Approaches to the Numerical Estimates of Grid Convergence of NSE in the Presence of Singularities

2018 ◽  
Vol 19 (3-4) ◽  
pp. 281-287
Author(s):  
Chenguang Zhang ◽  
Krishnaswamy Nandakumar
Keyword(s):  
Numerical Algorithms ◽  
Nonlinear Problems ◽  
Order Of Accuracy ◽  
One Dimensional ◽  
Accuracy Order ◽  
Uniform Grids ◽  
Grid Convergence ◽  
The Common ◽  
Spatial Grid ◽  
Different Levels

AbstractEvaluating the order of accuracy (order) is an integral part of the development and application of numerical algorithms. Apart from theoretical functional analysis to place bounds on error estimates, numerical experiments are often essential for nonlinear problems to validate the estimates in a reliable answer. The common workflow is to apply the algorithm using successively finer temporal/spatial grid resolutions ${\delta _i}$, measure the error ${\isin _i}$ in each solution against the exact solution, the order is then obtained as the slope of the line that fits $(\log {\isin _i}, \log {\delta _i})$. We show that if the problem has singularities like divergence to infinity or discontinuous jump, this common workflow underestimates the order if solution at regions around the singularity is used. Several numerical examples with different levels of complexity are explored. A simple one-dimensional theoretical model shows it is impossible to numerically evaluate the order close to singularity on uniform grids.

unrechtliche peinliche schmehung oder dem gemeinen nutz nuetzlich?Eine Fallstudie zur Normenkonkurrenz im Schmähschriftprozess des 16. Jahrhunderts

2020 ◽  
Vol 25 (1) ◽  
pp. 135-149
Author(s):  
Jan Siegemund
Keyword(s):  
Early Modern ◽  
Common Good ◽  
Public Places ◽  
Legal Norms ◽  
The Public ◽  
The Common ◽  
The Public Sphere ◽  
The City ◽  
Different Levels

AbstractLibel played an important and extraordinary role in early modern conflict culture. The article discusses their functions and the way they were assessed in court. The case study illustrates argumentative spaces and different levels of normative references in libel trials in 16th century electoral Saxony. In 1569, Andreas Langener – in consequence of a long stagnating private conflict – posted several libels against the nobleman Tham Pflugk in different public places in the city of Dresden. Consequently, he was arrested and charged with ‘libelling’. Depending on the reference to conflicting social and legal norms, he had therefore been either threatened with corporal punishment including his execution, or rewarded with laudations. In this case, the act of libelling could be seen as slander, but also as a service to the community, which Langener had informed about potentially harmful transgression of norms. While the common good was the highest maxim, different and sometimes conflicting legally protected interests had to be discussed. The situational decision depended on whether the articulated charges where true and relevant for the public, on the invective language, and especially on the quality and size of the public sphere reached by the libel.

Numerical investigation on a melt-blowing die with internal stabilizers

2019 ◽  
pp. 152808371986693 ◽  
Author(s):  
Changchun Ji ◽  
Yudong Wang ◽  
Yafeng Sun
Keyword(s):  
Average Velocity ◽  
Fiber Diameter ◽  
Measurement Data ◽  
Melt Blowing ◽  
One Dimensional ◽  
Temperature Decay ◽  
Slot Die ◽  
The Common ◽  
The One ◽  
Peak Value

In order to decrease the fiber diameter and reduce the energy consumption in the melt-blowing process, a new slot die with internal stabilizers was designed. Using computational fluid dynamics technology, the new slot die was investigated. In the numerical simulation, the calculation data were validated with the laboratory measurement data. This work shows that the new slot die could increase the average velocity on the centerline of the air-flow field by 6.9%, compared with the common slot die. Simultaneously, the new slot die could decrease the back-flow velocity and the rate of temperature decay in the region close to the die head. The new slot die could reduce the peak value of the turbulent kinetic energy and make the fiber movements more gradual. With the one-dimensional drawing model, it proves that the new slot die has more edge on the decrease of fiber diameter than the common slot die.

DESIGN ACTIVITY MODELING IN DISTRIBUTED KNOWLEDGE RESOURCES ENVIRONMENT

2011 ◽  
Vol 10 (01) ◽  
pp. 69-76 ◽  
Author(s):  
XUDONG DAI ◽  
XUEFEN MA ◽  
YOUBAI XIE
Keyword(s):  
Integrated Design ◽  
Knowledge Flow ◽  
Design Activity ◽  
Distributed Resources ◽  
Value Analysis ◽  
Knowledge Resources ◽  
Design Activities ◽  
Design Requirements ◽  
The Common ◽  
Different Levels

For the definition of knowledge flow, knowledge-flow control and knowledge-acquisition in integrated product design within distributed knowledge resources environment, this paper studies the structural modeling of design activity for integrated product design. The common features of integrated design in distributed resources environment are summarized as follows: centering on specific design requirements, organizing related design resources to perform design activities, outputting design results, carrying on value analysis of design results, and then making design decisions on the basis of value analysis. Based on the common features, a structural model of integrated design activities in distributed resources environment is built, which presents the structural expression of knowledge flow by defining the design requirements, the design resource input, the result output, the design activities, the relationship between the design activities, and the values of the design activities. Design activities at different levels are defined according to the design process models at different levels. A design activity that has been defined can be packaged into design components. The essence of integrated design lies in knowledge integration, which is to be realized by defining the input and output relationship between the design components and the knowledge components.

scholarly journals Influence of saprophages (Isopoda, Diplopoda) on leaf litter decomposition under different levels of humidification and chemical loading

2020 ◽  
Vol 28 (4) ◽  
pp. 384-389
Author(s):  
A. P. Pokhylenko ◽  
O. O. Didur ◽  
Y. L. Kulbachko ◽  
L. P. Bandura ◽  
S. A. Chernykh
Keyword(s):  
Leaf Litter ◽  
Litter Decomposition ◽  
Zinc Content ◽  
Leaf Litter Decomposition ◽  
Absolute Difference ◽  
Average Weight ◽  
Chemical Stress ◽  
Experimental Conditions ◽  
The Common ◽  
Different Levels

The paper presents a study about the influence of two saprophage groups (Isopoda, Diplopoda) on leaf litter decomposition under different levels of humidification and chemical stress. Because of their worldwide distribution, we focused on the common pillbug Armadillidium vulgare (Latreille, 1804) (Isopoda, Armadillidiidae), and the common millipede species Rossiulus kessleri (Lohmander, 1927) (Julida, Julidae). The function of environment creation by the given saprophages, as destructors of dead plant matter, supporting such ecosystem services as soil fertility improvement and nutrients’ turnover, is highlighted. To conduct the experiment, the animals were collected manually and using pitfall trapping. In order to bring the experimental conditions closer to the natural, the individuals were not sexed. The maximum consumption of leaf litter by woodlice was recorded in the conditions with adequate moisture (0.5 mL of distilled water per box) and amounted to 2.52 mg/10 individuals per day, which exceeds its consumption with low and increased moisture, respectively, by 1.82 and 1.24 times. As for the effect of interaction, the consumption of maple litter with optimal moisture (4.77 mg/10 individuals per day) was the greatest. The largest absolute difference between broad-leaved tree species in the average weight of leaf litter consumed by woodlice was between maple leaf litter and oak leaf litter, the minimum – between robinia leaf litter and oak leaf litter. According to the results of the obtained data (Diplopoda), it can be stated that there is a statistically significant effect of chemical stress and discrepancy of the average zinc content in the object of study (in Diplopoda and their faecal pellets). We found that the diet provided did not affect the distribution of zinc in Diplopoda under conditions of chemical stress. According to the results of pairwise comparisons, we determined that the zinc content in the Diplopoda clearly differs for control and almost every concentration of zinc sulfate solution – 0.03 and 0.15 g/L, the samples of which do not form a homogeneous group. The species composition, abundance and distribution in space of soil invertebrates are informative indicators which reflect the ecological state of soils, intensity in development of soil horizons as well as intensity of processes occurring in them.

scholarly journals SHORT COMMUNICATION: THE EFFECT OF TANNIN SOLUTION IN PERFORMING SUCCESFULL EGG MICROINJECTION ON AFRICAN CATFISH (Clarias gariepinus)

2009 ◽  
Vol 4 (2) ◽  
pp. 153
Author(s):  
Muhammad Hunaina Fariduddin Ath-thar ◽  
Komar Sumantadinata ◽  
Alimuddin Alimuddin
Keyword(s):  
Short Communication ◽  
Clarias Gariepinus ◽  
Standard Operating Procedure ◽  
African Catfish ◽  
Hatching Rate ◽  
The Common ◽  
Transgenic Embryos ◽  
The Individual ◽  
Breeding And Genetics ◽  
Different Levels

In order to successfully perform a gene transfer activity using microinjection, an individual egg is needed. The common standard operating procedure to collect the individual egg is by applying chemical solution to remove the sticky layer covering the egg surface. Among several available solutions, tannin is one of alternative substances that can be used in performing egg microinjection on African catfish. In this study, the effect of different dosages of tannin solution to remove the sticky layer of eggs was observed. The study was conducted at the Laboratory of Fish Breeding and Genetics, Bogor Agricultural University. Prior to microinjection, the eggs were treated with different dosages of tannin solution right after fertilization. There were four different levels of dosage used as the treatments i.e.: 0.3, 0.5, 0.7, and 0.9 ppm. After the treatments, each individual egg was injected using DNA pmâactin-hrGFP plasmid with a concentration of 20 μg/mL. The results showed that the dosage of 0.5 ppm of tannin was the most effective treatment compared to the other dosages. This dosage produced 71.4% hatching rate and 57.1% transgenic embryos respectively.

Solitary-wave solutions of nonlinear problems

1990 ◽  
Vol 331 (1617) ◽  
pp. 195-244 ◽  
Keyword(s):  
Fixed Point ◽  
Solitary Waves ◽  
Fixed Point Index ◽  
Fixed Point Theorems ◽  
Nonlinear Problems ◽  
One Dimensional ◽  
Propagating Waves ◽  
Model Equations ◽  
Permanent Form ◽  
General Method

A general method is presented for the exact treatment of analytical problems that have solutions representing solitary waves. The theoretical framework of the method is developed in abstract first, providing a range of fixed-point theorems and other useful resources. It is largely based on topological concepts, in particular the fixed-point index for compact mappings, and uses a version of positive-operator theory referred to Frechet spaces. Then three exemplary problems are treated in which steadily propagating waves of permanent form are known to be represented. The first covers a class of one-dimensional model equations that generalizes the classic Korteweg—de Vries equation. The second concerns two-dimensional wave motions in an incompressible but density-stratified heavy fluid. The third problem describes solitary waves on water in a uniform canal.

Semi-supervised learning using autodidactic interpolation on sparse representation-based multiple one-dimensional embedding

2019 ◽  
Vol 17 (03) ◽  
pp. 1950013 ◽  
Author(s):  
Hao Deng ◽  
Chao Ma ◽  
Lijun Shen ◽  
Chuanwu Yang
Keyword(s):  
Sparse Representation ◽  
Euclidean Distance ◽  
Main Idea ◽  
Classification Problem ◽  
Classification Performance ◽  
One Dimensional ◽  
Adaptive Interpolation ◽  
Shortest Distance ◽  
The Common ◽  
Sample Set

In this paper, we present a novel semi-supervised classification method based on sparse representation (SR) and multiple one-dimensional embedding-based adaptive interpolation (M1DEI). The main idea of M1DEI is to embed the data into multiple one-dimensional (1D) manifolds satisfying that the connected samples have shortest distance. In this way, the problem of high-dimensional data classification is transformed into a 1D classification problem. By alternating interpolation and averaging on the multiple 1D manifolds, the labeled sample set of the data can enlarge gradually. Obviously, proper metric facilitates more accurate embedding and further helps improve the classification performance. We develop a SR-based metric, which measures the affinity between samples more accurately than the common Euclidean distance. The experimental results on several databases show the effectiveness of the improvement.

scholarly journals Unusual Polyhydroxylated Steroids from the Starfish Anthenoides laevigatus, Collected off the Coastal Waters of Vietnam

Molecules ◽  
2020 ◽  
Vol 25 (6) ◽  
pp. 1440
Author(s):  
Alla A. Kicha ◽  
Dinh T. Ha ◽  
Timofey V. Malyarenko ◽  
Anatoly I. Kalinovsky ◽  
Roman S. Popov ◽  
...  
Keyword(s):  
Coastal Waters ◽  
2D Nmr ◽  
2D Nmr Spectroscopy ◽  
Cytotoxic Effects ◽  
One Dimensional ◽  
The Common ◽  
Polyhydroxylated Steroids ◽  
New Compounds ◽  
Ht 29 ◽  
Inhibit Cell Proliferation

Four new polyhydroxylated steroids 1–4 were isolated along with two previously known related steroids 5 and 6 from the methanolic extract of the starfish Anthenoides laevigatus collected off the coastal waters of Vietnam. Structures of new compounds were substantially elucidated by one-dimensional (1D) and two-dimensional (2D) NMR spectroscopy and HRESIMS techniques. Heptaol 1 and hexaol 2 contain the common 5α-cholestane skeleton, while hexaol 3 and heptaol 4 have the rare among starfish steroid compounds 5β-cholestane skeleton. Compounds 1, 5, and 6 do not show cytotoxic effects against normal JB6 Cl41 and cancer HT-29 and MDA-MB-231 cells, however they inhibit cell proliferation and colony formation of cancer HT-29 and MDA-MB-231 cells.

scholarly journals The development of biofilm architecture

2016 ◽  
Vol 472 (2188) ◽  
pp. 20150798 ◽  
Author(s):  
A. C. Fowler ◽  
T. M. Kyrke-Smith ◽  
H. F. Winstanley
Keyword(s):  
Bacterial Biofilm ◽  
Governing Equations ◽  
Biofilm Growth ◽  
One Dimensional ◽  
Direct Numerical Solution ◽  
The Common ◽  
Common Observation ◽  
The Stability ◽  
The One ◽  
A Free Boundary Problem

We extend the one-dimensional polymer solution theory of bacterial biofilm growth described by Winstanley et al . (2011 Proc. R. Soc. A 467 , 1449–1467 ( doi:10.1098/rspa.2010.0327 )) to deal with the problem of the growth of a patch of biofilm in more than one lateral dimension. The extension is non-trivial, as it requires consideration of the rheology of the polymer phase. We use a novel asymptotic technique to reduce the model to a free-boundary problem governed by the equations of Stokes flow with non-standard boundary conditions. We then consider the stability of laterally uniform biofilm growth, and show that the model predicts spatial instability; this is confirmed by a direct numerical solution of the governing equations. The instability results in cusp formation at the biofilm surface and provides an explanation for the common observation of patterned biofilm architectures.

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