Stationary states of boundary driven exclusion processes with nonreversible boundary dynamics

We prove a law of large numbers for the empirical density of one-dimensional, boundary driven, symmetric exclusion processes with different types of non-reversible dynamics at the boundary. The proofs rely on duality techniques

NIR/Optical Selected Local Mergers --- Spatial Density and sSFR Enhancement

Mergers play important roles in triggering the most active objects in the universe, including (U)LIRGs and QSOs. However, whether they are also important for the total stellar mass build-up in galaxies in general is unclear and controversial. The answer to that question depends on the merger rate and the average strength of merger induced star formation. In this talk, I will review studies on spatial density and sSFR enhancement of local mergers found in NIR/optical selected pair samples. In line with the current literature on galaxy formation/evolution, special attention will be paid to the dependence of the local merger rate and of the sSFR enhancement on four fundamental observables: (1) stellar mass, (2) mass ratio, (3) separation, and (4) environment.Comment: A review talk; 8 pages; to appear on the Conference Proceedings for "Galaxy Mergers in an Evolving Universe", held in Hualien, Taiwan (October 2011

Review of the "Bottom-Up" scenario

Thermalization of a longitudinally expanding color glass condensate with Bjorken boost invariant geometry is investigated within parton cascade BAMPS. Our main focus lies on the detailed comparison of thermalization, observed in BAMPS with that suggested in the Bottom-Up scenario. We demonstrate that the tremendous production of soft gluons via $gg \to ggg$, which is shown in the Bottom-Up picture as the dominant process during the early preequilibration, will not occur in heavy ion collisions at RHIC and LHC energies, because the back reaction $ggg\to gg$ hinders the absolute particle multiplication. Moreover, contrary to the Bottom-Up scenario, soft and hard gluons thermalize at the same time. The time scale of thermal equilibration in BAMPS calculations is of order \as^{-2} (\ln \as)^{-2} Q_s^{-1}. After this time the gluon system exhibits nearly hydrodynamic behavior. The shear viscosity to entropy density ratio has a weak dependence on $Q_s$ and lies close to the lower bound of the AdS/CFT conjecture.Comment: Quark Matter 2008 Proceeding

Mathematical modeling of thrombus formation in idealized models of aortic dissection: Initial findings and potential applications

Aortic dissection is a major aortic catastrophe with a high morbidity and mortality risk caused by the formation of a tear in the aortic wall. The development of a second blood filled region defined as the “false lumen” causes highly disturbed flow patterns and creates local hemodynamic conditions likely to promote the formation of thrombus in the false lumen. Previous research has shown that patient prognosis is influenced by the level of thrombosis in the false lumen, with false lumen patency and partial thrombosis being associated with late complications and complete thrombosis of the false lumen having beneficial effects on patient outcomes. In this paper, a new hemodynamics-based model is proposed to predict the formation of thrombus in Type B dissection. Shear rates, fluid residence time, and platelet distribution are employed to evaluate the likelihood for thrombosis and to simulate the growth of thrombus and its effects on blood flow over time. The model is applied to different idealized aortic dissections to investigate the effect of geometric features on thrombus formation. Our results are in qualitative agreement with in-vivo observations, and show the potential applicability of such a modeling approach to predict the progression of aortic dissection in anatomically realistic geometries

Metastability of finite state Markov chains: a recursive procedure to identify slow variables for model reduction

Consider a sequence $(\eta^N(t) :t\ge 0)$ of continuous-time, irreducible Markov chains evolving on a fixed finite set $E$, indexed by a parameter $N$. Denote by $R_N(\eta,\xi)$ the jump rates of the Markov chain $\eta^N_t$, and assume that for any pair of bonds $(\eta,\xi)$, $(\eta',\xi')$ $\arctan \{R_N(\eta,\xi)/R_N(\eta',\xi')\}$ converges as $N\uparrow\infty$. Under a hypothesis slightly more restrictive (cf. \eqref{mhyp} below), we present a recursive procedure which provides a sequence of increasing time-scales \theta^1_N, \dots, \theta^{\mf p}_N, $\theta^j_N \ll \theta^{j+1}_N$, and of coarsening partitions \{\ms E^j_1, \dots, \ms E^j_{\mf n_j}, \Delta^j\}, 1\le j\le \mf p, of the set $E$. Let \phi_j: E \to \{0,1, \dots, \mf n_j\} be the projection defined by \phi_j(\eta) = \sum_{x=1}^{\mf n_j} x \, \mb 1\{\eta \in \ms E^j_x\}. For each 1\le j\le \mf p, we prove that the hidden Markov chain $X^j_N(t) = \phi_j(\eta^N(t\theta^j_N))$ converges to a Markov chain on \{1, \dots, \mf n_j\}

Testing the transferability of regression equations derived from small sub-catchments to a large area in central Sweden

There is an ever increasing need to apply hydrological models to catchments where streamflow data are unavailable or to large geographical regions where calibration is not feasible. Estimation of model parameters from spatial physical data is the key issue in the development and application of hydrological models at various scales. To investigate the suitability of transferring the regression equations relating model parameters to physical characteristics developed from small sub-catchments to a large region for estimating model parameters, a conceptual snow and water balance model was optimised on all the sub-catchments in the region. A multiple regression analysis related model parameters to physical data for the catchments and the regression equations derived from the small sub-catchments were used to calculate regional parameter values for the large basin using spatially aggregated physical data. For the model tested, the results support the suitability of transferring the regression equations to the larger region.</p> <p style='line-height: 20px;'><b>Keywords: </b>water balance modelling,large scale, multiple regression, regionalisation</p