Using Graphing Calculators to Integrate Mathematics and Science

The computational, graphing, statistical and programming capabilities of today’s graphing calculators make it possible for teachers and students to explore aspects of functions and investigate real-world situations in ways that were previously inaccessible because of computational constraints. Many of the features of graphing calculators can be used to integrate topics from mathematics and science. Here we provide a few illustrations of activities that use the graphing, parametric graphing, regression, and recursion features of graphing calculators to study mathematics in science contexts

Load distribution in small world networks

In this paper we introduce a new model of data packet transport, based on a stochastic approach with the aim of characterizing the load distribution on complex networks. Moreover we analyze the load standard deviation as an index of uniformity of the distribution of packets within the network, to characterize the effects of the network topology. We measure such index on the model proposed by Watts and Strogatz as the redirection probability is increased. We find that the uniformity of the load spread is maximized in the intermediate region, at which the small world effect is observed and both global and local efficiency are high. Moreover we analyze the relationship between load centrality and degree centrality as an approximate measure of the load at the edges. Analogous results are obtained for the load variance computed at the edges as well as at the vertices.Comment: 6 pages, 5 figures. Included in conference proceedings International Conference PhysCon 2005 August 24-26, 2005, Saint Petersburg, RUSSI

Growth and social capital: an evolutionary model

In this paper, we analyze the role of cooperation between firms through a model of growth and social capital. In a growth model à la Solow we incorporate the set of resources that a relational network has at its disposals, as a distinct production factor, and thus examine its dissemination through evolutionary type processes in firm interactions. Dynamic analysis of the model demonstrates that cooperation is able to increase the productivity of factors, fostering a higher rate of growth in the long term. The most significant result is that scarcity of social capital can produce a general collapse of the economic system in areas in which long term growth is usually sustained by the learning by doing and spillover of knowledge phenomena. This conclusion leads to reconsider the role of local development economic policies that should concentrate on activities that promote repeated interaction between firms proven to be cooperative or that encourage the formation of technological consortia.Economic growth; Social capital; Networks; Evolutionary games

Application of ERTS-1 data to the protection and management of New Jersey's coastal environment

ERTS-1 imagery is being used by the New Jersey Department of Environmental Protection (NJDEP) to develop information products that will assist the state in optimally managing its coastal resources and in allocating funds. Interviews with NJDEP personnel have identified significant problem areas in the coastal zone, and the types of remote sensor derived information products that can be used in real-time decision making. Initial analyses of imagery from several successive ERTS-1 orbits have shown the extent, predominant drift, and dispersion characteristics of waste disposal in coastal New Jersey waters. Imagery (MSS Bands 4 and 5) for several orbits, shows that New-York Harbor tidal discharge extending as far south as Long Branch, New Jersey

Effective Transport Template for Particle Separation in Microfluidic Bumper Arrays

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.Microfluidic bumper arrays are increasingly being used for the size-based sorting of particle suspensions. The separation mechanism is based on the interaction between a spatially periodic array of obstacles and the suspended particles as they are driven through the obstacle lattice either by volume forces or by the Stokesian drag of the surrounding fluid. By this mechanism, a focused stream of suspended particles of different sizes entering the lattice splits into different currents, each entraining assigned ranges of particle dimensions, and each characterized by a specific angle with respect to the main device axis. In this work, we build up on recent results stemming from macrotransport process theory to derive a closed-form solution for the steady-state distribution of advecting-diffusing particles in the presence of anisotropic dispersion, which typically characterizes large-scale behavior of particle motion through the periodic lattice. Attention is focused on separation resolution, that ultimately controls the feasibility of the separation in specific applications

Dispersion phenomena in microchannels: Transition from Taylor-Aris to convection-dominated regime

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.This article addresses the qualitative and quantitative properties of solute transport and dispersion in microchannel of finite-length. As the Peclet number increases a transition from the Taylor-Aris to a new regime referred as convection dominated dispersion occurs, which is controlled by the velocity profile near the stagnation points at the solid walls. The properties characterizing dispersion dominated regime can be used for analytical purposes as a chromatographic-based velocimetry and for determining the eventual occurrence of slip at the solid walls of microchannels

Optimal Design of Silicon-based Chips for Piezo-induced Ultrasound Resonances in Embedded Microchannels

AbstractWe present a variational formulation of the governing equations and introduce global indicators to describe the behavior of acoustofluidic devices driven at resonance frequencies by means of a piezoelectric transducer. The individuation of the correct Lagrangian densities for the different parts constituting the device (the piezo transducer, the silicon walls, the fluid-filled microchannel, and the glass lid) allows for the introduction of the weak formulation used in the finite element discretization of the equations describing the system in its oscillatory regime. Additionally, the knowledge of the Lagrangian density leads to the derivation of the correct structure of the Hamiltonian density, i.e. the energy density, which is important for the quantification of the energy content of the whole system and its individual parts. Specifically, the energy content of the embedded microchannel is quantified by means of the acoustofluidic yield η defined as the ratio between the energy in the channel and the total energy. From the standpoint of acoustophoretic application, the introduction of the acoustophoretic mean orientation allows us to identify the frequencies for which an acoustophoretic effect, i.e. the lateral motion of particle dragged by the axial main flow, is particularly strong. Finally, the connection between the mechanical and electrical degrees of freedom of the system is addressed. This is important for proper determination of the dissipated power, and it may lead to the detection of resonance states by means of purely electrical measurements. Numerical simulations and preliminary experimental results show some features of the model introduced

The increasing temperature as driving force for spatial distribution patterns of Parapenaeus longirostris (Lucas 1846) in the Strait of Sicily (Central Mediterranean Sea)

The deep-water rose shrimp Parapenaeus longirostris (DPS), a demersal decapod representing the most important component of crustacean landings in the Mediterranean Sea, has been suggested as a species that may exhibit temperature-driven changes in the spatio-temporal dynamics. Considering that Mediterranean waters are warming up faster than oceans, understanding the relationships of DPS populations with temperature variations and the related changes in spatial patterns is absolutely key for its management. Using a long-term dataset covering 13-years from scientific surveys (International Bottom Trawl-Surveys in the Mediterranean, MEDITS; Italian national trawl surveys, GRUND) in the Strait of Sicily (central Mediterranean Sea), the annual DPS spatial patches and the depth distribution were investigated using geostatistical and quotient analyses. The patches dimension and depth range occupation were then related to sea temperature by using linear regression analysis. Results showed that both the dimension of DPS spatial patches and the depth distribution range occupied increased concurrently with temperature. Our findings corroborate that the ongoing sea warming widen areas suitable for this species and in which it can expand its spatial distribution