• 대한수학회논문집
• /
• 제26권2호
• /
• pp.273-289
• /
• 2011

In this paper we dene the concept of a conditional generalized Fourier-Feynman transform on very general function space $C_{a,b}$[0, T]. We then establish the existence of the conditional generalized Fourier-Feynman transform for functionals in a Fresnel type class. We also obtain several results involving the conditional transform. Finally we present functionals to apply our results. The functionals arise naturally in Feynman integration theories and quantum mechanics.

• 대한수학회논문집
• /
• 제37권3호
• /
• pp.749-763
• /
• 2022

Let C[0, T] denote an analogue of Weiner space, the space of real-valued continuous on [0, T]. In this paper, we investigate the translation of time interval [0, T] defining the analogue of Winer space C[0, T]. As applications of the result, we derive various relationships between the analogue of Wiener space and its product spaces. Finally, we express the analogue of Wiener measures on C[0, T] as the analogue of Wiener measures on C[0, s] and C[s, T] with 0 < s < T.

• Kyungpook Mathematical Journal
• /
• 제64권2호
• /
• pp.219-233
• /
• 2024

In this paper, we study the generalized Fourier-Feynman transform (GFFT) for functions on the general Wiener space C_a,b[0, T]. We establish an explicit evaluation formula for the analytic GFFT of bounded cylinder functions on C_a,b[0, T]. We start by examining certain cylinder functions which belong in a Banach algebra of bounded functions on C_a,b[0, T]. We then obtain an explicit formula for the analytic GFFT of the bounded cylinder functions.

• 멤브레인
• /
• 제12권4호
• /
• pp.207-215
• /
• 2002

한정된 미세공간에서의 제한확산(hindered diffusion)은 멤브레인 기공(pore)에서 입자들의 운동에 의해 결정되는 여과 메카니즘을 매우 미세한 수준에서 이해하는데 중요한 현상이다. 구형(spherical) 콜로이드 입자에 비해 보다 복잡한 형태(conformation)인 고분자사슬 구조를 갖는 다가전해질(polyelectrolyte)의 제한확산 거동에는 다양한 인자들이 관련되어 있기 때문에, 이론 접근은 물론 실험적 접근도 한층 어려운 것이 사실이다. 본 연구에서는, 슬릿형 미세기공에 한정되어 있는 단일한 다가전해질(single polyelectrolyte)에 coarse-grained bead spring model과 먼거리(long-range) 정전상호작용(electrostatic interaction)인 Debye-Huckel potential을 적용하여 분자시뮬레이션 기법인 브라운 동력학 모사를 수행하였다. 기공과 다가전해질 사슬(Polyelectrolyte chain)의 주어진 크기에서, 용액의 전해질 이온농도가 감소함에 따른 사슬의 신장(extension)효과는 제한확산계수를 감소시켰고, 기공 벽면의 하전성은 제한확산계수를 더욱 감소시켰다. 이는, 다가전해질 사슬(polyelectrolyte chain)의 입체적 장애(steric hindrance)와 함께 정전반발력이 미세기공에서의 확산이동을 억제함을 의미한다.

• 물과 미래
• /
• 제27권3호
• /
• pp.115-121
• /
• 1994

하구수리계에 있어서 점착성류사의 운동은 응결과 응집(aggregation) 현상에 의해 크게 좌우되며, 이들 현상에 의하여 의결된 입자들의 크기, 모양, 강도는 그 퇴적율과 그리고 부유류사와 오염물질의 변동과정에 영향을 미친다. 본 연구에서는 Brownian 운동에 의해 지배되는 이동성 부유영역과 중력에 의해 지배되는 정체성 부유영역으로 분리하여 점착성입자들의 응집과 응결과정을 모의하였다. 이동성 부유영역에 있어서는 Smoluchowski 모형중 입자들의 무작위 회전을 이용한 최대연쇄 모형으로 응집물질의 사영들을 도출하였으며, 그 회전반경에 의해 사영들의 쪽거리 차원을 구하였다. 저에성 부유영역에서의 응집물질(Brownian 영역을 벗어나 침강하는 응집물질)는 비구형 입자들의 침강으로 간주되어진다. 최종 침강속도 차이로 이들 응집물들은 재차 충돌, 결합하여 보다 큰 응집 입자들을 형성하며, 이들 최종 응집입자들의 사영이 모의되어진다. 최대 Feret's 직경과 Minkowski's sausage logic 개념들을 이용하여 모의되어진 사영들의 둘레 길이에 대하여 쪽거리 차원들을 구하였다.

• 한국입자에어로졸학회지
• /
• 제11권2호
• /
• pp.29-36
• /
• 2015

The purpose of this research is to find out the collection property of nanoparticle in diffusion filter to know particle size dispersion of nanomaterial using inertial force and principle of Brownian diffusion motion. We used inertial filters which are two different type and diffusion filters made by various kinds of Wiremesh and the different pieces of filter to compare with particle size distribution using NaCl particles. Finally, We made a conclusion as follows : (1) the bigger available charging volume is and the larger specific surface area of inertial filter is, the better collection efficiency is. (2) The higher wire-mesh number of filter is, the more collection efficiency of small particle is increasing because the wire of the higher Wiremesh number filter is thinner and denser. (3) The more pieces of wire-mesh filter, the more collection efficiency is increasing because it makes the residence time longer.

• 한국정보통신학회논문지
• /
• 제23권4호
• /
• pp.416-422
• /
• 2019

본 논문은 절차적함수를 이용하여 실시간으로 3차원 구름을 모델링하고 렌더링하는 알고리즘을 제안한다. 구름 모델링은 절차적 노이즈 함수인 fbm(Fractional Brownian Motion)을 변형하여 사용하며, 이 값을 대기의 수증기 밀도 값으로 이용한다. 이 밀도 값은 파라미터로 주어진 3가지 구름의 형태를 위해 변형되며 렌더링단계의 입력 값으로 들어간다. 레이마칭(ray marching)기법을 이용한 렌더링 단계에서는 이 밀도 값을 이용하여 구름의 색상을 결정하며 이때 밀도에 따른 빛의 감소 및 산란현상은 물리적으로 계산된다. 대기모델로 렌더링 된 하늘 위에 제안한 알고리즘에 의해 구현된 구름들이 블랜딩되며, 이 때 바람의 방향에 따라 구름이 움직이도록 한다. 제안된 구름 생성 및 렌더링은 GLSL언어를 이용해서 GPU상에서 구현되었다.

• Bulletin of the Korean Chemical Society
• /
• 제19권10호
• /
• pp.1068-1072
• /
• 1998

We present results of molecular dynamic (MD) simulations for the segmental motion of liquid n-butane as the base case for a consistent study for conformational transition from one rotational isomeric state to another in long chains of liquid n-alkanes. The behavior of the hazard plots for n-butane obtained from our MD simulations are compared with that for n-butane of Brownian dynamics study. The MD results for the conformational transition of n-butane by a Poisson process form the total first passage times are different from those from the separate t-g and g-t first passage times. This poor agreement is probably due to the failure of the detailed balance between the fractions of trans and gauche. The enhancement of the transitions t-g and g-t at short time regions are also discussed.

• Bulletin of the Korean Chemical Society
• /
• 제19권11호
• /
• pp.1217-1221
• /
• 1998

We present results of molecular dynamic (MD) simulations for the segmental motion of liquid n-heptadecane in order to investigate conformational transitions from one rotational isomeric state to another. The behavior of the hazard plots for n-heptadecane obtained from our MD simulations are compared with that for polymer of Brownian dynamics (BD) study. The transition rate at the ending dihedrals of the n-heptadecane chain is much higher than that at the central dihedrals. In the study of correlation between transitions of neighboring dihedrals, the large value of c2 implies that some 30% of the transitions of the second neighbors can be regarded as following transitions two bonds away in a correlated fashion. Finally the analysis of multiple transitions and the number of times occurred in the initial 0.005 ns are discussed.

• 대한기계학회논문집B
• /
• 제26권2호
• /
• pp.227-237
• /
• 2002

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 electrostatic force on a particle in the simulation cell was considered as a sum of electrostatic forces from other particles in the original cell and its replicate cells. We assumed that the electric charges accumulated on an aggregate were located on its center of mass, and aggregates were only charged with pre-charged primary particles. The morphological shape of aggregates was described in terms of the fractal dimension. In the simulation, 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. In the bipolar charge state, the average sizes of aggregates were larger than that of the uncharged state in the early and middle stages of aggregation process, but were almost the same as the case of the uncharged state in the final stage. On the other hand, in the unipolar charge state, the average size of aggregates and the dispersion of particle volume decreased with the increasing of the charge quantities.