Sub-10 nm colloidal lithography for integrated spin-photo-electronic devices

Colloidal lithography [1] is how patterns are reproduced in a variety of natural systems and is used more and more as an efficient fabrication tool in bio-, opto-, and nano-technology. Nanoparticles in the colloid are made to form a mask on a given material surface, which can then be transferred via etching into nano-structures of various sizes, shapes, and patterns [2,3]. Such nanostructures can be used in biology for detecting proteins [4] and DNA [5,6], for producing artificial crystals in photonics [7,8] and GHz oscillators in spin-electronics [9-14]. Scaling of colloidal patterning down to 10-nm and below, dimensions comparable or smaller than the main relaxation lengths in the relevant materials, including metals, is expected to enable a variety of new ballistic transport and photonic devices, such as spin-flip THz lasers [15]. In this work we extend the practice of colloidal lithography to producing large-area, near-ballistic-injection, sub-10 nm point-contact arrays and demonstrate their integration in to spin-photo-electronic devices.Comment: 15 pages, 5 figure

Perturbations of Spatially Closed Bianchi III Spacetimes

Motivated by the recent interest in dynamical properties of topologically nontrivial spacetimes, we study linear perturbations of spatially closed Bianchi III vacuum spacetimes, whose spatial topology is the direct product of a higher genus surface and the circle. We first develop necessary mode functions, vectors, and tensors, and then perform separations of (perturbation) variables. The perturbation equations decouple in a way that is similar to but a generalization of those of the Regge--Wheeler spherically symmetric case. We further achieve a decoupling of each set of perturbation equations into gauge-dependent and independent parts, by which we obtain wave equations for the gauge-invariant variables. We then discuss choices of gauge and stability properties. Details of the compactification of Bianchi III manifolds and spacetimes are presented in an appendix. In the other appendices we study scalar field and electromagnetic equations on the same background to compare asymptotic properties.Comment: 61 pages, 1 figure, final version with minor corrections, to appear in Class. Quant. Gravi

Swinging of red blood cells under shear flow

We reveal that under moderate shear stress (of the order of 0.1 Pa) red blood cells present an oscillation of their inclination (swinging) superimposed to the long-observed steady tanktreading (TT) motion. A model based on a fluid ellipsoid surrounded by a visco-elastic membrane initially unstrained (shape memory) predicts all observed features of the motion: an increase of both swinging amplitude and period (1/2 the TT period) upon decreasing the shear stress, a shear stress-triggered transition towards a narrow shear stress-range intermittent regime of successive swinging and tumbling, and a pure tumbling motion at lower shear stress-values.Comment: 4 pages 5 figures submitted to Physical Review Letter

An Introduction to Conformal Ricci Flow

We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the Conformal Ricci Flow Equations because of the role that conformal geometry plays in constraining the scalar curvature. These equations are analogous to the incompressible Navier-Stokes equations of fluid mechanics inasmuch as a conformal pressure arises as a Lagrange multiplier to conformally deform the metric flow so as to maintain the scalar curvature constraint. The equilibrium points are Einstein metrics with a negative Einstein constant and the conformal pressue is shown to be zero at an equilibrium point and strictly positive otherwise. The geometry of the conformal Ricci flow is discussed as well as the remarkable analytic fact that the constraint force does not lose derivatives and thus analytically the conformal Ricci equation is a bounded perturbation of the classical unnormalized Ricci equation. That the constraint force does not lose derivatives is exactly analogous to the fact that the real physical pressure force that occurs in the Navier-Stokes equations is a bounded function of the velocity. Using a nonlinear Trotter product formula, existence and uniqueness of solutions to the conformal Ricci flow equations is proven. Lastly, we discuss potential applications to Perelman's proposed implementation of Hamilton's program to prove Thurston's 3-manifold geometrization conjectures.Comment: 52 pages, 1 figur

Space/time noncommutative field theories and causality

As argued previously, amplitudes of quantum field theories on noncommutative space and time cannot be computed using naive path integral Feynman rules. One of the proposals is to use the Gell-Mann--Low formula with time-ordering applied before performing the integrations. We point out that the previously given prescription should rather be regarded as an interaction point time-ordering. Causality is explicitly violated inside the region of interaction. It is nevertheless a consistent procedure, which seems to be related to the interaction picture of quantum mechanics. In this framework we compute the one-loop self-energy for a space/time noncommutative \phi^4 theory. Although in all intermediate steps only three-momenta play a role, the final result is manifestly Lorentz covariant and agrees with the naive calculation. Deriving the Feynman rules for general graphs, we show, however, that such a picture holds for tadpole lines only.Comment: 16 pages, LaTeX, uses feynmf macros, one reference added; ooops, version 2 was an older one

On the D0D^0 -- DsD_s lifetime difference and τ→7π+ντ\tau\to 7\pi + \nu_\tau decays

In this paper we discuss some aspects of inclusive decays of charmed mesons and also decays of the $\tau$ lepton into $\nu_\tau + 7\pi$. We find that phase space effects are likely to explain the observed lifetime ratio $\tau(D_s^+) / \tau(D^0)$ = 1.17. In particular one need not appeal to a large annihilation contribution in the inclusive $D^0$ decay which, being absent in $D_s^+$ decays could also contribute to the enhanced $D^0$ decay rate relative to that of the $D_s^+$. Examining a separate problem, we find that the rate for $\tau\to \nu_\tau + 7\pi$ is almost completely dominated by the tiny phase space for the final eight particle state. Using an effective chiral Lagrangian to estimate the matrix element yields a branching ratio into the channel of interest far smaller than the present upper bound.Comment: No figure

Finishing of ABS-M30 Parts Manufactured with Fused Deposition Modeling with Focus on Dimensional Accuracy

Fused Deposition Modeling (FDM) parts are prone to process-related rough and wavy surfaces with stair-stepping effects whenever the parts produced have sloped or rounded geometries. These stair-stepping effects can be reduced by using a smaller slice height, but complete elimination is not possible. In this paper, FDM parts manufactured with the material ABS-M30 are finished using mass finishing methods. The mass finishing is done with a trough vibrator, which is comparatively gentle to the parts in comparison to other mass finishing technologies. The analysis discusses the surface-smoothing effect of finishing time and intensity on various part sizes and build orientations. In addition, the dimensional accuracy of the parts after the finishing process is examined.Mechanical Engineerin