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1.
In this study, we investigate three kinds of fractional differential models (distributed-order model, variable-order model and random-order model) for characterization of anomalous diffusion. The characteristics, physical advantages and potential applications of each model are highlighted. The numerical simulations also validate our analytical and comparison results. Furthermore, a generalized distributed-variable-order model and a more generalized distributed-variable-random-order model are proposed to combine the advantages of distributed-order model, variable-order model and random-order model. 相似文献
2.
Several models of prebiological systems are described and analyzed. The following models are characterized: a quasispecies model, a hypercycle model, a syser model (the term "syser" is an abbreviation of SYstem of SElf-Reproduction), a stochastic corrector model, a model of the origin of a primordial genome through spontaneous symmetry breaking. The quasispecies model analyzes the Darwinian evolution of information chains; this evolution is similar to the evolution of RNA molecules. Rather general estimates of the speed and efficiency of evolutionary processes can be obtained in the framework of the quasispecies model. We briefly describe the method for obtaining these estimates and the corresponding results. The hypercycle model considers the interaction of RNA chains and enzymes. The syser model characterizes a rather general scheme of the self-reproducing system, which is similar to the self-reproducing systems of biological cells. Syser includes a polynucleotide sequence, a replication enzyme, a translation enzyme, and other enzymes; these macromolecules are located inside the protocell. The stochastic corrector model describes the process of using a relatively small number of molecules of competing and cooperating replicators in protocells. The model of the origin of a primordial genome through spontaneous symmetry breaking characterizes an interesting and important process of the appearance of genotypes in protocells. This model was proposed and investigated by Takeuchi, Hogeweg, and Kaneko in 2017; we call it further “the THK model.” The current article characterizes and compares all these models. 相似文献
3.
A Simplified Neuronal Model for the Instigation and Propagation of Cortical Spreading Depression
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Huaxiong Huang Robert M. Miura & Wei Yao 《advances in applied mathematics and mechanics.》2011,3(6):759-773
In this paper, we construct a simplified neuronal model that is capable
of simulating the instigation of cortical spreading depression (CSD) and
propagation of a CSD wave. Our model is a simplification and extension of
a single neuron model proposed in the literature for studying the instigation
of CSD. Using the simplified neuronal model, we construct a network of these
simplified neurons. This network model shows that the propagation of a CSD
wave occurs naturally after it is instigated electrically or chemically.
Although the model is simple, the speed of the CSD wave predicted by our
model is consistent with experimentally observed values. Finally, our model
allows us to investigate the effects of specific ion channels on the spread
of a CSD wave. 相似文献
4.
锂离子电池的电化学模型对于电池特性分析和电池管理具有重要意义,但是准二维(P2D)模型复杂度太高,为了在保证模型精度的基础上尽量降低复杂度,本文提出了一种包含液相简化的P2D (LSP2D)模型,该模型首先基于电化学平均动力学将电池端电压化简成为仅耦合固相Li+浓度c_s和液相Li+浓度c_e的方程,然后进一步对表达c_s和c_e演化规律的偏微分方程进行抛物线近似化简,使得最终的模型由多项式组成.COMSOL仿真表明在放电倍率为1C时该模型与单粒子(SP)模型的估算精度和速度相当,但在放电倍率为3C时,该模型的估算时间比P2D模型减少了99.73%,与SP模型相当,估算精度相比SP模型有大幅度提升. 相似文献
5.
A dual-model method is proposed for correcting the calibration model. In the method, a primary calibration model is built using the spectra of a primary instrument and a correction model is established to describe the ratios between the predicted results from the spectra of different instruments. The prediction for the spectra of secondary instrument can be achieved by correcting the prediction of the primary model. A mathematical proof is described for the existence of the correction model, and the model is investigated using a near-infrared spectroscopic dataset of plant leaf samples measured on two instruments. The results show that a precise correction model is obtained and the model can be used to correct the predictions of the primary model. The correlation coefficients between the predicted and the reference ratios are above 0.9, and the prediction error after the correction is at the same level of the primary model. 相似文献
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This paper presents a car-following model that considers the asymmetric characteristic of the velocity differences of the vehicles in a traffic stream. The problems of the prevalent general force (GF) model and the full velocity difference (FVD) model were solved. Furthermore, the optimal velocity (OV) model, the GF model, and the FVD model are proved to be the special cases of the proposed asymmetric full velocity difference (AFVD) model. The mathematical model is presented, followed by simulation analysis which demonstrates the properties of the AFVD model. 相似文献
8.
Conditional Source-term Estimation (CSE) is a closure model for turbulence–chemistry interactions. This model uses the first-order CMC hypothesis to close the chemical reaction source terms. The conditional scalar field is estimated by solving an integral equation using inverse methods. It was originally developed and has been used extensively in non-premixed combustion. This work is the first application of this combustion model for a premixed flame. CSE is coupled with a Trajectory Generated Low-Dimensional Manifold (TGLDM) model for chemistry. The CSE-TGLDM combustion model is used in a RANS code to simulate a turbulent premixed Bunsen burner. Along with this combustion model, a similar model which relies on the flamelet assumption is also used for comparison. The results of these two approaches in the prediction of the velocity field, temperature and species mass fractions are compared together. Although the flamelet model is less computationally expensive, the CSE combustion model is more general and does not have the limiting assumption underlying the flamelet model. 相似文献
9.
Ya Bo Wu Ming Hui Fu Fang Yuan Cheng Huan Huan Fu 《General Relativity and Gravitation》2009,41(8):1677-1693
In this paper a more general phenomenological model is proposed on the basis of the Hobbit model in Cardone et al. (Phys Rev
D 69:083517, 2004). The main purpose of constructing our model is to make this model can not only mimic the ΛCDM model, but
also describe a four-phase smooth transition of the universe, namely the inflationary phase, a radiation-dominated phase,
a matter-dominated phase and a de Sitter-like phase. In order to check whether this model is a viable one, the evolutions
of the universe are respectively discussed in the two cases, and the possible physical interpretations for this model are
also respectively shown by using the scalar fields. Finally, the structure formations in our model are simply discussed for
the both cases, and the results given by us reconfirm that our model can be regarded as a fit to the ΛCDM model, if we choose
the proper conditions. 相似文献
10.
In the present paper, the two-dimensional Ising model with anisotropic nearest-neighbor, next-nearest-neighbor and four-spin interactions has been studied. The ground states and energy of the model have been obtained. The model is equivalent to an eight-vertex model on its dual lattice. In some special cases, the model can be solved exactly as a zero-field eight-vertex model or a free-fermion model. Explicit phase diagrams are obtained exactly. 相似文献
11.
This paper deals with a prediction problem of a new targeting variable corresponding to a new explanatory variable given a training dataset. To predict the targeting variable, we consider a model tree, which is used to represent a conditional probabilistic structure of a targeting variable given an explanatory variable, and discuss statistical optimality for prediction based on the Bayes decision theory. The optimal prediction based on the Bayes decision theory is given by weighting all the model trees in the model tree candidate set, where the model tree candidate set is a set of model trees in which the true model tree is assumed to be included. Because the number of all the model trees in the model tree candidate set increases exponentially according to the maximum depth of model trees, the computational complexity of weighting them increases exponentially according to the maximum depth of model trees. To solve this issue, we introduce a notion of meta-tree and propose an algorithm called MTRF (Meta-Tree Random Forest) by using multiple meta-trees. Theoretical and experimental analyses of the MTRF show the superiority of the MTRF to previous decision tree-based algorithms. 相似文献
12.
In the last few decades, nanoindentation has gained widespread acceptance as a technique for materials properties characterization at micron and submicron length scales. Accurate and precise characterization of material properties with a nanoindenter is critically dependent on the ability to correctly model the response of the test equipment in contact with the material. In dynamic nanoindention analysis, a simple Kelvin–Voigt model is commonly used to capture the viscoelastic response. However, this model oversimplifies the response of real viscoelastic materials such as polymers. A model is developed that captures the dynamic nanoindentation response of a viscoelastic material. Indenter tip-sample contact forces are modelled using a generalized Maxwell model. The results on a silicon elastomer were analysed using conventional two element Kelvin–Voigt model and contrasted to analysis done using the Maxwell model. The results show that conventional Kelvin–Voigt model overestimates the storage modulus of the silicone elastomer by ~30%. Maxwell model represents a significant improvement in capturing the viscoelastic material behaviour over the Voigt model. 相似文献
13.
We consider a vertex model on the simple-quartic lattice defined by line graphs on the lattice for which there is always an odd number of lines incident at a vertex. This is the odd 8-vertex model which has eight possible vertex configurations. We establish that the odd 8-vertex model is equivalent to a staggered8-vertex model. Using this equivalence we deduce the solution of the odd8-vertex model when the weights satisfy a free-fermion condition. It is found that the free-fermion model exhibits no phase transitions in the regime of positive vertex weights. We also establish the complete equivalence of the free-fermion odd 8-vertex model with the free-fermion 8-vertex model solved by Fan and Wu. Our analysis leads to several Ising model representations of thefree-fermion model with pure 2-spin interactions. 相似文献
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The paper presents a methodology for noise and vibration analysis of gear pumps and its application to an external gear pump for automotive applications. The methodology addresses the use of a combined numerical model and experimental analyses. The combined model includes a lumped-parameter model, a finite-element model and a boundary-element model. The lumped-parameter (LP) model regards the interior parts of the pump (bearing blocks and gears loaded by the pressure distribution and the driving torque), the finite element (FE) model regards the external parts of the pump (casing and end plates), while the boundary element (BE) model enables the estimation of the emitted noise in operational conditions. Based on experimental evidences, attention has been devoted to the modelling of the pump lubricant oil: the fluid–structure interaction between the oil and pump casing was taken into account. In the case of gear pumps all these important effects have to be considered in the same model in order to take their interactions into account. The model has been assessed using experiments: the experimental accelerations and acoustic pressure measured in operational conditions have been compared with the simulated data coming from the combined LP/FE/BE model. The combined model can be considered a very useful tool for design optimisation. 相似文献
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针对路网中的动态交通分配问题,采用高阶守恒模型(CHO)进行建模与数值研究,并推广高阶守恒模型二进二出路口的Riemann问题;同时将高阶守恒模型与动态网络加载(DNL)模型相结合,通过变分不等式对动态网络加载模型进行分析.数值模拟采用一阶有限体积法求解高阶守恒模型,同时采用梯度下降方法迭代求解动态网络加载模型的变分不等式问题,最终以动态用户最优条件为目标实现分配均衡.数值结果表明CHO模型与DNL模型结合解决动态交通分配问题是可行的,对传统模型的研究有一定的指导意义. 相似文献
18.
Using a graphical method we establish the exact equivalence of the partition function of aq-state nonintersecting string (NIS) model on an arbitrary planar, even-valenced, lattice with that of a q2-state Potts model on a related lattice. The NIS model considered in this paper is one in which the vertex weights are expressible as sums of those of basic vertex types, and the resulting Potts model generally has multispin interactions. For the square and Kagomé lattices this leads to the equivalence of a staggered NIS model with Potts models with anisotropic pair interactions, indicating that these NIS models have a first-order transition forq > 2. For the triangular lattice the NIS model turns out to be the five-vertex model of Wu and Lin and it relates to a Potts model with two- and three-site interactions. The most general model we discuss is an oriented NIS model which contains the six-vertex model and the NIS models of Stroganov and Schultz as special cases. 相似文献
19.
An Efficient Three-Dimensional Coupled Normal Mode Model and Its Application to Internal Solitary Wave Problems
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We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided. 相似文献
20.
Jonathan Raz Erik J. Fernandez John Gillespie 《Journal of magnetic resonance (San Diego, Calif. : 1997)》1997,127(2):173-183
Distortions in the FID and spin echo due to magnetic field inhomogeneity are proved to have a representation as the characteristic function of some probability distribution. In the special case that the distribution is Cauchy, the model reduces to the conventional Lorentzian model. A more general and flexible representation is presented using the Fourier transform of a logspline density. An algorithm for fitting the model is described, the performance of the model and algorithm is investigated in applications to real and simulated data sets, and the logspline approach is compared to a previous Hermitian spline approach and to the Lorentzian model. The logspline model is more parsimonious than the Hermitian spline model, provides a better fit to real data, and is much less biased than the Lorentzian model. 相似文献