arXiv subjects

Adrian Muntean

Publications and source records attributed to Adrian Muntean.

At least 91 records · Page 5Linked to original sources

arXiv2016

Corrector estimates for a thermo-diffusion model with weak thermal coupling

The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermo-diffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast microstructures. The terminology "weak thermal coupling" refers here to the variable scaling in terms of the small homogenization parameter of the heat conduction-diffusion interaction terms, while the "high-contrast" is thought particularly in terms of the heat conduction properties of the composite material. As main target, we justify the first-order terms of the multiscale asymptotic expansions in the presence of coupled fluxes, induced by the joint contribution of Sorret and Dufour-like effects. The contrasting heat conduction combined with cross coupling lead to the main mathematical difficulty in the system. Our approach relies on the method of periodic unfolding combined with a priori estimates for the thermal and concentration fields and for their coupled fluxes.

math.AP↗

arXiv2016

Large-time behavior of solutions to a thermo-diffusion system with Smoluchowski interactions

We prove the large time behavior of solutions to a coupled thermo-diffusion arising in the modelling of the motion of hot colloidal particles in porous media. Additionally, we also ensure the uniqueness of solutions of the target problem. The main mathematical difficulty is due to the presence in the right-hand side of the equations of products between temperature and concentration gradients. Such terms mimic the so-called thermodynamic Soret and Dufour effects. These are cross-coupling terms emphasizing in this context a strong interplay between heat conduction and molecular diffusion.

math.AP↗

arXiv2016

Blockage induced condensation controlled by a local reaction

We consider the set-up of stationary Zero Range models and discuss the onset of condensation induced by a local blockage on the lattice. We show that the introduction of a local feedback on the hopping rates allows to control the particle fraction in the condensed phase. This phenomenon results in a current vs. blockage parameter curve characterized by two non--analyticity points.

cond-mat.stat-mech↗

arXiv2016

Eulerian vs. Lagrangian analyses of pedestrian dynamics asymmetries in a staircase landing

Real-life, out-of-laboratory, measurements of pedestrian movements allow extensive and fully-resolved statistical analyses. However, data acquisition in real-life is subjected to the wide heterogeneity that characterizes crowd flows over time. Disparate flow conditions, such as co-flows and counter-flows at low and at high pedestrian densities, typically follow randomly one another. When analysing the data in order to study the dynamics and behaviour of pedestrians it is crucial to be able disentangle and to properly select (query) data from statistically homogeneous flow conditions in order to avoid spurious statistics and to enable qualitative comparisons. In this paper we extend our previous analysis on the asymmetric pedestrian dynamics on a staircase landing, where we collected a large statistical database of measurements from ad hoc continuous recordings. This contribution has a two-fold aim: first, method-wise, we discuss two possible approaches to query experimental datasets for homogeneous flow conditions. For given flow conditions, we can either agglomerate measurements on a time-frame basis (Eulerian queries) or on a trajectory basis (Lagrangian queries). Second, we employ these two different perspectives to further explore asymmetries in the pedestrian dynamics in our measurement site. We report cross-comparisons of statistics of pedestrian positions, velocities and accelerations vs. flow conditions as well as vs. Eulerian or Lagrangian approach.

physics.soc-ph↗

arXiv2016

Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities

In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and flux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of [Evers, Hille and Muntean. Journal of Differential Equations, 259:1068-1097, 2015] to settings where the dynamics are driven by interactions. In a forward-Euler-like approach, we construct a time-discretized version of the original problem and employ the results of [Evers, Hille and Muntean. Journal of Differential Equations, 259:1068-1097, 2015] as a building block within each subinterval. A limit solution is obtained as the mesh size of the time discretization goes to zero. Moreover, the limit is independent of the specific way of partitioning the time interval $[0,T]$. This paper is partially based on results presented in Chapter 5 of [Evers. PhD thesis, Eindhoven University of Technology, 2015], while a number of issues that were still open there, are now resolved.

math.AP↗

arXiv2016

Stationary currents in particle systems with constrained hopping rates

We study the effect on the stationary currents of constraints affecting the hopping rates in stochastic particle systems. In the framework of Zero Range Processes with drift within a finite volume, we discuss how the current is reduced by the presence of the constraint and deduce exact formulae, fully explicit in some cases. The model discussed here has been introduced in Ref. [1] and is relevant for the description of pedestrian motion in elongated dark corridors, where the constraint on the hopping rates can be related to limitations on the interaction distance among pedestrians.

cond-mat.stat-mech↗

arXiv2016

Effects of communication efficiency and exit capacity on fundamental diagrams for pedestrian motion in an obscure tunnel - a particle system approach

Fundamental diagrams describing the relation between pedestrians speed and density are key points in understanding pedestrian dynamics. Experimental data evidence the onset of complex behaviors in which the velocity decreases with the density and different logistic regimes are identified. This paper addresses the issue of pedestrians transport and of fundamental diagrams for a scenario involving the motion of pedestrians escaping from an obscure tunnel. We capture the effects of the communication efficiency and the exit capacity by means of two thresholds controlling the rate at which particles (walkers, pedestrians) move on the lattice. Using a particle system model, we show that in absence of limitation in communication among pedestrians we reproduce with good accuracy the standard fundamental diagrams, whose basic behaviors can be interpreted in terms of the exit capacity limitation. When the effect of a limited communication ability is considered, then interesting non-intuitive phenomena occur. Particularly, we shed light on the loss of monotonicity of the typical speed--density curves, revealing the existence of a pedestrians density optimizing the escape. We study both the discrete particle dynamics as well as the corresponding hydrodynamic limit (a porous medium equation and a transport (continuity) equation). We also point out the dependence of the effective transport coefficients on the two thresholds - the essence of the microstructure information.

cond-mat.stat-mech↗

arXiv2016

A lattice model of reduced jamming by barrier

We study an asymmetric simple exclusion process in a strip in the presence of a solid impenetrable barrier. We focus on the effect of the barrier on the residence time of the particles, namely, the typical time needed by the particles to cross the whole strip. We explore the conditions for reduced jamming when varying the environment (different drifts, reservoir densities, horizontal diffusion walks, etc.). Particularly, we discover an interesting non--monotonic behavior of the residence time as a function of the barrier length. Besides recovering by means of both the lattice dynamics and mean-field model well-known aspects like faster-is-slower effect and the intermittence of the flow, we propose also a birth-and-death process and a reduced one-dimensional model with variable barrier permeability to capture qualitatively the behavior of the residence time with respect to the parameters. We report our first steps towards the understanding to which extent the presence of obstacles can fluidize pedestrian and biological transport in crowded heterogeneous environments.

cond-mat.stat-mech↗

arXiv2016

A Note on Iterations-based Derivations of High-order Homogenization Correctors for Multiscale Semi-linear Elliptic Equations

This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working technique relies on monotone iterations combined with formal two-scale homogenization asymptotics. It can be adapted to handle more complex scenarios including for instance nonlinearities posed at the boundary of perforations and the vectorial case, when the model equations are coupled only through the nonlinear production terms.

math.AP↗

arXiv2015

Asymptotic analysis of a semi-linear elliptic system in perforated domains: well-posedness and correctors for the homogenization limit

In this study, we prove results on the weak solvability and homogenization of a microscopic semi-linear elliptic system posed in perforated media. The model presented here explores the interplay between stationary diffusion and both surface and volume chemical reactions in porous media. Our interest lies in deriving homogenization limits (upscaling) for alike systems and particularly in justifying rigorously the obtained averaged descriptions. Essentially, we prove the well-posedness of the microscopic problem ensuring also the positivity and boundedness of the involved concentrations and then use the structure of the two scale expansions to derive corrector estimates delimitating this way the convergence rate of the asymptotic approximates to the macroscopic limit concentrations. Our techniques include Moser-like iteration techniques, a variational formulation, two-scale asymptotic expansions as well as energy-like estimates.

math.AP↗

arXiv2015

Asymmetric pedestrian dynamics on a staircase landing from continuous measurements

We investigate via extensive experimental data the dynamics of pedestrians walking in a corridor-shaped landing in a building at Eindhoven University of Technology. With year-long automatic measurements employing a Microsoft KinectTM 3D-range sensor and ad hoc tracking techniques, we acquired few hundreds of thousands pedestrian trajectories in real-life conditions. Here we discuss the asymmetric features of the dynamics in the two walking directions with respect to the flights of stairs (i.e. ascending or descending). We provide a detailed analysis of position and speed fields for the cases of pedestrians walking alone undisturbed and for couple of pedestrians in counter-flow. Then, we show average walking velocities exploring all the observed combinations in terms of numbers of pedestrians and walking directions.

physics.soc-ph↗

arXiv2015

Residence time estimates for asymmetric simple exclusion dynamics on stripes

The target of our study is to approximate numerically and, in some particular physically relevant cases, also analytically, the residence time of particles undergoing an asymmetric simple exclusion dynamics on a stripe. The source of asymmetry is twofold: (i) the choice of boundary conditions (different reservoir levels) and (ii) the strong anisotropy from a nonlinear drift with prescribed directionality. We focus on the effect of the choice of anisotropy in the flux on the asymptotic behavior of the residence time with respect to the length of the stripe. The topic is relevant for situations occurring in pedestrian flows or biological transport in crowded environments, where lateral displacements of the particles occur predominantly affecting therefore in an essentially way the efficiency of the overall transport mechanism.

nlin.CG↗

arXiv2014

Mild solutions to a measure-valued mass evolution problem with flux boundary conditions

We investigate the well-posedness and approximation of mild solutions to a class of linear transport equations on the unit interval $[0,1]$ endowed with a linear discontinuous production term, formulated in the space $\mathcal{M}([0,1])$ of finite Borel measures. Our working technique includes a detailed boundary layer analysis in terms of a semigroup representation of solutions in spaces of measures able to cope with the passage to the singular limit where thickness of the layer vanishes. We obtain not only a suitable concept of solutions to the chosen measure-valued evolution problem, but also derive convergence rates for the approximation procedure and get insight in the structure of flux boundary conditions for the limit problem.

math.FA↗

arXiv2014

Upscaling of the dynamics of dislocation walls

We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open question raised by Geers et al. in [GPPS13]. The proof of the upscaling procedure (i.e. the discrete-to-continuum passage) relies on the gradient flow structure of both the discrete and continuous energies of dislocations set in a suitable evolutionary variational inequality framework. Moreover, the convexity and $Γ$-convergence of the respective energies are properties of paramount importance for our arguments.

math.AP↗

arXiv2014

Modelling with measures: Approximation of a mass-emitting object by a point source

We consider a linear diffusion equation on $Ω:=\mathbb{R}^2\setminus\bar{Ω_\mathcal{O}}$, where $Ω_\mathcal{O}$ is a bounded domain. The time-dependent flux on the boundary $Γ:=\partialΩ_\mathcal{O}$ is prescribed. The aim of the paper is to approximate the dynamics by the solution of the diffusion equation on the whole of $\mathbb{R}^2$ with a measure-valued point source in the origin and provide estimates for the quality of approximation. For all time $t$, we derive an $L^2([0,t];L^2(Γ))$-bound on the difference in flux on the boundary. Moreover, we derive for all $t>0$ an $L^2(Ω)$-bound and an $L^2([0,t];H^1(Ω))$-bound for the difference of the solutions to the two models.

math.AP↗

arXiv2014

A thermo-diffusion system with Smoluchowski interactions: well-posedness and homogenization

We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via two-scale convergence techniques, allows the investigation of deposition effects in porous materials in the presence of thermal gradients.

math.AP↗

arXiv2014

High statistics measurements of pedestrian dynamics

Understanding the complex behavior of pedestrians walking in crowds is a challenge for both science and technology. In particular, obtaining reliable models for crowd dynamics, capable of exhibiting qualitatively and quantitatively the observed emergent features of pedestrian flows, may have a remarkable impact for matters as security, comfort and structural serviceability. Aiming at a quantitative understanding of basic aspects of pedestrian dynamics, extensive and high-accuracy measurements of pedestrian trajectories have been performed. More than 100.000 real-life, time-resolved trajectories of people walking along a trafficked corridor in a building of the Eindhoven University of Technology, The Netherlands, have been recorded. A measurement strategy based on Microsoft Kinect\texttrademark has been used; the trajectories of pedestrians have been analyzed as ensemble data. The main result consists of a statistical descriptions of pedestrian characteristic kinematic quantities such as positions and fundamental diagrams, possibly conditioned to local crowding status (e.g., one or more pedestrian(s) walking, presence of co-flows and counter-flows).

physics.soc-ph↗

arXiv2014

Error control for the FEM approximation of an upscaled thermo-diffusion system with Smoluchowski interactions

We analyze a coupled system of evolution equations that describes the effect of thermal gradients on the motion and deposition of $N$ populations of colloidal species diffusing and interacting together through Smoluchowski production terms. This class of systems is particularly useful in studying drug delivery, contaminant transportin complex media, as well as heat shocks thorough permeable media. The particularity lies in the modeling of the nonlinear and nonlocal coupling between diffusion and thermal conduction. We investigate the semidiscrete as well as the fully discrete em a priori error analysis of the finite elements approximation of the weak solution to a thermo-diffusion reaction system posed in a macroscopic domain. The mathematical techniques include energy-like estimates and compactness arguments.

math.AP↗