Turbulent Contributions to Ohm's Law in Axisymmetric Magnetized Plasmas

The effect of magnetic turbulence in shaping the current density in axisymmetric magnetized plasma is analyzed using a turbulent extension of Ohm's law derived from the self-consistent action-angle transport theory. Besides the well-known hyper-resistive (helicity-conserving) contribution, the generalized Ohm's law contains an anomalous resistivity term, and a turbulent bootstrap-like term proportional to the current density derivative. The numerical solution of the equation for equilibrium and turbulence profiles characteristic of conventional and advanced scenarios shows that, trough "turbulent bootstrap" effect and anomalous resistivity turbulence can generate power and parallel current which are a sizable portion (about 20-25%) of the corresponding effects associated with the neoclassical bootstrap effect. The degree of alignment of the turbulence peak and the pressure gradient plays an important role in defining the steady-state regime. In fully bootstrapped tokamak, the hyper-resistivity is essential in overcoming the intrinsic limitation of the hollow current profile.Comment: 19 pages, 6 figures, journal pape

Gauge vortex dynamics at finite mass of bosonic fields

The simple derivation of the string equation of motion adopted in the nonrelativistic case is presented, paying the special attention to the effects of finite masses of bosonic fields of an Abelian Higgs model. The role of the finite mass effects in the evaluation of various topological characteristics of the closed strings is discussed. The rate of the dissipationless helicity change is calculated. It is demonstrated how the conservation of the sum of the twisting and writhing numbers of the string is recovered despite the changing helicity.Comment: considerably revised to include errata to journal versio

Large Scale Structures a Gradient Lines: the case of the Trkal Flow

A specific asymptotic expansion at large Reynolds numbers (R)for the long wavelength perturbation of a non stationary anisotropic helical solution of the force less Navier-Stokes equations (Trkal solutions) is effectively constructed of the Beltrami type terms through multi scaling analysis. The asymptotic procedure is proved to be valid for one specific value of the scaling parameter,namely for the square root of the Reynolds number (R).As a result large scale structures arise as gradient lines of the energy determined by the initial conditions for two anisotropic Beltrami flows of the same helicity.The same intitial conditions determine the boundaries of the vortex-velocity tubes, containing both streamlines and vortex linesComment: 27 pages, 2 figure

Helicity cascades in rotating turbulence

The effect of helicity (velocity-vorticity correlations) is studied in direct numerical simulations of rotating turbulence down to Rossby numbers of 0.02. The results suggest that the presence of net helicity plays an important role in the dynamics of the flow. In particular, at small Rossby number, the energy cascades to large scales, as expected, but helicity then can dominate the cascade to small scales. A phenomenological interpretation in terms of a direct cascade of helicity slowed down by wave-eddy interactions leads to the prediction of new inertial indices for the small-scale energy and helicity spectra.Comment: 7 pages, 8 figure

Primordial Magnetic Field Limits from Cosmic Microwave Background Bispectrum of Magnetic Passive Scalar Modes

Primordial magnetic fields lead to non-Gaussian signals in the cosmic microwave background (CMB) even at the lowest order, as magnetic stresses and the temperature anisotropy they induce depend quadratically on the magnetic field. In contrast, CMB non-Gaussianity due to inflationary scalar perturbations arises only as a higher order effect. Apart from a compensated scalar mode, stochastic primordial magnetic fields also produce scalar anisotropic stress that remains uncompensated till neutrino decoupling. This gives rise to an adiabatic-like scalar perturbation mode that evolves passively thereafter (called the passive mode). We compute the CMB reduced bispectrum ($b_{l_{_1}l_{_2}l_{_3}}$) induced by this passive mode, sourced via the Sachs-Wolfe effect, on large angular scales. For any configuration of bispectrum, taking a partial sum over mode-coupling terms, we find a typical value of $l_1(l_1+1)l_3(l_3+1) b_{l_{_1}l_{_2}l_{_3}} \sim 6-9 \times 10^{-16}$, for a magnetic field of $B_0 \sim 3$ nG, assuming a nearly scale-invariant magnetic spectrum . We also evaluate, in full, the bispectrum for the squeezed collinear configuration over all angular mode-coupling terms and find $l_1(l_1+1)l_3(l_3+1) b_{l_{_1}l_{_2}l_{_3}} \approx -1.4 \times 10^{-16}$. These values are more than $\sim 10^6$ times larger than the previously calculated magnetic compensated scalar mode CMB bispectrum. Observational limits on the bispectrum from WMAP7 data allow us to set upper limits of $B_0 \sim 2$ nG on the present value of the cosmic magnetic field of primordial origin. This is over 10 times more stringent than earlier limits on $B_0$ based on the compensated mode bispectrum.Comment: 9 page

``Smoke Rings'' in Ferromagnets

It is shown that bulk ferromagnets support propagating non-linear modes that are analogous to the vortex rings, or ``smoke rings'', of fluid dynamics. These are circular loops of {\it magnetic} vorticity which travel at constant velocity parallel to their axis of symmetry. The topological structure of the continuum theory has important consequences for the properties of these magnetic vortex rings. One finds that there exists a sequence of magnetic vortex rings that are distinguished by a topological invariant (the Hopf invariant). We present analytical and numerical results for the energies, velocities and structures of propagating magnetic vortex rings in ferromagnetic materials.Comment: 4 pages, 3 eps-figures, revtex with epsf.tex and multicol.sty. To appear in Physical Review Letters. (Postscript problem fixed.

The imprint of large-scale flows on turbulence

We investigate the locality of interactions in hydrodynamic turbulence using data from a direct numerical simulation on a grid of 1024^3 points; the flow is forced with the Taylor-Green vortex. An inertial range for the energy is obtained in which the flux is constant and the spectrum follows an approximate Kolmogorov law. Nonlinear triadic interactions are dominated by their non-local components, involving widely separated scales. The resulting nonlinear transfer itself is local at each scale but the step in the energy cascade is independent of that scale and directly related to the integral scale of the flow. Interactions with large scales represent 20% of the total energy flux. Possible explanations for the deviation from self-similar models, the link between these findings and intermittency, and their consequences for modeling of turbulent flows are briefly discussed

Syringe Pump

Our team was asked to design a syringe pump that would deliver fluid at a controlled flow rate to cells in a microfluidic device. The design process of our syringe pump proved to be a very dynamic one. The beginning research of both microfluidic devices and existing syringe pumps helped our team get an idea of ways we could implement existing aspects that work into our design. There were many existing devices that resembled the one that we were asked to make closely; however, due to our resources as students, we had to be a bit more creative in figuring out how to afford and assemble each component to the best of our abilities. Developing customer requirements was a huge step in the process of understanding what exactly you as our customer wanted to see delivered in our syringe pump. The main requirements of our pump were that it was able to deliver accurate shear stress values so that they could mimic those found in true physiology, that it was able to deliver an accurate flow rate to the device, that it was easily usable, and that it was compact to both fit in a desired location and have ease of mobility when needed to be moved to or from that location. Next, it was our job as the engineers to turn those requirements into quantitative engineering specifications that our device needed to meet via testing of the device once the prototype was finished. Once we determined what numbers needed to be hit to quantify the requirements set by you, we were able to create a network diagram of tasks in order to organize the design, manufacturing, and testing processes that we had ahead. Our design process then became a series of brainstorming via tools like a conjoint analysis, morphology, and Pugh matrices. We did these exercises in order to compile a multitude of ideas for each component of the pump to determine which combination of these ideas would produce the optimal pump that is attractive to the user and does the best job at meeting the customer specifications. We determined the main functions of our pump were inputting flow rate parameters on the interface, having a power source for the pushing mechanism, the physical pushing mechanism, and lastly the mechanism through which the fluid would be delivered into the tube. Ultimately, through the many exercises as well as iterations due to a multitude of realizations down the road, we settled upon using a stepper motor linear actuator for the pushing mechanism and a screen with buttons for the input from the user, powered by a 24 V DC Power Supply and connected by a needle attachment to the syringe. Next came acquiring the materials and aspects of the pump that were to be purchased from a manufacturer as well as designing the aspects that we were going to manufacture ourselves. The primary component of our design that we purchased was the FUYU stepper motor linear actuator, to which we programmed electrically and designed adapters to fit onto. Our electrical programming revolved around the Arduino UNO and the Sketch coding software. The chassis was our last component to design, and its main purpose was to keep the user safe from any potential harm from the pump and protect the pump from any water or other wear. When we had performed the Hazard Safety Assessment, we determined a lot of the risk involved the user having their hands in the pinch points as well as having the device fall on the user, both of which were mitigated by having a chassis that covered the pinch point and made the device more compact and mobile. Once we had those components designed, we determined how we would both manufacture and assemble the final prototype. These plans were surely dynamic as we changed materials and found new ways to better manufacture each piece. Critical changes included changing the chassis material from acrylic to polycarbonate, and thus changing the manufacturing process from laser jetting to water jetting to using a variety of saws to cut the pieces. Another critical change came after having manufactured the pusher block adapter, as we were sent back to the design process when the adapter did not perform the way we wanted it to. Additionally, the electrical side of our design manufacturing had to be iterated multiple times as we determined what was feasible and still effective for inputting the parameters. Our design changed from a 4 x 4 keypad to two buttons, one increasing the flow rate value and one decreasing the value. Once the prototype had been built, it was time to verify that we had made a device that met the customer specifications. We created protocols for how we would test these specifications and executed each of the four, the most time-consuming ones being the flow rate and shear stress tests. Our testing plans for shear stress included both an analytical COMSOL simulation through the solid model of the microfluidic device as well as physical testing of the velocity of the particles moving via the LabSmith Micro Particle Image Velocimetry microscope. The physical testing was to verify that our analytical model accurately displayed what velocity and thus shear stresses the cells in our microfluidic devices would be experiencing. Next, we tested flow rate via running water through our pump at specified flow rates for a given period of time, measuring the mass acquired on a sensitive scale to back-calculate what flow rate was actually being delivered. Additionally, we used a gauge to measure the displacement of our pusher block over a specified time to first ensure that the correct speed was being programmed to the motor. In terms of surface area testing, we simply used a ruler to measure the dimensions of the bottom of our chassis to verify it would fit in the desired location in the lab. Lastly, our ease of use testing included simply numbering the steps in the operations manual. Ultimately, our data showed that we did in fact create a pump that received an input and delivered a controllable flow rate and shear stress to the cells in the microfluidic devices, all while being compact and easily usable. After inputting a flow rate of 28.8 ml/hr, we measured the delivered flow rate to be 25.5 ml/hr, which was within our target percent error range of 15%. For shear stress, when entering a flow rate of 75.8 uL/hr, our physical testing showed a particle velocity of 295.6 um/s and our COMSOL velocity showed one of 358.91 um/s, putting these within range of our 20% error goal. We measured the bottom surface area of our pump to be 431.85 cm^2, which was well within our specification of 695 cm^2. Lastly, we measured 5 steps to program our device, which was our target specification. There were surely limitations to our data, as when flow rate decreased to smaller and smaller values it was increasingly harder to acquire data, and then additionally extremely difficult to have that data be accurate. Thus, at the flow rate of 0.76 uL/hr, which is the flow rate at which the pump will typically be used at, both the shear stress and flow rate specifications were not met via our testing. There are a multitude of reasons why our data may have been skewed, and we have plans for future testing to discover where errors might be introduced in our pump. Overall, our team learned much about the design process and grew as engineers while designing this syringe pump

Interference phenomena in scalar transport induced by a noise finite correlation time

The role played on the scalar transport by a finite, not small, correlation time, $\tau_u$, for the noise velocity is investigated, both analytically and numerically. For small $\tau_u$'s a mechanism leading to enhancement of transport has recently been identified and shown to be dominating for any type of flow. For finite non-vanishing $\tau_u$'s we recognize the existence of a further mechanism associated with regions of anticorrelation of the Lagrangian advecting velocity. Depending on the extension of the anticorrelated regions, either an enhancement (corresponding to constructive interference) or a depletion (corresponding to destructive interference) in the turbulent transport now takes place.Comment: 8 pages, 3 figure

Thermal detection of single e-h pairs in a biased silicon crystal detector

We demonstrate that individual electron-hole pairs are resolved in a 1 cm$^2$ by 4 mm thick silicon crystal (0.93 g) operated at $\sim$35 mK. One side of the detector is patterned with two quasiparticle-trap-assisted electro-thermal-feedback transition edge sensor (QET) arrays held near ground potential. The other side contains a bias grid with 20\% coverage. Bias potentials up to $\pm$ 160 V were used in the work reported here. A fiber optic provides 650~nm (1.9 eV) photons that each produce an electron-hole ($e^{-} h^{+}$) pair in the crystal near the grid. The energy of the drifting charges is measured with a phonon sensor noise $\sigma$ $\sim$0.09 $e^{-} h^{+}$ pair. The observed charge quantization is nearly identical for $h^+$'s or $e^-$'s transported across the crystal.Comment: 4 journal pages, 5 figure