Linear Boltzmann dynamics in a strip with large reflective obstacles: stationary state and residence time

The presence of obstacles modify the way in which particles diffuse. In cells, for instance, it is observed that, due to the presence of macromolecules playing the role of obstacles, the mean square displacement ofbiomolecules scales as a power law with exponent smaller than one. On the other hand, different situations in grain and pedestrian dynamics in which the presence of an obstacle accelerate the dynamics are known. We focus on the time, called residence time, needed by particles to cross a strip assuming that the dynamics inside the strip follows the linear Boltzmann dynamics. We find that the residence time is not monotonic with the sizeand the location of the obstacles, since the obstacle can force those particles that eventually cross the strip to spend a smaller time in the strip itself. We focus on the case of a rectangular strip with two open sides and two reflective sides and we consider reflective obstaclea into the strip

Residence time of symmetric random walkers in a strip with large reflective obstacles

We study the effect of a large obstacle on the so called residence time, i.e., the time that a particle performing a symmetric random walk in a rectangular (2D) domain needs to cross the strip. We observe a complex behavior, that is we find out that the residence time does not depend monotonically on the geometric properties of the obstacle, such as its width, length, and position. In some cases, due to the presence of the obstacle, the mean residence time is shorter with respect to the one measured for the obstacle--free strip. We explain the residence time behavior by developing a 1D analog of the 2D model where the role of the obstacle is played by two defect sites having a smaller probability to be crossed with respect to all the other regular sites. The 1D and 2D models behave similarly, but in the 1D case we are able to compute exactly the residence time finding a perfect match with the Monte Carlo simulations

Conditional expectation of the duration of the classical gambler problem with defects

The effect of space inhomogeneities on a diffusing particle is studied in the framework of the 1D random walk. The typical time needed by a particle to cross a one--dimensional finite lane, the so--called residence time, is computed possibly in presence of a drift. A local inhomogeneity is introduced as a single defect site with jumping probabilities differing from those at all the other regular sites of the system. We find complex behaviors in the sense that the residence time is not monotonic as a function of some parameters of the model, such as the position of the defect site. In particular we show that introducing at suitable positions a defect opposing to the motion of the particles decreases the residence time, i.e., favors the flow of faster particles. The problem we study in this paper is strictly connected to the classical gambler's ruin problem, indeed, it can be thought as that problem in which the rules of the game are changed when the gambler's fortune reaches a particular a priori fixed value. The problem is approached both numerically, via Monte Carlo simulations, and analytically with two different techniques yielding different representations of the exact result

Extrapolated shock fitting for two-dimensional flows on structured grids

Over the years the development of structured-grid shock-fitting techniques faced two main problems: the handling of a moving discontinuity on a fixed background grid and the capability of simulating complex flow configurations. In the proposed work, the authors present a new shock-fitting technique for structured-grid solvers that is capable of overcoming the limitations that affected the different approaches originally developed. The technique presented here removes the tight link between grid topology and shock topology, which characterizes previous shock fitting as well as front tracking methods. This significantly simplifies their implementation and more importantly reduces the computational overhead related to these geometrical manipulations. Interacting discontinuities and shocks interacting with a solid boundary are discussed and analyzed. Finally, a quantitative investigation of the error reduction obtained with the approach proposed via a global grid convergence analysis is presented

Free to move or trapped in your group: Mathematical modeling of information overload and coordination in crowded populations

We present modeling strategies that describe the motion and interaction of groups of pedestrians in obscured spaces. We start off with an approach based on balance equations in terms of measures and then we exploit the descriptive power of a probabilistic cellular automaton model. Based on a variation of the simple symmetric random walk on the square lattice, we test the interplay between population size and an interpersonal attraction parameter for the evacuation of confined and darkened spaces. We argue that information overload and coordination costs associated with information processing in small groups are two key processes that influence the evacuation rate. Our results show that substantial computational resources are necessary to compensate for incomplete information -- the more individuals in (information processing) groups the higher the exit rate for low population size. For simple social systems, it is likely that the individual representations are not redundant and large group sizes ensure that this non--redundant information is actually available to a substantial number of individuals. For complex social systems information redundancy makes information evaluation and transfer inefficient and, as such, group size becomes a drawback rather than a benefit. The effect of group sizes on outgoing fluxes, evacuation times and wall effects are carefully studied with a Monte Carlo framework accounting also for the presence of an internal obstacle

Preliminary study on the use of the 137 Cs method for soil erosion investigation in the pampean region of Argentina

Soil erosion is the most important degradation process in A rgentine. According to the estimation of 4.9 millon ha in Pampa Ondulada Region, 1.600.000 ha (36% of agricultural soils) are affected by the erosion. Field measurements of soil erosion and sediment deposition using classical techniques are difficult, time consuming, and expensive but indispensable to feed the prediction models for conservation practices design and fa rm planning. Many authors have reported that the measurement of fallout nuclides is useful tool to characterize geomorphical processes. Walling and He proposes models for conve rting 137Cs depletion/enrichment amounts to net soil loss/deposition. These models are based in the comparison between a reference 137Cs profile in a long term undisturbed site (control site) and the 137Cs profiles in the suspected eroded or deposited sites in the landscape. The aim of this study is to provide a complete and well representative set of data on the erosion intensity in topographical conditions for the Pampa Ondulada Region in A rgentine by using a tracer technique. The study area is a small watershed (about 300 ha), located in Arroyo del Tala medium basin, within Partido of San Pedro in Buenos Aires Province, Argentine. This paper presents a group of results from a detailed investigation of erosion and sediment delivery, within a 49 ha cultivated field study site in this watershed. The base of sampling strategy is the grid approach. A reference inventory, representing the local fallout input, was searched for at a site experiencing neither erosion nor deposition. Radiocaesium analyses were made at the Nuclear Regulatory Authority Laboratory by a GE Hp detector. To make an interpretation of 137Cs distribution of soil losses and sedimentation, the Mass Balance Model 2 was used (Walling and He 1997). The erosion/deposition rates from Mass Balance Model 2 are in the range of 0 to -30 t·ha-1·y-1 for erosion, and 0 to 19 t·ha-1·y-1 for deposition, and these values matched well, with the rates of erosion obtained by classical methods. The 137Cs spatial and depth distribution are showed in a map, and enabled to study the relationship of the erosion to the topography, and a good discrimination in subclasses within moderate erosion class and sedimentation class

Volatile lipophilic substances management in case of fatal sniffing.

Death due to inhalation of aliphatic hydrocarbons such as butane and propane is a particularly serious problem worldwide, resulting in several fatal cases of sniffing these volatile substances in order to "get high". Despite the number of cases published, there is not a unique approach to case management of fatal sniffing. In this paper we illustrate the volatile lipophilic substances management in a case of a prisoner died after sniffing a butane-propane gas mixture from prefilled camping stove gas canisters, discussing the comprehensive approach of the crime scene, the autopsy, histology and toxicology. A large set of accurate values of both butane and propane was obtained by gas chromatography-mass spectrometry analyzing the following post-mortem biological samples: peripheral blood, heart blood, vitreous humor, liver, lung, heart, brain/cerebral cortex, fat tissue, kidney, and allowed an in depth discussion about the cause of death. A key role is played by following the proper sampling approach during autopsy

Amyloid precursor protein drives down-regulation of mitochondrial oxidative phosphorylation independent of amyloid beta

Amyloid precursor protein (APP) and its extracellular domain, soluble APP alpha (sAPPα) play important physiological and neuroprotective roles. However, rare forms of familial Alzheimer’s disease are associated with mutations in APP that increase toxic amyloidogenic cleavage of APP and produce amyloid beta (Aβ) at the expense of sAPPα and other non-amyloidogenic fragments. Although mitochondrial dysfunction has become an established hallmark of neurotoxicity, the link between Aβ and mitochondrial function is unclear. In this study we investigated the effects of increased levels of neuronal APP or Aβ on mitochondrial metabolism and gene expression, in human SH-SY5Y neuroblastoma cells. Increased non-amyloidogenic processing of APP, but not Aβ, profoundly decreased respiration and enhanced glycolysis, while mitochondrial DNA (mtDNA) transcripts were decreased, without detrimental effects to cell growth. These effects cannot be ascribed to Aβ toxicity, since higher levels of endogenous Aβ in our models do not cause oxidative phosphorylation (OXPHOS) perturbations. Similarly, chemical inhibition of β-secretase decreased mitochondrial respiration, suggesting that non-amyloidogenic processing of APP may be responsible for mitochondrial changes. Our results have two important implications, the need for caution in the interpretation of mitochondrial perturbations in models where APP is overexpressed, and a potential role of sAPPα or other non-amyloid APP fragments as acute modulators of mitochondrial metabolism