Utilizing Multi-Level Concepts for Multi-Phase Modeling

In model-based systems engineering projects, engineers from multiple domains collaborate by establishing a common system model. Multi-level modeling is a technique that can be used to model the development from abstract ideas to concrete implementations. However, current multi-level modeling approaches are not adequate for processes with multiple modeling phases that might have to be rearranged later. In this paper, we introduce multi-phase modeling that utilizes concepts of multi-level modeling by considering a description of the expected phase ordering per domain. Constraints aware of this context can express that certain elements are only valid in specific phases without having to determine a concrete phase ordering for a particular model. This enables using multi-phase modeling in flexible workflows, adapting to changing requirements and the definition of access rules in domain notation. We show feasibility of this multi-phase modeling by applying it to multiple real-life systems engineering projects of the aerospace domain

Characterization of the pneumatic behavior of a novel spouted bed apparatus

Recently the importance of spouted bed technology has significantly increased in the context of drying processes as well as granulation, agglomeration or coating processes. Particulate systems concerning very fine or non spherical particles that are difficult to fluidize, often cannot be treated in conventional fluidized beds. In contrast to those fluidized beds, the spouted bed technology with its specific flow structure offers the opportunity of stable fluidization under controlled conditions. Within this work the fluid dynamics of a novel spouted bed with two adjustable gas inlets is investigated. By analysis of gas fluctuation spectra by means of a fast Fourier transformation algorithm, different operation regimes are identified and depicted graphically. Furthermore, continuum CFD-modeling of the granular solid phase motion by means of an Euler/Euler approach and comparisons with experimental obtained velocity vector fields by means of particle image velocimetry (PIV) measurements will be presented in this work

The Halo Occupation Distribution of Black Holes: Dependence on Mass

We investigate the halo occupation distribution (HOD) of black holes within a hydrodynamic cosmological simulation that directly follows black hole growth. Similar to the HOD of galaxies/subhalos, we find that the black hole occupation number can be described by the form N_BH proportional to 1+ (M_Host)^alpha where alpha evolves mildly with redshift indicating that a given mass halo (M_Host) at low redshift tends to host fewer BHs than at high redshift (as expected as a result of galaxy and BH mergers). We further divide the occupation number into contributions from black holes residing in central and satellite galaxies within a halo. The distribution of M_BH within halos tends to consist of a single massive BH (distributed about a peak mass strongly correlated with M_Host), and a collection of relatively low-mass secondary BHs, with weaker correlation with M_Host. We also examine the spatial distribution of BHs within their host halos, and find they typically follow a power-law radial distribution (i.e. much more centrally concentrated than the subhalo distribution). Finally, we characterize the host mass for which BH growth is feedback dominated (e.g. star formation quenched). We show that halos with M_Host > 3 * 10^12 M_sun have primary BHs that are feedback dominated by z~3 with lower mass halos becoming increasingly more affected at lower redshift.Comment: 10 pages, 7 figures, submitted to MNRA

Quasar Clustering in Cosmological Hydrodynamic Simulations: Evidence for mergers

We examine the clustering properties of a population of quasars drawn from fully hydrodynamic cosmological simulations that directly follow black hole growth. We find that the black hole correlation function is best described by two distinct components: contributions from BH pairs occupying the same dark matter halo ('1-halo term') which dominate at scales below 300 kpc/h, and contributions from BHs occupying separate halos ('2-halo term') which dominate at larger scales. From the 2-halo BH term we find a typical host halo mass for faint-end quasars (those probed in our simulation volumes) ranging from 10^11 to a few 10^12 solar masses from z=5 to z=1 respectively (consistent with the mean halo host mass). The BH correlation function shows a luminosity dependence as a function of redshift, though weak enough to be consistent with observational constraints. At small scales, the high resolution of our simulations allows us to probe the 1-halo clustering in detail, finding that the 1-halo term follows an approximate power law, lacking the characteristic decrease in slope at small scales found in 1-halo terms for galaxies and dark matter. We show that this difference is a direct result of a boost in the small-scale quasar bias caused by galaxies hosting multiple quasars (1-subhalo term) following a merger event, typically between a large central subgroup and a smaller, satellite subgroup hosting a relatively small black hole. We show that our predicted small-scale excess caused by such mergers is in good agreement with both the slope and amplitude indicated by recent small-scale measurements. Finally, we note the excess to be a strong function of halo mass, such that the observed excess is well matched by the multiple black holes of intermediate mass (10^7-10^8 solar masses) found in hosts of 4-8*10^11 solar masses, a range well probed by our simulations.Comment: 12 pages, 10 figures. Submitted to MNRA

Chemo-hygral model for asr expansion and its effects on fatigue lives of bridge slabs

For evaluating damages of structural concrete by alkali silica reaction (ASR), an analytical platform to rationally deal with the complex interaction of multi-scale chemo- physics events is being developed. For experimental verification of the predictive model proposed, ASR expansion tests under several magnitudes of confinement are conducted and the results are compared with the multi-scale simulation. It is experimentally found that the highly deviatoric compression may bring about isotropically confined ASR expansion. The poro-mechanics based multi-phase modeling can simulate this nonlinearity by considering the quasi-hydro static pressure of created ASR gels in concrete composites and its injection into the micro-pores. The investigated models are used for assessing the fatigue lives of RC bridge decks. It is shown that fatigue life can be longer with the ASR-induced expansions

Variational approximation of functionals defined on 1-dimensional connected sets: the planar case

In this paper we consider variational problems involving 1-dimensional connected sets in the Euclidean plane, such as the classical Steiner tree problem and the irrigation (Gilbert-Steiner) problem. We relate them to optimal partition problems and provide a variational approximation through Modica-Mortola type energies proving a $\Gamma$-convergence result. We also introduce a suitable convex relaxation and develop the corresponding numerical implementations. The proposed methods are quite general and the results we obtain can be extended to $n$-dimensional Euclidean space or to more general manifold ambients, as shown in the companion paper [11].Comment: 30 pages, 5 figure

Mathematical biomedicine and modeling avascular tumor growth

In this chapter we review existing continuum models of avascular tumor growth, explaining howthey are inter related and the biophysical insight that they provide. The models range in complexity and include one-dimensional studies of radiallysymmetric growth, and two-dimensional models of tumor invasion in which the tumor is assumed to comprise a single population of cells. We also present more detailed, multiphase models that allow for tumor heterogeneity. The chapter concludes with a summary of the different continuum approaches and a discussion of the theoretical challenges that lie ahead