Up in Smoke

This poem is about struggling with addition, and learning that often a controlled substance is controlling you and not the other way around

Three-dimensional spontaneous magnetic reconnection in neutral current sheets

Magnetic reconnection in an antiparallel uniform Harris current sheet equilibrium, which is initially perturbed by a region of enhanced resistivity limited in all three dimensions, is investigated through compressible magnetohydrodynamic simulations. Variable resistivity, coupled to the dynamics of the plasma by an electron-ion drift velocity criterion, is used during the evolution. A phase of magnetic reconnection amplifying with time and leading to eruptive energy release is triggered only if the initial perturbation is strongly elongated in the direction of current flow or if the threshold for the onset of anomalous resistivity is significantly lower than in the corresponding two-dimensional case. A Petschek-like configuration is then built up for \sim 100 Alfven times, but remains localized in the third dimension. Subsequently, a change of topology to an O-line at the center of the system (``secondary tearing'') occurs. This leads to enhanced and time-variable reconnection, to a second pair of outflow jets directed along the O-line, and to expansion of the reconnection process into the third dimension. High parallel current density components are created mainly near the region of enhanced resistivity.Comment: 22 pages, 14 figures (Figs. 3,9,10, and 14 as external GIF-Files

Analysis of unconstrained nonlinear MPC schemes with time varying control horizon

For discrete time nonlinear systems satisfying an exponential or finite time controllability assumption, we present an analytical formula for a suboptimality estimate for model predictive control schemes without stabilizing terminal constraints. Based on our formula, we perform a detailed analysis of the impact of the optimization horizon and the possibly time varying control horizon on stability and performance of the closed loop

Dynamo action in cellular convection

The dynamo properties of square patterns in Boussinesq Rayleigh-Benard convection in a plane horizontal layer are studied numerically. Cases without rotation and with weak rotation about a vertical axis are considered, particular attention being paid to the relation between dynamo action and the kinetic helicity of the flow. While the fluid layer is symmetric with respect to up-down reflections, the square-pattern solutions may or may not possess this vertical symmetry. Vertically symmetric solutions, appearing in the form of checkerboard patterns, do not possess a net kinetic helicity and we find them to be incapable of dynamo action at least up to magnetic Reynolds numbers of ≈ 12000. Vertically asymmetric squares, a secondary convection pattern appearing via the skewed varicose instability of rolls and being characterized by rising (descending) motion in the centers and descending (rising) motion near the boundaries, can in turn be devided into such that possess full horizontal square symmetry and others lacking also this symmetry. The flows lacking both the vertical and horizontal symmetries are particularly interesting in that they possess kinetic helicity and show kinematic dynamo action even without rotation. The generated magnetic fields are concentrated in vertically oriented filamentary structures near cell boundaries. The dynamos found in the nonrotating case are, however, always only kinematic, never nonlinear dynamos. Nonlinearly the back-reaction of the magnetic field then forces the flow into the basin of attraction of a roll-pattern solution incapable of dynamo action. But with rotation added parameter regions are found where a subtle balance between the Coriolis and Lorentz forces enables nonlinear dynamo action of stationary asymmetric squares. In some parameter regions this balance leads to nonlinear dynamos with flows in the form of oscillating squares or stationary modulated rolls

Energy transfer in Hall-MHD turbulence: cascades, backscatter, and dynamo action

Scale interactions in Hall MHD are studied using both the mean field theory derivation of transport coefficients, and direct numerical simulations in three space dimensions. In the magnetically dominated regime, the eddy resistivity is found to be negative definite, leading to large scale instabilities. A direct cascade of the total energy is observed, although as the amplitude of the Hall effect is increased, backscatter of magnetic energy to large scales is found, a feature not present in MHD flows. The coupling between the magnetic and velocity fields is different than in the MHD case, and backscatter of energy from small scale magnetic fields to large scale flows is also observed. For the magnetic helicity, a strong quenching of its transfer is found. We also discuss non-helical magnetically forced Hall-MHD simulations where growth of a large scale magnetic field is observed.Comment: 25 pages, 16 figure

Analysis of unconstrained nonlinear MPC schemes with time varying control horizon

For nonlinear discrete time systems satisfying a controllability condition, we present a stability condition for model predictive control without stabilizing terminal constraints or costs. The condition is given in terms of an analytical formula which can be employed in order to determine a prediction horizon length for which asymptotic stability or a performance guarantee is ensured. Based on this formula a sensitivity analysis with respect to the prediction and the possibly time varying control horizon is carried out.Comment: 7 pages, 4 figure

A multi-systems approach to human movement after ACL reconstruction: the cardiopulmonary system

The cardiopulmonary system plays a pivotal role in athletic and rehabilitative activities following anterior cruciate ligament reconstruction, along with serving as an important support for the functioning of other physiologic systems including the integumentary, musculoskeletal, and nervous systems. Many competitive sports impose high demands upon the cardiorespiratory system, which requires careful attention and planning from rehabilitation specialists to ensure athletes are adequately prepared to return to sport. Cardiopulmonary function following anterior cruciate ligament reconstruction (ACLR) can be assessed using a variety of methods, depending on stage of healing, training of the clinician, and equipment availability. Reductions in cardiovascular function may influence the selection and dosage of interventions that are not only aimed to address cardiopulmonary impairments, but also deficits experienced in other systems that ultimately work together to achieve goal-directed movement. The purpose of this clinical commentary is to present cardiopulmonary system considerations within a multi-physiologic systems approach to human movement after ACLR, including a clinically relevant review of the cardiopulmonary system, assessment strategies, and modes of cardiopulmonary training to promote effective, efficient movement. Level of evidence: 5