The effect of internal pressure on the tetragonal to monoclinic structural phase transition in ReOFeAs: the case of NdOFeAs

We report the temperature dependent x-ray powder diffraction of the quaternary compound NdOFeAs (also called NdFeAsO) in the range between 300 K and 95 K. We have detected the structural phase transition from the tetragonal phase, with P4/nmm space group, to the orthorhombic or monoclinic phase, with Cmma or P112/a1 (or P2/c) space group, over a broad temperature range from 150 K to 120 K, centered at T0 ~137 K. Therefore the temperature of this structural phase transition is strongly reduced, by about ~30K, by increasing the internal chemical pressure going from LaOFeAs to NdOFeAs. In contrast the superconducting critical temperature increases from 27 K to 51 K going from LaOFeAs to NdOFeAs doped samples. This result shows that the normal striped orthorhombic Cmma phase competes with the superconducting tetragonal phase. Therefore by controlling the internal chemical pressure in new materials it should be possible to push toward zero the critical temperature T0 of the structural phase transition, giving the striped phase, in order to get superconductors with higher Tc.Comment: 9 pages, 3 figure

Intrinsic phase separation in superconducting K0.8Fe1.6Se2 (Tc= 31.8 K) single crystals

Temperature dependent single-crystal x-ray diffraction (XRD) in transmission mode probing the bulk of the newly discovered K0.8Fe1.6Se2 superconductor (Tc = 31.8 K) using synchrotron radiation is reported. A clear evidence of intrinsic phase separation at 520 K between two competing phases, (i) a first majority magnetic phase with a ThCr2Si2-type tetragonal lattice modulated by the iron vacancy ordering and (ii) a minority non-magnetic phase having an in-plane compressed lattice volume and a weak superstructure, is reported. The XRD peaks due to the Fe vacancy ordering in the majority phase disappear by increasing the temperature at 580 K, well above phase separation temperature confirming the order-disorder phase transition. The intrinsic phase separation at 520K between a competing first magnetic phase and a second non-magnetic phase in the normal phase both having lattice superstructures (that imply different Fermi surface topology reconstruction and charge density) is assigned to a lattice-electronic instability of the K0.8Fe1.6Se2 system typical of a system tuned at a Lifshitz critical point of an electronic topological transition that gives a multi-gaps superconductor tuned a shape resonance.Comment: 10 pages, 4 figure

'I Want to, But I Also Need to' - Start-Ups Resulting from Opportunity and Necessity

When unemployed persons go into business, they often are characterized as necessity entrepreneurs, because push factors, namely their unemployment, likely prompted their decision. In contrast to this, business founders who have been previously employed represent opportunity entrepreneurs because pull factors provide the rationale for their decision. However, a data set of nearly 1,900 business start-ups by unemployed persons reveals that both kind of motivation can be observed among these start-ups. Moreover, a new type of entrepreneur emerges, motivated by both push and pull variables simultaneously. An analysis of the development of the businesses reflecting three different motivational types indicates a strong relationship between motives, survival rates and entrepreneurial development. We find in particular that start-ups out of opportunity and necessity have higher survival rates than do start-ups out of necessity, even if both types face the same duration of previous unemployment

Can you hear the fractal dimension of a drum?

Electromagnetics and Acoustics on a bounded domain are governed by the Helmholtz's equation; when such a domain is a [pre-]fractal described by means of a `just-touching' Iterated Function System (IFS) spectral decomposition of the Helmholtz's operator is self-similar as well. Renormalization of the Green's function proves this feature and isolates a subclass of eigenmodes, called ``diaperiodic'', whose waveforms and eigenvalues can be recursively computed applying the IFS to the initiator's eigenspaces. The definition of ``spectral dimension'' is given and proven to depend on diaperiodic modes only for a wide class of IFSs. Finally, asymptotic equivalence between box-counting and spectral dimensions in the fractal limit is proven. As the `self-similar' spectrum of the fractal is enough to compute box-counting dimension, positive answer is given to title question

Can you hear the fractal dimension of a drum?

Electromagnetics and Acoustics on a bounded domain are governed by the Helmholtz's equation; when such a domain is a [pre-]fractal described by means of a 'just-touching' Iterated Function System (IFS) spectral decomposition of the Helmholtz's operator is self-similar as well. Renormalization of the Green's function proves this feature and isolates a subclass of eigenmodes, called diaperiodic, whose waveforms and eigenvalues can be recursively computed applying the IFS to the initiator's eigenspaces. The definition of spectral dimension is given and proven to depend on diaperiodic modes only for a wide class of IFSS. Finally, asymptotic equivalence between box-counting and spectral dimensions in the fractal limit is proven. As the "self-similar" spectrum of the fractal is enough to compute box-counting dimension, positive answer is given to title question

Topological Calculus: between Algebraic Topology and Electromagnetic Fields

Topological behaviour of self-similar spectra for fractal domains is shown and applied to solve electromagnetic problems on fractal geometries, like for example the Sierpinski gasket.. Two different mathematical tools are employed: the Topological Calculus, which frames a topology-consistent, discrete counterpart to domains and operators and the Iterated Function Systems (IFSs) to produce fractals as limit sets of simple recursion mappings. Topological invariants and Analytical features of a set can be easily extracted from such a discrete model, even for complex geometries like fractal ones.One of the targets of this work is to show how recursion symmetries of a (pre-) fractal set, mathematically coded by "algebraic" relationships between its parts, are sole responsible for the self-similar distribution of its (laplacian) eigenvalues: no metric information is needed for this property to be observed.Another primary target is to show how Topological Calculus easily allows for an almost instantaneous discretization of contoinuum equations of any (topological) field theory. Investigating the natural modes of self-similar domains is important to many applications whose core geometry is prefractal or at least highly irregular. Most recently, transport and electromagnetic pehnomena were focused: IFS-generated waveguides, resonators and antennas(9) exhibiting multi-band properties. Such complex domains need careful mathematical formulations in order to transfer traditional-geometric properties to them; Topological Calculus is one of such discrete formulations

Spectral analysis of Šerpinskij carpet-like prefractal waveguides and resonators

Exact results on some modal properties of waveguides and resonators is studied, whose geometry is derived from "Šerpinskij carpet-like" prefractals (Serpinskij carpet and sponge; Menger sponge). The study is biased to the closed-form computation of specific resonances and eigenmodes (called "diaperiodic"), and to the relation existing between their topology and the existence of a finite set of transverse electromagnetic modes

Electromagnetic radiation from moving fractal sources: A plane-wave spectral approach

In this work the solution to the problem of electromagnetic radiation from (pre-) fractal antennas is performed by means of Plane-Wave field representation based on closed-form Fourier transforms of the self-similar current patterns. The generalization to the case of uniformly translating antennas is then accomplished through the Frame-Hopping Method by exploiting special-relativistic covariance properties of Plane-Wave spectra