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I use the example of the Earth's orbit to illustrate the principle behind the Akaike Information Criterion, and refute the misconception that the criterion, by definition, discards more complex models in favour of simpler ones.
The resistive magnetohydrodynamic (MHD) equations as usually defined in the quasineutral approximation refer to a system of 14 scalar equations in 14 scalar variables, hence are determined to be complete and soluble. These equations are a combination of Navier-Stokes and a subset of Maxwell's. However, one of the vector equations is actually an identity when viewed from the potential formulation of electrodynamics, hence does not determine any degrees of freedom. Only by reinstating Gauss's law does the system of equations become closed, allowing for the determination of both the current and mass flow velocity from the equations of motion. Results of a typical analysis of the proposed electromagnetic hydrodynamic model including the magnetization force are presented.
Applying Newtonian dynamics in five dimensions rather than four, to a universe that is closed, isotropic and expanding,suggests that under certain circumstances an additional and previously unidentified acceleration, a_A, can arise affecting the four dimensional motion of spacecraft. The two cases of this acceleration being either real or virtual are considered. In the real case, simple estimates of a_A are shown to be in partial agreement with reported acceleration anomalies from several Earth flybys and from the Pioneer spacecraft. However, these estimates do not fully reconcile with radio Doppler tracking data. The virtual case, by contrast, appears to overcome these and other difficulties with the real case, and is discussed in an addendum. Furthermore, the virtual case has an altitude dependence which makes detection of any anomaly unlikely above ~2000 km. Equations governing this additional acceleration have been derived from first principles, without the introduction of free parameters or new constants and without amendment to the law of gravity.
In this Chapter we deal with the attempts to measure the general relativistic gravitomagnetic Lense-Thirring effect with the Satellite Laser Ranging (SLR) technique applied to the existing LAGEOS and LAGEOS II terrestrial satellites and to the recently approved LARES.
Recently Zhang et al. [2008] presented a statistical study of sizes and relative geoeffectiveness of ICMEs (bodies of magnetic clouds) and preceding sheaths for 46 events responsible for intense (Dst < -100 nT) geomagnetic storms in 1996-2005 in which only a single ICME was responsible for generating the storm. Here we would like to comment several results and conclusions of this paper.
The anisotropic fluid equations governing a frictionless obliquely-flowing plasma around an essentially arbitrarily shaped three-dimensional ion-absorbing object in a strong magnetic field are solved analytically in the quasi-neutral drift-approximation, neglecting parallel temperature gradients. The effects of transverse displacements traversing the magnetic presheath are also quantified. It is shown that the parallel collection flux density dependence upon external Mach-number is $n_\infty c_s \exp[-1 -(M_{\parallel\infty}- M_\perp\cotθ)]$ where $θ$ is the angle (in the plane of field and drift velocity) of the object-surface to the magnetic-field and $M_{\parallel\infty}$ is the external parallel flow. The perpendicular drift, $\M_\perp$, appearing here consists of the external $\E\wedge\B$ drift plus a weighted sum of the ion and electron electron diamagnetic drifts that depends upon the total angle of the surface to the magnetic field. It is that somewhat counter-intuitive combination that an oblique (transverse) Mach probe experiment measures.
The goal of the recently approved space-based LARES mission is to measure the general relativistic Lense-Thirring effect in the gravitational field of the spinning Earth at a repeatedly claimed 1% accuracy by combining its node Omega with those of the existing LAGEOS and LAGEOS II laser-ranged satellites. In this paper we show that, in view of the lower altitude of LARES (h=1450 km) with respect to LAGEOS and LAGEOS II (h\approx 6000 km), the cross-coupling between the effect of the atmospheric drag, both neutral and charged, on the inclination of LARES and its classical node precession due to the Earth's oblateness may induce a 3-9% year^-1 systematic bias on the total relativistic precession. Since its extraction from the data will take about 5-10 years, such a perturbing effect may degrade the total accuracy of the test, especially in view of the large uncertainties in modeling the drag force.
Howard and Simnett (HS) employed a new technique for associating LASCO CMEs to SMEI ICMEs. In order to extrapolate the SMEI data back to the LASCO field of view they used nonlinear trajectories, dependent on a speed and direction, what is more realistic than the linear extrapolation with only one parameter (a speed). However, there are two errors and one mistake in their procedure: (1) HS used two free parameters of the direction, whereas only one can be freely selected, because the second is provided by SMEI data. As a result, the directions determined by HS are incorrect. (2) HS overlooked that, since the trajectory depends on more than one parameter, there is a broad set of trajectories, for various speeds and directions, matching the event, and thus a broad range of the onset times. HS select only one trajectory for each SMEI event. Therefore the associations made by them are incomplete, and they should be reexamined. As long as it is not done any conclusion about CMEs undetected by solar coronagraphs are premature. (3) HS made some mistake in determination of the SMEI speeds. The speeds given in their Table 1 are about twice as high as those demanded to obtain the onset times given in the table. It explains why the SMEI speed distribution is excessively shifted toward high speeds ; hence, there is no reason to search for a physical explanation.
In January 2004, the Stardust spacecraft flew through the dust of comet 81P/Wild 2 and captured specks of the cometary dust. On analysis of the comet 81P/Wild 2 samples, it was found that they contain materials found in the coldest and hottest region of the early solar nebula, strongly suggesting 'mixing' on the grandest scale. Here it is suggested that if microorganisms were present in the early solar nebula, as required by the hypothesis of cometary panspermia, then in the light of the Stardust findings, life was already present in the very material that formed the planetary bodies.
In this paper we put forward a proposal to use Near Earth Objects as radiation shield for deep space exploration. In principle these objects can provide also a spacious habitat for the astronauts and their supplies on their journeys. We undertake also a detailed assessment of this proposal for a mission from Earth to Mars.
This report presents new EOS and strength models for use in numerical hydrocode simulations of dust impacts on the NASA solar probe space vehicle. This spacecraft will be subjected to impact at velocities up to 300 km/s, producing pressures as high as 100 TPa and temperatures as high as 200 eV. Hence the material models must treat a variety of physical and chemical phenomena, including solid-solid transitions, melting and vaporization, chemical reactions, electronic excitation and ionization. The EOSPro code is used to develop tabular EOS that include these effects. The report discusses the theoretical methods used to create the new EOS tables and constitutive models for six materials--Al2O3, two porous carbon materials, fused SiO2, a silicone elastomer, and germanium--which will be used in the thermal protection shield (TPS) and solar cells, the components most vulnerable to dust impacts. It also presents the results of hydrocode simulations of dust impacts on the TPS and on glass targets. It discusses the importance of radiation contributions to the EOS and the importance of reactions between Al2O3 and carbon during impacts. It makes recommendations for additional work, including experiments for testing the accuracy and reliability of the hydrocode simulations as well as for improving and calibrating the material models.
Statistical properties of the Sun's photospheric turbulent magnetic field, especially those of the Active Regions (ARs), have been studied using the line-of-sight data from magnetograms taken by SOHO and several other instruments (see e.g. Abramenko et al (2002, 2003),Abramenko and Yurchyshyn (2010)). This includes structure functions and their exponents, flatness curves and correlation functions. In these works, the dependence of structure function exponents ($ζ_p$) of the order of the structure functions ($\it{p}$) was modeled using a non-intermittent K41 model. It is now well known that the ARs are highly turbulent and are associated with strong intermittent events. In this paper we compare some of the observations from Abramenko et al (2003) with the log-Poisson model (Biskamp 2003) used for modeling intermittent MHD turbulent flows. Next, we analyze the structure function data obtained from the direct numerical simulations (DNS) of homogeneous, incompressible 3D-MHD turbulence in three cases: sustained by forcing, freely decaying and a flow initially driven and later allowed to decay (case 3). The respective DNS replicate the properties seen in the plots of $ζ_p$ against $\it{p}$ of ARs. We also reproduce the trends and changes observed in intermittency in flatness [Abramenko and Yurchyshyn (2010)] and correlation functions [Abramenko et al (2003)] of ARs. It is suggested from this analysis that an AR in the onset phase of a flare can be treated as a forced 3D-MHD turbulent system in its simplest form and that the flaring stage is representative of decaying 3D-MHD turbulence. It is also inferred that significant changes in intermittency from the initial onset phase of a flare to its final peak flaring phase, are related to the time taken by the system to reach the initial onset phase.
Energetic (suprathermal) solar particles, accelerated in the interplanetary medium, contribute to the solar wind pressure, in particular during high solar activity periods. We estimated the effect of the increase of solar wind pressure due to suprathermal particles on magnetospheric transmissivity of galactic cosmic rays in the case of one recent solar event.
The Cosmic Rays propagation was studied in details using the HelMod-2D Monte Carlo code, that includes a general description of the diffusion tensor, and polar magnetic-field. The Numerical Approach used in this work is based on a set of Stochastic Differential Equations fully equivalent to the well know Parker Equation for the transport of Cosmic Rays. In our approach the Diffusion tensor in the frame of the magnetic field turbolence does not depends explicitly by Solar Latitude but varies with time using a diffusion parameter obtained by Neutron Monitors. The parameters of the Model were tuned using data during the solar Cycle 23 and Ulysses latitudinal Fast Scan in 1995. The actual parametrization is able to well reproduce the observed latitudinal gradient of protons and the southward shift of the minimum of latitudinal intensity. The description of the model is also available online at website www.helmod.org. The model was then applied on Pamela/Ulysses proton intensity from 2006 up to 2009. The model during this 4-year continous period agree well with both PAMELA (at 1 AU) and Ulysses data (at various solar distance and solar latitude). The agreement improves when considering the ratio between this data. Studies done also with particles with different charge (e.g. electrons) allow us to explain the presence (or not) of protons and electrons latitudinal gradients observed by Ulysses during the Latitudinal Fast Scan in 1995 and 2007.
The flat Harris current sheet model has become a powerful initial equilibrium in theory and simulation of magnetic reconnection in the magnetotail, at the magnetopause and also in multiple current sheet models of the heliosheath and astrophysics, where it is believed that such structures may become responsible for generation of turbulence and also high energy particles. Here we investigate the philosophy behind the Harris sheet in view of the physical conditions. The kinematic treatment in this note takes care of the different dynamics of ions and electrons.
The average (thermal) gyroradius of charged particles is re-examined from a quantum-mechanical point of view. The straight quantum-mechanical calculation clearly reproduces its conventionally used random-mean-square (rms) expectation value. The quasi-classical approach reproduces its mean expectation value as well thus confirming the purely classical calculation. It shows that the fluctuations in the gyroradius amount to 21.5% of its rms value. This fluctuation is, however, within the usual $\sqrt{2}$-"freedom" range of choice in the definition of the rms gyroradius respectively the mean thermal speed on which the rms value is based, its correct (nonrelativistic) value $v_t^2= 2T_\perp/m_e$ and its simplified version $v_t^2=T_\perp/m_e$.
Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. It is shown that through a parameter $α$, called the pathway parameter, one can connect generalized type-1 beta family of densities, generalized type-2 beta family of densities, and generalized gamma family of densities, in the scalar as well as the matrix cases, also in the real and complex domains. It is shown that when the model is applied to physical situations then the current hot topics of Tsallis statistics and superstatistics in statistical mechanics become special cases of the pathway model, and the model is capable of capturing many stable situations as well as the unstable or chaotic neighborhoods of the stable situations and transitional stages. The pathway model is shown to be connected to generalized information measures or entropies, power law, likelihood ratio criterion or $λ-$criterion in multivariate statistical analysis, generalized Dirichlet densities, fractional calculus, Mittag-Leffler stochastic process, Krätzel integral in applied analysis, and many other topics in different disciplines. The pathway model enables one to extend the current results on quadratic and bilinear forms, when the samples come from Gaussian populations, to wider classes of populations.
Determining the factor M(3000)F2 is very important for ionograms analysis obtained of Ionosonde. M(3000)F2 is the result of the maximum usable frequency (MUF), for to 3000 km distance, divided by the critical frequency of the F2 layer (FoF2). Nowadays, the graphic method to determine the M(3000)F2 is used in Havana station in the ionograms analysis. The purpose of this work is to implement an analytic method that allows us the direct obtaining of M(3000)F2, so it could be programmed and incorporated as part of ionograms elaboration process in Havana station. When is used a PC, some points in the ionogram can be determined. This dataset (f; h') are used to calculate analytically the factor M(3000)F2 . Comparison between the analytic method implemented and the old graphic method are shown. The new method is more accurate and the errors are diminished in the factor M(3000)F2.