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Sudden commencement associated discontinuities in interplanetary magnetic field observed by IMP 3 satellite, stressing shocks and tangential and rotational discontinuities
Plasma and magnetic field measurements of tangential discontinuities in solar wind by Pioneer 6, considering velocity shears and rotation of sun
Summary A new continuous‐discontinuous strategy for the computational modeling of crack propagation within the context of phase‐field models of fracture is presented. The method is designed to introduce and update a sharp crack surface within an evolving damage band and to enhance the kinematics of the finite element approximation accordingly. The proposed approach relies on three key elements. First, we propose the use of a crack length functional to provide a trigger for initiating a continuous to discontinuous transition. Next, the crack path identification is addressed by introducing the concept of an auxiliary damage field that varies with an extension of the sharp crack surface. The sharp crack surface is extended through an optimization algorithm, in which the difference between the auxiliary field and the actual damage field stemming from the phase‐field framework is minimized. Finally, a strong discontinuity is inserted in the wake of the diffuse crack tip with the extended finite element method, completing the continuous to discontinuous transition. Several benchmark problems in two‐dimensional quasi‐static fracture mechanics are presented to demonstrate the accuracy and robustness of the method.
Geomagnetic field sudden increases or storm sudden commencements are compared with measurements of electron content of the solar wind. The latter data are obtained by a radio propagation experiment, which measures the electron content along a radio path between transmitters on the ground and several spacecraft in solar orbit. Measurements were examined during time periods that included 40 of the geomagnetic disturbances (gmd) reported between January 1, 1966, and June 30, 1969. These studies indicate that some widely reported solar wind discontinuities have been detected by the radio propagation experiment. Eleven of the 40 gmd were classified as storm sudden commencements (ssc), which usually result when a shock in the solar wind strikes the magnetosphere. The relative timings of these 11 events are consistent with conclusions drawn from comparisons of experiment geometry to prevailing shock models. Compared to the nature of these 11 events, the characteristics of the solar-wind disturbances corresponding to the remaining 29 gmd were generally found to have been less favorable for detection by the radio propagation experiment, but sharp changes in the content were clearly evident at the time of several minor gmd.
It is proposed that the principal cause of the confined solar flare is the dissipation of magnetic energy at the many small-scale pre-existing tangential discontinuities in the local bipolar magnetic field. The discontinuities are a consequence of the continuous shuffling and intermixing of the footpoints of the bipolar field by the turbulent photospheric granules. The X-ray corona within the bipolar field is presumed to be a consequence of the continuing dissipation by reconnection at these discontinuities. A flare results when static deformation and/or internal agitation of the field stimulates the onset of rapid reconnection at the many small internal discontinuities. The discontinuities are partially exhausted by the flare, so that the post-flare X-ray emission of that particular loop is substantially below the pre-flare level for a period of some hours while the discontinuities are being rejuvenated.
Direct integration of the force-free field equation del x B = alpha B, in the simple case of the local deformation of a laminar field, produces field configurations containing tangential discontinuities (current sheets). Whereas continuous solutions allow only restricted field topologies, the discontinuities provide the necessary release from those restrictions in more general topologies. Magnetic fields in nature are strongly deformed by convection, so as to contain significant internal discontinuities. The bipolar magnetic fields containing the active X-ray corona of the sun are a case in point. It appears that the dissipation caused by the discontinuities may be the primary heat source producing the X-ray corona.
Interplanetary magnetic field reconnection at tangential discontinuities, discussing coincidence with proton temperature maxima in solar wind during magnetic storm
In this paper, we present a first-order Stress-Hybrid Virtual Element Method (SH-VEM) on six-noded triangular meshes for linear plane elasticity. Here, we adopt the Hellinger–Reissner variational principle to construct a weak equilibrium condition and a stress based projection operator. In each element, the stress projection operator is expressed in terms of the nodal displacements, which leads to a displacement based formulation. This stress-hybrid approach assumes a globally continuous displacement field while the stress field is discontinuous across each element. The stress field is initially represented by divergence-free tensor polynomials based on Airy stress functions, but we also present a formulation that uses a penalty term to enforce the element equilibrium conditions, referred to as the Penalty Stress-Hybrid Virtual Element Method (PSH-VEM). Numerical results are presented for PSH-VEM and SH-VEM, and we compare their convergence to the composite triangle FEM and B-bar VEM on benchmark problems in linear elasticity. The SH-VEM converges optimally in the L 2 norm of the displacement, energy seminorm, and the L 2 norm of hydrostatic stress. Furthermore, the results reveal that PSH-VEM converges in most cases at a faster rate than the expected optimal rate, but it requires the selection of a suitably chosen penalty parameter.
Conventional basin-by-basin approaches to calibrate hydrologic models are limited to gauged basins and typically result in spatially discontinuous parameter fields. Moreover, the consequent low calibration density in space falls seriously behind the need from present-day applications like high resolution river hydrodynamic modeling. In this study we calibrated three key parameters of the Variable Infiltration Capacity (VIC) model at every 1/8° grid-cell using machine learning-based maps of four streamflow characteristics for the conterminous United States (CONUS), with a total of 52,663 grid-cells. This new calibration approach, as an alternative to parameter regionalization, applied to ungauged regions too. A key difference made here is that we tried to regionalize physical variables (streamflow characteristics) instead of model parameters whose behavior may often be less well understood. The resulting parameter fields no longer presented any spatial discontinuities and the patterns corresponded well with climate characteristics, such as aridity and runoff ratio. The calibrated parameters were evaluated against observed streamflow from 704/648 (calibration/validation period) small-to-medium-sized catchments used to derive the streamflow characteristics, 3941/3809 (calibration/validation period) small-to-medium-sized catchments not used to derive the streamflow characteristics as well as five large basins. Comparisons indicated marked improvements in bias and Nash-Sutcliffe efficiency. Model performance was still poor in arid and semiarid regions, which is mostly due to both model structural and forcing deficiencies. Although the performance gain was limited by the relative small number of parameters to calibrate, the study and results here served as a proof-of-concept for a new promising approach for fine-scale hydrologic model calibrations.
Applying an external magnetic field to laser-driven inertial confinement fusion implosions is a promising approach for enhancing fusion yield. The field is compressed with the plasma, producing a magnetized hotspot that anisotropically suppresses thermal losses and traps alpha particles, making performance sensitive to the compressed field orientation. Here, we derive a simple, readily applicable analytic model that enables rapid evaluation of the compressed field topology and show that ablation into the hotspot amplifies the central field, while the ablated ice near the hotspot edge develops a decaying, radially bent field, with a discontinuity in the field direction. The radially bent field renders thermal insulation at the hotspot edge negligible and largely independent of the applied field strength, whereas insulation in the hotspot core still depends strongly on the applied field. Applying the model to non-axial initial field configurations, we find that an initially applied mirror field provides the greatest suppression, followed by the standard axial field.
Three-dimensional Helios plasma and field data are used to investigate the relative changes in direction of the velocity and magnetic field vectors across tangential discontinuities (TDs) in the solar wind at solar distances of 0.29-0.50 AU. It is found for TDs with large Delta-v and (Delta-B)/B that Delta-v and Delta-B are closely aligned with each other, in agreement with the unexpected results of previous studies of TDs observed at 1 AU and beyond. It is shown that this effect probably results from the destruction by the Kelvin-Helmholtz instability of TDs for which Delta-v and Delta-B are not aligned. The observed decrease in the number of interplanetary discontinuities with increasing solar distance may be associated with the growth of the Kelvin-Helmholtz instability with decreasing Alfven speed.
We developed a three-dimensional radiative transfer code for an ultra-relativistic background flow-field by using the Monte Carlo (MC) method in the context of gamma-ray burst (GRB) emission. For obtaining reliable simulation results in the coupled computation of MC radiation transport with relativistic hydrodynamics which can reproduce GRB emission, we validated radiative transfer computation in the ultra-relativistic regime and assessed the appropriate simulation conditions. The radiative transfer code was validated through two test calculations: (1) computing in different inertial frames and (2) computing in flow-fields with discontinuous and smeared shock fronts. The simulation results of the angular distribution and spectrum were compared among three different inertial frames and in good agreement with each other. If the time duration for updating the flow-field was sufficiently small to resolve a mean free path of a photon into ten steps, the results were thoroughly converged. The spectrum computed in the flow-field with a discontinuous shock front obeyed a power-law in frequency whose index was positive in the range from 1 to 10 MeV. The number of photons in the high-energy side decreased with the smeared shock front because the photons were less scattered immediately behind the shock wave due to the small electron number density. The large optical depth near the shock front was needed for obtaining high-energy photons through bulk Compton scattering. Even one-dimensional structure of the shock wave could affect the results of radiation transport computation. Although we examined the effect of the shock structure on the emitted spectrum with a large number of cells, it is hard to employ so many computational cells per dimension in multi-dimensional simulations. Therefore, a further investigation with a smaller number of cells is required for obtaining realistic high-energy photons with multi-dimensional computations.
The paper begins with a short overview of the recent work done in the field of discontinuous reinforced composites, focusing on the different parameters which influence the material behavior of discontinuous reinforced composites, as well as the various analysis approaches undertaken. Based on this overview it became evident that in order to investigate the enumerated effects in an efficient and comprehensive manner, an alternative approach to the computationally intensive finite-element based micromechanics approach is required. Therefore, an investigation is conducted to demonstrate the utility of utilizing the generalized method of cells (GMC), a semi-analytical micromechanics-based approach, to simulate the elastic and elastoplastic material behavior of aligned short fiber composites. The results are compared with simulations using other micromechanical based mean field models and finite element (FE) unit cell models found in the literature given elastic material behavior, as well as finite element unit cell and a new semianalytical elastoplastic shear lag model in the inelastic range. GMC is shown to definitely have a window of applicability when simulating discontinuously reinforced composite material behavior.
The paper begins with a short overview of the recent work done in the field of discontinuous reinforced composites, focusing on the different parameters which influence the material behavior of discontinuous reinforced composites, as well as the various analysis approaches undertaken. Based on this overview it became evident, that in order to investigate the enumerated effects in an efficient and comprehensive manner, an alternative approach to the computationally intensive finite-element based micromechanics approach is required. Therefore, an investigation is conducted to demonstrate the utility of utilizing the generalized method of cells (GMC), a semi-analytical micromechanics-based approach, to simulate the elastic and elastoplastic material behavior of aligned short fiber composites. The results are compared with (1) simulations using other micromechanical based mean field models and finite element (FE) unit cell models found in the literature given elastic material behavior, as well as (2) finite element unit cell and a new semianalytical elastoplastic shear lag model in the inelastic range. GMC is shown to definitely have a window of applicability when simulating discontinuously reinforced composite material behavior.
Here, we describe mathematical methods based on optimizing a modified non-linear flux function (MFF) to evaluate whether odd-parity perturbations affect the local closure of magnetic field lines in field-reversed configurations. Using the MFF methodology, quantitative formulas are derived that provide the shift of the field minimum and the threshold for field-line opening, a discontinuous change in field topology.
Large convective electric fields of the order of 10 mV/m (sometimes as high as 22 mV/m) are observed at rotational magnetopause discontinuities. These observations were made with the long cylindrical (179-m base line) probes carried on the ISEE 1 satellite. These electric field observations yield convective velocity magnitudes (equal to the cross product of the vector E and the vector B, the latter divided by the square of the magnitude of B) of the order of 150 km/s. In this format for the convective velocity magnitudes, some of these observations are similar to the high speed plasma velocity observations that were made at the magnetopause with the plasma experiment carried on the ISEE 1 satellite. It is shown that, for many of these magnetopause crossings, there exists a special moving coordinate system where the observed electric fields vanish. Such a unique reference system is often used in theoretical studies of magnetic discontinuities. This special coordinate system does not move at the local plasma velocity but moves instead at a velocity intermediate between the convective velocity and the local Alfven velocity. It is used here as a diagnostic tool for the experimental investigation of rotational discontinuities at the magnetopause.
The Harang discontinuity, the area separating the positive and negative bay regions in the midnight sector of the auroral zone, is a focal point for changes in behavior of many phenomena. Through this region the electric field rotates through the west from a basically northward field in the positive bay region to a basically southward field in the negative bay region, appearing as a reversal in a single axis measurement; 32 of these reversals have been identified in the OGO-6 data from November and December, 1969. The discontinuity is dynamic in nature, moving southward and steepening its latitudinal profile as magnetic activity is increased. As activity decreases it relaxes poleward and spreads out in latitudinal width. It occurs over several hours of magnetic local time. The boundary in the electric field data is consistent with the reversal of ground magnetic disturbances from a positive to negative bay condition. The discontinuity is present in the electric field data both during substorms and during quiet times and appears to define a pattern on which other effects can occur.
In order to extend the conventional baroclinic instability concept, one has to picture the growth process as resulting from the superposition of two neutrally stable baroclinic waves, an upper and a lower one, each wave propagating along a near-discontinuity in the potential vorticity (PV) field. The PV discontinuity for the lower wave is given by the non-uniformity of the thermal field at the ground, while the discontinuity for the upper wave is given by the contrast, in the 400 to 200 mb range, between the high-PV polar stratosphere and the low-PV subtropical troposphere. The horizontal PV radients mentioned are approximately opposed to each other, causing the wo waves to travel in the opposite direction. As Hoskins et al. (1985) show convincingly, a phase lock between the upper and lower wave may occur, coupled with a tendency toward mutual amplification. The conceptual model just outlined is particularly attractive to synoptic meteorologists because it does not require the two waves to be of initially small amplitude and thus does not fly in the face of observational evidence. This model, by allowing a finite perturbation velocity and a considerable range of relative phase speeds at the time when the upper and lower wave reach the proper phase lag for amplification, may lead to growth rates larger than those predicted by linear theory. aba R.J.F.