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Sociophysics Simulations II:Opinion Dynamics Dietrich Stau?er Institute for Theoretical Physics,Cologne University,D-50923K¨o ln,Euroland Abstract Individuals have opinions but can change them under the in?uence of others.The recent models of Sznajd (missionaries),of De?uant et al.(negotiators),and of Krause and Hegselmann (opportunists)are reviewed here,while the voter and Ising models,Galam’s majority rule and the Axelrod multicultural model were dealt with by other lecturers at this 8th Granada Seminar.1Introduction University professors know everything and are always right;lesser people change their opinion after interactions with others,as discussed in this re-view as well as in the lectures of Redner,Toral,and San Miguel.Missing at this Granada seminar was the Latan′e model [1,2]which is a generalized Ising model;simulations are reviewed in [3].Here we concentrate on the models of Sznajd [4],Krause and Hegselmann [5],and De?uant et al [6],all three of which di?er drastically in their de?nitions but give similar results,just as many variants of the Sznajd model were shown to have similar properties in an analytical approximation [7].For completeness we mention that the language bit-string models of part I of our review series can also be inter-preted as binary Axelrod models for multi-culturality:instead of taking over elements of another language,one may also replace elements of the native culture by those of another culture.On the other hand,the Latan′e model was already applied to languages in [8].In the next section we ?rst de?ne the three models in a uni?ed way,and then present,section by section,selected results.
2The Three Models
Each individual i (i =1,2,...N )has one opinion O i on one particular question.This opinion can be binary (0or 1),multivalued integer (O i =
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time Figure 1:Continuous opinions for 450million negotiators with everybody possibly connected to everybody:Two centrist parties ?ght for victory while much smaller extremist parties survive unharmed.From [9].1,2,...,Q )or continuous real (0≤O i ≤1).The neighbours j of individual i may be those on a square lattice,or on a Barab′a si-Albert network,or any other individual.Because of interactions between individuals i and j ,one of them or both may change opinion from one time step (t )to the next (t +1),according to rules to be speci?ed below.
“Bounded con?dence”[5,6]means that only people with similar opinions talk to each other.If in politics ?ve parties 1,2,3,4,5sit in parliament,traditionally ordered from left to right,then a left-centre coalition of 2and 3,or a rightist coalition of 3,4,and 5may work,while collaboration of the extremes 1and 5seldomly happen in formal coalition agreements.Thus we may assume that only parties talk to each other which di?er by not more than one opinion unit,or by ?Q units more generally for Q opinions,or by ?for real opinions between zero and one.If ?≥1,bounded con?dence is ignored;if ??1,con?dence is strongly bounded.This parameter ?thus
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opinion Final votes in Hegselmann-Krause (+) and Deffuant et al (x) model; eps=0.15; opinions scaled to 5
Figure 2:Final distribution of votes for 300,000opportunists (dashed line)and negotiators (solid line),with opinions scaled from 0to 5instead of the original interval [0,1]to facilitate comparison with missionaries,Fig.3.measures the tolerance for dissent or the openness to di?erent opinions.
The three models (each of which was studied in several variants)are missionaries [4],opportunists [5]and negotiators [6].
Missionaries of the Sznajd model convince all neighbours (within their con?dence bound)of their mission,particularly if two neighbouring mis-sionaries have the same opinion.For example,if on a square lattice two neighbours have the same opinion O =2out of Q =5possible opinions,and the con?dence bound is one unit,then they force their opinion 2onto all (at most six)lattice neighbours which before had opinions 1,2,or 3;they cannot convince neighbours with opinions 4or 5.
Opportunists of the Krause-Hegselmann model ask all their neighbours (within their con?dence bound)for their opinion,and then follow the arith-metic average of them.Thus for Q =5,a present opinion O i (t )=2of the considered individual and a con?dence bound of one unit,the new O i (t +1)
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opinion Final votes in Sznajd square lattice, five opinions, unit confidence bound, 300 x 300 people
Figure 3:Final distribution of votes for 301×301missionaries with discrete opinions 1,2,3,4,5and unit con?dence bound.Thus two neighbours of opinion 4convince all those neighbours to the same opinion 4which had opinions 3or 5before.
will be the rounded arithmetic average of all neighbour opinions except 4and 5.
Negotiators of De?uant et al.each select one discussion partner at one time step.If their opinions O i and O j di?er by less than the con?dence bound,their two opinions mutually get closer without necessarily agreeing completely.More precisely,O i shifts towards O j and O j shifts towards O i by a (rounded)amount μ|O j ?O i |,where the extreme case μ=0means rigid unchanging opinions,while μ=1/2gives immediate agreement.For example,for Q =5and μ=0.3,for a con?dence bound of three units,the pair O i =2,O j =5will become O i =3,O j =4.(If the opinion di?erence is only one unit,one of the two partner takes the opinion of the other.Thus a con?dence bound of only one unit makes less sense since then only this special case of one opinion jumping to the other remains,and
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f a i l u r e f r a c t i o n dimensionality Probability NOT to reach a consensus at Q = 3 (bottom) and 4 (top); 19^2, 7^3, 5^4, 5^5
Figure 4:Probability to ?nd no consensus with three (lower data)and four (upper data)possible missionary opinions,versus dimensionality.The tri-angular lattices is put at dimensionality 5/2.Opinion 0can only convince opinions )±1;all opinions are natural numbers.From [9].no mutual compromise as in negotiations.)Already two centuries ago,the mathematician Gauss (according to U.Krause)studied a similar problem:How do two opinions evolve if one discussion partner takes the arithmetic and the other takes the geometric average of the two opinions.
Particularly large populations can be simulated for the continuous ne-gotiator model of in?nite connection range,Fig.1.To plot the continuous opinions we binned them into 20intervals and show only the centrist inter-vals 10and 11and the extremists in intervals 1(+)and 2(x).More plots on the time dependence of negotiations are given in [6].
Basic programs for missionaries,opportunists and negotiators are pub-lished in my earlier reviews [10].
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Figure 5:Scaling of the number S of surviving opinions as a function of the number Q of possible discrete opinions and the number N of people,for missionaries.From L.da Fontura Costa,priv,comm.PRELIMINARY
3Consensus,Polarization or Fragmentation All three standard models give after su?ciently long time one of three types of results:We may ?nd one,two or more than two di?erent opinions surviving.The case of one opinion or consensus can also be called dictatorship.The case of two surviving opinions or polarization can also be called a balance of power between opposition and government.The case with three or more opinions or fragmentation can also be called anarchy,multi-party democracy,multiculturality or diversity.Thus the models themselves do not tell us whether the result is desirable or unwanted;this value judgement depends on the application and interpretation.
(Similarly,once we physicists have mastered the multiplication 3×5=15we can estimate that three bags,of ?ve oranges each,contain in total 15oranges,or that a room of 5meter length and 3meter width has an
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area of 15square meters.Both results are usually regarded as correct even though an orange does not have a surface of a square meter and a room of 15square meters may be regarded as too large for some and too small for other purposes.Thus one model,here multiplication,may have di?erent interpretations which can be judged di?erently.)
Figs.2and 3show this similarity:Continuous opinions for opportunists and for negotiators give three ?nal main opinions in Fig.2,and discrete opin-ions for missionaries do the same in Fig.3.The distribution of people among the three opinions may be di?erent,with very tiny groups having opinions between the main ones,or fringe opinions near zero and one not dying out for the continuous case.
For missionaries,not only square lattices have been simulated.The origi-nal one-dimensional chains are less interesting (similar to Ising models)since they do not have a phase transition (see next section).But for triangu-lar,simple cubic,and hypercubic in four and ?ve dimensions the results are about the same,Fig.4:For Q ≤3possible opinions,in most cases a consen-
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Q/N Scaled number S of final opinions versus scaled number Q of possible opinions, N = 10 to 10000
Figure 7:As Fig.5but for negotiators,from [17].sus is reached;for Q ≥4possible opinions,such a consensus is rare.(The con?dence bound is unity for all cases.)
This threshold of 3.5at unit con?dence interval (or ?=1/3.5)for mission-aries corresponds to a threshold of ?=1/2for negotiators [11]and ?=0.2for opportunists [12]with continuous opinions between zero and one:For larger ?one has consensus,for decreasing epsilon one has ?rst polarization into two opinions,and then fragmentation into three or more opinions,∝1/?.The negotiator threshold 1/2is quite general [11]except if the model is made very asymmetric [13].In summary:Reaching a consensus requires a strong willingness to listen to other opinions and to reach a compromise.For nego-tiators the results are well described by a theory [14].
Missionaries with continuous opinions seem to reach always a consensus
[15],independent of the con?dence bound ?.
Discrete instead of continuous opinions have the advantage that one can ?nd precisely whether or not two opinions agree,without a numerical cuto?depending on the precision of the computer.Particularly opportunists could
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now be simulated in much larger numbers[16].Also,now a?xed point is reached when all opinions agree or are out of reach from each other;real numbers never fully agree and thus prevent a?xed point.Moreover,now one has a maximum number Q of possible opinions,and the following scaling law is valid:If the number N of people is much larger than the number Q of possible opinions,then each opinion will?nd some followers,and the number S of surviving opinions agrees with Q.In the opposite limit of N?Q,each person may keep its own opinion if separated by more then?from the other opinions:S=N.It is easiest to take a unit con?dence interval,i.e.?=1/Q. Then for missionaries(Fig.5),opportunists(Fig.6)and negotiators(Fig.7) we get
S/Q=f(Q/N)
with a constant scaling function f for Q?N,and f=N/Q for Q?N, valid for large Q,S,N.
4Networks
Most simulations of opportunists and negotiators had in?nite connection range,i.e.each person could get into contact with all other persons,with the same probability.In contrast,the missionaries were usually simulated on lattices.Reality is in between these two extremes of nearest lattice neigh-bours and in?nitely distant neighbours.Small world networks[18]and in particular scale-free networks of Barab′a si-Albert type[19]have been used as the topological basis of opinion dynamics.The name scale-free means that there is no characteristic number k of neighbours for each site;instead the number of sites having k neighbours decays with a power-law in k like 1/k3.These networks are supposed to describe the empirical fact than with a rather small number of steps one can connect most people in the USA with most other people there via personal acquaintances.
Their history,often misrepresented,started in1941with Flory’s percola-tion theory on a Bethe lattice where each site has exactly k neighbours,with the same k for all sites;if the probability for two neighbours to be connected is larger than the percolation threshold p c=1/(k?1),one in?nite cluster of connected sites appears,coexisting with many small clusters including iso-lated sites.15years later Erd¨o s and R′e nyi modi?ed it such that each site is connected with a small probability with other sites,arbitrarily far away;this
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random graph belongs to the same“universality class”of mean-?eld perco-lation as Flory’s solution but now the number k of neighbours for each site ?uctuates according to a Poisson distribution.We get the desired1/k3law only by a very di?erent construction(the rich get richer;or powerful people attract even more supporters).We start with m sites all connected with each other.This network is then enlarged,adding one site per step.Each new site selects,among the already existing sites,exactly m neighbours,ran-domly with a probability proportional to the number of neighbours that site had already before.Once a new site has selected an old site as a neighbour, also the new site is neighbour to the old site:this neighbourhood relation is symmetric.A computer program published in[17]at the beginning contains this construction of the network.As a result,the probability that a site has k neighbours decays as1/k3for k≥m.
If one now wants to put opinion dynamics onto this network,one may waste much memory.With a million sites it is possible that one of them (typically one of the starting sites)has a large number of neighbours,of the order thousands.Then a neighbourhood table of size106×104is needed. Aleksiejuk[20]programmed a one-dimensional neighbourhood table to save memory,but this is di?cult to understand.It is much more practical,and does not change the results much,to switch from the above undirected net-works to directed networks:The new site still selects m neighbours from the old sites,but these m old sites do not have the new site as a neighbour:The neighbourhood relation has become asymmetric or directed.Similarly,a new member of a political party knows the heads of that party,but these heads don’t know the new member.Thus a hierarchy of directed relations is built up,which starts with the latest members of the network at the bottom and ends with the initial core members at the top.
Actually,Figs.6,7are for a directed scale-free network,but the undirected case with in?nite-range connectivity looks very similar[16]for opportunists. The simplicity of the scaling law makes it invariant against details of the network.
Also for other questions[21],negotiators with continuous opinions be-tween zero and one on a Barab′a si-Albert network showed little di?erence between directed and undirected neighbourhoods.Fig.8shows the resulting size distribution of opinion clusters.Such an opinion cluster is the set of people,not necessarily connected,having the same(within10?6)opinion. Consensus means everybody is in one opinion cluster;thus the opposite frag-mentation limit?=0.1is more interesting.If we increase systematically
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the network size,we see in Fig.8a peak moving to the right with increasing network size.This peak comes from large clusters,of the order of one per simulated network,which contain a positive fraction of the whole network.To the left of this peak,separated by a valley only for large networks,is the statistics for lots of small clusters,down to isolated people sharing their opinion with nobody else.The size distribution of these many small clusters is not much a?ected by the network size except that their statistics is better for larger networks.This cluster statistics is similar to percolation theory slightly above the threshold:One “in?nite”cluster coexists with many ?nite clusters.But our clusters are sets of agreeing people,not sets of neighbouring sites as in percolation theory.
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Figure 8:Size distribution of opinion clusters for negotiators on directed Barab′a si-Albert networks,with continuous opinions between zero and one and ?=0.1.All network sizes,from 100to 50,000,were simulated 100times.From [17].
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Figure 9:Transition width for missionaries with mixed global and local in-teraction,from [23].This width is de?ned as the interval in the initial con-centration of up opinions (Q =2square lattice)within which the fraction of samples ?nishing all up increases from 50to 70percent.
5Phase Transition
The simplest version of missionaries [4]has only Q =2possible opinions up and down,in which case bounded con?dence makes no sense and can be omitted.We always reach a consensus on the square lattice:Either everybody is up or everybody is down.If initially half of the opinions are up and the others are down,then after the simulation of many samples one ?nds
[22]that half of the samples are all up and half are all down.(For negotiators,the limit Q =2destroys the compromise part of shifting opinions somewhat and thus does not make sense.For opportunists we expect in this limit the same behaviour as for missionaries except that the dynamics is much faster:Each person takes the initial majority opinion.)
When we vary the initial up concentration away from 50percent,then
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for the small and intermediate sizes for which the standard missionary model reaches its?nal?xed point within reasonable time,the fraction of all-up sam-ples also moves away from50percent.Increasing the initial up concentration from40to60percent,we see[22]for small square lattices a slow increase of the fraction of up-samples,and for larger lattices this increase is somewhat steeper.Thus one might extrapolate that for in?nite lattices one has a sharp phase transition:For initial up concentrations below50percent all sam-ples?nish down,and for concentrations above50percent all samples?nish up.For the standard model the numerical evidence is meager due to small system sizes,but Schulze[23]combined the traditional nearest-neighbour in-teractions with global interactions similar to the nice mean-?eld theory of of Slanina and Lavi?c ka[24]:two people of arbitrary distance who agree in their opinions convince their nearest neighbours of this opinion.Then,as predicted[24],the times to reach the?nal?xed point are much shorter and their distribution decays exponentially.Thus larger lattices can be simulated and give in Fig.8a width of the transition varying as1/L in L×L squares, 10 In the simpli?cation[25]suggested by a third-year student,to allow al-ready one single missionary to convince the four square-lattice neighbours, one still has a complete consensus but no more a phase transition:The frac-tion of?nal up samples agrees with the initial concentration of up opinions, as found independently in simulation[26]and approximate theory[24];see Slanina lecture in this Seminar.Easier to understand is that in one dimen-sion,also this phase transition does not exist[4];this absence corresponds to the lack of phase transition in the one-dimensional Ising model of1925 which is so often mispronounced as Eyesing-Model by unhistorical speakers, instead of Eesing. 6Variants Numerous variants of the above standard models were published,and can be summarized here only shortly. Negotiators:The inventors of negotiators[6]published several alterna-tive,for example with unsymmetric opinion shifts as a result of compromise, with negotiators on a square lattice etc[27].For negotiators on scale-free networks,the network was made more realistic by increasing triangular re-lations(the friend of my neighbours is also my own friend);the qualitative 13 results remained unchanged[17].Opinions which di?er in their convincing power were simulated by Assmann[13],and the interactions of opinions on several di?erent aspects of life by Jacobmeier[28]. Missionaries:If you dislike the complete consensus enforced by mission-aries,just let their neighbours follow the convincing rule only with a high probability,or let a small minority of dissidents always be against the ma-jority.Then the full consensus is replaced by the more realistic widespread consensus[4,29].The role of neutrality in a three-opinion model,of opin-ion leaders,and of social temperature was studied by He et al[30].Sousa [31]showed that the network results are robust against the inclusion of more triangular relations(preceding paragraph)and that complete consensus can be avoided with Q>2.If the opinion dynamics starts already while the network is still growing not much is changed[32]. According to[33],the missionaries are part of a wider group of cellular automata giving about the same results;see also[7].Long-range interactions, decaying with a power law of the distance on a square lattice,still need to be explained[34].Frustration occurs if we switch from sequential to simultaneous updating and one person gets di?erent opinions simultaneously from di?erent pairs of missionaries[35].The time-dependent decay of the number of people who never changed their opinion is Ising-like only in one dimension[36].Other(dis-)similarities with Ising models are discussed in [37,38]. Opportunists:Fortunato[12]compared the threshold for?when the number of neighbour varies proportional to the total population to the case-where it is independent of the population size.Hegselmann and Krause[39] compared various alternative averages to the standard arithmetic average. 7Applications The most successful application of the missionary model were political elec-tions.This does not mean that we can predict which candidate will win the next elections.Neither can statistical physics predict which air molecules will hit my nose one minute from now;the laws of Boyle-Mariott and Gay-Lussac predict the pressure,i.e.the average number of molecules hitting my nose per picosecond.Similarly,many elections have shown a rather similar picture for the number of votes which one candidate gets(in case voters can select among numerous candidates,not among a few parties).The larger the 14 number v of votes is,the smaller is the number n(v)of candidates getting v votes.For intermediate v one has n(v)∝1/v while for large and small v, downward deviations are seen:Nobody gets more than100percent of the votes,and nobody gets half a vote.Missionaries on their way to the con-sensus?xed point on a Barab′a si-Albert network agreed well with Brazilian votes[40],and similar agreement was also found in modi?ed networks[41,31] and Indian elections.However,exceptions exist(S.Fortunato,https://www.doczj.com/doc/fd392888.html,m.). It would be interesting to check whether opportunists and negotiators also agree with Brazilian election results. If one person changes opinion,does this in?uence the whole community? This question,known as damage spreading in physics but invented in1969for genetics by Stuart Kau?man,was recently simulated in detail by Fortunato and the review[9]is still up-to-date. Readers may try to become rich by going into advertising:How can mass media in?uence opinion dynamics?For missionaries[26]the answer is clear: The larger the population is the less e?ort is needed to convince everybody to drink Coke instead of Pepsi;but the advertizing has to come early in the opinion formation process,not when most people have already made their choice.Again,analogous studies for opportunists and negotiators would be nice.Or perhaps you get rich with[42]. 8Summary Humans may dislike to be simulated like Ising spins,and clearly the brain is more complicated than one binary variable.But humans have been treated in this way since a long time:The astronomer Halley,known for his comet, tried to estimate human mortality already three centuries ago.Life insurance, health insurance,car insurance are present widespread examples of treating humans like inanimate particles with probabilistic behaviour,relying on the laws of large numbers.Whoever dislikes this treatment,should not blame todays sociophysicists for having started it.Already more than two millenia ago,Empedocles compared humans with?uids:Some are like wine and water,mixing well;others dislike each other,like oil and water(J.Mimkes, https://www.doczj.com/doc/fd392888.html,m.). 15 9Summary I thank my collaborators working on these models since the beginning of this millenium:S.Moss de Oliveira,A.O.Sousa,J.S.Andrade,A.A.Mor-eira,A.T.Bernardes,U.M.S.Costa,A.Araujo,R.Ochrombel,C.Schulze, J.Bonnekoh,P.M.C de Oliveira,H.Meyer-Ortmanns,S.Fortunato,P.Ass-mann,and N.Klietsch. 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Visit the following websites to learn more about this book: 46 Chapter 2 Sketching Chapter 2 Sketching A simulation project starts with the creation of a geometric model. T o be pro0cient at simulations, an engineer has to be pro0cient at geometric modeling 0rst. In a simulation project, it is not uncommon to take the majority of human-hours to create a geometric model, that is particularly true in a 3D simulation. A complex 3D geometry can be viewed as a collection of simpler 3D solid bodies. Each solid body is often created by 0rst drawi ng a sketch on a plane, and then the sketch i s used to generate the 3D soli d body usi ng tools such as extrude, revolve, sweep, etc. In turn, to be pro0cient at 3D bodies creation, an engineer has to be pro0cient at sketching 0rst. Purpose of the Chapter The purpose of this chapter is to provide exercises for the students so that they can be pro0cient at sketching using DesignModeler. Five mechanical parts are sketched in this chapters. Although each sketch is used to generate a 3D models, the generation of 3D models is so trivial that we should be able to focus on the 2D sketches without being distracted. More exercises of sketching will be provided in later chapters. About Each Section Each sketch of a mechani cal part wi ll be completed i n a secti on. Sketches i n the 0rst two secti ons are gui ded i n a step-by-step fashion. Section 1 sketches a cross section of W16x50; the cross section is then extruded to generate a solid model in 3D space. Section 2 sketches a triangular plate; the sketch is then extruded to generate a solid model in 3D space. Secti on 3 does not mean to provi de a hands-on case. It overvi ews the sketchi ng tools i n a systemati c way, attempting to complement what were missed in the 0rst two sections. Sections 4, 5, and 6 provide three cases for more exercises. Sketches in these sections are in a not-so-step-by-step fashion; we purposely leave some room for the students to 0gure out the details. Vibro-Acoustic Simulations Introduction Content A comparison of discrete element simulations and experiments for F sandpiles _composed of spherical particles Yanjie Li a ,Yong Xu a,*,Colin Thornton b a Department of Applied Mechanics,China Agricultural University,Beijing 100083,China b School of Engineering,University of Birmingham,Edgbaston,Birmingham B152TT,UK Received 11April 2005;received in revised form 1August 2005;accepted 6September 2005 Available online 18October 2005 Abstract Discrete element simulations,with the particle–particle interaction model based on classical contact mechanics theory between two non-adhesive spheres,were carried out and compared with F sandpile _experiments using spherical particles in order to assess the validation of the simulation data.The contact interaction model is a combination of Hertzian theory for the normal interaction and Mindlin–Deresiewicz theory for the tangential interaction.To ensure the consistency of the simulations with the experiments,the measurement of sliding friction,a key parameter in DEM simulations,was highlighted.A simple experimental method for establishing the value of the friction coefficient was proposed and used in measuring the friction of the rough glass beads and steel balls to be modelled in the simulations.The simulations were carried out for two cases according to particle arrangements:the first is quasi-two-dimensional (Q2D),with a smaller flat cuboidal box containing the spherical particles inside another box for discharge,and the second case is axisymmetric (3D).For both cases,simulations and experiments were carried out for assemblies of polydisperse rough glass beads under the same https://www.doczj.com/doc/fd392888.html,parisons were made that showed that the profiles and hence the measured angles of repose,in each case,were in good agreement,thus supporting the validity of the discrete element model used.Further numerical–experimental comparisons were carried out for 3D conical piles using smooth monodisperse steel balls and the same conclusions were obtained. D 2005Elsevier B.V .All rights reserved. Keywords:Discrete element method;Particles;Sandpiles;Angle of repose;Base pressure distribution 1.Introduction The Discrete Element Method has become a powerful numerical method for analysing discontinuous media since the important work by Cundall and Strack [1].Apart from the advances of applications in civil engineering with block element modelling,the particulate discrete element method for granular materials has developed rapidly in analysing both macroscopic and microscopic behaviours in many applica-tions in chemical engineering,agricultural engineering,etc.Progress has involved both model improvement and intensive simulations.Many investigators have proposed models modified from the original for specific applications.Thornton and Yin [2],Thornton [3,4]developed new particle interac- tion models for spherical particles based on contact mechanics for both nonadhesive and adhesive particles as well as for elastoplastic interactions.Oda et al.[5]modified the conventional linear spring–dashpot model by adding rolling resistance with which he analysed shear band phenomena.Han et al.[6]combined the discrete element method with the finite element method to simulate peen-forming processes.Williams et al.[7]developed a contact detection algorithm for particles with arbitrary geometries.Cleary [8]reported DEM simulations illustrating applications to various industrial processes. However,many researchers have done DEM simulations with their own models without experimental validation.Only a small number of studies have presented their predicted results in comparison with experimental data with enough specified parameters.The ambiguous parameter specification leads to theoretical uncertainty and thus restricts its applicability.For instance,the model based on classical contact mechanics between 0032-5910/$-see front matter D 2005Elsevier B.V .All rights reserved.doi:10.1016/j.powtec.2005.09.002 *Corresponding author.Tel.:+861062736514;fax:+861062736514.E-mail address:xuyong@https://www.doczj.com/doc/fd392888.html, (Y .Xu). Powder Technology 160(2005)219– 228 https://www.doczj.com/doc/fd392888.html,/locate/powtec ADS Fundamentals - 2002 LAB 4: AC Simulations Overview - This lab continues the amp_1900 project and uses the same sub-circuit as the previous lab. This exercise teaches the basics of AC simulation, including small signal gain and noise. It also shows many detailed features of the data display for controlling and manipulating data. OBJECTIVES ?Perform AC small signal and noise simulations. ?Adjust pin/wire labels. ?Sweep variables and write equations. ?Control plots, traces, datasets, and AC sources. Lab 4: AC Simulations 4-2 Table of Contents 1. Copy & Paste (Ctrl+C / Ctrl+V) from one design to another. (3) 2. Modify the copied circuit and pin labels (4) 3. Push and pop to verify the sub circuit. (5) 4. Set up an AC simulation with Noise. (5) 5. Simulate and list the noise data (5) 6. Control the output of equations and node voltages. (6) 7. Simulate without noise. (7) 8. Write a data display equation using a measurement equation (7) 9. Work with measurement and data display equations. (8) 10. Plot the phase and group delay for the ac analysis data (9) 11. Variable Info and the w hat function. (10) 12. OPTIONAL - Sweep Vcc (as if the battery voltage is decreasing) (11) 电力系统仿真软件PSS/E 的直流系统模型及其仿真 研究 黄莹，徐政，贺辉 ( 浙江大学电机系，浙江省杭州市310027) HVDC MODELS OF PSS/E AND THEIR APPLICABILITY IN SIMULATIONS HUA NG Ying ，XU Zheng ，HE Hui (Dept. of Electrical Engineering ，Zhejiang University ，Hangzhou 310027 ，Zhejiang Province ，China) ABS TRACT: The basic principle of dynamic simulation by power system simulation software PSS/E is presented in brief. The HVDC models in PSS/E can be divided into two kinds, in one kind the inductive transient processes in DC trans mission line and the dynamic characteristics of the high frequency DC controller are considered, and in the other kind the above mentioned processes and characteristics are not considered. The effectiveness and adaptability of these DC models are analyzed. Finally, the pseudo steady-state HVDC dynamic model CDC4 is studied in detail and is used to simulate the testing system. The simulation results show that the DC model of PSS/E can meet the need of the simulation of large scale A C/DC power systems, so it is available to apply PSS/E to the transient stability analysis of practical large scale A D/DC power system. KEY WORDS : PSS/E ；HVDC model ；Pseudo steady-state HVDC dynamic model ；HVDC dynamic characteristics ；Power system Measurements and simulations of transient characteristics of heat pipes Jaros?aw Legierski a ,Bogus?aw Wie ?cek a,* ,Gilbert de Mey b a Technical University of ?o ′dz ′,Institute of Electronics,ul.Wo ′lczanska 223,90-924?o ′dz ′,Poland b University of Ghent,Department of Electronics and Information Systems,Sint Pieternieuwstraat 41,9000Ghent,Belgium Received 1April 2004;received in revised form 13May 2005 Available online 5August 2005 Abstract The rejection of heat generated by components and circuits is a very important aspect in design of electronics sys-tems.Heat pipes are very e?ective,low cost elements,which can be used in cooling systems.This paper presents the modelling and measurements of the heat and mass transfer in heat pipes.The physical model includes the e?ects of liquid evaporation and condensation inside the heat pipe.The internal vapour ?ow was fully simulated using compu-tational ?uid dynamics.The theory has been compared with experimental measurements using thermographic camera and contact thermometers.The main purpose of this study is to determine the e?ective heat pipe thermal conductivity in transient state during start up the pipe operation and temperature increase.ó2005Elsevier Ltd.All rights reserved. 1.Introduction The investigations of heat pipes and their applica-tions into thermal management are known for years,but lately they have become more attractive to transport and dissipate heat in electronics [2,3,6,7].It is mainly due to the high e?ectiveness,small size and compact con-struction.Most of the previous research was made for static thermal conditions,and it resulted in getting the e?ective thermal resistance [6,7,9–11]. Heat pipe is a passive heat transfer device with a high e?ective thermal conductivity.The device is built up as hermetic container that is partially ?lled with a ?uid (typically water for electronic cooling design).The inner surfaces of the heat pipe have a capillary wicking mate- rial.The liquid in the pipe saturates the capillary wick.When one heats up the end of the pipe,the liquid at this place evaporates.Because evaporated medium in the heated section has a higher pressure than in the other part of the pipe,the vapour moves to the colder section,where it is cooled down and condensed.The condensed liquid is then transported back to the hot area thought the capillary wicks.This process causes a transport of heat and mass along the pipe [7,12]. In such a heat sink one can de?ne three sections:–evaporator,–condenser, –adiabatic region in the middle of the pipe. Usually,the heat pipe is modelled as a very high ther-mal conductivity element (k =50000W/m K)[5].The purpose of the measurements and simulations presented in this paper is to determine the e?ective thermal 0026-2714/$-see front matter ó2005Elsevier Ltd.All rights reserved.doi:10.1016/j.microrel.2005.06.003 * Corresponding author. E-mail address:wiecek@p.lodz.pl (B.Wie ?cek). Microelectronics Reliability 46(2006)109–115 https://www.doczj.com/doc/fd392888.html,/locate/microrel TERTS, a generic real-time gas turbine simulation environment W.P.J. Visser, M.J. Broomhead and J. van der Vorst Nationaal Nationaal Lucht- en Lucht- en Lucht- en Ruimtevaartlaboratorium Ruimtevaartlaboratorium National Aerospace Laboratory NLR NLR-TP-2002-069 TERTS, a generic real-time gas turbine simulation environment W.P.J. Visser, M.J. Broomhead and J. van der Vorst This report is based on a presentation held at the ASME IGTI TurboExpo 2001,New Orleans, June 4-7, 2001 and has also been published as ASME-2001-GT-446.The contents of this report may be cited on condition that full credit is given to NLR and the authors Customer:National Aerospace Laboratory NLR Working Plan number: V.2.A.3Owner:National Aerospace Laboratory NLR Division:Flight Distribution:Unlimited Classification title:Unclassified February 2002 864/JOURNAL OF ENGINEERING MECHANICS/SEPTEMBER2001 JOURNAL OF ENGINEERING MECHANICS /SEPTEMBER 2001/ 865 FIG. 1. Spiral Object in DEM FIG. 3.Calculation Cycle in DEM FIG. 2.Unfolded Figure of Spiral Line at r p 22 r =x ?y (5)?p p p y p ?1 ?=tan (6) p x p If r p is within the range between r spin and r spout ,the particle is able to contact the surface of the spiral. Fig.2shows an unfolded depiction of the spiral line at a distance r p from the z ?-axis.Assuming the spiral has no thick-ness,the distance between the center of the particle and the spiral surface perpendicular to the spiral surface d is given by p d = z ? ?cos ?(7) p p p ? ? 2? By comparing the distance given by (7)and the particle radius R p ,the contact can be judged between the particle and the spiral object d NASA/TM-2003-212145 A Collection of Nonlinear Aircraft Simulations in MATLAB Frederico R. Garza George Washington University Joint Institute for the Advancement of Flight Sciences Langley Research Center, Hampton, Virginia Eugene A. Morelli Langley Research Center, Hampton, Virginia January 2003 The NASA STI Program Office ... in Profile Since its founding, NASA has been dedicated to the advancement of aeronautics and space science. The NASA Scientific and Technical Information (STI) Program Office plays a key part in helping NASA maintain this important role. The NASA STI Program Office is operated by Langley Research Center, the lead center for NASA’s scientific and technical information. The NASA STI Program Office provides access to the NASA STI Database, the largest collection of aeronautical and space science STI in the world. The Program Office is also NASA’s institutional mechanism for disseminating the results of its research and development activities. These results are published by NASA in the NASA STI Report Series, which includes the following report types: ? TECHNICAL PUBLICATION. Reports of completed research or a major significant phase of research that present the results of NASA programs and include extensive data or theoretical analysis. Includes compilations of significant scientific and technical data and information deemed to be of continuing reference value. NASA counterpart of peer-reviewed formal professional papers, but having less stringent limitations on manuscript length and extent of graphic presentations. ? TECHNICAL MEMORANDUM. Scientific and technical findings that are preliminary or of specialized interest, e.g., quick release reports, working papers, and bibliographies that contain minimal annotation. Does not contain extensive analysis. ? CONTRACTOR REPORT. Scientific and technical findings by NASA-sponsored contractors and grantees. ?CONFERENCE PUBLICATION. Collected papers from scientific and technical conferences, symposia, seminars, or other meetings sponsored or co-sponsored by NASA. ? SPECIAL PUBLICATION. Scientific, technical, or historical information from NASA programs, projects, and missions, often concerned with subjects having substantial public interest. ? TECHNICAL TRANSLATION. English-language translations of foreign scientific and technical material pertinent to NASA’s mission. Specialized services that complement the STI Program Office’s diverse offerings include creating custom thesauri, building customized databases, organizing and publishing research results ... even providing videos. For more information about the NASA STI Program Office, see the following: ? Access the NASA STI Program Home Page at https://www.doczj.com/doc/fd392888.html, ? E-mail your question via the Internet to help@https://www.doczj.com/doc/fd392888.html, ? Fax your question to the NASA STI Help Desk at (301) 621-0134 ? Phone the NASA STI Help Desk at (301) 621-0390 ? Write to: NASA STI Help Desk NASA Center for AeroSpace Information 7121 Standard Drive Hanover, MD 21076-1320Finite Element Simulations with Ansys Workbench
VIBRO_1_DIRECT_simulations-ACTRAN振动声学直接频响分析理论
ACTRAN Training – VIBRO
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Pre-requisites - before going through this presentation, the reader should have read and understood the following presentations:
1_BASICS_General_Program_Organization.pdf; Workshop_BASICS_0_Edit_an_ACTRAN_input_file.pdf.
These slides present the basics materials, components and boundary conditions involved in a structural simulation in physical coordinates.
2
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The structural Materials
The visco-elastic and shell Component
The equivalent beam Component and Material
The discrete Component and Material
The Boundary Conditions
Meshing Criteria
3
Copyright Free Field TechnologiesA comparison of discrete element simulations
ADS Fundamentals - 2002_AC Simulations
电力系统仿真软件PSS-E的直流系统模型及其仿真研究
Measurements and simulations of transient characteristics of heat pipes
simulation
Three-Dimensional DEM Simulations of Bulk Handling by Screw Conveyors
A Collection of Nonlinear Aircraft Simulations in MATLAB
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