On SAT representations of XOR constraints

We study the representation of systems S of linear equations over the two-element field (aka xor- or parity-constraints) via conjunctive normal forms F (boolean clause-sets). First we consider the problem of finding an "arc-consistent" representation ("AC"), meaning that unit-clause propagation will fix all forced assignments for all possible instantiations of the xor-variables. Our main negative result is that there is no polysize AC-representation in general. On the positive side we show that finding such an AC-representation is fixed-parameter tractable (fpt) in the number of equations. Then we turn to a stronger criterion of representation, namely propagation completeness ("PC") --- while AC only covers the variables of S, now all the variables in F (the variables in S plus auxiliary variables) are considered for PC. We show that the standard translation actually yields a PC representation for one equation, but fails so for two equations (in fact arbitrarily badly). We show that with a more intelligent translation we can also easily compute a translation to PC for two equations. We conjecture that computing a representation in PC is fpt in the number of equations.Comment: 39 pages; 2nd v. improved handling of acyclic systems, free-standing proof of the transformation from AC-representations to monotone circuits, improved wording and literature review; 3rd v. updated literature, strengthened treatment of monotonisation, improved discussions; 4th v. update of literature, discussions and formulations, more details and examples; conference v. to appear LATA 201

A Simple Model for Reflection-Driven Spectral Evolution of Turbulence in the Corona and Inner Heliosphere

International audienceDissipation of turbulence is generally considered as a prime candidate for the heating and acceleration of solar wind from the corona throughout the heliosphere, due to radially evolving dissipation processes and/or cascading of energy to dissipation scales. In order to model the latter consistently, we must consider the evolution of cross-helicity when modeling the strength of the cascade, as the non-linear interactions causing it require counterstreaming waves. In this paper, we present a simple model of non-WKB wave reflection from large-scale gradients, and apply the resulting cross-helicity to evaluate the evolution of the turbulence spectrum up to 0.3 AU by using a phenomenological cascade model. The study is restricted to a cascade in perpendicular direction. We study the ability of this spectral flux to heat the solar wind, and its dependence on the frequency of the excited waves. We find that the cascade advances fast in the low corona, and has a strong frequency dependence. The heating rate is high close to the coronal base, but decreases very quickly. In the corona, the heating rate varies by an order of magnitude in the frequency range of 10-6 to 10-3 Hz, suggesting that the shape and range of the frequency spectrum has important implications on the solar wind modelin

Optimal NaOH dosage for sulfide minerals oxidation in alkaline leach

Abstract. Sodium hydroxide also known as NaOH is well known and extensively used reagent in mining and mineral processing. Processed ores generally contain a large amount of minerals. Ore minerals contain for example sulfate and sulfide. These sulfide minerals are just one group of minerals that occurs in ore. A common way to dissolve sulfides is to use acidic conditions (acid leaching). However, due to challenging mineral structure and preg robbing ores, the best leaching results can be achieved by using alkaline conditions (alkaline leaching). NaOH with sufficient amount of oxygen is an effective substance to use in alkaline leaching. In this thesis the aim is to find out the optimal NaOH dosage for sulfide containing concentrate to dissolve the metals from sulfide matrix. NaOH is an expensive reagent and that is why the dosage optimizing is one of the fundamental questions when it comes to the process planning, budgeting, and profitability. Sulfide dissolution is measured through the oxidation level of sulfides. Oxidation level of sulfide can be measured as sulfur oxidation when all sulfur of the ore is in sulfide form. Oxidation level of sulfur correlates with the oxidation products, like sulfate and thiosulfate. Also, the ratio between thiosulfate and sulfates can be used to see if the oxidation level is high enough or how well the process is balanced. The goal of this thesis is to provide an information on the basis of which the process can be adjusted to improve the cost-efficiency of the process. Knowing the optimal dosage will help the company to perform in the best possible way. The use of right dosage of chemicals reduces the environmental impact of the mining industry. In the best-case scenario dosage optimization will reduce reagent consumption and enables cleaner and more efficient processes in the future. The research material and results of this thesis were gathered during the industrial pilot. The pilot consisted of three continuously operating leaching reactors each with a volume of 2,7m3. Consumption of sodium hydroxide was monitored in various ways in order to get as accurate consumption estimate as possible. Based on sulfur content of the feed, the other reagents, such as oxygen, can also be adjusted to achieve the best oxidation rate. The optimal dosage of the sodium hydroxide can be estimated by comparing the sulfur oxidation rate and the concentration of the formed dissolution products

ENERGETIC PARTICLE DIFFUSION IN CRITICALLY BALANCED TURBULENCE

Observations and modeling suggest that the fluctuations in magnetized plasmas exhibit scale-dependent anisotropy, with more energy in the fluctuations perpendicular to the mean magnetic field than in the parallel fluctuations and the anisotropy increasing at smaller scales. The scale dependence of the anisotropy has not been studied in full-orbit simulations of particle transport in turbulent plasmas so far. In this paper, we construct a model of critically balanced turbulence, as suggested by Goldreich & Sridhar, and calculate energetic particle spatial diffusion coefficients using full-orbit simulations. The model uses an enveloped turbulence approach, where each two-dimensional wave mode with wavenumber k ⊥ is packed into envelopes of length L following the critical balance condition, Lk –2/3 ⊥, with the wave mode parameters changing between envelopes. Using full-orbit particle simulations, we find that both the parallel and perpendicular diffusion coefficients increase by a factor of two, compared to previous models with scale-independent anisotropy

Regular albuterol or nedocromil sodium — effects on airway subepithelial tenascin in asthma

AbstractBoth albuterol and nedocromil sodium have been recognized to possess certain anti-inflammatory properties. However, there are no data on the impact of these drugs on the pathophysiology of the bronchial extracellular matrix in asthma characterized by enhanced tenascin (Tn) expression, known to occur proportional to the severity of asthma. This paper reports data from a morphometric study on the effects of regular treatment with inhaled albuterol or nedocromil sodium on the extent of bronchial subepithelial deposition of Tn, collagen types III, IV, and VII and mucosal infiltration with macrophages.Thirty-two patients (14 women) with chronic asthma, aged 38·7 years (median) with a median forced expiratory volume in 1 sec (FEV1) of 74·4% predicted, were selected to undergo fibre-optic bronchoscopy with bronchial biopsies before and after 12 weeks of treatment with either inhaled albuterol 0·2 mg or nedocromil sodium 4 mg four times daily according to a double-blind protocol. Cryostat sections of the biopsy specimens were studied by indirect immunostaining techniques using monoclonal antibodies and computer-assisted quantitative image analysis.Albuterol treatment significantly reduced the median thickness of subepithelial Tn expression from 9·7 to 6·3 μm (P=0·023) and macrophage numbers in the epithelium (P=0·034), lamina propria (P=0·039) and entire mucosa (P=0·033), whereas nedocromil sodium had no effect. Expression of the collagen types was not affected by either treatment. There was no identifiable statistical difference between the two treatments for any of the outcome variables measured. Nevertheless, the results demonstrate that even a short-acting β2-agonist may exert anti-inflammatory potential sufficient to interfere with the basic mechanisms of asthma as shown by reduction of subepithelial Tn content and mucosal macrophage count

Drift induced perpendicular transport of solar energetic particles

Drifts are known to play a role in galactic cosmic ray transport within the heliosphere and are a standard component of cosmic ray propagation models. However, the current paradigm of solar energetic particle (SEP) propagation holds the effects of drifts to be negligible, and they are not accounted for in most current SEP modeling efforts. We present full-orbit test particle simulations of SEP propagation in a Parker spiral interplanetary magnetic field (IMF), which demonstrate that high-energy particle drifts cause significant asymmetric propagation perpendicular to the IMF. Thus in many cases the assumption of field-aligned propagation of SEPs may not be valid. We show that SEP drifts have dependencies on energy, heliographic latitude, and charge-to-mass ratio that are capable of transporting energetic particles perpendicular to the field over significant distances within interplanetary space, e.g., protons of initial energy 100 MeV propagate distances across the field on the order of 1 AU, over timescales typical of a gradual SEP event. Our results demonstrate the need for current models of SEP events to include the effects of particle drift. We show that the drift is considerably stronger for heavy ion SEPs due to their larger mass-to-charge ratio. This paradigm shift has important consequences for the modeling of SEP events and is crucial to the understanding and interpretation of in situ observations. © 2013. The American Astronomical Society. All rights reserved.

Early propagation of energetic particles across the mean field in turbulent plasmas

Propagation of energetic particles across the mean field direction in turbulent magnetic fields is often described as spatial diffusion. Recently, it has been suggested that initially the particles prop- agate systematically along meandering field lines, and only later reach the time-asymptotic diffusive cross-field propagation. In this paper, we analyse cross-field propagation of 1–100 MeV protons in composite 2D-slab turbulence superposed on a constant background magnetic field, using full-orbit particle simulations, to study the non-diffusive phase of particle propagation with a wide range of turbulence parameters. We show that the early-time non-diffusive propagation of the particles is consistent with particle propagation along turbulently meandering field lines. This results in a wide cross-field extent of the particles already at the initial arrival of particles to a given distance along the mean field direction, unlike when using spatial diffusion particle transport models. The cross-field extent of the particle distribution remains constant for up to tens of hours in turbulence environ- ment consistent with the inner heliosphere during solar energetic particle events. Subsequently, the particles escape from their initial meandering field lines, and the particle propagation across the mean field reaches time-asymptotic diffusion. Our analysis shows that in order to understand so- lar energetic particle event origins, particle transport modelling must include non-diffusive particle propagation along meandering field lines. Key words: Sun: particle emission – diffusion – magnetic fields – turbulenc

Evolution of kinklike fluctuations associated with ion pickup within reconnection outflows in the Earth's magnetotail

Magnetic reconnection (MR) in Earth's magnetotail is usually followed by a systemwide redistribution of explosively released kinetic and thermal energy. Recently, multispacecraft observations from the THEMIS mission were used to study localized explosions associated with MR in the magnetotail so as to understand subsequent Earthward propagation of MR outbursts during substorms. Here we investigate plasma and magnetic field fluctuations/structures associated with MR exhaust and ion-ion kink mode instability during a well documented MR event. Generation, evolution and fading of kinklike oscillations are followed over a distance of 70 000 km from the reconnection site in the midmagnetotail to the more dipolar region near the Earth. We have found that the kink oscillations driven by different ion populations within the outflow region can be at least 25 000 km from the reconnection site.Comment: 11 pages, 4 figure

Time dependence of Fe/O ratio within a 3D solar energetic particle propagation model including drift

Context. The intensity profiles of iron and oxygen in Solar Energetic Particle (SEP) events often display differences that result in a decreasing Fe/O ratio over time. The physical mechanisms behind this behaviour are not fully understood, but these observational signatures provide important tests of physical modelling efforts. Aims. In this paper we study the propagation of iron and oxygen SEP ions using a 3D model of propagation which includes the effect of guiding centre drift in a Parker spiral magnetic field. We derive time intensity profiles for a variety of observer locations and study the temporal evolution of the Fe/O ratio. Methods. We use a 3D full orbit test particle model which includes scattering. The configuration of the interplanetary magnetic field is a unipolar Parker spiral. Particles are released instantaneously from a compact region at two solar radii and allowed to propagate in 3D. Results. Both Fe and O experience significant transport across the magnetic field due to gradient and curvature drifts. We find that Fe ions drift more than O ions due to their larger mass-to-charge ratio, so that an observer that is not magnetically well connected to the source region will observe Fe arriving before O, for particles within the same range in energy per nucleon. As a result, for the majority of observer locations, the Fe/O ratio displays a decrease in time. Conclusions. We conclude that propagation effects associated with drifts produce a decay over time of the Fe/O ratio, qualitatively reproducing that observed in SEP event profiles