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This work introduces a method for preprocessing measurements of electrical impedance tomography to considerably reduce the effect uncertainties in the electrode contacts have on the reconstruction quality, without a need to explicitly estimate the contacts. The idea is to compute the Jacobian matrix of the forward map with respect to the contact strengths and project the electrode measurements and the forward map onto the orthogonal complement of the range of this Jacobian. Using the smoothened complete electrode model as the forward model, it is demonstrated that inverting the resulting projected equation with respect to only the internal conductivity of the examined body results in good quality reconstructions both when resorting to a single step linearization with a smoothness prior and when combining lagged diffusivity iteration with total variation regularization. The quality of the reconstructions is further improved if the range of the employed projection is also orthogonal to that of the Jacobian with respect to the electrode positions. These results hold even if the projections are formed at internal and contact conductivities that significantly differ from the true ones; it is numerically demonstrated that the orthogonal complement of the range of the contact Jacobian is almost independent of the conductivity parameters at which it is evaluated. In particular, our observations introduce a numerical technique for inferring whether a change in the electrode measurements is caused by a change in the internal conductivity or alterations in the electrode contacts, which has potential applications, e.g., in bedside monitoring of stroke patients. The ideas are tested both on simulated data and on real-world water tank measurements with adjustable contact resistances., Comment: 25 pages, 11 figures

The first partial boundary data complex geometrical optics based methods for electrical impedance tomography in three dimensions are developed, and tested, on simulated and experimental data. The methods provide good localization of targets for both absolute and time-difference imaging, when large portions of the domain are inaccessible for measurement. As most medical applications of electrical impedance tomography are limited to partial boundary data, the development of partial boundary algorithms is highly desirable. While iterative schemes have been used traditionally, their high computational cost makes them cost-prohibitive for applications that need fast imaging. The proposed algorithms require no iteration and provide informative absolute or time-difference images exceptionally quickly in under 2 seconds. Reconstructions are compared to reference reconstructions from standard linear difference imaging (30 seconds) and total variation regularized absolute imaging (several minutes) The algorithms perform well under high levels of noise and incorrect domain modeling., Comment: 10 pages, 9 figures, 1 table

Objective: To develop a fast image reconstruction method for stroke monitoring with electrical impedance tomography with image quality comparable to computationally expensive nonlinear model-based methods. Methods: A post-processing approach with graph convolutional networks is employed. Utilizing the flexibility of the graph setting, a graph U-net is trained on linear difference reconstructions from 2D simulated stroke data and applied to fully 3D images from realistic simulated and experimental data. An additional network, trained on 3D vs. 2D images, is also considered for comparison. Results: Post-processing the linear difference reconstructions through the graph U-net significantly improved the image quality, resulting in images comparable to, or better than, the time-intensive nonlinear reconstruction method (a few minutes vs. several hours). Conclusion: Pairing a fast reconstruction method, such as linear difference imaging, with post-processing through a graph U-net provided significant improvements, at a negligible computational cost. Training in the graph framework vs classic pixel-based setting (CNN) allowed the ability to train on 2D cross-sectional images and process 3D volumes providing a nearly 50x savings in data simulation costs with no noticeable loss in quality. Significance: The proposed approach of post-processing a linear difference reconstruction with the graph U-net could be a feasible approach for on-line monitoring of hemorrhagic stroke., Comment: 11 pages, 8 figures

The consecutive transients (CT) method is a diagnostics approach combining experimental and computational techniques to probe the plasma parameters of Charge Breeder Electron Cyclotron Resonance Ion Sources (CB-ECRIS). The method is based on short pulse injection of singly charged ions into the charge breeder plasma, and the measurement of the resulting transients of the charge bred multiply charged ions. Estimates for plasma density, average electron energy and characteristic times of ion confinement, electron impact ionization and charge exchange are then computationally derived from the experimental data. Here the CT method is applied for parametric studies of CBECRIS plasma. Potassium ions were charge bred with hydrogen support plasma, and the effects of varied microwave power, neutral gas pressure and magnetic field strength on the plasma parameters and charge breeding efficiency are presented. It is shown that the method is sufficiently sensitive to provide relevant information on changing plasma conditions with the control parameters. The neutral gas pressure had the strongest impact on the plasma parameters, and the results agree with trends obtained by using other diagnostic methods, e.g. the increase of plasma density with increased neutral gas pressure. Furthermore, the method can provide information inaccessible with other methods, such as the characteristic times of ion confinement, ionization and charge exchange, and the hierarchy between them. The results show that the peak charge breeding efficiency is obtained for the highest ion charge state for which the ionization time remains shorter than the charge exchange and the ion confinement times.

Objective: To present the first 3D CGO-based absolute EIT reconstructions from experimental tank data. Approach: CGO-based methods for absolute EIT imaging are compared to traditional TV regularized non-linear least squares reconstruction methods. Additional robustness testing is performed by considering incorrect model\textbf{}ing of domain shape. Main Results: The CGO-based methods are fast, and show strong robustness to incorrect domain modeling comparable to classic difference EIT imaging and fewer boundary artefacts than the TV regularized non-linear least squares reference reconstructions. Significance: This work is the first to demonstrate fully 3D CGO-based absolute EIT reconstruction on experimental data and also compares to TV-regularized absolute reconstruction. The speed (1-5 seconds) and quality of the reconstructions is encouraging for future work in absolute EIT., Comment: 23 pages, 7 figures, 3 tables

A new method for determining plasma parameters from beam current transients resulting from short pulse 1+ injection into a Charge Breeder Electron Cyclotron Resonance Ion Source (CB-ECRIS) has been developed. The proposed method relies on few assumptions, and yields the ionisation times $1/n_e\left\langle\sigma v\right\rangle^{\text{inz}}_{q\to q+1}$, charge exchange times $1/n_0\left\langle\sigma v\right\rangle^{\text{cx}}_{q\to q-1}$, the ion confinement times $\tau^q$, as well as the plasma energy contents $n_e\left\langle E_e\right\rangle$ and the plasma triple products $n_e \left\langle E_e\right\rangle \tau^q$. The method is based on fitting the current balance equation on the extracted beam currents of high charge state ions, and using the fitting coefficients to determine the postdictions for the plasma parameters via an optimisation routine. The method has been applied for the charge breeding of injected K$^+$ ions in helium plasma. It is shown that the confinement times of K$^{q+}$ charge states range from 2.6$^{+0.8}_{-0.4}$ ms to 16.4$^{+18.3}_{-6.8}$ ms increasing with the charge state. The ionisation and charge exchange times for the high charge state ions are 2.6$^{+0.5}_{-0.5}$ ms--12.6$^{+2.6}_{-3.2}$ ms and 3.7$^{+5.0}_{-1.6}$ ms--357.7$^{+406.7}_{-242.4}$ ms, respectively. The plasma energy content is found to be $2.5^{+4.3}_{-1.8}\times 10^{15}$ eV/cm$^3$., Comment: 31 pages, 11 figures. This is an author-created, un-copyedited version of an article accepted for publication in Plasma Sources Science and Technology. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it

The design, integration, testing, and launch of the first Finnish satellite Aalto-1 is briefly presented in this paper. Aalto-1, a three-unit CubeSat, launched into Sun-synchronous polar orbit at an altitude of approximately 500 km, is operational since June 2017. It carries three experimental payloads: Aalto Spectral Imager (AaSI), Radiation Monitor (RADMON), and Electrostatic Plasma Brake (EPB). AaSI is a hyperspectral imager in visible and near-infrared (NIR) wavelength bands, RADMON is an energetic particle detector and EPB is a de-orbiting technology demonstration payload. The platform was designed to accommodate multiple payloads while ensuring sufficient data, power, radio, mechanical and electrical interfaces. The design strategy of platform and payload subsystems consists of in-house development and commercial subsystems. The CubeSat Assembly, Integration & Test (AIT) followed Flatsat -- Engineering-Qualification Model (EQM) -- Flight Model (FM) model philosophy for qualification and acceptance. The paper briefly describes the design approach of platform and payload subsystems, their integration and test campaigns, and spacecraft launch. The paper also describes the ground segment & services that were developed by the Aalto-1 team., Comment: 41 pages, 16 figures, accepted to Acta Astronautica, 2021

The in-orbit results and lessons learned of the first Finnish satellite Aalto-1 are briefly presented in this paper. Aalto-1, a three-unit CubeSat which was launched in June 2017, performed AaSI (Aalto Spectral Imager), Radiation Monitor (RADMON), and Electrostatic Plasma Brake (EPB) missions. The satellite partly fulfilled its mission objectives and allowed to either perform or attempt the experiments. Although attitude control was partially functional, AaSI and RADMON were able to acquire valuable measurements. EPB was successfully commissioned but the tether deployment was not successful., Comment: 35 pages

Fundamental studies of excitation and non-linear evolution of kinetic instabilities of strongly nonequlibrium hot plasmas confined in open magnetic traps suggest new opportunities for fine-tuning of conventional electron cyclotron resonance (ECR) ion sources. These devices are widely used for the production of particle beams of high charge state ions. Operating the ion source in controlled turbulence regime allows increasing the absorbed power density and therefore the volumetric plasma energy content in the dense part of the discharge surrounded by the ECR surface, which leads to enhanced beam currents of high charge state ions. We report experiments at the ECR ion source at the JYFL accelerator laboratory, in which adopting of a new approach allows to increase the multicharged ion beam current up to two times, e.g. to 95 $\mu$A of O$^{7+}$ achieved with mere 280 W power at 11.56 GHz. A theoretical model supporting and explaining the experimental findings is presented. The study suggests that the controlled turbulence regime has the potential to enhance the beam currents of modern high-performance ion sources, including state-of-the-art superconducting devices., Comment: Submitted to Plasma Sources Sci. Tech

The first numerical implementation of a D-bar method in 3D using electrode data is presented. Results are compared to Calder\'on's method as well as more common TV and smoothness regularization-based methods. D-bar methods are based on tailor-made non-linear Fourier transforms involving the measured current and voltage data. Low-pass filtering in the non-linear Fourier domain is used to stabilize the reconstruction process. D-bar methods have shown great promise in 2D for providing robust real-time absolute and time-difference conductivity reconstructions but have yet to be used on practical electrode data in 3D, until now. Results are presented for simulated data for conductivity and permittivity with disjoint non-radially symmetric targets on spherical domains and noisy voltage data. The 3D D-bar and Calder\'on methods are demonstrated to provide comparable quality to their 2D CGO counterparts, and hold promise for real-time reconstructions., Comment: 29 pages, 13 figures, 6 tables

The production of negative ions in cesium sputter ion sources is generally considered to be a pure surface process. It has been recently proposed that ion pair production could explain the higher-than-expected beam currents extracted from these ion sources, therefore opening the door for laser-assisted enhancement of the negative ion yield. We have tested this hypothesis by measuring the effect of various pulsed diode lasers on the O$^-$ beam current produced from Al$_2$O$_3$ cathode of a cesium sputter ion source. It is expected that the ion pair production of O$^-$ requires populating the 5d electronic states of neutral cesium, thus implying that the process should be provoked only with specific wavelengths. Our experimental results provide evidence for the existence of a wavelength-dependent photo-assisted effect but cast doubt on its alleged resonant nature as the prompt enhancement of beam current can be observed with laser wavelengths exceeding a threshold photon energy. The beam current transients observed during the laser pulses suggest that the magnitude and longevity of the beam current enhancement depends on the cesium balance on the cathode surface. We conclude that the photo-assisted negative ion production could be of practical importance as it can more than double the extracted beam current under certain operational settings of the ion source., Comment: 12 pages, 13 figures

We give a simple proof of the strong maximum principle for viscosity subsolutions of fully nonlinear elliptic PDEs on the form $$ F(x,u,Du,D^2u) = 0 $$ under suitable structure conditions on the equation allowing for non-Lipschitz growth in the gradient terms. In case of smooth boundaries, we also prove the Hopf lemma, the boundary Harnack inequality and that positive viscosity solutions vanishing on a portion of the boundary are comparable with the distance function near the boundary. Our results apply to weak solutions of an eigenvalue problem for the variable exponent $p$-Laplacian.

This paper presents a simulation study of a permanent magnet electron cyclotron resonance ion source (ECRIS) with a minimum-B quadrupole magnetic field topology. The magnetic field is made to conform to conventional ECRIS with $B_\textrm{min}/B_\textrm{ECR}$ of 0.67 and a last closed magnetic isosurface of 1.86$B_\textrm{ECR}$ at 10 GHz. The distribution of magnetic field gradients parallel to the field, affecting the electron heating efficiency, cover a range from 0 to 13 T/m, being similar to conventional ECRIS. Therefore it is expected that the novel ion source produces warm electrons and high charge state ions in significant number. Single electron tracking simulations are used to estimate plasma flux distribution on the plasma chamber walls and to provide an estimate of the ion density profile at the extraction slit then used in ion optical simulations demonstrating high transmission through the low energy beam transport. The designed ion source is intended to study if the quadrupole field topology could produce high charge state beams in comparable intensities to conventional ECRIS and efficiently transport them through a low energy beamline, thus paving the way for a superconducting ARC-ECRIS using the same field topology. Furthermore, the prospects of the presented ion source design as an injector of a single-ended accelerator for ion beam analysis are discussed.

Further progress in the development of ECR ion sources (ECRIS) requires deeper understanding of the underlying physics. One of the topics that remains obscure, though being crucial for the performance of the ECRIS, is the electron energy distribution (EED). A well-developed technique of measuring the EED of electrons escaping axially from the magnetically confined plasma of an ECRIS was used for the study of EED in unstable mode of plasma confinement, i.e. in the presence of kinetic instabilities. The experimental data were recorded for pulsed and CW discharges with a room-temperature 14 GHz ECRIS at the JYFL accelerator laboratory. The measurements were focused on observing differences between the EED escaping from a stable and unstable plasmas. It was found that nonlinear phenomena alter the EED noticeably. The electron losses are enhanced in both unstable regime and with two-frequency heating suppressing the instabilities. It has been shown earlier that two-frequency heating boosts the ECRIS performance presumably owing to the suppression of instabilities. We report the observed changes in EED introduced by the secondary frequency in different regimes, including an off-resonance condition where the secondary frequency is lower than the minimum frequency satisfying the resonance condition for cold electrons at the magnetic field minimum. Finally, we suggest an experimental method of qualitative evaluation of the energy distribution of electrons confined in the magnetic trap using a method of measuring energy distribution of lost electrons during the plasma decay in pulsed operation of the ion source., Comment: Invited paper at Proceedings of the 18th International Conference on Ion Sources

The measurement of the axially lost electron energy distribution escaping from a minimum-B electron cyclotron resonance ion source in the range of 4-800 keV is reported. The experiments have revealed the existence of a hump at 150-300 keV energy, containing up to 15% of the lost electrons and carrying up to 30% of the measured energy losses. The mean energy of the hump is independent of the microwave power, frequency and neutral gas pressure but increases with the magnetic field strength, most importantly with the value of the minimum-B field. Experiments in pulsed operation mode have indicated the presence of the hump only when microwave power is applied, confirming that the origin of the hump is rf-induced momentum space diffusion. Possible mechanism of the hump formation is considered basing on the quasi-linear model of plasma-wave interaction., Comment: 13 pages, 18 figures, submitted to "Plasma Physics and Controlled Fusion"

Today, the near-Earth space is facing a paradigm change as the number of new spacecraft is literally sky-rocketing. Increasing numbers of small satellites threaten the sustainable use of space, as without removal, space debris will eventually make certain critical orbits unusable. A central factor affecting small spacecraft health and leading to debris is the radiation environment, which is unpredictable due to an incomplete understanding of the near-Earth radiation environment itself and its variability driven by the solar wind and outer magnetosphere. This paper presents the FORESAIL-1 nanosatellite mission, having two scientific and one technological objectives. The first scientific objective is to measure the energy and flux of energetic particle loss to the atmosphere with a representative energy and pitch angle resolution over a wide range of magnetic local times. To pave the way to novel model - in situ data comparisons, we also show preliminary results on precipitating electron fluxes obtained with the new global hybrid-Vlasov simulation Vlasiator. The second scientific objective of the FORESAIL-1 mission is to measure energetic neutral atoms (ENAs) of solar origin. The solar ENA flux has the potential to contribute importantly to the knowledge of solar eruption energy budget estimations. The technological objective is to demonstrate a satellite de-orbiting technology, and for the first time, make an orbit manoeuvre with a propellantless nanosatellite. FORESAIL-1 will demonstrate the potential for nanosatellites to make important scientific contributions as well as promote the sustainable utilisation of space by using a cost-efficient de-orbiting technology., Comment: 26 pages, 7 figures, 5 tables Published online in JGR: Space Physics on 21 May 2019

Multi-energy CT takes advantage of the non-linearly varying attenuation properties of elemental media with respect to energy, enabling more precise material identification than single-energy CT. The increased precision comes with the cost of a higher radiation dose. A straightforward way to lower the dose is to reduce the number of projections per energy, but this makes tomographic reconstruction more ill-posed. In this paper, we propose how this problem can be overcome with a combination of a regularization method that promotes structural similarity between images at different energies and a suitably selected low-dose data acquisition protocol using non-overlapping projections. The performance of various joint regularization models is assessed with both simulated and experimental data, using the novel low-dose data acquisition protocol. Three of the models are well-established, namely the joint total variation, the linear parallel level sets and the spectral smoothness promoting regularization models. Furthermore, one new joint regularization model is introduced for multi-energy CT: a regularization based on the structure function from the structural similarity index. The findings show that joint regularization outperforms individual channel-by-channel reconstruction. Furthermore, the proposed combination of joint reconstruction and non-overlapping projection geometry enables significant reduction of radiation dose., Comment: 29 pages. Final version: Switched to non-stacked bar graphs for added readability, fixed a typo in the abstract, split previous Figure 5 into 2 Figures (now 5 and 6) for better placement of Figures

Since 2001, the SPIRAL 1 facility has been one of the pioneering facilities in ISOL techniques for reaccelerating radioactive ion beams: the fragmentation of the heavy ion beams of GANIL on graphite targets and subsequent ionization in the Nanogan ECR ion source has permitted to deliver beams of gaseous elements (He, N, O, F, Ne, Ar, Kr) to numerous experiments. Thanks to the CIME cyclotron, energies up to 20 AMeV could be obtained. In 2014, the facility was stopped to undertake a major upgrade, with the aim to extend the production capabilities of SPIRAL 1 to a number of new elements. This upgrade, which is presently under commissioning, consists in the integration of an ECR booster in the SPIRAL 1 beam line to charge breed the beam of different 1+ sources. A FEBIAD source (the so-called VADIS from ISOLDE) was chosen to be the future workhorse for producing many metallic ion beams. The charge breeder is an upgraded version of the Phoenix booster which was previously tested in ISOLDE. The performances of the aforementioned ingredients of the upgrade (targets, 1+ source and charge breeder) have been and are still being optimized in the frame of different European projects (EMILIE, ENSAR and ENSAR2). The upgraded SPIRAL 1 facility will provide soon its first new beams for physics and further beam development are undertaken to prepare for the next AGATA campaign. The results obtained during the on-line commissioning period permit to evaluate intensities for new beams from the upgraded facility., Comment: 9 pages, 12 figures, conference proceedings of EMIS 2018, CERN, Geneva, to appear in Nuclear Instruments and Methods B

This paper is devoted to the efficient numerical solution of the Helmholtz equation in a two- or three-dimensional rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and trilinear finite elements on an orthogonal mesh yielding a separable system of linear equations. The main key to high performance is to employ the Fast Fourier transform (FFT) within a fast direct solver to solve the large separable systems. The computational complexity of the proposed FFT based direct solver is O(N log N) operations. Numerical results for both two- and three-dimensional problems are presented confirming the efficiency of the method discussed.

Launching orbital and suborbital rockets from a high altitude is beneficial because of e.g. nozzle optimisation and reduced drag. Aeroplanes and gas balloons have been used for the purpose. Here we present a concept where a balloon is filled with pure water vapour on ground so that it rises to the launch altitude. The system resembles a gas balloon because no onboard energy source is carried and no hard objects fall down. We simulate the ascent behaviour of the balloon. In the baseline simulation, we consider a 10 tonne rocket lifted to an altitude of 18 km. We model the trajectory of the balloon by taking into account steam adiabatic cooling, surface cooling, water condensation and balloon aerodynamic drag. The required steam mass proves to be only 1.4 times the mass of the rocket stage and the ascent time is around 10 minutes. For small payloads, surface cooling increases the relative amount of steam needed, unless insulation is applied to the balloon skin. The ground-filled steam balloon seems to be an attractive and sustainable method of lifting payloads such as rockets into high altitude., Comment: 17 pages, 13 figures, accepted to The Aeronautical Journal

This paper is concerned with the adaptation of alternating direction implicit (ADI) time discretization schemes for the numerical solution of partial integro-differential equations (PIDEs) with application to the Bates model in finance. Three different adaptations are formulated and their (von Neumann) stability is analyzed. Ample numerical experiments are provided for the Bates PIDE, illustrating the actual stability and convergence behaviour of the three adaptations.

The shape of a rotating electric solar wind sail under the centrifugal force and solar wind dynamic pressure is modeled to address the sail attitude maintenance and thrust vectoring. The sail rig assumes centrifugally stretched main tethers that extend radially outward from the spacecraft in the sail spin plane. Furthermore, the tips of the main tethers host remote units that are connected by auxiliary tethers at the sail rim. Here, we derive the equation of main tether shape and present both a numerical solution and an analytical approximation for the shape as parametrized both by the ratio of the electric sail force to the centrifugal force and the sail orientation with respect to the solar wind direction. The resulting shape is such that near the spacecraft, the roots of the main tethers form a cone, whereas towards the rim, this coning is flattened by the centrifugal force, and the sail is coplanar with the sail spin plane. Our approximation for the sail shape is parametrized only by the tether root coning angle and the main tether length. Using the approximate shape, we obtain the torque and thrust of the electric sail force applied to the sail. As a result, the amplitude of the tether voltage modulation required for the maintenance of the sail attitude is given as a torque-free solution. The amplitude is smaller than that previously obtained for a rigid single tether resembling a spherical pendulum. This implies that less thrusting margin is required for the maintenance of the sail attitude. For a given voltage modulation, the thrust vectoring is then considered in terms of the radial and transverse thrust components., Comment: 10 pages, 9 figures, Corrects bad layout in equations in the printed journal version

Why is invention strongly positively correlated with parental income not only in the US but also in Finland which displays low income inequality and high social mobility? Using data on 1.45M Finnish individuals and their parents, we find that: (i) the positive association between parental income and off-spring probability of inventing is greatly reduced when controlling for parental education; (ii) instrumenting for the parents having a MSc-degree using distance to nearest university reveals a large causal effect of parental education on offspring probability of inventing; and (iii) the causal effect of parental education has been markedly weakened by the introduction in the early 1970s of a comprehensive schooling reform. [Funding for this report was provided by the ERC, the Yrjö Jahnsson Foundation, and FORTE.]

European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a given model parameter variation range.

In Coulomb drag propulsion, a long high voltage tether or system of tethers gathers momentum from a natural plasma stream such as solar wind or ionospheric plasma ram flow. A positively polarised tether in the solar wind can be used for efficient general-purpose interplanetary propellantless propulsion (the electric solar wind sail or E-sail), whereas a negatively polarised tether in LEO can be used for efficient deorbiting of satellites (the plasma brake). Aalto-1 is a 3-U cubesat to be launched in May 2016. The satellite carries three scientific experiments including 100 m long Coulomb drag tether experiment. The tether is made of four 25 and 50 micrometre diameter aluminium wires that are ultrasonically bonded together every few centimetre intervals. The tether can be charged by an onboard voltage source up to one kilovolt positive and negative. The Coulomb drag is measured by monitoring the spin rate., Comment: Space Propulsion 2016 (Rome, 2-6 May 2016) proceedings paper, 7 pages, 6 figures. arXiv admin note: text overlap with arXiv:1404.7430

The electric solar wind sail (E-sail) is a way to propel a spacecraft by using the natural solar wind as a thrust source. The problem of secular spinrate change was identified earlier which is due to the orbital Coriolis effect and tends to slowly increase or decrease the sail's spinrate, depending on which way the sail is inclined with respect to the solar wind. Here we present an E-sail design and its associated control algorithm which enable spinrate control during propulsive flight by the E-sail effect itself. In the design, every other maintether ("T-tether") is galvanically connected through the remote unit with the two adjacent auxtethers, while the other maintethers ("I-tethers") are insulated from the tethers. This enables one to effectively control the maintether and auxtether voltages separately, which in turn enables spinrate control. We use a detailed numerical simulation to show that the algorithm can fully control the E-sail's spin state in real solar wind. The simulation includes a simple and realistic set of controller sensors: an imager to detect remote unit angular positions and a vector accelerometer. The imager resolution requirement is modest and the accelerometer noise requirement is feasible to achieve. The TI tether rig enables building E-sails that are able to control their spin state fully and yet are actuated by pure tether voltage modulation from the main spacecraft and requiring no functionalities from the remote units during flight., Comment: 28 pages, 10 figures, 3 tables, resubmitted version

Background: Nuclear self-consistent mean-field approaches are rooted in the density functional theory and, through the spontaneous symmetry breaking mechanism, allow for including important correlations, while keeping the simplicity of the approach. Because real ground states should have all symmetries of the nuclear Hamiltonian, these methods require subsequent symmetry restoration. Purpose: We implement and study Lipkin method of approximate variation after projection applied to the restoration of the translational or rotational symmetries. Methods: We use Lipkin operators up to quadratic terms in momenta or angular momenta with self-consistently determined values of the Peierls-Yoccoz translational masses or moments of inertia, respectively. Calculations based on Skyrme energy-density functional are performed for heavy, deformed, and paired nuclei. Results: In deformed nuclei, the Peierls-Yoccoz translational masses along three different principal-axes directions of the intrinsic system can be different, which illustrates different widths of the total-momentum distributions. Numerically, the differences are only of the order of a few per cent. For the rotational-symmetry restoration, the Lipkin method compares favorably with the exact angular-momentum projection, which requires much larger computational effort. Conclusions: The Lipkin method of translational and rotational symmetry restoration is a practical low-cost method of determining the corresponding correlation energies. It allows for a simultaneous restoration of several symmetries and can be relatively easily implemented in the standard self-consistent mean-field calculations, including those required for the parameter adjustments., Comment: 7 pages, 10 figures, version submitted to Physical Review C

We have performed self-consistent Skyrme Hartree-Fock-Bogolyubov calculations for nuclei close to $^{254}$No. Self-consistent deformations, including $\beta_{2,4,6,8}$ as functions of the rotational frequency, were determined for even-even nuclei $^{246,248,250}$Fm, $^{252,254}$No, and $^{256}$Rf. The quasiparticle spectra for N=151 isotones and Z=99 isotopes were calculated and compared with experimental data and the results of Woods-Saxon calculations. We found that our calculations give high-order deformations similar to those obtained for the Woods-Saxon potential, and that the experimental quasiparticle energies are reasonably well reproduced., Comment: 6 pages, 2 figures; ICFN5 conference proceedings

Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or multidimensional parabolic problems of the convection-diffusion type and generalizations thereof. An overview of various operator splitting methods is presented for the efficient numerical solution of these problems. Splitting schemes of the Alternating Direction Implicit (ADI) type are discussed for multidimensional problems, e.g. given by stochastic volatility (SV) models. For jump models Implicit-Explicit (IMEX) methods are considered which efficiently treat the nonlocal jump operator. For American options an easy-to-implement operator splitting method is described for the resulting linear complementarity problems. Numerical experiments are presented to illustrate the actual stability and convergence of the splitting schemes. Here European and American put options are considered under four asset price models: the classical Black-Scholes model, the Merton jump-diffusion model, the Heston SV model, and the Bates SV model with jumps.