Coprime invariable generation and minimal-exponent groups

A finite group $G$ is \emph{coprimely-invariably generated} if there exists a set of generators $\{g_1, ..., g_u\}$ of $G$ with the property that the orders $|g_1|, ..., |g_u|$ are pairwise coprime and that for all $x_1, ..., x_u \in G$ the set $\{g_1^{x_1}, ..., g_u^{x_u}\}$ generates $G$. We show that if $G$ is coprimely-invariably generated, then $G$ can be generated with three elements, or two if $G$ is soluble, and that $G$ has zero presentation rank. As a corollary, we show that if $G$ is any finite group such that no proper subgroup has the same exponent as $G$, then $G$ has zero presentation rank. Furthermore, we show that every finite simple group is coprimely-invariably generated. Along the way, we show that for each finite simple group $S$, and for each partition $\pi_1, ..., \pi_u$ of the primes dividing $|S|$, the product of the number $k_{\pi_i}(S)$ of conjugacy classes of $\pi_i$-elements satisfies $\prod_{i=1}^u k_{\pi_i}(S) \leq \frac{|S|}{2| Out S|}.

A decomposition of the Jacobian of a Humbert-Edge curve

A \textit{Humbert-Edge curve of type} $n$ is a non-degenerate smooth complete intersection of $n-1$ diagonal quadrics. Such a curve has an interesting geometry since it has a natural action of the group $(\mathbb{Z}/2\mathbb{Z})^n$. We present here a decomposition of its Jacobian variety as a product of Prym-Tyurin varieties, and we compute the kernel of the corresponding isogeny.Comment: 9 pages, comments welcome! To appear in Contemporary Mathematic

The Metaphor: a Literary Tool Lent to the Architectural Design. Theoretical References, Research Method and Practical Experience in Teaching Activity

The design process in Architectural Design Studio’s first classes for students is often based on images that are erroneously used as references by copying some formal choices. In the most general sense, this issue is related to a gap between architectural culture and society, as architecture is considered a virtual and consumable object. Those problems could be faced with an old but still effective tool that is the metaphor. Architecture is mainly known by images, and each image has a visible and an invisible part; the latter concerns the culture that underlies it. The paper assumes the metaphor is a design tool that can be helpful in the initial stages of the design process as it allows anyone to quickly connect images, ideas, and experiences, getting deeper into the invisible part of images. Since the metaphor is mainly a linguistic agent, most of the studies concern the use of the metaphor in the field of theoretical criticism and for reviewing other projects. The paper proposes to integrate this approach by investigating the metaphor to support the transfer of shapes and figures between different architectures. Furthermore, the proposed process foresees a permanent part based on the type of dynamic and more mobile part where metaphorical thinking finds space. Therefore, two types of use of the metaphor are put forward: the first interprets existing buildings by recognising both linguistic metaphors used by the critics and those crystallized in the architectural form; the second instead stimulates students to use visual metaphors in determining the shape and volume of the project

Breaking degeneracy in jet dynamics: multi-epoch joint modelling of the BL Lac PKS 2155-304

Supermassive black holes can launch powerful jets which can be some of the most luminous multi-wavelength sources; decades after their discovery their physics and energetics are still poorly understood. The past decade has seen a dramatic improvement in the quality of available data, but despite this improvement the semi-analytical modelling of jets has advanced slowly: simple one-zone models are still the most commonly employed method of interpreting data, in particular for AGN jets. These models can roughly constrain the properties of jets but they cannot unambiguously couple their emission to the launching regions and internal dynamics, which can be probed with simulations. However, simulations are not easily comparable to observations because they cannot yet self-consistently predict spectra. We present an advanced semi-analytical model which accounts for the dynamics of the whole jet, starting from a simplified parametrization of Relativistic Magnetohydrodynamics in which the magnetic flux is converted into bulk kinetic energy. To benchmark the model we fit six quasisimultaneous, multi-wavelength spectral energy distributions of the BL Lac PKS 2155-304 obtained by the TANAMI program, and we address the degeneracies inherent to such a complex model by employing a state-of-the-art exploration of parameter space, which so far has been mostly neglected in the study of AGN jets. We find that this new approach is much more effective than a single-epoch fit in providing meaningful constraints on model parameters.Comment: Accepted for publication on MNRA

Ptychographic reconstruction of attosecond pulses

We demonstrate a new attosecond pulse reconstruction modality which uses an algorithm that is derived from ptychography. In contrast to other methods, energy and delay sampling are not correlated, and as a result, the number of electron spectra to record is considerably smaller. Together with the robust algorithm, this leads to a more precise and fast convergence of the reconstruction.Comment: 12 pages, 7 figures, the MATLAB code for the method described in this paper is freely available at http://figshare.com/articles/attosecond_Extended_Ptychographyc_Iterative_Engine_ePIE_/160187

Three-dimensional charge transport mapping by two-photon absorption edge transient-current technique in synthetic single-crystalline diamond

We demonstrate the application of two-photon absorption transient current technique to wide bandgap semiconductors. We utilize it to probe charge transport properties of single-crystal Chemical Vapor Deposition (scCVD) diamond. The charge carriers, inside the scCVD diamond sample, are excited by a femtosecond laser through simultaneous absorption of two photons. Due to the nature of two-photon absorption, the generation of charge carriers is confined in space (3-D) around the focal point of the laser. Such localized charge injection allows to probe the charge transport properties of the semiconductor bulk with a fine-grained 3-D resolution. Exploiting spatial confinement of the generated charge, the electrical field of the diamond bulk was mapped at different depths and compared to an X-ray diffraction topograph of the sample. Measurements utilizing this method provide a unique way of exploring spatial variations of charge transport properties in transparent wide-bandgap semiconductors.Comment: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Applied Physics Letters and may be found at https://doi.org/10.1063/1.509085

Preasymptotic multiscaling in the phase-ordering dynamics of the kinetic Ising model

The evolution of the structure factor is studied during the phase-ordering dynamics of the kinetic Ising model with conserved order parameter. A preasymptotic multiscaling regime is found as in the solution of the Cahn-Hilliard-Cook equation, revealing that the late stage of phase-ordering is always approached through a crossover from multiscaling to standard scaling, independently from the nature of the microscopic dynamics.Comment: 11 pages, 3 figures, to be published in Europhys. Let

Attosecond screening dynamics mediated by electron-localization

Transition metals with their densely confined and strongly coupled valence electrons are key constituents of many materials with unconventional properties, such as high-Tc superconductors, Mott insulators and transition-metal dichalcogenides. Strong electron interaction offers a fast and efficient lever to manipulate their properties with light, creating promising potential for next-generation electronics. However, the underlying dynamics is a fast and intricate interplay of polarization and screening effects, which is poorly understood. It is hidden below the femtosecond timescale of electronic thermalization, which follows the light-induced excitation. Here, we investigate the many-body electron dynamics in transition metals before thermalization sets in. We combine the sensitivity of intra-shell transitions to screening effects with attosecond time resolution to uncover the interplay of photo-absorption and screening. First-principles time-dependent calculations allow us to assign our experimental observations to ultrafast electronic localization on d-orbitals. The latter modifies the whole electronic structure as well as the collective dynamic response of the system on a timescale much faster than the light-field cycle. Our results demonstrate a possibility for steering the electronic properties of solids prior to electron thermalization, suggesting that the ultimate speed of electronic phase transitions is limited only by the duration of the controlling laser pulse. Furthermore, external control of the local electronic density serves as a fine tool for testing state-of-the art models of electron-electron interactions. We anticipate our study to facilitate further investigations of electronic phase transitions, laser-metal interactions and photo-absorption in correlated electron systems on its natural timescale