Search results for "geometrical [transition]"
showing 10 items of 50 documents
COULD STUDY AND PLAY OF CHESS IMPROVE SOCIAL INTERACTIONS? RE PORT OF AN ITALIAN CASE STUDY.
2012
Aim of this work is to improve the social interactions within a math classrooms (6 th grade), introducing a chess activity during the curricula hours. The theoretical framework upon which this research is based consists of: Vygotsky’s Theory of child developmen t (Vygotsky, 1986), the knowledge objectification theory (Radford, 2006) and theory of configural concepts (a personal review of Fischbein’s theory of figural concepts). We will discuss the results of an experimentation that has the purpose to create an appropriate environment wher e the students develop the abilities to solve and pose problems.
Meeting the Discipline-Culture Framework of Physics Knowledge: A Teaching Experience in Italian Secondary School
2014
The paper deals with physics teaching/learning in high school. An investigation in three upper secondary school classes in Italy explored the reactions of students to a structuring lecture on optics within the discipline-culture (DC) framework that organises physics knowledge around four interrelated fundamental theories of light. The lecture presented optics as an unfolding conceptual discourse of physicists regarding the nature of light. Along with the knowledge constructed in a school course of a scientific lyceum, the students provided epistemological comments, displaying their perception of physics knowledge presented in the classroom. Students’ views and knowledge were investigated by…
A perfect Fresnel acoustic reflector implemented by a Fano-resonant metascreen
2018
We propose a perfectly reflecting acoustic metasurface which is designed by replacing the curved segments of the traditional Fresnel reflector by flat Fano-resonant sub-wavelength unit cells. To preserve the original Fresnel focusing mechanism, the unit cell phase follows a specific phase profile which is obtained by applying the generalized Snell's law and Fermat's principle. The reflected curved phase fronts are thus created at the air-metasurface boundary by tailoring the metasurface dispersion as dictated by Huygens' principle. Since the unit cells are implemented by sub-wavelength double slit-shaped cavity resonators, the impinging sound waves are perfectly reflected producing acoustic…
Spectral anomalies in focused waves of different Fresnel numbers
2004
Light propagation induces remarkable changes in the spectrum of focused diffracted beams. We show that spectral changes take place in the vicinity of phase singularities in the focal region of spatially coherent, polychromatic spherical waves of different Fresnel numbers. Instead of the Debye formulation, we use the Kirchhoff integral to evaluate the focal field accurately. We find that as a result of a decrease in the Fresnel number, some cylindrical spectral switches are geometrically transformed into conical spectral switches.
White-light Fourier transformer with low chromatic aberration.
1992
A simple Fourier transformation system working with broadband parallel illumination is presented. The proposed setup, consisting of two on-axis zone plates and an achromatic objective, allows us to obtain the achromatic Fourier transform representation of the input at a finite distance with a low chromatic aberration. The discussion of the system, using the Fresnel diffraction theory, leads to an analytical expression to evaluate the transversal and longitudinal chromatic aberrations. It is shown that the resulting chromatic aberrations for typical values of the involved parameters are less than 1% over the entire visible spectrum.
Focal squeeze in axicons
2005
The on-axis irradiance distribution of a truncated conical wavefront is evaluated in terms of the Fresnel number of the focusing geometry. In agreement with geometrical optics, a focal line of increasing intensity is generated for extremely high Fresnel numbers. Otherwise clear deviations may be observed for the position of the maximum irradiance along the optical axis. A remarkable focal squeeze appears and, for decreasing Fresnel numbers, this effect manifests stronger. An analytical formula is provided for the fast evaluation of the focal squeeze.
Focal-shift formula in apodized nontelecentric focusing systems
2007
A single analytical formulation for evaluating the focal shift in any apodized nontelecentric focusing setup is reported. The formulation is also useful in the case of imaged paraxial beams. We show explicitly that the magnitude of the focal shift is determined by only one parameter that depends on the effective width of the pupil filter and its axial position. To illustrate our approach we examine different focusing setups.
Liquid-liquid phase coexistence in gold clusters. 2D or not 2D?
2006
The thermodynamics of gold cluster anions (${\mathrm{Au}}_{N}^{\ensuremath{-}}$, $N=11,\dots{},14$) is investigated using quantum molecular dynamics. Our simulations suggest that ${\mathrm{Au}}_{N}^{\ensuremath{-}}$ may exhibit a novel, freestanding planar liquid phase which dynamically coexists with a normal three-dimensional liquid. Upon cooling with experimentally realizable cooling rates, the entropy-favored three-dimensional liquid clusters often supercool and solidify into the ``wrong'' dimensionality. This indicates that experimental validation of theoretically predicted ${\mathrm{Au}}_{N}^{\ensuremath{-}}$ ground states might be more complicated than hitherto expected.
Exploring Gravitational Lensing
2019
In this article, we discuss the idea of gravitational lensing, from a systematic, historical and didactic point of view. We show how the basic lensing equation together with the concepts of geometrical optics opens a space of implications that can be explored along different dimensions. We argue that Einstein explored the idea along different pathways in this space of implication, and that these explorations are documented by different calculational manuscripts. The conceptualization of the idea of gravitational lensing as a space of exploration also shows the feasibility of discussing the idea in the classroom using some of Einstein's manuscripts.
WIGNER TRANSFORM METHODS IN INCLUSIVE ELECTRON SCATTERING FROM NUCLEI
1984
A multiple scattering series for deep inelastic leptoninduced reactions is derived by using semiclassical Wigner transform methods. In contrast to the usual Glauber theory there is no limitation for the energy loss since a time-dependent formulation is used throughout. A simple parametrization of the generalized profile function yields a closed analytical expression for the longitudinal and transverse response function of p-shell nuclei. Comparison is made with the Saclay data for -'• C. I Introduction It is common knowledge that geometrical optics is valid if the wavelength of the scattering wave is small compared to the dimensions of the scatterer. Under these conditions the phase-space d…