EXISTENCE AND UNIQUENESS OF RENORMALIZED SOLUTIONS FOR A CLASS OF DEGENERATE PARABOLIC EQUATIONS

This article discusses the existence and uniqueness of renormalized solutions for a class of degenerate parabolic equations b（u）t - div（a（u, u）） = H（u）（f ＋ divg）.

RENORMALIZED SOLUTIONS OF ELLIPTIC EQUATIONS WITH ROBIN BOUNDARY CONDITIONS

In the present paper, we consider elliptic equations with nonlinear and nonlao mogeneous Robin boundary conditions of the type {-div（B（x,u）△u） = f in Ω,u=0 on Гo, B（x,u）Vu·n^-＋γ（x）h（u） = 9 on Г1,where f and g are the element of L^1（Ω） and L^1（Г1）, respectively. We define a notion of renormalized solution and we prove the existence of a solution. Under additionM assumptions on the matrix field B we show that the renormalized solution is unique.

SOLUTIONS OF GINZBURG-LANDAU EQUATIONS WITH WEIGHT AND MINIMIZERS OF THE RENORMALIZED ENERGY

In this paper, it is proved that for any given d non-degenerate local minimum points of the renormalized energy of weighted Ginzburg-Landau eqautions, one can find solutions to the Ginzburg-Landau equations whose vortices tend to these d points. This provides the connections between solutions of a class of Ginzburg-Landau equations with weight and minimizers of the renormalized energy.

Renormalized Coordinate Stretching: A Generalization of Shoot and Fit with Application to Stellar Structure

The standard shooting and fitting algorithm for non-linear two-point boundary value problems derives from conventional coordinate perturbation theory. We generalize the algorithm using the renormalized perturbation theory of strained coordinates. This allows for the introduction of an arbitrary function, which may be chosen to improve numerical convergence. An application to a problem in stellar structure exemplifies the algorithm and shows that, when used in conjunction with the standard procedure, it has superior convergence compared to the standard one alone.

Investigating the Potential of Quasi-One-Dimensional Organic Crystals of TTT(TCNQ)2 for Thermoelectric Applications

The purpose of this paper is to present the results of investigations on quasi-one-dimensional organic crystals of tetrathiotetracene-tetracyanoquinodi- methane (TTT(TCNQ)2) from the prospective of thermoelectric applications. The calculations were performed after analytical expressions, obtained in the frame of a physical model, more detailed than the model presented earlier by authors. The main Hamiltonian of the model includes the electronic and phonon part, electron-phonon interactions and the impurity scattering term. In order to estimate the electric charge transport between the molecular chains, the physical model was upgraded to the so-called three-dimen- sional (3D) physical model. Numeric computations were performed to determine the electrical conductivity, Seebeck coefficient, thermal conductivity, thermoelectric power factor and thermoelectric figure-of-merit as a function on charge carrier concentrations, temperatures and impurity concentrations. A detailed analysis of charge-lattice interaction, consisting of the exploration of the Peierls structural transition in TCNQ molecular chains of TTT(TCNQ)2 was performed. As result, the critical transition temperature was determined. The dispersion of renormalized phonons was examined in detail.

Mapping rice cropping systems using Landsat-derived Renormalized Index of Normalized Difference Vegetation Index （RNDVI） in the Poyang Lake Region, China

Mapping rice cropping systems with optical imagery in multiple cropping regions is challenging due to cloud contamination and data availability; development of a phenology-based algorithm with a reduced data demand is essential. In this study, the Landsat-derived Renorma- lized Index of Normalized Difference Vegetation Index （RNDVI） was proposed based on two temporal windows in which the NDVI values of single and early （or late） rice display inverse changes, and then applied to discriminate rice cropping systems. The Poyang Lake Region （PLR）, characterized by a typical cropping system of single cropping rice （SCR, or single rice） and double cropping rice （DCR, including early rice and late rice）, was selected as a testing area. The results showed that NDVI data derived from Landsat time-series at eight to sixteen days captures the temporal development of paddy rice. There are two key phenological stages during the overlapping growth period in which the NDVI values of SCR and DCR change inversely, namely the ripening phase of early rice and the growing phase of single rice as well as the ripening stage of single rice and the growing stage of late rice. NDVI derived from scenes in two temporal windows, specifically early August and early October, was used to construct the RNDVI for discriminating rice cropping systems in the polder area of the PLR, China. Comparison with ground truth data indicates high classification accuracy. The RNDVI approach highlights the inverse variations of NDVI values due to the difference of rice growth between two temporal windows. This makes the discrimination of rice cropping systems straightforward as it only needs to distinguish whether the candidate rice typeis in the period of growth （RNDVI 〈 0） or senescence （RNDVI 〉 0）.

Entropy and Renormalized Solutions for Nonlinear Elliptic Problem Involving Variable Exponent and Measure Data

We give an existence result of entropy and renormalized solutions for strongly nonlinear elliptic equations in the framework of Sobolev spaces with variable exponents of the type： -div （a（x, u,▽u）＋φ（u））＋g（x, u,▽u）=μ, where the right-hand side belongs to L^1（Ω）＋W^-1,p＇（x）（Ω）, -div（a（x, u,▽u）） is a Leray-Lions operator defined from W^-1,p＇（x）（Ω） into its dual and φ∈C^0（R,R^N）. The function g（x, u,▽u） is a non linear lower order term with natural growth with respect to ｜▽u｜ satisfying the sign condition, that is, g（x, u,▽u）u ≥ 0.

Tunable caging of excitation in decorated Lieb-ladder geometry with long-range connectivity

Controlled Aharonov-Bohm caging of wave train is reported in a quasi-one-dimensional version of Lieb geometry with next-nearest-neighbor hopping integral within the tight-binding framework.This longer-wavelength fluctuation is considered by incorporating periodic,quasi-periodic or fractal kind of geometry inside the skeleton of the original network.This invites exotic eigenspectrum displaying a distribution of flat band states.Also a subtle modulation of external magnetic flux leads to a comprehensive control over those non-resonant modes.Real space renormalization group method provides us an exact analytical prescription for the study of such tunable imprisonment of excitation.The non-trivial tunability of external agent is important as well as challenging in the context of experimental perspective.

First-principles study of the bandgap renormalization and optical property ofβ-LiGaO_(2)

Theβ-LiGaO_(2)with an orthorhombic wurtzite-derived structure is a candidate ultrawide direct-bandgap semiconductor.In this work,using the non-adiabatic Allen-Heine-Cardona approach,we investigate the bandgap renormalization arising from electron-phonon coupling.We find a sizable zero-point motion correction of-0.362 eV to the gap atΓ,which is dominated by the contributions of long-wavelength longitudinal optical phonons.The bandgap ofβ-LiGaO_(2)decreases monotonically with increasing temperature.We investigate the optical spectra by comparing the model Bethe-Salpether equation method with the independent-particle approximation.The calculated optical spectra including electron-hole interactions exhibit strong excitonic effects,in qualitative agreement with the experiment.The contributing interband transitions and the binding energy for the excitonic states are analyzed.

Stability of the topological quantum critical point between multi-Weyl semimetal and band insulator

One could tune a topological double-Weyl semimetal or a topological triple-Weyl semimetal to become a topologically trivial insulator by opening a band gap.This kind of quantum phase transition is characterized by the change of certain topological invariant.A new gapless semimetallic state emerges at each topological quantum critical point.Here we perform a renormalization group analysis to investigate the stability of such critical points against perturbations induced by random scalar potential and random vector potential.We find that the quantum critical point between double-Weyl semimetal and band insulator is unstable and can be easily turned into a compressible diffusive metal by any type of weak disorder.The quantum critical point between triple-Weyl semimetal and band insulator flows to a stable strong-coupling fixed point if the system contains a random vector potential merely along the z-axis,but becomes a compressible diffusive metal when other types of disorders exist.

Effects of quantum quench on entanglement dynamics in antiferromagnetic Ising model

We study the relationship between quench dynamics of entanglement and quantum phase transition in the antiferromagnetic Ising model with the Dzyaloshinskii–Moriya(DM)interaction by using the quantum renormalization-group method and the definition of negativity.Two types of quench protocols(i)adding the DM interaction suddenly and(ii)rotating the spins around x axis are considered to drive the dynamics of the system,respectively.By comparing the behaviors of entanglement in both types of quench protocols,the effects of quench on dynamics of entanglement are studied.It is found that there is the same characteristic time at which the negativity firstly reaches its maximum although the system shows different dynamical behaviors.Especially,the characteristic time can accurately reflect the quantum phase transition from antiferromagnetic to saturated chiral phases in the system.In addition,the correlation length exponent can be obtained by exploring the nonanalytic and scaling behaviors of the derivative of the characteristic time.

Pacman Renormalization in Siegel Parameters of Bounded Type

A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorially periodic rotation number in the main cardioid of the Mandelbrot set. It is already known that it can be defined a Pacman renormalization operator such that for Siegel pacmen, with combinatorially periodic rotation numbers, the operator is compact, analytic and has a unique fixed point, at which it is hyperbolic with one-dimensional unstable manifold. In this paper we observe that this Pacman renormalization operator is compact and analytic at any Siegel Pacman or Siegel map with combinatorially bounded rotation number. This allows us to define a renormalization operator on the hybrid classes of the standard Siegel pacmen to which we built its horseshoe where the operator is topologically semiconjugated to the left shift on the space of bi-infinite sequences of natural numbers bounded by some constant.

Mechanism of local scour around submarine pipelines based on numerical simulation of turbulence model

The mechanism of local scour around submarine pipelines is studied numerically based on a renormalized group （RNG） turbulence model. To validate the numerical model, the equilibrium profiles of local scour for two cases are simulated and compared with the experimental data. It shows that the RNG turbulence model can give an appropriate prediction for the configuration of equilibrium scour hole, and it is applicable to this situation. The local scour mechanism around submarine pipelines including the flow structure, shear stress distribution and pressure field is then analyzed and compared with experiments. For further comparison and validation, especially for the flow structure, a numerical calculation employing the large eddy simulation （LES） is also conducted. The numerical results of RNG demonstrate that the critical factor governing the equilibrium profile is the seabed shear stress distribution in the case of bed load sediment transport, and the two-equation RNG turbulence model coupled with the law of wall is capable of giving a satisfying estimation for the bed shear stress. Moreover, the piping phenomena due to the great difference of pressure between the upstream and downstream parts of pipelines and the vortex structure around submarine pipelines are also simulated successfully, which are believed to be the important factor that lead to the onset of local scour.

Phonons near Peierls Structural Transition in Quasi-One-Dimensional Organic Crystals of TTF-TCNQ

The Peierls structural transition in quasi-one-dimensional organic crystals of TTF-TCNQ is investigated in the frame of a more complete physical model. The two most important electron-phonon interaction mechanisms are taken into account simultaneously. One is similar of that of deformation potential and the other is of polaron type. For simplicity, the 2D crystal model is considered. The renormalized phonon spectrum and the phonon polarization operator are calculated in the random phase approximation for different temperatures. The effects of interchain interaction on renormalized acoustic phonons and on the Peierls critical temperature are analyzed.

Properties of ground state and anomalous quantum fluctuations in one-dimensional polaron-soliton systems-the effects of electron-two-phonon interaction and non-adiabatic quantum correlations

Based on the Holstein model Hamiltonian of one-dimensional molecular crystals, by making use of the expansion approach of the correlated squeezed-coherent states of phonon instead of the two-phonon coherent state expansion scheme, the properties of the ground state and the anomalous quantum fluctuations are investigated in a strongly coupled electron-phonon system with special consideration of the electron-two-phonon interaction. The effective renormalization （ai） of the displacement of the squeezed phonons with the effect of the squeezed-coherent states of phonon and both the electron-displaced pbonon and the polaron-squeezed phonon correlations have been combined to obtain the anomalous quantum fluctuations for the corrections of the coherent state. Due to these non-adiabatic correlations, the effective displacement parameter ai is larger than the ordinary parameter ai （0） In comparison with the electron-one-phonon interaction （g） corrected as oig, we have found the electron-two-phonon interaction （gl） corrected as ai2gi is enhanced significantly. For this reason, the ground state energy （E（2）） contributed by the electron-two-phonon interaction is more negative than the single-phonon case （E01）） and the soliton solution is more stable. At the same time, the effects of the electron-two-phonon interaction greatly increase the polaron energy and the quantum fluctuations. Furthermore, in a deeper level, we have considered the effect of the polaron-squeezed phonon correlation （f-correlation）. Since this correlation parameter f 〉 1, this effect will strengthen the electron-one and two-phonon interactions by fai9 and f2ai2g1, respectively. The final results show that the ground state energy and the polaron energy will appear more negative further and the quantum fluctuations will gain further improvement.

EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF PARABOLIC EQUATIONS WITH NATURAL GROWTH TERMS AND L^1 DATA

We study a class of nonlinear parabolic equations of the type：δb（u）/δt-div（a（x,t,u）△u）＋y（u）｜△u｜^2=f,where the right hand side belongs to L^1（Q）, b is a strictly increasing C^1-function and -div（a（x, t, u）△u） is a Leray-Lions operator. The function g is just assumed to be continuous on R and to satisfy a sign condition. Without any additional growth assumption on u, we prove the existence of a renormalized solution.

对无机化学教材的处理与分析

对无机化学教材的处理与分析屠昆岗（苏州铁道师范学院化学系，苏州２１５００９）无机化学是化学系第一门专业基础课，在学生以后的学习中起着十分重要的作用。它的任务不仅是给学生打好理论基础和实验基础，而且要培养学生具有分析问题和解决化学问题的能力。几年来我们...

Weak Solutions of a Class of Strongly Degenerate Quasilinear Parabolic Equations

In this paper, we show the existence of the renormalized solutions and the entropy solutions of a class of strongly degenerate quasilinear parabolic equations.

Assessment of Turbulence Models on Bridge-Pier Scour Using Flow-3D

The main purpose of this paper is to analyze the influence of different turbulence flow models on scouring pit of bridge-pier. Flow-3D software is applied in line with the purpose. The key motivation for this study is to contribute to the Flow-3D software by means of some modification and adjustment in the sediment scour model and shallow water model. An assessment of turbulence model adopted with the parameters of the Melville experiment to estimate the maximum scour-depth was performed. In the simulation results, the alternate eddy formation and shedding were repeated while the Karman vortex street formed behind the pier for the large eddy simulation LES turbulence model is more realistic in the flow phenomenon. The results of the scour development of large eddy simulation (LES) turbulence model were found to be more satisfied than the Renormalized group (RNG) turbulence model and close to the prior experiment results. The simulated scour results were significantly different with the observed data collected from previous literature in the reason of some unsuitability of meshing method in Flow-3D software.

Metal-Insulator Transition of Peierls Type in Quasi-One-Dimensional Crystals of TTT₂I₃

We investigate the metal-insulator transition in quasi-one-dimensional organic crystals of tetrathiotetracene-iodide, TTT2I3, in the 2D model. A crystal physical model is applied which takes into account two the most important hole-phonon interaction mechanisms. One is similar to that of deformation potential and the other is of polaron type. The scattering on defects is also considered and it is crucial for the explanation of the transition. The phonon polarization operator and the renormalized phonon spectrum are calculated in the random phase approximation for different temperatures applying the method of Green functions. We show that the transition is of Peierls type. The effect of lattice distortion on the dispersion of renormalized acoustic phonons is analyzed.