Daniel R. Parisi

Solving differential equations with unsupervised neural networks

Abstract A recent method for solving differential equations using feedforward neural networks was applied to a non-steady fixed bed non-catalytic solid–gas reactor. As neural networks have universal approximation capabilities, it is possible to postulate them as solutions for a given DE problem that defines an unsupervised error. The training was performed using genetic algorithms and the gradient descent method. The solution was found with uniform accuracy (MSE ∼10−9) and the trained neural network provides a compact expression for the analytical solution over the entire finite domain. The problem was also solved with a traditional numerical method. In this case, solution is known only over a discrete grid of points and its computational complexity grows rapidly with the size of the grid. Although solutions in both cases are identical, the neural networks approach to the DE problem is qualitatively better since, once the network is trained, it allows instantaneous evaluation of solution at any desired number of points spending negligible computing time and memory.

Clogging transition of many-particle systems flowing through bottlenecks

When a large set of discrete bodies passes through a bottleneck, the flow may become intermittent due to the development of clogs that obstruct the constriction. Clogging is observed, for instance, in colloidal suspensions, granular materials and crowd swarming, where consequences may be dramatic. Despite its ubiquity, a general framework embracing research in such a wide variety of scenarios is still lacking. We show that in systems of very different nature and scale -including sheep herds, pedestrian crowds, assemblies of grains, and colloids- the probability distribution of time lapses between the passages of consecutive bodies exhibits a power-law tail with an exponent that depends on the system condition. Consequently, we identify the transition to clogging in terms of the divergence of the average time lapse. Such a unified description allows us to put forward a qualitative clogging state diagram whose most conspicuous feature is the presence of a length scale qualitatively related to the presence of a finite size orifice. This approach helps to understand paradoxical phenomena, such as the faster-is-slower effect predicted for pedestrians evacuating a room and might become a starting point for researchers working in a wide variety of situations where clogging represents a hindrance.

Faster-is-slower effect in escaping ants revisited: ants do not behave like humans

In this work we studied the trajectories, velocities and densities of ants when egressing under controlled levels of stress produced by a chemical repellent at different concentrations. We found that, unlike other animals escaping under life-and-death conditions and pedestrian simulations, ants do not produce a higher density zone near the exit door. Instead, ants are uniformly distributed over the available space allowing for efficient evacuations. Consequently, the faster-is-slower effect observed in ants (Soria et al., 2012) is clearly of a different nature to that predicted by de social force model. In the case of ants, the minimum evacuation time is correlated with the lower probability of taking backward steps. Thus, as biological model ants have important differences that make their use inadvisable for the design of human facilities.

Efficient Egress of Escaping Ants Stressed with Temperature

In the present work we investigate the egress times of a group of Argentine ants (Linepithema humile) stressed with different heating speeds. We found that the higher the temperature ramp is, the faster ants evacuate showing, in this sense, a group-efficient evacuation strategy. It is important to note that even when the life of ants was in danger, jamming and clogging was not observed near the exit, in accordance with other experiments reported in the literature using citronella as aversive stimuli. Because of this clear difference between ants and humans, we recommend the use of some other animal models for studying competitive egress dynamics as a more accurate approach to understanding competitive egress in human systems.

Modeling steady-state heterogeneous gas–solid reactors using feedforward neural networks

Abstract A new method for solving gas–solid heterogeneous reactors is proposed. Mass balance inside the pellet (numerical integration of a differential equations system) is replaced by an analytical function, which functionality corresponds to an adequate trained three-layer feedforward neural network. The global reaction rate evaluated by using this function includes the complex phenomena of simultaneous diffusion and chemical reaction into the solid. The methodology was successfully applied to the steam reforming of methane. Both methods are compared. Results of the reactor simulation are very similar in both cases but the one that used neural networks is about 20 times faster. The method proposed could also be applied to any type of two-phase heterogeneous reactors.

Flow of pedestrians through narrow doors with different competitiveness

We report a thorough analysis of the intermittent flow of pedestrians through a narrow door. The observations include five different sets of evacuation drills with which we have investigated the effect of door size and competitiveness on the flow dynamics. Although the outcomes are in general compatible with the existence of the faster-is-slower effect, the temporal evolution of the instantaneous flow rate provides evidence of new features. These stress the crucial role of the number of people performing the tests, which has an influence on the obtained results. Once the transients at the beginning and end of the evacuation are removed, we have found that the time lapses between the passage of two consecutive pedestrians display heavy-tailed distributions in all the scenarios studied. Meanwhile, the distribution of burst sizes decays exponentially; this can be linked to a constant probability of finding a long-lasting clog during the evacuation process. Based on these results, a discussion is presented on the caution that should be exercised when measuring or describing the intermittent flow of pedestrians through narrow doors.

“Faster Is Slower” Effect in Granular Flows

We investigate the faster is slower (FIS) effect for a granular flow system which consist of a quasi two-dimensional hopper placed on a vibrating inclined plane. Increasing the angle of the plane (θ) is similar to increasing the driving force in the social force model. We measured the distribution of the time intervals between two successive particles (dt) and found that for narrow exits (3 particle diameter) it displays a power-law tail with a negative exponent α, were | α | < 2, indicating that the mean dt is not defined. Hence, we proposed to use α as a measure of the ability of the system not to develop long-lasting blockages and in this sense, the FIS effect was observed for the experimental granular system. This is the first experimental evidence of the FIS effect in granular flows. Moreover, our results suggest that a different approach might be necessary to quantify the evacuation time for pedestrians since its mean may not be defined for highly competitive crowd systems.

Experimental characterization of collision avoidance in pedestrian dynamics

In the present paper, the avoidance behavior of pedestrians was characterized by controlled experiments. Several conflict situations were studied considering different flow rates and group sizes in crossing and head-on configurations. Pedestrians were recorded from above, and individual two-dimensional trajectories of their displacement were recovered after image processing. Lateral swaying amplitude and step lengths were measured for free pedestrians, obtaining similar values to the ones reported in the literature. Minimum avoidance distances were computed in two-pedestrian experiments. In the case of one pedestrian dodging an arrested one, the avoidance distance did not depend on the relative orientation of the still pedestrian with respect to the direction of motion of the first. When both pedestrians were moving, the avoidance distance in a perpendicular encounter was longer than the one obtained during a head-on approach. It was found that the mean curvature of the trajectories was linearly anticorrelated with the mean speed. Furthermore, two common avoidance maneuvers, stopping and steering, were defined from the analysis of the acceleration and curvature in single trajectories. Interestingly, it was more probable to observe steering events than stopping ones, also the probability of simultaneous steering and stopping occurrences was negligible. The results obtained in this paper can be used to validate and calibrate pedestrian dynamics models.

Pedestrian collective motion in competitive room evacuation

When a sizable number of people evacuate a room, if the door is not large enough, an accumulation of pedestrians in front of the exit may take place. This is the cause of emerging collective phenomena where the density is believed to be the key variable determining the pedestrian dynamics. Here, we show that when sustained contact among the individuals exists, density is not enough to describe the evacuation, and propose that at least another variable –such as the kinetic stress– is required. We recorded evacuation drills with different degrees of competitiveness where the individuals are allowed to moderately push each other in their way out. We obtain the density, velocity and kinetic stress fields over time, showing that competitiveness strongly affects them and evidencing patterns which have been never observed in previous (low pressure) evacuation experiments. For the highest competitiveness scenario, we detect the development of sudden collective motions. These movements are related to a notable increase of the kinetic stress and a reduction of the velocity towards the door, but do not depend on the density.

Clogging Transition of Vibration-Driven Vehicles Passing through Constrictions

We report experimental results on the competitive passage of elongated self-propelled vehicles rushing through a constriction. For the chosen experimental conditions, we observe the emergence of intermittencies similar to those reported previously for active matter passing through narrow doors. Noteworthy, we find that, when the number of individuals crowding in front of the bottleneck increases, there is a transition from an unclogged to a clogged state characterized by a lack of convergence of the mean clog duration as the measuring time increases. It is demonstrated that this transition-which was reported previously only for externally vibrated systems such as colloids or granulars-appears also for self-propelled agents. This suggests that the transition should also occur for the flow through constrictions of living agents (e.g., humans and sheep), an issue that has been elusive so far in experiments due to safety risks.