ISEE Measurements Research Articles

Large Deviations for the Annealed Ising Model on Inhomogeneous Random Graphs: Spins and Degrees

We prove a large deviations principle for the total spin and the number of edges under the annealed Ising measure on generalized random graphs. We also give detailed results on how the annealing over the Ising model changes the degrees of the vertices in the graph and show how it gives rise to interesting correlated random graphs.

Ferromagnetic Ising measures on large locally tree-like graphs

We consider the ferromagnetic Ising model on a sequence of graphs GnGn converging locally weakly to a rooted random tree. Generalizing [Probab. Theory Related Fields 152 (2012) 31–51], under an appropriate “continuity” property, we show that the Ising measures on these graphs converge locally weakly to a measure, which is obtained by first picking a random tree, and then the symmetric mixture of Ising measures with ++ and −− boundary conditions on that tree. Under the extra assumptions that GnGn are edge-expanders, we show that the local weak limit of the Ising measures conditioned on positive magnetization is the Ising measure with ++ boundary condition on the limiting tree. The “continuity” property holds except possibly for countable many choices of ββ, which for limiting trees of minimum degree at least three, are all within certain explicitly specified compact interval. We further show the edge-expander property for (most of) the configuration model graphs corresponding to limiting (multi-type) Galton–Watson trees.

Critical Ising on the Square Lattice Mixes in Polynomial Time

The Ising model is widely regarded as the most studied model of spin-systems in statistical physics. The focus of this paper is its dynamic (stochastic) version, the Glauber dynamics, introduced in 1963 and by now the most popular means of sampling the Ising measure. Intensive study throughout the last three decades has yielded a rigorous understanding of the spectral-gap of the dynamics on \({\mathbb{Z}^2}\) everywhere except at criticality. While the critical behavior of the Ising model has long been the focus for physicists, mathematicians have only recently developed an understanding of its critical geometry with the advent of SLE, CLE and new tools to study conformally invariant systems.A rich interplay exists between the static and dynamic models. At the static phase-transition for Ising, the dynamics is conjectured to undergo a critical slowdown: At high temperature the inverse-gap is O(1), at the critical β c it is polynomial in the side-length and at low temperature it is exponential. A seminal series of papers verified this on \({\mathbb{Z}^2}\) except at β = β c where the behavior remained a challenging open problem.Here we establish the first rigorous polynomial upper bound for the critical mixing, thus confirming the critical slowdown for the Ising model in \({\mathbb{Z}^2}\) . Namely, we show that on a finite box with arbitrary (e.g. fixed, free, periodic) boundary conditions, the inverse-gap at β = β c is polynomial in the side-length. The proof harnesses recent understanding of the scaling limit of the critical Fortuin-Kasteleyn representation of the Ising model together with classical tools from the analysis of Markov chains.

The weak limit of Ising models on locally tree-like graphs

We consider the Ising model with inverse temperature β and without external field on sequences of graphs G n which converge locally to the k-regular tree. We show that for such graphs the Ising measure locally weakly converges to the symmetric mixture of the Ising model with + boundary conditions and the − boundary conditions on the k-regular tree with inverse temperature β. In the case where the graphs G n are expanders we derive a more detailed understanding by showing convergence of the Ising measure conditional on positive magnetization (sum of spins) to the + measure on the tree.

Rapid density fluctuations in the solar wind

Abstract. Electron density fluctuations (up to 2.5 Hz) in the solar wind have been studied, using the EFW experiment on the Cluster spacecraft, which measures density through measurements of the biased probe potentials relative to the spacecraft. The density fluctuation spectra obtained from the EFW probe potential variations are compared to earlier, OGO 5, measurements of ion density fluctuations and ISEE measurements of electron density fluctuations, and are consistent with them. The electric fields corresponding to the electron density fluctuations are extremely small compared with what would be obtained if the electron fluctuations were not cancelled out by nearly equal ion density fluctuations. This is consistent with the nature of ion acoustic waves. In agreement with ISEE work, the fluctuations are proportional to the ambient density. Correlation with magnetic fluctuations is weak, essentially nonexistent during part of the period studied. This might be expected as magnetic fluctuations are known to be nearly incompressible, but even the correlation with fluctuations in the magnitude of B is very small. However, many structures which apparently are pressure balance structures are found. Pressure balance structures are the nearly perpendicular propagation limit of ion acoustic waves. As ion acoustic waves are strongly damped in plasmas like the solar wind at least if the plasma is taken as Maxwellian, it has always been a puzzle as to why they are found there. We speculate that these waves are created by mode conversion from magnetic fluctuations, and may represent part of the dissipation process for these.

Current fluctuations in the Earth's magnetosphere caused by lower-hybrid-drift turbulence

Nonlinear calculations of the anomalous electrical conductivity in the plasma of the earth's plasma mantle, the tail plasma sheet boundary layer and the ionospheric F-region density-trough are presented provided that lower-hybrid-drift turbulence exists. It is shown that in these regions the stabilization of the wave growth is mainly caused by current relaxation. Further, the fluctuations of the electrical currents are estimated via Ampère's and Ohm's laws. It is found that the lower-hybrid-drift turbulence causes maximum anomalous collision frequencies of the order of 10 −2 Hz in the magnetosphere. The maximum current fluctuations are about 3 10 −9 A/m 2. The theoretical results are in agreement with ISEE and Prognoz-8 measurements.

The oscillatory behavior of the high-temperature expansion of Dyson's hierarchical model: A renormalization group analysis

We calculate 800 coefficients of the high-temperature expansion of the magnetic susceptibility of Dyson's hierarchical model with a Landau-Ginzburg measure. Log-periodic corrections to the scaling laws appear as in the case of a Ising measure. The period of oscillation appears to be a universal quantity given in good approximation by the logarithm of the largest eigenvalue of the linearized RG transformation, in agreement with a possibility suggested by K. Wilson and developed by Niemeijer and van Leeuwen. We estimate $\gamma $ to be 1.300 (with a systematic error of the order of 0.002) in good agreement with the results obtained with other methods such as the $\epsilon $-expansion. We briefly discuss the relationship between the oscillations and the zeros of the partition function near the critical point in the complex temperature plane.

Characterization of small‐scale structures at the magnetopause from ISEE measurements

High‐resolution data (covering up to 8 Hz) from the flux gate magnetometers on the two ISEE spacecraft are used to analyze ultralow‐frequency (ULF) fluctuations observed at the magnetopause and in the adjacent layers. Intersatellite correlations are computed to show that the same structure can be identified in the fluctuations observed on both spacecraft when the interspacecraft distance is small. Then the possibility of deducing the velocity of the structure from two‐point measurements is discussed; it is shown that it can be estimated only in certain cases.

Suprathermal electrons at Earth's bow shock

A hot, suprathermal population of electrons is often present near the Earth's bow shock. The overall morphology of this hot population as observed with the Los Alamos/Garching fast plasma experiments on ISEE 1 and 2 in the energy range from 1 to 20 keV is much as described previously by others working primarily with more energetic particle measurements. In particular, at energies below 20 keV the flux of suprathermal electrons is most intense immediately downstream from the shock and decreases in intensity with increasing penetration into the magnetosheath. Upstream fluxes of electrons in this energy range are generally considerably weaker than are the downstream fluxes. The major new results from our ISEE measurements are as follows: (1) The suprathermal electrons are commonly found downstream from perpendicular and quasi‐perpendicular portions of the shock but not downstream from quasi‐parallel portions. (2) The suprathermal electron spectrum extends smoothly out of the shocked solar wind spectrum generally as a power law in energy with an exponent in the range from −3 to −4. (3) Angular distributions for the suprathermal electrons are generally isotropic immediately downstream of the shock ramp, but an anisotropy perpendicular to the magnetic field usually develops with increasing penetration into the magnetosheath. (4) Suprathermal electrons are often first observed within the shock layer itself as a field‐aligned beam escaping upstream. We interpret these observations in terms of a qualitative model wherein the suprathermal electrons are accelerated out of the solar wind thermal and halo populations as the solar wind convects across perpendicular portions of the shock. Subsequently, the suprathermal electrons leak back upstream along the magnetic field to form the backstreaming fluxes of energetic electrons commonly observed in the Earth's foreshock region. Although the mechanism of acceleration is presently uncertain, we believe it is unlikely that these electrons are accelerated by magnetic mirroring of upstream electrons at the shock or that they result from a simple adiabatic mapping of electron distributions from upstream to downstream.

Simultaneous polar cap and magnetotail observations of intense polar rain

Six prolonged episodes of intense polar rain with average or above average temperatures occured during the four‐month period from mid‐February to mid‐June 1978. Electrons with energies up to 1 keV are observed throughout these events, and 9‐keV electrons occasionally are detected. To investigate whether this intense polar rain is accelerated within the magnetosphere, we compare DMSP F2 electron measurements made at low altitudes over the polar cap with near‐simultaneous ISEE 1 electron measurements made in the northern tail lobe at distances between 10 and 22.6 RE. In some cases, the electron spectra measured at low altitude are nearly identical to those measured in the tail lobe. In other cases, intensities are similar, but the phase space densities measured by DMSP exceed those measured by ISEE at energies above 500 eV. The episodes with extremely similar spectra show that intense polar rain can pass through the tail lobes without undergoing acceleration between 22.6 RE and 800 km altitude. Three‐dimensional ISEE measurements of electron distribution functions suggest that the field‐aligned pitch angle anisotropy of the tail lobe electron population may account for most if not all of the differences when the spectra do not match.

The boundary layers as the primary transport regions of the Earth's magnetotail

A comprehensive survey of ISEE and IMP LEPEDEA plasma measurements in the earth's magnetotail reveals that the magnetospheric boundary layer and the plasma sheet boundary layer are the primary transport regions there. These plasma measurements also distinguish various components of the plama sheet, including the central plasma sheet and plasma sheet boundary layer. A significant new result reported here is the existence of cold‐and hot‐plasma components that are spatially copresent within the central plasma sheet. Such plasma components cannot be explained merely by temporal variations in spectra involving the entire plasma sheet. Contributions to a low‐temperature component of the plasma sheet enter directly from the boundary layer located along the magnetotail flanks. Field‐aligned flows predominate within the plasma sheet boundary layer, which is almost always present and is located near the northern and southern border of the plasma sheet. The plasma sheet boundary layer comprises highly anisotropic ion distributions, including counterstreaming ion beams, that evolve into the hot, isotropic component of the plasma sheet. Tailward acceleration regions generate these ion beams with plasma input from the magnetospheric boundary layer. Antisunward flowing ion beams, at E/q < 1 kV and of ionospheric composition, are frequently observed in the plasma sheet boundary layer and in the tail lobes. These ion beams are likely accelerated at low altitude over the polar cap and especially along auroral field lines. An ionospheric component of the plasma sheet is supplied from this source via the plasma sheet boundary layer. On the basis of a survey of ∼2000 three‐dimensional velocity distribution functions sampled by the ISEE LEPEDEA in the magnetotail we find that interpretations based solely on moments parameters are inevitably inadequate for inferring plasma sources and acceleration processes. We find that earthward flowing ions or counterstreaming beams are often observed near expansive phase onset under conditions for which antisunward ion flow is predicted by the near‐earth neutral line model of magnetospheric substorms. Magnetotail plasma flows sampled out to 38 RE and reported as typical of onset and recovery of magnetospheric substorms can only be adequately understood by considering spatial and temporal variations of the boundary layers described above.

Dynamics of the 1054 UT March 22, 1979, substorm event: CDAW 6

The physical processes involved in the transfer of energy from the solar wind to the magnetosphere, and release associated with substorms, have been examined in a sequence of Coordinated Data Analysis Workshops (CDAW 6). Magnetic storms of March 22 and 31, 1979, were chosen to study the problem, using a data base from 13 spacecraft and about 130 ground‐based magnetometers. This paper describes the March 22 storm, in particular the large, isolated substorm at 1054 UT which followed an interval of magnetic calm. We summarize the observations in the solar wind, in various regions of the magnetosphere, and at the ground, synthesizing these observations into a description of the substorm development. We then give our interpretation of these observations and test their consistency with the reconnection model. The substorm appears to have been generated by a southward turning of the interplanetary magnetic field associated with a current sheet crossing. Models of ionospheric currents derived from ground data show the substorm had three phases of development. During the first phase, a two‐celled convection current system developed in the polar cap as synchronous spacecraft on the nightside recorded an increasingly taillike field and the ISEE measurements show that the near‐earth plasma sheet thinned. In the second phase, possibly triggered by sudden changes in the solar wind, a one‐celled current system was added to the first, enhancing the westward electrojet. During this phase the synchronous orbit field became more dipolar, and the plasma sheet magnetic field turned strongly southward as rapid tailward flow developed soon after expansion onset, suggesting that a neutral line formed in the near‐earth plasma sheet with subsequent plasmoid ejection. In the third phase, which occurred after interplanetary magnetic field turned northward, the magnetospheric current systems decayed as the plasma sheet expanded and the flow turned earthward. The data from this event support the notion that substorms include two major processes of energy dissipation: one directly driven by the solar wind and one driven by release of energy stored in the geomagnetic tail. The near‐tail data suggest that one or more neutral lines formed earthward of the ISEE spacecraft. However, all the signatures of plasma flow and energetic particles can be explained only by postulating a complex series of events. While this reconnection picture represents the interpretations of many of the CDAW 6 participants, it is not a consensus viewpoint.

Magnetic turbulence and diffusion processes in the magnetopause boundary layer

The thickness of the magnetopause boundary layer can be explained by anomalous cross‐field diffusion of magnetosheath protons resonating with either electrostatic or electromagnetic waves (Tsurutani and Thorne, 1982). Whereas the first mechanism was favored by these authors on the basis of ISEE measurements, GEOS data, which are obtained when the magnetosphere is contracted, seem to show that the second one may be more important, at least during disturbed conditions. The special relationship which exists between the proton resonant energy and the frequency of right‐handed electromagnetic waves leads to a preferential diffusion of protons of a few keV. The ability of electromagnetic waves to evacuate the energy dissipated during the generation of turbulence is also discussed.