Operator interpretation of resonances generated by some operator matrices

We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct a family of non-selfadjoint operators which reproduce certain parts of the transfer-function spectrum including resonances situated on the unphysical sheets neighboring the physical sheet. On this basis, completeness and basis properties for the root vectors of the transfer function (including those for the resonances) are proved.Comment: LaTeX, 15 pages, no figures; Contribution to Proceedings of the Mark Krein International Conference on Operator Theory and Applications, Odessa, August 18-22, 199

Generation of highly symmetric, cylindrically convergent shockwaves in water

We report on pulsed power driven, exploding copper wire array experiments conducted to generate cylindrical convergent shockwaves in water employing μs risetime currents >550 kA in amplitude and with stored energies of >15 kJ—a substantial increase over previous results. The experiments were carried out on the recently constructed Mega-Ampere-Compression-and-Hydrodynamics facility at Imperial College London in collaboration with colleagues of Technion, Israel. 10 mm diameter arrays consisting of 60 × 130 μm wires were utilized, and the current and voltage diagnostics of the load region suggested that ∼8 kJ of energy was deposited in the wires (and the load region close to the wires) during the experiments, resulting in the formation of dense, highly resistive plasmas that rapidly expanded driving the shockwaves in water. Laser-backlit framing images of the shockfront were obtained at radii 50:1. Framing images and streak photographs showed that the velocity of the shockwave reached ∼7.5 km s−1 at 0.1 mm from the axis. 2D hydrodynamic simulations that match the experimentally obtained implosion trajectory suggest that pressures >1 Mbar are produced within 10 μm of the axis along with water densities of 3gcm−3 and temperatures of many 1000 s of Kelvin. Under these conditions, Quotidian Equation of State suggests that a strongly coupled plasma with an ionization fraction of ∼0.7 would be formed. The results represent a “stepping stone” in the application of the technique to drive different material samples into high pressure, warm dense matter regimes with compact, university scale generators, and provide support in scaling the technique to multi-mega ampere currents

Human Milk Warming Temperatures Using a Simulation of Currently Available Storage and Warming Methods.

Human milk handling guidelines are very demanding, based upon solid scientific evidence that handling methods can make a real difference in infant health and nutrition. Indeed, properly stored milk maintains many of its unique qualities and continues to be the second and third best infant feeding alternatives, much superior to artificial feeding. Container type and shape, mode of steering, amount of air exposure and storage temperature may adversely affect milk stability and composition. Heating above physiological temperatures significantly impacts nutritional and immunological properties of milk. In spite of this knowledge, there are no strict guidelines regarding milk warming. Human milk is often heated in electrical-based bottle warmers that can exceed 80°C, a temperature at which many beneficial human milk properties disappear. High temperatures can also induce fat profile variations as compared with fresh human milk. In this manuscript we estimate the amount of damage due to overheating during warming using a heat flow simulation of a regular water based bottle warmer. To do so, we carried out a series of warming simulations which provided us with dynamic temperature fields within bottled milk. We simulated the use of a hot water-bath at 80°C to heat bottled refrigerated milk (60 ml and 178 ml) to demonstrate that large milk portions are overheated (above 40°C). It seems that the contemporary storage method (upright feeding tool, i.e. bottle) and bottle warming device, are not optimize to preserve the unique properties of human milk. Health workers and parents should be aware of this problem especially when it relates to sick neonates and preemies that cannot be directly fed at the breast

Large volume warming simulation after 300 seconds.

<p>The dominant and average temperature is 36°C with layers of higher temperature up to the layer just below the contact with the air where the maximal temperature reaches 53°C. The milk volume having temperature of 40–53°C is approximately 25% of the total volume. The minimal temperature of the milk is 32°C.</p

Large volume warming simulation after 420 seconds.

<p>The average temperature is 46°C with large islets of 49°C and small islets of 59°C that are located in the upper interface with the water bath. The temperature of the entire milk volume is above 42°C which is just above the recommended heating temperature (40°C).</p

Water bottle warmer model.

<p>The model includes milk volume (60 ml or 180ml) indicated as spotted area and upper part filled with air. The bottle height is either 49 mm or 140mm, including the nipple, with total bottle volume either 107 ml or 324ml. The plastic interface (bottle) is indicated in waves, the milk volume is indicated in dots and the heat bath of water is indicated in stripes.</p

Small volume warming simulation after 420 seconds.

<p>The dominant and average temperature is 63°C, with small islets of 60°C and thin islets of 69°C located at the upper interface with the water bath. The minimal temperature of the milk is 60°C.</p