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Phonons in MoSe2/WSe2 van der Waals heterobilayer

2021

We report first-principles calculations of the structural and vibrational properties of the synthesized two-dimensional van der Waals heterostructures formed by single-layers dichalcogenides MoSe2 and WSe2. We show that, when combining these systems in a periodic two-dimensional heterostructures, the intrinsic phonon characteristics of the free-standing constituents are to a large extent preserved but, furthermore, exhibit shear and breathing phonon modes that are not present in the individual building blocks. These peculiar modes depend strongly on the weak vdW forces and has a great contibution to the thermal properties of the layered materials. Besides these features, the departure of fl…

Computing variations of entropy and redundancy under nonlinear mappings not preserving the signal dimension: quantifying the efficiency of V1 cortex

2021

In computational neuroscience, the Efficient Coding Hypothesis argues that the neural organization comes from the optimization of information-theoretic goals [Barlow Proc.Nat.Phys.Lab.59]. A way to confirm this requires the analysis of the statistical performance of biological systems that have not been statistically optimized [Renart et al. Science10, Malo&Laparra Neur.Comp.10, Foster JOSA18, Gomez-Villa&Malo J.Neurophysiol.19]. However, when analyzing the information-theoretic performance, cortical magnification in the retina-cortex pathway poses a theoretical problem. Cortical magnification stands for the increase the signal dimensionality [Cowey&Rolls Exp. Brain Res.74]. Conventional mo…

General Theory: Topological Aspects

2009

In Chapter 1, we have analyzed the structure of pip-spaces from the algebraic point of view only, (i.e., the compatibility relation). Here we will discuss primarily the topological structure given by the partial inner product itself. The aim is to tighten the definitions so as to eliminate as many pathologies as possible. The picture that emerges is reassuringly simple: Only two types of pip-spaces seem sufficiently regular to have any practical use, namely lattices of Hilbert spaces (LHS) or Banach spaces (LBS), that we have introduced briefly in the Introduction. Our standard reference on locally convex topological vector spaces (LCS) will be the textbook of Kothe [Kot69]. In addition, fo…

Design and Implementation of a Tool for Analysing Student Products When They Solve Fermi Problems

2017

In this chapter, we present a tool for analysing the work of secondary-level students from two different schools when they solve a type of Fermi problem. The tool is based on the characterisation of the concepts, procedures and language used to construct the models. Our results show that the proposed tool is useful to describe the models and to distinguish different aspects between the models produced by students without any previous modelling experience and those obtained by students who were already acquainted with working on modelling activities.

Optimal control of the Schrödinger equation with two or three levels

2007

In this paper, we present how techniques of “control theory”, “sub-Riemannian geometry” and “singular Riemannian geometry” can be applied to some classical problems of quantum mechanics and yield improvements to some previous results.

Paschen β line shape studies in low-temperature plasmas

2003

Line shape calculations and measurements of the Paschen β line of hydrogen (λ=12818 Å) are reported. Measurements were performed at electron densities of the plasma between 1015 cm-3 and 1016 cm-3. A wall-stabilized arc operated at atmospheric pressure in a helium-hydrogen gas mixture was applied as the excitation source. The radiation of the plasma, originating from nearly homogeneous plasma layers, in the end-on direction, was analyzed. A grating spectrometer equipped with a CCD detector was used for the radiation detection. The measured line profiles are compared with results of available experimental and theoretical Stark broadening data e.g. based on simulation techniques, applied also…

Optical study of gallium and nitrogen polarity layers of GaN grown on sapphire

2003

A confocal Raman spectroscopic study was carried out on either side of an intentionally grown GaN inversion domain boundary between a pair of strips with opposite (Ga- or N-) polarity. It is shown that the Raman spectra on the N-polarity side displays an A1(TO) mode, prohibited by symmetry considerations, meanwhile on Ga-polarity material this peak is absent, indicating a lower density of defects present in this region. The Raman spectra reveal that in the lateral direction, the change in structural quality accross the inversion domain boundary is rather continuous and extends along 4 ± 1 μm. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Emmy Noether’s Triumphal Years

2020

When Emmy Noether returned from the September 1929 conference in Prague – where she and Hasse surely spoke about their mutual mathematical interests – she belatedly answered a postcard he had sent here.

Appendix: Feynman rules

2010

Multiparametric Rational Solutions of Order N to the KPI Equation and the Explicit Case of Order 3

2021

We present multiparametric rational solutions to the Kadomtsev-Petviashvili equation (KPI). These solutions of order N depend on 2N − 2 real parameters. Explicit expressions of the solutions at order 3 are given. They can be expressed as a quotient of a polynomial of degree 2N(N +1)−2 in x, y and t by a polynomial of degree 2N(N +1) in x, y and t, depending on 2N − 2 real parameters. We study the patterns of their modulus in the (x,y) plane for different values of time t and parameters.