Trajectory-correction propulsion system Patent

Spacecraft trajectory correction propulsion syste

INTERNATIONAL AGRICULTURAL TRADE DISPUTES: CASE STUDIES IN NORTH AMERICA

International Relations/Trade,

Kinetic Vlasov Simulations of collisionless magnetic Reconnection

A fully kinetic Vlasov simulation of the Geospace Environment Modeling (GEM) Magnetic Reconnection Challenge is presented. Good agreement is found with previous kinetic simulations using particle in cell (PIC) codes, confirming both the PIC and the Vlasov code. In the latter the complete distribution functions $f_k$ ($k=i,e$) are discretised on a numerical grid in phase space. In contrast to PIC simulations, the Vlasov code does not suffer from numerical noise and allows a more detailed investigation of the distribution functions. The role of the different contributions of Ohm's law are compared by calculating each of the terms from the moments of the $f_k$. The important role of the off--diagonal elements of the electron pressure tensor could be confirmed. The inductive electric field at the X--Line is found to be dominated by the non--gyrotropic electron pressure, while the bulk electron inertia is of minor importance. Detailed analysis of the electron distribution function within the diffusion region reveals the kinetic origin of the non--gyrotropic terms

Numerical electrokinetics

A new lattice method is presented in order to efficiently solve the electrokinetic equations, which describe the structure and dynamics of the charge cloud and the flow field surrounding a single charged colloidal sphere, or a fixed array of such objects. We focus on calculating the electrophoretic mobility in the limit of small driving field, and systematically linearise the equations with respect to the latter. This gives rise to several subproblems, each of which is solved by a specialised numerical algorithm. For the total problem we combine these solvers in an iterative procedure. Applying this method, we study the effect of the screening mechanism (salt screening vs. counterion screening) on the electrophoretic mobility, and find a weak non-trivial dependence, as expected from scaling theory. Furthermore, we find that the orientation of the charge cloud (i. e. its dipole moment) depends on the value of the colloid charge, as a result of a competition between electrostatic and hydrodynamic effects.Comment: accepted for publication in Journal of Physics Condensed Matter (proceedings of the 2012 CODEF conference

Phase Separation in Charge-Stabilized Colloidal Suspensions: Influence of Nonlinear Screening

The phase behavior of charge-stabilized colloidal suspensions is modeled by a combination of response theory for electrostatic interparticle interactions and variational theory for free energies. Integrating out degrees of freedom of the microions (counterions, salt ions), the macroion-microion mixture is mapped onto a one-component system governed by effective macroion interactions. Linear response of microions to the electrostatic potential of the macroions results in a screened-Coulomb (Yukawa) effective pair potential and a one-body volume energy, while nonlinear response modifies the effective interactions [A. R. Denton, \PR E {\bf 70}, 031404 (2004)]. The volume energy and effective pair potential are taken as input to a variational free energy, based on thermodynamic perturbation theory. For both linear and first-order nonlinear effective interactions, a coexistence analysis applied to aqueous suspensions of highly charged macroions and monovalent microions yields bulk separation of macroion-rich and macroion-poor phases below a critical salt concentration, in qualitative agreement with predictions of related linearized theories [R. van Roij, M. Dijkstra, and J.-P. Hansen, \PR E {\bf 59}, 2010 (1999); P. B. Warren, \JCP {\bf 112}, 4683 (2000)]. It is concluded that nonlinear screening can modify phase behavior but does not necessarily suppress bulk phase separation of deionized suspensions.Comment: 14 pages of text + 9 figure

An exactly solvable toy model that mimics the mode coupling theory of supercooled liquid and glass transition

A toy model is proposed which incorporates the reversible mode coupling mechanism responsible for ergodic-nonergodic transition with trivial Hamiltonian in the mode coupling theory (MCT) of structural glass transition. The model can be analyzed without relying on uncontrolled approximations inevitable in the current MCT. The strength of hopping processes can be easily tuned and the ideal glass transition is reproduced only in a certain range of the strength. On the basis of the analyses of our model we discuss about a sharp ergodic-nonergodic transition and its smearing out by "hopping".Comment: 5 pages, 2 ps-figures, inappropriate terms replace

Complexity Bounds for Ordinal-Based Termination

`What more than its truth do we know if we have a proof of a theorem in a given formal system?' We examine Kreisel's question in the particular context of program termination proofs, with an eye to deriving complexity bounds on program running times. Our main tool for this are length function theorems, which provide complexity bounds on the use of well quasi orders. We illustrate how to prove such theorems in the simple yet until now untreated case of ordinals. We show how to apply this new theorem to derive complexity bounds on programs when they are proven to terminate thanks to a ranking function into some ordinal.Comment: Invited talk at the 8th International Workshop on Reachability Problems (RP 2014, 22-24 September 2014, Oxford

Nonlinear Screening and Effective Electrostatic Interactions in Charge-Stabilized Colloidal Suspensions

A nonlinear response theory is developed and applied to electrostatic interactions between spherical macroions, screened by surrounding microions, in charge-stabilized colloidal suspensions. The theory describes leading-order nonlinear response of the microions (counterions, salt ions) to the electrostatic potential of the macroions and predicts microion-induced effective many-body interactions between macroions. A linear response approximation [Phys. Rev. E 62, 3855 (2000)] yields an effective pair potential of screened-Coulomb (Yukawa) form, as well as a one-body volume energy, which contributes to the free energy. Nonlinear response generates effective many-body interactions and essential corrections to both the effective pair potential and the volume energy. By adopting a random-phase approximation (RPA) for the response functions, and thus neglecting microion correlations, practical expressions are derived for the effective pair and triplet potentials and for the volume energy. Nonlinear screening is found to weaken repulsive pair interactions, induce attractive triplet interactions, and modify the volume energy. Numerical results for monovalent microions are in good agreement with available ab initio simulation data and demonstrate that nonlinear effects grow with increasing macroion charge and concentration and with decreasing salt concentration. In the dilute limit of zero macroion concentration, leading-order nonlinear corrections vanish. Finally, it is shown that nonlinear response theory, when combined with the RPA, is formally equivalent to the mean-field Poisson-Boltzmann theory and that the linear response approximation corresponds, within integral-equation theory, to a linearized hypernetted-chain closure.Comment: 30 pages, 8 figures, Phys. Rev. E (in press

Iron porphyrin molecules on Cu(001): Influence of adlayers and ligands on the magnetic properties

The structural and magnetic properties of Fe octaethylporphyrin (OEP) molecules on Cu(001) have been investigated by means of density functional theory (DFT) methods and X-ray absorption spectroscopy. The molecules have been adsorbed on the bare metal surface and on an oxygen-covered surface, which shows a $\sqrt{2}\times2\sqrt{2}R45^{\circ}$ reconstruction. In order to allow for a direct comparison between magnetic moments obtained from sum-rule analysis and DFT we calculate the dipolar term $7$, which is also important in view of the magnetic anisotropy of the molecule. The measured X-ray magnetic circular dichroism shows a strong dependence on the photon incidence angle, which we could relate to a huge value of $7$, e.g. on Cu(001) $7$ amounts to -2.07\,\mbo{} for normal incidence leading to a reduction of the effective spin moment $m_s + 7$. Calculations have also been performed to study the influence of possible ligands such as Cl and O atoms on the magnetic properties of the molecule and the interaction between molecule and surface, because the experimental spectra display a clear dependence on the ligand, which is used to stabilize the molecule in the gas phase. Both types of ligands weaken the hybridization between surface and porphyrin molecule and change the magnetic spin state of the molecule, but the changes in the X-ray absorption are clearly related to residual Cl ligands.Comment: 17 figures, full articl