Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations

We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process.     

Asymmetric phase diagram and phase separation in Pr0.5−δCa0.2+δSr0.3MnO3 (−0.04δ0.04)

We present electric and magnetic properties of polycrystalline Pr_0.5−δCa_0.2+δSr_0.3MnO₃, for δ between −0.04 and 0.04, where the hole concentration is n=0.5+δ. In this series, we study the effects of moving n away from 0.5 on both, the phase diagram and phase separated state. We found that the low temperature ferromagnetic fraction X_FM continuously decreases when n increases. As a result, the samples with n<0.5 (large X_FM) exhibit metallic resistivity at low T while for n>0.5 the insulating state predominates. We construct a detailed T–n phase diagram showing the asymmetries around half-doping.     

Strong,large distance impurity dipole interaction in KNbO3 single crystals

It is found that the unrelaxed impurity dipoles can arrange themselves linearly in the structure joining each other end-to-end in pseudocubic [110] direction at the tetragonal to the orthorhombic phase transition. It is shown that this alignment precedes the domain formation at the phase transition, which implies quick movements of the dipoles in the structure, and a strong dipolar interaction. The experiments with the application of dc fields to the crystals showed that the dipolar interaction becomes stronger with the field. The dipoles can see each other across the existing domain walls implying the large distance nature of the interaction. The observation of impurity clusters arranged in pseudocubic [110] direction confirmed the large distance nature of the interaction. It is concluded that this strong, large distance interaction is very interesting in as much as such an interaction of dipoles forms the basis of ferroelectricity.     

Local Lead–Lag Relationships and Nonlinear Granger Causality: An Empirical Analysis

The Granger causality test is essential for detecting lead–lag relationships between time series. Traditionally, one uses a linear version of the test, essentially based on a linear time series regression, itself being based on autocorrelations and cross-correlations of the series. In the present paper, we employ a local Gaussian approach in an empirical investigation of lead–lag and causality relations. The study is carried out for monthly recorded financial indices for ten countries in Europe, North America, Asia and Australia. The local Gaussian approach makes it possible to examine lead–lag relations locally and separately in the tails and in the center of the return distributions of the series. It is shown that this results in a new and much more detailed picture of these relationships. Typically, the dependence is much stronger in the tails than in the center of the return distributions. It is shown that the ensuing nonlinear Granger causality tests may detect causality where traditional linear tests fail.     

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

GIS Partial Discharge Pattern Recognition Based on a Novel Convolutional Neural Networks and Long Short-Term Memory

Distinguishing the types of partial discharge (PD) caused by different insulation defects in gas-insulated switchgear (GIS) is a great challenge in the power industry, and improving the recognition accuracy of the relevant models is one of the key problems. In this paper, a convolutional neural network and long short-term memory (CNN-LSTM) model is proposed, which can effectively extract and utilize the spatiotemporal characteristics of PD input signals. First, the spatial characteristics of higher-level PD signals can be obtained through the CNN network, but because CNN is a deep feedforward neural network, it does not have the ability to process time-series data. The PD voltage signal is related to the time dimension, so LSTM saves and analyzes the previous voltage signal information, realizes the modeling of the time dependence of the data, and improves the accuracy of the PD signal pattern recognition. Finally, the pattern recognition results based on CNN-LSTM are given and compared with those based on other traditional analysis methods. The results show that the pattern recognition rate of this method is the highest, with an average of 97.9%, and its overall accuracy is better than that of other traditional analysis methods. The CNN-LSTM model provides a reliable reference for GIS PD diagnosis.     

Seeded Ising Model and Distributed Biometric Template Storage and Matching

It is known that a variant of Ising model, called Seeded Ising Model, can be used to recover the information content of a biometric template from a fraction of information therein. The method consists in reconstructing the whole template, which is called the intruder template in this paper, using only a small portion of the given template, a partial template. This reconstruction method may pose a security threat to the integrity of a biometric identity management system. In this paper, based on the Seeded Ising Model, we present a systematic analysis of the possible security breach and its probability of accepting the intruder templates as genuine. Detailed statistical experiments on the intruder match rate are also conducted under various scenarios. In particular, we study (1) how best a template is divided into several small pieces called partial templates, each of which is to be stored in a separate silo; (2) how to do the matching by comparing partial templates in the locked-up silos, and letting only the results of these intra-silo comparisons be sent to the central tallying server for final scoring without requiring the whole templates in one location at any time.     

Numerical simulations of partial elements excitation for hemispherical high-intensity focused ultrasound phased transducer

The hemispherical phased transducer maximizes the coverage of the skull and the ultrasonic energy per unit area of the skull is minimized, thereby reducing the risk of skull burns, but the transducer has a small focal area adjustment range, increasing the focal length of treatment is an urgent question for this type of transducer. In this paper, a three-dimensional high-intensity focused ultrasound (HIFU) transcranial propagation model is established based on the human head structure. The finite difference time domain (FDTD) is combined with the Westervelt acoustic wave nonlinear propagation equation and Penne's biological heat conduction equation for numerical simulation of the sound pressure field and temperature field. Forming a treatable focal area in a small-opening hemispherical transducer with a small amount of numerical simulation calculation focusing at a set position to determine the minimum partial excitation area ratio of focusing. And then, applying these preliminary results to a large-opening diameter hemispherical transducer and the temperature field formed by it or full excitation is studied. The results show that the focus area with the excitation area ratio of less than 22% moves forward to the transducer side when the excitation sound is formed. When the excitation area ratio is greater than or equal to 23%, it focuses at the set position. In the case of partial incentives, using 23% of the partial array, the adjustable range of the treatable focal area formed in the three-dimensional space is larger than that of the full excitation.     

Photoinduced Ordering Transition in Microdroplets of Liquid Crystals with Azo‐Dendrimer

Ordering transitions are observed in azo‐dendrimer‐dissolved nematic liquid crystal (NLC) droplets dispersed in a glycerol matrix. The dendrimer molecules are spontaneously attached at the interface between NLC and glycerol, so that the nematic directors orient perpendicular to the interface, in the radial configuration. Photoisomerization makes the directors be tangential to the interface, in a photoinduced ordering transition from radial to bipolar structure. Similar experiments are conducted both in cholesteric (Ch) and smectic‐A (SmA) LC droplets. Complicated photoinduced ordering transitions are also observed in Ch and SmA droplets, and the associated molecular orientation changes are discussed. Photoisomerizable azo‐dendrimer molecules provide a possible way to control orientation, even in microdroplet systems in which the interface cannot be treated by conventional surface agents.