arXiv subjects

Adrian Muntean

Publications and source records attributed to Adrian Muntean.

At least 55 records · Page 3Linked to original sources

arXiv2021

A Mesoscopic Lattice Model for Morphology Formation in Ternary Mixtures with Evaporation

We develop a mesoscopic lattice model to study the morphology formation in interacting ternary mixtures with evaporation of one component. As concrete application of our model, we wish to capture morphologies as they are typically arising during fabrication of organic solar cells. In this context, we consider an evaporating solvent into which two other components are dissolved, as a model for a 2-component coating solution that is drying on a substrate. We propose a 3-spins dynamics to describe the evolution of the three interacting species. As main tool, we use a Monte Carlo Metropolis-based algorithm, with the possibility of varying the system's temperature, mixture composition, interaction strengths, and evaporation kinetics. The main novelty is the structure of the mesoscopic model -- a bi-dimensional lattice with periodic boundary conditions and divided in square cells to encode a mesoscopic range interaction among the units. We investigate the effect of the model parameters on the structure of the resulting morphologies. Finally, we compare the results obtained with the mesoscopic model with corresponding ones based on an analogous lattice model with a short range interaction among the units, i.e. when the mesoscopic length scale coincides with the microscopic length scale of the lattice.

cond-mat.stat-mech↗

arXiv2021

Towards a quantitative reduction of the SIR epidemiological model

Motivated by our intention to use SIR-type epidemiological models in the context of dynamic networks as provided by large-scale highly interacting inhomogeneous human crowds, we investigate in this framework possibilities to reduce the classical SIR model to a representative evolution model for a suitably chosen observable. For selected scenarios, we provide practical {\em a priori} error bounds between the approximate and the original observables. Finally, we illustrate numerically the behavior of the reduced models compared to the original ones.

cond-mat.stat-mech↗

arXiv2021

Well-posedness of a coupled system of Skorohod-like stochastic differential equations

We study the well-posedness of a coupled system of Skorohod-like stochastic differential equations with reflecting boundary condition. The setting describes the evacuation dynamics of a mixed crowd composed of both active and passive pedestrians moving through a domain with obstacles, fire and smoke. As main working techniques, we use compactness methods and the Skorohod's representation of solutions to SDEs posed in bounded domains. This functional setting is a new point of view in the field of modeling and simulation pedestrian dynamics. The main challenge is to handle the coupling in the model equations together with the multiple-connectedness of the domain and the pedestrian-obstacle interaction.

math.PR↗

arXiv2021

A multiscale quasilinear system for colloids deposition in porous media: Weak solvability and numerical simulation of a near-clogging scenario

We study the weak solvability of a quasilinear reaction-diffusion system nonlinearly coupled with an linear elliptic system posed in a domain with distributed microscopic balls in $2D$. The size of these balls are governed by an ODE with direct feedback on the overall problem. The system describes the diffusion, aggregation, fragmentation, and deposition of populations of colloidal particles of various sizes inside a porous media made of prescribed arrangement of balls. The mathematical analysis of the problem relies on a suitable application of Schauder's fixed point theorem which also provides a convergent algorithm for an iteration method to compute finite difference approximations of smooth solutions to our multiscale model. Numerical simulations illustrate the behavior of the local concentration of the colloidal populations close to clogging situations.

math.AP↗

arXiv2020

A moving boundary approach of capturing diffusants penetration into rubber: FEM approximation and comparison with laboratory measurements

We propose a moving-boundary scenario to model the penetration of diffusants into dense and foamed rubbers. The presented modelling approach recovers experimental findings related to the diffusion of cyclohexane and the resulting swelling in a piece of material made of ethylene propylene diene monomer rubber (EPDM). The main challenge is to find out relatively simple model components which can mimic the mechanical behavior of the rubber. Such special structure is identified here so that the computed penetration depths of the diffusant concentration are within the range of experimental measurements. We investigate two cases: a dense rubber and a rubber foam, both made of the same matrix material. After a brief discussion of scaling arguments, we present a finite element approximation of the moving boundary problem. To overcome numerical difficulties due to the \textit{a priori} unknown motion of the diffusants penetration front, we transform the governing model equations from the physical domain with moving unknown boundary to a fixed fictitious domain. We then solve the transformed equations by the finite element method and explore the robustness of our approximations with respect to relevant model parameters. Finally, we discuss numerical estimations of the expected large-time behavior of the material.

math.NA↗

arXiv2020

Deterministic reversible model of non-equilibrium phase transitions and stochastic counterpart

N point particles move within a billiard table made of two circular cavities connected by a straight channel. The usual billiard dynamics is modified so that it remains deterministic, phase space volumes preserving and time reversal invariant. Particles move in straight lines and are elastically reflected at the boundary of the table, as usual, but those in a channel that are moving away from a cavity invert their motion (rebound), if their number exceeds a given threshold T. When the geometrical parameters of the billiard table are fixed, this mechanism gives rise to non--equilibrium phase transitions in the large N limit: letting T/N decrease, the homogeneous particle distribution abruptly turns into a stationary inhomogeneous one. The equivalence with a modified Ehrenfest two urn model, motivated by the ergodicity of the billiard with no rebound, allows us to obtain analytical results that accurately describe the numerical billiard simulation results. Thus, a stochastic exactly solvable model that exhibits non-equilibrium phase transitions is also introduced.

cond-mat.stat-mech↗

arXiv2020

When diffusion faces drift: consequences of exclusion processes for bi--directional pedestrian flows

Stochastic particle--based models are useful tools for describing the collective movement of large crowds of pedestrians in crowded confined environments. Using descriptions based on the simple exclusion process, two populations of particles, mimicking pedestrians walking in a built environment, enter a room from two opposite sides. One population is passive -- being unaware of the local environment; particles belonging to this group perform a symmetric random walk. The other population has information on the local geometry in the sense that as soon as particles enter a visibility zone, a drift activates them. Their self-propulsion leads them towards the exit. This second type of species is referred here as active. The assumed crowdedness corresponds to a near--jammed scenario. The main question we ask in this paper is: Can we induce modifications of the dynamics of the active particles to improve the outgoing current of the passive particles? To address this question, we compute occupation number profiles and currents for both populations in selected parameter ranges. Besides observing the more classical faster--is--slower effect, new features appear as prominent like the non--monotonicity of currents, self--induced phase separation within the active population, as well as acceleration of passive particles for large--drift regimes of active particles.

cond-mat.stat-mech↗

arXiv2020

Anticipation decides on lane formation in pedestrian counterflow -- a simulation study

Human crowds base most of their behavioral decisions upon anticipated states of their walking environment. We explore a minimal version of a lattice model to study lanes formation in pedestrian counterflow. Using the concept of horizon depth, our simulation results suggest that the anticipation effect together with the presence of a small background noise play an important role in promoting collective behaviors in a counterflow setup. These ingredients facilitate the formation of seemingly stable lanes and ensure the ergodicity of the system.

nlin.CG↗

arXiv2020

Global weak solvability, Continuous dependence on data and large time growth of swelling moving interfaces

We prove a global existence result for weak solutions to a one-dimensional free boundary problem with flux boundary conditions describing swelling along a halfline. Additionally, we show that solutions are not only unique but also depend continuously on data and parameters. The key observation is that the structure of our system of partial differential equations allows us to show that the moving a priori unknown interface never disappears. As main ingredients of the global existence proof, we rely on a local weak solvability result for our problem, uniform estimates of the solution, integral estimates on quantities defined at the free boundary, as well as a fine pointwise lower bound for the position of the moving boundary. Some of the estimates are time-independent. They allow us to explore the large time behavior of the position of the moving boundary. The approach is specific to one-dimensional settings.

math.AP↗

arXiv2019

Uniqueness and stability with respect to parameters of solutions to a fluid-like driven system for active-passive pedestrian dynamics

We study a system of parabolic equations consisting of a double nonlinear parabolic equations of Forchheimer type coupled with a semilinear parabolic equations. The system describes a fluid-like driven system for active-passive pedestrian dynamics. The structure of the nonlinearity of the coupling allows us to prove the uniqueness of solutions. We provide also stability estimates of solutions with respect to selected parameters.

math.AP↗

arXiv2019

Colloidal Transport in Locally Periodic Evolving Porous Media -- An Upscaling Exercise

We derive an upscaled model describing the aggregation and deposition of colloidal particles within a porous medium allowing for the possibility of local clogging of the pores. At the level of the pore scale, we extend an existing model for colloidal dynamics including the evolution of free interfaces separating colloidal particles deposited on solid boundaries (solid spheres) from the colloidal particles transported through the gaseous parts of the porous medium. As a result of deposition, the solid spheres grow reducing therefore the space available for transport in the gaseous phase. Upscaling procedures are applied and several classes of macroscopic models together with effective transport tensors are obtained, incorporating explicitly the local growth of the solid spheres. The resulting models are solved numerically and various simulations are presented. In particular, they are able to detect clogging regions, and therefore, can provide estimates on the storage capacity of the porous matrix.

math.AP↗

arXiv2019

Weak solvability a fluid-like driven system for active-passive pedestrian dynamics

We study the question of weak solvability for a nonlinear coupled parabolic system that models the evolution of a complex pedestrian flow. The main feature is that the flow is composed of a mix of densities of active and passive pedestrians that are moving with different velocities. We rely on special energy estimates and on the use a Schauder's fixed point argument to tackle the existence of solutions to our evolution problem.

math.AP↗

arXiv2019

A semidiscrete Galerkin scheme for a coupled two-scale elliptic-parabolic system: well-posedness and convergence approximation rates

In this paper, we study the numerical approximation of a coupled system of elliptic-parabolic equations posed on two separated spatial scales. The model equations describe the interplay between macroscopic and microscopic pressures in an unsaturated heterogeneous medium with distributed microstructures as they often arise in modeling reactive flow in cementitious-based materials. Besides ensuring the well-posedness of our two-scale model, we design two-scale convergent numerical approximations and prove a priori error estimates for the semidiscrete case. We complement our analysis with simulation results illustrating the expected behaviour of the system.

math.AP↗

arXiv2019

A lattice model for active--passive pedestrian dynamics: a quest for drafting effects

We study the pedestrian escape from an obscure corridor using a lattice gas model with two species of particles. One species, called passive, performs a symmetric random walk on the lattice, whereas the second species, called active, is subject to a drift guiding the particles towards the exit. The drift mimics the awareness of some pedestrians of the geometry of the corridor and of the location of the exit. We provide numerical evidence that, in spite of the hard core interaction between particles -- namely, there can be at most one particle of any species per site, -- adding a fraction of active particles in the system enhances the evacuation rate of all particles from the corridor. A similar effect is also observed when looking at the outgoing particle flux, when the system is in contact with an external particle reservoir that induces the onset of a steady state. We interpret this phenomenon as a discrete space counterpart of the drafting effect typically observed in a continuum set--up as the aerodynamic drag experienced by pelotons of competing cyclists.

physics.soc-ph↗

arXiv2019

A pore-scale study of transport of inertial particles by water in porous media

We study the transport of inertial particles in water flow in porous media. Our interest lies in understanding the accumulation of particles including the possibility of clogging. We propose that accumulation can be a result of hydrodynamic effects: the tortuous paths of the porous medium generate regions of dominating strain/vorticity, which favour the accumulation/dispersion of the inertial particles. Numerical simulations show that essentially two accumulation regimes are identified: for low and for high flow velocities. When particles accumulate in high-velocity regions, at the entrance of a pore throat, a clog is formed. The formation of a clog significantly modifies the flow, as the partial blockage of the pore causes a local redistribution of pressure. This redistribution can divert the upstream water flow into neighbouring pores. Moreover, we show that accumulation in high velocity regions occurs in heterogeneous media, but not in homogeneous media, where we refer to homogeneity with respect to the distribution of the pore throat diameters.

physics.flu-dyn↗

arXiv2019

Modelling, Simulation and Parameter Identification of Active Pollution Reduction with Photovoltaic Asphalt

We develop and implement a numerical model to simulate the effect of photovoltaic asphalt on reducing the concentration of nitrogen monoxide due to the presence of heavy traffic in an urban environment. The contributions in this paper are threefold: we model and simulate the spread and breakdown of pollution in an urban environment, we provide a parameter estimation process that can be used to find missing parameters, and finally, we train and compare this simulation with different data sets. We analyze the results and provide an outlook on further research.

math.NA↗

arXiv2019

Homogenization of a pseudo-parabolic system via a spatial-temporal decoupling: upscaling and corrector estimates for perforated domains

In this paper, we determine the convergence speed of an upscaling of a pseudo-parabolic system containing drift terms with scale separation of size $ε\ll 1$. Both the upscaling and convergence speed determination exploit a natural spatial-temporal decomposition, which splits the pseudo-parabolic system into a spatial elliptic partial differential equation and a temporal ordinary differential equation. We extend the applicability to space-time domains that are a product of spatial and temporal domains, such as a time-independent perforated spatial domain. Finally, for special cases we show convergence speeds for global times, i.e. $t \in \mathbf{R}_+$, by using time intervals that converge to $\mathbf{R}_+$ as $ε\downarrow 0$.

math.AP↗

arXiv2018

Analysis of a projection method for the Stokes problem using an $\varepsilon$-Stokes approach

We generalize pressure boundary conditions of an $\varepsilon$-Stokes problem. Our $\varepsilon$-Stokes problem connects the classical Stokes problem and the corresponding pressure-Poisson equation using one parameter $\varepsilon>0$. For the Dirichlet boundary condition, it is proven in K. Matsui and A. Muntean (2018) that the solution for the $\varepsilon$-Stokes problem converges to the one for the Stokes problem as $\varepsilon$ tends to 0, and to the one for the pressure-Poisson problem as $\varepsilon$ tends to $\infty$. Here, we extend these results to the Neumann and mixed boundary conditions. We also establish error estimates in suitable norms between the solutions to the $\varepsilon$-Stokes problem, the pressure-Poisson problem and the Stokes problem, respectively. Several numerical examples are provided to show that several such error estimates are optimal in $\varepsilon$. Our error estimates are improved if one uses the Neumann boundary conditions. In addition, we show that the solution to the $\varepsilon$-Stokes problem has a nice asymptotic structure.

math.AP↗