Diffusion System Research Articles

Bifurcations in a General Delay Sel’kov–Schnakenberg Reaction–Diffusion System

The dynamics of a delay Sel’kov–Schnakenberg reaction–diffusion system are explored. The existence and the occurrence conditions of the Turing and the Hopf bifurcations of the system are found by taking the diffusion coefficient and the time delay as the bifurcation parameters. Based on that, the existence of codimension-2 bifurcations including Turing–Turing, Hopf–Hopf and Turing–Hopf bifurcations are given. Using the center manifold theory and the normal form method, the universal unfolding of the Turing–Hopf bifurcation at the positive constant steady-state is demonstrated. According to the universal unfolding, a Turing–Hopf bifurcation diagram is shown under a set of specific parameters. Furthermore, in different parameter regions, we find the existence of the spatially inhomogeneous steady-state, the spatially homogeneous and inhomogeneous periodic solutions. Discretization of time and space visualizes these spatio-temporal solutions. In particular, near the critical point of Hopf–Hopf bifurcation, the spatially homogeneous periodic and inhomogeneous quasi-periodic solutions are found numerically.

Thermo-physical phase field model of laser powder melting additive manufacturing of 2D layered stainless steel structures

Additive manufacturing (AM) techniques based on laser melting of metal powders are experiencing tremendous growth and are rapidly becoming the preferred processing approach for metal parts. However, the effect of the different processing variables on microstructural and mechanical property outcomes is not yet fully understood. Modeling and simulation can provide an inexpensive and expedient way to probe the large parameter space and identify the most important correlations between processing degrees of freedom and output products. In this work, we develop a two dimensional thermo-physical phase model of laser melting additive manufacturing that captures solidification and melting, heterogeneous nucleation, and oriented grain growth to simulate layered microstructures grown by melting a metal layer connected to the underlying substrate by a set of orientation relations. The model solves the Allen-Cahn and heat diffusion system of equations on structured meshes, and simulates the motion of a laser spot across the specimen through a sequence of successive passes. The simulations best replicate the formation of columnar structures, as under high-power laser conditions or under rapid solidification kinetics, in good qualitative agreement with experimental observations. Our approach connects processing variables with the microstructural outcomes, thus capturing the effect of important inputs such as laser spot size, laser scan speed, and cross hatch fraction on grain size and structure.

Series of configurational movements: User activities in technology generalization

The detailed studies of adoption and user activities indicate that continuous alterations accompany the proliferation of new technology, yet diffusion theory and system change-oriented frameworks portray the spread of technologies across a social or sociotechnical system with relatively few changes. To better reconcile the two orientations, we introduce a series of configurational movements (SCM) as a conceptual register for the generalization of new technology in society. We elaborate on the SCM with an over-a-decade-long investigation into heat pumps in Finland, one of the globally furthest progressed energy transitions. The process has thus far involved nine configurational movements, each featuring a change in the character of the technology, the ecology of actors relevant to it, and the contexts in which the technology spreads. SCM analysis further surfaces eight user activity types that have shaped how the technology, its deployment, and its markets have evolved: Adoption and routine use, adaption and adjustment, championing, user innovation, community building, peer intermediation, market creation and production of legitimating discourse on heat pumps. In all, the generalization features significant shifts in user practices, the technology, and societal impact throughout the process, not only during its early phases, instilling energy system wide change.

A case study of the multifaceted therapeutic approach of VIPomas

Neuroendocrine tumors, arising from neuroendocrine cells, a group of malignant tumors capable of secreting peptides and biogenic amines, are differentiated as either diffuse endocrine system (DES) or gastroentero-pancreatic neuroendocrine tumors (GEP-NET). The latter are rare tumors that synthesize various substances, leading to the onset of certain generalized symptoms

Almost periodic traveling waves for a nonlocal dispersal system

This paper mainly deals with the monotonicity, stability, uniqueness and existence for almost periodic traveling waves to a nonlocal dispersal system. The difference from some previous works is mainly reflected in diffusion terms. First, the comparison principle of nonlocal diffusion equations is built by the contradiction method and some analysis techniques. Moreover, the difficulty of establishing the monotonicity to almost periodic traveling waves for the emergence of system is solved by introducing the standard partial ordering in matrices and some analysis techniques. Therefore, the results for the stability and existence for periodic traveling waves to nonlocal diffusion equations are extended to almost periodic systems, and those conclusions related to almost periodic traveling waves for scalar equations with Laplace diffusion are generalized to nonlocal diffusion systems.

Corrosion and Mechanical Properties of Multi Principal Element Alloys Designed By Using Diffusion Couples

The efficient exploration of novel alloy chemistries is crucial for advancing the development of new materials. Diffusion-controlled synthesis of gradient alloys is an intelligent approach for creating phase diagrams and to effectively identify potential material combinations with tailored properties.This project focusses on the design of quaternary multi-principle-element alloys (MPEAs) using diffusion couples. Our diffusion system contains an equimolar ternary alloy (FeNiCr) and additional single diffusing elements e.g. Mn and Mo. We determined the optimal temperature ranges for the diffusion thermal treatment by means of ThermoCalc simulations with the aim to form single-phase MPEAs. Microstructure and chemical characterization of the diffusion couples were performed by means of scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDX). For most alloy couples, the diffusion zone contained a single-phase alloy matrix with diffusion-induced compositional gradient as well as precipitation phases. This heterogeneity makes the diffusion couples interesting materials to investigate local mechanical and corrosion properties. Thus, local corrosion properties were examined using Atomic Force Microscopy (AFM) and Scanning Electrochemical Microscopy (SECM). Nanoindentation was used for the analysis of local mechanical properties.Based on the results of the local corrosion analysis, we have selected single-phase alloy chemistries along the diffusion zone and reproducibly synthesized these alloys in bulk for detailed corrosion studies by means of potentiodynamic polarization and SECM.The presentation will briefly summarize our methodology and motivation for using diffusion couples as an efficient tool for exploring phase diagrams of MPEAs in the search for new alloy chemistries and the results of our correlative study on the mechanical and corrosion properties of these materials.

To intervene or not: the game of recycled water use for residents with different preferences.

Recycled water contributes to sustainable development by providing a unified approach to wastewater treatment and rational water supply. However, the environmental benefit-sharing feature of recycled water may encourage some residents to show "free-rider" behavior. In this study, the evolutionary game model was applied to a game system consisting of two types of people, environmental preference and risk aversion. We analyzed internal and external factors and conducted a numerical simulation to seek both players' behavior evolutionary and stabilization trends. The study found that interventions are indispensable during recycled water use's initial and intermediate stages. Moreover, interventions should be tailored to different stages. In the initial stage, the benefits of co-use and the recycled water scientific information should be advertised. In the intermediate and mature stages, it is necessary to increase the trust coefficient or knowledge base of decided people who belong to early adopters of the recycled water diffusion system.

Selectable diffusion direction with topologically protected edge modes

Topological insulators provide great potential to control diffusion phenomena as well as waves. In addition to the thermal localization and robust decay as reported, the topological edge states with higher degree of freedom offers a route to control directional diffusion. Here, we show that the direction of thermal diffusion can be selected by the contributions of the topologically protected edge modes in a honeycomb-shaped structure. Considering the thermal diffusion between the nearest neighboring sites of the honeycomb-shaped unit cells, the cells allow unidirectional heat balance from a macroscopic perspective when we set the structure to the temperature corresponding to the edge mode type. Moreover, this diffusion system is found to be immune to defects owing to the robustness of topological states. Our work points to exciting avenues for controlling diffusion phenomena.

Reaction–diffusion systems with nonlinear sources of different intensity in the case of a multiple root without quasimonotonicity condition

We consider a boundary value problem for a singularly perturbed system of two second-order ordinary differential equations with different powers of a small parameter at the second derivatives without requiring the right-hand sides to be quasimonotonic. The specific feature of the problem is that one of the two equations in the degenerate system has a double root. It is proved that for sufficiently small values of a small parameter, the problem has a solution of the boundary layer type. A condition is obtained that replaces the quasimonotonicity condition and expands the class of problems to which the results of the work are applicable.

Parameter estimation for network-organized Turing system based on convolution neural networks

Turing dynamics mainly focuses on non-homogeneous self-adaptive spatial patterns of reaction diffusion systems in a continuous space. If defining the diffusion environment as network structure, then network patterns are available under Turing instability conditions. In allusion to parameter estimation for network Turing-instable systems, this paper proposes a new recognition method using artificial neural networks. When diffusion occurs on quadrilateral lattice networks, a deep convolutional neural network (CNN) is built to invert the unknown parameters. The results on training set and validation set indicate that the CNN model exhibits great robustness without overfitting and gradient explosion. Meanwhile, the prediction performance on two test sets is excellent, with average relative errors of the estimators ending up at 0.68% and 1.04%, respectively. When diffusion occurs on non-regular networks, a spatial domain graph convolutional network (GCN) is established, which is slightly less robust than the CNN. The average relative error of the estimators on both test sets ends up between 1.1% and 2.8%, which is still in the ideal range.

Laplace transform-homotopy perturbation method for fractional time diffusive predator–prey models in ecology

In this paper, we consider some reaction–diffusion systems arising from two-component predator–prey models with various kinetics ranging from prey-dependent, ratio-dependent functional responses and subdiffusion. The goal of the present work is to simulate the time-dependent predator–prey model of Lotka–Volterra. Analytical solutions of this model are performed using the Laplace transform-homotopy perturbation method. The proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The fact that the proposed technique solves nonlinear problems without using Adomian’s polynomials can be considered as a clear advantage of this algorithm over the decomposition method. We show all the possible equilibria and examine their stability in line with the ecological parameters. Numerical simulations of the diffusive predator–prey model in one-, two- and three-dimensions are given to compare and demonstrate the asymptotic behaviour of the time-dependent reaction–diffusion systems. The results show that proposed technique is a powerful tool to solve systems of nonlinear ordinary and partial differential equations of predator–prey models in ecology.

Exploring the impact of a moving sink in a reaction–diffusion system: exact dynamics for two simple potentials

Exploring the impact of a moving sink in a reaction–diffusion system: exact dynamics for two simple potentials

The increasing strength of higher-order interactions may homogenize the distribution of infections in Turing patterns

The spatial pattern of epidemic is one key metric describing epidemiological spread features, beneficial to formulation of the intervention measures. Networked reaction–diffusion (RD) systems have become popular to mathematically portray such patterns due to discrete distribution of human habitat. However, most of the current research focused on diffusion along pairwise interactions. Effect of diffusion along higher-order interactions is still understood poorly. To this end, in the paper, based on one classic SIR epidemic RD model, we study its Turing instability in simplicial complexes and analyze the impact of the simplex strength on Turing patterns. It is found by theoretical analysis and simulation that the distribution of infections in patterns tends to become homogeneity with the increase of the simplex strength, i.e., infection density of most nodes concentrates near the steady state. Obviously, for a newly emerging epidemic, such homogeneous scenario is unfavorable to epidemic control. Because it may lead to the decentralized allocation of limited resources, which is not enough to contain epidemic. In contrast, heterogeneous scenario that nodes with low and high infection density prominently distribute in two sides of steady state allows to put all limited resources into the targeted treatment of nodes with high infection density. Our findings link epidemic control with higher-order interactions and may provide a new insight into intervening epidemic from higher-order networks.

Vallée de la Roya and its opaque infrastructures of transit. Inhabiting the border.

This paper offers a closer look at the French-Italian border and its violence. The border in the Vallée de la Roya restores some conditions of rurality, transit, and danger to which the migratory route is confronted. In this context, different genealogies of displacement, social fabrics and spatial forms are forced to coexist and resist situations of crisis in different ways, contributing to ongoing processes of dematerialisation of the border. At the southern French-Italian border and specifically in the valley emerge new forms of spaces and practices of holding, as the simultaneous and ambivalent conflict between support and hostility, mobility and immobility, visibility and invisibility. The progressive increase of transits and the subsequent enclosure of the internal frontier engender dispersed and mobile massive militarisation as well as important acts of reception. The valley and the experience of Le Camping encompass a new fragment of the infrastructure of solidarity that explains its performativity as a transnational dispositive of protection, enabling transits through the informal, diffuse, and opaque system of collective resistances of architecture.

Nonlinear diffusion system for simultaneous restoration and binarization of degraded document images

Existing diffusion models can only do tasks for either restoration or binarization of degraded document images; in this paper, we pay close attention to the problem of simultaneous restoration and binarization. We first introduce a model of image formation for degraded document images, which decomposes a degraded document image into the product of background and foreground components. Then a weakly coupled nonlinear diffusion system is developed for simultaneous restoration and binarization of degraded document images. In this diffusion system, the first equation is used to estimate background component and the second equation is responsible for the foreground component. The restored and binarized images are finally obtained by the estimated background and foreground components, respectively. Two coupled diffusion equations are solved alternately by explicit finite differencing. The proposed model is tested on some degraded document images that represent five types of typical degradations including bleed-through, complex background, page stains, stamps and smeared ink, and is compared with eight closely related models for degraded document binarization, qualitatively and quantitatively. Experimental results illustrate that the proposed model has shown promising results in terms of restoration and binarization of degrade document images.

Novel Aspects in Pattern Formation Arise from Coupling Turing Reaction–Diffusion and Chemotaxis

Recent experimental studies on primary hair follicle formation and feather bud morphogenesis indicate a coupling between Turing-type diffusion driven instability and chemotactic patterning. Inspired by these findings we develop and analyse a mathematical model that couples chemotaxis to a reaction–diffusion system exhibiting diffusion–driven (Turing) instability. While both systems, reaction–diffusion systems and chemotaxis, can independently generate spatial patterns, we were interested in how the coupling impacts the stability of the system, parameter region for patterning, pattern geometry, as well as the dynamics of pattern formation. We conduct a classical linear stability analysis for different model structures, and confirm our results by numerical analysis of the system. Our results show that the coupling generally increases the robustness of the patterning process by enlarging the pattern region in the parameter space. Concerning time scale and pattern regularity, we find that an increase in the chemosensitivity can speed up the patterning process for parameters inside and outside of the Turing space, but generally reduces spatial regularity of the pattern. Interestingly, our analysis indicates that pattern formation can also occur when neither the Turing nor the chemotaxis system can independently generate pattern. On the other hand, for some parameter settings, the coupling of the two processes can extinguish the pattern formation, rather than reinforce it. These theoretical findings can be used to corroborate the biological findings on morphogenesis and guide future experimental studies. From a mathematical point of view, this work sheds a light on coupling classical pattern formation systems from the parameter space perspective.

Komunikasi Inovasi dan Perilaku Adopsi Sorgum Bioguma di Kabupaten Langkat

Innovation communication is an approach in development communication that aims to introduce an innovation to the community so that it creates a certain effect as something useful. One of the innovations created by the government is sorghum bioguma as an alternative commodity for the purpose of food diversification. This study aims to analyze the innovation communication model of sorghum bioguma; analyze the innovation communication channels of sorghum bioguma; and analyzing the adoption behavior of sorghum bioguma in Pasar VI Kwala Mencirim village, Sei Bingai sub-district, Langkat Regency, North Sumatra. The informants in this study were the Balai Pengkajian Teknologi Pertanian Sumatera Utara (BPTP Sumut) and farmers in Pasar VI Kwala Mencirim village. The research was conducted using a qualitative approach with descriptive methods. The theory used is Everett M Rogers' diffusion of innovation and Ban and Hawkins' Agricultural Extension. Data collection techniques were carried out by interviews, observation and documentation. The results of the study indicated: Communication of sorghum bioguma innovations carried out by BPTP Sumut through four activities namely carrying out coordination, involving farmer groups, making demonstration plots, and carrying out technical guidance. These four activities are a model of a centralized diffusion system, which means the spread of innovation is carried out linearly from the central government to farmers; The innovation communication channels used by BPTP Sumut are interpersonal, group, audio-visual, and social media communication channels. Interpersonal communication is the most effective channel in changing farmers' attitudes; Farmers in Pasar VI Kwala Mencirim adopt unsustainable. This decision was included in the type of active rejection, which means that the farmers had tried the sorghum bioguma innovation but then decided not to adopt it because there was no economic advantage.

Unified gas-kinetic particle method for frequency-dependent radiation transport

This paper proposes a unified gas-kinetic particle (UGKP) method for the frequency-dependent photon transport process. The photon transport is a typical multiscale process governed by the nonlinear radiative transfer equations (RTE). The flow regime of photon transport varies from the ballistic regime to the diffusive regime with respect to optical depth and photon frequency. The UGKP method is an asymptotic preserving (AP) scheme and a regime adaptive scheme. The teleportation error is significantly reduced, and the computational efficiency is remarkably improved in the diffusive regime. Distinguished from the standard multigroup treatment, the proposed UGKP method solves the frequency space in a non-discretized way. Therefore the Rosseland diffusion system can be precisely preserved in the optically thick regime. Taking advantage of the local integral solution of RTE, the distribution of the emitted photon can be constructed from its macroscopic moments. The Monte Carlo particles in the UGKP method need only be tracked before their first collision events, and a re-sampling process is performed to close the photon distribution for each time step. The high computational cost of calculating excessive scattering events can be saved, especially in the optically thick regime. The proposed UGKP method is implicit and removes the light speed constraint on the time step. The particle tracking approach combining the implicit formulation makes the proposed UGKP method an efficient solution algorithm for frequency-dependent radiative transfer problems. We demonstrate with numerical examples the capability of the proposed multi-frequency UGKP method.

Spatiotemporal patterns of reaction–diffusion systems with advection mechanisms on large-scale regular networks

This paper primarily investigates the dynamics behaviour of reaction–diffusion systems with advection mechanisms on network structures. Introducing the advection mechanism from continuous space to network structure, this study uses the Laplacian matrix of a directed network to describe it and sets up a network-organized reaction–diffusion system with directed migration mechanism based on this. Firstly, we derived the Turing instability conditions of the system under certain restrictions. We then focus on the Turing dynamical of the system on a type of composite circular networks and a type of composite torus networks. Furthermore, through numerical methods, we reveal the existence of travelling Turing patterns in the system under various circumstances, including the significant case where the system only has diffusion behaviours but no directed migration. Simultaneously, the result of numerical simulations shows that on the network structures presented in this paper, increasing the global directed migration strength promotes homogeneity among the connected nodes; increasing the difference of directed migration strengths between two groups is conducive to the occurrence of Turing instability.

Robustness of quantum spin Hall effect-inspired edge modes depending on C6 symmetry in topological diffusion systems

We investigate the robustness of a quantum spin Hall effect-inspired topological edge modes in a thermal diffusion system consisting of honeycomb-shaped structures. The robustness of the edge modes deteriorates because of the contributions of C6 symmetry breaking, thus resulting in the appearance of a large gap at the band-crossing point in the decay rate spectra. An interaction between more than two boundaries also leads to poor robustness, whereas strong C6 symmetry breaking improves the robustness deteriorated by such boundary interactions. Our study provides a guide for designing a robust edge mode with a desired decay rate in topological diffusion systems.