On Recurrent Reachability for Continuous Linear Dynamical Systems

The continuous evolution of a wide variety of systems, including continuous-time Markov chains and linear hybrid automata, can be described in terms of linear differential equations. In this paper we study the decision problem of whether the solution $\boldsymbol{x}(t)$ of a system of linear differential equations $d\boldsymbol{x}/dt=A\boldsymbol{x}$ reaches a target halfspace infinitely often. This recurrent reachability problem can equivalently be formulated as the following Infinite Zeros Problem: does a real-valued function $f:\mathbb{R}_{\geq 0}\rightarrow\mathbb{R}$ satisfying a given linear differential equation have infinitely many zeros? Our main decidability result is that if the differential equation has order at most $7$, then the Infinite Zeros Problem is decidable. On the other hand, we show that a decision procedure for the Infinite Zeros Problem at order $9$ (and above) would entail a major breakthrough in Diophantine Approximation, specifically an algorithm for computing the Lagrange constants of arbitrary real algebraic numbers to arbitrary precision.Comment: Full version of paper at LICS'1

Treatment of sanitary sewer overflow with fixed media bioreactors

Fixed media bioreactors (biofilters) are a promising and proven technology used for wastewater treatment in unsewered rural areas. As an on-site treatment system, it cart potentially provide high treatment efficiency with a relatively low cost and maintenance. This research expanded the application of fixed media bioreactors and tested their feasibility in the treatment of sanitary sewer overflows (SSO) at high hydraulic loading of 0.2 m/h. Sand, peat, and textile (felt) were used as media to treat simulated 6-h peak flows for a 25-year SSO event in the city of Columbus, Ohio. The influent SSO was a mixture of primary sludge from a wastewater treatment plant diluted with tap water. The efficiency of treatment was measured as changes in the concentrations of biochemical oxygen demand (BOD5), chemical oxygen demand (COD), and total suspended solids (TSS). Sand as a filter medium had the best removal of organic matter with average 84% reduction of BOD5 and 90% of COD. The TSS removal was more than 90% in all media. Peat and felt were,somewhat more efficient than the sand in the TSS removal. The media type and influent BOD5 concentration were two major factors that impacted the treatment of BOD5 (p<0.007). For the treatment of COD, significant factors were media type, influent concentration, and time course of loading in each SSO event (ps <= 0.001)

Effect of pressure on the quantum spin ladder material IPA-CuCl3

Inelastic neutron scattering and bulk magnetic susceptibility studies of the quantum S=1/2 spin ladder system IPA-CuCl3 are performed under hydrostatic pressure. The pressure dependence of the spin gap $\Delta$ is determined. At $P=1.5$ GPa it is reduced to $\Delta=0.79$ meV from $\Delta=1.17$ meV at ambient pressure. The results allow us to predict a soft-mode quantum phase transition in this system at P$_\mathrm{c}\sim 4$ GPa. The measurements are complicated by a proximity of a structural phase transition that leads to a deterioration of the sample.Comment: 5 pages, 4 figure

Small ball probability, Inverse theorems, and applications

Let $\xi$ be a real random variable with mean zero and variance one and $A={a_1,...,a_n}$ be a multi-set in $\R^d$. The random sum $$S_A := a_1 \xi_1 + ... + a_n \xi_n$$ where $\xi_i$ are iid copies of $\xi$ is of fundamental importance in probability and its applications. We discuss the small ball problem, the aim of which is to estimate the maximum probability that $S_A$ belongs to a ball with given small radius, following the discovery made by Littlewood-Offord and Erdos almost 70 years ago. We will mainly focus on recent developments that characterize the structure of those sets $A$ where the small ball probability is relatively large. Applications of these results include full solutions or significant progresses of many open problems in different areas.Comment: 47 page

Nanoimprint lithography of Al nanovoids for deep-UV SERS.

Deep-ultraviolet surface-enhanced Raman scattering (UV-SERS) is a promising technique for bioimaging and detection because many biological molecules possess UV absorption lines leading to strongly resonant Raman scattering. Here, Al nanovoid substrates are developed by combining nanoimprint lithography of etched polymer/silica opal films with electron beam evaporation, to give a high-performance sensing platform for UV-SERS. Enhancement by more than 3 orders of magnitude in the UV-SERS performance was obtained from the DNA base adenine, matching well the UV plasmonic optical signatures and simulations, demonstrating its suitability for biodetection.We acknowledge financial support from EPSRC grant EP/G060649/1, EP/I012060/1, EP/J007552/1, ERC grant LINASS 320503.This is the final version of the article. It first appeared from ACS via http://dx.doi.org/10.1021/am505511

Coupled cavity QED for coherent control of photon transmission (I): Green function approach for hybrid systems with two-level doping

This is the first one of a series of our papers theoretically studying the coherent control of photon transmission along the coupled resonator optical waveguide (CROW) by doping artificial atoms for various hybrid structures. We will provide the several approaches correspondingly based on Green function, the mean field method and spin wave theory et al. In the present paper we adopt the two-time Green function approach to study the coherent transmission photon in a CROW with homogeneous couplings, each cavity of which is doped by a two-level artificial atom. We calculate the two-time correlation function for photon in the weak-coupling case. Its poles predict the exact dispersion relation, which results in the group velocity coherently controlled by the collective excitation of the doping atoms. We emphasize the role of the population inversion of doping atoms induced by some polarization mechanism.Comment: 11 pages, 9 figure

Construction of the free energy landscape by the density functional theory

On the basis of the density functional theory, we give a clear definition of the free energy landscape. To show the usefulness of the definition, we construct the free energy landscape for rearrangement of atoms in an FCC crystal of hard spheres. In this description, the cooperatively rearranging region (CRR) is clealy related to the hard spheres involved in the saddle between two adjacent basins. A new concept of the simultaneously rearranging region (SRR) emerges naturally as spheres defined by the difference between two adjacent basins. We show that the SRR and the CRR can be determined explicitly from the free energylandscape.Comment: 11 pages, 3 figures, submitted to J. Chem. Phy

Anisotropic Neutron Spin Resonance in Superconducting BaFe1.9_{1.9}Ni0.1_{0.1}As2_2

We use polarized inelastic neutron scattering to show that the neutron spin resonance below $T_c$ in superconducting BaFe$_{1.9}$Ni$_{0.1}$As$_2$ ($T_c=20$ K) is purely magnetic in origin. Our analysis further reveals that the resonance peak near 7~meV only occurs for the planar response. This challenges the common perception that the spin resonance in the pnictides is an isotropic triplet excited state of the singlet Cooper pairs, as our results imply that only the $S_{001}=\pm1$ components of the triplet are involved

Self-aligned colloidal lithography for controllable and tuneable plasmonic nanogaps.

Au nanoparticles (NPs) deposited on a substrate function as ring shaped colloidal shadow masks. Using e-beam evaporation of gold, nanometer sized gaps are formed as a result. The size of these gaps can be accurately tuned by controlling the thickness of the gold deposition, thereby tuning the plasmonic coupling of the NPs with the substrate. The clean cavity produced between the Au NPs and the Au film provides an excellent SERS platform for trace molecule detection.The authors acknowledge the fi nancial support of this research from EPSRC grant EP/G060649/1, EP/I012060/1, and ERC grant LINASS 320503. FB acknowledges support from the Winton Pro-gramme for the Physics of Sustainability.This article was originally published in Small, 2015, DOI: 10.1002/smll.201402639