl)}ethenyl groups as NLO-chromophores, which are parts the polymer backbones. Polymer 7 is soluble in common organic solvents such as acetone and N,N-dimethylformamide. It showed thermal stability up to 300 ${^{\circ}C}$ in thermogravimetric analysis with glasstransition temperature obtained from differential scanning calorimetry near 134 ${^{\circ}C}$. The second harmonic generation (SHG) coefficient ($d_33$) of poled polymer film at the 1560 nm fundamental wavelength was around 6.74 x $10^{-9}$ esu. The dipole alignment exhibited high thermal stability up to the glass-transition temperature ($Tg$), and there was no SHG decay below 135 ${^{\circ}C}$ because of the partial main-chain character of polymer structure, which is acceptable for NLO device applications.