Particlization in hybrid models

In hybrid models, which combine hydrodynamical and transport approaches to describe different stages of heavy-ion collisions, conversion of fluid to individual particles, particlization, is a non-trivial technical problem. We describe in detail how to find the particlization hypersurface in a 3+1 dimensional model, and how to sample the particle distributions evaluated using the Cooper-Frye procedure to create an ensemble of particles as an initial state for the transport stage. We also discuss the role and magnitude of the negative contributions in the Cooper-Frye procedure.Comment: 18 pages, 28 figures, EPJA: Topical issue on "Relativistic Hydro- and Thermodynamics"; version accepted for publication, typos and error in Eq.(1) corrected, the purpose of sampling and change from UrQMD to fluid clarified, added discussion why attempts to cancel negative contributions of Cooper-Frye are not applicable her

Nonequilibrium dynamics in scalar hybrid models

We study by numerical simulations the transition from the metastable "false vacuum" to the broken symmetry phase in the preheating stage after cosmic inflation in a scalar hybrid model. We take quantum fluctuations and their back reaction into account by applying a one-loop bubble-resummation.Comment: 5 pages, 4 figures, contribution to the conference Strong and Electroweak Matter (SEWM2004), Helsinki, Finland, 16-19 June 200

Hybrid Models with Deep and Invertible Features

We propose a neural hybrid model consisting of a linear model defined on a set of features computed by a deep, invertible transformation (i.e. a normalizing flow). An attractive property of our model is that both p(features), the density of the features, and p(targets | features), the predictive distribution, can be computed exactly in a single feed-forward pass. We show that our hybrid model, despite the invertibility constraints, achieves similar accuracy to purely predictive models. Moreover the generative component remains a good model of the input features despite the hybrid optimization objective. This offers additional capabilities such as detection of out-of-distribution inputs and enabling semi-supervised learning. The availability of the exact joint density p(targets, features) also allows us to compute many quantities readily, making our hybrid model a useful building block for downstream applications of probabilistic deep learning.Comment: ICML 201

Decompactifications and Massless D-Branes in Hybrid Models

A method of determining the mass spectrum of BPS D-branes in any phase limit of a gauged linear sigma model is introduced. A ring associated to monodromy is defined and one considers K-theory to be a module over this ring. A simple but interesting class of hybrid models with Landau-Ginzburg fibres over CPn are analyzed using special Kaehler geometry and D-brane probes. In some cases the hybrid limit is an infinite distance in moduli space and corresponds to a decompactification. In other cases the hybrid limit is at a finite distance and acquires massless D-branes. An example studied appears to correspond to a novel theory of supergravity with an SU(2) gauge symmetry where the gauge and gravitational couplings are necessarily tied to each other.Comment: PDF-LaTeX, 34 pages, 2 mps figure

Hybrid modelling of individual movement and collective behaviour

Mathematical models of dispersal in biological systems are often written in terms of partial differential equations (PDEs) which describe the time evolution of population-level variables (concentrations, densities). A more detailed modelling approach is given by individual-based (agent-based) models which describe the behaviour of each organism. In recent years, an intermediate modelling methodology – hybrid modelling – has been applied to a number of biological systems. These hybrid models couple an individual-based description of cells/animals with a PDEmodel of their environment. In this chapter, we overview hybrid models in the literature with the focus on the mathematical challenges of this modelling approach. The detailed analysis is presented using the example of chemotaxis, where cells move according to extracellular chemicals that can be altered by the cells themselves. In this case, individual-based models of cells are coupled with PDEs for extracellular chemical signals. Travelling waves in these hybrid models are investigated. In particular, we show that in contrary to the PDEs, hybrid chemotaxis models only develop a transient travelling wave

Distributed control of urban traffic networks using hybrid models

Urban traffic control poses a challenging problem in terms of coordinating the different traffic lights that can be used in order to influence the traffic flow. Model based control requires hybrid systems models consisting of interacting fluid flow Petri net models for controlled and uncontrolled intersections, and cell transmission models for links connecting the intersections. This paper proposes a simulation based distributed model predictive control algorithm for solving this problem