Simulation of phase boundaries using constrained cell models

Despite impressive advances, precise simulation of fluid-fluid and fluid-solid phase transitions still remains a challenging task. The present work focuses on the determination of the phase diagram of a system of particles that interact through a pair potential, ?(r), which is of the form ?(r)?=?4?[(σ/r)(2n)?-?(σ/r)(n)] with n?=?12. The vapor-liquid phase diagram of this model is established from constant-pressure simulations and flat-histogram techniques. The properties of the solid phase are obtained from constant-pressure simulations using constrained cell models. In the constrained cell model, the simulation volume is divided into Wigner-Seitz cells and each particle is confined to moving in a single cell. The constrained cell model is a limiting case of a more general cell model which is constructed by adding a homogeneous external field that controls the relative stability of the fluid and the solid phase. Fluid-solid coexistence at a reduced temperature of 2 is established from constant-pressure simulations of the generalized cell model. The previous fluid-solid coexistence point is used as a reference point in the determination of the fluid-solid phase boundary through a thermodynamic integration type of technique based on histogram reweighting. Since the attractive interaction is of short range, the vapor-liquid transition is metastable against crystallization. In the present work, the phase diagram of the corresponding constrained cell model is also determined. The latter is found to contain a stable vapor-liquid critical point and a triple point.     

Orbital-decomposed electronic and magnetic properties of the double perovskite Sr2FeReO6

The detailed orbital-decomposed electronic structures and magnetic properties of the double perovskite Sr₂FeReO₆ have been studied using the first-principles projector augmented wave (PAW) potential within the generalized gradient approximation (GGA). Both occupied and unoccupied s and three p states of Fe³⁺ ion are located far away from the Fermi level, while all up-spin states and most down-spin states are completely filled for the s and three p states of Re⁵⁺ ion. The octahedral crystal field of the oxygen atoms around transition-metal (TM) sites splits the five-fold degenerate d states of the free TM atoms into triply degenerate t_2g states with smaller bonding-antibonding splitting and doubly degenerate e_g states with larger bonding-antibonding splitting. The Fe³⁺ and Re⁵⁺ ions are in the states (3d⁵, S=5/2) and (5d², S=1) with magnetic moments 3.70 and −0.86μ_B, respectively and thus antiferromagnetic coupling via oxygen between them. There are no direct interactions between two nearest Fe-Fe or Re-Re pairs, whereas along each Fe-O-Re-O-Fe or Re-O-Fe-O-Re chains, the hybridizations between Fe 3d and 4s, O 2s and 2p, as well as Re 5p, 5d and 6s orbitals are fairly significant.     

Output-sensitive results on convex hulls,extreme points,and related problems

We use known data structures for ray-shooting and linear-programming queries to derive new output-sensitive results on convex hulls, extreme points, and related problems. We show that thef-face convex hull of ann-point setP in a fixed dimensiond≥2 can be constructed in time; this is optimal if for some sufficiently large constantK. We also show that theh extreme points ofP can be computed in time. These results are then applied to produce an algorithm that computes the vertices of all the convex layers ofP inO(n ^2−γ) time for any constant . Finally, we obtain improved time bounds for other problems including levels in arrangements and linear programming with few violated constraints. In all of our algorithms the input is assumed to be in general position. This research was supported by a Killam Predoctoral Fellowship and an NSERC Postgraduate Scholarship.     

Construction and Borel summability of planar 4-dimensional euclidean field theory

We use the methods of [1] to show that the planar part of the renormalized perturbation theory for ₄ ⁴ -euclidean field theory is Borel-summable on the asymptotically free side of the theory. The Borel sum can therefore be taken as a rigorous definition of theN limit of a massiveN×N matrix model with a +trg ⁴ interaction, hence with wrong sign ofg. Our construction is relevant for a solution of the ultra-violet problem for planar QCD. We also propose a program for studying the structure of the renormalons singularities within the planar world.     

Study on the lifetime and attenuation properties of microbubbles coated with carboxylic acid salts

Four kinds of surfactants, sodium laurate, sodium myristate, sodium palmitate and sodium oleate were used to study the effects of surfactant coatings on the lifetime and attenuation of microbubbles. The changes in the size distribution of microbubbles prepared with these surfactants in saline were measured with a Coulter Multisizer (Coulter Electronics Ltd., Luton, UK). Frequency characteristics of ultrasonic attenuation of the microbubble suspensions were measured between 400 kHz and 6 MHz. From the changes in attenuation in the microbubble suspensions over time, it was found that the lifetime of microbubbles in a suspension also depends on the frequency of the irradiating ultrasound. The effect of surfactants on the frequency characteristics of attenuation was also studied, and characteristics of the surfactant coating, including shell elasticity and shell friction parameters were calculated from the measurement results. Microbubbles produced with sodium palmitate had the longest lifetime and the smallest average size. The shell had very little effect on the ultrasonic properties of microbubbles produced with sodium palmitate, suggesting that the sodium palmitate microbubbles behaved ultrasonically as free microbubbles.     

陶瓷/VDF-TrFE 0-3型铁电复合物的三阶非线性介电系数

在自建的非线性介电测试装置上测得了Ｐ笔ＶＤＦ－ＴｒＦＥ共聚物形成的０－３型铁电复合物厚片的三阶非线性介电系数ε３。研究发现,三种复合物的ε３都随陶瓷组分含量的上升而增大,测试场强升高,测得的ε３值减小,但对高陶瓷含量（Φ〉０．０４）的ＢＴ／ＶＤＦ－ＴｒＦＥ和ＰＺ／ＶＤＦ－ＴｒＦＥ复合物则在６ＭＶ／ｍ场强下出现极小值,二相都被预极化的复合物小于仅陶瓷相被预极化的ε３值,ＰＺＴ／ＶＤＦ－ＴｒＦＥ复合物     

Quantitative vibration amplitude measurement with time-averaged digital speckle pattern interferometry

A new method of using time-averaged digital speckle pattern interferometry for the quantitative measurement of vibration amplitude was developed. Signal processing techniques especially the Hilbert transformation for quantitative evaluation of the Bessel fringes obtained in time-averaged digital speckle pattern interferometry were explored. The quadrature signal after Hilbert transformation is equivalent to a 90° phase-shifted interferogram for a monotonically increasing or decreasing phase function. An algorithm was developed for Bessel fringe contrast enhancement and phase extraction. The techniques were tested numerically and experimentally. Sub-fringe quantification of the time-averaged vibration fringes is realised with the proposed method. Compared with the commonly used phase shift method which requires a minimum of two images for image processing, this method requires only one fringe pattern for data extraction.     

An Experimental Approach to Correcting Counting Errors in the Aerodynamic Particle Sizer (APS Model 3310)

This paper describes the different ways of analyzing the output of a real-time device for measuring and counting airborne particles, the aerodynamic particle sizer (APS). This instrument is very widely used in aerosol research throughout the world. It is a time-of-flight instrument in which a particle's measured transit time in the changing flow in a jet passing between two laser beams is converted to its aerodynamic diameter. As the particle passes between the two laser beams, two signal processors, the small particle processor (SPP) and the large particle processor (LPP), independently provide measures of the particle's transit time from the light pulses that are produced. This information is related to the aerodynamic particle diameter of the particle (d_ae) by means of calibration against ‘unit’ density (1000 kg/m³) spheres. If more than one particle is involved in the analysis of particle transit time, then it gives rise to coincidence effects, resulting in ‘phantom’ particle generation. The SPP is known to generate phantom counts, while the LPP is known to reduce phantom counts. A new method is described in this paper that gives guidance on how to deal with such coincidence problems. The principle is that it relies on additional information to obtain ‘correction factors’. In this case, well-established theory for the aspiration efficiencies of thin-walled aerosol sampling probes has been used along with corresponding experimental data obtained in a wind tunnel using the APS. Results using this method are compared with various other methods that have been tried in the past. The paper provides insights on to how the user can operate the APS to avoid counting errors like those described, and the advantages and limitations of different correction methods are discussed.     

Estimation of eardrum acoustic pressure and of ear canal length from remote points in the canal

Sound pressure distributions in the human ear canal, whether unoccluded or occluded with ear molds, were studied using a probe tube technique. On average, for frequencies below 6 kHz, the measuring probe tube had to be placed within 8 mm of the vertical plane containing the top of the eardrum (TOD), determined optically, in order to obtain sound pressure magnitudes within 6 dB of "eardrum pressure." To obtain that accuracy in all of the eight subjects studied, the probe had to be within 6 mm of the TOD. Since probe location relative to the drum has to be known, a purely acoustic method was developed which can be conveniently used to localize the probe-tip position, utilizing the standing wave property of the sound pressure in the ear canal. The acoustically estimated "drum location" generally lay between the optically determined vertical planes containing the TOD and the umbo. On average, the "drum location" fell 1 mm medial to the TOD. Of the 32 estimates made acoustically in various occluded and unoccluded conditions in 14 subjects, 30 estimates lay within a +/- 2-mm range of this average.