Collisionless Magnetic Reconnection in Space Plasmas

Magnetic reconnection requires the violation of the frozen-in condition which ties gyrating charged particles to the magnetic field inhibiting diffusion. Ongoing reconnection has been identified in near-Earth space as being responsible for the excitation of substorms, magnetic storms, generation of field aligned currents and their consequences, the wealth of auroral phenomena. Its theoretical understanding is now on the verge of being completed. Reconnection takes place in thin current sheets. Analytical concepts proceeded gradually down to the microscopic scale, the scale of the electron skin depth or inertial length, recognizing that current layers that thin do preferentially undergo spontaneous reconnection. Thick current layers start reconnecting when being forced by plasma inflow to thin. For almost half a century the physical mechanism of reconnection has remained a mystery. Spacecraft in situ observations in combination with sophisticated numerical simulations in two and three dimensions recently clarified the mist, finding that reconnection produces a specific structure of the current layer inside the electron inertial (also called electron diffusion) region around the reconnection site, the X line. Onset of reconnection is attributed to pseudo-viscous contributions of the electron pressure tensor aided by electron inertia and drag, creating a complicated structured electron current sheet, electric fields, and an electron exhaust extended along the current layer. We review the general background theory and recent developments in numerical simulation on collisionless reconnection. It is impossible to cover the entire field of reconnection in a short space-limited review. The presentation necessarily remains cursory, determined by our taste, preferences, and knowledge. Only a small amount of observations is included in order to support the few selected numerical simulations.Comment: Review pape

Numerical Tests of Fast Reconnection in Weakly Stochastic Magnetic Fields

We study the effects of turbulence on magnetic reconnection using 3D numerical simulations. This is the first attempt to test a model of fast magnetic reconnection in the presence of weak turbulence proposed by Lazarian & Vishniac (1999). This model predicts that weak turbulence, generically present in most of astrophysical systems, enhances the rate of reconnection by reducing the transverse scale for reconnection events and by allowing many independent flux reconnection events to occur simultaneously. As a result the reconnection speed becomes independent of Ohmic resistivity and is determined by the magnetic field wandering induced by turbulence. To quantify the reconnection speed we use both an intuitive definition, i.e. the speed of the reconnected flux inflow, as well as a more sophisticated definition based on a formally derived analytical expression. Our results confirm the predictions of the Lazarian & Vishniac model. In particular, we find that Vrec Pinj^(1/2), as predicted by the model. The dependence on the injection scale for some of our models is a bit weaker than expected, i.e. l^(3/4), compared to the predicted linear dependence on the injection scale, which may require some refinement of the model or may be due to the effects like finite size of the excitation region. The reconnection speed was found to depend on the expected rate of magnetic field wandering and not on the magnitude of the guide field. In our models, we see no dependence on the guide field when its strength is comparable to the reconnected component. More importantly, while in the absence of turbulence we successfully reproduce the Sweet-Parker scaling of reconnection, in the presence of turbulence we do not observe any dependence on Ohmic resistivity, confirming that our reconnection is fast.Comment: 22 pages, 20 figure

On the Complexity of Two Dimensional Commuting Local Hamiltonians

The complexity of the commuting local Hamiltonians (CLH) problem still remains a mystery after two decades of research of quantum Hamiltonian complexity; it is only known to be contained in NP for few low parameters. Of particular interest is the tightly related question of understanding whether groundstates of CLHs can be generated by efficient quantum circuits. The two problems touch upon conceptual, physical and computational questions, including the centrality of non-commutation in quantum mechanics, quantum PCP and the area law. It is natural to try to address first the more physical case of CLHs embedded on a 2D lattice, but this problem too remained open apart from some very specific cases [Aharonov and Eldar, 2011; Hastings, 2012; Schuch, 2011]. Here we consider a wide class of two dimensional CLH instances; these are k-local CLHs, for any constant k; they are defined on qubits set on the edges of any surface complex, where we require that this surface complex is not too far from being "Euclidean". Each vertex and each face can be associated with an arbitrary term (as long as the terms commute). We show that this class is in NP, and moreover that the groundstates have an efficient quantum circuit that prepares them. This result subsumes that of Schuch [Schuch, 2011] which regarded the special case of 4-local Hamiltonians on a grid with qubits, and by that it removes the mysterious feature of Schuch\u27s proof which showed containment in NP without providing a quantum circuit for the groundstate and considerably generalizes it. We believe this work and the tools we develop make a significant step towards showing that 2D CLHs are in NP

Fast Magnetic Reconnection and Spontaneous Stochasticity

Magnetic field-lines in astrophysical plasmas are expected to be frozen-in at scales larger than the ion gyroradius. The rapid reconnection of magnetic flux structures with dimensions vastly larger than the gyroradius requires a breakdown in the standard Alfv\'en flux-freezing law. We attribute this breakdown to ubiquitous MHD plasma turbulence with power-law scaling ranges of velocity and magnetic energy spectra. Lagrangian particle trajectories in such environments become "spontaneously stochastic", so that infinitely-many magnetic field-lines are advected to each point and must be averaged to obtain the resultant magnetic field. The relative distance between initial magnetic field lines which arrive to the same final point depends upon the properties of two-particle turbulent dispersion. We develop predictions based on the phenomenological Goldreich & Sridhar theory of strong MHD turbulence and on weak MHD turbulence theory. We recover the predictions of the Lazarian & Vishniac theory for the reconnection rate of large-scale magnetic structures. Lazarian & Vishniac also invoked "spontaneous stochasticity", but of the field-lines rather than of the Lagrangian trajectories. More recent theories of fast magnetic reconnection appeal to microscopic plasma processes that lead to additional terms in the generalized Ohm's law, such as the collisionless Hall term. We estimate quantitatively the effect of such processes on the inertial-range turbulence dynamics and find them to be negligible in most astrophysical environments. For example, the predictions of the Lazarian-Vishniac theory are unchanged in Hall MHD turbulence with an extended inertial range, whenever the ion skin depth $\delta_i$ is much smaller than the turbulent integral length or injection-scale $L_i.$Comment: 31 pages, 5 figure

Cogent: uniqueness types and certifying compilation

This paper presents a framework aimed at significantly reducing the cost of proving functional correctness for low-level operating systems components. The framework is designed around a new functional programming language, Cogent. A central aspect of the language is its uniqueness type system, which eliminates the need for a trusted runtime or garbage collector while still guaranteeing memory safety, a crucial property for safety and security. Moreover, it allows us to assign two semantics to the language: The first semantics is imperative, suitable for efficient C code generation, and the second is purely functional, providing a user-friendly interface for equational reasoning and verification of higher-level correctness properties. The refinement theorem connecting the two semantics allows the compiler to produce a proof via translation validation certifying the correctness of the generated C code with respect to the semantics of the Cogent source program. We have demonstrated the effectiveness of our framework for implementation and for verification through two file system implementations

Glitch Poetics:Critical Sensory Realism in Contemporary Language Practice

A practice-based research project that introduces the term "Glitch Poetics" as a mode for reading and writing in the digital age: this term overlaps different creative (and uncreative) writing methodologies, and forges new lines of connection between "new media" and the literary and textual. The work is relevant to fields such as Literary Theory, Experimental Writing, Electronic Literature and New Media Art. The research methodology was interdisciplinary, including: synthesising key conceptualisations of "glitch" from media theoretical areas such as media archaeology and software studies, and new media art practitioners such as Rosa Menkman, with those of historical approaches to 'poetics'; performing close readings of contemporary literature, performance and other artistic language practices; and producing art works that move between live performance, exposition and textual practice. Over the course of 4 years, the project achieved a significant level of depth, concluding that "glitches" offer a moment of correspondence between the (already diverse) concerns of poetics and those of critical media practices, forming new disciplinary allegiances and necessitating new hybrid forms of critique. In recent published material I have also illustrated how this critical framework can be deployed to analyse influential books and artworks alongside emerging technologies. The new term "Glitch Poetics" gained traction through a publications in national specialist media, such as Art Monthly, Resonance FM and Poetry Wales, and was developed through interdisciplinary contexts including invited talks at Transmediale festival, Onassis centre in Athens, academic appearances at conferences for new media, literature and poetics, and as a chapter in the Bloomsbury Handbook of Electronic Literature. The practice-based components were commissioned by the Bluecoat and FACT, and a final outcome was developed into a publication with Entr'acte records in Antwerp, streamed in its entirety on The Wire website

Coronal magnetic energy release by current sheet reconnection

In this thesis we investigate the rapid release of energy in the solar corona, with a particular view to understanding the solar flare in which magnetic reconnection is thought to play a key role. A review of existing reconnection solutions is given in Chapters 2 and 3, with new analytic and numeric results are presented in subsequent chapters. Although much of the work in this thesis is computational, numerical investigations are always motivated theoretically. In Chapters 4 and 5 several aspects of two dimensional reconnection are investigated using a periodic time-dependent incompressible code. One of the main points is to check the veracity of the analytic solution of Craig and Henton (1995) by running the code from general initial conditions. Other aspects of 2-D merging covered include the tearing mode instability, osculation and the effects of finite compressibility. We employ a 3-D time-dependent code, in Chapter 4, to check that the analytically predicted spine and fan forms develop from general initial conditions. Scalings with resistivity of the associated current structures are also investigated. Most of the analytic work so far has revolved around single null magnetic configurations. Chapter 6 focuses on reconnection solutions in the presence of multiple nulls. Finally, we look at an application of the analytic theory in the context of particle acceleration. In Chapter 7 we trace proton orbits using a physically plausible analytic current sheet solution

The Centripetal Network: How the Internet Holds Itself Together, and the Forces Tearing It Apart

Two forces are in tension as the Internet evolves. One pushes toward interconnected common platforms; the other pulls toward fragmentation and proprietary alternatives. Their interplay drives many of the contentious issues in cyberlaw, intellectual property, and telecommunications policy, including the fight over network neutrality for broadband providers, debates over global Internet governance, and battles over copyright online. These are more than just conflicts between incumbents and innovators, or between openness and deregulation. Their roots lie in the fundamental dynamics of interconnected networks. Fortunately, there is an interdisciplinary literature on network properties, albeit one virtually unknown to legal scholars. The emerging field of network formation theory explains the pressures threatening to pull the Internet apart, and suggests responses. The Internet as we know it is surprisingly fragile. To continue the extraordinary outpouring of creativity and innovation that the Internet fosters, policy-makers must protect its composite structure against both fragmentation and excessive concentration of power. This paper, the first to apply network formation models to Internet law, shows how the Internet pulls itself together as a coherent whole. This very process, however, creates and magnifies imbalances that encourage balkanization. By understanding how networks behave, governments and other legal decision-makers can avoid unintended consequences and target their actions appropriately. A network-theoretic perspective holds great promise to inform the law and policy of the information economy