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We present a general framework for producing families of harmonic maps from the unit ball into the Euclidean sphere starting from a fixed harmonic map. In particular, our analysis provides a theoretical background for a generalized radial projection which was recently introduced by Nakauchi. Our approach is based on work of Toth who established a machinery that generates eigenmaps between spheres from a given eigenmap. Finally, we point out how these families of harmonic maps can be used to construct solutions to associated variational problems such as intrinsic biharmonic and triharmonic maps, $p$-harmonic maps as well as extrinsic polyharmonic maps.
We demonstrate a tandem lens optical setup, comprising two diffractive optics, that focuses a high-power ultrafast laser with a shaped on-axis intensity profile, producing a meter-long Bessel focus. The intended use of the optical setup is to produce a laser-ionized plasma source for plasma wakefield acceleration. By controlling the on-axis intensity, the density profile of the plasma ramps at the entrance and exit of the plasma can be tailored to optimize matching of the electron beam into the plasma. In addition to demonstrating the optical system, we describe the algorithm used to calculate the lens phases and present detailed calculations of the lenses' expected performance.
In this work, the straight flux rope in the model of giant flares on magnetars (Meng et al. 2014) was replaced with a curved one and the equilibrium behavior of the flux rope was investigated. Two footpoints of the flux rope are anchored to the spherical surface of magnetar. The forces acting on the flux rope include magnetic tension, magnetic pressure, curvature force, gravity. The equilibrium in the flux rope, so as in the global configuration, is achieved as these forces offset each other. Changes in the background environment drive the configuration to evolve through a set of equilibria in a quasi-static fashion until the critical point is reached and the loss of equilibrium in the configuration occurs, invoking a giant flare. We establish a criterion to identify magnetars capable of producing giant flares. Among the four forces, the curvature force as well as the magnetic compression tend to expel the flue rope outward. In a given magnetic configuration, the curvature force and magnetic compression are proportional to the square of the current intensity of the flux rope, which is determined by the frozen-flux condition and background magnetic field strength. We find that only
We present a scheme for producing intense $μ^+$ and $μ^-$ lepton beams that could be utilized in a future muon-muon or muon-ion collider, as well as for other applications. The scheme makes use of BACKscattered GAMMas On Nucleons (BACKGAMMON). Current accelerator infrastructures could be utilized to produce the muon beams, such as the Electron-Ion Collider (EIC) at Brookhaven National Laboratory in the United States. We discuss the implementation of BACKGAMMON at the EIC.
The article focuses on word (or string) attractors, which are sets of positions related to the text compression efficiency of the underlying word. The article presents two combinatorial algorithms based on Suffix automata or Directed Acyclic Word Graphs. The first algorithm decides in linear time whether a set of positions on the word is an attractor of the word. The second algorithm generates an attractor for a given word in a greedy manner. Although this problem is NP-hard, the algorithm is efficient and produces very small attractors for several well-known families of words.
Landforms such as sand dunes act as roughness elements to Atmospheric Boundary Layer (ABL) flows, triggering the development of new scales of turbulent motions. These turbulent motions, in turn, energize and kick-up sand particles, influencing sediment transport and ultimately the formation and migration of dunes -- with knock on consequences for dust emission. While feedbacks between flow and form have been studied at the scale of dunes, research has not examined how the development of an Internal Boundary Layer (IBL) over the entire dune field influences sediment-transporting turbulence. Here, we deploy large-eddy simulation of an ABL encountering a natural roughness transition: the sand dunes at White Sands National Park, New Mexico. We analyze turbulence producing motions and how they change as the IBL grows over the dune field. Frequency spectrum and Reynolds shear stress profiles show that IBL thickness determines the largest scales of turbulence. More, the developing IBL enhances the frequency, magnitude and duration of sweep and ejection events -- turbulence producing motions whose peaks systematically migrate away from the wall as the IBL thickens. Because sweep and ejecti
We develop the foundations of a general framework for producing optimal upper and lower bounds on the sum $\sum_p a_p$ over primes $p$, where $(a_n)_{x/2<n\le x}$ is an arbitrary non-negative sequence satisfying Type I and Type II estimates. Our lower bounds on $\sum_p a_p$ depend on a new sieve method, which is non-iterative and uses all of the Type I and Type II information at once. We also give a complementary general procedure for constructing sequences $(a_n)$ satisfying the Type I and Type II estimates, which in many cases proves that our lower bounds on $\sum_p a_p$ are best possible. A key role in both the sieve method and the construction method is played by the geometry of special subsets of $\mathbb{R}^k$. This allows us to determine precisely the ranges of Type I and Type II estimates for which an asymptotic for $\sum_p a_p$ is guaranteed, that a substantial Type II range is always necessary to guarantee a non-trivial lower bound for $\sum_p a_p$, and to determine the optimal bounds in some naturally occurring families of parameters from the literature. We also demonstrate that the optimal upper and lower bounds for $\sum_p a_p$ exhibit many discontinuities with resp
Neural networks are typically black-boxes that remain opaque with regards to their decision mechanisms. Several works in the literature have proposed post-hoc explanation methods to alleviate this issue. This paper proposes LMAC-TD, a post-hoc explanation method that trains a decoder to produce explanations directly in the time domain. This methodology builds upon the foundation of L-MAC, Listenable Maps for Audio Classifiers, a method that produces faithful and listenable explanations. We incorporate SepFormer, a popular transformer-based time-domain source separation architecture. We show through a user study that LMAC-TD significantly improves the audio quality of the produced explanations while not sacrificing from faithfulness.
For a prime $p$ congruent to three modulo four, we prove that there exists a smooth curve of genus five in characteristic $p$ that is supersingular. We produce this curve as an unramified double cover of a curve of genus three. We conjecture that the setting of unramified double covers of curves of genus three also produces supersingular curves of genus five when $p$ is congruent to one modulo four, and we computationally verify this conjecture for primes less than $100$. These results can be viewed as a generalization of work of Ekedahl and of Harashita, Kudo, and Senda.
Software bills of materials (SBOM) promise to become the backbone of software supply chain hardening. We deep-dive into 6 tools and the accuracy of the SBOMs they produce for complex open-source Java projects. Our novel insights reveal some hard challenges for the accurate production and usage of SBOMs.
The mechanism of multinucleon transfer (MNT) reactions for producing neutron-rich heavy nuclei around N = 126 is investigated within two different theoretical frameworks: dinuclear system (DNS) model and isospin-dependent quantum molecular dynamics (IQMD) model. The effects of mass asymmetry relaxation, N=Z equilibration, and shell closures on production cross sections of neutron-rich heavy nuclei are investigated. For the first time, the advantages for producing neutron-rich heavy nuclei around N = 126 is found in MNT reactions based on 238U target. We propose the reactions with 238U target for producing unknown neutron-rich heavy nuclei around N = 126 in the future.
In this paper, we introduce a certain method to construct polynomials producing many absolute pseudoprimes. By this method, we give new polynomials producing absolute pseudoprimes with any fixed number of prime factors which can be viewed as a generalization of Chernick's result. By the similar method, we give another type of polynomials producing many absolute pseudoprimes. As concrete examples, we tabulate the counts of such numbers of our forms.
We present a statistical result on the properties of solar source regions that have produced 57 fastest front-side coronal mass ejections (CMEs) (speed 1500 km/s) occurred from 1996 June to 2007 January. The properties of these fast-CME-producing regions, 35 in total, are compared with those of all 1143 active regions (ARs) in the period studied. An automated method, based on SOHO/MDI magnetic synoptic charts, is used to select and characterize the ARs. For each AR, a set of parameters are derived including the areas (positive, negative and total, denoted by A_P, A_N and A_T respectively), the magnetic fluxes (positive, negative and total, F_P, F_N and F_T respectively), the average magnetic field strength (B_avg), quasi-elongation (e) characterizing the overall shape of the AR, the number and length of polarity inversion lines (PILs, or neutral lines, N_PIL and L_PIL respectively), and the average and maximum of magnetic gradient on the PILs (GOP_avg and GOP_max respectively). Our statistical analysis shows a general trend between the scales of an AR and the likelihood of producing a fast CME, i.e., the larger the geometric size (A_T), the larger the magnetic flux (F_T), the stron
This is the second paper in a series where we examine the physics of pair producing gaps in low-luminosity accreting supermassive black hole systems. In this paper, we carry out time-dependent self-consistent fully general relativistic 1D PIC simulations of the gap, including full inverse Compton scattering and photon tracking. Similar to the previous paper, we find a highly time-dependent solution where a macroscopic vacuum gap can open quasi-periodically, producing bursts of $e^\pm$ pairs and high energy radiation. We present the light curve, particle and photon spectra from this process. Using an empirical scaling relation, we rescale the parameters to the inferred values at the base of the jet in M87, and find that the observed TeV flares could potentially be explained by this model under certain parameter assumptions.
The multinucleon transfer process is one promising approach for producing neutron-rich heavy nuclei. The favorable projectile-target combinations play a key role in experiments. As one important approach to investigate the multinucleon transfer process, one new version of the dinuclear system (DNS) model is developed. The improved version of the DNS model is shown in detail. Based on deformation degree of freedom in the improved DNS model, one way of calculating excitation energies of primary fragments is proposed. And the remarkable improvements for describing experimental data of producing trans-uranium nuclei is noticed. To produce trans-uranium nuclei, the collisions of 48Ca, 136Xe, and 238U projectiles with the 238U target are investigated within the improved DNS model. Based on the potential energy surface, the influence of projectiles on the probabilities of transferring neutrons and protons from the projectiles to the target are studied. One behavior is found that the transfer probabilities strongly depend on the projectiles in the neutron stripping process, while relatively weak projectile dependence is noticed in the proton transferring process. The 136Xe and 238U project
We propose a novel method for producing very-neutron-rich hypernuclei and corresponding resonance states by employing charge-exchange reactions via pp($^{12}$C, $^{12}$N $K^+$)n$Λ$ with single-charge-exchange and ppp($^{9}$Be, $^{9}$C $K^+$)nn$Λ$ with double-charge-exchange, both of which produce $ΛK^+$ in a target nucleus. The feasibility of producing very-neutron-rich hypernuclei using the proposed method was analysed by applying an ultra-relativistic quantum molecular dynamics model to a $^6$Li+$^{12}$C reaction at 2 $A$ GeV. The yields of very-neutron-rich hypernuclei, signal-to-background ratios, and background contributions were investigated. The proposed method is a powerful tool for studying very-neutron-rich hypernuclei and resonance states with a hyperon for experiments employing the Super-FRS facility at FAIR and HFRS facility at HIAF.
treePL uses a penalised likelihood approach to produce a dated phylogeny in a maximum likelihood framework. Since its publication in 2012, few resources have been developed to explain how to use it properly. In this guide, I provide a step-by-step protocol for producing a dated phylogeny using treePL, based on my experience building a large dated phylogeny with it and conducting additional tests on a smaller phylogeny. I also provide the necessary data to reproduce one of the example phylogenies presented. I compare these treePL phylogenies to BEAST2-built counterparts. Even though I cannot explain precisely how treePL works, the evidence discussed in this guide suggest that the empirical protocol presented is reliable.
We survey the known group properties that a sequence of finite groups or group actions needs to satisfy to admit subsets of bounded cardinality producing expander Cayley or Schreier graphs. We prove that an infinite amenable group and solvable groups of bounded derived length do not produce expander Schreier graphs, generalizing with easier proofs results of Lubotzky and Weiss for Cayley graphs. In particular, the poor expansion properties of a group action cannot in general be detected by looking at the abelian sections or at the representations above the stabilizer of a point.
By using an econometric approach this paper looks at the evolution of the world wine industry in the period 1961-2005. A particular stylized fact is the appearance of nontraditional producing and exporting countries of wine from the beginning of the nineties. We show that the success of these new producing and exporting countries can be explained by the importance of the demand from non-producing countries with little or no tradition of wine consumption, relative to the world demand. This stylized fact is consistent with a testable implication of the switching cost literature and to the best of our knowledge this is the first time that this implication is tested.
Sufficiently strong electric fields can produce charged-particle pairs via the Schwinger effect. We argue that steep matter-density gradients, as can arise in neutron star interiors, would analogously produce neutrino-antineutrino pairs. We then discuss observational signatures of these gradient-produced (anti)neutrinos and how they could provide new probes of neutron-star structure and baryon-dense QCD.