Construction of nested space-filling designs

New types of designs called nested space-filling designs have been proposed for conducting multiple computer experiments with different levels of accuracy. In this article, we develop several approaches to constructing such designs. The development of these methods also leads to the introduction of several new discrete mathematics concepts, including nested orthogonal arrays and nested difference matrices.Comment: Published in at http://dx.doi.org/10.1214/09-AOS690 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization

In this article, we study an analog of the Bj\"orling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $\gamma$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $\gamma$, find an isothermic surface that is tangent to $\gamma$ and that has $v$ and $w$ as principal directions of curvature. We prove that solutions to that problem can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is sampled along $\gamma$, and passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.Comment: 29 pages, some figure

Approximation of conformal mappings using conformally equivalent triangular lattices

Consider discrete conformal maps defined on the basis of two conformally equivalent triangle meshes, that is edge lengths are related by scale factors associated to the vertices. Given a smooth conformal map $f$, we show that it can be approximated by such discrete conformal maps $f^\epsilon$. In particular, let $T$ be an infinite regular triangulation of the plane with congruent triangles and only acute angles (i.e.\ $<\pi/2$). We scale this tiling by $\epsilon>0$ and approximate a compact subset of the domain of $f$ with a portion of it. For $\epsilon$ small enough we prove that there exists a conformally equivalent triangle mesh whose scale factors are given by $\log|f'|$ on the boundary. Furthermore we show that the corresponding discrete conformal maps $f^\epsilon$ converge to $f$ uniformly in $C^1$ with error of order $\epsilon$.Comment: 14 pages, 3 figures; v2 typos corrected, revised introduction, some proofs extende

Ge quantum dot arrays grown by ultrahigh vacuum molecular beam epitaxy on the Si(001) surface: nucleation, morphology and CMOS compatibility

Issues of morphology, nucleation and growth of Ge cluster arrays deposited by ultrahigh vacuum molecular beam epitaxy on the Si(001) surface are considered. Difference in nucleation of quantum dots during Ge deposition at low (<600 deg C) and high (>600 deg. C) temperatures is studied by high resolution scanning tunneling microscopy. The atomic models of growth of both species of Ge huts---pyramids and wedges---are proposed. The growth cycle of Ge QD arrays at low temperatures is explored. A problem of lowering of the array formation temperature is discussed with the focus on CMOS compatibility of the entire process; a special attention is paid upon approaches to reduction of treatment temperature during the Si(001) surface pre-growth cleaning, which is at once a key and the highest-temperature phase of the Ge/Si(001) quantum dot dense array formation process. The temperature of the Si clean surface preparation, the final high-temperature step of which is, as a rule, carried out directly in the MBE chamber just before the structure deposition, determines the compatibility of formation process of Ge-QD-array based devices with the CMOS manufacturing cycle. Silicon surface hydrogenation at the final stage of its wet chemical etching during the preliminary cleaning is proposed as a possible way of efficient reduction of the Si wafer pre-growth annealing temperature.Comment: 30 pages, 11 figure

A Microscopic Mechanism for Muscle's Motion

The SIRM (Stochastic Inclined Rods Model) proposed by H. Matsuura and M. Nakano can explain the muscle's motion perfectly, but the intermolecular potential between myosin head and G-actin is too simple and only repulsive potential is considered. In this paper we study the SIRM with different complex potential and discuss the effect of the spring on the system. The calculation results show that the spring, the effective radius of the G-actin and the intermolecular potential play key roles in the motion. The sliding speed is about $4.7\times10^{-6}m/s$ calculated from the model which well agrees with the experimental data.Comment: 9 pages, 6 figure

Efficiency optimization in a correlation ratchet with asymmetric unbiased fluctuations

The efficiency of a Brownian particle moving in periodic potential in the presence of asymmetric unbiased fluctuations is investigated. We found that there is a regime where the efficiency can be a peaked function of temperature, which proves that thermal fluctuations facilitate the efficiency of energy transformation, contradicting the earlier findings (H. kamegawa et al. Phys. Rev. Lett. 80 (1998) 5251). It is also found that the mutual interplay between asymmetry of fluctuation and asymmetry of the potential may induce optimized efficiency at finite temperature. The ratchet is not most efficiency when it gives maximum current.Comment: 10 pages, 7 figure

An Empirical Air-to-Ground Channel Model Based on Passive Measurements in LTE

In this paper, a recently conducted measurement campaign for unmanned-aerial-vehicle (UAV) channels is introduced. The downlink signals of an in-service long-time-evolution (LTE) network which is deployed in a suburban scenario were acquired. Five horizontal and five vertical flight routes were considered. The channel impulse responses (CIRs) are extracted from the received data by exploiting the cell specific signals (CRSs). Based on the CIRs, the parameters of multipath components (MPCs) are estimated by using a high-resolution algorithm derived according to the space-alternating generalized expectation-maximization (SAGE) principle. Based on the SAGE results, channel characteristics including the path loss, shadow fading, fast fading, delay spread and Doppler frequency spread are thoroughly investigated for different heights and horizontal distances, which constitute a stochastic model.Comment: 15 pages, submitted version to IEEE Transactions on Vehicular Technology. Current status: Early acces

Sensitive Chemical Compass Assisted by Quantum Criticality

The radical-pair-based chemical reaction could be used by birds for the navigation via the geomagnetic direction. An inherent physical mechanism is that the quantum coherent transition from a singlet state to triplet states of the radical pair could response to the weak magnetic field and be sensitive to the direction of such a field and then results in different photopigments in the avian eyes to be sensed. Here, we propose a quantum bionic setup for the ultra-sensitive probe of a weak magnetic field based on the quantum phase transition of the environments of the two electrons in the radical pair. We prove that the yield of the chemical products via the recombination from the singlet state is determined by the Loschmidt echo of the environments with interacting nuclear spins. Thus quantum criticality of environments could enhance the sensitivity of the detection of the weak magnetic field.Comment: 4 pages, 3 figure

Soil Quality of the Land Under Coffee-Based Farming System (Case Study at Sumberjaya, West Lampung)

Forest conversion to coffee-based farming systems has raised concern among many stakeholders since it may create serious impact to the deterioration of forest functions, declining soil productivity in particular and land degradation in general. Study on the impact of forest conversion on changes of soil quality, and the role of coffee for soil quality recovery has been conducted at Bodong and Laksana Sub Village of Sumberjaya Village, West Lampung. In Laksana, the observed landuse consisted of young (&lt; 3 years) coffee plantation, mature (&gt; 10 years) coffee, mix farming (multistrata), caliandra and forest, while in Bodong are young and mature coffee plantations and forest. The soil quality parameters used in this experiment were soil organic matter status and soil physical properties. Changes of soil quality as affected by forest conversion to coffee farming depends on soil resistance (resilience to structural break down). Soils with low resistance are easier to degrade than those with high soil resistance. The mix (multistarata) system shows better impact on soil quality than monoculture system does

On the Stability and Structural Dynamics of Metal Nanowires

This article presents a brief review of the nanoscale free-electron model, which provides a continuum description of metal nanostructures. It is argued that surface and quantum-size effects are the two dominant factors in the energetics of metal nanowires, and that much of the phenomenology of nanowire stability and structural dynamics can be understood based on the interplay of these two competing factors. A linear stability analysis reveals that metal nanocylinders with certain magic conductance values G=1, 3, 6, 12, 17, 23, 34, 42, 51, 67, 78, 96, ... times the conductance quantum are exceptionally stable. A nonlinear dynamical simulation of nanowire structural evolution reveals a universal equilibrium shape consisting of a magic cylinder suspended between unduloidal contacts. The lifetimes of these metastable structures are also computed.Comment: 8 pages, 6 figure