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Wolfgang Bock

Publications and source records attributed to Wolfgang Bock.

At least 37 records · Page 2Linked to original sources
arXiv2021

Disease contagion models coupled to crowd motion and mesh-free simulation

Modeling and simulation of disease spreading in pedestrian crowds has been recently become a topic of increasing relevance. In this paper, we consider the influence of the crowd motion in a complex dynamical environment on the course of infection of the pedestrians. To model the pedestrian dynamics we consider a kinetic equation for multi-group pedestrian flow based on a social force model coupled with an Eikonal equation. This model is coupled with a non-local SEIS contagion model for disease spread, where besides the description of local contacts also the influence of contact times has been modelled. Hydrodynamic approximations of the coupled system are derived. Finally, simulations of the hydrodynamic model are carried out using a mesh-free particle method. Different numerical test cases are investigated including uni- and bi-directional flow in a passage with and without obstacles.

math.DS↗
arXiv2021

Optimal Control for Tuberculosis with Exogenous Reinfection and Stigmatization

The effect of stigmatization is hindering the control of diseases. Especially in the case of exogenous reinfection, this effect can play a massive role. We develop in this paper, based on a tuberculosis model of Feng et.al. a model with exogenous reinfection and stigmatization. As in the base model, in presence of exogenous reinfection there exists multiple endemic equilibria. We solve an optimal control problem for a case scenario and show that both types of measures, those fighting stigmatization but also direct disease control have to be invoked.

math.OC↗
arXiv2019

The Edwards Model for fBm Loops and Starbursts

We extend Varadhan's construction of the Edwards polymer model to fractional Brownian loops and fractional Brownian starbursts. We show that, as in the fBm case, the Edwards density under a renormalizaion is an integrable function for the case H<= 1/d.

math-ph↗
arXiv2019

Convex topological algebras via linear vector fields and Cuntz algebras

Realization by linear vector fields is constructed for any Lie algebra which admits a biorthogonal system and for its any suitable representation. The embedding into Lie algebras of linear vector fields is analogous to the classical Jordan-Schwinger map. A number of examples of such Lie algebras of linear vector fields is computed. In particular, we obtain examples of the twisted Heisenberg-Virasoro Lie algebra and the Schrödinger-Virasoro Lie algebras among others. More generally, we construct an embedding of an arbitrary locally convex topological algebra into the Cuntz algebra.

math.FA↗
arXiv2019

Dynamical Properties of Gaussian Chains and Rings with Long Range Interactions

Various authors have invoked discretized fractional Brownian (fBm) motion as a model for chain polymers with long range interaction of monomers along the chain. We show that for these, in contrast to the Brownian case, linear forces are acting between all pairs of constituents, attractive for small Hurst index H and mostly repulsive when H is larger than 1/2. In the second part of this paper we extend this study to periodic fBm and related models with a view to ring polymers with long range interactions.

math-ph↗
arXiv2019

Fractional Periodic Processes: Properties and an Application of Polymer Form Factors

In this paper we introduce and study three classes of fractional periodic processes. An application to ring polymers is investigated. We obtain a closed analytic expressions for the form factors, the Debye functions and their asymptotic decay. The relation between the end-to-halftime and radius of gyration is computed for these classes of periodic processes.

math-ph↗
arXiv2019

Integral Representation of Generalized Grey Brownian Motion

In this paper we investigate the representation of a class of non Gaussian processes, namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic process which is a solution of a certain stochastic differential equation. In particular the underlying process can be seen as a non Gaussian extension of the Ornstein-Uhlenbeck process, hence generalizing the representation results of Muravlev as well as Harms and Stefanovits to the non Gaussian case.

math.PR↗
arXiv2018

An Agent Based Modeling of Spatially Inhomogeneous Host-Vector Disease Transmission

In this article we consider a microscopic model for host-vector disease transmission based on configuration space analysis. Using Vlasov scaling we obtain the corresponding mesoscopic (kinetic) equations, describing the density of susceptible and infected compartments in space. The resulting system of equations can be seen as a generalization to a spatial SISUV model.

q-bio.PE↗
arXiv2018

Compartmental Spatial Multi-Patch Deterministic and Stochastic Models for Dengue

Dengue is a vector-borne viral disease increasing dramatically over the past years due to improvement in human mobility. The movement of host individuals between and within the patches are captured via a residence-time matrix. A system of ordinary differential equations (ODEs) modeling the spatial spread of disease among the multiple patches is used to create a system of stochastic differential equations (SDEs). Numerical solutions of the system of SDEs are compared with the deterministic solutions obtained via ODEs.

q-bio.PE↗
arXiv2018

Stochastic Quantization for the Edwards Measure of Fractional Brownian Motion with $Hd=1$

In this paper we construct a Markov process which has as invariant measure the fractional Edwards measure based on a $d$-dimensional fractional Brownian motion, with Hurst index $H$ in the case of $Hd=1$. We use the theory of classical Dirichlet forms. However since the corresponding self-intersection local time of fractional Brownian motion is not Meyer-Watanabe differentiable in this case, we show the closability of the form via quasi translation invariance of the fractional Edwards measure along shifts in the corresponding fractional Cameron-Martin space.

math-ph↗
arXiv2017

Analysis of Stochastic Quantization for the fractional Edwards Measure

We analyse a diffusion process whose invariant measure is the fractional polymer or Edwards measure for fractional Brownian motion in dimension $d\in\mathbb{N}$ with Hurst parameter $H\in(0,1)$ fulfilling $dH < 1$. We make use of a construction of the diffusion via Dirichlet form techniques in infinite dimensional (Gaussian) analysis. By providing a Fukushima decomposition for the stochastic quantization of the fractional Edwards measure we prove that the constructed process solves weakly a stochastic differential equation in infinite dimension for quasi-all starting points. Moreover, the solution process is driven by an Ornstein--Uhlenbeck process taking values in an infinite dimensional distribution space and is unique, in the sense that the underlying Dirichlet form is Markov unique. The equilibrium measure, which is by construction the fractional Edwards measure, is specified to be an extremal Gibbs state and therefore, the constructed stochastic dynamics is time ergodic. The studied stochastic differential equation provides in the language of polymer physics the dynamics of the bonds, i.e. stochastically spoken the noise of the process. An integration leads then to polymer paths. We show that if one starts with a continuous polymer configuration the integrated process stays almost surely continuous during the time evolution.

math.PR↗
arXiv2016

Stochastic Quantization for the fractional Edwards Measure

We prove the existence of a diffusion process whose invariant measure is the fractional polymer or Edwards measure for fractional Brownian motion in dimension $d\in\mathbb{N}$ with Hurst parameter $H\in(0,1)$ fulfilling $dH < 1$. The diffusion is constructed via Dirichlet form techniques in infinite dimensional (Gaussian) analysis. Moreover, we show that the process is invariant under time translations.

math-ph↗
arXiv2015

Scaling Properties of Weakly Self-Avoiding Fractional Brownian Motion in One Dimension

We use an off-lattice discretization of fractional Brownian motion and a Metropolis Algorithm to determine the asymptotic scaling of this discretized fractional Brownian motion under the influence of an excluded volume as in the Edwards and Domb-Joyce models. We find a good agreement between the Flory index describing the scaling of end-to-end length with a mean field formula proposed earlier for this class of models.

physics.comp-ph↗