Dynamics of genuine multipartite correlations in open quantum systems

We propose a measure for genuine multipartite correlations suited for the study of dynamics in open quantum systems. This measure is contextual in the sense that it depends on how information is read from the environment. It is used to study an interacting collective system of atoms undergoing phase transitions as external parameters are varied. We show that the steady state of the system can have a significant degree of genuine multipartite quantum and classical correlations, and that the proposed measure can serve as a witness of critical behavior in quantum systems.Comment: 5 pages, 3 figure

Numerical study of the effect of structure and geometry on van der Waals forces

We use multipolar expansions to find the force on a gold coated sphere above a gold substrate; we study both an empty gold shell and a gold coated polystyrene sphere. We find four characteristic separation ranges. In the first region, which for the empty gold shell occurs for distances, d, smaller than the thickness of the coating, the result agrees with that on a solid gold sphere and varies as d^(-2); for larger separations there is a region where the force behaves as if the coating is strictly two dimensional and varies as d^(-5/2); in the third region the dependence is more unspecific; in the forth region when d is larger than the radius, the force varies as d^(-4). For homogeneous objects of more general shapes we introduce a numerical method based on the solution of an integral equation for the electric field over a system of objects with arbitrary shapes. We study the effect of shape and orientation on the van der Waals interaction between an object and a substrate and between two objects.Comment: 8 pages, presented in the QFEXT07 conference, submitted to Journal of Physics

Ecological Engineering in a New Town Development: DrainageDesign in The Woodlands, Texas

This paper presents a comparative study of two different drainage designs in a 10,930-ha new town development of The Woodlands, Texas. Open surface drainage by shallow grassed swales was used in the first two subdivisions that were developed with ecological approaches. Open surface drainage mimics the natural flow regime and is regarded to mitigate development impacts on watershed. In other later subdivisions, the drainage design shifted back to a conventional stormwater drainage system, that is, curb and gutter, drop inlet, and underground piping, known to concentrate stormwater and lead to downstream flooding. The objective of this study is to compare The Woodlands’ two drainage systems on their correlation with downstream floods. Two sub-watersheds within The Woodlands that used different drainage designs were compared. U.S. Geological Survey stream data from the gauge station at the outlet of each sub-watershed were used for analysis. Geographic Information System was used to quantify the development conditions. Correlation analysis was performed using measured precipitation and streamflow data. Results show that open drainage watershed generated less storm runoff than the conventional drainage watershed, given the similar impervious area in both watersheds. Furthermore, the open surface drainage watershed responded to rainfall in a way similar to its predevelopment natural forest conditions, indicating effective flood mitigation post development. In contrast, in the conventional drainage watershed, the precipitation–streamflow correlations increased enormously after development. The open drainage system presents an advantage over the conventional drainage one in mitigating flood problems in urban development

Non-Markovian effect on the quantum discord

We study the non-Markovian effect on the dynamics of the quantum discord by exactly solving a model consisting of two independent qubits subject to two zero-temperature non-Markovian reservoirs, respectively. Considering the two qubits initially prepared in Bell-like or extended Werner-like states, we show that there is no occurrence of the sudden death, but only instantaneous disappearance of the quantum discord at some time points, in comparison to the entanglement sudden death in the same range of the parameters of interest. It implies that the quantum discord is more useful than the entanglement to describe quantum correlation involved in quantum systems.Comment: 5 pages, 5 figure

Efficient 5-axis CNC trochoidal flank milling of 3D cavities using custom-shaped cutting tools

A novel method for trochoidal flank milling of 3D cavities bounded by free-form surfaces is proposed. Existing 3D trochoidal milling methods use on-market milling tools whose shape is typically cylindrical or conical, and is therefore not well-suited for meeting fine milling tolerances required for finishing of benchmark free-form surfaces like blades or blisks. In contrast, our variational framework incorporates the shape of the tool into the optimization cycle and looks not only for the trochoidal milling paths, but also for the shape of the tool itself. High precision quality is ensured by firstly designing flank milling paths for the side surfaces that delimit the motion space, in which the trochoidal milling paths are further computed. Additionally, the material removal rate is maximized with the cutter-workpiece engagement being constrained under a given tolerance. Our framework also supports multi-layer approach that is necessary to handle deep cavities. The ability and efficacy of the proposed method are demonstrated by several industrial benchmarks, showing that our approach meets fine machining tolerances using only a few trochoidal paths.RYC-2017-2264

Natural Realizations of Seesaw in Mini-Warped Minimal SO(10)

The minimal SUSY SO(10) GUT models with {\bf 10}, {\bf 126} and {\bf 210} Higgs and only renormalizable couplings has been shown to provide a simple way to understand the neutrino mixings as well as the ratio $\Delta m^2_\odot/\Delta m^2_A$ in terms of quark mixing parameter $\theta_{Cabibbo}$, provided neutrino masses are described by type II seesaw formula. However, in this minimal picture, it is impossible to realize type II dominance with renormalizable couplings in 4-dimensions. We show that this problem can be cured by embedding this model into a warped 5-dimensional space time with warping between the Planck and the GUT scale, where both type II as well as mixed seesaw formulae can be realized in a natural manner without expanding the Higgs sector. These models also avoid the possible problem of threshold effects associated with large Higgs representations since the theory above the GUT scale is now strongly coupled.Comment: 20 pages and one figur

Automatic fitting of conical envelopes to free-form surfaces for flank CNC machining

We propose a new algorithm to detect patches of free-form surfaces that can be well approximated by envelopes of a rotational cone under a rigid body motion. These conical envelopes are a preferable choice from the manufacturing point of view as they are, by-definition, manufacturable by computer numerically controlled (CNC) machining using the efficient flank (peripheral) method with standard conical tools. Our geometric approach exploits multi-valued vector fields that consist of vectors in which the point-surface distance changes linearly. Integrating such vector fields gives rise to a family of integral curves, and, among them, linear segments that further serve as conical axes are quickly extracted. The lines that additionally admit tangential motion of the associated cone along the reference geometry form a set of candidate lines that are sequentially clustered and ordered to initialize motions of a rigid truncated cone. We validate our method by applying it on synthetic examples with exact envelopes, recovering correctly the exact solutions, and by testing it on several benchmark industrial datasets, detecting manufacturable conical envelope patches within fine tolerances

Magnetic Field Control of the Quantum Chaotic Dynamics of Hydrogen Analogues in an Anisotropic Crystal Field

We report magnetic field control of the quantum chaotic dynamics of hydrogen analogues in an anisotropic solid state environment. The chaoticity of the system dynamics was quantified by means of energy level statistics. We analyzed the magnetic field dependence of the statistical distribution of the impurity energy levels and found a smooth transition between the Poisson limit and the Wigner limit, i.e. transition between regular Poisson and fully chaotic Wigner dynamics. Effect of the crystal field anisotropy on the quantum chaotic dynamics, which manifests itself in characteristic transitions between regularity and chaos for different field orientations, was demonstrated.Comment: 4 pages, 4 figure

Characterizing envelopes of moving rotational cones and applications in CNC machining

Motivated by applications in CNC machining, we provide a characterization of surfaces which are enveloped by a one-parametric family of congruent rotational cones. As limit cases, we also address ruled surfaces and their offsets. The characterizations are higher order nonlinear PDEs generalizing the ones by Gauss and Monge for developable surfaces and ruled surfaces, respectively. The derivation includes results on local approximations of a surface by cones of revolution, which are expressed by contact order in the space of planes. To this purpose, the isotropic model of Laguerre geometry is used as there rotational cones correspond to curves (isotropic circles) and higher order contact is computed with respect to the image of the input surface in the isotropic model. Therefore, one studies curve-surface contact that is conceptually simpler than the surface-surface case. We show that, in a generic case, there exist at most six positions of a fixed rotational cone that have third order contact with the input surface. These results are themselves of interest in geometric computing, for example in cutter selection and positioning for flank CNC machining.RYC-2017-2264

The Casimir effect for parallel plates at finite temperature in the presence of one fractal extra compactified dimension

We discuss the Casimir effect for massless scalar fields subject to the Dirichlet boundary conditions on the parallel plates at finite temperature in the presence of one fractal extra compactified dimension. We obtain the Casimir energy density with the help of the regularization of multiple zeta function with one arbitrary exponent and further the renormalized Casimir energy density involving the thermal corrections. It is found that when the temperature is sufficiently high, the sign of the Casimir energy remains negative no matter how great the scale dimension $\delta$ is within its allowed region. We derive and calculate the Casimir force between the parallel plates affected by the fractal additional compactified dimension and surrounding temperature. The stronger thermal influence leads the force to be stronger. The nature of the Casimir force keeps attractive.Comment: 14 pages, 2 figure