Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer

Many coherence transfer experiments in Nuclear Magnetic Resonance Spectroscopy, involving network of coupled spins, use temporary spin-decoupling to produce desired effective Hamiltonians. In this paper, we show that significant time can be saved in producing an effective Hamiltonian, if spin-decoupling is avoided. We provide time optimal pulse sequences for producing an important class of effective Hamiltonians in three spin networks. These effective Hamiltonians are useful for coherence transfer experiments and implementation of quantum logic gates in NMR quantum computing. It is demonstrated that computing these time optimal pulse sequences can be reduced to geometric problems that involve computing sub-Riemannian geodesics on Homogeneous spaces

Compressible flow structures interaction with a two-dimensional ejector: a cold-flow study

An experimental study has been conducted to examine the interaction of compressible flow structures such as shocks and vortices with a two-dimensional ejector geometry using a shock-tube facility. Three diaphragm pressure ratios ofP4 =P1 = 4, 8, and 12 have been employed, whereP4 is the driver gas pressure andP1 is the pressure within the driven compartment of the shock tube. These lead to incident shock Mach numbers of Ms = 1:34, 1.54, and 1.66, respectively. The length of the driver section of the shock tube was 700 mm. Air was used for both the driver and driven gases. High-speed shadowgraphy was employed to visualize the induced flowfield. Pressure measurements were taken at different locations along the test section to study theflow quantitatively. The induced flow is unsteady and dependent on the degree of compressibility of the initial shock wave generated by the rupture of the diaphragm

Soft Spheres Make More Mesophases

We use both mean-field methods and numerical simulation to study the phase diagram of classical particles interacting with a hard-core and repulsive, soft shoulder. Despite the purely repulsive interaction, this system displays a remarkable array of aggregate phases arising from the competition between the hard-core and shoulder length scales. In the limit of large shoulder width to core size, we argue that this phase diagram has a number of universal features, and classify the set of repulsive shoulders that lead to aggregation at high density. Surprisingly, the phase sequence and aggregate size adjusts so as to keep almost constant inter-aggregate separation.Comment: 4 pages, 2 included figure

Numerical Simulation of Illumination and Thermal Conditions at the Lunar Poles Using LOLA DTMs

We are interested in illumination conditions and the temperature distribution within the upper two meters of regolith near the lunar poles. Here, areas exist receiving almost constant illumination near areas in permanent shadow, which were identified as potential exploration sites for future missions. For our study a numerical simulation of the illumination and thermal environment for lunar near-polar regions is needed. Our study is based on high-resolution, twenty meters per pixel and 400 x 400 km large polar Digital Terrain Models (DTMs), which were derived from Lunar Orbiter Laser Altimeter (LOLA) data. Illumination conditions were simulated by synthetically illuminating the LOLA DTMs using the horizon method considering the Sun as an extended source. We model polar illumination for the central 50 x 50 km subset and use it as an input at each time-step (2 h) to evaluate the heating of the lunar surface and subsequent conduction in the sub-surface. At surface level we balance the incoming insolation with the subsurface conduction and radiation into space, whereas in the sub-surface we consider conduction with an additional constant radiogenic heat source at the bottom of our two-meter layer. Density is modeled as depth-dependent, the specific heat parameter as temperature-dependent and the thermal conductivity as depth- and temperature-dependent. We implemented a fully implicit finite-volume method in space and backward Euler scheme in time to solve the one-dimensional heat equation at each pixel in our 50 x 50 km DTM. Due to the non-linear dependencies of the parameters mentioned above, Newton's method is employed as the non-linear solver together with the Gauss-Seidel method as the iterative linear solver in each Newton iteration. The software is written in OpenCL and runs in parallel on the GPU cores, which allows for fast computation of large areas and long time scales