Replica Bounds by Combinatorial Interpolation for Diluted Spin Systems

In two papers Franz et al. proved bounds for the free energy of diluted random constraints satisfaction problems, for a Poisson degree distribution (Franz and Leone in J Stat Phys 111(3–4):535–564, 2003) and a general distribution (Franz et al. in J Phys A 36(43), 10967, 2003). Panchenko and Talagrand (Probab Theo Relat Fields 130(3):319–336, 2004) simplified the proof and generalized the result of Franz and Leone (J Stat Phys 111(3–4):535–564, 2003) for the Poisson case. We provide a new proof for the general degree distribution case and as a corollary, we obtain new bounds for the size of the largest independent set (also known as hard core model) in a large random regular graph. Our proof uses a combinatorial interpolation based on biased random walks (Salez in Combin Probab Comput 25(03):436–447, 2016) and allows to bypass the arguments in Franz et al. (J Phys A 36(43):10967, 2003) based on the study of the Sherrington–Kirkpatrick (SK) model.     

Three-stage auto-ignition of n-heptane and methyl-cyclohexane mixtures at lean conditions in a flat piston rapid compression machine

One approach to enhancing the thermal efficiency of combustion systems is to burn fuels at ultra-lean conditions (equivalence ratio below 0.5). It has been recently reported that the auto-ignition of some hydrocarbon fuels, under specific temperature, pressure, and mixture conditions, releases heat in three distinctive stages. The three auto-ignition stages can be divided as a first low-temperature auto-ignition stage with conventional low temperature, and a high-temperature stage separated into two sub-stages. This study presents ignition delay time measurements of n-heptane and methyl-cyclohexane (MCH) mixtures in a flat piston rapid compression machine (RCM) under ultra-lean conditions. It provides experimental evidence of three-stage auto-ignition. This phenomenon of delayed high-temperature heat release is seldom reported in the literature and this is the first time to be reported for these types of fuels. The experiments cover two binary n-heptane/MCH mixtures of 15/85 and 70/30 by volume, pressures of 11 bar and 16 bar, temperature range of 700 to 900 K, and equivalence ratio of 0.4. The RCM optical access was utilized for high-speed chemiluminescence imaging. Detailed chemical kinetic simulations in a homogenous batch reactor with variable volume were conducted to further interrogate the three-stage auto-ignition phenomenon. Chemiluminescence shows that three-stage auto-ignition occurs in the adiabatically compressed end-gas, which indicates that this phenomenon is chemically-driven and is not induced by a thermal stratification in the RCM experiments. The model predicts the features of three-stage auto-ignition, which were experimentally observed at temperatures approximately below 750 K. As expected, significant discrepancies are observed in the ignition delays of experiment and simulation in the negative temperature coefficient (NTC) region. The simulation of the n-heptane/MCH 70/30 mixture shows better agreement with experiments in the Positive Temperature Coefficient (PTC) region compared to the 15/85 mixture.     

Response of bare 1-3 piezocomposite array to localized electrical excitation

The theoretical response of a 1-3 piezocomposite plate submitted to localized electrical excitation was studied with the theory of guided waves. The theoretical modeling was based on the global matrix method, and the piezocomposite material was considered as a homogeneous medium. To validate the theoretical results, experimental displacement measurements were performed with an interferometric probe on two piezocomposite plates, one with a single element and one with an array of electrodes. The measured response on the single-element plate was mainly supported by the S0 and S3 modes of the plate. Homogenization limits of the composite in terms of frequency and wave number are defined on the basis of data from this sample. Within these limits, the piezocomposite material operates as a homogeneous medium, and comparison between theoretical and experimental results allows the equivalent electroacoustic parameters to be evaluated. A second sample was measured to study the effects of the electrode array on the electroacoustic response of the plate. Two kinds of electrical excitation were studied.     

铅蓄冷材料的二级脉冲管制冷机研究

采用多级方案是高频脉冲管制冷机获得低于20 K以下制冷温度的主要方法,以不锈钢金属丝网为蓄冷材料的二级高频脉冲管制冷机,实验已经达到了20 K以下温度.理论上讲,由于热容大,以铅为主的蓄冷材料比不锈钢更适合40～10 K温区工作,这在低频回热制冷机中得到了证明.本文介绍了我们采用不同铅球和铅网为低温蓄冷材料的研究结果.实验表明,小铅球对于高频脉冲管制冷机是不很合适的,导致制冷温度的明显升高.镀铅的不锈钢丝网和已有不锈钢丝网的性能相似,可进一步深入研究.该研究对于20 K以至更低温度的高频回热制冷机研究有一定的借鉴意义.     

Outcome of laryngeal and velopharyngeal biofeedback treatment in children and young adults: A pilot study

A relatively new management strategy for the treatment of voice disorders is the use of laryngeal (LB) and velopharyngeal biofeedback (VB). The main purpose of the present pilot study is to document the outcome of vocal and velopharyngeal performances after a well-defined LB and VB treatment. Four subjects were studied pretreatment (1 week before LB or VB treatment) and posttreatment (1 week after the LB or VB treatment). To measure and compare the effect of LB and VB, objective and subjective assessment techniques were used. Perceptual voice assessment included a perceptual rating of the voice using the GRBAS scale. Furthermore, the vocal quality in this population is modeled by means of the Dysphonia Severity Index. For the objective assessment of nasal resonance, the Nasometer and the Glatzel test were used. A perceptual evaluation of speech, the Gutzmann test, and the tests from Bzoch were used as subjective assessment techniques. Both patients selected for LB and VB treatment showed improvement of their performances. The resulting improvement, as measured by means of an objective approach, is in agreement with the perceived (auditory) improvement of voice and resonance. The use of LB and VB treatment in patients, especially in some subjects who are not responding to traditional voice or velopharyngeal therapy, must be encouraged.     

Direct Minimization of the least-squares spectral element functional – Part I: Direct solver

This paper describes an equivalent but improved least-squares formulation for the numerical approximation of the solution of partial differential equations. Instead of using variational analysis to impose the conditions for minimizing the residual, the residuals are minimized directly, thus leading to a method we will denote by Direct Minimization (DM). DM circumvents setting up the normal equations which consists of matrix–matrix multiplications. Matrix–matrix multiplications are expensive, may lead to loss of accuracy and destroy the sparsity pattern present in the original system. The condition number of the DM formulation is the square root of the condition number which would be obtained if variational analysis was employed. An element-by-element procedure will be presented which allows for parallelization of DM. A computational comparison between DM and the conventional least-squares formulation based on variational analysis will be presented.     

Ultrabroadband conical emission generated from the ultraviolet up to the far-infrared during the optical filamentation in air

Ultraviolet and infrared conical emissions were observed during the filamentation in air of powerful femtosecond laser pulses produced by a portable terawatt laser system. The broadband spectrum was measured from 200 nm up to 14 microm and covered the complete optical transmission window of the atmosphere. The angularly resolved spectrum showed some X-wave structure across the frequency range analyzed. However, we demonstrated that the strong conical emission observed in the mid- and far-infrared is mainly owing to the four-wave mixing between the pump pulse and its blueshifted conical emission.     

Unique continuation results for Ricci curvature and applications

Unique continuation results are proved for metrics with prescribed Ricci curvature in the setting of bounded metrics on compact manifolds with boundary, and in the setting of complete conformally compact metrics on such manifolds. Related to this issue, an isometry extension property is proved: continuous groups of isometries at conformal infinity extend into the bulk of any complete conformally compact Einstein metric. Relations of this property with the invariance of the Gauss–Codazzi constraint equations under deformations are also discussed.     

Modeling urban street patterns

Urban street patterns form planar networks whose empirical properties cannot be accounted for by simple models such as regular grids or Voronoi tesselations. Striking statistical regularities across different cities have been recently empirically found, suggesting that a general and detail-independent mechanism may be in action. We propose a simple model based on a local optimization process combined with ideas previously proposed in studies of leaf pattern formation. The statistical properties of this model are in good agreement with the observed empirical patterns. Our results thus suggest that in the absence of a global design strategy, the evolution of many different transportation networks indeed follows a simple universal mechanism.     

Nonlinear evolution of anisotropic cosmological power

There has been growing interest in the possibility of testing more precisely the assumption of statistical isotropy of primordial density perturbations. If it is to be tested with galaxy surveys at distance scales < or = 10 Mpc, then nonlinear evolution of anisotropic power must be understood. To this end, we calculate the angular dependence of the power spectrum to third order in perturbation theory for a primordial power spectrum with a quadrupole dependence on the wave vector direction. Our results suggest that primordial power anisotropies will be suppressed by < or = 7% in the quasilinear regime. We also show that the skewness in the statistically anisotropic theory differs by no more than 1% from that in the isotropic theory.