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In this paper we study the existence of sections of universal bundles on rational homogeneous varieties -- called nestings -- classifying them completely in the case in which the Lie algebra of the automorphism group of the variety is simple of classical type. In particular we show that, under this hypothesis, nestings do not exist unless there exists a proper algebraic subgroup of the automorphism group acting transitively on the base variety., Comment: Major revision of the exposition. To appear in Tranformation Groups

We link small modifications of projective varieties with a ${\mathbb C}^*$-action to their GIT quotients. Namely, using flips with centers in closures of Bia{\l}ynicki-Birula cells, we produce a system of birational equivariant modifications of the original variety, which includes those on which a quotient map extends from a set of semistable points to a regular morphism. The structure of the modifications is completely described for the blowup along the sink and the source of smooth varieties with Picard number one with a ${\mathbb C}^*$-action which has no finite isotropy for any point. Examples can be constructed upon homogeneous varieties with a ${\mathbb C}^*$-action associated to short grading of their Lie algebras., Comment: 29 pages, 7 figures

We prove LeBrun--Salamon conjecture in the following situation: if $X$ is a contact Fano manifold of dimension $2n+1$ whose group of automorphisms is reductive of rank $\geq \max(2,(n-3)/2)$ then $X$ is the adjoint variety of a simple group. The rank assumption is fulfilled not only by the three series of classical linear groups but also by almost all the exceptional ones., Comment: Minor changes committed

As a natural extension of the theory of uniform vector bundles on Fano manifolds, we consider uniform principal bundles, and study them by means of the associated flag bundles, as their natural projective geometric realizations. In this paper, we develop the necessary background and prove some theorems that are flag bundle counterparts of some of the central results in the theory of uniform vector bundles.

In-space plasma propulsion is today a necessity for the economic competitiveness of commercial satellites. In plasma thrusters the impulse is imparted by a mesothermal plasma jet where ions drift a supersonic velocities. Compact multi-electrode systems for ion acceleration are studied by a combination of analytical calculations and computer simulations. The results show exahust speeds of 140 km/s can be reached with specific impulses higher than unsual plasma thrusters. Additionally, the ion velocity distribution functions of the plasma jet exhasut obtained with retarded field energy analyzers that can be used to cross validate the results of numerical simulations.

The dynamic structure factor and other dynamic characteristics of strongly coupled one-component plasmas have been studied [Yu. V. Arkhipov et al., Phys. Rev. Lett. 119, 045001 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.045001] using the self-consistent version of the method of moments. Within any version of the latter, the system dielectric function satisfies all involved sum rules and other exact relations automatically, and the advantage of this version is that, in addition, the dynamic characteristics (the dynamic structure factor, the dispersion, and decay parameters of the collective modes) are all expressed in terms of the static ones (the static structure factor) without any adjustment to the simulation data. The approach outlined in the aforementioned Letter is justified in detail and applied mainly to the classical Coulomb systems achieving satisfactory agreement with new numerical simulation data. It is shown how the realm of applicability of the method can be extended to partly degenerate and multicomponent systems, even to simple liquids. Some additional theoretical results are presented in the Supplemental Material.

We introduce a simple thrust stand for the direct measurement of the millinewton impulses or thrusts delivered by small thrusters intended for in-space electric propulsion. The thruster under test, with a weight below 1.5 kg, is disposed on a horizontal platform and its impulse is measured as an overweight by using a strain gauge cell physically protected from the ambient plasma and vacuum conditions. This system provides ten thrust readings per second with noise peak to peak amplitudes of 0.10–0.18 mN. The calibration procedures to verify its dynamic response to time dependent thrusts in the range of 0–15 mN using control weights as well as its minimum thrust sensitivity δTs = 0.3 mN are discussed. Additionally, its simple conception permits a plain data reduction and analysis of steady state and low frequency thrust transients. This thrust stand was employed under low pressure and plasma ambient conditions to measure the steady impulses delivered by the Alternative Low Power Hybrid Ion Engine (ALPHIE) of 0.4–4.0 mN with absolute errors ΔT = ±0.3 mN. Finally, the experimental results show that a control electric voltage governs the ALPHIE thruster throttle.

In this paper we consider the 15‐dimensional rational homogeneous variety of Picard number one F4(4), and provide a characterization of it in terms of its variety of minimal rational tangents.

In the framework of the problem of characterizing complete flag manifolds by their contractions, the complete flags of type $F_4$ and $G_2$ satisfy the property that any possible tower of Bott-Samelson varieties dominating them birationally deforms in a nontrivial moduli. In this paper we illustrate the fact that, at least in some cases, these deformations can be explained in terms of automorphisms of Schubert varieties, providing variations of certain isotropic structures on them. As a corollary, we provide a unified and completely algebraic proof of the characterization of complete flag manifolds in terms of their contractions., New version with additional results

[EN] Several sum rules and other exact relations are employed to determine both the static and the dynamic properties of strongly coupled, partially and completely degenerate one-component plasmas. Emphasis is placed on the electron gas, both at zero and finite temperatures. The procedure is based on the self-consistent method of moments, recently developed in Phys. Rev. Lett., 2017, 119, 045001, that provides a neat expression for the loss function valid at strong couplings. An input value of the method in its classical version is the static structure factor, whose accuracy is shown to insignificantly affect the resulting numerical data. Starting from the Cauchy-Bunyakovsky-Schwarz inequality, a criterion is proposed to verify the quality of various approaches to the evaluation of the static characteristics of one-component, strongly coupled plasmas., This research was supported by Grants PTsF‐BR05236730, AP05132333 and AP05132677 (Ministry of Education and Science, Kazakhstan), No. BO1366-10 (Deutsche Forschungsgemeinschaft, Germany), and Grant No. ESP2013-41078R (Ministerio de Economía y Competitividad, Spain).

A pseudoeffective divisor is said to have a weak Zariski decomposition if it can be, up to a birational transformation, numerically written as the sum of a nef and an effective divisor. In this paper we consider the problem of the existence of a weak Zariski decomposition for each pseudoeffective divisor on a variety $$X= \mathbb {P}(\fancyscript{E})$$ , where $$\fancyscript{E}$$ is a vector bundle on a smooth complex projective variety $$Z$$ of Picard number one. We prove the existence of such a decomposition in a number of meaningful situations.

The main aim of this paper is the analysis of the feasibility of employing permanent magnets for the multipactor mitigation in a coaxial waveguide. First, the study of a coaxial line immersed in a uniform axial magnetic field shows that multipactor can be suppressed at any RF if the external magnetic field is strong enough. Both theoretical simulations and experimental tests validate this statement. Next, multipactor breakdown of a coaxial line immersed in a hollow cylindrical permanent magnet is analyzed. Numerical simulations show that multipactor can be suppressed in a certain RF range. The performed experimental test campaign demonstrates the capability of the magnet to avoid the multipactor electron multiplication process., This work was supported by the European Regional Development Fund-A Way of Making Europe. The review of this paper was arranged by Editor R. Carter.

We present here some conjectures on the diagonalizability of uniform principal bundles on rational homogeneous spaces, that are natural extensions of classical theorems on uniform vector bundles on the projective space, and study the validity of these conjectures in the case of classical groups., Comment: 20 pages, 8 tables

A Fano manifold $$X$$ with nef tangent bundle is of Flag-Type if it has the same kind of elementary contractions as a complete flag manifold. In this paper we present a method to associate a Dynkin diagram $$\mathcal {D}(X)$$ with any such $$X$$ , based on the numerical properties of its contractions. We then show that $$\mathcal {D}(X)$$ is the Dynkin diagram of a semisimple Lie group. As an application we prove that Campana–Peternell conjecture holds when $$X$$ is a Flag-Type manifold whose Dynkin diagram is $$A_n$$ , i.e. we show that $$X$$ is the variety of complete flags of linear subspaces in $$\mathbb {P}^n$$ .

Plasmas evolve under sharp conditions such as localized currents, charge separation and absorption or emission of particles. The plasma-wall interaction is one of these singularities. Numerical methods based upon differences usually fail under these abrupt boundary conditions leading to new spurious noise and singularities of numerical nature. Here, we extend the path-sum integral numerical method to account for abrupt boundary conditions in plasma drift-diffusion equations. The boundary-path-integral solution also shows the advantages of the smoothing affects of the diffusive short-time propagators for unbounded domains. The proposed scheme is free of artificial numerical smoothing functions to mask sharp behaviours. This stable, robust and grid-free algorithm is applied to test cases of plasma-wall interaction with an advancing scheme that simultaneously copes with disparate electron and ion time scales. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The electric charge transport through the two-grid systems of the Alternative Low Power Ion Engine is studied using a particle-in-cell (PIC) code. In this plasma thruster design, the ionizing electrons from the only cathode and the ions extracted from the ionization chamber flow in opposite directions through the open spaces of its grids. This configuration differs from classical gridded ion engines where only positive ions are accelerated. The electric charge transport is simulated, and the results are in agreement with previous experimental observations. The numerical simulations are performed for a single beamlet domain in a 2D axial symmetry, and only two aligned holes of the grid system are studied. The extracted ions move outwards from the ionization chamber reaching supersonic velocities of 43–51 km/s which are controlled by an acceleration voltage. The ionizing electrons from the only cathode are accelerated along the opposite direction and achieve energies in the range of 400–600 eV inside the ionization chamber. Additionally, the PIC simulations predict the development of an electric field close to the exit section of the thruster not observed previously because of the practical limitations of experiments. The imbalance of electric charge in the region where the electrons are injected from the only cathode creates a positive field that further accelerates the electric charges, preventing low energy ions from the plasma stream from returning to the plasma thruster.

Recently there has been renewed interest among differential geometers in the theory of Engel structures. We introduce holomorphic analogues of these structures, and pose the problem of classifying projective manifolds admitting them. Besides providing their basic properties and presenting two series of examples, we classify those satisfying certain positivity conditions.

We classify rank two Fano bundles over the Grassmannian of lines G ( 1 , 4 ) . In particular we show that the only non-split rank two Fano bundle over G ( 1 , 4 ) is, up to a twist, the universal quotient bundle Q . This completes the classification of rank two Fano bundles over Grassmannians of lines.

As an application of a recent characterization of complete flag manifolds as Fano manifolds having only ${\mathbb P}^1$-bundles as elementary contractions, we consider here the case of a Fano manifold $X$ of Picard number one supporting an unsplit family of rational curves whose subfamilies parametrizing curves through a fixed point are rational homogeneous, and we prove that $X$ is homogeneous. In order to do this, we first study minimal sections on flag bundles over the projective line, and discuss how Grothendieck's theorem on principal bundles allows us to describe a flag bundle upon some special sections., Comment: To appear in J. Math. Pures Appl

In this paper we study smooth complex projective varieties X containing a Grassmannian of lines $${{\mathbb G}(1, r)}$$ which appears as the zero locus of a section of a rank two nef vector bundle E. Among other things we prove that the bundle E cannot be ample.

A well known result of Miyaoka asserts that a complex projective manifold is uniruled if its cotangent bundle restricted to a general complete intersection curve is not nef. Using the Harder-Narasimhan filtration of the tangent bundle, it can moreover be shown that the choice of such a curve gives rise to a rationally connected foliation of the manifold. In this note we show that, conversely, a movable curve can be found so that the maximal rationally connected fibration of the manifold may be recovered as a term of the associated Harder-Narasimhan filtration of the tangent bundle., An error in the argumentation has been corrected

It is a well-known fact that families of minimal rational curves on rational homogeneous manifolds of Picard number one are uniform, in the sense that the tangent bundle to the manifold has the same splitting type on each curve of the family. In this note we prove that certain --stronger-- uniformity conditions on a family of minimal rational curves on a Fano manifold of Picard number one allow to prove that the manifold is homogeneous.

The main goal of this letter is the analysis of the multipactor effect within a coaxial waveguide structure when an external axial dc magnetic field is applied. We have designed and manufactured a coaxial waveguide sample that has been immersed within a long solenoid. Numerical and experimental results confirm a significant change in the RF breakdown behavior with regard to the case without the axial dc magnetic field, as well as the existence of single- and double-surface multipactor regimes. Good agreement between theory and experimental data has been found., Manuscript received January 23, 2012; accepted January 31, 2012. Date of publication March 16, 2012; date of current version April 20, 2012. This work was supported in part by the Spanish Government through R&D project TEC2010-21520-C04-01. The review of this letter was arranged by Editor E. A. Gutierrez-D.

The present paper provides a geometric characterization of complete flag varieties for semisimple algebraic groups. Namely, if $X$ is a Fano manifold whose all elementary contractions are $\mathbb P^1$-fibrations then $X$ is isomorphic to the complete flag manifold $G/B$ where $G$ is a semi-simple Lie algebraic group and $B$ is a Borel subgroup of $G$., Comment: 30 pages, minor issues corrected. To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze

We present a path-integral-like method to numerically solve drift-diffusion equations for plasma physics. The algorithm uses short-time propagators as approximate Green's functions that tend to smooth typical discontinuities arising in plasma dynamics as, for instance, the effects of plasma-wall interaction or localized particle flows. The usual numerical schemes based on differences may fail to represent these abrupt conditions by inducing numerical viscosities and instabilities. However, the robust mesli-free computational integral method has been proved to be unconditionally stable in the simple case of no imposed restrictions by boundary conditions. The extension of the method to deal with boundary value problems is analysed. The advancing scheme is also useful to deal with the merging of natural discontinuities in the system as those induced by the effects of electromagnetic fields generated by charge separation as well as for the existence of two differentiated plasma regimes. In any case, the kinetic equation may have drift and/or diffusion coefficients that are likewise discontinuous. The method works almost being numerically insensitive to these discontinuities, leading to feasible physically meaningful solutions. The scheme works as an effective integral kinetic operator even for Fokker-Planck equations connecting two different dynamical statistics, like Maxwell-Bolt.zmann and Fermi- Dirac ones. It is robust to describe spatially heterogeneous plasmas.

This paper presents some mathematical models for distribution of goods in logistic networks based on spectral analysis of complex networks. Given a steady distribution of a finished product, some numerical algorithms are presented for computing the weights in a multiplex logistic network that reach the equilibrium dynamics with high convergence rate. As an application, the logistic networks of Germany and Spain are analyzed in terms of their convergence rates. We are living in a global-scale world. Globalization is the process of international integration of products, ideas, culture, and science that has changed our way of understanding the world. Advances in communication and transportation that took place along the last Century allowed shortening the distances and making that our society moved from the local-scale to a global scale, generating new interdependences of economic, political, social, and cultural activities along the world. This process also has affected the business and commerce processes and the way that traditional trade is performed, changing from buying and selling to our closest neighbors to exchanging products with costumers in any country in the world. This change in the commerce's scales forces a new way of distributing the goods that has shifted from the direct supplier to costumer perspective to a new distributed point of view. Supply chain management (SCM),11 which is also known as Logistics Network Analysis, is a part of the Operational Research that has been extensively studied in recent years to analyze the newly distributed perspective of commerce arises from the Globalization. In this new approach, the classic point-to-point distribution that directly connects the supplier (the factory) with the final costumer is replaced by the use of logistic networks and distributed global-scale transportation. This paper presents some mathematical models for distribution of several products simultaneously by using multiplex networks analysis, and some effective algorithms are included in order to spot the optimal logistic network, in terms of distribution rate.

In this paper we classify rank two Fano bundles $\cE$ on Fano manifolds satisfying $H^2(X,\Z)\cong H^4(X,\Z)\cong\Z$. The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization ${\mathbb{P}}(\cE)$, that allows us to obtain the cohomological invariants of $X$ and $\cE$. As a by-product we discuss Fano bundles associated to congruences of lines, showing that their varieties of minimal rational tangents may have several linear components.

In this work we deal with vector bundles of rank two on a Fano manifold $X$ with $b_2=b_4=1$. We study the nef and pseudoeffective cones of the corresponding projectivizations and how these cones are related to the decomposability of the vector bundle. As consequences, we obtain the complete list of $\mathbb{P}^1$-bundles over $X$ that have a second $\mathbb{P}^1$-bundle structure, classify all the uniform rank two vector bundles on this class of Fano manifolds and show the stability of indecomposable Fano bundles (with one exception on $\mathbb{P}^2$)., Updated version with an issue corrected

The thresholds for the electron multiplication in both multipactor and the so-called collisional multipactor microwave discharges are calculated by means of an individual particle model. The simulations are restricted to low and intermediate gas pressures, where the collisional mean-free path of electrons is of the same order or larger than the characteristic dimension of the system. Thus, the charge multiplication is caused by both the electron impact ionization of the neutral gas and the secondary electron emission by electron collisions at the surfaces. The charge avalanche is simulated by the numerical integration of the trajectories of electrons up to the characteristic time for the space-charge buildup. The electron dynamics is described by the stochastic Langevin equations where the collisional scatter of electrons is incorporated by means of a random force, while the microwave electric field and the friction are deterministic forces. The physical properties of materials at the walls are considered by means of realistic models deduced from experimental data fitting, while the constant collision frequency model is used for elastic and inelastic electron collisions with neutral atoms. Previous results for low pressure electron multipactor are recovered, and for pressures corresponding to collisional multipactor the predictions of this simple model are in agreement with both the experimental results and particle in cell and Monte Carlo simulations. Finally, physical conditions under which the charge multiplication develops and the limitations for higher pressures of the proposed model are also discussed.

This is the author’s version of a work that was accepted for publication in Simulation Modelling Practice and Theory. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Simulation Modelling Practice and Theory, 16, 9, (2008) http://dx.doi.org/10.1016/j.simpat.2008.08.002, In this paper we present two software tools for the simulation of electron multiplication processes in radio frequency (RF) waveguides. The electric discharges are caused by the multiplication of a small initial number of electrons. These are accelerated by the RF field and produce new electrons either by collisions with the walls of the waveguide (ripping new electrons from them), or by ionization of the neutral atoms of a gas inside the device. MEST allows simulating the Multipactor effect, a discharge produced in vacuum and generated by the collision of the electrons with the walls. CEST simulates the discharge when in addition a neutral gas is present in the waveguide, at pressures lower than ground levels (often denominated Corona discharge). The main characteristic of both tools is that they implement individual-based, microscopic models, where every electron is individually represented and tracked. In the case of MEST, the simulation is discrete-event, as the trajectory of each electron can be computed analytically. In CEST we use a hybrid simulation approach. The trajectory of each electron is governed by the Langevin stochastic differential equations that take into account a deterministic RF electric force and the random interaction with the neutral atom background. In addition, wall and ionizing collisions are modelled as discrete events. The tools allow performing batches of simulations with different wall coating materials and gases, and have produced results in good agreement with experimental and theoretical data. The different output forms generated at run-time have proven to be very useful in order to analyze the different discharge processes. The tools are valuable for the selection of the most promising coating materials for the construction of the waveguide, as well as for the identification of safe operating parameters., Work sponsored by the ESA, TRP activity program 17025/03/NL/EC: Surface Treatment and Coating.

Going one step further in Zak's classification of Scorza varieties with secant defect equal to one, we characterize the Veronese embedding of $\P^n$ given by the complete linear system of quadrics and its smooth projections from a point as the only smooth irreducible complex and non-degenerate projective subvarieties of $\P^N$ that can be projected isomorphically into $\P^{2n}$ when $N\geq\binom{n+2}{2}-2$., Comment: To appear in Bulletin of the London Mathematical Society

This paper is concerned with a sufficient criterion to guarantee that a given foliation on a normal variety has algebraic and rationally connected leaves. Following ideas from a preprint of Bogomolov-McQuillan and using recent works of Langer and Graber-Harris-Starr, we give a clean, short and simple proof of previous results. Apart from a new vanishing theorem for vector bundles in positive characteristic, our proof employs only standard techniques of Mori theory and does not make any reference to the more involved properties of foliations in characteristic p. We apply the result to show that Q-Fano varieties with unstable tangent bundles always admit a sequence of partial rational quotients naturally associated to the Harder-Narasimhan filtration., Minor simplification. A few typos and an obvious issue in the main statement are fixed

The expression for electron impact ionization rate by a Maxwellian electron population drifting with respect to a uniform neutral atom background is derived. Depending on electron temperature, drift speeds between one to five times electron thermal velocity produce increments in the ionization rate from two to seven orders of magnitude. Local ionization takes place over shorter distances than predicted for nondrifting electron populations and the results agree with previous experimental evidence on ionizing plasma double layers and electron attracting sheaths.