Two-dimensional Discrete Model Research Articles

Numerical investigation on the thermal performance of a molten salt tank under different electric heating method

Two-tank molten salt (MS) thermal energy storage (TES) technology is an efficient and widely used energy storage technology. This study develops a two-dimensional discrete model (2DIM) using the Modelica language to accurately and quickly represent molten salt temperature distribution and heat loss, applicable to system-level analysis in thermal power systems. It also uncovers variations in heat loss, cooling rate, and required auxiliary electric heating power across different tank volumes, liquid levels, and MS temperatures, offering guidance for optimizing design, energy management, and operational strategies. Additionally, the study examined the impact of different electric heater placements on the performance of the thermal storage system. The results show that heating the gas inside the tank is more effective than traditional direct electric heating, reducing molten salt heat loss by 25.89 % and increasing energy storage efficiency by 0.17 %.The research provide a reference for the study of efficient utilization of TES tank in different thermal systems.

Construction of a Two-Dimensional Discrete Dislocation Model to Describe the Plastic Deformation Process of a Single Crystal

Construction of a Two-Dimensional Discrete Dislocation Model to Describe the Plastic Deformation Process of a Single Crystal

Fracture Network Analysis of Karstified Subis Limestone Build-Up in Niah, Sarawak

Understanding complex carbonate fracture networks and karstification at various geological scales is challenging, especially with limited multi-scale datasets. This paper aims to reduce uncertainty in the fracture architecture of Central Luconia karstified reservoirs by narrowing observational gaps between seismic and well data by using the discrete fracture models of exposed limestone outcrops as analogues for the subsurface carbonate reservoir. An outcrop-based fracture network characterisation of a near-surface paleo-karst at Subis Limestone combined with lineament analysis was conducted to extract fracture parameters. The karst structure was first delineated using a digital elevation map and outcrop examination. Then, topology analysis was performed, following the creation of two-dimensional discrete fracture models. Two main fracture sets oriented northeast–southwest and northwest–southeast and 79 potential dolines were identified. Fracture intersections, northeast–southwest major orientations, and drainage systems highly influenced the karst features. The Subis Limestone fracture model revealed that the highest number of fractures and total length of fractures were concentrated in the northern part of the Subis Limestone build-up (X: 250–350, Y: 150–250) and became denser towards the northwest direction of the outcrop (X: 600–800). The fractures in the Subis paleo-karsts appear isolated, with I-nodes ranging from 0.74 to 0.94. Hence, it is crucial to incorporate matrix porosity into multiple scales of fracture network modelling to improve upscaling and the modelling of fracture–vug networks, as well as to minimise the underestimation of discrete fracture networks in fractured and karstified limestone.

Optimal design in bionic wear-resistant structures by multiscale DEM simulation

To address the problems of long optimization times of bionic wear-resistant structures in discrete element simulation. We established two-dimensional homoscale discrete element simulation models for four biomimetic structures, along with their respective abrasive wear computational models. We then deliberated upon their wear behavior in relation to the structural morphology, contact constraints, contact force, and wear volume during the wear process. The study found that the shedding of brittle wear body surface abrasives had little effect on the substrate of the bionic structure. Based on the above findings, a multi-scale/cross-level study of the interaction between biological wear surface structure and abrasive was conducted. The findings evince that utilization of a multi-scale computational model ensures the precise examination of the mechanical response of a material to external forces, while also economizing computational time. Finally, the design of the conical bionic structure is optimized based on the multi-scale/cross-level computational model. The results show that the conical bionic structure has good wear resistance when the abrasive grain size is small and when the monomer spacing is not larger than the monomer width. The bionic structure/abrasive interaction multi-scale numerical simulation system established in this paper reduces the complexity of dynamic numerical simulation of wear behavior on the surface of wear- resistant organisms, improves the calculation efficiency, and provides an important research means and method for optimizing the design of bionic wear-resistant parts.

Topological-numerical analysis of a two-dimensional discrete neuron model.

We conduct computer-assisted analysis of a two-dimensional model of a neuron introduced by Chialvo in 1995 [Chaos, Solitons Fractals 5, 461-479]. We apply the method of rigorous analysis of global dynamics based on a set-oriented topological approach, introduced by Arai et al. in 2009 [SIAM J. Appl. Dyn. Syst. 8, 757-789] and improved and expanded afterward. Additionally, we introduce a new algorithm to analyze the return times inside a chain recurrent set. Based on this analysis, together with the information on the size of the chain recurrent set, we develop a new method that allows one to determine subsets of parameters for which chaotic dynamics may appear. This approach can be applied to a variety of dynamical systems, and we discuss some of its practical aspects.

New duality relation for the discrete Gaussian SOS model on a torus

We construct a new duality for two-dimensional discrete Gaussian models. It is based on a known one-dimensional duality and on a mapping, implied by the Chinese remainder theorem, between the sites of an N × M torus and those of a ring of NM sites. The duality holds for an arbitrary translation-invariant interaction potential between the height variables on the torus. It leads to pairs of mutually dual potentials and to a temperature inversion according to . When is isotropic, duality renders an anisotropic . This is the case, in particular, for the potential that is dual to an isotropic nearest-neighbor potential. In the thermodynamic limit, this dual potential is shown to decay with distance according to an inverse square law with a quadrupolar angular dependence. There is a single pair of self-dual potentials . At the self-dual temperature the height–height correlation can be calculated explicitly; it is anisotropic and diverges logarithmically with distance.

Two-dimensional discrete-time laser model with chaos and bifurcations

<abstract><p>We explore the local dynamical characteristics, chaos and bifurcations of a two-dimensional discrete laser model in $ \mathbb{R}_+^2 $. It is shown that for all $ a $, $ b $, $ c $ and $ p $, model has boundary fixed point $ P_{0y}(0, \frac{p}{c}) $, and the unique positive fixed point $ P^+_{xy}(\frac{ap-bc}{ab}, \frac{b}{a}) $ if $ p > \frac{b c}{a} $. Further, local dynamical characteristics with topological classifications for the fixed points $ P_{0y}(0, \frac{p}{c}) $ and $ P^+_{xy}(\frac{ap-bc}{ab}, \frac{b}{a}) $ have explored by stability theory. It is investigated that flip bifurcation exists for the boundary fixed point $ P_{0y}(0, \frac{p}{c}) $, and also there exists a flip bifurcation if parameters vary in a small neighborhood of the unique positive fixed point $ P^+_{xy}(\frac{ap-bc}{ab}, \frac{b}{a}) $. Moreover, it is also explored that for the fixed point $ P^+_{xy}(\frac{ap-bc}{ab}, \frac{b}{a}) $, laser model undergoes a Neimark-Sacker bifurcation, and in the meantime stable invariant curve appears. Numerical simulations are implemented to verify not only obtain results but also exhibit complex dynamics of period $ -2 $, $ -3 $, $ -4 $, $ -5 $, $ -8 $ and $ -9 $. Further, maximum lyapunov exponents along with fractal dimension are computed numerically to validate chaotic behavior of the laser model. Lastly, feedback control method is utilized to stabilize chaos exists in the model.</p></abstract>

МОДЕЛИРОВАНИЕ ВОЗБУЖДЕНИЯ ПОВЕРХНОСТНЫХ ПЛАЗМОН-ПОЛЯРИТОНОВ В ПРЯМОУГОЛЬНОМ НАНОРЕЗОНАТОРЕ НА ОСНОВЕ ЗОЛОТА

This paper considers the modeling of surface plasmon polaritons excitation in a limited nanostructure on the basis of a two-dimensional area discrete model, the area interacts with the oscillator. The nanostructure is a rectangle defined on the metal surface at the interface of the gold–silicon oxide, the surface plasmon–polaritons are excited by an electromagnetic radiation point source located above the metal surface. The dynamics of radiation point source is described by a discrete version of the Van der Pol equation with a small nonlinearity of the source parameters. The parameters of the goldsilicon oxide structure (the wave phase speed, the radiation source frequency, the characteristic time in the system, etc.) will be received from the dispersion relation for surface plasmon–polaritons at a single metal–dielectric interface. The distributions of the wave field in the structure will be analyzed at different positions of the point oscillator and different coupling coefficients of the wave field with the oscillators. The resonant wave field mode composition at different positions of the point oscillator and different coupling coefficients will be found using the two-dimensional Fourier transform of the wave field, the time evolution of excited modes of the wave field amplitudes will be also analyzed. In conclusion, the paper gives applicability limits of the considered model for studying the surface plasmon polaritons excitation in a limited nanostructure.

Effects of feedback control in small-world neuronal networks interconnected according to a human connectivity map

In this work, we consider a phenomenological two-dimensional discrete model coupled in a structure of a clustered network to investigate the suppression of neuronal synchronization in a complex network. We constructed a network according to a weighted human connectivity matrix and an adjacency matrix that carries small-world properties. The coupling between neurons is inserted through a chemical synapse term and a neuronal activation function. The neuronal synchronization is measured by the Kuramoto order parameter. We intend to achieve the suppression of burst phase synchronization, and for that, we use a mathematical tool, based on the technique of deep brain stimulation, which consists of applying an external signal to the network after a certain time, causing the bursts to desynchronize. Our results are efficient when applying the feedback method both in the global network and in the cortical regions. We have seen that for cortical regions, synchronization is more difficult to suppress, however, by slightly increasing the perturbation, we are able to achieve the desired effect. This shows that it is possible to use the control efficiently in isolated cortical areas, therefore, we present a new alternative to conventional methods, avoiding to apply the control to the entire network to obtain the same results.

The synchronization of discrete quantum chaotic maps with uncertainty via compensated control technique

In this work, a two-dimensional discrete map model based on quantum game is introduced, and its dynamics are investigated. Moreover, the stability condition of Nash equilibrium is also analyzed. In addition, the synchronization control of discrete chaotic maps with uncertainties is studied, and a new dynamical compensation control (DCC) technique is presented by constructing a dynamical compensator. At a result, the influence of the uncertain term can be suppressed effectively. Compared with the previous synchronous control approaches, the proposed method avoids the complex derivation and amplification operation, because it does not use Lyapunov function, and the controller design is simple and the proposed scheme is well verified.

Adaptive conservative time integration for transport in fractured porous media

The time step of an explicit time integration scheme for solving time-dependent hyperbolic partial differential equations in a finite volume method (FVM) framework is restricted by the Courant–Friedrichs–Lewy (CFL) criterion. Conventional time stepping integrates all grid cells with the same time step. This causes unnecessary computational costs when wave speeds and/or grid spacing vary considerably throughout the domain, and a few critical cells dictate the global time step, although most cells could be advanced with a much larger time step. Adaptive time stepping overcomes this issue by allowing different local time step sizes for each grid cell. The adaptive conservative time integration (ACTI) scheme is a recently developed adaptive time stepping method which relies on local time steps that are equal to the largest time step divided by powers of two.This work extends the ACTI scheme to tracer transport in fractured porous media. When fluid velocity within highly permeable fractures is higher than in the rock matrix and local grid refinement is applied around fractures, the CFL restriction would require prohibitively small time steps in the vicinity of fractures. For two-dimensional discrete fracture and matrix models of fracture patterns we demonstrate that ACTI reduces the computational cost by orders of magnitude compared to global time stepping while retaining solution accuracy. Empirically, we show that ACTI is stable in combination with a first-order explicit flux discretization scheme. Since combination with a standard higher-order MUSCL scheme can lead to spurious oscillations in the solution, we propose a modified MUSCL scheme relying on advection of an inclined reconstruction (MUSCL-AIR).

A 2D discrete moisture diffusion model for simulating desiccation fracturing of soil

The desiccation fracturing of soil is widespread, which affects the migration of rainwater in the soil, and the stability of slopes or other projects. This paper proposes a simple two-dimensional (2D) discrete moisture diffusion model considering the influence of fractures on moisture migration. The moisture diffusion model is used in conjunction with the finite discrete element method (FDEM) to create a 2D discrete moisture diffusion-fracture coupling model, which is implemented in a GPU parallel multiphysics finite-discrete element software, namely MultiFracS. The coupled model is made up of three parts: a 2D discrete moisture diffusion model that takes into account the influence of fractures on moisture migration, a shrinkage deformation and stress computation, and an FDEM fracture mechanical computation. First, the moisture distribution in the system is analyzed using the moisture diffusion model. The shrinkage stress resulting from the moisture change is then computed. Finally, the shrinkage stress is added to the governing equation of FDEM to perform the fracture mechanical computation. Desiccation fracturing of the soil can be modeled using the processes outlined above. The paper firstly verifies the correctness of the 2D discrete moisture diffusion model to deal with the moisture migration in a continuous media, a media with impervious fractures or permeable fractures. Then, we give a principle that is used to determine the moisture exchange coefficient of the unbroken joint element through the parameter sensitivity analysis. Moreover, typical shrinkage deformation and stress problems and soil desiccation fracturing experiments are simulated. The simulation results are in good agreement with the analytical solutions and experiment results, verifying the effectiveness of the 2D discrete moisture diffusion-fracture coupling model to deal with shrinkage deformation and stress problems and the desiccation fracturing of soil. The coupled model provides a powerful solution tool to study the desiccation fracturing of soil.

Continuous non-autonomous memristive Rulkov model with extreme multistability* *Project supported by the National Natural Science Foundation of China (Grant Nos. 12172066, 61801054, and 51777016), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20160282), and the Postgraduate Research and Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX21 2823).

Based on the two-dimensional (2D) discrete Rulkov model that is used to describe neuron dynamics, this paper presents a continuous non-autonomous memristive Rulkov model. The effects of electromagnetic induction and external stimulus are simultaneously considered herein. The electromagnetic induction flow is imitated by the generated current from a flux-controlled memristor and the external stimulus is injected using a sinusoidal current. Thus, the presented model possesses a line equilibrium set evolving over the time. The equilibrium set and their stability distributions are numerically simulated and qualitatively analyzed. Afterwards, numerical simulations are executed to explore the dynamical behaviors associated to the electromagnetic induction, external stimulus, and initial conditions. Interestingly, the initial conditions dependent extreme multistability is elaborately disclosed in the continuous non-autonomous memristive Rulkov model. Furthermore, an analog circuit of the proposed model is implemented, upon which the hardware experiment is executed to verify the numerically simulated extreme multistability. The extreme multistability is numerically revealed and experimentally confirmed in this paper, which can widen the future engineering employment of the Rulkov model.

Bifurcation and chaos in a one mass discrete time vocal fold dynamical model

In this article, we are going to study the stability and bifurcation of a two-dimensional discrete time vocal fold model. The existence and local stability of the unique fixed point of the model is investigated. It is shown that a Neimark-Sacker bifurcation occurs and an invariant circle will appear. We give sufficient conditions for this system to be chaotic in the sense of Marotto. Numerically it is shown that our model has positive Lyapunov exponent and is sensitive dependence on initial conditions. Some numerical simulations are presented to illustrate our theoretical results.

Research progress of elastic topological materials

Topological insulators, originated in quantum systems, are recently generalized to electromagnetic, acoustic, and elastic wave fields due to interesting wave controlling provides, such as unidirectional and dissipationless energy transportation. This new kind of materials provide unprecedented possibilities for engineering wave flows. This paper will introduce the basic theory of topological insulators and summarize the research progress of topological insulators in elastic fields. Based on one-dimensional and two-dimensional discrete models, preliminary concepts of topological insulators, such as Dirac cone, band inversion, Berry curvatures, topological invariants, are introduced. The design and progress of valley Hall insulators, Chern insulators as well as spin Hall insulators are introduced afterward, followed by discussions on high-order topological insulators. The last part of this paper covers topological phenomena in static mechanics, including topological solitons and toplogical zero energy modes.

Performance Analysis of Cognitive Radio Networks With Burst Dynamics

The impact of the traffic characteristics of secondary users (SUs) on the performance of cognitive radio networks (CRNs) should be understood for designing operation rules. This paper focuses on multi-type burst services and network congestion problem in CRNs and evaluates the QoS of SUs based on multiple cross-layer considerations. A two-state Markov-modulate Bernoulli process (MMBP-2) is adopted to model packet flows of SUs with different burst degrees in CRNs. We propose a two-dimensional discrete queuing model to consider spectrum access, burstiness of traffic, network congestion, channel environment, user activity and finite buffer. We construct an iterative algorithm to compute the steady-state distribution of the proposed queuing model and determine the performance metrics like the throughput, the average delay, the average queue length and the total packet loss probability. Numerical analysis evaluates the QoS of SUs under different burst environments.

Discrete element modelling of desiccation cracking in thin clay layer under different basal boundary conditions

This study aims to investigate the effect of basal boundary conditions on the initiation and propagation of desiccation cracking along the vertical direction in thin clay layer using discrete element method (DEM). A two-dimensional discrete model was proposed considering shrinkage kinetics and property change during the drying process. Different basal boundary constraints were simulated by applying bond between the soil particles and the fixed base particles of difference sizes. The simulation results were compared with the laboratory experiments. The results showed that the model can reproduce the main trend of desiccation process. Larger base particles produced more cracks in the specimen. Both cracks initiated from the top surface and cracks initiated from the bottom soil-base interface were observed and discriminated in the simulation. The model revealed the development of bottom-initiated cracks and unpenetrated cracks beneath the surface that may be neglected in traditional cracking simulations. The study suggests that the different initiation position of cracks is associated with the change of force distribution inside the specimen. Moreover, the effects of different boundary properties (the geometrical roughness, the frictional coefficient and the bond strength), particle density change and evaporation gradient on model performance were investigated.

Equivalent Permeability Distribution for Fractured Porous Rocks: Correlating Fracture Aperture and Length

Estimating equivalent permeability at grid block scale of numerical models is a critical issue for large-scale fractured porous rocks. However, it is difficult to constrain the permeability distributions for equivalent fracture models as these are strongly influenced by complex fracture properties. This study quantitatively investigated equivalent permeability distributions for fractured porous rocks, considering the impact of the correlated fracture aperture and length model. Two-dimensional discrete fracture models are generated with varied correlation exponent ranges from 0.5 to 1, which indicates different geomechanical properties of fractured porous rock. The equivalent fracture models are built by the multiple boundary upscaling method. Results indicate that the spatial distribution of equivalent permeability varied with the correlation exponent. When the minimum fracture length and the number of fractures increase, the process that the diagonal equivalent permeability tensor components change from a power law like to a lognormal like and to a normal-like distribution slows down as the correlation exponent increases. The average dimensionless equivalent permeability for the equivalent fracture models is well described by an exponential relationship with the correlation exponent. A power law model is built between the equivalent permeability of equivalent fracture models and fracture density of discrete fracture models for the correlated aperture-length models. The results demonstrate that both the fracture density and length-aperture model influence the equivalent permeability of equivalent fracture models interactively.

Aeroelastic dynamic response of elastic aircraft with consideration of two-dimensional discrete gust excitation

Design loads generally require a one-dimensional discrete gust profile without consideration of the spanwise effect, and this profile cannot represent the true gust field exactly. For a high aspect ratio aircraft, two-dimensional gusts may cause critical load conditions, and approaches for calculating dynamic responses under two-dimensional discrete gust excitation are rarely presented. In this paper, a spanwise non-uniform vertical discrete gust field is established based on a one-dimensional ‘1-cos’ gust profile in reference to a DARPA proposal, while frequency and hybrid approaches to the dynamic response analysis of flexible aircraft under this two-dimensional gust excitation are presented. Solution techniques have been applied to a high aspect ratio aircraft to assess the different response characteristics with a comparison between one-dimensional and two-dimensional discrete gust field conditions. The results show that the two-dimensional discrete gust model produces a higher bending moment than that of the one-dimensional condition. Therefore, the critical load conditions that are derived from the two-dimensional discrete gust for high aspect ratio aircraft should be seriously considered. According to the analysis, an active control scheme to alleviate the bending loads caused by the two-dimensional gust is designed, and alleviation effects in different gust conditions are compared.

Performance Analysis of Licensed-Assisted Access to Unlicensed Spectrum in LTE Release 13

This paper studies and analyzes the performance of the licensed-assisted access (LAA) scheme introduced by 3GPP in LTE Release 13, and adopted by 3GPP in LTE Release 14, which is called 3GPP LAA scheme for short. Considering the characteristics that the 3GPP LAA scheme is different from other LAA schemes and IEEE 802.11 distributed coordination function (DCF) protocol in WiFi systems, the 3GPP LAA scheme is modeled as a new two-dimensional discrete Markov model, and the collision probability and the channel occupancy utilization are further derived based on the proposed model. To more deeply analyze the performance of the 3GPP LAA scheme by comparisons, we also derive the expressions of the same performance indices for the linear backoff based LAA scheme proposed in this paper and the fixed contention window based LAA scheme mentioned in existing literatures. The simulation and numerical results prove the validity of the proposed Markov chain model, and also show that the 3GPP LAA scheme is the friendliest one to WiFi networks among the three LAA schemes, whereas its total channel occupancy utilization is the lowest when the number of LAA small base stations (SBSs) is little and that is the highest when large. However, the other two LAA schemes are still the graceful coexistence, which is defined as the scheme where the interference to WiFi users caused by LAA SBSs coexisting with them is not more than that caused by other WiFi APs replacing the LAA SBSs.