Current moments of 1D ASEP by duality

We consider the exponential moments of integrated currents of 1D asymmetric simple exclusion process using the duality found by Sch\"utz. For the ASEP on the infinite lattice we show that the $n$th moment is reduced to the problem of the ASEP with less than or equal to $n$ particles.Comment: 13 pages, no figur

Interactive Whiteboard Technology within the Kindergarten Visual Arts Classroom

The purpose of this document is to design and record a Kindergarten visual arts unit using the Activboard to determine how student achievement, motivation, and interest are impacted. Methods of data collection include both observational recording and student interviews. The Activboard facilitates a highly interactive study of the art curriculum and data collected throughout the unit indicates a positive impact on student achievement, motivation, and interest

A smoke generator system for aerodynamic flight research

A smoke generator system was developed for in-flight vortex flow studies on the F-18 high alpha research vehicle (HARV). The development process included conceptual design, a survey of existing systems, component testing, detailed design, fabrication, and functional flight testing. Housed in the forebody of the aircraft, the final system consists of multiple pyrotechnic smoke cartridges which can be fired simultaneously or in sequence. The smoke produced is ducted to desired locations on the aircraft surface. The smoke generator system (SGS) has been used successfully to identify vortex core and core breakdown locations as functions of flight condition. Although developed for a specific vehicle, this concept may be useful for other aerodynamic flight research which requires the visualization of local flows

Is play disappearing? Instances of no-play in children\u27s neighbourhoods: Implications for learning, development and curriculum

This paper presents data from the Irish Neighbourhood Play Study that explored children’s engagement in play. The data raises concerns around recorded instances of no-play in play environments. The instances of no-play were recorded during peak play time periods including weekend and afterschool hours. This data raises the critical question: Are today’s children being afforded sufficient time to play? Both the quality of opportunity to play and the quantity of time afforded to children to engage in play are important factors in children’s learning and development (Fisher, Hirsh-Pasek, Golinkoff, Singer & Berk, 2011; Whitebread, 2012). The data from the Irish Neighbourhood Play Study indicates that children may not be spending enough time playing in their neighbourhoods. In discussing the data, this paper evolves to explore the thesis that schools should attend to this absence of play by providing play-based education. A justification for play-based approaches within the school experience is underpinned by an evidence-based defense of the centrality of play within children’s academic and holistic development

Child\u27s play the developmental benefits of the play choices of modern children: Implications for school curricula

This paper presents data from the Irish Neighbourhood Play Study. The Irish Neighbourhood Play Study explored the play choices of children from 0 to 15 years of age. This paper reports the findings on the play choices of children and these are presented alongside the levels of engagement within each play type. Construction Play, Motor Play, Fantasy (Imaginative) Play and Social Play are all applied as broad categories with detailed data presented that drills down into what elements of play children are choosing within each category. The developmental benefits of each play type are then explored and discussed. These findings are viewed through an educational lens and contextualised within a curricular context. The critical questions arising from the findings concern the developmental benefits inherent to the types of play children choose for themselves and how these developmental benefits translate to the school context. This paper discusses these critical questions and suggests possible implications for school curricula when adopting play-based approaches

Maine\u27s Marine Invasion

The Asian shore crab. Dead man\u27s fingers. Bonamia oyster disease. These are just a few of the non-native species that have been documented along the Maine coast. This fact sheet summarizes the concerns and actions of Maine\u27s stakeholders regarding species invasions and associated problems

Universal Results for Correlations of Characteristic Polynomials: Riemann-Hilbert Approach

We prove that general correlation functions of both ratios and products of characteristic polynomials of Hermitian random matrices are governed by integrable kernels of three different types: a) those constructed from orthogonal polynomials; b) constructed from Cauchy transforms of the same orthogonal polynomials and finally c) those constructed from both orthogonal polynomials and their Cauchy transforms. These kernels are related with the Riemann-Hilbert problem for orthogonal polynomials. For the correlation functions we obtain exact expressions in the form of determinants of these kernels. Derived representations enable us to study asymptotics of correlation functions of characteristic polynomials via Deift-Zhou steepest-descent/stationary phase method for Riemann-Hilbert problems, and in particular to find negative moments of characteristic polynomials. This reveals the universal parts of the correlation functions and moments of characteristic polynomials for arbitrary invariant ensemble of $\beta=2$ symmetry class.Comment: 34page

The determinant representation for quantum correlation functions of the sinh-Gordon model

We consider the quantum sinh-Gordon model in this paper. Using known formulae for form factors we sum up all their contributions and obtain a closed expression for a correlation function. This expression is a determinant of an integral operator. Similar determinant representations were proven to be useful not only in the theory of correlation functions, but also in the matrix models.Comment: 21 pages, Latex, no figure

The One-dimensional KPZ Equation and the Airy Process

Our previous work on the one-dimensional KPZ equation with sharp wedge initial data is extended to the case of the joint height statistics at n spatial points for some common fixed time. Assuming a particular factorization, we compute an n-point generating function and write it in terms of a Fredholm determinant. For long times the generating function converges to a limit, which is established to be equivalent to the standard expression of the n-point distribution of the Airy process.Comment: 15 page