Transport of Brownian particles confined to a weakly corrugated channel

We investigate the average velocity of Brownian particles driven by a constant external force when constrained to move in two-dimensional, weakly-corrugated channels. We consider both the geometric confinement of the particles between solid walls as well as the soft confinement induced by a periodic potential. Using perturbation methods we show that the leading order correction to the marginal probability distribution of particles in the case of soft confinement is equal to that obtained in the case of geometric confinement, provided that the (configuration) integral over the cross-section of the confining potential is equal to the width of the solid channel. We then calculate the probability distribution and average velocity in the case of a sinusoidal variation in the width of the channels. The reduction on the average velocity is larger in the case of soft channels at small P\'eclet numbers and for relatively narrow channels and the opposite is true at large P\'eclet numbers and for wide channels. In the limit of large P\'eclet numbers the convergence to bulk velocity is faster in the case of soft channels. The leading order correction to the average velocity and marginal probability distribution agree well with Brownian Dynamics simulations for the two types of confinement and over a wide range of P\'eclet numbers

When are two Dedekind sums equal?

A natural question about Dedekind sums is to find conditions on the integers $a_1, a_2$, and $b$ such that $s(a_1,b) = s(a_2, b)$. We prove that if the former equality holds then $b \ | \ (a_1a_2-1)(a_1-a_2)$. Surprisingly, to the best of our knowledge such statements have not appeared in the literature. A similar theorem is proved for the more general Dedekind-Rademacher sums as well, namely that for any fixed non-negative integer $n$, a positive integer modulus $b$, and two integers $a_1$ and $a_2$ that are relatively prime to $b$, the hypothesis $r_n (a_1,b)= r_n (a_2,b)$ implies that $b \ | \ (6n^2+1-a_1a_2)(a_2-a_1)$.Comment: 6 page

语言分类系统、真值间隔和不可通约性 — 对库恩关于不可通约性的分类学解释之重建

摘要：通常所接受对库恩有关不可通约性的分类学解释的理解建立在不可译性概念之上，因而是相当不完善的。为了弥补此不足，本文在分类之逻辑语义理论 (a logical-semantic theory of taxonomy)、真值语义理论 (a semantic theory of truth-value)，以及跨语言交流的真值条件理论 (a truth-value conditional theory of cross-language communication) 之基础上，对库恩有关不可通约性的分类学解释进行了重建。根据这种重建，如果两个科学语言具有不相匹配的分类结构，则当一科学语言的核心语句在其所属语境中具有真值、而在另一科学语言之语境中考虑缺乏真值时，这两种科学语言乃不可通约。通过这种重建，库恩对于不可通约性的成熟解释并非基于保真 (truth-preserving) 可译性或不可译性的概念，而是基于保留真值状态 (truth-value-preserving) 的跨语言交流概念之上。这种重建使得库恩有关不可通约性的解释更具坚实的理论基础、也在概念上更加完整。

Linear Algebra with Applications : An adaptation for MAT223 UTM

1. System of Linear Equations2. Matrix Algebra3. Determinants and Diagonalization4. Vector Geometry5. Vector SpaceThis open textbook is an adaptation of Linear Algebra with Applications by W. Keith Nicholson. The original book can be found and downloaded from Lyryx.com. Five topics are covered here: system of linear equations, matrix algebra, determinants and diagonalization, vector geometry and vector space. It's suitable for beginners who are interested in learning linear algebra. Readers will have the opportunity to work through H5P elements embedded in every chapter to check their understanding of core concepts on their own. Reader's note: Xinli Wang left UTM in 2020 August so this book no longer reflects MAT133 accurately. Readers are welcome to use it as an additional resource for learning linear algebra

The effect of inhibiting glycinamide ribonucleotide formyl transferase on the development of neural tube in mice

mRNA gel picture. (TIF 878 kb

Experimental and Theoretical Study on the OH-Reaction Kinetics and Photochemistry of Acetyl Fluoride (CH3C(O)F), an Atmospheric Degradation Intermediate of HFC-161 (C2H5F)

The direct reaction kinetic method of low pressure fast discharge flow (DF) with resonance fluorescence monitoring of OH (RF) has been applied to determine rate coefficients for the overall reactions OH + C2H5F (EtF) (1) and OH + CH3C(O)F (AcF) (2). Acetyl fluoride reacts slowly with the hydroxyl radical, the rate coefficient at laboratory temperature is k(2)(300 K) = (0.74 +/- 0.05) x 10(-14) cm(3) molecule(-1) s(-1) (given with 2 sigma statistical uncertainty). The temperature dependence of the reaction does not obey the Arrhenius law and it is described well by the two-exponential rate expression of k(2)(300-410 K) = 3.60 x 10(-3) exp(-10500/T) + 1.56 x 10(-13) exp(-910/T) cm(3) molecule(-1) s(-1). The rate coefficient of k(1) = (1.90 +/- 0.19) x 10(-13) cm(3) molecule(-1) s(-1) has been determined for the EtF-reaction at room temperature (T = 298 K). Microscopic mechanisms for the OH + CH3C(O)F reaction have also been studied theoretically using the ab initio CBS-QB3 and G4 methods. Variational transition state theory was employed to obtain rate coefficients for the OH + CH3C(O)F reaction as a function of temperature on the basis of the ab initio data. The calculated rate coefficients are in good agreement with the experimental data. It is revealed that the reaction takes place predominantly via the indirect H-abstraction mechanism involving H-bonded prereactive complexes and forming the nascent products of H2O and the CH2CFO radical. The non-Arrhenius behavior of the rate coefficient at temperatures below 500 K is ascribed to the significant tunneling effect of the in-the-plane H-abstraction dynamic bottleneck. The production of FC(O)OH + CH3 via the addition/elimination mechanism is hardly competitive due to the significant barriers along the reaction routes. Photochemical experiments of AcF were performed at 248 nm by using exciplex lasers. The total photodissociation quantum yield for CH3C(O)F has been found significantly less than unity; among the primary photochemical processes, C-C bond cleavage is by far dominating compared with CO-elimination. The absorption spectrum of AcF has also been determined by displaying a strong blue shift compared with the spectra of aliphatic carbonyls. Consequences of the results on atmospheric chemistry have been discussed

流動性の連動性に関する論文三編

要約のみTohoku University金﨑芳輔課

On the rolling motion of viscous fluid on a rigid surface

This thesis considers two closely related problems. First, the influence of insoluble surfactant at a moving contact line is considered. This work is mostly motivated by the air entrainment during the coating process where there is a three-phase contact point (e.g., air, liquid and solid). For moving contact line problems, when the fluid is assumed to be an incompressible Newtonian fluid and a no-slip boundary condition is enforced at the solid boundary, the non-integrable stress singularity arises at the contact line, which is physically unrealistic. The contact angle of 180° is considered as a special case in which the singularity is absent. The previous work showed that there exists a non-singular local solution in the vicinity of the contact line for any capillary number. A simplified asymptotic model is used here to find a global solution with a 180° contact angle. Also the effects of insoluble surfactant are checked and numerical results show there exists a critical capillary number above which there is no steady state solution. The second problem is viscous droplets rolling down a non-wettable inclined plane. The recent experiments show that the contact angle is very large (close to 180°) when a droplet rolls on a super-hydrophobic surface. The biharmonic boundary element method (BBEM) is used to implement numerical simulations of rolling motion. The numerical results agree well with the experimental results and theoretical prediction. Numerical evidence is also found that the stress singularity at the contact line is alleviated with a 180° contact angle. For droplets with insoluble surfactant on the surface, the finite volume method is used to track the evolution of surfactant. It shows that the rolling motion is retarded because of Marangoni force due to nonuniform concentration distribution of surfactant

Transport properties of Brownian particles confined to a narrow channel by a periodic potential

We investigate the transport of Brownian particles in a two-dimensional potential under the action of a uniform external force. The potential is periodic in one direction and confines the particle to a narrow channel of varying cross-section in the other direction. We apply the standard long-wave asymptotic analysis in the narrow dimension and show that the leading order term is equivalent to that obtained previously from a direct extension of the Fick-Jacobs approximation. We also show that the confining potential has similar effects on the transport of Brownian particles to those induced by a solid channel. Finally, we compare the analytical results with Brownian dynamics simulations in the case of a sinusoidal variation of the width of the parabolic potential in the cross-section. We obtain excellent agreement for the marginal probability distribution, the average velocity of the Brownian particles and the asymptotic dispersion coefficient, over a wide range of Peclet numbers

Active snort rules and the needs for computing resources: Computing resources needed to activate different numbers of snort rules

This project was designed to discover the relationship between the number of enabled rules maintained by Snort and the amount of computing resources necessary to operate this intrusion detection system (IDS) as a sensor. A physical environment was set up to loosely simulate a network and an IDS sensor monitoring it. The experiment was conducted in five trials. A different number of Snort rules was enabled in each trial and the corresponding utilization of computing resources was measured. Remarkable variation and a clear trend of CPU usage were observed in the experiment