构造孤子方程的Weierstrass椭圆函数解的一个新方法

利用具有Weierstrass椭圆函数解的方程，首先获得了投影Riccati方程的两组新解.由于投影Riccati方程可用于多种具孤子解的非线性演化方程的求解，因而得到了一个可以构造这些方程的Weierstrass椭圆函数解的新方法. 关键词： Weierstrass椭圆函数解 投影Riccati方程 非线性演化方程     

Boussinesq-Burgers方程新的精确解

基于改进的投影Riccati方程的解,提出一种新的构造非线性演化方程精确解的方法.通过这种方法,我们得导到了Boussinesq-Burgers方程各种类型的精确解,包括Jacobi和Weierstrass周期函数解.这种方法与数学软件Maple结合,简单易行,有助于探索其他非线性演化方程的精确解.     

(2+1)维 Zakharov-Kuznetsov 方程的精确解和孤子结构

在符号计算软件Maple的帮助下,利用改进的Riccati方程映射法得到了(2+1)维Zakharov-Kuznetsov方程(ZK)的新显式精确解. 根据得到的解,研究了ZK方程的特殊孤子结构. 关键词： 改进的Riccati方程映射法 Zakharov-Kuznetsov方程 精确解 孤子结构     

非线性演化方程椭圆函数解的一种简单求法及其应用

非线性演化方程的许多行波解可以写成满足投影Riccati方程的两个基本函数的多项式形式.利用这一性质，通过建立一般的椭圆方程与投影Riccati方程解之间的关系，导出了一个构造这些解的新方法.该方法对类型Ⅰ的方程和类型Ⅱ的方程均有效，同时也回答了如何求出非线性演化方程分式形式椭圆函数解的问题. 关键词： 非线性演化方程 椭圆函数解     

构造非线性发展方程无穷序列复合型精确解的一种方法

为了获得非线性发展方程新的无穷序列复合型精确解,给出了Riccati方程的Bäcklund变换和解的非线性叠加公式,符号计算系统Mathematica的帮助下,以广义Boussinesq方程为应用实例,获得了无穷序列复合型精确解.这里包括双曲函数、三角函数与有理函数复合解、双曲函数与三角函数复合解等几种新的无穷序列复合型精确解.该方法在构造非线性发展方程无穷序列复合型精确解方面具有普遍意义. 关键词： 非线性发展方程 非线性叠加公式 Riccati方程 无穷序列精确解     

非线性发展方程的Riemann theta 函数等几种新解

为了构造非线性发展方程的复合型无穷序列精确解, 获得了第二种椭圆方程的Riemann theta 函数等几种新解.在此基础上,利用第二种椭圆方程与Riccati方程的Bäcklund变换和解的非线性叠加公式, 借助符号计算系统 Mathematica, 以mKdV方程为应用实例, 构造了该方程的复合型无穷序列新精确解.这里包括Riemann theta 函数、Jacobi椭圆函数、双曲函数、 三角函数和有理函数,通过几种形式构成的复合型无穷序列新精确解. 关键词： 第二种椭圆方程 Riccati方程 非线性发展方程 Riemann theta 函数无穷序列解     

构造非线性发展方程无穷序列类孤子精确解的一种方法

辅助方程法已构造了非线性发展方程的有限多个新精确解. 本文为了构造非线性发展方程的无穷序列类孤子精确解, 分析总结了辅助方程法的构造性和机械化性特点. 在此基础上,给出了一种辅助方程的新解与Riccati方程之间的拟Bäcklund变换. 选择了非线性发展方程的两种形式解,借助符号计算系统 Mathematica,用改进的(2+1) 维色散水波系统为应用实例,构造了该方程的无穷序列类孤子新精确解. 这些解包括无穷序列光滑类孤子解, 紧孤立子解和尖峰类孤立子解.     

Degasperis-Procesi 方程的无穷序列尖峰孤立波解

本文为了构造非线性发展方程的无穷序列尖峰精确解,给出了Riccati方程的Bäcklund 变换和解的非线性叠加公式,并借助符号计算系统Mathematica,用Degasperis-Procesi方程为应用实例,构造了无穷序列尖峰孤立波解和无穷序列尖峰周期解. 关键词： Riccati方程 解的非线性叠加公式 尖峰孤立波解 Degasperis-Procesi 方程     

利用耦合的Riccati方程组构造微分-差分方程精确解

通过引入耦合的Riccati方程组得到一个构造非线性微分-差分方程精确解的代数方法.作为实例,将该方法应用到了一般格子方程,相对论的Toda格子方程和(2+1)维Toda格子方程.借助符号计算软件Mathematica,获得了这些方程的扭结型孤波解和复数解.该方法也适合求解其他非线性微分-差分方程的精确解. 关键词： 耦合Riccati方程组 格子方程 相对论的Toda格子方程 (2+1)维Toda格子方程     

用Riccati方程构造非线性差分微分方程新的精确解

把Riccati方程应用到非线性差分微分方程求解领域,并相结合与一种函数变换,借助符号计算系统Mathematica构造了修正的Volterra方程和一般格子方程新的精确孤立波解和三角函数解. 关键词： Riccati方程 函数变换 非线性差分微分方程 孤立波解     

AC losses dependence on a CuNi layer location in NbTi CICC

In the frame of the ITER fusion program, large Cable In Conduit Cables (CICC) made with NbTi superconductors are foreseen for the poloidal field system. These coils are pulsed and so subjected to fast variations in magnetic field. Superconductors have then to be designed in order to reduce AC losses to an acceptable level. A solution could be to insert a copper nickel resistive barrier in the copper stabilizer surrounding the filamentary area of the composite. The purpose of this barrier is to reduce interstrand coupling currents. In order to predict the effect of this barrier on AC losses, a modeling of a 36 strands CICC has been realized. According to this code, the ability of the resistive barrier to reduce coupling currents is dependent on its location. For this study, three CICC with three barrier locations, from the inner to the outer diameter of the copper crown stabilizer, have been produced. AC losses have been measured and compared to our numerical model.     

宽波段单色仪多级谱高精度波长定标

通常利用单色仪输出的单色光对空间遥感光谱仪进行波长定标。提出以空间遥感光谱仪的置信度为标准,来评价宽波段单色仪高精度波长定标精度的方法。通过对仪器精度的分析,分别求出单色仪的波长的重复性误差和偏差。应用高压汞灯的本征谱和光栅衍射多级谱作为定标谱线,避免更换灯源带来的误差。通过粗细定标相结合的方法,缩短扫描时间,并且运用高斯拟合对波峰进行精确定位,缩小误差。最后利用高次拟合得到的关系式,测出单色仪波长精度,计算出空间遥感光谱仪定标的置信度。以1.5 M单色仪为例,单色仪在200～840 nm波段内波长精度±0.016 nm,则空间遥感光谱仪的波长精度达到±0.050 nm的置信度为99.82%。     

Whole-field analysis of uniaxial tensile tests by Moiré interferometry

Moiré interferometry—a high sensitivity whole-field optical technique—was used to follow the evolution of the deformation process of an aluminium sample subjected to a uniaxial tensile test. This technique allowed us to measure the two in-plane displacement components undergone by the sample, to evaluate the strain, stress and rotation fields, and to appreciate the trends in the deformation pattern that characterized the different stages of the test. Through a subtraction process between fields obtained at two different load levels, we were able to identify the area where strains began to localize and to observe the appearance of the diffuse neck.     

Thermo-chemical modelling of a village cookstove for design improvement

Cookstove operation comprises three basic processes, namely combustion of firewood, natural air draft due to the buoyancy induced by the temperature difference between the hearth and its surroundings, and heat transfer to the pot, stove body and surrounding atmosphere. Owing to the heterogenous and unsteady burning of solid fuel, there exist nonlinear and dynamic interrelationships among these process parameters. A steady-state analytical model of the cookstove operation is developed for its design improvement by splitting the hearth into three zones to study char combustion, volatile combustion and heat transfer to the pot bottom separately. It comprises a total of seven relations corresponding to a thorough analysis of the three basic processes. A novel method is proposed to model the combustion of wood to mimic the realities closely. Combustion space above the fuel bed is split into 1000 discrete parts to study the combustion of volatiles by considering a set of representative volatile gases. Model results are validated by comparing them with a set of water boiling tests carried on a traditional cookstove in the laboratory. It is found that the major thrust areas to improve the thermal performance are combustion of volatiles and the heat transfer to the pot. It is revealed that the existing design dimensions of the traditional cookstove are close to their optimal values. Addition of twisted-tape inserts in the hearth of the cookstove shows an improvement in the thermal performance due to increase in the heat transfer coefficient to the pot bottom and improved combustion of volatiles.     

Numbers,scale and symbols: the public understanding of nanotechnology

Nanotechnology will be an increasing part of the everyday lives of most people in the world. There is a general recognition that few people understand the implications of the technology, the technology itself or even the definition of the word. This lack of understanding stems from a lack of knowledge about science in general but more specifically difficulty in grasping the size scale and symbolism of nanotechnology. A potential key to informing the general public is establishing the ability to comprehend the scale of nanotechnology. Transitioning from the macro to the nanoscale seems to require an ability to comprehend scales of one-billion. Scaling is a skill not common in most individuals and tests of their ability to extrapolate size based upon scaling a common object demonstrates that most individuals cannot scale to the extent needed to make the transition to nanoscale. Symbolism is another important vehicle to providing the general public with a basis to understand the concepts of nanotechnology. With increasing age, individuals are able to draw representations of atomic scale objects, but these tend to be iconic and the different representations not easily translated. Ball and stick models are most recognized by the public, which provides an opportunity to present not only useful symbolism but also a reference point for the atomic scale.     

Inference and Learning in a Latent Variable Model for Beta Distributed Interval Data

Latent Variable Models (LVMs) are well established tools to accomplish a range of different data processing tasks. Applications exploit the ability of LVMs to identify latent data structure in order to improve data (e.g., through denoising) or to estimate the relation between latent causes and measurements in medical data. In the latter case, LVMs in the form of noisy-OR Bayes nets represent the standard approach to relate binary latents (which represent diseases) to binary observables (which represent symptoms). Bayes nets with binary representation for symptoms may be perceived as a coarse approximation, however. In practice, real disease symptoms can range from absent over mild and intermediate to very severe. Therefore, using diseases/symptoms relations as motivation, we here ask how standard noisy-OR Bayes nets can be generalized to incorporate continuous observables, e.g., variables that model symptom severity in an interval from healthy to pathological. This transition from binary to interval data poses a number of challenges including a transition from a Bernoulli to a Beta distribution to model symptom statistics. While noisy-OR-like approaches are constrained to model how causes determine the observables’ mean values, the use of Beta distributions additionally provides (and also requires) that the causes determine the observables’ variances. To meet the challenges emerging when generalizing from Bernoulli to Beta distributed observables, we investigate a novel LVM that uses a maximum non-linearity to model how the latents determine means and variances of the observables. Given the model and the goal of likelihood maximization, we then leverage recent theoretical results to derive an Expectation Maximization (EM) algorithm for the suggested LVM. We further show how variational EM can be used to efficiently scale the approach to large networks. Experimental results finally illustrate the efficacy of the proposed model using both synthetic and real data sets. Importantly, we show that the model produces reliable results in estimating causes using proofs of concepts and first tests based on real medical data and on images.     

Illusion and reality in the quantum world

Often considered as the last ‘encyclopedist’, Henri Poincaré died one hundred years ago. If he was a prominent man in 1900 French Society, his heritage is not so clearly recognised, particularly in France. Among his too often misunderstood works is his contribution to the theory of relativity, mainly because it is almost never presented within Poincaré's general approach to science, including his philosophical writings. Our aim is therefore to provide an historical account of the main steps (experimental as well as theoretical) which led Poincaré to contribute to the theory of relativity. Starting from the optical experiments which led to the inconsistency of the classical (Galilean) composition law for velocities to explain light propagation, we introduce the FitzGerald and Lorentz contraction which was viewed as the ‘sole hypothesis’ to explain the Michelson and Morley experiment. We then show that Poincaré's contribution starts with a discussion of the principles governing the mechanics and was built step by step up to express in all its generality the principle of relativity. Poincaré thus showed the invariance of the Maxwell equations under the Lorentz transformation. In doing so, he also discovered the right composition law for velocities. Poincaré's approach to philosophy is detailed to help the reader to understand what a theory meant to him.     

Pressure effects on inter‐ and intramolecular vibrations in hydrogen‐bonded L‐ascorbic acid crystal

Pressure effects on the Raman spectra due to the inter‐ and intramolecular vibrations of the L ‐ascorbic acid crystal were studied. The intensity of the Raman bands due to the intermolecular vibrations varies in three different ways by application of pressure. The bands of the first group become stronger, those of the second one become weaker and the third group shows no prominent change in their intensity with increasing pressure. The bands due to the intermolecular vibrations show a blue shift, while the bands due to the intramolecular vibrations shift to the blue or red depending on the vibrational modes by application of pressure. The bands assigned to the O H stretching vibrations shift to the red, the bands assigned to the CO and CC stretching vibrations shift a little to the red and the bands assigned to the other vibrations shift to the blue under high pressure. The following conclusions were derived. (1) The hydrogen bonds forming helixes become stronger and the isolated hydrogen bond becomes weaker with increasing pressure. (2) The bands of the first group owing to the intermolecular vibrations are ascribed to the vibrations related to the helix hydrogen bonds and the second group bands to the isolated hydrogen bond. (3) The CO stretching vibration couples with the CC stretching vibration. (4) The phase transitions take place at 1.8 and 4 GPa in the crystal. Copyright © 2007 John Wiley & Sons, Ltd.     

Inactivation of the enveloped virus phi6 with hydrodynamic cavitation

The COVID −19 pandemic reminded us that we need better contingency plans to prevent the spread of infectious agents and the occurrence of epidemics or pandemics. Although the transmissibility of SARS-CoV-2 in water has not been confirmed, there are studies that have reported on the presence of infectious coronaviruses in water and wastewater samples. Since standard water treatments are not designed to eliminate viruses, it is of utmost importance to explore advanced treatment processes that can improve water treatment and help inactivate viruses when needed. This is the first study to investigate the effects of hydrodynamic cavitation on the inactivation of bacteriophage phi6, an enveloped virus used as a SARS-CoV-2 surrogate in many studies. In two series of experiments with increasing and constant sample temperature, virus reduction of up to 6.3 logs was achieved. Inactivation of phi6 at temperatures of 10 and 20 °C occurs predominantly by the mechanical effect of cavitation and results in a reduction of up to 4.5 logs. At 30 °C, the reduction increases to up to 6 logs, where the temperature-induced increased susceptibility of the viral lipid envelope makes the virus more prone to inactivation. Furthermore, the control experiments without cavitation showed that the increased temperature alone is not sufficient to cause inactivation, but that additional mechanical stress is still required. The RNA degradation results confirmed that virus inactivation was due to the disrupted lipid bilayer and not to RNA damage. Hydrodynamic cavitation, therefore, has the potential to inactivate current and potentially emerging enveloped pathogenic viruses in water at lower, environmentally relevant temperatures.     

Computation of aeolian tone from a circular cylinder using source models

The generation of aeolian tones from a two-dimensional circular cylinder situated in a uniform cross-flow is investigated. The major emphasis here is placed on identifying the important noise generation mechanisms. Acoustic-viscous splitting techniques are utilized to compute modelled acoustic source terms and their corresponding acoustic fields. The incompressible Reynolds averaged Navier-Stokes equation is used to compute the near-field viscous flow solution, from which modelled acoustic source terms are extracted based on an approximation to the Lighthill’s stress tensor. Acoustic fields are then computed with an acoustic solver to solve the linearized Euler equations forced by the modelled source terms. Computations of the acoustic field based on the approximated Lighthill’s stress tensor are shown to be in good agreement with those computed from the surface dipole sources obtained using Curle’s solution to the acoustic analogy. It is shown in this paper that the stress tensor source term in the streamwise direction makes a comparable, but slightly larger contribution to the overall radiated field, compared with that due to the stress tensor in the direction normal to the mean flow. In addition, it is shown that shear sources, which arise due to the interaction between the fluctuating velocity and the background steady mean velocity, make the greatest contribution to the acoustic field, while the self-noise sources, which represents the interaction between the fluctuating velocities, is shown to be comparably negligible.