Deterministic-statistical analysis of a structural-acoustic system

The purpose of this paper is to develop an efficient approach for vibro-acoustic analysis. Being simple and representative, an exited plate-acoustic system is selected as a validation case for the vibro-acoustic analysis as the system presents one two-dimensional statistical component (modal dense structure panel—plate) connected to the other component (deterministic acoustic volume—cavity) through the area junction over a surface domain, rather than at a line boundary. Potential industrial applications of the system vibro-acoustic analysis would be in acoustic modelling of vehicle body panels such as the cabin roof panel, and door panels for the boom noise analysis.A new deterministic-statistical analysis approach is proposed from a combination or hybrid of deterministic analysis and statistical energy analysis (SEA) approaches. General theory of the new deterministic-statistical analysis approach is introduced. The main advantage of the new deterministic-statistical analysis approach is its possibility in place of the time consuming Monte Carlo simulation. In order to illustrate and validate the new deterministic-statistical analysis approach, three approaches of the deterministic analysis, the statistical energy analysis and the new deterministic-statistical analysis are then applied to conduct the plate-acoustic system modelling, and their results will be compared. The vibro-acoustic energy coupling characteristic of the plate-acoustic system will be studied. The most suitable frequency range for the new approach will be identified in consideration of computational accuracy, information and speed.     

Antiferromagnets in a field and ferromagnets in a random field

A new mean field approach for antiferromagnets in a field is shown to be equivalent to a mean field treatment of ferromagnets in a random field. Phase diagrams of the two systems are analogous.     

Magnetic field homogeneity: a new approach to orthogonalizing and optimizing shim gradients

A new approach to optimizing shim coil currents for magnetic resonance magnets is presented. The new approach orthogonalizes the shim coil gradients to allow a simple one-dimensional optimization for each orthogonalized "composite shim." The technique demands no specialized equipment, requiring only the acquisition of simple one-dimensional NMR spectra. Examples from two high-resolution NMR spectrometers are presented, where the shim currents found by the new algorithm provide higher resolution than was obtained by the spectrometer vendor's installation engineers using field-mapping techniques. The examples shown demonstrate the advantages of the technique for high-resolution NMR, but we expect the approach will also find application in a broad variety of areas including imaging and in vivo spectroscopy.     

一个新的三维混沌系统的分析、电路实现及同步

中心流形理论提供了一个将高维系统降维研究的方法，应用该理论研究了一个新的混沌系统的基本特性，给出中心流形上流方程，分析这个新的混沌系统的叉式分岔.通过构建电路实现了该混沌系统,从而验证了系统的混沌行为，证实了混沌吸引子的存在.同时说明了由于电路信号频率与数值信号频率的不同所带来的数值仿真与物理实现之间在应用上有着重要区别.最后利用单变量反馈控制方法实现了新系统的同步控制，并给出了完整的同步实现电路. 关键词： 三维混沌系统 中心流形 电路实现 同步     

Optimized electron–optical system of a static mass-spectrometer for simultaneous isotopic and chemical analysis

A new approach to control the linear dimensions of analytical electrophysical systems is suggested. This approach uses the lens properties of electron–optical elements with a curvilinear axis. It is shown that such an approach can be effectively applied, in particular, to synthesize ion–optical systems (IOSs) for static magnetic mass spectrometers and can be implemented owing to off-axis fundamental points, the “poles” of an electron–optical system, introduced earlier by one of the authors. The capabilities of the new approach are demonstrated with the synthesis of the IOS of a static mass spectrometer dedicated for isotopic and chemical analysis with an increased resolution. A new IOS not only provides desired high ion–optical parameters at decreased dimensions of the mass spectrometer as a whole but also makes it possible to loosen requirements for the manufacturing accuracy of IOS main elements.     

An efficient approach of unsteady flamelet modeling of a cross-flow-jet combustion system using LES

Steady flamelet models have been widely used in turbulent combustion simulations because of their simplicity, efficiency, yet physics-based nature. They are, however, unable to handle slow chemical and physical processes such as pollutant formation. Unsteady flamelet models have been shown to be able to provide accurate predictions especially for pollutants, but their implementations are usually not as straightforward as for the steady models, and additional assumptions are involved. One relatively straightforward approach of implementing the unsteady flamelet model is to tabulate the time history of unsteady flamelet solutions. This often leads to flamelet libraries of large sizes because of increased dimensions for the new physics. The purpose of this paper is to introduce a new and efficient approach of tabulating unsteady flamelet solutions in the LES of complex systems, here demonstrated in simulations of a cross-flow-jet combustion system. This approach employs Taylor series expansions to represent the time history of unsteady flamelet solutions. Compared with other approaches, the new approach retains the efficiency and simplicity benefits of steady flamelet models but possesses the accuracy of unsteady flamelet models. Various issues associated with the formulation and implementation of this approach are discussed, which include the selection of the base solution, the order of accuracy of the expansion, and the treatment of simultaneous wall heat losses and heat transfer through thermal radiation. This approach is validated in large eddy simulations of a cross-flow-jet combustion system. Good agreement with experiments is obtained for both temperature and NO concentration, as well as for major species.     

Stability of the BA Network: a New Approach to Rigorous Proof

We propose a new approach to rigorously prove the existence of the steady-state degree distribution for the BA network. The approach is based on a vector Markov chain of vertex numbers in the network evolving process. This framework provides a rigorous theoretical basis for the rate equation approach which has been widely applied to many problems in the field of complex networks, e.g., epidemic spreading and dynamic synchronization.     

Measurement of a broad range of Gaussian laser beam diameters using various periodic and aperiodic rulings

A novel analytical approach is proposed for an accurate estimation of a broad range of Gaussian laser beam diameters. The new approach, based on the Fourier transform and the convolution operations, is used to study the performance of most recently proposed periodic and aperiodic rulings. Further, for applications that require extremely small beam diameter measurements, a new Ronchi-like ruling is proposed; while for applications requiring large beam diameters measurements, various aperiodic non-Ronchi rulings are proposed. Furthermore, for spot-size measurement applications, which range from very small to very large beam diameters, a new single aperiodic exponential ruling is proposed. This new ruling eliminates the necessity of using a large number of rulings for measuring a broad range of beam diameters.     

Nonlinear pulse propagation: a time-transformation approach

We present a time-transformation approach for studying the propagation of optical pulses inside a nonlinear medium. Unlike the conventional way of solving for the slowly varying amplitude of an optical pulse, our new approach maps directly the input electric field to the output one, without making the slowly varying envelope approximation. Conceptually, the time-transformation approach shows that the effect of propagation through a nonlinear medium is to change the relative spacing and duration of various temporal slices of the pulse. These temporal changes manifest as self-phase modulation in the spectral domain and self-steepening in the temporal domain. Our approach agrees with the generalized nonlinear Schr?dinger equation for 100 fs pulses and the finite-difference time-domain solution of Maxwell's equations for two-cycle pulses, while producing results 20 and 50 times faster, respectively.     

Statistical properties of a harmonic plus a delta-potential

For a singular but solvable potential we test a new variational approach for calculating statistical properties of quantum systems proposed recently by Feynman and Kleinert. We consider a potential consisting of a sum of a harmonic oscillator and a delta-potential. We solve the Schrödinger equation analytically, calculate exact free energies and particle densities, and compare with the variational approach. We find good agreement in a wide range of temperature and strength of the delta-potential.     

Optimized swimmer tracking system based on a novel multi-related-targets approach

Robust tracking is a crucial step in automatic swimmer evaluation from video sequences. We designed a robust swimmer tracking system using a new multi-related-targets approach. The main idea is to consider the swimmer as a bloc of connected subtargets that advance at the same speed. If one of the subtargets is partially or totally occluded, it can be localized by knowing the position of the others. In this paper, we first introduce the two-dimensional direct linear transformation technique that we used to calibrate the videos. Then, we present the classical tracking approach based on dynamic fusion. Next, we highlight the main contribution of our work, which is the multi-related-targets tracking approach. This approach, the classical head-only approach and the ground truth are then compared, through testing on a database of high-level swimmers in training, national and international competitions (French National Championships, Limoges 2015, and World Championships, Kazan 2015). Tracking percentage and the accuracy of the instantaneous speed are evaluated and the findings show that our new appraoach is significantly more accurate than the classical approach.     

On a method of computation of scattering amplitudes and on ionization of hydrogen atoms

The general expressions for the scattering amplitudes due to Das have been rederived following a new approach. It is possible in this approach to improve the results considerably. Ionization of hydrogen atoms by electrons and positrons has also been considered.     

On the equilibrium equation for a generalized biological membrane energy by using a shape optimization approach

A mechanical equilibrium equation of a vesicle membrane under a generalized elastic bending energy is obtained in this paper. Moreover, the derivation of this equilibrium equation is based on some shape optimization tools. This approach is new and more concise than the tensorial tools used previously for this problem.     

Principle of an a priori use of symmetries in the theory of nonlinear waves

The principle of an a priori use of symmetries is proposed as a new approach to solving nonlinear problems on the basis of a reasonable complication of mathematical models. Such a complication often causes an additional symmetry and, hence, opens up possibilities for finding new analytical solutions. The application of group analysis to the problems of nonlinear acoustics is outlined. The potentialities of the proposed approach are illustrated by exact solutions, which are of interest for wave theory.     

Dynamical equations and a new analytical approach in lattice gauge theories

A new analytical approach in lattice gauge theories is presented. It is based on the use of the dynamical equations of the theory. The new method is used to discuss the phase structure of abelian lattice gauge systems, the results show that the new approach is an effective one.     

Strength Function in Continuum with a Square Integrable Basis

We present a new approach to describe the three-body continuum with a square integrable basis and show some examples to assess its efficiency. The formulation is done elegantly in the hyperspherical formalism and the tail behavior is appropriately corrected with use of the Green??s function. The efficiency of this approach is shown in a simple solvable problem by calculating the electric dipole strength function of a three-body system and comparing it to that obtained with the complex scaling method, which is widely used for calculating the strength function.     

Cancer detection on a cell-by-cell basis using a fractal dimension analysis

We show that the application of imaging and pattern recognition techniques developed for basic heavy ion research has useful applications in medical imaging. In particular, we utilize the fractal dimension of the perimeter surface of cell sections as a new observable to characterize cells of different types. We propose that it is possible to distinguish cancerous from healthy cells with the aid of this new approach. As a first application we show in an exploratory study that it is possible to perform this distinction between patients with hairy-cell lymphocytic leukemia and those with normal blood lymphocytes.     

A new approach to asymmetric feedback in a segmented broad area diode laser

We present the demonstration of a non-critical setup for asymmetric feedback in a segmented broad area diode laser. We compare the dependence of the beam quality on the position of the dispersive element for standard spectral beam combining and our new non-critical setup. We find that our new approach is significantly less critical to the position of the dispersive element. It is shown that we can displace the dispersive element by at least 50% of the focal length of the collimating lens away from the Fourier plane without compromising performance. Furthermore, our approach provides the same high beam quality as is possible using off-axis spectral beam combining. This provides the possibility of achieving a high beam quality in a more compact setup than previously possible.