text:
Alfresco discussion and collaboration. Stick around a few hours after asking a question.
Official support for Enterprise subscribers: support.alfresco.com.
Join in the conversation by getting an IRC client and connecting to #alfresco at Freenode. Our you can use the IRC web chat.
More information about the channel is in the wiki.
More help is available in this list of resources.
2018-07-27 06:41:53 GMT <qwebirc30253> good morning
2018-07-27 06:41:56 GMT <qwebirc30253> Previously we are using two different projects for platform and share, now converted to AIO project getting an issue of dependencies, showing like Noclassfound even though dependencies exist in pom.xml (parent folder), tried like adding dependencies in platform module pom.xml but then also getting the same issue. Where exactly dependencies need to add for Java class of platform module is needed to aid in parent poem or modu
2018-07-27 06:42:47 GMT <qwebirc30253> pom**
2018-07-27 07:04:07 GMT <ashley_> Hello All
2018-07-27 07:05:03 GMT <ashley_> I am want get user's group details using javascript in alfresco process service, can you please share any link is available
2018-07-27 07:05:15 GMT <ashley_> i used GroupInfo=userInfoBean.getPrimaryGroup(userID);
2018-07-27 07:05:33 GMT <ashley_> but its getting empty
2018-07-27 07:09:04 GMT <ashley_> and Caused by: org.activiti.engine.ActivitiException: Exception while invoking TaskL istener: couldn't find a variable type that is able to serialize com.activiti.mo Exception
2018-07-27 10:03:26 GMT <ashley_> Can anyone help me on this please
2018-07-27 10:17:23 GMT <yreg> ashley_, I bet your chances would be higher if you open a support case, or ask in the activiti bitter channel
2018-07-27 10:17:33 GMT <yreg> *gitter
2018-07-27 10:17:50 GMT <yreg> Or probably even better if post your question to community.alfresco.com
2018-07-27 10:18:49 GMT <yreg> You may not get a prompt response but I bet you would probably get some constructive interraction
2018-07-27 10:42:40 GMT <alfbot> Tichodroma: Sent 2 weeks, 6 days, 19 hours, and 59 minutes ago: <AFaust> From within ALfresco you can use the search.solrAdminHTTPCLient bean for that...
2018-07-27 10:42:41 GMT <alfbot> Tichodroma: Sent 2 weeks, 6 days, 19 hours, and 58 minutes ago: <AFaust> Alfresco already use that to call the SUMMARY action
2018-07-27 10:44:48 GMT <hi-ko> AFaust: I'm still struggeling with douple encoded url in aos. I saw your comment in https://issues.alfresco.com/jira/browse/ACE-5259
2018-07-27 10:47:02 GMT <AFaust> My comment? You mean a different JIRA issue than this one, because I can't see a comment of mine in there
2018-07-27 10:47:54 GMT <AFaust> But I have encountered such issues in the past, yes
2018-07-27 10:48:04 GMT <hi-ko> What I'm wondering: the url is already encoded. so encodeURI(url) is not a fix but the issue. I see in action.js in dlA_internalEditOnlineAos(response) the onlineEditUrlAos property is already encoded but I don't understand were the onlineEditUrlAos comes from
2018-07-27 10:48:34 GMT <hi-ko> sorry this https://issues.alfresco.com/jira/browse/ALF-21758
2018-07-27 10:48:44 GMT <AFaust> I have one situation at a customer where only a single user is affected by this (despite all using the same Alfresco and the same Office version, and the entire system of the user having been completely rebuildt based on their standard image)
2018-07-27 10:49:38 GMT <AFaust> Ah yes, that ALF-21758 was for the same customer, though a different constellation
2018-07-27 10:50:56 GMT <hi-ko> So - to address the issue I have to find out where the url / onlineEditUrlAos comes from. this determines if the url should be encoded or not
2018-07-27 10:51:53 GMT <AFaust> I backported the code from 201701 GA for my customer, and that solved the issue of ALF-21758 for them, though they still had one user where Office would introduce a double encoded URL somewhere (Alfresco not at fault - I looked at all network packages and it is Office that generates the double-encoded URL)
2018-07-27 10:53:00 GMT <hi-ko> you backported which part? the action.js?
2018-07-27 10:53:27 GMT <AFaust> Yes
2018-07-27 10:53:38 GMT <AFaust> The _aos_tryToLaunchOfficeByMsProtocolHandler
2018-07-27 10:55:55 GMT <hi-ko> but encodeURI(url) is the issue in my case. Only reverting back to plain url works. so when I debug action.js the url is already encoded
2018-07-27 10:58:45 GMT <hi-ko> a - sorry I was on github share-old - my fault. in https://github.com/Alfresco/share/ it's again location.href = protocolHandler + ':ofe%7Cu%7C' + url; as I expected ...
2018-07-27 10:58:46 GMT <alfbot> Title:GitHub - Alfresco/share: Alfresco Share (at github.com)
2018-07-27 10:59:48 GMT <hi-ko> So in share 5.1.x this should be assumed as a bug and worked by accident
2018-07-27 11:01:14 GMT <hi-ko> AFaust: did you understand where the url comes from?
2018-07-27 11:03:17 GMT <AFaust> from alfresco.js onlineEditUrlAos()
2018-07-27 11:04:05 GMT <AFaust> using the webdavUrl of the record as the base, and falling back to a UUID based URL if webdavUrl is too long
2018-07-27 11:35:21 GMT <hi-ko> strange - webdav url is taken from /share/proxy/alfresco/slingshot/doclib2/node/workspace/SpacesStore/ details and this is already url encoded. for me this is fine so far with encoding again in actions.js. I'm wondering why this worked in the past ...
2018-07-27 11:36:07 GMT <hi-ko> AFaust: thanks for your input.
2018-07-27 11:47:33 GMT <qwebirc30253> with SDK 3.0.1 in documentlist-min.js is not loading
2018-07-27 11:50:13 GMT <qwebirc30253> I just changed documentlist-min.js for showing custom metadata template,then after changes I restarted server the changes are showing changed file is not loading from res
2018-07-27 11:55:00 GMT <angelborroy> qwebirc30253 why are you modifying a minimized JS file?
2018-07-27 11:55:44 GMT <angelborroy> You could modify documentlist.js in your Alfresco SDK 3 project and then maven will minify the file for you
2018-07-27 11:55:56 GMT <angelborroy> Anyway modifying directly Alfresco resources is discouraged
2018-07-27 11:58:08 GMT <qwebirc30253> angelborroy, I thought for customization we need change in -min.js that's why
2018-07-27 11:59:07 GMT <angelborroy> what do you want to modify?
2018-07-27 12:00:40 GMT <qwebirc30253> added metadata template to show document status in documentlist js file beside social icons
2018-07-27 12:04:16 GMT <angelborroy> qwebirc30253 probably this can help you to understand how to extend Alfresco
2018-07-27 12:04:17 GMT <angelborroy> https://github.com/angelborroy/alfresco-add-menu-sample
2018-07-27 12:04:18 GMT <alfbot> Title:GitHub - angelborroy/alfresco-add-menu-sample: Ejemplo para crear un menú en la Biblioteca de Documentos de Alfresco Share (at github.com)
2018-07-27 12:04:28 GMT <angelborroy> Unluckily it's only available in Spanish
2018-07-27 12:08:42 GMT <qwebirc30253> @angelborroy I will go through those link. thq
2018-07-27 12:17:55 GMT <AxelFaust> Grrrml.... struggling with a weird error in my Docker init shell script for almost 2 hours know, and error output does not make any sense... Likely a single stray character somewhere missing with the entire file structure.
2018-07-27 12:26:23 GMT <yreg> AxelFaust, can you elaborate ?
2018-07-27 12:27:50 GMT <AxelFaust> The error reported meeting EOF at line X looking for some specific input. Thing is, line X was far away from any EOF (still 30 lines to go), and that line was even commented out in some of my re-tries
2018-07-27 12:28:37 GMT <AxelFaust> It was unclear which command was being run that may have tried to match more than its intended arguments due to an unterminated parameter string, since none of my debug echo statements triggered
2018-07-27 12:28:50 GMT <yreg> Could it be a hidden char ?
2018-07-27 12:29:28 GMT <yreg> Try deleting the line instead of commenting or make sure you are pointing to the right location using the full path for your entrypoint
2018-07-27 12:29:51 GMT <AxelFaust> No - it turned out (just fixed that error) to be a ` at the end of a variable assignment based on a piped set of utils
2018-07-27 12:30:04 GMT <yreg> You obviously can avoid having to re-build the image every time by simply mounting the newly edited file as volume
2018-07-27 12:30:10 GMT <yreg> It would save you some time
2018-07-27 12:30:11 GMT <AxelFaust> Yeah, I deleted the whole block the line was in to see if I got a different error message
2018-07-27 12:34:57 GMT <AxelFaust> On to the next error(s)...
2018-07-27 12:37:32 GMT <yreg> Good luck
2018-07-27 12:37:57 GMT <alfresco-discord> <mbui> So we're having some issues with some users performing actions that takes long time (enough for a client side timeout) to process. Such as moving/copying files, extracting ZIP-files etc.
2018-07-27 12:38:51 GMT <yreg> @mbui FYI the action should continue to run on the backend
2018-07-27 12:38:58 GMT <alfresco-discord> <mbui> First the user gets an error message on the client side timeout. And when they're attempting the action again (cause they think the previous failed) it may say something like "File already exists" or something similar. Because it has processed.
2018-07-27 12:39:59 GMT <yreg> @mbui you can always increase timeout limit, but be careful to keep it reasonable just not to Hog youtomcaq threadpool
2018-07-27 12:40:01 GMT <alfresco-discord> <mbui> Yes, my point is that this is very confusing for the users. I was thinking a way to solve this by polling the BatchJob (I'm assuming those processes are run as batch jobs, havn't checked). Instead of waiting for the answer.
2018-07-27 12:41:06 GMT <yreg> Moving/copying/deleting are not processed as batch jobs
2018-07-27 12:41:06 GMT <alfresco-discord> <mbui> But it feels like this should be a very common use case? It should be intuitive OOTB in my opinion 😃
2018-07-27 12:43:10 GMT <alfresco-discord> <mbui> well, that's unfortunate 😃
2018-07-27 12:44:34 GMT <alfresco-discord> <mbui> So, would one approach be to wrap those actions as batch jobs and then create a webscript which polls the job for the progress? 🤔
2018-07-27 12:46:39 GMT <yreg> Too much effort in my opinion for too less added value
2018-07-27 12:47:46 GMT <yreg> I wouldn't expect to hit such case in day to day operations .. maybe just once or twice a year for some restructuring of the repo or something ...
2018-07-27 12:56:00 GMT <alfresco-discord> <mbui> Depends on the use case of the business logic I guess. In this particular case they are using Alfresco as case mananagement. It's not unusual that they have folders with several hundreds or maybe even thousands of files in which they may want to move/copy etc.
2018-07-27 13:01:20 GMT <yreg> In my experience few hundreds should never be an issue (on reasonably performant systems)
2018-07-27 13:01:28 GMT <AxelFaust> As far as I remember, the biggest impact of those big copy / move / unzip operations is typically the lookup of rules to execute (due to inheritance of rules)
2018-07-27 13:01:41 GMT <AxelFaust> And yes, a reasonably fast system should not have issues with a few hundred
2018-07-27 13:02:19 GMT <yreg> I would discourage from moving several thousands as regular day to day task because it generates a lot of overhead (referring to solr indexing as well)
2018-07-27 13:03:01 GMT <yreg> In my experience that can cause solr to lag behind
2018-07-27 13:03:15 GMT <yreg> And full reindex to take much longer than should
2018-07-27 13:04:11 GMT <AxelFaust> At one of my customers we have implemented a feature of "background actions" for the Share UI, i.e. via an AOP approach, operations known to take a long time are being moved to a background process, and the client receives an ID (NodeRef) of a status object to check for progress. A small popup + progress bar on the lower right side of the Share UI then tracks those action(s)
2018-07-27 13:05:27 GMT <AxelFaust> Though that obviously only supports our custom actions
2018-07-27 13:10:18 GMT <alfresco-discord> <mbui> AxelFaust: That sounds like a neat feature. So only the user who executed the action will see the progress? And the progress will still be available if they accidently closes the browser, change page or logs out+in?
2018-07-27 13:23:43 GMT <AxelFaust> mbui: yes
2018-07-27 16:00:38 GMT <alfresco-discord> <mbui> Anyone know how to create a FTS query which searches for a property (that consists of a collection) which has an empty collection?
2018-07-27 16:03:17 GMT <yreg> @mbui have you tried ISNULL:'property-qname' ?
2018-07-27 16:03:46 GMT <alfresco-discord> <mbui> yreg: yes, does not work.
2018-07-27 16:06:39 GMT <yreg> Can you create a behaviour to convert those empty collections to a null value <grin> ?
2018-07-27 16:08:11 GMT <alfresco-discord> <mbui> I've found a node which has the property wpsmail-v2:attachmentsCache set to an empty collection. This crashes the document library. Want to find if there's other similar nodes in the system.
2018-07-27 16:08:35 GMT <alfresco-discord> <mbui> https://i.gyazo.com/86356046743cf23aa50489be8a885102.png
2018-07-27 16:10:28 GMT <yreg> Just out of curiosity, have you confirmed it was actually an empty collection, not a collection with a single empty string ?
2018-07-27 16:18:05 GMT <alfresco-discord> <mbui> Yes
2018-07-27 16:18:38 GMT <yreg> I think it should be fairly possible to craft a DB query to get all of them
2018-07-27 16:22:50 GMT <alfresco-discord> <mbui> Not optimal, but the query ISNOTNULL:'wpsmail-v2:attachmentsCache' and then iterating the result and filtering all the ones that has node.properties["wpsmail-v2:attachmentsCache"].length == 0 did the work. However that approach is quite limited maxItems.
2018-07-27 16:23:42 GMT <yreg> You can paginate
2018-07-27 17:39:53 GMT <alfresco-discord> <mbui> I guess it's a generel bug in Share. This happens only in "Detailed view" in the document library. My guess is that the client always crashes if you have a property that contains an empty collection. I've reported this to Alfresco support.
2018-07-27 17:41:55 GMT <alfresco-discord> <mbui> The crash happens in documentlist.js: https://i.gyazo.com/2f9548b8cf6d87b74d05893fdfaf3c45.png
2018-07-27 18:12:07 GMT <manav> hello all
2018-07-27 18:12:57 GMT <manav> I'm trying hot reload java code in alfresco sdk 2.2
2018-07-27 18:13:42 GMT <manav> @ECHO OFF set springloadedfile=springloaded-1.2.5.RELEASE.jar IF "%MAVEN_OPTS%" == "" ( ECHO The environment variable 'MAVEN_OPTS' is not set, setting it for you SET MAVEN_OPTS=-javaagent:springloaded-1.2.5.RELEASE.jar -noverify -Xdebug -Xms256m -Xmx2G -Xms256m -Xmx2G -XX:PermSize=300m ) ECHO MAVEN_OPTS is set to '%MAVEN_OPTS%' mvn clean install -Pamp-to-war
2018-07-27 18:14:15 GMT <manav> above code is in my run.bat
2018-07-27 18:16:00 GMT <manav> alfresco server is getting started, but the changes in java code is not getting reflected..
2018-07-27 18:40:29 GMT <mark_____> Hi Guys, I'm switching from LDAP to LDAPS, I've imported the certificate, changed the port in the config and added ldap.authentication.java.naming.security.protocol=ssl, is there any steps I'm missing?
2018-07-27 18:45:37 GMT <mark_____> Failed to communicate with ldaps://xxx.yyy.local:636. Reason javax.naming.CommunicationException, simple bind failed: xxx.yyy.local:636, javax.net.ssl.SSLHandshakeException, sun.security.validator.ValidatorException: PKIX path building failed: sun.security.provider.certpath.SunCertPathBuilderException: unable to find valid certification path to requested target, sun.security.validator.ValidatorException, PKIX path building faile
2018-07-27 18:45:52 GMT <mark_____> not sure if that makes sense to anyone :|
2018-07-27 22:43:15 GMT <mark_____> anyone about?
2018-07-27 23:19:29 GMT <alfresco-discord> <Mark> You need to configure an ssl trust relationship. Meaning you import the ldap server's certificate into a keystore for trust entries (a truststore)
2018-07-27 23:21:35 GMT <alfresco-discord> <Mark> Instructions start at "ldap.authentication.java.naming.security.protocol" on this page: https://docs.alfresco.com/5.1/concepts/auth-ldap-props.html
2018-07-27 23:21:37 GMT <alfbot> Title:LDAP configuration properties | Alfresco Documentation (at docs.alfresco.com)
The other logs are at http://esplins.org/hash_alfresco


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Fine structure of oscillons in the spherically symmetric
Ethan P. Honda
Klein-Gordon model
Applied Research Laboratories, The University of Texas at Austin, Austin, Texas 78758
Matthew W. Choptuik
CIAR Cosmology and Gravity Program, Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1 and Center for Relativity, University of Texas at Austin, Texas 78712-1081 Received 26 September 2001; published 8 April 2002 We present results from a study of the fine structure of oscillon dynamics in the 3 1 spherically symmetric Klein-Gordon model with a symmetric double-well potential. We show that in addition to the previously understood longevity of oscillons, there exists a resonant and critical behavior which exhibits a time-scaling law. The mode structure of the critical solutions is examined, and we also show that the upper bound to oscillon formation in r 0 space is either nonexistent or higher than previously believed. Our results are generated using a novel technique for implementing nonreflecting boundary conditions in the finite difference solution of wave equations. The method uses a coordinate transformation which blueshifts and ''freezes'' outgoing radiation. The frozen radiation is then annihilated via dissipation explicitly added to the finite-difference scheme, with very little reflection into the interior of the computational domain. DOI: 10.1103/PhysRevD.65.084037 PACS number s : 04.25.Dm, 04.40.Nr, 11.10.Lm, 11.27. d
There is a long history in physics and mathematics of trying to find new nontrivial solutions to nonlinear wave equations. The literature on the subject goes back at least as far as 1845 when Russell published a paper about a surface wave he witnessed travel for almost two miles in a shallow water channel the first scientifically reported soliton 1 . Since then there has been much effort directed toward understanding stable localized solutions to nonlinear wave equations: the classical kink soliton, topological defects monopoles, cosmic strings, and domain walls 2 , and nontopological defects such as Q balls 3,4 are but a few examples. However, localized but unstable solutions have been discussed much less frequently and in this paper we focus our attention on one such solution, the oscillon. The definition of oscillon varies slightly depending on context, but here we refer to localized, time-dependent, unstable, spherically symmetric solutions to the nonlinear Klein-Gordon equation. Although oscillons are unstable, their lifetimes are long compared to a dynamical time. Oscillons were originally discovered by Bogolyubskii and Makhan'kov 5,6 who called them ''pulsons'' , and were later studied in more detail by Gleiser 7 and by Copeland et al. 8 . Oscillons can be formed via the collapse of field configurations initial data that interpolate between two vacuum and ) of a symmetric double well potential states ( SDWP .1 In spherical symmetry, such a configuration is a bubble, where the interpolating region is the bubble ''wall'' that separates the two vacuum states at some characteristic as the large-r radius where in this work we always use
1 Asymmetric double well potentials can also produce oscillons, but here we consider only the SDWP.
vacuum state . An oscillon formed this way typically has three distinct stages in its evolution. First, immediately following the bubble collapse a large percentage of its energy is radiated away. As will be discussed below, this can happen either through localized field oscillations, or through bounces ¯ reminiscent of the 1 1 dimensional kink-antikink (KK ) scattering 9 . After the initial radiative phase, the solution settles into the oscillon stage. Here the field is localized with a shape roughly that of an origin-centered Gaussian, with the field value asymptotically approaching the large-r vacuum state. Because of the asymmetry of the potential about either the large-r vacuum minimum, the field oscillates about such that the time-averaged value of the field lies between the two vacua, i.e., where ••• T 1 T •••dt as in 8 . For typical initial field configura0 tions the energy of the oscillon is slowly radiated away, approaching a specific ''plateau'' value. In the third and final stage of evolution, the oscillon stops oscillating and disperses, radiating away its remaining energy. Much of the original excitement about oscillons arose from the fact that their long lifetimes could potentially alter the dynamics of a cosmological phase transition. However, since oscillons are unstable, their ability to affect such a phase transition depends crucially on their lifetimes. Previous studies by Copeland et al. 8 used dynamical grid methods to study oscillon dynamics and treated the initial radius, r 0 , of the bubble shell of radiation as a free parameter. These studies showed not only that oscillon lifetimes can be comparable to the age of the universe at the grand unified theory GUT scale , but that oscillons are formed from a wide range of initial bubble radii. However, the computational demands of the dynamical grid methods employed in 8 prevented a detailed study of the r 0 parameter space. A key problem in the accurate, long-time simulation of oscillons is the treatment of boundary conditions at the outer
©2002 The American Physical Society
0556-2821/2002/65 8 /084037 12 /$20.00
65 084037-1
edge, r r max , of the computational domain. It is standard practice in the computational solution of nonlinear field equations to use finite difference techniques applied to functions defined on a lattice of grid points. If a static, finite-sized domain is used i.e. if r max is fixed, then one needs to employ a method that minimizes the amount of radiation energy that is artificially reflected at r r max . With massless scalar fields, and in spherical symmetry, this can be done quite easily simply by imposing a discrete version of an ''outgoing radiation,'' or Sommerfeld, condition. However, for the case of massive scalar fields, or more generally, for fields with nontrivial dispersion relations, the Sommerfeld condition is only approximate, and its use generically results in significant reflection at r r max , and subsequent contamination of the interior solution. A surefire fix for the outer-boundary problem is to use a dynamically growing grid as in 8 , so that r max rmax(t), and lattice points are continuously added to extend the computational domain as needed. Alternatively, compactified coordinates or coordinates which propagate outward faster than any characteristic speed in the problem can be used, but in these cases, new grid points also need to be continuously added to the mesh in order to maintain adequate resolution of solution features. These methods are somewhat more efficient than the use of a static mesh with r max chosen so that no signals reach the outer boundary during the integration period of interest, T. However, for long-lived solutions, the mesh soon becomes quite large, and the computation time tends to be proportional to T 2 . Recently, Gleiser and Sornborger 10 introduced an adiabatic damping method which adds an explicit damping term to the equations of motion, and which has been shown to absorb outgoing massive radiation extremely well in 1D spherical and 2D cylindrical simulations. Here we present an alternative approach for dealing with outgoing massive scalar fields which is quite general and quite different from previously used methods of which we are aware. The technique involves the use of a specially chosen coordinate system that ''freezes'' and blueshifts outgoing radiation in a relatively thin layer located away from the central region where the dynamics of principal interest unfold. The addition of a standard type of finite-difference dissipation 11 then ''quenches'' the blueshifted, frozen radiation, and very little energy is reflected back into the interior region. This approach, like that described in 10 , has the advantage that a static and uniform finite-difference mesh can be used, so that computational time scales linearly with the integration period, T. Our new technique was crucially important to our discovery and detailed study of fine structure in a well-known and still much studied nonlinear system. Specifically, we have found strong evidence for a family of resonant oscillon solutions in the SDWP model. Each of these solutions appears to possess a single unstable mode in perturbation theory, and by tuning the family parameter, r 0 , in the vicinity of a specific resonance, we can tune away that mode, producing oscillons which live longer and longer as we tune closer and closer to the precise resonant value, r à . This leads to a view 0 of oscillons as being analogous to the type I critical solutions
which have been discovered in the context of gravitational collapse 12 , and as in that case, we find compelling evidence for power-law scaling of the oscillon lifetime, : cr r0 rà 0
where c r is an overall scale factor set by the particular resonance, and r is a resonance-dependent exponent which is presumably the reciprocal Lyapunov exponent associated with the resonance's single unstable mode. In addition, contrary to previous claims 8,10 , we see no hard evidence for an upper bound on r 0 beyond which oscillons are no longer generated via collapse of Gaussian data. In particular we find strong evidence for resonances for r 0 6.5, well above the limit r 0 4.2 quoted in 8,10 . Moreover, we relate the existence of these ''large-r 0 '' resonances to the ''bouncing'' behavior observed in the 1 1 kinkantikink study of Campbell et al. 9 . The remainder of the paper is organized as follows. In Sec II we introduce a new coordinate system in which to solve nonlinear wave equations using finite differences. We examine the conformal structure induced by our new coordinates, as well as the characteristics of the resulting wave equation. In Sec. III we discuss the new properties of oscillons that were discovered during our study. In particular, we observe resonances in the parameter space which obey a time-scaling law, and we construct a sample resonant solution via a nonradiative ansatz Secs. III A and III B, respectively . Finally, in Sec. III C we discuss oscillons and resonant solutions found outside the bounds of the parameter space previously explored. Sec. IV summarizes our results and is followed by two appendixes that discuss the details of the finite difference equations Appendix A and the testing of the code Appendix B .
We are interested in the self-interacting scalar field theory described by the (3 1)-dimensional action S d 4x g 1 g 2 V 2
where we take V( ) to be a symmetric double well potential2 VS 1 4
and g to be the metric of flat spacetime in spherical symmetry, written in standard spherical polar coordinates (˜ ,r ,˜ , ˜ ): t˜
This is identical to using V( ) ( /4)( 2 m 2 / ) 2 and introducing dimensionless variables r ˜ m, t ˜ m, and r t /m) .
˜ ds 2
˜ r d˜ 2 dr 2 ˜ 2 d˜ 2 sin2˜ d ˜ 2 . t
We now introduce a new radial coordinate, r, which interpor lates between the old radial coordinate, ˜ , at small ˜ and an r outgoing null coordinate at large ˜ . Specifically, we take r ˜ t, t ˜ r r ˜ ˜ , , f r t, 5 6 7 8
In the nomenclature of the ADM formalism, is the lapse function, while is the radial component of the shift vector. In the work which follows, we have adopted the following specific form for f (r): f r where 1 tanh r c / /2 12 1 tanh r r c / /2 , 11
where f (r) is a monotonically increasing function which smoothly interpolates between 0 and 1 at some characteristic cutoff, r c , so that f (r)→0 for r r c , and f (r)→1 for r r c . We call (t,r) monotonically increasingly boosted MIB coordinates. The MIB system reduces to the original spherical coordinates, (˜ ,r ), for r r c , but as discussed bet˜ low, in the r r c region, both outgoing and ingoing from r r c ) radiation tends to be ''frozen'' in the transition layer, r r c . Furthermore, since the outgoing radiation is blueshifted as it propagates into the transition region, r r c , application of standard finite-difference dissipation operators can then quench it with minimal reflection back into the interior of the computational domain. In general, MIB coordinates will not cover all of the (˜ ,r ) t˜ half plane. However, given that f (r) is monotonically increasing, the determinant of the Jacobian of the transformation is nonzero for all t such that t max f (r) . Thus, for this range of t, the transformation to and from the standard spherical coordinate system is well defined, and although a coordinate singularity inevitably forms as t→ past timelike infinity , this has no effect on the forward evolution of initial data given at t 0. We also note that in order that our MIB coordinates be regular at r 0 so that there is no conical singularity at the origin , we must also demand that f (0) 0. Our coordinate choice results in the following spherically symmetric, 3 1, or Arnowitt-Deser-Misner ADM 13 form: ds 2
is chosen to satisfy the regularity condition at r 0. It is now instructive to consider the conformal structure of the MIB hypersurfaces. This is done by applying Eqs. 8 to the standard conformal compactification on Minkowski space, ˜ ˜ tan (T R)/2 where T and R are the axes in t r the conformal diagram; see 14 or 15 , and then plotting curves of constant r and t. The constant-t hypersurfaces are everywhere spacelike and all reach spatial infinity, i o . Although constant-r surfaces for r r c appear at first glance to be null, a closer look see insets of Fig. 1 reveals that they are indeed everywhere timelike and do not ever reach future null infinity, J . The equation of motion for the scalar field which results from the action 2 is 1 g gg a(
1 )/ , and
which with Eqs. 9 , 10 , give r ˙ 1 r b
2 2
r 2b 2
˙ b b
1 , 14
a ,
dt 2 2a 2 dtdr a 2 dr 2 sin2 d
r 2b 2 d where a t,r 1
f r t,
b t,r
f r
t r
where ˙ t and r . These equations are familiar from the ADM formalism as applied to the spherically symmetric Klein-Gordon field coupled to the general relativistic gravitational field 16 . However, in the current case, instead of dynamically evolving metric functions, the metric components a, b, , and are a priori fixed functions of (t,r) that resulted from a coordinate transformation of flat spacetime. Clearly, characteristic speeds for the massless KleinGordon field V( ) 0 bound the inward or outward speed group velocities of any radiation in a self-interacting field V( ) 0 . Characteristic analysis of the massless KleinGordon equation with metric 9 yields local propagation speeds , 17
f r 1 f r t
FIG. 1. Conformal diagram showing surfaces of constant r dotted lines and lines of constant t dashed lines . Lines of constant t look exactly like the constant-t hypersurfaces of Minkowski space, whereas the lines of constant r behave much differently. For r r c , it appears as if the constant-r surfaces are null. However, as insets A, B, and C show, the constant-r lines do not become null do not intersect future null infinity , but rather are everywhere timelike.
FIG. 3. Plot of characteristic speeds, (r ,100), where r and t are radial MIB coordinates in units where r c is set to unity.
where and are the outgoing and ingoing characteristic speeds, respectively 16,17 see Fig. 2 . For r r c , the propagation of scalar radiation in (t,r) or (˜ ,r ) coordinates t˜ is essentially identical. However, as illustrated in Fig. 3, and as can be deduced from Eqs. 17 and 10 , for r r c both the ingoing and the outgoing characteristic velocities go to zero as t→ as the inverse power of t). Thus, any radiation incident on this region will effectively be trapped, or ''frozen in.'' It is this property of the MIB system that enables the effective implementation of nonreflecting boundary conditions. As discussed further in Appendix A, an additional key
ingredient is the application of Kreiss-Oliger-style dissipation 11 to the difference equations. This dissipation efficiently quenches the trapped outgoing radiation, which as mentioned above tends to be blueshifted to the lattice scale on a dynamical time scale. Finally, we note that, as is evident from Fig. 3, the ''absorbing layer'' in the MIB system i.e. the region in which the characteristic speeds are 0) expands both outward and inward as t increases. This means that for fixed r c , the absorbing layer will eventually encroach on the interior region r r c and ruin the calculation. However, the rate at which the layer expands is roughly logarithmic in t, so, in practice, this fact should not significantly impact the viability of the method. For arbitrarily large final integration times, T, computational cost will scale as T ln T. However, the calculations described here all used the same values of the grid param5), so that for all practical eters (r max 60, r c 54, and purposes, the computational cost is linear in the integration time. The ability of the system to trap and absorb outgoing radiation is relatively insensitive to the choice of both and r c and was observed to work well for varying amounts of outgoing radiation Appendix B and Figs. 16 and 17 below .
FIG. 2. Plot of the characteristic velocities as a function of the MIB coordinates r and t in units where r c is set to unity. and are the outgoing and ingoing characteristic speeds respectively. is taken to be → /r c 0.0893 corresponding to the system used in this article . Characteristic velocities are plotted for times t 0, 1, 10, and 100 (t 100 is larger than the lifetime of the longest lived solution studied in this work . As r→1, we have (t ,r ) O(1/t ).
Copeland et al. 8 showed quite clearly that oscillons formed for a wide range of initial bubble radii, r 0 . They even caught a glimpse of the fine structure in the model—which in large part motivated this study—but they did not explore this fine structure of the parameter space in detail. With the efficiency of our new code, we have been able to explore parameter space much more thoroughly, which in turn has yielded additional insights into the dynamical nature of oscillons. Following 7 we use a Gaussian profile for initial data where the fields at the core and outer boundary values are set (t, ) to the vacuum values, (t,0) c 1 and o 1 respectively, and the field interpolates between them at a characteristic radius, r 0 : 0,r
o c o
r 2 /r 2 . 0
FIG. 4. Plot of oscillon lifetime versus initial bubble radius for 2.0 r 0 5.0. Each of the 125 resonances is resolved to one part in 1014.
Keeping c and o constant, but varying r 0 , we have a one parameter family of solutions to explore. Figure 4 shows the behavior of the oscillon lifetime as a function of r 0 in the range 2.0 r 0 5.0. We discuss three main findings that are distinct from previous work: the existence of resonances and their time scaling properties, the mode structure of the resonant solutions, and the existence of oscillons outside the parameter-space region 2 r 0 5.
A. Resonances and time scaling
FIG. 6. Top plot shows the envelope of (t,0) for r à r0 0 displaying bifurcate behavior around the r à 2.335 resonance 0 ( r 0 10 14); the solid curve is the envelope barely above resonance 15 modulations while the dotted line is the envelope barely below resonance 14 modulations . Bottom plot shows the energy radiated as a function of time through the surface containing the oscillon as defined in Appendix B. The increases in the energy radiated are synchronized with the modulation in the field.
In contrast to Fig. 7 of Copeland et al. 8 , the most obvious new feature seen in Fig. 4 is the appearance of the 125 resonances which rise above the overall lifetime profile. These resonances also seen in Fig. 5 become visible only after carefully resolving the parameter space. Upon finetuning r 0 to about 1 part in 1014 we noticed interesting bifurcate behavior about the resonances Fig. 6, top . The
FIG. 5. Plot of oscillon lifetime versus initial bubble radius for 2.27 r initial 2.29. The three resonances shown occur at r * 0 * 2.2805, r 1 2.2838, and r * 2.2876. Each resonance separates 2 the parameter space into regions with n and n 1 modulations; the 's correspond to oscillons with no modulations, the triangles to oscillons with one modulation, the squares to two modulations, and the circles to three modulations.
field oscillates with a period T 4.6 for all oscillons so the individual oscillations cannot be seen in the plot, but it is the lower-frequency modulation that is of interest here.3 The top figure shows the envelope of (t,0) on both sides of a resonance dotted and solid curves . We see that the large period modulation that exists for all typical oscillons disappears late in the lifetime of the oscillon as r 0 is brought closer to a resonant value, r à . On one side of r à the modulation returns 0 0 before the oscillon disperses referred to as supercritical and shown with the solid curve , while on the other side of r à the 0 modulation does not return and the the oscillon simply disperses referred to as subcritical and shown with the dotted curve . For resonances where r à 2.84, the subcritical solu0 tions appear on the r 0 r à side of the resonance and the 0 supercritical solutions appear on the r 0 r à side of the reso0 nance. The opposite is true for resonances where r à 2.84, 0 i.e. the subcritical solutions appear on the r 0 r à side of the 0 resonance and the supercritical solutions appear on the r 0 r à side of the resonance. This bifurcate behavior does not 0 manifest itself until r 0 is quite close to r à . In practice then, to 0 locate a resonant value, r à , we first maximize the oscillon 0 lifetime using a three point extremization routine golden section search with bracketing interval of 0.62, 18 until we have computed an interval whose end points exhibit the two distinct behaviors just described. Once a resonance has been thus bracketed, we switch to a standard bisection search, and subsequently locate the resonance to close to machine precision. Although we can see from Fig. 6 that the modulation is directly linked to the resonant solution, it is
In dimensionful coordinates, ˜ and ˜ , the period would be ˜ r t T 4.6m 1 . In general, to recover proper dimensions, lengths and times are multiplied by m 1 and energies by m 1 .
FIG. 7. Plot of time scaling T versus ln r0 rà for the r 0 0 2.335 resonance. The top line triangles displays the scaling behavior for supercritical evolutions, r 0 r à , while the bottom line 0 ( 's shows the scaling for subcritical calculations, r 0 r à . The 0 exponents measured by the slopes of the lines are both approximately equal to 30. The offset in the two curves represents the time spent by supercritical oscillons in executing the final modulation shown in Fig. 6.
FIG. 8. Plot of critical exponents for each resonance. There are vs r à two values of for each resonance. The top plot displays 0 à while the lower plot displays vs r 0 . The uncertainties are estimated from running the entire parameter space surveys at two resolutions, N N r 1449 and N N r 1025 and estimating the error, N N .
not obvious why this is so. However, if we look at the relationship between the modulation in the field top and the power radiated by the oscillon bottom , we see that they are clearly synchronized. The behavior of these resonant solutions may not be sur¯ prising to those familiar with the 1 1 KK scattering studied using the same model 9 . Campbell et al. showed that after the ''prompt radiation'' phase—the initial release of radiation upon collision of a kink and antikink—the remaining radiation was emitted from the decay of what they referred to as ''shape'' oscillations. The ''shape modes'' were driven by the ¯ contribution to the field ''on top'' of the K and K soliton solutions. Since the exact closed-form solution for the ideal ¯ nonradiative KK interaction is not known, initial data aimed at generating such an interaction is generally only approximate, and the ''surplus'' or deficit field is responsible for exciting the shape modes. The energy stored in the shape modes slowly decays away as the kink and antikink interact and eventually the solution disperses. In our case, we believe the large period modulation represents the excitation of a similar ''shape mode'' superimposed on a periodic, nonradiative, localized oscillating solution. On either side of a resonance in the r 0 parameter space, the solution is on the threshold of having one more shape mode oscillation. If this is the case, then, as we tune r 0 →r à , we are, in effect, tuning away the single unstable shape 0 mode, and thus should expect that the oscillon lifetime will obey a scaling law such as that seen in type I solutions in critical gravitational collapse 12 . Figure 7 shows a plot of oscillon lifetime versus ln r0 rà for the r 0 2.335 . . . 0 resonance , and we can see quite clearly that there is a scalln r0 rà , for the lifetime of the solution as ing law, T 0 measured on either side of the resonance. We denote for for the the scaling exponent on the r 0 r à side, and 0 scaling exponent on the r 0 r à side. Although we observe 0
lifetime scaling for each resonance, the scaling exponent per se varies from resonance to resonance; a plot of the scaling exponents, and , versus the critical initial bubble radius can be seen in Fig. 8. For all resonances we find . Finally we note that, by analogy with the case of type I critical gravitational collapse, we expect that the scaling exponents, , are simply the reciprocal Lyapunov exponents associated with each resonance's single unstable mode. In addition we note that, for any resonance, if we were able to infinitely fine-tune r 0 to r à , we would expect the oscillon 0 lifetime to go to infinity.
B. Mode structure
Assuming that periodic, nonradiative solutions to Eq. 13 exist, we should be able to construct them by inserting an ansatz of the form t,r
n 1
r cos n t
in the equations of motion and solving the resulting system of ordinary differential equations obtained from matching cos(n t) terms: r2
/r 2
3 2
m, 2
1 4 r2
m,p,q 0
n 2
p q
/r 2
3 3 2 1 4
q n,
p q
n, m
p q
FIG. 9. Critical solution n (r) for n 0,1,2,3,4) obtained from the Fourier-decomposed PDE data ( 's overlaid with n (r) obtained by shooting Eqs. 20 and 21 solid curves . The Fourierdecomposed PDE data overlies the shooting solution everywhere.
Equations 20 and 21 can also be obtained by inserting ansatz 19 into the action and varying with respect to the n 19 . This set of ordinary differential equations can be solved by ''shooting,'' where the quantities n (0) are the shooting parameters. Unfortunately, we were unable to construct a method that self-consistently computed ; the best we could achieve was to solve Eqs. 20 and 21 for a given which we measured from the partial differential equation PDE solution. For ease of comparison of the results obtained from the periodic ansatz with those generated via solution of the PDEs, we Fourier decomposed the PDE results. This was done by taking the solution during the interval of time when the large period modulation disappears (1200 t 1800 for the oscillon in Fig. 6, for example and constructing fast Fourier transforms FFTs of at each grid point, r i . Specifically, at each r i , the amplitude of each Fourier mode was obtained from a FFT which used a time series, (t n ,r i ), n t const. Keeping only 1,2, . . . ,4096 with t n 1 t n the first five modes in the expansion 19 , we compare the Fourier decomposed PDE data with the shooting solution see Fig. 9 . It should be noted that although the value for was determined from the PDE solution, the shooting algorithm still involved a five-dimensional search for the the shooting parameters, n (0), n 0, . . . ,4. The close correspondence of the curves shown in Fig. 9 strongly suggests that the resonant solutions i.e. in the limit as r 0 →r à ) ob0 served in the PDE calculations are indeed consistent with the periodic, nonradiative oscillon ansatz 19 . By examining the three most dominant components of the power spectrum of (t,0), Fig. 10, we can see that during the ''no-modulation'' epoch, the amplitude of each Fourier mode becomes constant. Although the specific plot is for the core amplitude, r 0, we note that this behavior holds for all r. Again, this is consistent with the view that as we tune r 0 to r à , the oscillon phase of the evolution is better and better 0 described by a one-mode unstable ''intermediate attractor.'' As discussed previously, this is precisely reminiscent of the type I critical phenomena studied in critical gravitational collapse, particularly the collapse of a real, massive scalar field
FIG. 10. Power spectra of the core amplitude, (t,0), for the oscillons barely above and below the r 0 2.335 resonance. The power measured in each frequency regime slowly diminishes as the oscillon radiates away much of its energy until approximately t 1100 where the oscillon enters a nonradiative state and all the components of the power spectrum become constant.
as studied by Brady et al. 12 , where the intermediate attractors are unstable, periodic, ''oscillon stars'' discovered earlier by Seidel and Suen 20 .
C. "Bounce… windows to more oscillons
Lastly, we consider the existence of oscillons generated by Gaussian initial data with r 0 5. The oscillons explored by Copeland et al. were restricted to the parameter-space region 2 r 0 5, and in fact it was concluded that there was an upper bound, r 0 4.2, beyond which evolution of Gaussian data would not result in an oscillon phase 10 . However, we have found that oscillons can form for r 0 5, and that they do so by a rather interesting mechanism. ¯ Again, from the 1 1 dimensional K scattering studies of Campbell et al., it is well known that a kink and antikink in interaction often ''bounce'' many times before either dispersing or falling into an unstable bound state. Here, a bounce occurs when the kink and antikink reflect off one another, stop after propagating a short distance, and then recollapse. We find that such behavior occurs in the (3 1) dimensional case as well, but now the unstable bound state is an oscillon. For larger r 0 , instead of remaining within r 2.5 after reflection through r 0 as occurs for 2 r 0 5), the bubble wall travels out to larger r typically 3 r 6), stops, then recollapses, shedding away large amounts of energy in the process see Fig. 11 . Thus in this system, as with the ¯ 1 1 KK model, there are regions of parameter space which constitute ''bounce windows.'' Within such regions, the bounces allow the bubble to radiate away large amounts of energy. The bubble then recollapses, effectively producing a new initial configuration albeit with a different shape with a smaller effective r 0 . Within these ''windows'' both oscillons and resonances similar to those observed for 2 r 0 4.6) can be observed inset of Fig. 12 .
computed and those generated via finite-difference solution of the PDEs. Finally, we have showed that oscillons can form from bubbles with energies higher than had previously been assumed, through a mechanism analogous to the bounce windows found in the 1 1 case of kink-antikink scattering. We note that the use of MIB or related coordinates, in conjunction with finite-difference dissipation techniques, should result in a generally applicable strategy for formulating nonreflecting boundary conditions for finite-difference solution of wave equations. The method has already been used in the study of axisymmetric oscillon collisions 21 , and attempts are under way to use similar techniques in the context of 3D numerical relativity and 2D and 3D ocean acoustics.
FIG. 11. Plot of (t,0) for r 0 7.25 displaying extremely nonlinear and unpredictable behavior during the ''bouncing'' phase for t 60), after which the field settles into a typical oscillon evolution. Once in the oscillon regime, the period is approximately T 4.6, and the first two modulations of the field can be seen envelope maxima at t 105 and t 200). IV. CONCLUSIONS ACKNOWLEDGMENTS
Using a new technique for implementing nonreflecting boundary conditions for finite-differenced evolutions of nonlinear wave equations, we have conducted an extensive parameter space survey of bubble dynamics described by a spherically symmetric Klein-Gordon field with a symmetric double-well potential. We have found that the parameter space of the model exhibits resonances wherein the lifetimes of the intermediate-phase ''oscillons'' diverge as one approaches a resonance. We have conjectured that these resonances are single-mode unstable solutions, analogous to type I solutions in critical gravitational collapse, and have presented evidence that their lifetimes satisfy the type of scaling law which is to be expected if this is so. In addition, we have independently computed resonant solutions starting from an ansatz of periodicity, and have demonstrated good agreement between the solutions thereby
We thank Philip J. Morrison for useful discussions on the exact nonradiative oscillon solutions. We also thank Marcelo Gleiser and Andrew Sornborger for useful input on many oscillon issues. This research was supported by NSF grant PHY9722088, a Texas Advanced Research Projects Grant, and by NSERC. The bulk of the computations described here were carried out on the vn.physics.ubc.ca Beowulf cluster, which was funded by the Canadian Foundation for Innovation, with operations support from NSERC, and from the Canadian Institute for Advanced Research. Some computations were also carried out using the Texas Advanced Computing Center's SGI Cray SV-1 aurora.hpc.utexas.edu and SGI Cray T3E lonestar.hpc.utexas.edu.
Equations 14 , 15 , 16 are solved using two-level second order in both space and time finite difference approximations on a static uniform spatial mesh: ri i 1 r, i 1,2, . . . ,I, A1
where I is the total number of mesh points r r max . I 1 A2
TABLE I. Two-level finite difference operators. Here we have adopted a standard finite-difference notation: f in f "(n 1) t,(i 1) r…. Operator
f n rfi b n r fi n rfi n tfi d n t fi
Definition ( 3 f in 4 f in 1 f in 2 )/2 r (3 f in 4 f in 1 f in 2 )/2 r ( f in 1 f in 1 )/2 r ( f in 1 f in )/ t ( f in 1 f in )/ t n f in 2 f in 2 dis 6 f i n 4( f i 1 f in 1 )]/16 t ( f in 1 f in )/2
n O( r 2 ) rf i n O( r 2 ) rf i n O( r 2 ) rf i n 1/2 O( t 2 ) tf i n 1/2 O( t 2 ) tf i
FIG. 12. Plot of oscillon lifetime versus initial radius of bubble for 4.22 r 0 9. Although there seem to be no oscillons in the range 4.6 r 0 6, it is clear that oscillons and resonances do exist for higher initial bubble radii, r 0 6.5.
n tfi
n 1/2 i
O( t 2 )
FIG. 13. Fundamental field (r) in the freeze-out region at t 0, 57, 75, and 270. The characteristic speeds of the radiation →0 as r→r c here, r c 56) and the wavelength of the radiation is blueshifted to the lattice Nyquist limit, 2 r. The Kreiss-Oliger dissipation explicitly added to the finite difference equations subsequently ''quenches'' the field.
FIG. 14. Typical convergence factor, C f 4h 2h 2 / 2h composed from the solution at three differh 2 , for the field ent discretizations value of 4 indicates second order convergence . The l 2 norm ••• 2 is defined by v 2 (N 1 iN 1 v i ) 1/2. Extensive convergence testing was performed throughout r 0 space and the above plot is representative of all the tests performed.
f i
The scale of discretization is set by r and t r, where we fixed the Courant factor, , to 0.5 as we changed the base discretization. r Using the operators from Table I, r˜ a, r nr n 1 r n , and rb ˜ , the difference equations applied in the interior of r the mesh, i 2,3, . . . ,I 1, are
n d t n i
a a
n 1
is fixed by regularity:
n 1
˜3 r
˜2 r
a a
ii n
To update , we use a discrete versions of the equation for ˙ which follows from the definition of :
˙ b 2 b
i 1,2, . . . ,I.
n d t n i t r
d t
n i
These equations are solved using an iterative scheme and explicit dissipation of the type advocated by Kreiss and Oliger 11 . The dissipative term, incorporated in the operator d , is essentially a fourth spatial derivative multiplied by t ( r) 3 so that the truncation error of the difference scheme remains O( r 2 , t 2 ). Although the results discussed in this paper were not sensitive to the choice of dis , we always used dis 0.1. The temporal difference operator, d , is used t as an approximation to t everywhere in the interior of the computational domain, except for next-to-extremal points, where t is used because the grid values f in 2 or f in 2 are not defined. At the inner boundary, r 0, we use O( r 2 ) forward spatial differences to evolve :
FIG. 15. Plot of energy contained in oscillon dashed line , energy radiated dotted line , and total energy solid line . The total energy of the system is a constant of motion and is numerically conserved to within a few tenths of a percent. The energy contained within the bubble drops rapidly during the initial radiative phase and plateaus around E 43m/ during the quasistable ''oscillon'' phase.
region are efficiently and stably annihilated by the dissipation which is explicitly added to the difference scheme Fig. 13 . In fact, there is a loss of resolution and second order convergence for r r c , but this does not affect the stability or convergence of the solution for r r c . Figure 14 shows a convergence test for the field for r r c /2 over roughly six crossing times. Extensive convergence testing was performed throughout r 0 space and Fig. 14 is representative of all the tests performed. Since we are solving Eq. 13 in flat spacetime, it is very simple to monitor energy conservation. The spacetime admits a timelike Killing vector, t , so we t T . We monitor the flux of have a conserved current, J J through a surface constructed from two adjacent spacelike ( 1,0,0,0) , and hypersurfaces for r r c with normals n (0,a 1 ,0,0) . To an ''end cap'' at r r O with normal n obtain the the conserved energy at a time, t f , the energy contained in the bubble,
FIG. 16. Plot comparing the OBC solid lines and MIB dotted lines solutions to ''ideal'' solutions for r 0 2.4,2.8,3.5,4. These values were chosen to reasonably cover the region of interest in r 0 space and test the system with varying amounts of outgoing radiation at r 0 4 almost four times the mass of a typical oscillon enters the region r r c ). The OBC solutions are obtained using a massless outgoing boundary condition, the MIB solutions are obtained by solving the system in spherical MIB coordinates, and the ideal solutions are obtained by evolving the solution in standard (r,t) coordinates on a grid large enough to ensure no reflection off the outer boundary. The error estimates are obtained from the l 2 norm of the difference between the trial solutions OBC or MIB and the ideal solution, ideal 2 . Contamination of the OBC solution is observed at two crossing times, t 120, where the error estimate increases by over three orders of magnitude.
E bubble 4
rO 0
r 2b 2
2a 2
where the integrand is evaluated at time t f , is added to the total radiated energy, E rad 4
tf 0
r 2b 2
At the outer boundary, r r max , our specific choice of boundary conditions and discretizations thereof have little impact; due to the use of MIB coordinates and Kreiss-Oliger dissipation, almost none of the outgoing scalar field reaches the outer edge of the computational domain. Nevertheless, we imposed discrete versions of the usual Sommerfeld conditions for a massless scalar field on and :
n t n i t b r
I n
n i
b r
One might think that ''freezing'' outgoing radiation on a static uniform mesh would lead to a ''bunching-up'' of the wave-train from the oscillating source, which would then result in a loss of resolution, numerical instabilities, and an eventual breakdown of the code. However, this turns out not to be the case; all outgoing radiation is ''frozen'' around r r c , but the steep gradients which subsequently form in this
where the integrand is evaluated at r r O ). The sum, E total E bubble E rad , remains conserved to within a few tenths of a percent4 through 250 000 iterations see Fig. 15 . Although monitoring energy conservation is a very important test, it says little about whether there is reflection of the field off the outer boundary, r r max , or the region r r c . To check the efficacy of our technique for implementing nonreflecting boundary conditions, we compare the MIB results to those obtained with two other numerical schemes. The first alternate method involves evolution of Eq. 13 in (˜ ,r ) cot˜ ordinates on a grid with r max sufficiently large that radiation never reaches the outer boundary large-grid solutions . For a given discretization scale, results from this approach serve as near-ideal reference solutions, since the solution is guaranteed to be free of contamination from reflection off the outer boundary. The second method involves evolution on a grid with the same r max adopted in the MIB calculation, but with discrete versions of massless Sommerfeld outgoing radiation conditions applied at r r max . We refer to the results thus generated as outgoing boundary condition OBC solutions, and since we know that these solutions do have error resulting from reflections from r r max , they demonstrate what can go wrong when a solution is contaminated by reflected radiation. Treating the large-grid solution as ideal, Fig. 16 compares log10 ideal 2 of both MIB and OBC solutions for four different values of r 0 , showing the consis4 A few hundredths of a percent if measured relative to the energy remaining after the initial radiative burst from the collapse.
FIG. 17. Plot comparing the OBC solid lines and MIB dotted lines solutions to ''ideal'' solutions for different . The OBC solutions are obtained using a massless outgoing boundary condition, the MIB solutions are obtained by solving the system in spherical MIB coordinates, and the ideal solutions are obtained by evolving the solution in standard (r,t) coordinates on a grid large enough to ensure no reflection off the outer boundary. The error estimates are obtained from the l 2 norm of the difference between the trial solutions OBC or MIB and the ideal solution, ideal 2 . Contamination of the OBC solution is observed at two crossing times, t 120, where the error estimate increases by over three orders of magnitude. Note that while some reflection is seen in 1 MIB solution, no reflection is observed for 2 8. The l 2 norm of the difference between the MIB and the ideal solutions increases with increasing . This is due to the slight differences between the coordinate systems i.e. a 1, b 1, and 0 for the MIB system ; these differences increase with larger .
FIG. 18. (t,0) versus time for the large-grid solution triangles , MIB solution solid curves , and OBC solution dashed curves . The solutions all agree before 2t crossing , but the OBC solution begins to drift away from the ideal solution after 2t crossing . The error in the OBC solution is due to radiation that is reflected off the outer boundary hence needing two crossing times to return to r 0 to contaminate the oscillon . All pictures span the same area, 0.075 by t 0.5.
tency of the system across the region of interest in r 0 space. It should be noted that by increasing r 0 more energy is shed away during the initial bubble collapse up to almost four times the mass of a typical oscillon at r 0 4). In each plot there is a steep increase in the OBC solution error three orders of magnitude around t 125, which is at roughly two crossing times again, r max 60 and r c 54). This implies that some radiation emitted from the initial collapse reached the outer boundary and reflected back into the region r
rO . There is no such behavior found in any MIB solutions. Figure 17 shows the insensitivity of the system to the choice of ; although there is some reflection observed in the MIB 1, for 2 8 no reflection is observed. system when The system is also insensitive to the choice of r c , again assuming that r c is chosen such that the ''freeze-out'' region does not encroach on the region of interest. Lastly, for a more direct look at the field itself, we can see (t,0) for large-grid triangles , MIB solid curves , and OBC dashed curves solutions in Fig. 18. Initially, both the MIB and OBC solutions agree with the large-grid solution extremely well. However, after two crossing times the OBC solution starts to substantially diverge from the ideal solution, while the MIB results remain in very good agreement with the ideal calculations. In summary, the MIB solution conserves energy, converges quadratically in the mesh spacing as expected , and produces results which are equivalent—at the level of truncation error—to large-grid reference solutions. At the same time, the MIB approach is considerably more computationally efficient than dynamical- or large-grid techniques.
1 J.S. Russell, in Report of the Fourteenth Meeting of the British Association for the Advancement of Science John Murray, London, 1845 . 2 A. Vilenkin, Phys. Rep. 121, 263 1985 . 3 R. Friedberg, T.D. Lee, and A. Sirlin, Phys. Rev. D 13, 2739 1976 . 4 S. Coleman, Nucl. Phys. B262, 263 1985 . 5 I.L. Bogolyubskii and V.G. Makhan'kov, JETP Lett. 24, 12 1976 .
6 I.L. Bogolyubskii and V.G. Makhan'kov, JETP Lett. 25, 107 1977 . 7 M. Gleiser, Phys. Rev. D 49, 2978 1994 . ¨ 8 E.J. Copeland, M. Gleiser, and H.R. Muller, Phys. Rev. D 52, 1920 1995 . 9 D.K. Campbell, J.F. Schonfeld, and C.A. Wingate, Physica D 9, 1 1983 . 10 M. Gleiser and A. Sornborger, Phys. Rev. E 62, 1368 2000 . 11 H.-O. Kreiss and J. Oliger, ''Methods for the Approximate
ETHAN P. HONDA AND MATTHEW W. CHOPTUIK Solution of Time Dependent Problems,'' Global Atmospheric Research Program Publication No. 10, World Meteorological Organization, Case Postale No. 1, CH-1211 Geneva 20, Switzerland, 1973. ´ 12 M.W. Choptuik, T. Chmaj, and P. Bizon, Phys. Rev. Lett. 77, 424 1996 ; P.R. Brady, C.M. Chambers, and S.M.C.V. Goncalves, Phys. Rev. D 56, 6057 1997 ; S.H. Hawley and M.W. Choptuik, ibid. 62, 104024 2000 . 13 R. Arnowitt, S. Deser, and C.W. Misner, in Gravitation: An Introduction to Current Research, edited by L. Witten Wiley, New York, 1962 ; C.W. Misner, K.S. Thorne, and J.A. Wheeler, Gravitation W.H. Freeman, San Francisco, 1973 . 14 S.W. Hawking and G. Ellis, The Large Scale Structure of Space-Time Cambridge University Press, Cambridge, En-
PHYSICAL REVIEW D 65 084037 gland, 1973 . 15 R. Wald, General Relativity The University of Chicago Press, Chicago, 1984 . 16 M.W. Choptuik, Ph.D. dissertation, The University of British Columbia, 1986. 17 R. Courant and D. Hilbert, Methods of Mathematical Physics Wiley and Sons, New York, 1962 , Vol. II. 18 W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C, 2nd ed. Cambridge University Press, Cambridge, England, 1994 . 19 P.J. Morrison private communication . 20 E. Seidel and W.-M. Suen, Phys. Rev. Lett. 66, 1659 1991 . 21 E.P. Honda, Ph.D. dissertation, The University of Texas at Austin, 2000.


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Looking for a company which can design/develop web app similar to www.lumen5.com excluding the enterprise features. Please have a look at all the features thoroughly before bidding on this project and wasting the time. I will be required all the features. Plus, a feature of converting text to voice over. User can select the voice (male/female) as well
Hi, :) Need quality writer/researcher that will rewrite this article: obdadvisor .com/how-to-reset-check-engine-light (remove space before .com) Must be done with care and passion. It is not a mere inauthentic article-spinning attempt. Points: 1) Done in MS Word. No more then 1300 words. 2) Layout is to be decently exact. At least 80% identical
I am looking for a person who can market website http://techtutorialz.com. Looking for SEO, Social media , Digital marketing. Please visit http://[войдите, чтобы посмотреть URL] to understand the requirement before placing bid.
I am looking for Tutorials, Articles, Interview Questions, Sample resumes on AWS Please visit http://[войдите, чтобы посмотреть URL] to understand the requirement before placing bid.
I need SEO for a new Health and Wellness website http://[войдите, чтобы посмотреть URL] For some keywords low competition (you can choose from the site or suggest new ones) Tell me if you can provide me with guaranteed result. NO result, No payment. Please send me your plan in details. I don't read generic proposal. Thanks in advance.
We have two web services which give us JSON data. One API gives us the store list and another one gives us printers data for each store. The printers data contains printers DNS. These DNS does not respond to HTTP protocol. But these DNS respond when we ping them from terminal or command prompt using ping. Now we have to create the front-end using Angular
cant login or sign up a user also may need some php work
Já tenho o site montado e funcionando, mas minhas propagandas não ficaram bem expostas, então preciso de ajuda no layout. Também não tenho fontes de trafego, face, youtube entre outros Em resumo é isso preciso de alguém que me ajude no visual do site, no encaixe das propagandas e criação de mídias sociais
...(please see Excel attached). Characters: There must be 9 characters, including the main one. Each character must represent a number of the enneagram (https://www.integrative9.com/enneagram/introduction/) and each character must interact between each fo them according to how each personality number woud be expected to interact with. It is not needed to