Nanoimprinted substrates for high-yield production of topological insulator nanoribbons

We present a growth process mediated by nanoimprinted nanostructures specifically for producing bismuth selenide (Bi₂Se₃) topological insulator nanoribbons with a high yield. In this process, topological insulator nanostructures are grown on nanoimprinted gratings by using a nanoparticle-catalyzed vapor–liquid–solid mechanism. In comparison with the growth processes performed on flat and randomly rough substrates, such a nanograting-mediated growth method produces topological insulator nanoribbons with a higher yield (～15?000 nanoribbons/mm²), a narrower average ribbon width (w _avg<60 nm), and a higher uniformity in ribbon width (σ<30 nm); effectively suppresses the formation of other unwanted morphologies; and also results in the axial growth of nanoribbons along specific in-plane directions relative to pre-structured gratings. Such technical merits of nanograting-mediated growth are attributed to the preferential nucleation of Bi₂Se₃ crystal seeds and the concomitant pinning of catalytic nanoparticles at ordered grating edges. Finally, Aharonov–Bohm interference oscillations in the magnetoresistance were observed and demonstrated the coherent transport of electrons through topological surface states of Bi₂Se₃ nanoribbons. This growth process in combination with large-area nanoimprint lithography could serve as an important foundation for nanomanufacturing topological insulator nanoribbons with controllable feature size, large-area uniformity, and ordering, suitable for applications in future low-dissipation nanoelectronics.     

Computing inertia sets using atoms

We consider the problem of computing inertia sets for graphs. By using tools for combining the inertia sets of smaller graphs we can reduce this problem to understanding the inertia sets for three-connected graphs that are not joins. We term such graphs atoms and give the inertia sets for all atoms on at most seven vertices. This can be used to compute the inertia sets for all graphs on at most seven vertices.     

Additive Hermitian idempotent preservers between operator algebras

Let L be an additive map between (real or complex) matrix algebras sending $n\times n$ Hermitian idempotent matrices to $m\times m$ Hermitian idempotent matrices. We show that there are nonnegative integers $p,q$ with $n(p+q)=r\le m$ and an $m\times m$ unitary matrix U such that$L(A)=U[(I_p?A)\oplus (I_q?A^t)\oplus 0_{m?r}]U^{?},\text{for any}n\times n\text{Hermitian}A\text{with rational trace}.$ We also extend this result to the (complex) von Neumann algebra setting, and provide a supplement to the Dye-Bunce-Wright Theorem asserting that every additive map of Hermitian idempotents extends to a Jordan ?-homomorphism.     

On the stability of the open-string QED neutron and dark matter

The European Physical Journal A - Efficient neutron transport is a key ingredient to the performance of ultracold neutron (UCN) sources, important to meeting the challenges placed by high precision...     

On constrained multivariate splines and their approximations

Summary The variational formulation of multivariate spline functions is generalized to include cases where the function has to satisfy inequality constraints such as positivity and convexity. Condition for existence and uniqueness of a solution is given. Approximation to the solution can be obtained by solving the variational problem in a finite dimensional subspace. Conditions for convergence and error estimates of the approximations are presented, both for interpolation problems and smoothing problems. The general theory is illustrated by specific examples including the volume-matching problem and the one-sided thin plate spline.This research is partially supported by the U.S. Army Contract No. DAAG 29-77-G-0207, and by NSF Grant No. MCS-8101836Part of this paper is based on Chapters 2 and 3 of the author's Ph. D. thesis. The author would like to express his sincere thanks to Professor Grance Wahba and to two referees for many helpful comments     

Detecting and Diagnostic Checking Multivariate Conditional Heteroscedastic Time Series Models

Two tests for multivariate conditional heteroscedastic models are proposed. One is based on the cross-correlations of standardized squared residuals and the other is a score (Lagrange multiplier) test. The cross-correlations test can be used to detect the presence of multivariate conditional heteroscedasticity whereas the other test can be used for diagnostic checking. Simulation studies on the size and power of the test statistics are reported. The application of the tests is illustrated by an example using the S & P 500 and Sydney All Ordinary Indexes.     

Analytic soliton solutions of cubic‐quintic Ginzburg‐Landau equation with variable nonlinearity and spectral filtering in fiber lasers

In fiber lasers, the study of the cubic‐quintic complex Ginzburg‐Landau equations (CGLE) has attracted much attention. In this paper, four families (kink solitons, gray solitons, Y‐type solitons and combined solitons) of exact soliton solutions for the variable‐coefficient cubic‐quintic CGLE are obtained via the modified Hirota method. Appropriate parameters are chosen to investigate the properties of solitons. The influences of nonlinearity and spectral filtering effect are discussed in these obtained exact soliton solutions, respectively. Methods to amplify the amplitude and compress the width of solitons are put forward. Numerical simulation with split‐step Fourier method and fourth‐order Runge‐Kutta algorithm are carried out to validate some of the analytic results. Transformation from the variable‐coefficient cubic‐quintic CGLE to the constant coefficients one is proposed. The results obtained may have certain applications in soliton control in fiber lasers, and may have guiding value in experiments in the future.