Inapproximability of the Standard Pebble Game and Hard to Pebble Graphs

Pebble games are single-player games on DAGs involving placing and moving pebbles on nodes of the graph according to a certain set of rules. The goal is to pebble a set of target nodes using a minimum number of pebbles. In this paper, we present a possibly simpler proof of the result in [CLNV15] and strengthen the result to show that it is PSPACE-hard to determine the minimum number of pebbles to an additive $n^{1/3-\epsilon}$ term for all $\epsilon > 0$, which improves upon the currently known additive constant hardness of approximation [CLNV15] in the standard pebble game. We also introduce a family of explicit, constant indegree graphs with $n$ nodes where there exists a graph in the family such that using constant $k$ pebbles requires $\Omega(n^k)$ moves to pebble in both the standard and black-white pebble games. This independently answers an open question summarized in [Nor15] of whether a family of DAGs exists that meets the upper bound of $O(n^k)$ moves using constant $k$ pebbles with a different construction than that presented in [AdRNV17].Comment: Preliminary version in WADS 201

Mini-Computer Control of Electrical Energy Demand

Electrical power demand control results in huge dollar savings for the medium to large user. Meramec Mining Company realizes an average $4,500.00 savings from an average$150,000.00 monthly charge because of demand control efforts. This paper discusses the planning, designing, implementing, and auditing of the mini-computer system at Meramec Mining Company. No detailed discussion of the actual computer coding is included

Crosstalk between nanotube devices: contact and channel effects

At reduced dimensionality, Coulomb interactions play a crucial role in determining device properties. While such interactions within the same carbon nanotube have been shown to have unexpected properties, device integration and multi-nanotube devices require the consideration of inter-nanotube interactions. We present calculations of the characteristics of planar carbon nanotube transistors including interactions between semiconducting nanotubes and between semiconducting and metallic nanotubes. The results indicate that inter-tube interactions affect both the channel behavior and the contacts. For long channel devices, a separation of the order of the gate oxide thickness is necessary to eliminate inter-nanotube effects. Because of an exponential dependence of this length scale on dielectric constant, very high device densities are possible by using high-k dielectrics and embedded contacts

Ultrafast dynamics of a magnetic antivortex - Micromagnetic simulations

The antivortex is a fundamental magnetization structure which is the topological counterpart of the well-known magnetic vortex. We study here the ultrafast dynamic behavior of an isolated antivortex in a patterned Permalloy thin-film element. Using micromagnetic simulations we predict that the antivortex response to an ultrashort external field pulse is characterized by the production of a new antivortex as well as of a temporary vortex, followed by an annihilation process. These processes are complementary to the recently reported response of a vortex and, like for the vortex, lead to the reversal of the orientation of the antivortex core region. In addition to its fundamental interest, this dynamic magnetization process could be used for the generation and propagation of spin waves for novel logical circuits.Comment: 4 pages, 4 figures. To be published in Physical Review B (R

The magnetoelectrochemical switch

In the field of spintronics, the archetype solid-state two-terminal device is the spin valve, where the resistance is controlled by the magnetization configuration. We show here how this concept of spin-dependent switch can be extended to magnetic electrodes in solution, by magnetic control of their chemical environment. Appropriate nanoscale design allows a huge enhancement of the magnetic force field experienced by paramagnetic molecular species in solutions, which changes between repulsive and attractive on changing the electrodes' magnetic orientations. Specifically, the field gradient force created within a sub-100-nm-sized nanogap separating two magnetic electrodes can be reversed by changing the orientation of the electrodes' magnetization relative to the current flowing between the electrodes. This can result in a breaking or making of an electric nanocontact, with a change of resistance by a factor of up to 103. The results reveal how an external field can impact chemical equilibrium in the vicinity of nanoscale magnetic circuits

Angular-dependence of magnetization switching for a multi-domain dot: experiment and simulation

We have measured the in-plane angular variation of nucleation and annihilation fields of a multi-domain magnetic single dot with a microsquid. The dots are Fe/Mo(110) self-assembled in UHV, with sub-micron size and a hexagonal shape. The angular variations were quantitatively reproduced by micromagnetic simulations. Discontinuities in the variations are observed, and shown to result from bifurcations related to the interplay of the non-uniform magnetization state with the shape of the dot.Comment: 4 pages, 4 figures, for submission as a regular articl

Three-dimensional magnetic flux-closure patterns in mesoscopic Fe islands

We have investigated three-dimensional magnetization structures in numerous mesoscopic Fe/Mo(110) islands by means of x-ray magnetic circular dichroism combined with photoemission electron microscopy (XMCD-PEEM). The particles are epitaxial islands with an elongated hexagonal shape with length of up to 2.5 micrometer and thickness of up to 250 nm. The XMCD-PEEM studies reveal asymmetric magnetization distributions at the surface of these particles. Micromagnetic simulations are in excellent agreement with the observed magnetic structures and provide information on the internal structure of the magnetization which is not accessible in the experiment. It is shown that the magnetization is influenced mostly by the particle size and thickness rather than by the details of its shape. Hence, these hexagonal samples can be regarded as model systems for the study of the magnetization in thick, mesoscopic ferromagnets.Comment: 12 pages, 11 figure