Coefficient D3 Research Articles

Pattern dynamics of a predator–prey system with cross-diffusion, Allee effect and generalized Holling IV functional response

In this paper, a diffusive predator–prey model with Allee effect and functional response of generalized Holling type IV is established. The complex pattern dynamics of and bifurcation phenomena of system are analyzed by using linear stability analyses and bifurcation theory, etc. Corresponding to spiral pattern, spot pattern or spot–stripe mix pattern and chaotic pattern, respectively, the conditions that arise Hopf instability, Turing instability and Hopf–Turing instability of constant positive steady solutions of reaction–diffusion system are presented. The impacts of Allee effect and cross-diffusion on pattern formations of the system are further discussed. Particularly, provided that cross-diffusion is absent, there will not appear the formation of Turing pattern, that is, Turing pattern is only driven by cross-diffusions. Addressed to the different pattern formations involving in cross-diffusion and Allee effect, overall numerical simulations are provided when the spatial dimension is two and the theoretical results are demonstrated. It is revealed that the larger Allee effect constant A and the cross-diffusion coefficient d4 are advantageous for the appearing of formation of Turing pattern, while the cross-diffusion coefficient d3 suppresses the formation of Turing pattern with its increasing.

Robust approach to depth of anaesthesia assessment based on hybrid transform and statistical features

To develop an accurate and efficient depth of anaesthesia (DoA) assessment technique that could help anaesthesiologists to trace the patient's anaesthetic state during surgery, a new automated DoA approach was proposed. It applied wavelet-Fourier analysis (WFA) to extract the statistical characteristics from an anaesthetic electroencephalogram (EEG) signal and to design a new DoA index. In this proposed method, firstly, the wavelet transform was applied to a denoised EEG signal, and a fast Fourier transform was then applied to the wavelet detail coefficient D3. Ten statistical features were extracted and analysed, and from these, five features were selected for designing a new index for the DoA assessment. Finally, a new DoA (WFA DoA ) was developed and compared with the most popular bispectral index (BIS) monitor. The results from the testing set showed that there were very high correlations between the WFA DoA and the BIS index during the awake, light and deep anaesthetic stages. In the case of poor signal quality, the BIS index and the WFA DoA were also tested, and the obtained results demonstrated that the WFA DoA could indicate the DoA values, while the BIS failed to show valid outputs for those situations.

Relation of Experimental Features of P-Even, T-Odd Asymmetries in Ternary Nuclear Fission Induced by Cold Polarized Neutrons to Triple and Quintuple Scalar Correlations

In employing the concept of the isotropy of space, the coefficients D of P-even, T-odd asymmetry in the angular distributions of prescission alpha particles emitted as third particles in the ternary fission of nonoriented target nuclei that is induced by polarized cold neutrons are expressed in the lowest orders of perturbation theory in the neutron polarization vector in terms of two P-even scalar coefficients D3 and D5 associated with, respectively, triple and quintuple correlations depending on the unit vectors kα, kLF, and σn, which determine the features of the coefficients being studied. On the basis of the above representation, the experimental values of the coefficients D3 and D5 are determined by using the experimental values of D and the angular distributions of alpha particles emitted in the analogous reaction induced by unpolarized neutrons. The resulting coefficients D3 and D5 are compared with the analogous coefficients found by means of the classical method of trajectory calculations and by means of quantum-mechanical fission theory relying on the concept that it is the rotational mechanism that is responsible for the appearance of the asymmetries being studied. It turns out that the classical method, which disregards the interference between fission amplitudes for different S-wave neutron resonances, leads to an irremovable contradiction between the calculated coefficient D3 and the analogous experimental coefficient for the 233U target nucleus. In the case of employing the quantum-mechanical approach, it is concluded that three-body calculations of the Coriolis interaction—perturbed amplitude of the angular distributions of alpha particles moving in the Coulomb fields of fission fragments are required for the 233U target nucleus.

Non-invasive prediction of the tumor growth rate using advanced diffusion models in head and neck squamous cell carcinoma patients.

We assessed parameters of advanced diffusion weighted imaging (DWI) models for the prediction of the tumor growth rate in 55 head and neck squamous cell carcinoma (HNSCC) patients. The DWI acquisition used single-shot spin-echo echo-planar imaging with 12 b-values (0−2000). We calculated 14 DWI parameters using mono-exponential, bi-exponential, tri-exponential, stretched exponential and diffusion kurtosis imaging models. We directly measured the tumor growth rate from two sets of different-date imaging data. We divided the patients into a discovery group (n = 40) and validation group (n = 15) based on their MR acquisition dates. In the discovery group, we performed univariate and multivariate regression analyses to establish the multiple regression equation for the prediction of the tumor growth rate using diffusion parameters. The equation obtained with the discovery group was applied to the validation group for the confirmation of the equation's accuracy. After the univariate and multivariate regression analyses in the discovery-group patients, the estimated tumor growth rate equation was established by using the significant parameters of intermediate diffusion coefficient D2 and slow diffusion coefficient D3 obtained by the tri-exponential model. The discovery group's correlation coefficient between the estimated and directly measured tumor growth rates was 0.74. In the validation group, the correlation coefficient (r = 0.66) and intra-class correlation coefficient (0.65) between the estimated and directly measured tumor growth rates were respectively good. In conclusion, advanced DWI model parameters can be a predictor for determining HNSCC patients’ tumor growth rate.

가중 퍼지소속함수 기반 신경망과 웨이블릿 변환을 이용한 심실 빈맥/세동 검출

This paper presents an approach to classify normal and ventricular tachycardia/fibrillation(VT/VF) from the Creighton University Ventricular Tachyarrhythmia Database(CUDB) using the neural network with weighted fuzzy membership functions(NEWFM) and wavelet transforms. In the first step, wavelet transforms are used to obtain the detail coefficients at levels 3 and 4. In the second step, all of detail coefficients d3 and d4 are classified into four intervals, respectively, and then the standard deviations of the specific intervals are used as eight numbers of input features of NEWFM. NEWFM classifies normal and VT/VF beats using eight numbers of input features, and then the accuracy rate is 90.1%.

Inelastic interchannel collisions of pulses in optical fibers in the presence of third-order dispersion

We study the effect of third-order dispersion on the interaction between two solitons from different frequency channels in an optical fiber. The interaction may be viewed as an inelastic collision in which energy is lost to continuous radiation owing to nonzero third-order dispersion. We develop a perturbation theory with two small parameters: the third-order dispersion coefficient d3 and the reciprocal of the interchannel frequency difference 1/Ω. In the leading order the amplitude of the emitted radiation is proportional to d3/Ω2, and the source term for this radiation is identical to the one produced by perturbation of the second-order dispersion coefficient. The only other effects up to the third order are shifts in the soliton’s phase and position. Our results show that the statistical description of soliton propagation in a given channel influenced by interaction with a quasi-random sequence of solitons from other channels is similar to the description of soliton propagation in fibers with weak disorder in the second-order dispersion coefficient.

Ionic structure in a binary fluid

The tracer diffusion coefficient D3+ of the trivalent lanthanide cation 153Gd3+ is studied in mixtures of isobutyric acid, water and 5*10-4 M Gd(NO3)3 using an open-ended capillary tube. These data are given over the complete composition range at T-Tc=0.171 K. The coefficients D3+ are combined with the shear viscosity eta of the electrolyte. The results are discussed in terms of the Einstein-Stokes law; our analysis suggests three different behaviours of the diffusing entity in the mixtures and it is based on the preferential solvation phenomenon.

Development of electron avalanches in argon-an exact Boltzmann equation analysis

Development of the electron avalanche in argon has been studied at E/N=141, 283 and 566 Td by two exact Boltzmann equation methods, a Fourier expansion (FE) of the distribution function of electrons by Tagashira et al. (1978), and a direct estimation of moments (DEM) of the electron density distribution in the real space by starting from a Boltzmann equation. Elastic momentum transfer, total electronic excitation and ionisation collisions are considered. The electron swarm parameters obtained by FE agree exactly with those by DEM, justifying the expansion used in FE, and the swarm parameters obtained by two-term expansion (TE) are in good agreement with those obtained by the exact FE and DEM except the longitudinal diffusion coefficient DL and a higher order coefficient D3 at E/N=566 Td and the transverse diffusion coefficient DT at all the E/N studied, suggesting that the disagreement with DL and D3 is due simply to breakdown of TE at high E/N but the disagreement with DT is due to more essential insufficiency in TE. The electron velocity distributions are also obtained and discussed.

Sintering of Zinc Sulfide

The mechanisms of the sintering of ZnS were determined by measurement of the rate of growth of the necks between polycrystalline spheres. In vacuum (10−6 mm Hg) at temperatures higher than 600° C the mechanism of sintering is that of volume diffusion with coefficient Dv, = 1.06 × 10−2 exp (‐26,400/RT); below 600°C surface diffusion predominates, with coefficient D3, = 9.14 × 10‐3 exp (‐5700/RT). In Zn vapor (10−2 mm Hg) between 550° and 650°C the predominating mechanism of sintering is surf ace diffusion, D3, = 7.06 × 10−2 exp (‐8600/RT). It has been found that in an argon atmosphere the diffusion coefficient is much lower.