scholarly journals Effective resistance is more than distance: Laplacians, Simplices and the Schur complement

2022 ◽  
Author(s):  
Karel Devriendt
Keyword(s):  
Schur Complement ◽  
Effective Resistance

Analysis between graph-based and Power Transfer Distribution Factors (PTDF)-based model reduction methods in Electric Power Systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Diego A. Monroy-Ortiz ◽  
Sergio A. Dorado-Rojas ◽  
Eduardo Mojica-Nava ◽  
Sergio Rivera
Keyword(s):  
Power Systems ◽  
Power System ◽  
Model Reduction ◽  
Electrical Power ◽  
Schur Complement ◽  
Power Transfer ◽  
Electrical Power System ◽  
Admittance Matrix ◽  
Test Beds ◽  
Power Transfer Distribution Factors

Abstract This article presents a comparison between two different methods to perform model reduction of an Electrical Power System (EPS). The first is the well-known Kron Reduction Method (KRM) that is used to remove the interior nodes (also known as internal, passive, or load nodes) of an EPS. This method computes the Schur complement of the primitive admittance matrix of an EPS to obtain a reduced model that preserves the information of the system as seen from to the generation nodes. Since the primitive admittance matrix is equivalent to the Laplacian of a graph that represents the interconnections between the nodes of an EPS, this procedure is also significant from the perspective of graph theory. On the other hand, the second procedure based on Power Transfer Distribution Factors (PTDF) uses approximations of DC power flows to define regions to be reduced within the system. In this study, both techniques were applied to obtain reduced-order models of two test beds: a 14-node IEEE system and the Colombian power system (1116 buses), in order to test scalability. In analyzing the reduction of the test beds, the characteristics of each method were classified and compiled in order to know its advantages depending on the type of application. Finally, it was found that the PTDF technique is more robust in terms of the definition of power transfer in congestion zones, while the KRM method may be more accurate.

scholarly journals Integrable and Chaotic Systems Associated with Fractal Groups

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 237
Author(s):  
Rostislav Grigorchuk ◽  
Supun Samarakoon
Keyword(s):  
Operator Algebras ◽  
Probabilistic Approach ◽  
Schur Complement ◽  
Automata Theory ◽  
Random Schrödinger Operators ◽  
Rational Maps ◽  
Holomorphic Dynamics ◽  
Von Neumann ◽  
Intermediate Growth ◽  
Quasi Crystals

Fractal groups (also called self-similar groups) is the class of groups discovered by the first author in the 1980s with the purpose of solving some famous problems in mathematics, including the question of raising to von Neumann about non-elementary amenability (in the association with studies around the Banach-Tarski Paradox) and John Milnor’s question on the existence of groups of intermediate growth between polynomial and exponential. Fractal groups arise in various fields of mathematics, including the theory of random walks, holomorphic dynamics, automata theory, operator algebras, etc. They have relations to the theory of chaos, quasi-crystals, fractals, and random Schrödinger operators. One important development is the relation of fractal groups to multi-dimensional dynamics, the theory of joint spectrum of pencil of operators, and the spectral theory of Laplace operator on graphs. This paper gives a quick access to these topics, provides calculation and analysis of multi-dimensional rational maps arising via the Schur complement in some important examples, including the first group of intermediate growth and its overgroup, contains a discussion of the dichotomy “integrable-chaotic” in the considered model, and suggests a possible probabilistic approach to studying the discussed problems.

scholarly journals Augmented Lagrangian preconditioners for the Oseen–Frank model of nematic and cholesteric liquid crystals

2021 ◽  
Author(s):  
Jingmin Xia ◽  
Patrick E. Farrell ◽  
Florian Wechsung
Keyword(s):  
Liquid Crystals ◽  
Augmented Lagrangian ◽  
Augmented Lagrangian Method ◽  
Mass Matrix ◽  
Unit Length ◽  
Mesh Size ◽  
Schur Complement ◽  
Cholesteric Liquid Crystals ◽  
Multigrid Algorithm ◽  
The Cost

AbstractWe propose a robust and efficient augmented Lagrangian-type preconditioner for solving linearizations of the Oseen–Frank model arising in nematic and cholesteric liquid crystals. By applying the augmented Lagrangian method, the Schur complement of the director block can be better approximated by the weighted mass matrix of the Lagrange multiplier, at the cost of making the augmented director block harder to solve. In order to solve the augmented director block, we develop a robust multigrid algorithm which includes an additive Schwarz relaxation that captures a pointwise version of the kernel of the semi-definite term. Furthermore, we prove that the augmented Lagrangian term improves the discrete enforcement of the unit-length constraint. Numerical experiments verify the efficiency of the algorithm and its robustness with respect to problem-related parameters (Frank constants and cholesteric pitch) and the mesh size.

scholarly journals The aesthetics of political resistance: On silent politics

Thesis Eleven ◽  
2021 ◽  
pp. 072551362110351
Author(s):  
Katariina Kaura-aho
Keyword(s):  
Political Action ◽  
Effective Resistance ◽  
Representative Democracy ◽  
Political Resistance ◽  
Starting Point ◽  
The Aesthetic ◽  
Aesthetic Meaning ◽  
Political Subversion

This article analyses the aesthetics of silent political resistance by focusing on refugees’ silent political action. The starting point for the analysis is Jacques Rancière’s philosophy and his theorisation of the aesthetics of politics. The article enquires into the aesthetic meaning of silent refugee activism and interprets how refugees’ silent acts of resistance can constitute aesthetically effective resistance to what can be called the ‘speech system’ of statist, representative democracy. The article analyses silence as a political tactic and interprets the emancipatory meaning of silent politics for refugees. It argues that refugees’ silent acts of political resistance can powerfully affect aesthetic, political subversion in prevailing legal-political contexts.

Schur complement spectral bounds for large hybrid FETI-DP clusters and huge three-dimensional scalar problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zdeněk Dostál ◽  
Tomáš Brzobohatý ◽  
Oldřich Vlach
Keyword(s):  
Condition Number ◽  
Three Dimensional ◽  
Schur Complement ◽  
Decomposition Methods ◽  
Stiffness Matrices ◽  
Spectral Bounds ◽  
Schur Complements ◽  
Linear Problems ◽  
Primal Method ◽  
Large Clusters

Abstract Bounds on the spectrum of Schur complements of subdomain stiffness matrices with respect to the interior variables are key ingredients of the convergence analysis of FETI (finite element tearing and interconnecting) based domain decomposition methods. Here we give bounds on the regular condition number of Schur complements of “floating” clusters arising from the discretization of 3D Laplacian on a cube decomposed into cube subdomains. The results show that the condition number of the cluster defined on a fixed domain decomposed into m × m × m cube subdomains connected by face and optionally edge averages increases proportionally to m. The estimates support scalability of unpreconditioned H-FETI-DP (hybrid FETI dual-primal) method. Though the research is most important for the solution of variational inequalities, the results of numerical experiments indicate that unpreconditioned H-FETI-DP with large clusters can be useful also for the solution of huge linear problems.

scholarly journals Seed production of barnyardgrass (Echinochloa crus-galli) in response to time of emergence in cotton and rice

2011 ◽  
Vol 150 (6) ◽  
pp. 717-724 ◽  
Author(s):  
M. V. BAGAVATHIANNAN ◽  
J. K. NORSWORTHY ◽  
K. L. SMITH ◽  
P. NEVE
Keyword(s):  
United States ◽  
Seed Production ◽  
Herbicide Resistance ◽  
Crop Production ◽  
Integrated Management ◽  
Resistance Management ◽  
Simulation Models ◽  
Effective Resistance ◽  
Southern United States

SUMMARYThe spread of herbicide resistance in barnyardgrass (Echinochloa crus-galli(L.) Beauv.) poses a serious threat to crop production in the southern United States. A thorough knowledge of the biology of barnyardgrass is fundamental for designing effective resistance-management programmes. In the present study, seed production of barnyardgrass in response to time of emergence was investigated in cotton and rice, respectively, in Fayetteville and Rohwer, Arkansas, over a 2-year period (2008–09). Barnyardgrass seed production was greater when seedlings emerged with the crop, but some seed production was observed even if seedlings emerged several weeks after crop emergence. Moreover, barnyardgrass seed production was highly variable across environments. When emerging with the crop (0 weeks after crop emergence (WAE)), barnyardgrass producedc. 35 500 and 16 500 seeds/plant in cotton, andc. 39 000 and 2900 seeds/plant in rice, in 2008 and 2009, respectively. Seed production was observed when seedlings emerged up to 5 WAE (2008) or 7 WAE (2009) in cotton and up to 5 WAE (2008, 2009) in rice; corresponding seed production wasc. 2500 and 1500 seeds/plant in cotton, andc. 14 700 and 110 seeds/plant in rice, in 2008 and 2009, respectively. The results suggest that cultural approaches that delay the emergence of barnyardgrass or approaches that make the associated crop more competitive will be useful in integrated management programmes. In the context of herbicide resistance management, it may be valuable to prevent seed return to the seedbank, irrespective of cohorts. The findings are vital for parameterizing herbicide resistance simulation models for barnyardgrass.

Specific Susceptibility to HCN and the amount of HCN recovered from Fumigated Insects

1951 ◽  
Vol 42 (2) ◽  
pp. 399-418 ◽  
Author(s):  
S. Pradhan ◽  
S. C. Bhatia
Keyword(s):  
Body Weight ◽  
Water Content ◽  
Relative Position ◽  
Surface Resistance ◽  
Internal Resistance ◽  
Effective Resistance ◽  
The Body ◽  
Effective Dosage ◽  
Adult Females ◽  
The Dead

The relationship was studied between susceptibility of a number of different species of insects to HCN fumigation and the recovery of HCN from them immediately after fumigation.The test insects used were Tribolium castaneum, seventh stage caterpillars of Corcyra cephalonica, first-and second-instar nymphs of Drosicha sp., third-and fourthinstar nymphs of Drosicha sp. and adult females of Drosicha sp.The apparatus and methods used in the fumigation and in the recovery of HCN from the fumigated insects are fully described.Preliminary expsriments showed that the processes of distillation and redistillation did not affect the recovery of HCN but that the result obtained for recovery from distillation could be affected if some volatile reducing substance were produced and carried over to the distillate. It was found that this did actually take place in the case of one of the test insects—T. castaneum—but that redistillation got rid of the impurity.In the main experiments it was shown that, on the assumption that the concentration of HCN to which insects are exposed is the effective dosage, the susceptibility of the test insects varied in the following descending order : firstand second-stage nymphs of Drosicha sp. > third- and fourth-stage nymphs of Drosicha sp.>C. cephalonica> T. castaneum>the adult females of Drosicha sp.When the same insects were arranged in descending order of the quantities of HCN recovered per 100 gm. of body weight, the order was identical except for the nymphs of Drosicha sp. which occupied a different relative position. The two categories of nymphs of Drosicha sp. were found to occupy a different relative position again with regard to the other three test insects when exposed to a superlethal concentration and assessed for recovery of HCN per 100 gr. body weight.Parallel batches of T. castaneum and C. cephalonica were fumigated and the HCN was recovered from the dead and survivors. More HCN was recovered from the dead insects than from those that survived.Both recovery and sorption of HCN were estimated separately in parallel batches of insects (adult females of Drosicha sp. and C. cephalonica). Recovery was found to be less than sorption showing that a part of the HCN absorbed is converted into a non-recoverable state. Further, that the weight of HCN sorbed per gram body weight of adult females of Drosicha sp. is much less than in the case of C. cephalonica under similar conditions of fumigation and that the amount of HCN converted into non-recoverable products is less in Drosicha adults than in C. cephalonica.A comparison of the water content of T. castaneum, C. cephalonica and Drosicha sp. (adults) showed that there was a positive correlation between water content and higher susceptibility to HCN and greater recovery of HCN was also indicated. It is suggested that this may be a factor in the “ Surface Resistance ” of an insec to a fumigant.The observations of previous workers that larger amounts are sorbed by or recovered (after fumigation) from more susceptible species than for those less susceptible was corroborated by the results obtained with C. cephalonica, T. castaneum and adult females of Drosicha sp. but not with those from nymphs of Drosicha sp.When dosage-mortality graphs were prepared by taking the amount of HCN recovered per gram body weight as an index of internal dose, the order of resistance of different test insects based on this new criterion was found to be entirely different from that based on the usual criterion of the concentration of HCN in the fumatorium being the index of effective dosage.These apparently anomalous observations may be explained by assuming that the resistance shown by an insect in an actual fumigation operation, i.e., to the concentration of HCN to which it is exposed (external dose) is what may be called the total “ Effective Resistance ” and that this “ Effective Resistance ” is the resultant of (a) “ Surface Resistance ” to the entry of fumigant and (b) “ Internal Resistance ” to the amount of HCN which actually gains entry into the body in some way or other. Thus the “Effective Resistance ” of an insect may be due to a combination either of low “ Surface Resistance ” and high “ Internal Resistance ”, giving a very low “ Effective Resistance ” as in the case of C. cephalonica, or vice versa giving the maximum “ Effective Resistance ” as in adult females of Drosicha sp. The lower recovery of HCN from the nymphs of Drosicha sp., although they were more susceptible to fumigation than C. cephalonica, is explained by their higher “ Surface Resistance ” combined with a very much lower “ Internal Resistance ”, leading to a lower “ Effective Resistance ”.

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