Relativistic current collection by a cylindrical Langmuir probe

The current I to a cylindrical Langmuir probe with a bias Φp satisfying β≡eΦp/mec2∼O(1) is discussed. The probe is considered at rest in an unmagnetized plasma composed of electrons and ions with temperatureskTe∼kTi≪mec2. For small enough radius, the probe collects the relativistic orbital-motion-limited (OML) current I OML , which is shown to be larger than the non-relativistic result; the OML current is proportional to β1/2 and β3/2 in the limits β≪1 and β≫1, respectively. Unlike the non-relativistic case, the electron density can exceed the unperturbed density value. An asymptotic theory allowed to compute the maximum radius of the probe to collect OML current, the sheath radius for probe radius well below maximum and how the ratio I/I OML drops below unity when the maximum radius is exceeded. A numerical algorithm that solves the Vlasov-Poisson system was implemented and density and potential profiles presented. The results and their implications in a possible mission to Jupiter with electrodynamic bare tethers are discussed density value. An asymptotic theory allowed to compute the maximum radius of the probe to collect OML current, the sheath radius for probe radius well below maximum and how the ratio I/IOML drops below unity when the maximum radius is exceeded. A numerical algorithm that solves the Vlasov-Poisson system was implemented and density and potential profiles presented. The results and their implications in a possible mission to Jupiter with electrodynamic bare tethers are discussed.

Curvature and velocity of methane-air Bunsen flame tips

PIV and photographic recording are used to measure the velocity of the fresh gas and the shape of the reaction layer in a region around the tip of a methane- air Bunsen flame attached to a cylindrical burner. The results compare well with numerical simulations carried out with an infinite activation energy reaction model. The experimental and numerical results confirm that the well-known linear relation between flame velocity and flame stretch derived from asymptotic theory for weakly curved and strained flames is valid for small and moderate values of the flame stretch if the modified definition of stretch introduced by Echekki and Mungal (Proc Combust Inst 23:455–461,1990) and Poinsot et al. (Combust Sci Technol 81:45–73,1992) is used. However, the relation between flame velocity and modified stretch ceases to be linear and approaches a square root law for large values of the stretch, when the curvature of the flame tip becomes large compared to the inverse of the thickness of a planar flame

Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss

Sequential estimation of the success probability p in inverse binomial sampling is considered in this paper. For any estimator pˆ , its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters a and b for pˆ

p , respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as p→0, and which guarantee that, for any p∈(0,1), the risk is lower than its asymptotic value. This allows selecting the required number of successes, r, to meet a prescribed quality irrespective of the unknown p. In addition, the proposed estimators are shown to be approximately minimax when a/b does not deviate too much from 1, and asymptotically minimax as r→∞ when a=b.

Assortative and modular networks are shaped by adaptive synchronization processes

Modular organization and degree-degree correlations are ubiquitous in the connectivity structure of biological, technological, and social interacting systems. So far most studies have concentrated on unveiling both features in real world networks, but a model that succeeds in generating them simultaneously is needed. We consider a network of interacting phase oscillators, and an adaptation mechanism for the coupling that promotes the connection strengths between those elements that are dynamically correlated. We show that, under these circumstances, the dynamical organization of the oscillators shapes the topology of the graph in such a way that modularity and assortativity features emerge spontaneously and simultaneously. In turn, we prove that such an emergent structure is associated with an asymptotic arrangement of the collective dynamical state of the network into cluster synchronization.

Surface Impedance Characterization for UTD Based Solution with IBC for Surface Fields on a Dielectric-Coated PEC Circular Cylinder

A novel formulation for the surface impedance characterization is introduced for the canonical problem of surface fields on a perfect electric conductor (PEC) circular cylinder with a dielectric coating due to a electric current source using the Uniform Theory of Diffraction (UTD) with an Impedance Boundary Condition (IBC). The approach is based on a TE/TM assumption of the surface fields from the original problem. Where this surface impedance fails, an optimization is performed to minimize the error in the SD Green?s function between the original problem and the equivalent one with the IBC. This new approach requires small changes in the available UTD based solution with IBC to include the geodesic ray angle and length dependence in the surface impedance formulas. This asymptotic method, accurate for large separations between source and observer points, in combination with spectral domain (SD) Green?s functions for multidielectric coatings leads to a new hybrid SD-UTD with IBC to calculate mutual coupling among microstrip patches on a multilayer dielectric-coated PEC circular cylinder. Results are compared with the eigenfunction solution in SD, where a very good agreement is met.

Surface Impedance Characterization for Mutual Coupling Calculation of Patches on a Dielectric-Coated PEC Circular Cylinder

A novel formulation for the surface impedance characterization is introduced for the canonical problem of surface fields on a perfect electric conductor (PEC) circular cylinder with a dielectric coating due to a electric current source using the Uniform Theory of Diffraction (UTD) with an Impedance Boundary Condition (IBC). The approach is based on a TE/TM assumption of the surface fields from the original problem. Where this surface impedance fails, an optimization is performed to minimize the error in the SD Green?s function between the original problem and the equivalent one with the IBC. This asymptotic method, accurate for large separations between source and observer points, in combination with spectral domain (SD) Green?s functions for multidielectric coatings leads to a new hybrid SD-UTD with IBC to calculate mutual coupling among microstrip patches on a multilayer dielectric-coated PEC circular cylinder. Results are compared with the eigenfunction solution in SD, where a very good agreement is met.

Modeling the evolution of item rating networks using time-domain preferential attachment

The understanding of the structure and dynamics of the intricate network of connections among people that consumes products through Internet appears as an extremely useful asset in order to study emergent properties related to social behavior. This knowledge could be useful, for example, to improve the performance of personal recommendation algorithms. In this contribution, we analyzed five-year records of movie-rating transactions provided by Netflix, a movie rental platform where users rate movies from an online catalog. This dataset can be studied as a bipartite user-item network whose structure evolves in time. Even though several topological properties from subsets of this bipartite network have been reported with a model that combines random and preferential attachment mechanisms [Beguerisse Díaz et al., 2010], there are still many aspects worth to be explored, as they are connected to relevant phenomena underlying the evolution of the network. In this work, we test the hypothesis that bursty human behavior is essential in order to describe how a bipartite user-item network evolves in time. To that end, we propose a novel model that combines, for user nodes, a network growth prescription based on a preferential attachment mechanism acting not only in the topological domain (i.e. based on node degrees) but also in time domain. In the case of items, the model mixes degree preferential attachment and random selection. With these ingredients, the model is not only able to reproduce the asymptotic degree distribution, but also shows an excellent agreement with the Netflix data in several time-dependent topological properties.

Theory of a probe in a strong magnetic field

An asymptotic analysis of the Langmuir-probe problem in a quiescent, fully ionized plasma in a strong magnetic field is performed, for electron cyclotron radius and Debye length much smaller than probe radius, and this not larger than either ion cyclotron radius or mean free path. It is found that the electric potential, which is not confined to a sheath, controls the diffusion far from the probe; inside the magnetic tube bounded by the probe cross section the potential overshoots to a large value before decaying to its value in the body of the plasma. The electron current is independent of the shape of the body along the field and increases with ion temperature; due to the overshoot in the potential, (1) the current at negative voltages does not vary exponentially, (2) its magnitude is strongly reduced by the field, and (3) the usual sharp knee at space potential, disappears. In the regions of the C-V diagram studied the ion current is negligible or unaffected by the field. Some numerical results are presented.The theory, which fails beyond certain positive voltage, fields useful results for weak fields, too.

Caracterización de la impedancia de superficie para el cálculo del acoplo mutuo en un cilindro circular conductor cubierto por una dieléctrico multicapa

A novel formulation for the surface impedance characterization is introduced for the canonical problem of surface fields on a perfect electric conductor (PEC) circular cylinder with a dielectric coating due to a electric current source using the Uniform Theory of Diffraction (UTD) with an Impedance Boundary Condition (IBC). The approach is based on a TE/TM assumption of the surface fields from the original problem. Where this surface impedance fails, an optimization is performed to minimize the error in the SD Green's function between the original problem and the equivalent one with the IBC. This new approach requires small changes in the available UTD based solution with IBC to include the geodesic ray angle and length dependence in the surface impedance formulas. This asymptotic method, accurate for large separations between source and observer points, in combination with spectral domain (SD) Green's functions for multidielectric coatings leads to a new hybrid SD-UTD with IBC to calculate mutual coupling among microstrip patches on a multilayer dielectric-coated PEC circular cylinder. Results are compared with the eigenfunction solution in SD, where a very good agreement is met.

Far wake structure in rarefied plasma flows past charged bodies

The asymptotic structure of the far-wake behind a charged body in a rarefied plasma flow is investigated under the assumption of small ion-to-electron temperature ratio and of flow speed hypersonic with respect to the ions but not with respect to the electrons. It is found that waves are excited even if the flow is subacoustic (flow velocity less than the ion-acoustic speed). For both superacoustic and subacoustic velocities a steep wave front develops separating the weakly perturbed, quasineutral plasma ahead, from the region behind where ion waves appear. Near the axis a trailing front develops;the region between this and the axis is quasineutral for superacoustic speeds. The decay laws in all of these regions, the self-similar structure of the fronts and the general character of the waves are determined.The damping of the waves and special flow detail for bodies large and small compared with the Debye length are discussed. A nonlinear analysis of the leading wave front in superacoustic flow is carried out. A hyperacoustic equivalence principle is presented.

Self-similar motion of laser fusion plasmas. Absorption in an unbounded plasma

The one-dimensional motion generated in a cold, infinite, uniform plasma of density na by the absorption, in a certain plane, of a linear pulse of energy per unit time and area = 4>0t/r, 0< t< r, is considered, the analysis allows for thermal conduction and viscosity of ions and electrons, their energy exchange, and an electron heat flux limiter The resulting motion is self-similar and governed by a single nondimensional parameter a«(n0 2T/0)2/3 Detailed asymptotic results are obtained for both a < l and a > l , the general behavior of the solution for arbitrary a is discussed The analysis can be extended to the case of a plasma initially occupying a half-space, and throws light on how to optimize the hydrodynamics of laser fusion plasmas Known approximate results corresponding to motion of a plasma submitted to constant irradiation (<()) are recovered in the present work under appropriate limiting processes

Self-consistent, nonlocal electron heat flux at arbitrary ion charge number

A single, nonlocal expression for the electron heat flux, which closely reproduces known results at high and low ion charge number 2, and “exact” results for the local limit at all 2, is derived by solving the kinetic equation in a narrow, tail-energy range. The solution involves asymptotic expansions of Bessel functions of large argument, and (Z-dependent)order above or below it, corresponding to the possible parabolic or hyperbolic character of the kinetic equation; velocity space diffusion in self-scattering is treated similarly to isotropic thermalization of tail energies in large Z analyses. The scale length H characterizing nonlocal effects varies with Z, suggesting an equal dependence of any ad hoc flux limiter. The model is valid for all H above the mean-free path for thermal electrons.

Current collection by an active spherical electrode in an unmagnetized plasma

A theoretical model for the steady-state response of anodic contactors that emit a plasma current Ii and collect electrons from a collisionless, unmagnetized plasma is presented. The use of a (kinetic) monoenergetic population for the attracted species, well known in passive probe theory, gives both accuracy and tractability to the theory. The monoenergetic population is proved to behave like an isentropic fluid with radial plus centripetal motion, allowing direct comparisons with ad hoc fluid models. Also, a modification of the original monoenergetic equations permits analysis of contactors operating in orbit-limited conditions. Besides that, the theory predicts that, only for plasma emissions above certain threshold current a presheath/double layer/core structure for the potential is formed (the core mode), while for emissions below that threshold, a plasma contactor behaves exactly as a positive-ion emitter with a presheath/sheath structure (the no-core mode). Ion emitters are studied as a particular case. Emphasis is placed on obtaining dimensionless charts and approximate asymptotic laws of the current-voltage characteristic.

The orbital-motion-limited regime of cylindrical Langmuir probes

An asymptotic analysis of electron collection at high bias Fp serves to determine the domain of validity of the orbital-motion-limited regime of cylindrical Langmuir probes, which is basic for the workings of conductive bare tethers. The radius of a wire collecting OML current in an unmagnetized plasma at rest cannot exceed a value, Rmax , which is found to exhibit a minimum as a function of Fp ; atFp values of interest, Rmax is already increasing and is larger than the electron Debye length lDe . The breakdown of the regime relates to conditions far fromthe probe, at electron energies comparable to the ion thermal energy, kTi ; Rmax is found to increase with Ti . It is also found that ~1! the maximumwidth of a thin tape, if used instead of a wire, is 4Rmax ; ~2! the electron thermal gyroradius must be larger than both R and lDe for magnetic effects to be negligible; and ~3! conditions applying to the tether case are such that trapped-orbit effects are negligible.

Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss

Sequential estimation of the success probability $p$ in inverse binomial sampling is considered in this paper. For any estimator $\hatvap$, its quality is measured by the risk associated with normalized loss functions of linear-linear or inverse-linear form. These functions are possibly asymmetric, with arbitrary slope parameters $a$ and $b$ for $\hatvap < p$ and $\hatvap > p$ respectively. Interest in these functions is motivated by their significance and potential uses, which are briefly discussed. Estimators are given for which the risk has an asymptotic value as $p \rightarrow 0$, and which guarantee that, for any $p \in (0,1)$, the risk is lower than its asymptotic value. This allows selecting the required number of successes, $\nnum$, to meet a prescribed quality irrespective of the unknown $p$. In addition, the proposed estimators are shown to be approximately minimax when $a/b$ does not deviate too much from $1$, and asymptotically minimax as $\nnum \rightarrow \infty$ when $a=b$.