Dinger Model Research Articles

Stability of the one electron atom Schrödinger model with magnetic field in two dimensions

Stability of the one electron atom Schrödinger model with magnetic field in two dimensions

Mechanical and thermal properties of Si3N4 ceramics prepared by gelcasting using high-solid-loading slurries

In this study, according to the Dinger model, aqueous Si3N4 slurries with a solid loading of 63 vol% and a viscosity lower than 1.0 Pa s were successfully prepared using two-grade Si3N4 powders with D50 = 7.2 μm and 9.4 μm as starting materials. These resulting slurries exhibited good rheological properties and suspension stability. Notably, the presence of β-Si3N4 seeds existed in the starting materials effectively reduced the nucleation barrier by transforming homogeneous nucleation into heterogeneous nucleation. Consequently, it facilitated the reconstructive phase transformation of α-Si3N4 to β-Si3N4, promoted the anisotropic growth of β-Si3N4 nucleation, and resulted in the final formation of the bimodal microstructure. This unique microstructure significantly enhanced the mechanical properties of Si3N4 ceramics, resulting in a high flexural strength of 1011.4 MPa and a fracture toughness of 14.8 MPa m1/2. These excellent properties were achieved through the combination of gelcasting and gas pressure sintering. Simultaneously, the Si3N4 ceramics exhibited a low thermal conductivity of 47.7 W m−1 K−1, mainly owing to the low density of 95.3 %, the presence of low-thermal-conductivity silicate-based noncrystalline substances, and the possible existence of lattice oxygen in Si3N4 crystals.

Determining concrete properties for different optimized combined concrete mixtures: Novel mathematical approach

Gradation of the granular skeleton significantly influences almost all of the concrete performances. The main purpose of this research work is to develop a mathematical model to characterize the properties of various dry concrete mixtures. The starting point of this work is to propose a single equation to describe continuous aggregate gradations, by combining several ideal grading curves used to design different concrete mixtures, to achieve higher freedom in optimizing the particle-size distribution (PSD) of a concrete mixture. At the design procedure stage, the concrete constituents are selected so that the overall grading of the mix closely follows a given ideal grading curve for specific properties. Using the gradation equation afore-mentioned, a mathematical framework is established to outline several intrinsic factors in the optimized granular skeleton of concrete, characterized by a wide range of particle sizes. The factors developed, directly measured based on the PSD, include the specific surface area and the fineness modulus of the combined grading of the concrete mix particles, as well as the ratio between the granular fractions determined either by area or by weight, and the surface area of the total concrete mixture. The resulting model expressions relate the characteristics of the size distribution of the concrete skeleton, to the parameters in the proposed gradation equation, in particular the distribution exponent. The proposed model could be implemented in the study of the solid phase of concrete, design aggregate gradation to meet certain requirements, or even predict some attributes of the dry concrete mixture. • A unified equation of well-known optimal particle size distributions is developed. • A model is proposed to accurately calculate some properties of the concrete mixes. • The distribution exponent in the proposed equation is the most relevant parameter. • Optimal PSDs are fractal and converge mathematically to the Fung & Dinger model. • The proposed model is suitable for systems with a wide range of particle sizes.

Classification of Ultra-high Performance Concrete (UHPC)

Ultra-high performance concrete (UHPC) been an advanced concrete introduced as reactive powder concrete (RPC) over twenty years ago, is now being employed for use in the construction industry of some developed countries like China, Germany and United States of America. Its excellent properties in structural performance and durability make it the civil engineering material that will reshape the future of the construction industry in terms of structural performance; and this paper aims at helping construction experts and developing countries to understand and accept UHPC for use in everyday construction works. The paper gives an in-depth review on the classification of UHPCs based on mix proportion and mechanical properties. Firstly, the mixture design and the mechanical properties of UHPC were discussed. Then UHPC was classified into different types based on mechanical properties and the manufacturer’s modification of the ingredients used for reactive powder concrete or multi-scale cement composite production. This review shows that Funk and Dinger model (also known as Modified Andreasen and Andersen model (MAA)) is the most accepted and widely used mix design method for UHPC. It also revealed that UHPC’s compressive strength, tensile strength and flexural strength are in excess of 150, 7 and 40 MPa respectively. It further classified UHPC into BCV®, BSI®, Cemtec®, Ceracem, Ductal, DURA and UHPC with coarse aggregate; and this classification (especially UHPC with coarse aggregate) is a good sign that local materials can be incorporated into UHPC by developing countries for cost minimisation.

Classification of Ultra-high Performance Concrete (UHPC)

Ultra-high performance concrete (UHPC) been an advanced concrete introduced as reactive powder concrete (RPC) over twenty years ago, is now being employed for use in the construction industry of some developed countries like China, Germany and United States of America. Its excellent properties in structural performance and durability make it the civil engineering material that will reshape the future of the construction industry in terms of structural performance; and this paper aims at helping construction experts and developing countries to understand and accept UHPC for use in everyday construction works. The paper gives an in-depth review on the classification of UHPCs based on mix proportion and mechanical properties. Firstly, the mixture design and the mechanical properties of UHPC were discussed. Then UHPC was classified into different types based on mechanical properties and the manufacturer’s modification of the ingredients used for reactive powder concrete or multi-scale cement composite production. This review shows that Funk and Dinger model (also known as Modified Andreasen and Andersen model (MAA)) is the most accepted and widely used mix design method for UHPC. It also revealed that UHPC’s compressive strength, tensile strength and flexural strength are in excess of 150, 7 and 40 MPa respectively. It further classified UHPC into BCV®, BSI®, Cemtec®, Ceracem, Ductal, DURA and UHPC with coarse aggregate; and this classification (especially UHPC with coarse aggregate) is a good sign that local materials can be incorporated into UHPC by developing countries for cost minimisation.

Study on Film Formation Properties of SiC Slurry

Two kinds of silicon carbide (SiC) powders with median diameters of 0.60μm and 2.04μm were selected as raw materials, and uniformly dispersed SiC coating film solutions were prepared through different particle grading. The effects of gradation ratio and dispersant tetramethylammonium hydroxide (TMAH) on the dispersibility and rheology of SiC coating films were studied, and the effect of dispersant content on the film forming properties of the slurry was discussed. When the fine powder and coarse powder grading mass ratio is 3:7, the particle size distribution of the mixed powder is closest to the theoretical distribution of the Dinger model. At this time, the slurry has good rheology and high particle bulk density. When 0.4% TMAH is added, the viscosity of the slurry is the lowest. When TMAH is added in an amount of 0.1 to 0.2%, the slurry has good film-forming properties.

Unidirectional transport of wave packets through tilted discrete breathers in nonlinear lattices with asymmetric defects.

We consider the transfer of lattice wave packets through a tilted discrete breather (TDB) in opposite directions in the discrete nonlinear Schrödinger model with asymmetric defects, which may be realized as a Bose-Einstein condensate trapped in a deep optical lattice, or as optical beams in a waveguide array. A unidirectional transport mode is found, in which the incident wave packets, whose energy belongs to a certain interval between full reflection and full passage regions, pass the TDB only in one direction, while in the absence of the TDB, the same lattice admits bidirectional propagation. The operation of this mode is accurately explained by an analytical consideration of the respective energy barriers. The results suggest that the TDB may emulate the unidirectional propagation of atomic and optical beams in various settings. In the case of the passage of the incident wave packet, the scattering TDB typically shifts by one lattice unit in the direction from which the wave packet arrives, which is an example of the tractor-beam effect, provided by the same system, in addition to the rectification of incident waves.

On S-matrix factorization of the Landau-Lifshitz model

We consider the three-particle scattering S-matrix for the Landau-Lifshitz model by directly computing the set of the Feynman diagrams up to the second order. We show, following the analogous computations for the non-linear Schr\"{o}dinger model, that the three-particle S-matrix is factorizable in the first non-trivial order.

Form factors of the operators at the boundary in quantum nonlinear Schr?dinger model

For the nonlinear Schrdinger model with an integrable open boundary, the scalar products of Bethe eigenstates and form factors of operators at the boundary are calculated. The results are represented as determinants of usual functions with parameters of the model.

Integrability of the generalized multi-component Fermi quantum derivative nonlin ear Schrdinger model

With the help of Lax operator, the monodromy matrix is constructed, and the Hamiltonian is obtained. By using algebraic Bethe ansatz method, it has been shown t hat the monodromy matrix satisfies the Yang-Baxter equation on both a finite in terval and an infinite interval. So the integrability of this model is proved.

Gap and out-gap breathers in a binary modulated discrete nonlinear Schr�dinger model

We consider a modulated discrete nonlinear Schrodinger (DNLS) model with alternating on-site potential, having a linear spectrum with two branches separated by a ‘forbidden’ gap. Nonlinear localized time-periodic solutions with frequencies in the gap and near the gap -- discrete gap and out-gap breathers (DGBs and DOGBs) -- are investigated. Their linear stability is studied varying the system parameters from the continuous to the anti-continuous limit, and different types of oscillatory and real instabilities are revealed. It is shown, that generally DGBs in infinite modulated DNLS chains with hard (soft) nonlinearity do not possess any oscillatory instabilities for breather frequencies in the lower (upper) half of the gap. Regimes of ‘exchange of stability’ between symmetric and antisymmetric DGBs are observed, where an increased breather mobility is expected. The transformation from DGBs to DOGBs when the breather frequency enters the linear spectrum is studied, and the general bifurcation picture for DOGBs with tails of different wave numbers is described. Close to the anti-continuous limit, the localized linear eigenmodes and their corresponding eigenfrequencies are calculated analytically for several gap/out-gap breather configurations, yielding explicit proof of their linear stability or instability close to this limit.

Bunching of fluxons in a long Josephson junction with surface losses.

It is known that the sine-Gordon model of a long Josephson junction with a surface-loss term predicts a spatially oscillating trailing tail of a strongly contracted fluxon. In the present work, it is demonstrated that this should give rise to bunched (bound) states of fluxons, although the onset of the bunching drastically differs from the standard situation recently investigated in terms of the perturbed nonlinear Schro\ifmmode\ddot\else\textasciidieresis\fi{}dinger model. Influence of the bunching on the I-V characteristic of an annular junction with a finite number of trapped fluxons is analyzed qualitatively. It is demonstrated that the bunching may set in with a small hysteresis, and it increases voltage at a given current. The latter effect has been observed in most recent experiments with the annular junction.

Non-perturbative calculation of theS-matrix of the non-linear Schr�dinger model in the strong coupling regime

A non-perturbative scheme for the calculation of theS-matrix in quantum field theory is applied to the non-linear Schrodinger model, which is analytically solvable. We present numerical results, which demonstrate that the method works successfully in the weak but more importantly also in the strong coupling regime.

Fermionic perturbation theory for the statistical mechanics of the nonlinear Schr�dinger model

A fermionic perturbation theory is developed for the statistical mechanics of the nonlinear Schrodinger model. The theory is based on an interacting-fermion picture of the Bethe wave function. The inner product of the Bethe wave function is explicitly evaluated, and a simple graphical representation of it is given. The basic equations obtained for the free energy agree with those of Yang and Yang. In particular, the present theory gives a clear-cut meaning to the ɛ function of Yang and Yang: It represents a fermion energy at finite temperatures.