Big Problem-Small Solution: Nanotechnology-Based Sealing Fluid

2018 ◽  
Author(s):  
Larry Todd ◽  
Matthew Cleveland ◽  
Kevin Docherty ◽  
James Reid ◽  
Kenneth Cowan ◽  
...  
Keyword(s):  
Small Solution

scholarly journals The Concepts of Well-Posedness and Stability in Different Function Spaces for the 1D Linearized Euler Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Stefan Balint ◽  
Agneta M. Balint
Keyword(s):  
Euler Equation ◽  
Function Space ◽  
Euler Equations ◽  
Small Perturbation ◽  
Function Spaces ◽  
Well Posedness ◽  
Small Solution ◽  
Null Solution ◽  
Linearized Euler Equations ◽  
The Stability

This paper considers the stability of constant solutions to the 1D Euler equation. The idea is to investigate the effect of different function spaces on the well-posedness and stability of the null solution of the 1D linearized Euler equations. It is shown that the mathematical tools and results depend on the meaning of the concepts “perturbation,” “small perturbation,” “solution of the propagation problem,” and “small solution, that is, solution close to zero,” which are specific for each function space.

scholarly journals Verifying a Solver for Linear Mixed Integer Arithmetic in Isabelle/HOL

2020 ◽  
pp. 233-250
Author(s):  
Ralph Bottesch ◽  
Max W. Haslbeck ◽  
Alban Reynaud ◽  
René Thiemann
Keyword(s):  
Linear Programming ◽  
Branch And Bound ◽  
Decision Procedure ◽  
Simplex Algorithm ◽  
Upper Bounds ◽  
Mixed Integer ◽  
Small Solution ◽  
Code Generator ◽  
Integer Arithmetic ◽  
Termination Proofs

AbstractWe implement a decision procedure for linear mixed integer arithmetic and formally verify its soundness in Isabelle/HOL. We further integrate this procedure into one application, namely into , a formally verified certifier to check untrusted termination proofs. This checking involves assertions of unsatisfiability of linear integer inequalities; previously, only a sufficient criterion for such checks was supported. To verify the soundness of the decision procedure, we first formalize the proof that every satisfiable set of linear integer inequalities also has a small solution, and give explicit upper bounds. To this end we mechanize several important theorems on linear programming, including statements on integrality and bounds. The procedure itself is then implemented as a branch-and-bound algorithm, and is available in several languages via Isabelle’s code generator. It internally relies upon an adapted version of an existing verified incremental simplex algorithm.

The Effects of Cathodic Reagent Concentration and Small Solution Volumes on the Corrosion of Copper in Dilute Nitric Acid Solutions

CORROSION ◽  
10.5006/2655 ◽  
2017 ◽  
Vol 74 (3) ◽  
pp. 326-336 ◽  
Author(s):  
J. Turnbull ◽  
R. Szukalo ◽  
M. Behazin ◽  
D. Hall ◽  
D. Zagidulin ◽  
...  
Keyword(s):  
Nitric Acid ◽  
Cross Sections ◽  
Focused Ion Beam ◽  
Ion Beam ◽  
Exposure Period ◽  
Geologic Repository ◽  
Small Solution ◽  
High Level Nuclear Waste ◽  
Nitrate And Nitrite ◽  
High Level

The exposure conditions experienced by copper-coated high-level nuclear waste containers in a deep geologic repository will evolve with time. An early exposure period involving the gamma irradiation of aerated humid vapor could lead to the formation of nitric acid condensed in limited volumes of water on the container surface. The evolution of the corrosion processes under these conditions have been studied using pH measurements in limited volumes of water containing various concentrations of nitric acid. The extent and morphology of corrosion was examined using scanning electron microscopy on surfaces and on focused ion beam cut cross sections. The composition of corrosion products was determined by energy dispersive x-ray analyses and Raman spectroscopy. In the absence of dissolved oxygen only minor corrosion was observed with the reduction of nitric acid inhibited by the formation of either chemisorbed nitrate and nitrite species or the formation of a thin cuprite (Cu2O) layer. When the solution was aerated, both oxygen and nitric acid acted as cathodic reagents. After extensive exposure periods corrosion was stifled by the formation of corrosion product deposits of Cu2O, CuO (tenorite), and Cu2NO3(OH)3 (rouaite).

scholarly journals A Full Automatic Device for Sampling Small Solution Volumes in Photometric Titration Procedure Based on Multicommuted Flow System

2007 ◽  
Vol 2007 ◽  
pp. 1-6
Author(s):  
Sivanildo S. Borges ◽  
Gláucia P. Vieira ◽  
Boaventura F. Reis
Keyword(s):  
Flow System ◽  
Sodium Hydroxide Solution ◽  
Glass Tube ◽  
Automatic Device ◽  
Vertical Position ◽  
Good Precision ◽  
Small Solution ◽  
Relative Standard ◽  
Photometric Titration ◽  
Solution Volume

In this work, an automatic device to deliver titrant solution into a titration chamber with the ability to determine the dispensed volume of solution, with good precision independent of both elapsed time and flow rate, is proposed. A glass tube maintained at the vertical position was employed as a container for the titrant solution. Electronic devices were coupled to the glass tube in order to control its filling with titrant solution, as well as the stepwise solution delivering into the titration chamber. The detection of the titration end point was performed employing a photometer designed using a green LED (λ= 545 nm) and a phototransistor. The titration flow system comprised three-way solenoid valves, which were assembled to allow that the steps comprising the solution container loading and the titration run were carried out automatically. The device for the solution volume determination was designed employing an infrared LED (λ= 930 nm) and a photodiode. When solution volume delivered from proposed device was within the range of 5 to 105μl, a linear relationship (R = 0.999) between the delivered volumes and the generated potential difference was achieved. The usefulness of the proposed device was proved performing photometric titration of hydrochloric acid solution with a standardized sodium hydroxide solution and using phenolphthalein as an external indicator. The achieved results presented relative standard deviation of 1.5%.

scholarly journals An Ultrahigh Sensitive Microwave Microfluidic System for Fast and Continuous Measurements of Liquid Solution Concentrations

Sensors ◽  
2021 ◽  
Vol 21 (17) ◽  
pp. 5816
Author(s):  
Piotr Słobodzian ◽  
Krzysztof Szostak ◽  
Katarzyna Skowronek ◽  
Laura Jasińska ◽  
Karol Malecha
Keyword(s):  
Low Cost ◽  
Calibration Procedure ◽  
Liquid Solution ◽  
Microfluidic System ◽  
Industrial Applications ◽  
Small Solution ◽  
Lab On Chip ◽  
Ultrahigh Sensitivity ◽  
Concentration Changes ◽  
Solution Intake

In this paper, we describe a low-cost microwave microfluidic system of ultrahigh sensitivity for detecting small changes in the concentration of polar solutions (liquid dielectrics) in the 2.4 GHz ISM band. Its principle of operation is based on microwave interferometry, which is implemented using planar microstrip lines and integrated microwave components. The key features of this system include small solution intake (<200 µL per measurement), short time of measurement (ca. 20 ms), ultrahigh sensitivity of concentration changes (up to 55 dB/%), and low error of measurement (below 0.1%). The ultrahigh sensitivity was proven experimentally by measurements of the fat content of milk. In addition, it is a user-friendly system due to an effortless and fast calibration procedure. Moreover, it can be made relatively compact (<20 cm2) and features low power consumption (200 mW). Thus, the proposed system is perfect for industrial applications, especially for highly integrated lab-on-chip devices.

scholarly journals Global Small Solution to the 2D MHD System with a Velocity Damping Term

2015 ◽  
Vol 47 (4) ◽  
pp. 2630-2656 ◽  
Author(s):  
Jiahong Wu ◽  
Yifei Wu ◽  
Xiaojing Xu
Keyword(s):  
Damping Term ◽  
Small Solution ◽  
Mhd System
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