scholarly journals Note: Boundary homogenization for a circle with periodic absorbing arcs. Exact expression for the effective trapping rate

2015 ◽  
Vol 143 (22) ◽  
pp. 226101 ◽  
Author(s):  
Alexei T. Skvortsov ◽  
Alexander M. Berezhkovskii ◽  
Leonardo Dagdug
Keyword(s):  
Exact Expression ◽  
Trapping Rate

Rate Constants, Reactive Flux

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Correlation Function ◽  
Rate Constant ◽  
Cross Sections ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Exact Expression ◽  
Reaction Cross ◽  
Dividing Surface ◽  
Definition Of ◽  
Reactive Flux

This chapter discusses a direct approach to the calculation of the rate constant k(T) that bypasses the detailed state-to-state reaction cross-sections. The method is based on the calculation of the reactive flux across a dividing surface on the potential energy surface. Versions based on classical as well as quantum mechanics are described. The classical version and its relation to Wigner’s variational theorem and recrossings of the dividing surface is discussed. Neglecting recrossings, an approximate result based on the calculation of the classical one-way flux from reactants to products is considered. Recrossings can subsequently be included via a transmission coefficient. An alternative exact expression is formulated based on a canonical average of the flux time-correlation function. It concludes with the quantum mechanical definition of the flux operator and the derivation of a relation between the rate constant and a flux correlation function.

scholarly journals scSorter: assigning cells to known cell types according to marker genes

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Hongyu Guo ◽  
Jun Li
Keyword(s):  
Real Data ◽  
Cell Types ◽  
Exact Expression ◽  
Marker Genes ◽  
Specific Marker ◽  
Sequencing Data ◽  
Reference Dataset ◽  
Over Expression ◽  
Higher Power ◽  
Cell Type Specific

AbstractOn single-cell RNA-sequencing data, we consider the problem of assigning cells to known cell types, assuming that the identities of cell-type-specific marker genes are given but their exact expression levels are unavailable, that is, without using a reference dataset. Based on an observation that the expected over-expression of marker genes is often absent in a nonnegligible proportion of cells, we develop a method called scSorter. scSorter allows marker genes to express at a low level and borrows information from the expression of non-marker genes. On both simulated and real data, scSorter shows much higher power compared to existing methods.

scholarly journals A Head Formulation for the Steady-State Analysis of Water Distribution Systems Using an Explicit and Exact Expression of the Colebrook–White Equation

Water ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1163
Author(s):  
Mengning Qiu ◽  
Avi Ostfeld
Keyword(s):  
Steady State ◽  
Distribution System ◽  
Distribution Systems ◽  
Water Distribution ◽  
Solution Method ◽  
Water Distribution System ◽  
Academic Research ◽  
Exact Expression ◽  
Contamination Source

Steady-state demand-driven water distribution system (WDS) solution is the bedrock for much research conducted in the field related to WDSs. WDSs are modeled using the Darcy–Weisbach equation with the Swamee–Jain equation. However, the Swamee–Jain equation approximates the Colebrook–White equation, errors of which are within 1% for ϵ/D∈[10−6,10−2] and Re∈[5000,108]. A formulation is presented for the solution of WDSs using the Colebrook–White equation. The correctness and efficacy of the head formulation have been demonstrated by applying it to six WDSs with the number of pipes ranges from 454 to 157,044 and the number of nodes ranges from 443 to 150,630. The addition of a physically and fundamentally more accurate WDS solution method can improve the quality of the results achieved in both academic research and industrial application, such as contamination source identification, water hammer analysis, WDS network calibration, sensor placement, and least-cost design and operation of WDSs.

scholarly journals An exact expression of positive periodic solution for a first-order singular equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yun Xin ◽  
Xiaoxiao Cui ◽  
Jie Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Lower Bounds ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Positive Periodic Solution ◽  
Exact Expression ◽  
Upper And Lower Bounds ◽  
Singular Equation ◽  
First Order

Abstract The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

scholarly journals Flume Experiments Evaluating the Efficacy of a Large Wood Trap Featuring Horizontal Rods

Water ◽  
2021 ◽  
Vol 13 (13) ◽  
pp. 1837
Author(s):  
Mayuko Furukawa ◽  
Daizo Tsutsumi ◽  
Hironori Muto ◽  
Taro Uchida ◽  
Takuro Suzuki ◽  
...  
Keyword(s):  
Relative Length ◽  
Large Wood ◽  
Basic Information ◽  
Trapping Rate ◽  
Supply Rate ◽  
Flume Experiments ◽  
Water And Sediment ◽  
Constant Rate

Large wood (LW) disasters, which often accompany sediment-related disasters, occur worldwide. To prevent and mitigate such disasters, we developed a unique LW trap featuring horizontal rods aligned with the flow. When LW enters the trap, it is scooped up by the rods and thus separated from water and sediment. We explored trapping efficacy using a flume of slope 0.087. Water circulated at a constant rate of 1.8 L/s, LW was added to the flow, and the trapping rates were measured. We focused on the relative wood length (Lw) with respect to the horizontal rod spacing (Sr), the number of LW units supplied, and the supply rate. A longer relative length (Lw/Sr) of LW was associated with a higher trapping rate. The trapping rate was also high when the LW number or supply rate was high. The critical Lw/Sr value was 1.5; below this value, LW was not trapped. This study yields the basic information needed to design traps featuring horizontal rods to mitigate LW-related disasters.

The dimension of self-affine fractals II

1992 ◽  
Vol 111 (1) ◽  
pp. 169-179 ◽  
Author(s):  
K. J. Falconer
Keyword(s):  
Exact Expression ◽  
Singular Value ◽  
Compact Set ◽  
Value Functions ◽  
Affine Transformations ◽  
Box Counting ◽  
Box Counting Dimension ◽  
Almost All

AbstractA family {S1, ,Sk} of contracting affine transformations on Rn defines a unique non-empty compact set F satisfying . We obtain estimates for the Hausdorff and box-counting dimensions of such sets, and in particular derive an exact expression for the box-counting dimension in certain cases. These estimates are given in terms of the singular value functions of affine transformations associated with the Si. This paper is a sequel to 4, which presented a formula for the dimensions that was valid in almost all cases.

Stochastic resonance for a fractional oscillator with random trichotomous mass and random trichotomous frequency

2017 ◽  
Vol 31 (30) ◽  
pp. 1750231 ◽  
Author(s):  
Lifeng Lin ◽  
Huiqi Wang ◽  
Suchuan Zhong
Keyword(s):  
Stochastic Resonance ◽  
Exact Expression ◽  
Order Moment ◽  
Periodic Signal ◽  
Transformation Technique ◽  
First Order ◽  
Fractional Oscillator ◽  
Trichotomous Noise ◽  
Output Amplitude ◽  
Fractional System

The stochastic resonance (SR) phenomena of a linear fractional oscillator with random trichotomous mass and random trichotomous frequency are investigate in this paper. By using the Shapiro–Loginov formula and the Laplace transformation technique, the exact expression of the first-order moment of the system’s steady response is derived. The numerical results demonstrate that the evolution of the output amplitude is nonmonotonic with frequency of the periodic signal, noise parameters and fractional order. The generalized SR (GSR) phenomena, including single GSR (SGSR) and doubly GSR (DGSR), and trebly GSR (TGSR), are detected in this fractional system. Then, the GSR regions in the [Formula: see text] plane are determined through numerical calculations. In addition, the interaction effect of the multiplicative trichotomous noise and memory can diversify the stochastic multiresonance (SMR) phenomena, and induce reverse-resonance phenomena.

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