Developing number sense with Fingu: a preschooler’s embodied mathematics during interactions with a multi-touch digital game

Early number sense, including subitizing and composition, is a foundation for mathematics, and bodies, especially fingers, are integral to number sense. Multi-touch technology offers innovative opportunities for developing and studying number sense, especially using conceptually congruent gestures that match the mathematics. However, there have been few investigations of the development of early number sense, particularly in embodied forms. Therefore, this mixed-methods study explores a preschooler’s development of early number sense during a month of interactions with the multi-touch digital mathematics game Fingu. Key findings related to the development of early number sense include relevance of configuration and quantity, relationships among gestures and quantities, and development of estimation and precision. This research adds new perspectives to our understandings of early number sense research and practice, calling for consideration of embodiment and conceptually congruent gestures

Pressure of thermal excitations in superfluid helium

We find the pressure, due to the thermal excitations of superfluid helium, at the interface with a solid. The separate contributions of phonons, $R^-$ rotons and $R^+$ rotons are derived. The pressure due to $R^-$ rotons is shown to be negative and partially compensates the positive contribution of $R^+$ rotons, so the total roton pressure is positive but several times less than the separate $R^-$ and $R^+$ roton contributions. The pressure of the quasiparticle gas is shown to account for the fountain effect in $HeI I$. An experiment is proposed to observe the negative pressure due to $R^-$ rotons.Comment: 14 pages, 4 figure

Non-Riemannian Gravity and the Einstein-Proca System

We argue that all Einstein-Maxwell or Einstein-Proca solutions to general relativity may be used to construct a large class of solutions (involving torsion and non-metricity) to theories of non-Riemannian gravitation that have been recently discussed in the literature.Comment: 9 pages Plain Tex (No Figures), Letter to Editor Classical and Quantum Gravit

Isomorphism between Non-Riemannian gravity and Einstein-Proca-Weyl theories extended to a class of Scalar gravity theories

We extend the recently proved relation between certain models of Non-Riemannian gravitation and Einstein- Proca-Weyl theories to a class of Scalar gravity theories. This is used to present a Black-Hole Dilaton solution with non-Riemannian connection.Comment: 13 pages, tex file, accepted in Class. Quant. Gra

An axially symmetric solution of metric-affine gravity

We present an exact stationary {\it axially symmetric} vacuum solution of metric-affine gravity (MAG) which generalises the recently reported spherically symmetric solution. Besides the metric, it carries nonmetricity and torsion as post-Riemannian geometrical structures. The parameters of the solution are interpreted as mass and angular momentum and as dilation, shear and spin charges.Comment: 5 pages, RevTe

Evolution of a pulse of noninteracting quasiparticles with dispersion and initial angular width

The evolution of a pulse of noninteracting quasiparticles, caused by their different velocities and angular distribution of momenta, is studied theoretically. Equations are found that describe the shape of the pulse surface at any time. The time of the beginning, end and duration of the density of the quasiparticle energy flux is determined at a general spatial point. The quasiparticle energy density is considered at all times and positions, and it is shown that the region of high energy density, in the middle of the pulse, is equal to the initial energy density under certain conditions. These theoretical results are discussed in relation to experimental data on the evolution of a pulse of noninteracting phonons in superfluid helium

Electron-phonon interaction via Pekar mechanism in nanostructures

We consider an electron-acoustic phonon coupling mechanism associated with the dependence of crystal dielectric permittivity on the strain (the so-called Pekar mechanism) in nanostructures characterized by strong confining electric fields. The efficiency of Pekar coupling is a function of both the absolute value and the spatial distribution of the electric field. It is demonstrated that this mechanism exhibits a phonon wavevector dependence similar to that of piezoelectricity and must be taken into account for electron transport calculations in an extended field distribution. In particular, we analyze the role of Pekar coupling in energy relaxation in silicon inversion layers. Comparison with the recent experimental results is provided to illustrate its potential significance

Strong-Pinning Effects in Low-Temperature Creep: Charge-Density Waves in TaS_3

Nonlinear conduction in the quasi-one dimensional conductor o-TaS_3 has been studied in the low-temperature region down to 30 mK. It was found that at temperatures below a few Kelvins the current-voltage (I-V) characteristics consist of several branches. The temperature evolution of the I-V curve proceeds through sequential freezing-out of the branches. The origin of each branch is attributed to a particular strong pinning impurity type. Similar behavior is expected for other physical systems with collective transport (spin-density waves, Wigner crystals, vortex lattices in type-II superconductors etc.) in the presence of strong pinning centers.Comment: 11 pages, 3 ps figures, Revtex, To be published in Phys. Rev. Letters (1997