Brownian motion of anisotropic particles in microgravity

심규락,정성근,( William V. Meyer ),( Ronald J. Sicker ),( Dan Brown ),이창수 한국공업화학회 2019 한국공업화학회 연구논문 초록집 Vol.2019 No.0

In the universe, Brownian motion is fascinating phenomena that give great impact in the field of science and engineering. On earth, it is experimentally difficult to observe original Brownian motion of anisotropic particle due to buoyancy-driven force and sedimentation. Their original 3-dimensional (3D) Brownian motion is replaced by quasi 2-dimensional (2D) motion at long time scale because the colloidal particles usually settle down in a liquid due to gravity. Here we report the observation of 3D rotational Brownian motion of anisotropic colloidal particle in International Space Station (ISS) with the Light microscopy module (LMM). We find that the hydrophobic surface enhance their 3D rotational Brownian motion. Our observation is the measurement of 3D rotational Brownian motion of an anisotropic colloidal particle in microgravity where one can connect the combined effects of shape with the amount of a hydrophobic surface present.

Optical Tracking of Three-Dimensional Brownian Motion of Nanoparticles

C. K. Choi,K. D. Kihm 한국가시화정보학회 2005 한국가시화정보학회지 Vol.3 No.1

Novel optical techniques are presented for three-dimensional tracking of nanoparticles; Optical Serial Sectioning Microscopy (OSSM) and Ratiometric Total Internal Reflection Fluorescent Microscopy (R-TIRFM). OSSM measures optically diffracted particle images, the so-called Point Spread Function (PSF), and determines the defocusing or line-of-sight location of the imaged particle measured from the focal plane. The line-of-sight Brownian motion detection using the OSSM technique is proposed in lieu of the more cumbersome two-dimensional Brownian motion tracking on the imaging plane as a potentially more effective tool to nonintrusively map the temperature fields for nanoparticle suspension fluids. On the other hand, R-TIRFM is presented to experimentally examine the classic theory on the near-wall hindered Brownian diffusive motion. An evanescent wave field from the total internal reflection of a 488-㎚ bandwidth of an argon-ion laser is used to provide a thin illumination field of an order of a few hundred nanometers from the wall. The experimental results show good agreement with the lateral hindrance theory, but show discrepancies from the normal hindrance theory. It is conjectured that the discrepancies can be attributed to the additional hindering effects, including electrostatic and electro-osmotic interactions between the negatively charged tracer particles and the glass surface.

Estimation of drift parameter and change point via Kalman-Bucy filter for linear systems with signal driven by a fractional Brownian motion and observation driven by a Brownian motion

Mahendra Nath Mishra,Bhagavatula Lakshmi Surya Prakasa Rao 대한수학회 2018 대한수학회지 Vol.55 No.5

We study the estimation of the drift parameter and the change point obtained through a Kalman-Bucy filter for linear systems with signal driven by a fractional Brownian motion and the observation driven by a Brownian motion.

ESTIMATION OF DRIFT PARAMETER AND CHANGE POINT VIA KALMAN-BUCY FILTER FOR LINEAR SYSTEMS WITH SIGNAL DRIVEN BY A FRACTIONAL BROWNIAN MOTION AND OBSERVATION DRIVEN BY A BROWNIAN MOTION

Mishra, Mahendra Nath,Rao, Bhagavatula Lakshmi Surya Prakasa Korean Mathematical Society 2018 대한수학회지 Vol.55 No.5

We study the estimation of the drift parameter and the change point obtained through a Kalman-Bucy filter for linear systems with signal driven by a fractional Brownian motion and the observation driven by a Brownian motion.

Application of GTH-like algorithm to Markov modulated Brownian motion with jumps

Hong, Sung-Chul,Ahn, Soohan The Korean Statistical Society 2021 Communications for statistical applications and me Vol.28 No.5

The Markov modulated Brownian motion is a substantial generalization of the classical Brownian Motion. On the other hand, the Markovian arrival process (MAP) is a point process whose family is dense for any stochastic point process and is used to approximate complex stochastic counting processes. In this paper, we consider a superposition of the Markov modulated Brownian motion (MMBM) and the Markovian arrival process of jumps which are distributed as the bilateral ph-type distribution, the class of which is also dense in the space of distribution functions defined on the whole real line. In the model, we assume that the inter-arrival times of the MAP depend on the underlying Markov process of the MMBM. One of the subjects of this paper is introducing how to obtain the first passage probabilities of the superposed process using a stochastic doubling algorithm designed for getting the minimal solution of a nonsymmetric algebraic Riccatti equation. The other is to provide eigenvalue and eigenvector results on the superposed process to make it possible to apply the GTH-like algorithm, which improves the accuracy of the doubling algorithm.

Global uniform boundary Harnack principle with explicit decay rate and its application

Kim, P.,Song, R.,Vondracek, Z. North-Holland Pub. Co ; Elsevier Science Ltd 2014 Stochastic processes and their applications Vol.124 No.1

In this paper, we consider a large class of subordinate Brownian motions X via subordinators with Laplace exponents which are complete Bernstein functions satisfying some mild scaling conditions at zero and at infinity. We first discuss how such conditions govern the behavior of the subordinator and the corresponding subordinate Brownian motion for both large and small time and space. Then we establish a global uniform boundary Harnack principle in (unbounded) open sets for the subordinate Brownian motion. When the open set satisfies the interior and exterior ball conditions with radius R>0, we get a global uniform boundary Harnack principle with explicit decay rate. Our boundary Harnack principle is global in the sense that it holds for all R>0 and the comparison constant does not depend on R, and it is uniform in the sense that it holds for all balls with radii r@?R and the comparison constant depends neither on D nor on r. As an application, we give sharp two-sided estimates for the transition densities and Green functions of such subordinate Brownian motions in the half-space.

Optical Tracking of Three-Dimensional Brownian Motion of Nanoparticles

Choi C. K.,Kihm K.D. The Korean Society of Visualization 2005 한국가시화정보학회지 Vol.3 No.1

Novel optical techniques are presented for three-dimensional tracking of nanoparticles; Optical Serial Sectioning Microscopy (OSSM) and Ratiometric Total Internal Reflection Fluorescent Microscopy (R-TIRFM). OSSM measures optically diffracted particle images, the so-called Point Spread Function (PSF), and dotermines the defocusing or line-of-sight location of the imaged particle measured from the focal plane. The line-of-sight Brownian motion detection using the OSSM technique is proposed in lieu of the more cumbersome two-dimensional Brownian motion tracking on the imaging plane as a potentially more effective tool to nonintrusively map the temperature fields for nanoparticle suspension fluids. On the other hand, R-TIRFM is presented to experimentally examine the classic theory on the near-wall hindered Brownian diffusive motion. An evanescent wave field from the total internal reflection of a 488-nm bandwidth of an argon-ion laser is used to provide a thin illumination field of an order of a few hundred nanometers from the wall. The experimental results show good agreement with the lateral hindrance theory, but show discrepancies from the normal hindrance theory. It is conjectured that the discrepancies can be attributed to the additional hindering effects, including electrostatic and electro-osmotic interactions between the negatively charged tracer particles and the glass surface.

Oscillation of harmonic functions for subordinate Brownian motion and its applications

Kim, P.,Lee, Y. North-Holland Pub. Co ; Elsevier Science Ltd 2013 Stochastic processes and their applications Vol.123 No.2

In this paper, we establish an oscillation estimate of nonnegative harmonic functions for a pure-jump subordinate Brownian motion. The infinitesimal generator of such subordinate Brownian motion is an integro-differential operator. As an application, we give a probabilistic proof of the following form of relative Fatou theorem for such subordinate Brownian motion X in a bounded κ-fat open set; if u is a positive harmonic function with respect to X in a bounded κ-fat open set D and h is a positive harmonic function in D vanishing on D<SUP>c</SUP>, then the non-tangential limit of u/h exists almost everywhere with respect to the Martin-representing measure of h.

단일 나노입자의 다중 물리량의 평가를 위한 입자 모션 트랙킹 알고리즘

박예은,강지윤,박민수,노효웅,박홍식 한국센서학회 2022 센서학회지 Vol.31 No.3

The physical properties of biomaterials are important for their isolation and separation from body fluids. In particular, the precise evaluationof the multi-physical properties of single biomolecules is essential in that the correlation between physical and biological properties of specific biomolecule. However, the majority of scientific equipment, can only determine specific-physical properties of single nanoparticles, making the evaluation of the multi-physical properties difficult. The improvement of analytical techniques for the evaluation of multi-physical properties is therefore required in various research fields. In this study, we developed a motion-tracking algorithm to evaluate the multi-physical properties of single-nanoparticles by analyzing their behavior. We observed the Brownian motion and electric-field-induced drift of fluorescent nanoparticles injected in a microfluidic chip with two electrodes using confocal microscopy. The proposed algorithm is able to determine the size of the nanoparticles by i) removing the background noise from images, ii) tracking the motion of nanoparticles using the circular-Hough transform, iii) extracting the mean squared displacement (MSD) of the tracked nanoparticles, and iv) applying the MSD to the Stokes-Einstein equation. We compared the evaluated size of the nanoparticles with the size measured by SEM. We also determined the zeta-potential and surface-charge density of the nanoparticles using the extracted electrophoretic velocity and the Helmholtz-Smoluchowski equation. The proposed motion-tracking algorithm could be employed in various fields related to biomaterial analysis, such as exosome analysis

Some Limit Theorems for Fractional Levy Brownian Motions on Rectangles in the Plane

Hwang, Kyo-Shin,Kang, Soon-Bok,Park, Yong-Kab,Jeon, Tae-Il,Oh, Ho-Seh The Korean Statistical Society 1999 Journal of the Korean Statistical Society Vol.28 No.1

In this paper we establish some limit theorems for a two-parameter fractional Levy Brownian motion on rectangles in the Euclidean plane via estimating upper bounds of large deviation probabilities on suprema of the two-parameter fractional Levy Brownian motion.