Miracle-dz/UniFAR-FTUs huggingface dataset:
Analysis of the discharge channel structure upon nanosecond electrical explosion of wires

The structure of the discharge channel during nanosecond wire explosions has been studied using laser probing. Wires of 25μm diameter and 12mm length were exploded in air and vacuum by 10kA current pulse having a 50A∕ns rate of rise. Upon electrical explosion of thin wires in the air, the development of shock waves was observed. The propagation of shock waves was analyzed, and it was possible to draw conclusions on the location of the flow of most of the current in the volume of the discharge channel. This permitted distinguishing between two scenarios (shunting and internal) of the interelectrode gap breakdown development. The scenario depends to a large extent on the properties of the exploding wire material. The same two scenarios are valid upon electrical explosion of wire in vacuum. Moreover, if secondary breakdown develops in the internal scenario, the value of the energy deposition in the wire material during explosion in vacuum may be comparable with that found during explosion in air.
On the stability and uniform persistence of a discrete model of Nicholson's blowflies

Abstract Consider the delay difference equation N n+1 − Nn = −δ N n + pN n−k e −aN n −k , n = 0, 1, 2, …, (1) which is a discrete analogue of the delay differential equation N (t) = −δN(t) + pN(t − τ)e −aN(t−τ) , t ≥ 0 (cf. [8]). We show that when p ≤ δ, the zero solution of (1) is uniformly asymptotically stable and every non-negative solution of(1) tends to zero as n → ∞, while for p > δ, (1) is uniformly persistent. Moreover, if in addition to p > δ we also have [(1 − δ) − k −1 − 1] ln( p /δ) ≤ 1, then every positive solution of (1) tends to the positive equilibrium N * = (1/ a ) ln( p /δ).
SAW*-ALGEBRAS ARE ESSENTIALLY NON-FACTORIZABLE

Abstract In this paper, we solve a question of Simon Wassermann, whether the Calkin algebra can be written as a C*-tensor product of two infinite dimensional C*-algebras. More generally, we show that there is no surjective *-homomorphism from a SAW*-algebra onto C*-tensor product of two infinite dimensional C*-algebras.
Production of Carbon Nanoparticles Using Pulsed Arc Discharge Triggered by Dielectric Breakdown in Water

This paper describes a simple production method for carbon nanoparticles by pulsed arc discharge in water, which is triggered by the electrical breakdown of water between graphite electrodes. High-resolution transmission electron microscopy (HRTEM) observation revealed that the main products obtained by the proposed method were onion-like nanoparticles; while carbon nanotubes were not formed. The carbon nanoonions uniformly dispersed in water forming micron-sized aggregates. The effects of the arc discharge mode (dc or pulse) on the nanoparticle formation mechanism are discussed.
Optical Reflectivity and Band Structure of ZnS 1 − x Se x Mixed Crystals

Optical reflectivity measurements on mixed crystals of the system ${\mathrm{ZnS}}_{1\ensuremath{-}x}{\mathrm{Se}}_{x} (0l~xl~1)$ were made at room temperature in the energy region of 2.5 to 9.5 eV. Indirect as well as direct optical transitions were observed in the ${\ensuremath{\epsilon}}_{2}$ spectra computed by a Kramers-Kronig analysis. Considering the complete series of mixed crystals, the very complex structure of the observed spectra can only be explained assuming separated energy bands for the different components of these mixed crystals.
Determination of non-compactly supported electromagnetic potentials in an unbounded closed waveguide

We study the inverse problem of determining a magnetic Schrodinger operator in an unbounded closed waveguide from boundary measurements. We consider this problem with a general closed waveguide in the sense that we only require our unbounded domain to be contained into an infinite cylinder. In this context we prove unique recovery of general bounded and non-compactly supported electromagnetic potentials modulo gauge invariance. By assuming that the electromagnetic potentials are known on the neighborhood of the boundary outside a compact set, we even prove the unique determination of the electromagnetic potential from measurements restricted to a bounded subset of the infinite boundary. Finally, in the case of a waveguide taking the form of an infinite cylindrical domain, we prove the recovery of general electromagnetic potentials from partial data corresponding to restriction of Neumann boundary measurements to slightly more than half of the boundary. We establish all these results by mean of suitable complex geometric optics solutions and Carleman estimates suitably designed for our problem stated in an unbounded domain and with bounded electromagnetic potentials.
Cyclotron oscillations of plasma in an inhomogeneous magnetic field

Chapter I considers cyclotron oscillations of an equilibrium plasma (the cyclotron heating problem). It is devoted mainly to the analysis of processes that lead to energy exchange between oscillations and a plasma in cyclotron resonance in an inhomogeneous magnetic field. According to present-day concepts, such an exchange is effected by excitation of modulated beams. The oscillations due to individual beams are analogous to the known Van Kampen waves. In the presence of a thermal spread of the plasma-particle velocity, the interference quenches these oscillations. As a result, the energy drawn by the plasma from the cyclotron wave takes on a thermal (random) form. An appendix (at the end of the article) traces the analogy with Cerenkov resonance in an inhomogeneous plasma and with surface absorption of the oscillations incident on an abrupt plasma boundary (anomalous skin effect). Chapter II summarizes earlier results on the analysis of the stability of a plasma not in thermal equilibrium situated in the inhomogeneous field of a magnetic trap. It was shown in the earlier papers that, depending on the conditions on the plasma boundaries, an increase in the inhomogeneity of the magnetic field can lead to either a lowering of the increment of the unstable natural oscillations (oscillation-reflecting boundaries), or to their total stabilization (absorbing boundaries). Two approaches to the investigation of stability are compared in the review, viz., analysis of the natural oscillations and an investigation of the evolution of the initial perturbations with time.
Periodic Inhibition of Living Pacemaker Neurons (ii): Influences of Driver Rates and Transients and of Nondriven Postsynaptic Rates

This paper discusses synaptic inhibition of one pacemaker neuron by another, using data from living synapses. Spike discharges were assimilated to point processes. Inhibitory rate scale and behavior form. (i) Forms (p:q locked and others) with similar prevalent spectral components assembled monotonically with p:q. Between different lockings, intermittent, messy and other intermittent forms staggered characteristically; hoppings were interspersed. (ii) Locked, intermittent and messy forms occupied about 1/3 each of the rate scale. Individually, the 1:1, 2:1 and 1:2 locked domains were the widest, and seemed continuous; individual intermittent and messy domains were very narrow. Step-like inhibitory transients induced abrupt postsynaptic changes opposing them, which over- or under-shot and slowly returned in either orderly or complicated (chaotic? ) ways to steady states. Input-output relations around inhibitory trains resembled those of first-order lead-lag systems distorted by asymmetric sensitivity to change and saturation. Postsynaptic natural discharges separated into "slow" less variable, and "fast" more variable categories with somewhat different inhibited behaviors. Formal modeling is introduced by summarizing comparable models, the data-assumption discrepancies, and reasonable conjectures as to eventual models.
Modular Group Representations in Combinatorial Quantization with Non-Semisimple Hopf Algebras

Let $\Sigma_{g,n}$ be a compact oriented surface of genus $g$ with $n$ open disks removed. The algebra $\mathcal{L}_{g,n}(H)$ was introduced by Alekseev-Grosse-Schomerus and Buffenoir-Roche and is a combinatorial quantization of the moduli space of flat connections on $\Sigma_{g,n}$. Here we focus on the two building blocks $\mathcal{L}_{0,1}(H)$ and $\mathcal{L}_{1,0}(H)$ under the assumption that the gauge Hopf algebra $H$ is finite-dimensional, factorizable and ribbon, but not necessarily semisimple. We construct a projective representation of $\mathrm{SL}_2(\mathbb{Z})$, the mapping class group of the torus, based on $\mathcal{L}_{1,0}(H)$ and we study it explicitly for $H = \overline{U}_q(\mathfrak{sl}(2))$. We also show that it is equivalent to the representation constructed by Lyubashenko and Majid.
Hodge structure on the cohomology of the moduli space of Higgs bundles

We study the moduli space of Higgs bundles on a compact Riemann surface. It was shown by Thaddeus and Hausel (in rank 2) and Markman (in general rank) that the rational cohomology ring of this space is generated by universal classes. In this paper, we use their results to compute the Hodge structure on the cohomology of this moduli space. We show that the natural Hodge structure on H^k is pure of weight k.
Transformation properties for Dyson’s rank function

At the 1987 Ramanujan Centenary meeting Dyson asked for a coherent group-theoretical structure for Ramanujan's mock theta functions analogous to Hecke's theory of modular forms. Many of Ramanujan's mock theta functions can be written in terms of $R(\zeta,q)$, where $R(z,q)$ is the two-variable generating function of Dyson's rank function and $\zeta$ is a root of unity. Building on earlier work of Watson, Zwegers, Gordon and McIntosh, and motivated by Dyson's question, Bringmann, Ono and Rhoades studied transformation properties of $R(\zeta,q)$. In this paper we strengthen and extend the results of Bringmann, Rhoades and Ono, and the later work of Ahlgren and Treneer. As an application we give a new proof of Dyson's rank conjecture and show that Ramanujan's Dyson rank identity modulo $5$ from the Lost Notebook has an analogue for all primes greater than $3$. The proof of this analogue was inspired by recent work of Jennings-Shaffer on overpartition rank differences mod $7$.
Low-energy electrons in Saturn's inner magnetosphere and their role in interchange injections

[1] Since the days of Pioneer 11 and the Voyager missions, electrons have shown an unexplained peak in the data at approximately 7.5 Saturn radii (RS). To investigate this peak, we examine near-equatorial electron energy flux data (±10°) from the Cassini Plasma Spectrometer Electron Spectrometer from 1 July 2004 through 10 August 2007. When these data are plotted versus L shell, a peak between L = 7.5 and L = 8 appears in the electron data in the 12–100 eV range. We show that this peak is associated with interchange injections. The electrons are separated into trapped (70°–110°) pitch angles and field-aligned (0°–20° and 160°–180°) pitch angles. The field-aligned electrons show stronger fluxes than the trapped electrons in the 12–100 eV range during these injections. In SLS3 coordinates, the trapped electrons peak at longitudes between 45° and 240° at 7–8 RS with a smaller peak occurring between 310° and 360° SLS3 longitudes that penetrates to 6–5 RS. The field-aligned electrons, however, show no SLS3 dependence.
A nested dissection approach to modeling transport in nanodevices: Algorithms and applications

Modeling nanoscale devices quantum mechanically is a computationally challenging problem where new methods to solve the underlying equations are in a dire need. In this paper, we present an approach to calculate the charge density in nanoscale devices, within the context of the nonequilibrium Green's function approach. Our approach exploits recent advances in using an established graph partitioning approach. The developed method has the capability to handle open boundary conditions that are represented by full self‐energy matrices required for realistic modeling of nanoscale devices. Our method to calculate the electron density has a reduced complexity compared with the established recursive Green's function approach. As an example, we apply our algorithm to a quantum well superlattice and a carbon nanotube, which are represented by a continuum and tight binding Hamiltonian, respectively, and demonstrate significant speedup over the recursive method. Copyright © 2013 John Wiley & Sons, Ltd.
The use of distance sampling and mark‐resight to estimate the local density of wildlife populations

We used distance sampling (line transects) and mark‐resight to estimate habitat and local area (area size, range: 3.9–44.5 ha) population density of ungulates. The distance sampling study was performed on fallow deer (Dama dama), roe deer (Capreolus capreolus) and wild boar (Sus scrofa) in a mediterranean forest. The mark‐resight study was performed on a roe deer population in a hilly area of the Apennines. The first study allowed us to estimate the animal density into four different habitats (deciduous oak wood, evergreen oak wood, maquis and open areas with domestic‐pine woods). The between habitat differences of population density are large for the three species: fallow deer are more abundant in the open areas (22.22 heads/km2, c.i. 12.42–39.74), roe deer in the deciduous oak wood (14.50 heads/km2, c.i. 7.01–30.10) and wild boar in both the open areas (11.29 heads/km2, c.i. 4.86–26.20) and evergreen oak wood (10.42 heads/km2, c.i. 6.78–16.02). The roe deer population in the Apennines is characterized by large between‐zone variations of population density (range: 1997: 13.25–131.31, 1998: 29.06–78.01, 1999: 10.67–88.58). Moreover, trends of local zones may be quite different with respect to the average trend of a wider study area, suggesting a well‐defined short‐scale spatial structure for this population. We conclude that both survey methods may be very useful in population assessment, but they need intense field effort and careful statistical design. Care needs to be taken to satisfy the assumptions of the statistical models. Copyright © 2002 John Wiley & Sons, Ltd.
General characteristics of hot plasma and energetic particles in the Saturnian magnetosphere: Results from the Voyager spacecraft

The low energy charged particle (LECP) experiment on the Voyager 1 and 2 spacecraft made measurements of the intensity, energy spectra, and spatial distributions of ions (30 keV ≲ E ≲ 150 MeV) and electrons (22 keV ≲ E ≲ 20 MeV) during encounters with the Saturnian magnetosphere in November 1980 and August 1981, respectively. Detailed analysis of the data has revealed the following: (1) Energetic ions are present in the interplanetary medium both upstream (to ∼200 Rs) and off the dawn bow shock (to ∼400 Rs) of the magnetosphere, with maximum energies ∼100 keV. (2) Low-energy (≳22 keV) electrons are generally depleted inward of L ∼ 10 Rs, while low-energy (≳30 keV) ions are greatly enhanced in the same region. (3) The composition of low-energy ions is most likely dominated by protons in the outer magnetosphere but is consistent with oxygen in the inner (L ≲ 9) magnetosphere. (4) The ion spectrum is described well by the κ distribution with characteristic temperatures kTH ranging from ∼15 to ∼55 keV; the hot plasma region is generally confined between the L shells of Tethys and Rhea but exhibits substantial variability. (5) The electron energy spectrum at L ≲ 10 develops a secondary peak at E ≳ 200 keV that shifts to higher (∼1 MeV) energies inside the orbits of Enceladus and Mimas, indicative of electron resonance interactions with the planetary satellites. (6) There is a noon-dawn asymmetry in ion and electron intensities with peak fluxes near the Rhea-Dione L shells at local morning; this is the region in local time where Saturn kilometric radiation is modulated by the presence of Dione. (7) The ion energy density (≳30 keV) represents a significant fraction of the field energy density in the outer magnetosphere of the planet (L ≳ 13 Rs), with values of β ranging from 0.1 up to ∼4, when projected to the equator. (8) Comparison of electron and ion intensities measured by Voyagers 1 and 2 in the inner (L ≲ 6) magnetosphere at common points in B, L space shows that the radiation belts are substantially stable over periods of ∼9 months; both ion and electron intensities compared well with Pioneer 11 observations in 1979. It is evident from the results that the inner satellites of Saturn play a dominant role in the determination of intensity and spectral features of energetic particles at L ≲ 10. These aspects of the data are discussed in the context of proposed physical mechanisms expected to be operating within the magnetosphere of Saturn.
ESTIMATION AND COMPUTATION WITH MATRICES OVER FINITE FIELDS

The matrix group recognition project is a worldwide effort to produce efficient algorithms for working with arbitrary matrix groups over finite fields (see [3, 6]). Such groups are potentially very large in comparison to the input length, and dealing with them using deterministic methods is impractical. When a generating set for a group is input into a computer, a constructive recognition algorithm names the group and finds an efficient mapping between the input generators and a set of ‘standard generators’. This allows various important questions to be answered quickly. Constructive recognition is a major natural goal in computational group theory. To recognise an arbitrary group, there are two tasks to perform. The first is to decompose the group into smaller components if possible, and work recursively. The second is to deal with irreducible cases, which in this case are the finite simple groups. This paper addresses constructive recognition of matrix groups from ‘both ends’: on the one hand, we give an improved analysis of the Norton irreducibility test, part of the MEAT-AXE algorithm (see [1]), by providing a lower bound of the form a1 − a2q for the proportion of primary cyclic matrices in M(c, qb), where a1, a2 are constants depending only on q, b. To achieve this, we generalise the Kung–Stong cycle index (see [2, 7]) to compute a generating function for the proportion. On the other hand, we solve a particular family of base cases for the constructive recognition recursion, by extending the work of Magaard et al. [4] to provide a Las Vegas algorithm for constructive recognition of classical groups in irreducible representations of moderate degree. When the degree of the representation is large, existing black-box methods are effective. On the other hand, when the degree is equal to the natural degree, there are specific methods to address the problem.
Analogues of Auslander–Yorke theorems for multi-sensitivity

We study multi-sensitivity and thick sensitivity for continuous surjective selfmaps on compact metric spaces. Our main result states that a minimal system is either multi-sensitive or an almost one-to-one extension of its maximal equicontinuous factor. This is an analog of the Auslander–Yorke dichotomy theorem: a minimal system is either sensitive or equicontinuous. Furthermore, we introduce the concept of a syndetically equicontinuous point, and we prove that a transitive system is either thickly sensitive or contains syndetically equicontinuous points, which is a refinement of another well-known result of Akin, Auslander and Berg.
Spectral dimension and diffusion in multiscale spacetimes

Starting from a classical-mechanics stochastic model encoded in a Langevin equation, we derive the natural diffusion equation associated with three classes of multiscale spacetimes (with weighted, ordinary, and "q-Poincar\'e" symmetries). As a consistency check, the same result is obtained by inspecting the propagation of a quantum-mechanical particle in a disordered environment. The solution of the diffusion equation displays a time-dependent diffusion coefficient and represents a probabilistic process, classified according to the statistics of the noise in the Langevin equation. We thus illustrate, also with pictorial aids, how spacetime geometries can be more completely catalogued not only through their Hausdorff and spectral dimension, but also by a stochastic process. The spectral dimension of multifractional spacetimes is then computed and compared with what was found in previous studies, where a diffusion equation with some open issues was assumed rather than derived. These issues are here discussed and solved, and they point towards the model with q-Poincar\'e symmetries.
Invertible Carnot Groups

Abstract We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the J2-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity. A more general characterization of inversion invariant bi-Lipschitz homogeneity for certain non-fractal metric spaces is also provided.
Vacuum wavelength calibration of frequency-stabilized He-Ne lasers used in commercial laser interferometers

We report on the calibration results of the wavelength of the lasers used in commercial laser interferometers, including the vacuum wavelength deviation from its nominal value, the vacuum wavelength stability, the repeatability of stabilized wavelength, and the secular change of these properties, by analyzing the calibration data accumulated for more than two decades. We present an experimental method of calibrating the frequency of laser interferometers. We also propose a proper time interval and an appropriate uncertainty expression for the vacuum wavelength calibration of the laser interferometers.
Numerical Bifurcation and Spectral Stability of Wavetrains in Bidirectional Whitham Models

We consider several different bidirectional Whitham equations that have recently appeared in the literature. Each of these models combines the full two‐way dispersion relation from the incompressible Euler equations with a canonical shallow water nonlinearity, providing nonlocal model equations that may be expected to exhibit some of the interesting high‐frequency phenomena present in the Euler equations that standard “long‐wave” theories fail to capture. Of particular interest here is the existence and stability of periodic traveling wave solutions in such models. Using numerical bifurcation techniques, we construct global bifurcation diagrams for each system and compare the global structure of branches, together with the possibility of bifurcation branches terminating in a “highest” singular (peaked/cusped) wave. We also numerically approximate the stability spectrum along these bifurcation branches and compare the stability predictions of these models. Our results confirm a number of analytical results concerning the stability of asymptotically small waves in these models and provide new insights into the existence and stability of large amplitude waves.
Graph Relations and Constrained Homomorphism Partial Orders

We consider constrained variants of graph homomorphisms such as embeddings, monomorphisms, full homomorphisms, surjective homomorpshims, and locally constrained homomorphisms. We also introduce a new variation on this theme which derives from relations between graphs and is related to multihomomorphisms. This gives a generalization of surjective homomorphisms and naturally leads to notions of R-retractions, R-cores, and R-cocores of graphs. Both R-cores and R-cocores of graphs are unique up to isomorphism and can be computed in polynomial time. The theory of the graph homomorphism order is well developed, and from it we consider analogous notions defined for orders induced by constrained homomorphisms. We identify corresponding cores, prove or disprove universality, characterize gaps and dualities. We give a new and significantly easier proof of the universality of the homomorphism order by showing that even the class of oriented cycles is universal. We provide a systematic approach to simplify the proofs of several earlier results in this area. We explore in greater detail locally injective homomorphisms on connected graphs, characterize gaps and show universality. We also prove that for every $d\geq 3$ the homomorphism order on the class of line graphs of graphs with maximum degree $d$ is universal.