Entanglement Entropy: Helicity versus Spin

For a massive spin 1/2 field, we present the reduced spin and helicity density matrix, respectively, for the same pure one particle state. Their relation has also been developed. Furthermore, we calculate and compare the corresponding entanglement entropy for spin and helicity within the same inertial reference frame. Due to the distinct dependence on momentum degree of freedom between spin and helicity states, the resultant helicity entropy is different from that of spin in general. In particular, we find that both helicity entanglement for a spin eigenstate and spin entanglement for a right handed or left handed helicity state do not vanish and their Von Neumann entropy has no dependence on the specific form of momentum distribution as long as it is isotropic.Comment: 3 pages, title changed, typos corrected, version to appear in Int. J. Quant. In

Optimal surface profile design of deployable mesh reflectors via a force density strategy

Based on a force density method coupled with optimal design of node positions, a novel approach for optimal surface profile design of mesh reflectors is presented. Uniform tension is achieved by iterations on coefficients of force density. The positions of net nodes are recalculated in each iteration so that the faceting RMS error of the reflector surface is minimized. Applications of both prime focus and offset configurations are demonstrated. The simulation results show the effectiveness of the proposed approach

Microstructural stability and lattice misfit characterization of nimonic 263

Nimonic 263 has been selected as a candidate header/piping material of advanced ultra-supercritical (A-USC) boilers for the next generation of fossil fuel power plant. Experimental assessments on the microstructural stability of this material are presented in this paper. Microstructural evolution has been quantified by high resolution field emission SEM and TEM. Electron diffraction and the combined XRD and Gaussian peak-fitting have been applied to investigate the coherency and lattice misfit between the gamma prime precipitates and the gamma matrix. The microstructure subjected to solution and hardening treatment consists of gamma-matrix and a network of carbide precipitates along the grain boundaries. Large quantities of fine gamma prime-Ni3(Ti,Al) precipitates were observed, with an average size of 17 nm and coherent with the matrix lattice. The overall misfit has been quantified to be 0.28%. After long term aging at 700 and 725 °C for various periods up to 20,000 hours, gamma prime was still the predominant precipitate and mostly coherent with the matrix. A few needle-shape eta-Ni3Ti intermetallic precipitates were found in the grain boundary regions. The gamma prime size has grown progressively to 78 nm, accompanied by the gamma-gamma prime constrained misfit increasing to 0.50%. Moreover, the M23C6-type grain boundary carbides were found to have experienced morphological evolution, including the nucleation of Widmanstatten-type needles and their initial growth towards the matrix

Towards a Critical Contemporary Design in Historic Settings: Reclaiming the Inherent Relationship between the Old and the New, Reclaiming Continuity in Differentiation

Contemporary design in historic settings is a public concern as it fundamentally impacts the protection of historic resources, which specifically refers to new constructions in historical and existing context. At the core of design in historic settings lies the issues of studying, interpreting, and expressing the relationship between the old and the new. This thesis intends to address some of the limitations in how architectural designers approach these issues in historic settings and propose alternative design strategies. The strategies include analysis and methodology to integrate preservation philosophies with architectural design. They aim to produce new designs in historic settings which could go beyond the dichotomy between “strict preservation” and “strict differentiation” and to find a balance between “copies” and “experiments”. The thesis intends to reclaim a common ground between preservation and design. It reclaims an inherent relationship between the old and the new by proposing three alternative strategies to position design in historic preservation as both a creative and conservative act

Behavior of Different Sizes of Strontium Titanate Substrates in Electrochemical Modifications

In our previous atomic force microscopy (AFM) studies of 5 mm x 5 mm single crystal SrTiO3 (STO(100)) substrates, rutile TiO2 crystals were found on the substrates surfaces after electrochemical modification. These crystals were found mainly in the area of contact between the substrate and the gold-coated alligator clip that was not supposed to be immersed into the electrolyte and that served as a connection between the STO working electrode and the potentiostat circuit. The size and density of the crystals were found to depend on electrochemical potential, its polarity, the length of modifying time, and the total electrical charge that passed during electrochemical modification. In this work, larger size (10 mm x 10 mm) SrTiO3 substrates were used for electrochemical modification and the number of gold-STO contacts were varied to test for the ability to spatially pattern rutile TiO2 particles on STO. Eighteen (10 mm x 10 mm) STO samples were subjected to electrochemical treatments similar to the ones applied to the smaller substrates. When the STO working electrode was clipped with a single alligator clip, anodic currents were measured, albeit at levels that were lower than ones found in our previous work. While darkening of the electrodes in the areas of contact was visually observable, no rutile TiO2 crystals were found on the surface as verified by XRD. When anodically polarized, the STO working electrodes clipped with two alligator clips showed an unusual behavior, passing cathodic currents during the entire modification period. While such behavior is not fully understood, it has been found that the polarity of the current correlated with the level to which the electrodes were dipped in 1 M NaOH electrolyte such that the direction of the electrical current switched from cathodic at low levels of submersion to anodic when the STO electrodes were more deeply immersed into the electrolyte. It should also be noted that the magnitude of the cathodic current was sometimes not very different from the one that corresponded to the instrument background (measured by short circuiting the cell by detaching the potentiostat lead from the working electrode)

Behavior of Different Sizes of Strontium Titanate Substrates in Electrochemical Modifications

In our previous atomic force microscopy (AFM) studies of 5 mm x 5 mm single crystal SrTiO3 (STO(100)) substrates, rutile TiO2 crystals were found on the substrates surfaces after electrochemical modification. These crystals were found mainly in the area of contact between the substrate and the gold-coated alligator clip that was not supposed to be immersed into the electrolyte and that served as a connection between the STO working electrode and the potentiostat circuit. The size and density of the crystals were found to depend on electrochemical potential, its polarity, the length of modifying time, and the total electrical charge that passed during electrochemical modification. In this work, larger size (10 mm x 10 mm) SrTiO3 substrates were used for electrochemical modification and the number of gold-STO contacts were varied to test for the ability to spatially pattern rutile TiO2 particles on STO. Eighteen (10 mm x 10 mm) STO samples were subjected to electrochemical treatments similar to the ones applied to the smaller substrates. When the STO working electrode was clipped with a single alligator clip, anodic currents were measured, albeit at levels that were lower than ones found in our previous work. While darkening of the electrodes in the areas of contact was visually observable, no rutile TiO2 crystals were found on the surface as verified by XRD. When anodically polarized, the STO working electrodes clipped with two alligator clips showed an unusual behavior, passing cathodic currents during the entire modification period. While such behavior is not fully understood, it has been found that the polarity of the current correlated with the level to which the electrodes were dipped in 1 M NaOH electrolyte such that the direction of the electrical current switched from cathodic at low levels of submersion to anodic when the STO electrodes were more deeply immersed into the electrolyte. It should also be noted that the magnitude of the cathodic current was sometimes not very different from the one that corresponded to the instrument background (measured by short circuiting the cell by detaching the potentiostat lead from the working electrode)

Effect of the Min system on timing of bacterial cell division

In this work, we analyze the effect of the Min protein system on timing of cell division. We do this in a quantitative way by comparing the cell division waiting time of wild type and min

Well-posedness and Ill-posedness of the Nonlinear Beam Equation

The dissertation consists of two parts, Well-posedness and ill-posedness for the nonlinear beam equation and Strichartz estimates of the beam equation on the domains. In the first part, we will work to introduce the further studies of Strichartz estimates with initial data both in homogeneous Sobolev spaces $\\dot{H}^s\ imes\\dot{H}^{s-2}$ and in inhomogeneous Sobolev space ${H}^s\ imes{H}^{s-2}$. We take advantage of the Strichartz estimates to build well-posedness theorems of the nonlinear beam equations for rough data by the Picard iteration method. We will apply these methods on the nonlinear beam equation with ``energy critical, subcritical and ``energy supercritical cases. Since the beam equation does not satisfy finite speed propagation, we introduce the further result of the fractional chain rule to deal with the ``energy super critical case. We obtain the global well-posedness with initial data in homogeneous Sobolev space $\\dot{H}^s\ imes\\dot{H}^{s-2}$ and local well-posedness with initial data in inhomogeneous Sobolev space ${H}^s\ imes{H}^{s-2}$. At the same time, we extend the range of order $s$. With the global existence for small data, we prove the scattering and asymptotic completeness result for the nonlinear beam equation. Last we prove the nonlinear beam equation is ill-posed in defocusing case $\\omega=-1$ when $