Disentangling the Entangled Linkages of Relative Magnetic Helicity

Magnetic helicity, $H$, measures magnetic linkages in a volume. The early theoretical development of helicity focused on magnetically closed systems in $\mathcal{V}$ bounded by $\mathcal{S}$. For magnetically closed systems, $\mathcal{V}\in\mathbb{R}^3=\mathcal{V}+\mathcal{V}^*$, no magnetic flux threads the boundary, $\hat{\boldsymbol{n}}\cdot\boldsymbol{B}|_\mathcal{S}=0$. Berger and Field (1984) and Finn and Antonsen (1985) extended the definition of helicity to relative helicity, $\mathcal{H}$, for magnetically open systems where magnetic flux may thread the boundary. Berger (1999,2003) expressed this relative helicity as two gauge invariant terms that describe the self helicity of magnetic field that closes inside $\mathcal{V}$ and the mutual helicity between the magnetic field that threads the boundary $\mathcal{S}$ and the magnetic field that closes inside $\mathcal{V}$. The total magnetic field that permeates $\mathcal{V}$ entangles magnetic fields that are produced by current sources $\boldsymbol{J}$ in $\mathcal{V}$ with magnetic fields that are produced by current sources $\boldsymbol{J}^*$ in $\mathcal{V}^*$. Building on this fact, we extend Berger's expressions for relative magnetic helicity to eight gauge invariant quantities that simultaneously characterize both of these self and mutual helicities and attribute their origins to currents $\boldsymbol{J}$ in $\mathcal{V}$ and/or $\boldsymbol{J}^*$ in $\mathcal{V}^*$, thereby disentangling the domain of origin for these entangled linkages. We arrange these eight terms into novel expressions for internal and external helicity (self) and internal-external helicity (mutual) based on their domain of origin. The implications of these linkages for interpreting magnetic energy is discussed and new boundary observables are proposed for tracking the evolution of the field that threads the boundary.Comment: 27 pages, 2 figure

What is the relationship between photospheric flow fields and solar flares?

We estimated photospheric velocities by separately applying the Fourier Local Correlation Tracking (FLCT) and Differential Affine Velocity Estimator (DAVE) methods to 2708 co-registered pairs of SOHO/MDI magnetograms, with nominal 96-minute cadence and ~2" pixels, from 46 active regions (ARs) from 1996-1998 over the time interval t45 when each AR was within 45^o of disk center. For each magnetogram pair, we computed the average estimated radial magnetic field, B; and each tracking method produced an independently estimated flow field, u. We then quantitatively characterized these magnetic and flow fields by computing several extensive and intensive properties of each; extensive properties scale with AR size, while intensive properties do not depend directly on AR size. Intensive flow properties included moments of speeds, horizontal divergences, and radial curls; extensive flow properties included sums of these properties over each AR, and a crude proxy for the ideal Poynting flux, the total |u| B^2. Several magnetic quantities were also computed, including: total unsigned flux; a measure of the amount of unsigned flux near strong-field polarity inversion lines, R; and the total B^2. Next, using correlation and discriminant analysis, we investigated the associations between these properties and flares from the GOES flare catalog, when averaged over both t45 and shorter time windows, of 6 and 24 hours. We found R and total |u| B^2 to be most strongly associated with flares; no intensive flow properties were strongly associated with flares.Comment: 57 pages, 13 figures; revised content; added URL to manuscript with higher-quality image

A multi-step nucleation process determines the kinetics of prion-like domain phase separation

The nucleation mechanisms of biological protein phase separation are poorly understood. Here, the authors perform time-resolved SAXS experiments with the low-complexity domain (LCD) of hnRNPA1 and uncover multiple kinetic regimes on the micro- to millisecond timescale. Initially, individual proteins collapse. Nucleation then occurs via two steps distinguished by their protein cluster size distributions

On the analysis of sedimentation velocity in the study of protein complexes

Sedimentation velocity analytical ultracentrifugation has experienced a significant transformation, precipitated by the possibility of efficiently fitting Lamm equation solutions to the experimental data. The precision of this approach depends on the ability to account for the imperfections of the experiment, both regarding the sample and the instrument. In the present work, we explore in more detail the relationship between the sedimentation process, its detection, and the model used in the mathematical data analysis. We focus on configurations that produce steep and fast-moving sedimentation boundaries, such as frequently encountered when studying large multi-protein complexes. First, as a computational tool facilitating the analysis of heterogeneous samples, we introduce the strategy of partial boundary modeling. It can simplify the modeling by restricting the direct boundary analysis to species with sedimentation coefficients in a predefined range. Next, we examine factors related to the experimental detection, including the magnitude of optical aberrations generated by out-of-focus solution columns at high protein concentrations, the relationship between the experimentally recorded signature of the meniscus and the meniscus parameter in the data analysis, and the consequences of the limited radial and temporal resolution of the absorbance optical scanning system. Surprisingly, we find that large errors can be caused by the finite scanning speed of the commercial absorbance optics, exceeding the statistical errors in the measured sedimentation coefficients by more than an order of magnitude. We describe how these effects can be computationally accounted for in SEDFIT and SEDPHAT

Large-Scale Spatial Cross-Calibration of Hinode/SOT-SP and SDO/HMI

We investigate the cross-calibration of the Hinode/SOT-SP and SDO/HMI instrument meta-data, specifically the correspondence of the scaling and pointing information. Accurate calibration of these datasets gives the correspondence needed by inter-instrument studies and learning-based magnetogram systems, and is required for physically-meaningful photospheric magnetic field vectors. We approach the problem by robustly fitting geometric models on correspondences between images from each instrument's pipeline. This technique is common in computer vision, but several critical details are required when using scanning slit spectrograph data like Hinode/SOT-SP. We apply this technique to data spanning a decade of the Hinode mission. Our results suggest corrections to the published Level 2 Hinode/SOT-SP data. First, an analysis on approximately 2,700 scans suggests that the reported pixel size in Hinode/SOT-SP Level 2 data is incorrect by around 1%. Second, analysis of over 12,000 scans show that the pointing information is often incorrect by dozens of arcseconds with a strong bias. Regression of these corrections indicates that thermal effects have caused secular and cyclic drift in Hinode/SOT-SP pointing data over its mission. We offer two solutions. First, direct co-alignment with SDO/HMI data via our procedure can improve alignments for many Hinode/SOT-SP scans. Second, since the pointing errors are predictable, simple post-hoc corrections can substantially improve the pointing. We conclude by illustrating the impact of this updated calibration on derived physical data products needed for research and interpretation. Among other things, our results suggest that the pointing errors induce a hemispheric bias in estimates of radial current density.Comment: Under revisions at ApJ

Density-matrix formalism with three-body ground-state correlations

A density-matrix formalism which includes the effects of three-body ground- state correlations is applied to the standard Lipkin model. The reason to consider the complicated three-body correlations is that the truncation scheme of reduced density matrices up to the two-body level does not give satisfactory results to the standard Lipkin model. It is shown that inclusion of the three-body correlations drastically improves the properties of the ground states and excited states. It is pointed out that lack of mean-field effects in the standard Lipkin model enhances the relative importance of the three-body ground-state correlations. Formal aspects of the density-matrix formalism such as a relation to the variational principle and the stability condition of the ground state are also discussed. It is pointed out that the three-body ground-state correlations are necessary to satisfy the stability condition

On computational approaches for size-and-shape distributions from sedimentation velocity analytical ultracentrifugation

Sedimentation velocity analytical ultracentrifugation has become a very popular technique to study size distributions and interactions of macromolecules. Recently, a method termed two-dimensional spectrum analysis (2DSA) for the determination of size-and-shape distributions was described by Demeler and colleagues (Eur Biophys J 2009). It is based on novel ideas conceived for fitting the integral equations of the size-and-shape distribution to experimental data, illustrated with an example but provided without proof of the principle of the algorithm. In the present work, we examine the 2DSA algorithm by comparison with the mathematical reference frame and simple well-known numerical concepts for solving Fredholm integral equations, and test the key assumptions underlying the 2DSA method in an example application. While the 2DSA appears computationally excessively wasteful, key elements also appear to be in conflict with mathematical results. This raises doubts about the correctness of the results from 2DSA analysis

Dyson Equation Approach to Many-Body Greens Functions and Self-Consistent RPA, First Application to the Hubbard Model

An approach for particle-hole correlation functions, based on the so-called SCRPA, is developed. This leads to a fully self-consistent RPA-like theory which satisfies the $f$-sum rule and several other theorems. As a first step, a simpler self-consistent approach, the renormalized RPA, is solved numerically in the one-dimensional Hubbard model. The charge and the longitudinal spin susceptibility, the momentum distribution and several ground state properties are calculated and compared with the exact results. Especially at half filling, our approach provides quite promising results and matches the exact behaviour apart from a general prefactor. The strong coupling limit of our approach can be described analytically.Comment: 35 pages, 18 Figures, Feynman diagrams as 10 additional eps-files, revised and enhanced version, accepted in Phys. Rev.

Indefinite and Bidirectional Near Infrared Nanocrystal Photoswitching

Materials whose luminescence can be switched by optical stimulation drive technologies ranging from superresolution imaging1-4, nanophotonics5, and optical data storage6-8, to targeted pharmacology, optogenetics, and chemical reactivity9. These photoswitchable probes, including organic fluorophores and proteins, are prone to photodegradation, and often require phototoxic doses of ultraviolet (UV) or visible light. Colloidal inorganic nanoparticles have significant stability advantages over existing photoswitchable materials, but the ability to switch emission bidirectionally, particularly with NIR light, has not been reported with nanoparticles. Here, we present 2-way, near-infrared (NIR) photoswitching of avalanching nanoparticles (ANPs), showing full optical control of upconverted emission using phototriggers in the NIR-I and NIR-II spectral regions useful for subsurface imaging. Employing single-step photodarkening10-13 and photobrightening12,14-18, we demonstrate indefinite photoswitching of individual nanoparticles (>1000 cycles over 7 h) in ambient or aqueous conditions without measurable photodegradation. Critical steps of the photoswitching mechanism are elucidated by modeling and by measuring the photon avalanche properties of single ANPs in both bright and dark states. Unlimited, reversible photoswitching of ANPs enables indefinitely rewritable 2D and 3D multi-level optical patterning of ANPs, as well as optical nanoscopy with sub-{\AA} localization superresolution that allows us to distinguish individual ANPs within tightly packed clusters.Comment: 15 pages, 5 figure