arXiv subjects

Adrian Muntean

Publications and source records attributed to Adrian Muntean.

At least 109 records · Page 6Linked to original sources

arXiv2014

Multiscale Modeling of Colloidal Dynamics in Porous Media: Capturing Aggregation and Deposition Effects

We investigate the influence of multiscale aggregation and deposition on the colloidal dynamics in a saturated porous medium. At the pore scale, the aggregation of colloids is modeled by the Smoluchowski equation. Essentially, the colloidal mass is distributed between different size clusters. We treat these clusters as different species involved in a diffusion-advection-reaction mechanism. This modeling procedure allows for different material properties to be varied between the different species, specifically the rates of diffusion, aggregation, deposition as well as the advection velocities. We apply the periodic homogenization procedure to give insight into the effective coefficients of the upscaled model equations. Benefiting from direct access to microstructural information, we capture by means of 2D numerical simulations the effect of aggregation on the deposition rates recovering this way both the blocking and ripening regimes reported in the literature.

math.AP↗

arXiv2014

Parameter Estimation of Social Forces in Crowd Dynamics Models via a Probabilistic Method

Focusing on a specific crowd dynamics situation, including real life experiments and measurements, our paper targets a twofold aim: (1) we present a Bayesian probabilistic method to estimate the value and the uncertainty (in the form of a probability density function) of parameters in crowd dynamic models from the experimental data; and (2) we introduce a fitness measure for the models to classify a couple of model structures (forces) according to their fitness to the experimental data, preparing the stage for a more general model-selection and validation strategy inspired by probabilistic data analysis. Finally, we review the essential aspects of our experimental setup and measurement technique.

physics.data-an↗

arXiv2013

Is adding charcoal to soil a good method for CO2 sequestration? - Modeling a spatially homogeneous soil

Carbon sequestration is the process of capture and long-term storage of atmospheric carbon dioxide (CO2) with the aim to avoid dangerous climate change. In this paper, we propose a simple mathematical model (a coupled system of nonlinear ODEs) to capture some of the dynamical effects produced by adding charcoal to fertile soils. The main goal is to understand to which extent charcoal is able to lock up carbon in soils. Our results are preliminary in the sense that we do not solve the CO2 sequestration problem. Instead, we do set up a flexible modeling framework in which the interaction between charcoal and soil can be tackled by means of mathematical tools. We show that our model is well-posed and has interesting large-time behaviour. Depending on the reference parameter range (e.g. type of soil) and chosen time scale, numerical simulations suggest that adding charcoal typically postpones the release of CO2.

math.AP↗

arXiv2013

Pedestrians moving in dark: Balancing measures and playing games on lattices

We present two conceptually new modeling approaches aimed at describing the motion of pedestrians in obscured corridors: * a Becker-Döring-type dynamics * a probabilistic cellular automaton model. In both models the group formation is affected by a threshold. The pedestrians are supposed to have very limited knowledge about their current position and their neighborhood; they can form groups up to a certain size and they can leave them. Their main goal is to find the exit of the corridor. Although being of mathematically different character, the discussion of both models shows that it seems to be a disadvantage for the individual to adhere to larger groups. We illustrate this effect numerically by solving both model systems. Finally we list some of our main open questions and conjectures.

physics.soc-ph↗

arXiv2013

Large-time behavior of a two-scale semilinear reaction-diffusion system for concrete sulfatation

We study the large-time behavior of (weak) solutions to a two-scale reaction-diffusion system coupled with a nonlinear ordinary differential equations modeling the partly dissipative corrosion of concrete (/cement)-based materials with sulfates. We prove that as $t\to\infty$ the solution to the original two-scale system converges to the corresponding two-scale stationary system. To obtain the main result we make use essentially of the theory of evolution equations governed by subdifferential operators of time-dependent convex functions developed combined with a series of two-scale energy-like time-independent estimates.

math.AP↗

arXiv2013

Crowds reaching targets by maximizing entropy: a Clausius-Duhem inequality approach

In this paper we propose the use of concepts from thermodynamics in the study of crowd dynamics. Our continuous model consists of the continuity equation for the density of the crowd and a kinetic equation for the velocity field. The latter includes a nonlocal term that models interactions between individuals. To support our modelling assumptions, we introduce an inequality that resembles the Second Law of Thermodynamics, containing an entropy-like functional. We show that its time derivative equals a positive dissipation term minus a corrector term. The latter term should be small for the time derivative of the entropy to be positive. In case of isotropic interactions the corrector term is absent. For the anisotropic case, we support the claim that the corrector term is small by simulations for the corresponding particle system. They reveal that this term is sufficiently small for the entropy still to increase. Moreover, we show that the entropy converges in time towards a limit value.

math.AP↗

arXiv2013

The effect of perception anisotropy on particle systems describing pedestrian flows in corridors

We consider a microscopic model (a system of self-propelled particles) to study the behaviour of a large group of pedestrians walking in a corridor. Our point of interest is the effect of anisotropic interactions on the global behaviour of the crowd. The anisotropy we have in mind reflects the fact that people do not perceive (i.e. see, hear, feel or smell) their environment equally well in all directions. The dynamics of the individuals in our model follow from a system of Newton-like equations in the overdamped limit. The instantaneous velocity is modelled in such a way that it accounts for the angle under which an individual perceives another individual. We investigate the effects of this perception anisotropy by means of simulations, very much in the spirit of molecular dynamics. We define a number of characteristic quantifiers (including the polarization index and Morisita index) that serve as measures for e.g. organization and clustering, and we use these indices to investigate the influence of anisotropy on the global behaviour of the crowd. The goal of the paper is to investigate the potentiality of this model; extensive statistical analysis of simulation data, or reproducing any specific real-life situation are beyond its scope.

physics.soc-ph↗

arXiv2013

Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry's law and time-dependent Dirichlet data

We study the large-time behavior of the free boundary position capturing the one-dimensional motion of the carbonation reaction front in concrete-based materials. We extend here our rigorous justification of the $\sqrt{t}$-behavior of reaction penetration depths by including non-linear effects due to deviations from the classical Henry's law and time-dependent Dirichlet data.

math.AP↗

arXiv2012

Can cooperation slow down emergency evacuations?

We study the motion of pedestrians through obscure corridors where the lack of visibility hides the precise position of the exits. Using a lattice model, we explore the effects of cooperation on the overall exit flux (evacuation rate). More precisely, we study the effect of the buddying threshold (of no--exclusion per site) on the dynamics of the crowd. In some cases, we note that if the evacuees tend to cooperate and act altruistically, then their collective action tends to favor the occurrence of disasters.

physics.soc-ph↗

arXiv2012

Dynamics of pedestrians in regions with no visibility - a lattice model without exclusion

We investigate the motion of pedestrians through obscure corridors where the lack of visibility (due to smoke, fog, darkness, etc.) hides the precise position of the exits. We focus our attention on a set of basic mechanisms, which we assume to be governing the dynamics at the individual level. Using a lattice model, we explore the effects of non-exclusion on the overall exit flux (evacuation rate). More precisely, we study the effect of the buddying threshold (of no-exclusion per site) on the dynamics of the crowd and investigate to which extent our model confirms the following pattern revealed by investigations on real emergencies: If the evacuees tend to cooperate and act altruistically, then their collective action tends to favor the occurrence of disasters.

physics.soc-ph↗

arXiv2012

Distributed space scales in a semilinear reaction-diffusion system including a parabolic variational inequality: A well-posedness study

This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: $x$ - macro and $y$ - micro. The system's origin connects to the modeling of concrete corrosion in sewer concrete pipes. It consists of three partial differential equations which are mass-balances of concentrations, as well as, one ordinary differential equation tracking the damage-by-corrosion. The system is semilinear, partially dissipative, and coupled via the solid-water interface at the microstructure (pore) level. The structure of the model equations is obtained in \cite{tasnim1} by upscaling of the physical and chemical processes taking place within the microstructure of the concrete. Herein we ensure the positivity and $L^\infty-$bounds on concentrations, and then prove the global-in-time existence and uniqueness of a suitable class of positive and bounded solutions that are stable with respect to the two-scale data and model parameters. The main ingredient to prove existence include fixed-point arguments and convergent two-scale Galerkin approximations.

math.AP↗

arXiv2012

Macroscopic corrosion front computations of sulfate attack in sewer pipes based on a micro-macro reaction-diffusion model

We consider a two-scale reaction diffusion system able to capture the corrosion of concrete with sulfates. Our aim here is to define and compute two macroscopic corrosion indicators: typical pH drop and gypsum profiles. Mathematically, the system is coupled, endowed with micro-macro transmission conditions, and posed on two different spatially-separated scales: one microscopic (pore scale) and one macroscopic (sewer pipe scale). We use a logarithmic expression to compute values of pH from the volume averaged concentration of sulfuric acid which is obtained by resolving numerically the two-scale system (microscopic equations with direct feedback with the macroscopic diffusion of one of the reactants). Furthermore, we also evaluate the content of the main sulfatation reaction (corrosion) product---the gypsum---and point out numerically a persistent kink in gypsum's concentration profile. Finally, we illustrate numerically the position of the free boundary separating corroded from not-yet-corroded regions.

math.NA↗

arXiv2011

Single and two-scale sharp-interface models for concrete carbonation -- Asymptotics and numerical approximation

We investigate the fast-reaction asymptotics for a one-dimensional reaction-diffusion (RD) system describing the penetration of the carbonation reaction in concrete. The technique of matched-asymptotics is used to show that the RD system leads to two distinct classes of sharp-interface models, that correspond to different scalings in a small parameter εrepresenting the fast-reaction. Here εis the ratio between the characteristic scale of the diffusion of the fastest species and the one of the carbonation reaction. We explore three conceptually different scaling regimes (in terms of ε) of the effective diffusivities of the driving chemical species. The limiting models include one-phase and two-phase generalised Stefan moving-boundary problems as well as a nonstandard two-scale (micro-macro) moving-boundary problem -- the main result of the paper. Numerical results, supporting the asymptotics, illustrate the behavior of the concentration profiles for relevant parameter regimes.

cond-mat.mtrl-sci↗

arXiv2011

Rigorous Homogenization of a Stokes-Nernst-Planck-Poisson Problem for various Boundary Conditions

We perform the periodic homogenization (i.e. $\eps\to 0$) of the non-stationary Stokes-Nernst-Planck-Poisson system using two-scale convergence, where $\eps$ is a suitable scale parameter. The objective is to investigate the influence of \textsl{different boundary conditions and variable choices of scalings in $\eps$} of the microscopic system of partial differential equations on the structure of the (upscaled) limit model equations. Due to the specific nonlinear coupling of the underlying equations, special attention has to be paid when passing to the limit in the electrostatic drift term. As a direct result of the homogenization procedure, various classes of upscaled model equations are obtained.

math.AP↗

arXiv2011

Semi-discrete finite difference multiscale scheme for a concrete corrosion model: approximation estimates and convergence

We propose a semi-discrete finite difference multiscale scheme for a concrete corrosion model consisting of a system of two-scale reaction-diffusion equations coupled with an ode. We prove energy and regularity estimates and use them to get the necessary compactness of the approximation estimates. Finally, we illustrate numerically the behavior of the two-scale finite difference approximation of the weak solution.

math.NA↗

arXiv2011

Corrector estimates for the homogenization of a locally-periodic medium with areas of low and high diffusivity

We prove an upper bound for the convergence rate of the homogenization limit $ε\to 0$ for a linear transmission problem for a advection-diffusion(-reaction) system posed in areas with low and high diffusivity, where $ε$ is a suitable scale parameter. On this way, we justify the formal homogenization asymptotics obtained by us earlier by proving an upper bound for the convergence rate (a corrector estimate). The main ingredients of the proof of the corrector estimate include integral estimates for rapidly oscillating functions with prescribed average, properties of the macroscopic reconstruction operators, energy bounds and extra two-scale regularity estimates. The whole procedure essentially relies on a good understanding of the analysis of the limit two-scale problem.

math-ph↗

arXiv2011

A free-boundary problem for concrete carbonation: Rigorous justification of the $\sqrt{t}$-law of propagation

We study a one-dimensional free-boundary problem describing the penetration of carbonation fronts (free reaction-triggered interfaces) in concrete. A couple of decades ago, it was observed experimentally that the penetration depth versus time curve (say $s(t)$ vs. $t$) behaves like $s(t)=C\sqrt{t}$ for sufficiently large times $t > 0$ (with $C$ a positive constant). Consequently, many fitting arguments solely based on this experimental law were used to predict the large-time behavior of carbonation fronts in real structures, a theoretical justification of the $\sqrt{t}$-law being lacking until now. %This is the place where our paper contributes: The aim of this paper is to fill this gap by justifying rigorously the experimentally guessed asymptotic behavior. We have previously proven the upper bound $s(t)\leq C'\sqrt{t}$ for some constant $C'$; now we show the optimality of the rate by proving the right nontrivial lower estimate, i.e. there exists $C">0$ such that $s(t)\geq C"\sqrt{t}$. Additionally, we obtain weak solutions to the free-boundary problem for the case when the measure of the initial domain vanishes. In this way, our mathematical model is now allowing for the appearance of a moving carbonation front -- a scenario that until was hard to handle from the analysis point of view.

math-ph↗

arXiv2010

Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence

We explore the homogenization limit and rigorously derive upscaled equations for a microscopic reaction-diffusion system modeling sulfate corrosion in sewer pipes made of concrete. The system, defined in a periodically-perforated domain, is semi-linear, partially dissipative and weakly coupled via a non-linear ordinary differential equation posed on the solid-water interface at the pore level. Firstly, we show the well-posedness of the microscopic model. We then apply homogenization techniques based on two-scale convergence for an uniformly periodic domain and derive upscaled equations together with explicit formulae for the effective diffusion coefficients and reaction constants. We use a boundary unfolding method to pass to the homogenization limit in the non-linear ordinary differential equation. Finally, besides giving its strong formulation, we also prove that the upscaled two-scale model admits a unique solution.

math.AP↗