Moderate deviations for random field Curie-Weiss models

The random field Curie-Weiss model is derived from the classical Curie-Weiss model by replacing the deterministic global magnetic field by random local magnetic fields. This opens up a new and interestingly rich phase structure. In this setting, we derive moderate deviations principles for the random total magnetization $S_n$, which is the partial sum of (dependent) spins. A typical result is that under appropriate assumptions on the distribution of the local external fields there exist a real number $m$, a positive real number $\lambda$, and a positive integer $k$ such that $(S_n-nm)/n^{\alpha}$ satisfies a moderate deviations principle with speed $n^{1-2k(1-\alpha)}$ and rate function $\lambda x^{2k}/(2k)!$, where $1-1/(2(2k-1)) < \alpha < 1$.Comment: 21 page

Characterizing Van Kampen Squares via Descent Data

Categories in which cocones satisfy certain exactness conditions w.r.t. pullbacks are subject to current research activities in theoretical computer science. Usually, exactness is expressed in terms of properties of the pullback functor associated with the cocone. Even in the case of non-exactness, researchers in model semantics and rewriting theory inquire an elementary characterization of the image of this functor. In this paper we will investigate this question in the special case where the cocone is a cospan, i.e. part of a Van Kampen square. The use of Descent Data as the dominant categorical tool yields two main results: A simple condition which characterizes the reachable part of the above mentioned functor in terms of liftings of involved equivalence relations and (as a consequence) a necessary and sufficient condition for a pushout to be a Van Kampen square formulated in a purely algebraic manner.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

Variational bounds for the shear viscosity of gelling melts

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 $k\ge 2\nu-\beta$. 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.Comment: 5 pages; CHANGES: typos corrected, some references added; version as publishe

Unfolding-based Diagnosis of Systems with an Evolving Topology

We propose a framework for model-based diagnosis of systems with mobility and variable topologies, modelled as graph transformation systems. Generally speaking, model-based diagnosis is aimed at constructing explanations of observed faulty behaviours on the basis of a given model of the system. Since the number of possible explanations may be huge, we exploit the unfolding as a compact data structure to store them, along the lines of previous work dealing with Petri net models. Given a model of a system and an observation, the explanations can be constructed by unfolding the model constrained by the observation, and then removing incomplete explanations in a pruning phase. The theory is formalised in a general categorical setting: constraining the system by the observation corresponds to taking a product in the chosen category of graph grammars, so that the correctness of the procedure can be proved by using the fact that the unfolding is a right adjoint and thus it preserves products. The theory should hence be easily applicable to a wide class of system models, including graph grammars and Petri nets

Torn Between Two Plates: Exhumation of the Cer Massif (Internal Dinarides) as a Far‐Field Effect of Carpathian Slab Rollback Inferred From 40 Ar/ 39 Ar Dating and Cross Section Balancing

Abstract Extension across the southern Pannonian Basin and the internal Dinarides is characterized by Oligo‐Miocene metamorphic core complexes (MCCs) exhumed along mylonitic low‐angle extensional shear zones. Cer MCC at the transition between Dinarides and Pannonian Basin occupies a structural position within the distal‐most Adriatic thrust sheet and originates from two different tectonic processes: Late Cretaceous‐Paleogene nappe‐stacking during a continent‐continent collision with Adria in a lower plate position, and exhumation related to Miocene extension driven by the Carpathian slab‐rollback. Structural data and a balanced cross section across the Cer massif show linking of the exhuming shear zone to a breakaway fault, which reactivated the early Late Cretaceous most internal nappe contact. Paleozoic greenschist‐to amphibolite‐grade lithologies surround a polyphase intrusion composed of I‐ and S‐type granites and were exhumed along a shear zone characterized by top‐N transport. Thermobarometric analyses indicate an intrusion depth of 7–8 km of the Oligocene I‐type granite; cooling below ∼500°C occurred at 25.4 ± 0.6 Ma (1σ) yielded by 40 Ar/ 39 Ar dating of hornblende. Biotite and white mica from this intrusion as well as from the mylonitic shear zone yield 40 Ar/ 39 Ar cooling ages of 17–18 Ma independent of the used techniques (in situ laser ablation, single‐grain total fusion, single‐grain step heating, and multi‐grain step heating). White mica from the S‐type granite yield an 40 Ar/ 39 Ar cooling age of 16.7 ± 0.1 Ma (1σ). Associated dikes intruding the shear zone were also affected by N‐S extension resulting in the exhumation of the MCC, which was triggered by the opening of the Pannonian back‐arc basin in response to the Carpathian slab‐rollback.Plain Language Summary Horizontal stretching of continental plates induces thinning of the crustal upper part, melting of rocks, the sinking of the land surface, and formation of large basins. One of the world's best‐studied basins formed by such a process is the Central European Pannonian Basin. This basin is surrounded by the mountain belts of the Alps, Carpathians, and Dinarides. We have studied rocks between the Pannonian Basin and the southerly adjacent Dinaride Mountains, where rocks deposited in the basin are found right next to rocks that were initially about 7–8 km deep in the crust. These rocks are separated by a shear zone, along which they were brought to the surface. We have dated the activity of the shear zone by measuring concentrations of radioactive isotopes and their decay products contained in deformed minerals. The shear zone was active at a time when the Pannonian Basin started to open due to tectonic processes further NE underneath the Carpathian mountain chain. We also found evidence that the shear zone, which brought metamorphic rocks upwards was formerly one that brought rocks downwards into the crust during an earlier phase of mountain building, predating basin formation.Key Points Activity along the shear zone exhuming Cer metamorphic core complex in the internal Dinarides was dated by 40 Ar/ 39 Ar geochronology to ∼17 Ma Exhumation was facilitated by extensional reactivation of Late Cretaceous‐Paleogene nappe contacts resulting from Adria‐Europe collision Extensional reactivation of the thrusts is interpreted as a far‐field effect of Oligo‐Miocene Carpathian slab rollbac