Zippelius, Annette

[["dc.bibliographiccitation.artnumber","041505"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Physical Review. E"],["dc.bibliographiccitation.volume","65"],["dc.contributor.author","Broderix, K."],["dc.contributor.author","Mueller, P."],["dc.contributor.author","Zippelius, Annette"],["dc.date.accessioned","2018-11-07T10:31:02Z"],["dc.date.available","2018-11-07T10:31:02Z"],["dc.date.issued","2002"],["dc.description.abstract","A simple Rouse-type model, generalized to incorporate the effects of chemical cross-links, is used to obtain a theoretical prediction for the critical behavior of the normal-stress coefficients Psi(1) and Psi(2) in polymeric liquids when approaching the gelation transition from the sol side. While the exact calculation shows Psi(2)=0, a typical result for these types of models, an additional scaling ansatz is used to demonstrate that Psi(1) diverges with a critical exponent l=k+z. Here, k denotes the critical exponent of the shear viscosity and z the exponent governing the divergence of the time scale in the Kohlrausch decay of the shear-stress relaxation function. For cross-links distributed according to mean-field percolation, this scaling relation yields l=3, in accordance with an exact expression for the first normal-stress coefficient based on a replica calculation. Alternatively, using three-dimensional percolation for the cross-link ensemble we find the value lapproximate to4.9. Results on time-dependent normal-stress response are also presented."],["dc.identifier.doi","10.1103/PhysRevE.65.041505"],["dc.identifier.isi","000175146400035"],["dc.identifier.pmid","12005827"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/44004"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Amer Physical Soc"],["dc.relation.issn","1539-3755"],["dc.title","Normal stresses at the gelation transition"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","279"],["dc.bibliographiccitation.issue","1-4"],["dc.bibliographiccitation.journal","Physica A Statistical Mechanics and its Applications"],["dc.bibliographiccitation.lastpage","289"],["dc.bibliographiccitation.volume","302"],["dc.contributor.author","Broderix, K."],["dc.contributor.author","Lowe, H."],["dc.contributor.author","Mueller, P."],["dc.contributor.author","Zippelius, Annette"],["dc.date.accessioned","2018-11-07T11:19:21Z"],["dc.date.available","2018-11-07T11:19:21Z"],["dc.date.issued","2001"],["dc.description.abstract","Within the framework of a simple Rouse-type model we present exact analytical results for dynamical critical behaviour on the sol side of the gelation transition. The stress-relaxation function is shown to exhibit a stretched-exponential long-time decay. The divergence of the static shear viscosity is governed by the critical exponent k = phi - beta, where phi is the (first) crossover exponent of random resistor networks, and P is the critical exponent for the gel fraction. We also derive new results on the behaviour of normal stress coefficients. (C) 2001 Published by Elsevier Science B.V."],["dc.identifier.doi","10.1016/S0378-4371(01)00471-X"],["dc.identifier.isi","000173004500027"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/55253"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Elsevier Science Bv"],["dc.publisher.place","Amsterdam"],["dc.relation.conference","2nd Minerva Workshop on Frontiers in the Physics of Complex Systems"],["dc.relation.eventlocation","DEAD SEA, ISRAEL"],["dc.relation.issn","0378-4371"],["dc.title","Anomalous stress relaxation in random macromolecular networks"],["dc.type","conference_paper"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","325"],["dc.bibliographiccitation.issue","2"],["dc.bibliographiccitation.journal","The European Physical Journal. E, Soft Matter"],["dc.bibliographiccitation.lastpage","331"],["dc.bibliographiccitation.volume","12"],["dc.contributor.author","Kuntzel, M."],["dc.contributor.author","Lowe, H."],["dc.contributor.author","Mueller, P."],["dc.contributor.author","Zippelius, Annette"],["dc.date.accessioned","2018-11-07T10:35:45Z"],["dc.date.available","2018-11-07T10:35:45Z"],["dc.date.issued","2003"],["dc.description.abstract","Starting from a Zimm model, we study self-diffusion in a solution of crosslinked monomers. We focus on the effects of the hydrodynamic interaction on the dynamics and the critical behaviour at the sol-gel point. Hydrodynamic interactions cause the clusters' diffusion constant to depend not only on the cluster's size but also on the cluster's shape --in contrast to the Rouse model. This gives rise to a non-trivial scaling of the Kirkwood diffusion constant averaged over all clusters of fixed size n, (D) over cap (n) similar to n(-(b) over bar) with (b) over cap = 1/d(s) -1/2 given in terms of the spectral dimension d(s) of critical percolation clusters. The long-time decay of the incoherent scattering function is determined by the diffusive motion of the largest clusters. This implies the critical vanishing D-eff similar to epsilon(a) of the cluster-averaged effective diffusion constant at the gel point with exponent a = (3/2 -tau + 1/d(s))/sigma."],["dc.identifier.doi","10.1140/epje/i2003-10066-x"],["dc.identifier.isi","000186890500013"],["dc.identifier.pmid","15007668"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/45162"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Springer"],["dc.relation.issn","1292-895X"],["dc.relation.issn","1292-8941"],["dc.title","Diffusion of gelation clusters in the Zimm model"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","011510"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Physical Review. E"],["dc.bibliographiccitation.volume","63"],["dc.contributor.author","Broderix, K."],["dc.contributor.author","Lowe, H."],["dc.contributor.author","Mueller, P."],["dc.contributor.author","Zippelius, Annette"],["dc.date.accessioned","2018-11-07T09:38:30Z"],["dc.date.available","2018-11-07T09:38:30Z"],["dc.date.issued","2001"],["dc.description.abstract","Shear relaxation and dynamic density fluctuations are studied within a Rouse model, generalized to include the effects of permanent random crosslinks. We derive an exact correspondence between the static shear viscosity and the resistance of a random resistor network. This relation allows us to compute the static shear viscosity exactly for uncorrelated crosslinks. For more general percolation models, which are amenable to a scaling description, it yields the scaling relation k = phi - beta for the critical exponent of the shear viscosity. Here beta is the thermal exponent for the gel fraction, and phi is the crossover exponent of the resistor network. The results on the shear viscosity are also used in deriving upper and lower bounds on the incoherent scattering function in the long-time limit, thereby corroborating previous results."],["dc.identifier.isi","000166404900048"],["dc.identifier.pmid","11304269"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/33076"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","American Physical Soc"],["dc.relation.issn","1063-651X"],["dc.title","Critical dynamics of gelation"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","014905"],["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","The Journal of Chemical Physics"],["dc.bibliographiccitation.volume","122"],["dc.contributor.author","Lowe, H."],["dc.contributor.author","Mueller, P."],["dc.contributor.author","Zippelius, Annette"],["dc.date.accessioned","2018-11-07T08:41:45Z"],["dc.date.available","2018-11-07T08:41:45Z"],["dc.date.issued","2005"],["dc.description.abstract","In order to study rheological properties of gelling systems in dilute solution, we investigate the viscosity and the normal stresses in the Zimm model [B. H. Zimm, J. Chem. Phys. 24, 269 (1956)]. for randomly cross-linked monomers. The distribution of cluster topologies and sizes is assumed to be given either by Erdos-Renyi random graphs or three-dimensional bond percolation. Within this model the critical behavior of the viscosity and of the first normal stress coefficient is determined by the power-law scaling of their averages over clusters of a given size n with n. We investigate these scaling relations numerically and conclude that the scaling exponents are independent of the hydrodynamic interaction strength. The numerically determined exponents agree well with experimental data for branched polymers. However, we show that this traditional model of polymer physics is not able to yield a critical divergence at the gel point of the viscosity for a polydisperse dilute solution of gelation clusters. A generally accepted scaling relation for the Zimm exponent of the viscosity is thereby disproved. (C) 2005 American Institute of Physics."],["dc.identifier.doi","10.1063/1.1813433"],["dc.identifier.isi","000226698500065"],["dc.identifier.pmid","15638698"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/19536"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Amer Inst Physics"],["dc.relation.issn","1089-7690"],["dc.relation.issn","0021-9606"],["dc.title","Rheology of gelling polymers in the Zimm model"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","051313"],["dc.bibliographiccitation.issue","5"],["dc.bibliographiccitation.journal","Physical Review. E"],["dc.bibliographiccitation.volume","70"],["dc.contributor.author","Herbst, O."],["dc.contributor.author","Mueller, P."],["dc.contributor.author","Otto, Markus"],["dc.contributor.author","Zippelius, Annette"],["dc.date.accessioned","2018-11-07T10:44:28Z"],["dc.date.available","2018-11-07T10:44:28Z"],["dc.date.issued","2004"],["dc.description.abstract","We present event-driven simulations of a granular gas of inelastic hard disks with incomplete normal restitution in two dimensions between vibrating walls (without gravity). We measure hydrodynamic quantities such as the stress tensor, density and temperature profiles, as well as velocity distributions. Relating the local pressure to the local temperature and local density, we construct a local constitutive equation. For strong inelasticities the local constitutive relation depends on global system parameters, like the volume fraction and the aspect ratio. For moderate inelasticities the constitutive relation is approximately independent of the system parameters and can hence be regarded as a local equation of state, even though the system is highly inhomogeneous with heterogeneous temperature and density profiles arising as a consequence of energy injection. With respect to local velocity distributions we find that they do not scale with the square root of the local granular temperature. Moreover the high-velocity tails are different for the distribution of the x and the y components of the velocity, and even depend on the position in the sample, the global volume fraction, and the coefficient of restitution."],["dc.identifier.doi","10.1103/PhysRevE.70.051313"],["dc.identifier.isi","000225970500034"],["dc.identifier.pmid","15600609"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/47272"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Amer Physical Soc"],["dc.relation.issn","1550-2376"],["dc.relation.issn","1539-3755"],["dc.title","Local equation of state and velocity distributions of a driven granular gas"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","46002"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","EPL"],["dc.bibliographiccitation.volume","78"],["dc.contributor.author","Koehler, C. H."],["dc.contributor.author","Loewe, H."],["dc.contributor.author","Mueller, P."],["dc.contributor.author","Zippelius, Annette"],["dc.date.accessioned","2018-11-07T11:06:30Z"],["dc.date.available","2018-11-07T11:06:30Z"],["dc.date.issued","2007"],["dc.description.abstract","We study shear stress relaxation for a gelling melt of randomly crosslinked, interacting monomers. We derive a lower bound for the static shear viscosity eta, which implies that it diverges algebraically with a critical exponent k >= 2 nu - beta. Here, nu and beta are the critical exponents of percolation theory for the correlation length and the gel fraction. In particular, the divergence is stronger than in the Rouse model, proving the relevance of excluded-volume interactions for the dynamic critical behaviour at the gel transition. Precisely at the critical point, our exact results imply a Mark-Houwink relation for the shear viscosity of isolated clusters of fixed size. Copyright (C) EPLA, 2007."],["dc.identifier.doi","10.1209/0295-5075/78/46002"],["dc.identifier.isi","000247233900012"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/52326"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Epl Association, European Physical Society"],["dc.relation.issn","0295-5075"],["dc.title","Variational bounds for the shear viscosity of gelling melts"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.artnumber","041303"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Physical Review. E"],["dc.bibliographiccitation.volume","72"],["dc.contributor.author","Herbst, O."],["dc.contributor.author","Mueller, P."],["dc.contributor.author","Zippelius, Annette"],["dc.date.accessioned","2018-11-07T10:55:35Z"],["dc.date.available","2018-11-07T10:55:35Z"],["dc.date.issued","2005"],["dc.description.abstract","We performed event-driven simulations of a two-dimensional granular gas between two vibrating walls and directly measured the local heat flux and local energy dissipation in the stationary state. Describing the local heat flux as a function of the coordinate x in the direction perpendicular to the driving walls, we test a generalization of Fourier's law, q(x)=-kappa del T(x)+mu del rho(x), by relating the local heat flux to the local gradients of the temperature and density. This ansatz accounts for the fact that heat flux can also be generated by density gradients, not only by temperature gradients. Assuming the transport coefficients kappa and mu to be independent of x, we check the validity of this assumption and test the generalized Fourier law in the simulations. Both kappa and mu are determined for different system parameters, in particular, for a wide range of coefficients of restitution. We also compare our numerical results to existing hydrodynamic theories. Agreement is found for kappa for very small inelasticities only, i.e., when the gradients are small. Beyond this region, kappa and mu exhibit a striking nonmonotonic behavior. This may hint that hydrodynamics to Navier-Stokes order cannot be applied to moderately inelastic vibrated systems."],["dc.identifier.doi","10.1103/PhysRevE.72.041303"],["dc.identifier.isi","000232930600019"],["dc.identifier.pmid","16383369"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/49819"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","American Physical Soc"],["dc.relation.issn","1539-3755"],["dc.title","Local heat flux and energy loss in a two-dimensional vibrated granular gas"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","S1659"],["dc.bibliographiccitation.issue","20"],["dc.bibliographiccitation.journal","Journal of Physics Condensed Matter"],["dc.bibliographiccitation.lastpage","S1680"],["dc.bibliographiccitation.volume","17"],["dc.contributor.author","Lowe, H."],["dc.contributor.author","Mueller, P."],["dc.contributor.author","Zippelius, Annette"],["dc.date.accessioned","2018-11-07T10:59:54Z"],["dc.date.available","2018-11-07T10:59:54Z"],["dc.date.issued","2005"],["dc.description.abstract","The dynamics of randomly crosslinked liquids is addressed via Rouse-type and Zimm-type models with crosslink statistics taken either from bond percolation or Erdos-Renyi random graphs. While the Rouse-type model isolates the effects of the random connectivity on the dynamics of molecular clusters, the Zimm-type model also accounts for hydrodynamic interactions on a preaveraged level. The incoherent intermediate scattering function is computed in thermal equilibrium; its critical behaviour near the: sol-gel transition is analysed and related to the scaling of cluster diffusion constants at the critical point. Second, non-equilibrium dynamics is studied by. looking at stress relaxation in a simple shear flow. Anomalous stress relaxation and critical rheological properties are derived. Some of the results contradict long-standing scaling arguments, which are shown to be flawed by inconsistencies."],["dc.identifier.doi","10.1088/0953-8984/17/20/002"],["dc.identifier.isi","000230246800003"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/50804"],["dc.notes.status","zu prüfen"],["dc.notes.submitter","Najko"],["dc.publisher","Iop Publishing Ltd"],["dc.relation.issn","1361-648X"],["dc.relation.issn","0953-8984"],["dc.title","Dynamics of gelling liquids: a short survey"],["dc.type","review"],["dc.type.internalPublication","yes"],["dc.type.peerReviewed","yes"],["dc.type.status","published"],["dspace.entity.type","Publication"]]