Children’s Use of a ‘Time Line’ to Indicate When Events Occurred

Children who allege abuse are often asked to provide temporal information such as when the events occurred. Yet, young children often have difficulty recalling temporal information due to their limited knowledge of temporal patterns and linguistic capabilities. As time is an abstract concept (we cannot see it), some investigators have begun to use ‘time-lines’ or pictorial representations of time to aid children. Yet, there is no published research testing whether children are able to use time-lines and whether they can provide adequate temporal information using them. We tested whether children could indicate the time-of-day of events using a pictorial time-line and then compared their responses to their parents’. Seven- to 8-year-olds were most consistent with parental estimates while 4-year-olds were least consistent. Responses from the 5- to 6-year-olds depended on the temporal task. Guessing and using general knowledge to estimate the time-of-day were ruled out, and so children were genuinely drawing on episodic memory when making time-line judgments. Thus, there was a developmental progression in children’s use of physical representations to communicate abstract information. These results are promising for the use of the time-line in forensic settings but much more research is needed

Numerical aspects of nonlinear Schrodinger equations in the presence of caustics

The aim of this text is to develop on the asymptotics of some 1-D nonlinear Schrodinger equations from both the theoretical and the numerical perspectives, when a caustic is formed. We review rigorous results in the field and give some heuristics in cases where justification is still needed. The scattering operator theory is recalled. Numerical experiments are carried out on the focus point singularity for which several results have been proven rigorously. Furthermore, the scattering operator is numerically studied. Finally, experiments on the cusp caustic are displayed, and similarities with the focus point are discussed.Comment: 20 pages. To appear in Math. Mod. Meth. Appl. Sc

Role Differences in the Perception of Injustice

The current dissertation examined role differences in the perception of injustice; specifically, differences in how victims and offenders respond to a situation that they both agree is unfair. Past research has demonstrated that role affects reactions to transgressions and injustice, including recall of transgressions, and attributions of blame and responsibility (e.g., Baumeister, Stillwell, & Wotman, 1990; Mikula, Athenstaedt, Heschgl, & Heimgartner, 1998). However, to date, little work has examined role differences in perceptions of why an event is perceived as unfair (i.e., how an injustice is framed) or how justice should be restored. These were the perceptions I focused on in the present thesis. I also examined potential concerns that may motivate victims' and offenders' justice reactions, as well as the potential interaction between role and relationship quality in predicting justice reactions. In Studies 1 and 2, several of the predicted role differences in concerns were found; however, these did not lead to the expected differences in framing and restoration. In Study 1, using a vignette methodology, I found differences primarily in how victims and offenders believed justice should be restored. Overall, the significant role effects showed an accommodating response pattern (e.g., offenders proposed punishment more than did victims and neutral observers, whereas victims recommended minimal compensation more than did offenders and neutral observers), inconsistent with previous research and my hypotheses. Study 2, which employed a sample of romantic couples, substantiated the accommodating pattern found in Study 1. Study 3, which sampled a broader range of relationships, also showed i \ examples of accommodating reactions. In addition, Study 3 provided some support for the hypothesized interaction between role and relationship quality, such that responses were more accommodating as relationship quality increased. For example, offenders more strongly endorsed methods of restoration such as offender apology and recognition of the relationship with increasing relationship quality. Overall, the results from this dissertation support the general notion that victims and offenders respond to injustice differently, and, in-line with previous research on other justice-related responses (e.g., Mikula et at, 1998), suggest that victims and offenders show an other-serving, accommodating tendency in justice reactions when relationship quality is high

Time--Splitting Schemes and Measure Source Terms for a Quasilinear Relaxing System

Several singular limits are investigated in the context of a $2 \times 2$ system arising for instance in the modeling of chromatographic processes. In particular, we focus on the case where the relaxation term and a $L^2$ projection operator are concentrated on a discrete lattice by means of Dirac measures. This formulation allows to study more easily some time-splitting numerical schemes

Remote Predictive Mapping 5. Using a Lidar Derived DEM to Test the Influence of Variable Overburden Thickness and Bedrock on Drainage and Basin Morphology

A 4–m lidar digital elevation model (DEM) provides sufficient resolution to examine the impact of variable till cover on the incision history of multiple small (5 km2) catchments in eastern Canada.  The study site was selected because it has homogeneous bedrock geology that dips parallel to the land surface, is tectonically stable, has undergone common base level changes, and has a common ice history, with variable overburden thickness, from thin cover in the west to thick cover in the east. Basin morphometrics were compared for similar-size basins that have variable till cover thicknesses. Basins with thicker till cover are wider and show differences in hypsometries compared to those where till cover is thin. Two basins representing end members of till thickness were measured for stream discharge and water chemistry. Thick till  (> 1 m) on the eastern half of North Mountain retards infiltration sufficiently to promote overland flow and accelerate incision relative to areas with thinner till.  Till thickness and continuity therefore are expected to impede the achievement of steadiness and may also delay stream power law relationships in larger catchments until till cover has been effectively eroded.SOMMAIREUn modèle altimétrique numérique (MAN) par lidar 4 m offre une résolution suffisante pour étudier l'impact des divers dépôts de till sur l'histoire de l'érosion linéaire de multiples petits (5 km2) bassins versants dans l'Est du Canada.  Le site d'étude a été choisi parce que sa géologie est homogène et que son pendage est parallèle à la surface du sol, qu’il est tectoniquement stable, qu’il a subi des changements similaires du niveau de base d’érosion, de même qu’ une histoire glaciaire similaire, avec une épaisseur de mort-terrain variable, d’une couverture mince à l'ouest jusqu'à une couverture épaisse à l'est. La morphométrie du bassin a été comparée à celle de bassins de taille semblable aux épaisseurs de till variables.  Les bassins aux couvertures de till plus épaisses sont plus larges et montrent des différences hypsométriques comparé  à ceux aux couvertures minces.  Deux bassins représentant les termes extrêmes de l'épaisseur du till ont été mesurées quant au débit du courant et à la chimie de l'eau.  Les till épais (>1 m) sur la moitié est du mont Nord retardent l'infiltration, ce qui favorise l'écoulement en surface et accélèrent l’érosion linéaire par rapport aux zones couvertes de couches de till plus minces.  On s’attend donc à ce que l'épaisseur de la couche de till et sa continuité agissent comme une entrave à la stabilité et puissent aussi retarder les effets de la loi de puissance de l’écoulement dans les grands bassins récepteurs jusqu'à ce que la couverture de till a été effectivement érodée

A nonlinear drift which leads to κ\kappa-generalized distributions

We consider a system described by a Fokker-Planck equation with a new type of momentum-dependent drift coefficient which asymptotically decreases as $-1/p$ for a large momentum $p$. It is shown that the steady-state of this system is a $\kappa$-generalized Gaussian distribution, which is a non-Gaussian distribution with a power-law tail.Comment: Submitted to EPJB. 8 pages, 2 figures, dedicated to the proceedings of APFA

Structure preserving schemes for mean-field equations of collective behavior

In this paper we consider the development of numerical schemes for mean-field equations describing the collective behavior of a large group of interacting agents. The schemes are based on a generalization of the classical Chang-Cooper approach and are capable to preserve the main structural properties of the systems, namely nonnegativity of the solution, physical conservation laws, entropy dissipation and stationary solutions. In particular, the methods here derived are second order accurate in transient regimes whereas they can reach arbitrary accuracy asymptotically for large times. Several examples are reported to show the generality of the approach.Comment: Proceedings of the XVI International Conference on Hyperbolic Problem

Using Fill Terraces to Understand Incision Rates and Evolution of the Colorado River in Eastern Grand Canyon, Arizona

The incision and aggradation of the Colorado River in eastern Grand Canyon through middle to late Quaternary time can be traced in detail using well-exposed fill terraces dated by a combination of optically stimulated luminescence, uranium series, and cosmogenic nuclide dating. This fluvial history provides the best bedrock incision rate for this important landscape and highlights the complications and advantages of fill terrace records for understanding river long-profile evolution and incision. The use of fill terraces, as distinct from strath terraces, for calculating incision rates is complicated by the cyclic alluviation and incision they record. In the example of the Grand Canyon this has led to various rates being reported by different workers and rates that tend to be overestimates in shorter records. We illustrate that a meaningful long-term bedrock incision rate of 140 m/m.y. can be extracted from the Grand Canyon record by linking episodes when the Colorado River is floored on bedrock. Variable incision rates reported in the greater region may be, to some degree, due to inconsistent calculations. Our data also highlight that the Colorado River has been a mixed alluvial-bedrock river through both time and space and has been a bedrock river for less than half of its Pleistocene history. This strong temporal variation, combined with the varying bedrock the river encounters on its path, heightens the challenge of understanding the tectonic, climatic, and drainage integration controls on the form and evolution of the Colorado River’s long profile