A Lagrangian kinetic model for collisionless magnetic reconnection

A new fully kinetic system is proposed for modeling collisionless magnetic reconnection. The formulation relies on fundamental principles in Lagrangian dynamics, in which the inertia of the electron mean flow is neglected in the expression of the Lagrangian, rather then enforcing a zero electron mass in the equations of motion. This is done upon splitting the electron velocity into its mean and fluctuating parts, so that the latter naturally produce the corresponding pressure tensor. The model exhibits a new Coriolis force term, which emerges from a change of frame in the electron dynamics. Then, if the electron heat flux is neglected, the strong electron magnetization limit yields a hybrid model, in which the electron pressure tensor is frozen into the electron mean velocity.Comment: 15 pages, no figures. To Appear in Plasma Phys. Control. Fusio

The Hamiltonian structure and Euler-Poincar\'{e} formulation of the Vlasov-Maxwell and gyrokinetic systems

We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with a modified Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincar\'{e} theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models and Casimir type stability methods. [1] H. Cendra et. al., Journal of Mathematical Physics 39, 3138 (1998)Comment: 36 pages, 1 figur

Self-sustaining sound in collisionless, high-beta plasma

Using analytical theory and hybrid-kinetic numerical simulations, we demonstrate that, in a collisionless plasma, long-wavelength ion-acoustic waves (IAWs) with amplitudes $\delta n/n_0 \gtrsim 2/\beta$ (where $\beta\gg{1}$ is the ratio of thermal to magnetic pressure) generate sufficient pressure anisotropy to destabilize the plasma to firehose and mirror instabilities. These kinetic instabilities grow rapidly to reduce the pressure anisotropy by pitch-angle scattering and trapping particles, respectively, thereby impeding the maintenance of Landau resonances that enable such waves' otherwise potent collisionless damping. The result is wave dynamics that evince a weakly collisional plasma: the ion distribution function is near-Maxwellian, the field-parallel flow of heat resembles its Braginskii form (except in regions where large-amplitude magnetic mirrors strongly suppress particle transport), and the relations between various thermodynamic quantities are more `fluid-like' than kinetic. A nonlinear fluctuation-dissipation relation for self-sustaining IAWs is obtained by solving a plasma-kinetic Langevin problem, which demonstrates suppressed damping, enhanced fluctuation levels, and weakly collisional thermodynamics when IAWs with $\delta n/n_0 \gtrsim 2/\beta$ are stochastically driven. We investigate how our results depend upon the scale separation between the wavelength of the IAW and the Larmor radius of the ions, and discuss briefly their implications for our understanding of turbulence and transport in the solar wind and the intracluster medium of galaxy clusters.Comment: 25 pages, 10 figures, Journal of Plasma Physics, in pres

The Role of RUNX2 in Osteosarcoma Oncogenesis

Osteosarcoma is an aggressive but ill-understood cancer of bone that predominantly affects adolescents. Its rarity and biological heterogeneity have limited studies of its molecular basis. In recent years, an important role has emerged for the RUNX2 “platform protein” in osteosarcoma oncogenesis. RUNX proteins are DNA-binding transcription factors that regulate the expression of multiple genes involved in cellular differentiation and cell-cycle progression. RUNX2 is genetically essential for developing bone and osteoblast maturation. Studies of osteosarcoma tumours have revealed that the RUNX2 DNA copy number together with RNA and protein levels are highly elevated in osteosarcoma tumors. The protein is also important for metastatic bone disease of prostate and breast cancers, while RUNX2 may have both tumor suppressive and oncogenic roles in bone morphogenesis. This paper provides a synopsis of the current understanding of the functions of RUNX2 and its potential role in osteosarcoma and suggests directions for future study

Fluctuation dynamo in a weakly collisional plasma

The turbulent amplification of cosmic magnetic fields depends upon the material properties of the host plasma. In many hot, dilute astrophysical systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity of particle--particle collisions allows departures from local thermodynamic equilibrium. These departures exert anisotropic viscous stresses on the plasma motions that inhibit their ability to stretch magnetic-field lines. We present a numerical study of the fluctuation dynamo in a weakly collisional plasma using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous (Braginskii) stress. When the stress is limited to values consistent with a pressure anisotropy regulated by firehose and mirror instabilities, the Braginskii-MHD dynamo largely resembles its MHD counterpart. If instead the parallel viscous stress is left unabated -- a situation relevant to recent kinetic simulations of the fluctuation dynamo and to the early stages of the dynamo in a magnetized ICM -- the dynamo changes its character, amplifying the magnetic field while exhibiting many characteristics of the saturated state of the large-Prandtl-number (${\rm Pm}\gtrsim{1}$) MHD dynamo. We construct an analytic model for the Braginskii-MHD dynamo in this regime, which successfully matches magnetic-energy spectra. A prediction of this model, confirmed by our simulations, is that a Braginskii-MHD plasma without pressure-anisotropy limiters will not support a dynamo if the ratio of perpendicular and parallel viscosities is too small. This ratio reflects the relative allowed rates of field-line stretching and mixing, the latter of which promotes resistive dissipation of the magnetic field. In all cases that do exhibit a dynamo, the generated magnetic field is organized into folds that persist into the saturated state and bias the chaotic flow to acquire a scale-dependent spectral anisotropy.Comment: 62 pages, 25 figures, 1 table, accepted for publication to Journal of Plasma Physic

Teaching introductory undergraduate Physics using commercial video games

Commercial video games are increasingly using sophisticated physics simulations to create a more immersive experience for players. This also makes them a powerful tool for engaging students in learning physics. We provide some examples to show how commercial off-the-shelf games can be used to teach specific topics in introductory undergraduate physics. The examples are selected from a course taught predominantly through the medium of commercial video games.Comment: Accepted to Physics Education, Fig1 does not render properly in this versio

An adaptive technique for content-based image retrieval

We discuss an adaptive approach towards Content-Based Image Retrieval. It is based on the Ostensive Model of developing information needs—a special kind of relevance feedback model that learns from implicit user feedback and adds a temporal notion to relevance. The ostensive approach supports content-assisted browsing through visualising the interaction by adding user-selected images to a browsing path, which ends with a set of system recommendations. The suggestions are based on an adaptive query learning scheme, in which the query is learnt from previously selected images. Our approach is an adaptation of the original Ostensive Model based on textual features only, to include content-based features to characterise images. In the proposed scheme textual and colour features are combined using the Dempster-Shafer theory of evidence combination. Results from a user-centred, work-task oriented evaluation show that the ostensive interface is preferred over a traditional interface with manual query facilities. This is due to its ability to adapt to the user's need, its intuitiveness and the fluid way in which it operates. Studying and comparing the nature of the underlying information need, it emerges that our approach elicits changes in the user's need based on the interaction, and is successful in adapting the retrieval to match the changes. In addition, a preliminary study of the retrieval performance of the ostensive relevance feedback scheme shows that it can outperform a standard relevance feedback strategy in terms of image recall in category search