Yueh-Yi Lai; Wen-Kai Tai
2008-01-01
Synthesis of transition textures is essential for displaying visually acceptable appearances on a terrain. This investigation presents a modified method for synthesizing the transition texture to be tiled on a terrain. All transition pattern types are recognized for a number of input textures. The proposed modified patch-based sampling texture synthesis approach, using the extra feature map of the input source and target textures for patch matching, can synthesize any transition texture on a succession pattern by initializing the output texture using a portion of the source texture enclosed in a transition cut. The transition boundary is further enhanced to improve the visual effect by tracing out the integral texture elements. Either the Game of Life model or Wang tiles method are exploited to present a good-looking profile of successions on a terrain for tiling transition textures. Experimental results indicate that the proposed method requires few input textures, yet synthesizes numerous tileable transition textures, which are useful for obtaining a vivid appearance of a terrain.
Synthesis and materialization of a reaction-diffusion French flag pattern
Zadorin, Anton S.; Rondelez, Yannick; Gines, Guillaume; Dilhas, Vadim; Urtel, Georg; Zambrano, Adrian; Galas, Jean-Christophe; Estevez-Torres, André
2017-10-01
During embryo development, patterns of protein concentration appear in response to morphogen gradients. These patterns provide spatial and chemical information that directs the fate of the underlying cells. Here, we emulate this process within non-living matter and demonstrate the autonomous structuration of a synthetic material. First, we use DNA-based reaction networks to synthesize a French flag, an archetypal pattern composed of three chemically distinct zones with sharp borders whose synthetic analogue has remained elusive. A bistable network within a shallow concentration gradient creates an immobile, sharp and long-lasting concentration front through a reaction-diffusion mechanism. The combination of two bistable circuits generates a French flag pattern whose 'phenotype' can be reprogrammed by network mutation. Second, these concentration patterns control the macroscopic organization of DNA-decorated particles, inducing a French flag pattern of colloidal aggregation. This experimental framework could be used to test reaction-diffusion models and fabricate soft materials following an autonomous developmental programme.
Size-controlled synthesis of Cu2O nanoparticles via reaction-diffusion
Badr, Layla; Epstein, Irving R.
2017-02-01
Copper (I) oxide nanoparticles are synthesized by a simple reaction-diffusion process involving Cu+ ions and sodium hydroxide in gelatin. The mean diameter and the size dispersion of the nanoparticles can be controlled by two experimental parameters, the percent of gelatin in the medium and the hydroxide ion concentration. UV-visible spectroscopy, transmission electron microscopy and X-ray diffraction are used to analyze the size, morphology, and chemical composition of the nanoparticles generated.
Contrast negation and texture synthesis differentially disrupt natural texture appearance.
Balas, Benjamin
2012-01-01
Natural textures have characteristic image statistics that make them discriminable from unnatural textures. For example, both contrast negation and texture synthesis alter the appearance of natural textures even though each manipulation preserves some features while disrupting others. Here, we examined the extent to which contrast negation and texture synthesis each introduce or remove critical perceptual features for discriminating unnatural textures from natural textures. We find that both manipulations remove information that observers use for distinguishing natural textures from transformed versions of the same patterns, but do so in different ways. Texture synthesis removes information that is relevant for discrimination in both abstract patterns and ecologically valid textures, and we also observe a category-dependent asymmetry for identifying an "oddball" real texture among synthetic distractors. Contrast negation exhibits no such asymmetry, and also does not impact discrimination performance in abstract patterns. We discuss our results in the context of the visual system's tuning to ecologically relevant patterns and other results describing sensitivity to higher-order statistics in texture patterns.
Micro-Texture Synthesis by Phase Randomization
Bruno Galerne
2011-09-01
Full Text Available This contribution is concerned with texture synthesis by example, the process of generating new texture images from a given sample. The Random Phase Noise algorithm presented here synthesizes a texture from an original image by simply randomizing its Fourier phase. It is able to reproduce textures which are characterized by their Fourier modulus, namely the random phase textures (or micro-textures.
Feature-aware natural texture synthesis
Wu, Fuzhang
2014-12-04
This article presents a framework for natural texture synthesis and processing. This framework is motivated by the observation that given examples captured in natural scene, texture synthesis addresses a critical problem, namely, that synthesis quality can be affected adversely if the texture elements in an example display spatially varied patterns, such as perspective distortion, the composition of different sub-textures, and variations in global color pattern as a result of complex illumination. This issue is common in natural textures and is a fundamental challenge for previously developed methods. Thus, we address it from a feature point of view and propose a feature-aware approach to synthesize natural textures. The synthesis process is guided by a feature map that represents the visual characteristics of the input texture. Moreover, we present a novel adaptive initialization algorithm that can effectively avoid the repeat and verbatim copying artifacts. Our approach improves texture synthesis in many images that cannot be handled effectively with traditional technologies.
Using texture synthesis in fractal pattern design
无
2006-01-01
Traditional fractal pattern design has some disadvantages such as inability to effectively reflect the characteristics of real scenery and texture. We propose a novel pattern design technique combining fractal geometry and image texture synthesis to solve these problems. We have improved Wei and Levoy (2000)'s texture synthesis algorithm by first using two-dimensional autocorrelation function to analyze the structure and distribution of textures, and then determining the size of L neighborhood.Several special fractal sets were adopted and HSL (Hue, Saturation, and Light) color space was chosen. The fractal structure was used to manipulate the texture synthesis in HSL color space where the pattern's color can be adjusted conveniently. Experiments showed that patterns with different styles and different color characteristics can be more efficiently generated using the new technique.
Comments on "Steganography Using Reversible Texture Synthesis".
Zhou, Hang; Chen, Kejiang; Zhang, Weiming; Yu, Nenghai
2017-04-01
Message hiding in texture image synthesis is a novel steganography approach by which we resample a smaller texture image and synthesize a new texture image with a similar local appearance and an arbitrary size. However, the mirror operation over the image boundary is flawed and is easy to attack. We propose an attacking method on this steganography, which can not only detect the stego-images but can also extract the hidden messages.
Khan, Easir A.
2010-12-15
Core-shell micromembrane reactors are a novel class of materials where a catalyst and a shape-selective membrane are synergistically housed in a single particle. In this work, we report the synthesis of micrometer -sized core-shell particles containing a catalyst core and a thin permselective zeolite shell and their application as a micromembrane reactor for the selective hydrogenation of the 1-hexene and 3,3-dimethyl-1-butene isomers. The bare catalyst, which is made from porous silica loaded with catalytically active nickel, showed no reactant selectivity between hexene isomers, but the core-shell particles showed high selectivities up to 300 for a 1-hexene conversion of 90%. © 2010 American Chemical Society.
Image completion algorithm based on texture synthesis
Zhang Hongying; Peng Qicong; Wu Yadong
2007-01-01
A new algorithm is proposed for completing the missing parts caused by the removal of foreground or background elements from an image of natural scenery in a visually plausible way.The major contributions of the proposed algorithm are: (1) for most natural images, there is a strong orientation of texture or color distribution.So a method is introduced to compute the main direction of the texture and complete the image by limiting the search to one direction to carry out image completion quite fast; (2) there exists a synthesis ordering for image completion.The searching order of the patches is denned to ensure the regions with more known information and the structures should be completed before filling in other regions; (3) to improve the visual effect of texture synthesis, an adaptive scheme is presented to determine the size of the template window for capturing the features of various scales.A number of examples are given to demonstrate the effectiveness of the proposed algorithm.
Wavelet and Blend maps for texture synthesis
Du Jin-Lian
2011-04-01
Full Text Available blending is now a popular technology for large realtime texture synthesis .Nevertheless, creating blend map during rendering is time and computation consuming work. In this paper, we exploited a method to create a kind of blend tile which can be tile together seamlessly. Note that blend map is in fact a kind of image, which is Markov Random Field, contains multiresolution signals, while wavelet is a powerful way to process multiresolution signals, we use wavelet to process the traditional blend tile. After our processing steps, the result blend tile become smooth and suitable for tiling, with no important features lost. Using this kind blend tile, many computation resources for computing blend map during texture synthesizing is saved. The experimental results shows that our method may successfully process many traditional blend tiles.
Contrast-negation and texture synthesis differentially disrupt natural texture appearance
Benjamin J Balas
2012-11-01
Full Text Available Natural textures have characteristic image statistics that make them discriminable from unnatural textures. For example, both contrast-negation and texture synthesis alter the appearance of natural textures even though each manipulation preserves some features while disrupting others. Here, we examined the extent to which contrast-negation and texture synthesis each introduce or remove critical perceptual features for discriminating unnatural textures from natural textures. We find that both manipulations remove information that observers use for distinguishing natural textures from transformed versions of the same patterns, but do so in different ways. Texture synthesis removes information that is relevant for discrimination in both abstract patterns and ecologically valid textures, and we also observe a category-dependent asymmetry for identifying an oddball real texture among synthetic distractors. Contrast negation exhibits no such asymmetry, and also does not impact discrimination performance in abstract patterns. We discuss our results in the context of the visual system’s tuning to ecologically relevant patterns and other results describing sensitivity to higher-order statistics in texture patterns.
Method of Direct Texture Synthesis on Arbitrary Surfaces
Fu-Li Wu; Chun-Hui Mei; Jiao-Ying Shi
2004-01-01
A direct texture synthesis method on arbitrary surfaces is proposed in this paper. The idea is to recursively map triangles on surface to texture space until the surface is completely mapped. First, the surface is simplified and a tangential vector field is created over the simplified mesh. Then, mapping process searches for the most optimal texture coordinates in texture sample for each triangle, and the textures of neighboring triangles are blended on the mesh. All synthesized texture triangles are compressed to an atlas. Finally, the simplified mesh is subdivided to approach the initial surface. The algorithm has several advantages over former methods:it synthesizes texture on surface without local parameterization; it does not need partitioning surface to patches;and it does not need a particular texture sample. The results demonstrate that the new algorithm is applicable to a wide variety of texture samples and any triangulated surfaces.
Texture synthesis via the matching compatibility between patches
WANG WenCheng; LIU FeiTong; HUANG PeiJie; WU EnHua
2009-01-01
A new patch-based texture synthesis method is presented in this paper.By the method,a set of patches that can be matched with a sampled patch for growing textures effectively,called the matching compatibility between patches,is generated first for each patch,and the set is further optimized by culling the patches that may cause synthesis conflicts.In this way,similarity measurement calculation for selecting suitable patches in texture synthesis can be greatly saved,and synthesis conflicts between neighbouring patches are substantially reduced.Furthermore,retrace computation is Integrated in the synthesis process to improve the texture quality.As a result,the new method can produce high quality textures as texture optimization,the best method to date for producing good textures,and run in a time complexity linear to the size of the output texture.Experimental results show that the new method can interactively generate a large texture in 1024 × 1024 pixels,which is very difficult to achieve by existing methods.
Anisotropic 3D texture synthesis with application to volume rendering
Laursen, Lasse Farnung; Ersbøll, Bjarne Kjær; Bærentzen, Jakob Andreas
2011-01-01
We present a novel approach to improving volume rendering by using synthesized textures in combination with a custom transfer function. First, we use existing knowledge to synthesize anisotropic solid textures to fit our volumetric data. As input to the synthesis method, we acquire high quality....... This method is applied to a high quality visualization of a pig carcass, where samples of meat, bone, and fat have been used to produce the anisotropic 3D textures....
Higher order SVD analysis for dynamic texture synthesis.
Costantini, Roberto; Sbaiz, Luciano; Süsstrunk, Sabine
2008-01-01
Videos representing flames, water, smoke, etc., are often defined as dynamic textures: "textures" because they are characterized by the redundant repetition of a pattern and "dynamic" because this repetition is also in time and not only in space. Dynamic textures have been modeled as linear dynamic systems by unfolding the video frames into column vectors and describing their trajectory as time evolves. After the projection of the vectors onto a lower dimensional space by a singular value decomposition (SVD), the trajectory is modeled using system identification techniques. Synthesis is obtained by driving the system with random noise. In this paper, we show that the standard SVD can be replaced by a higher order SVD (HOSVD), originally known as Tucker decomposition. HOSVD decomposes the dynamic texture as a multidimensional signal (tensor) without unfolding the video frames on column vectors. This is a more natural and flexible decomposition, since it permits us to perform dimension reduction in the spatial, temporal, and chromatic domain, while standard SVD allows for temporal reduction only. We show that for a comparable synthesis quality, the HOSVD approach requires, on average, five times less parameters than the standard SVD approach. The analysis part is more expensive, but the synthesis has the same cost as existing algorithms. Our technique is, thus, well suited to dynamic texture synthesis on devices limited by memory and computational power, such as PDAs or mobile phones.
Automatic Quality Measurement and Parameter Selection for Example-based Texture Synthesis
Laursen, Lasse Farnung; Clemmensen, Line Katrine Harder; Bærentzen, Jakob Andreas
cover research to directly estimate specific texture synthesis parameters, such as patch size and iteration convergence, based on input textures. We also examine various similarity measures and evaluate their effectiveness. The goal for each measure is to properly evaluate how well the resulting...... far, automatically selecting parameters suitable for synthesis has been a relatively unexplored topic. In effect, this makes texture synthesis supervised rather than fully automatic. In this technical paper, we propose automatic parameter optimization methods for example based texture synthesis. We...... synthesis compares to the original input. A good similarity measure will enable the search for the optimal texture synthesis parameters by maximizing the quality of the synthesis as a function of parameters. We apply presented methods to a state of the art texture synthesis algorithm, namely the one...
Perspective texture synthesis based on improved energy optimization.
Syed Muhammad Arsalan Bashir
Full Text Available Perspective texture synthesis has great significance in many fields like video editing, scene capturing etc., due to its ability to read and control global feature information. In this paper, we present a novel example-based, specifically energy optimization-based algorithm, to synthesize perspective textures. Energy optimization technique is a pixel-based approach, so it's time-consuming. We improve it from two aspects with the purpose of achieving faster synthesis and high quality. Firstly, we change this pixel-based technique by replacing the pixel computation with a little patch. Secondly, we present a novel technique to accelerate searching nearest neighborhoods in energy optimization. Using k- means clustering technique to build a search tree to accelerate the search. Hence, we make use of principal component analysis (PCA technique to reduce dimensions of input vectors. The high quality results prove that our approach is feasible. Besides, our proposed algorithm needs shorter time relative to other similar methods.
Langevin Equations for Reaction-Diffusion Processes
Benitez, Federico; Duclut, Charlie; Chaté, Hugues; Delamotte, Bertrand; Dornic, Ivan; Muñoz, Miguel A.
2016-09-01
For reaction-diffusion processes with at most bimolecular reactants, we derive well-behaved, numerically tractable, exact Langevin equations that govern a stochastic variable related to the response field in field theory. Using duality relations, we show how the particle number and other quantities of interest can be computed. Our work clarifies long-standing conceptual issues encountered in field-theoretical approaches and paves the way for systematic numerical and theoretical analyses of reaction-diffusion problems.
Realistic Data-Driven Traffic Flow Animation Using Texture Synthesis.
Chao, Qianwen; Deng, Zhigang; Ren, Jiaping; Ye, Qianqian; Jin, Xiaogang
2017-01-11
We present a novel data-driven approach to populate virtual road networks with realistic traffic flows. Specifically, given a limited set of vehicle trajectories as the input samples, our approach first synthesizes a large set of vehicle trajectories. By taking the spatio-temporal information of traffic flows as a 2D texture, the generation of new traffic flows can be formulated as a texture synthesis process, which is solved by minimizing a newly developed traffic texture energy. The synthesized output captures the spatio-temporal dynamics of the input traffic flows, and the vehicle interactions in it strictly follow traffic rules. After that, we position the synthesized vehicle trajectory data to virtual road networks using a cage-based registration scheme, where a few traffic-specific constraints are enforced to maintain each vehicle's original spatial location and synchronize its motion in concert with its neighboring vehicles. Our approach is intuitive to control and scalable to the complexity of virtual road networks. We validated our approach through many experiments and paired comparison user studies.
Video Texture Synthesis Based on Flow-Like Stylization Painting
Qian Wenhua
2014-01-01
Full Text Available The paper presents an NP-video rendering system based on natural phenomena. It provides a simple nonphotorealistic video synthesis system in which user can obtain a flow-like stylization painting and infinite video scene. Firstly, based on anisotropic Kuwahara filtering in conjunction with line integral convolution, the phenomena video scene can be rendered to flow-like stylization painting. Secondly, the methods of frame division, patches synthesis, will be used to synthesize infinite playing video. According to selection examples from different natural video texture, our system can generate stylized of flow-like and infinite video scenes. The visual discontinuities between neighbor frames are decreased, and we also preserve feature and details of frames. This rendering system is easy and simple to implement.
Reaction-Diffusion Automata Phenomenology, Localisations, Computation
Adamatzky, Andrew
2013-01-01
Reaction-diffusion and excitable media are amongst most intriguing substrates. Despite apparent simplicity of the physical processes involved the media exhibit a wide range of amazing patterns: from target and spiral waves to travelling localisations and stationary breathing patterns. These media are at the heart of most natural processes, including morphogenesis of living beings, geological formations, nervous and muscular activity, and socio-economic developments. This book explores a minimalist paradigm of studying reaction-diffusion and excitable media using locally-connected networks of finite-state machines: cellular automata and automata on proximity graphs. Cellular automata are marvellous objects per se because they show us how to generate and manage complexity using very simple rules of dynamical transitions. When combined with the reaction-diffusion paradigm the cellular automata become an essential user-friendly tool for modelling natural systems and designing future and emergent computing arch...
Fluctuation in nonextensive reaction-diffusion systems
Wu Junlin; Chen Huaijun [Department of Physics, Shaanxi Normal University, Xian 710062 (China)
2007-05-15
The density fluctuation in a nonextensive reaction-diffusion system is investigated, where the nonequilibrium stationary-state distribution is described by the generalized Maxwell-Boltzmann distribution in the framework of Tsallis statistics (or nonextensive statistics). By using the density operator technique, the nonextensive pressure effect is introduced into the master equation and thus the generalized master equation is derived for the system. As an example, we take the{sup 3}He reaction-diffusion model inside stars to analyse the nonextensive effect on the density fluctuation and we find that the nonextensive parameter q different from one plays a very important role in determining the characteristics of the fluctuation waves.
Approximating parameters in nonlinear reaction diffusion equations
Robert R. Ferdinand
2001-07-01
Full Text Available We present a model describing population dynamics in an environment. The model is a nonlinear, nonlocal, reaction diffusion equation with Neumann boundary conditions. An inverse method, involving minimization of a least-squares cost functional, is developed to identify unknown model parameters. Finally, numerical results are presented which display estimates of these parameters using computationally generated data.
Reaction diffusion equations with boundary degeneracy
Huashui Zhan
2016-03-01
Full Text Available In this article, we consider the reaction diffusion equation $$ \\frac{\\partial u}{\\partial t} = \\Delta A(u,\\quad (x,t\\in \\Omega \\times (0,T, $$ with the homogeneous boundary condition. Inspired by the Fichera-Oleinik theory, if the equation is not only strongly degenerate in the interior of $\\Omega$, but also degenerate on the boundary, we show that the solution of the equation is free from any limitation of the boundary condition.
Reaction-Diffusion in the NEURON Simulator
Robert A. McDougal
2013-11-01
Full Text Available In order to support research on the role of cell biological principles (genomics, proteomics, signaling cascades and reaction dynamics on the dynamics of neuronal response in health and disease, NEURON has developed a Reaction-Diffusion (rxd module in Python which provides specification and simulation for these dynamics, coupled with the electrophysiological dynamics of the cell membrane. Arithmetic operations on species and parameters are overloaded, allowing arbitrary reaction formulas to be specified using Python syntax. These expressions are then transparently compiled into bytecode that uses NumPy for fast vectorized calculations. At each time step, rxd combines NEURON's integrators with SciPy’s sparse linear algebra library.
Reaction-diffusion pulses: a combustion model
Campos, Daniel [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Llebot, Josep Enric [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Fort, Joaquim [Dept. de FIsica, Univ. de Girona, Campus de Montilivi, 17071 Girona, Catalonia (Spain)
2004-07-02
We focus on a reaction-diffusion approach proposed recently for experiments on combustion processes, where the heat released by combustion follows first-order reaction kinetics. This case allows us to perform an exhaustive analytical study. Specifically, we obtain the exact expressions for the speed of the thermal pulses, their maximum temperature and the condition of self-sustenance. Finally, we propose two generalizations of the model, namely, the case of several reactants burning together, and that of time-delayed heat conduction. We find an excellent agreement between our analytical results and simulations.
Reaction-diffusion in the NEURON simulator.
McDougal, Robert A; Hines, Michael L; Lytton, William W
2013-01-01
In order to support research on the role of cell biological principles (genomics, proteomics, signaling cascades and reaction dynamics) on the dynamics of neuronal response in health and disease, NEURON's Reaction-Diffusion (rxd) module in Python provides specification and simulation for these dynamics, coupled with the electrophysiological dynamics of the cell membrane. Arithmetic operations on species and parameters are overloaded, allowing arbitrary reaction formulas to be specified using Python syntax. These expressions are then transparently compiled into bytecode that uses NumPy for fast vectorized calculations. At each time step, rxd combines NEURON's integrators with SciPy's sparse linear algebra library.
Galactic disks as reaction-diffusion systems
Smolin, L
1996-01-01
A model of a galactic disk is presented which extends the homogeneous one zone models by incorporating propagation of material and energy in the disk. For reasonable values of the parameters the homogeneous steady state is unstable to the development of inhomogeneities, leading to the development of spatial and temporal structure. At the linearized level a prediction for the length and time scales of the patterns is found. These instabilities arise for the same reason that pattern formation is seen in non-equilibrium chemical and biological systems, which is that the positive and negative feedback effects which govern the rates of the critical processes act over different distance scales, as in Turing's reaction-diffusion models. This shows that patterns would form in the disk even in the absence of gravitational effects, density waves, rotation, shear and external perturbations. These nonlinear effects may thus explain the spiral structure seen in the star forming regions of isolated flocculent galaxies.
Laser Spot Detection Based on Reaction Diffusion
Vázquez-Otero, Alejandro; Khikhlukha, Danila; Solano-Altamirano, J. M.; Dormido, Raquel; Duro, Natividad
2016-01-01
Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations. PMID:26938537
Laser Spot Detection Based on Reaction Diffusion
Alejandro Vázquez-Otero
2016-03-01
Full Text Available Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations.
Realization of texture synthesis algorithm based on mixed programming via COM
Qin, Rizhao; Pu, Yuanyuan; Xu, Dan; Chen, Hong
2012-01-01
This paper analyzes the respective characteristics of VS2005 and MATLAB and their performances and introduces several methods of mixed programming. Then, the paper discusses the advantages and great applications of texture synthesis from sample (TSFS) and Image Quilting algorithm which is a typical algorithm of TSFS. Further, the paper realizes the Image Quilting algorithm by using mixed programming between VS2005 and MATLAB2007a via COM. We can perceive that mixed programming via COM that is used in developing texture synthesis program can not only speeds up its efficiency and reliability, but also strengthen the convenience of operation and visualization. Finally, the paper summarizes the relationship between texture synthesis parameters and synthesis effects from the experiment.
Real-Time Texture Synthesis Using s-Tile Set
Feng Xue; You-Sheng Zhang; Ju-Lang Jiang; Min Hu; Xin-Dong Wu; Rong-Gui Wang
2007-01-01
This paper presents a novel method of generating a set of texture tiles from samples, which can be seamlessly tiled into arbitrary size textures in real-time. Compared to existing methods, our approach is simpler and more advantageous in eliminating visual seams that may exist in each tile of the existing methods, especially when the samples have elaborate features or distinct colors. Texture tiles generated by our approach can be regarded as single-colored tiles on each orthogonal direction border, which are easier for tiling and more suitable for sentence tiling. Experimental results demonstrate the feasibility and effectiveness of our approach.
Chemical computing with reaction-diffusion processes.
Gorecki, J; Gizynski, K; Guzowski, J; Gorecka, J N; Garstecki, P; Gruenert, G; Dittrich, P
2015-07-28
Chemical reactions are responsible for information processing in living organisms. It is believed that the basic features of biological computing activity are reflected by a reaction-diffusion medium. We illustrate the ideas of chemical information processing considering the Belousov-Zhabotinsky (BZ) reaction and its photosensitive variant. The computational universality of information processing is demonstrated. For different methods of information coding constructions of the simplest signal processing devices are described. The function performed by a particular device is determined by the geometrical structure of oscillatory (or of excitable) and non-excitable regions of the medium. In a living organism, the brain is created as a self-grown structure of interacting nonlinear elements and reaches its functionality as the result of learning. We discuss whether such a strategy can be adopted for generation of chemical information processing devices. Recent studies have shown that lipid-covered droplets containing solution of reagents of BZ reaction can be transported by a flowing oil. Therefore, structures of droplets can be spontaneously formed at specific non-equilibrium conditions, for example forced by flows in a microfluidic reactor. We describe how to introduce information to a droplet structure, track the information flow inside it and optimize medium evolution to achieve the maximum reliability. Applications of droplet structures for classification tasks are discussed.
Voter Model Perturbations and Reaction Diffusion Equations
Cox, J Theodore; Perkins, Edwin
2011-01-01
We consider particle systems that are perturbations of the voter model and show that when space and time are rescaled the system converges to a solution of a reaction diffusion equation in dimensions $d \\ge 3$. Combining this result with properties of the PDE, some methods arising from a low density super-Brownian limit theorem, and a block construction, we give general, and often asymptotically sharp, conditions for the existence of non-trivial stationary distributions, and for extinction of one type. As applications, we describe the phase diagrams of three systems when the parameters are close to the voter model: (i) a stochastic spatial Lotka-Volterra model of Neuhauser and Pacala, (ii) a model of the evolution of cooperation of Ohtsuki, Hauert, Lieberman, and Nowak, and (iii) a continuous time version of the non-linear voter model of Molofsky, Durrett, Dushoff, Griffeath, and Levin. The first application confirms a conjecture of Cox and Perkins and the second confirms a conjecture of Ohtsuki et al in the ...
Speed ot travelling waves in reaction-diffusion equations
Benguria, R D; Méndez, V
2002-01-01
Reaction diffusion equations arise in several problems of population dynamics, flame propagation and others. In one dimensional cases the systems may evolve into travelling fronts. Here we concentrate on a reaction diffusion equation which arises as a simple model for chemotaxis and present results for the speed of the travelling fronts. (Author)
Speed ot travelling waves in reaction-diffusion equations
Benguria, R.D.; Depassier, M.C. [Facultad de Fisica, Pontificia Universidad Catolica de Chile, Avda. Vicuna Mackenna 4860, Santiago (Chile); Mendez, V. [Facultat de Ciencies de la Salut, Universidad Internacional de Catalunya, Gomera s/n 08190 Sant Cugat del Valles, Barcelona (Spain)
2002-07-01
Reaction diffusion equations arise in several problems of population dynamics, flame propagation and others. In one dimensional cases the systems may evolve into travelling fronts. Here we concentrate on a reaction diffusion equation which arises as a simple model for chemotaxis and present results for the speed of the travelling fronts. (Author)
QUENCHING PROBLEMS OF DEGENERATE FUNCTIONAL REACTION-DIFFUSION EQUATION
无
2006-01-01
This paper is concerned with the quenching problem of a degenerate functional reaction-diffusion equation. The quenching problem and global existence of solution for the reaction-diffusion equation are derived and, some results of the positive steady state solutions for functional elliptic boundary value are also presented.
Pei, Soo-Chang; Zeng, Yi-Chong; Chang, Ching-Hua
2004-03-01
This work presents a novel algorithm using color contrast enhancement and lacuna texture synthesis is proposed for the virtual restoration of ancient Chinese paintings. Color contrast enhancement based on saturation and de-saturation is performed in the u'v'Y color space, to change the saturation value in the chromaticity diagram, and adaptive histogram equalization then is adopted to adjust the luminance component. Additionally, this work presents a new patching method using the Markov Random Field (MRF) model of texture synthesis. Eliminating undesirable aged painting patterns, such as stains, crevices, and artifacts, and then filling the lacuna regions with the appropriate textures is simple and efficient. The synthesization procedure integrates three key approaches, weighted mask, annular scan and auxiliary, with neighborhood searching. These approaches can maintain a complete shape and prevent edge disconnection in the final results. Moreover, the boundary between original and synthesized paintings is seamless, and unable to distinguish in which the undesirable pattern appears.
Research and Implementation of the Practical Texture Synthesis Algorithms
孙家广; 周毅
1991-01-01
How to generate pictures real and esthetic objects is an important subject of computer graphics.The techniques of mapping textures onto the surfaces of an object in the 3D space are efficient approaches for the purpose.We developed and implemented algorithms for generating objects with appearances stone,wood grain,ice lattice,brick,doors and windows on Apollo workstations.All the algorithms have been incorporated into the 3D grometry modelling system (GEMS) developed by the CAD Center of Tsinghua University.This paper emphasizes the wood grain and the ice lattice algorithms.
LAGRANGE STABILITY IN MEAN SQUARE OF STOCHASTIC REACTION DIFFUSION EQUATIONS
无
2006-01-01
This work is devoted to the discussion of stochastic reaction diffusion equations and some new theorems on Lagrange stability in mean square of the solution are established via Lyapunov method which is nothing to be done in the past.
Physarum machines: encapsulating reaction-diffusion to compute spanning tree
Adamatzky, Andrew
2007-12-01
The Physarum machine is a biological computing device, which employs plasmodium of Physarum polycephalum as an unconventional computing substrate. A reaction-diffusion computer is a chemical computing device that computes by propagating diffusive or excitation wave fronts. Reaction-diffusion computers, despite being computationally universal machines, are unable to construct certain classes of proximity graphs without the assistance of an external computing device. I demonstrate that the problem can be solved if the reaction-diffusion system is enclosed in a membrane with few ‘growth points’, sites guiding the pattern propagation. Experimental approximation of spanning trees by P. polycephalum slime mold demonstrates the feasibility of the approach. Findings provided advance theory of reaction-diffusion computation by enriching it with ideas of slime mold computation.
NONLINEAR SINGULARLY PERTURBED PREDATOR-PREY REACTION DIFFUSION SYSTEMS
MoJiaqi; TangRongrong
2004-01-01
A class of nonlinear predator-prey reaction diffusion systems for singularly perturbedproblems are considered. Under suitable conditions, by using theory of differential inequalitiesthe existence and asymptotic behavior of solution for initial boundary value problems arestudied.
Multiresolution stochastic simulations of reaction-diffusion processes.
Bayati, B; Chatelain, P.; Koumoutsakos, P.
2008-01-01
Stochastic simulations of reaction-diffusion processes are used extensively for the modeling of complex systems in areas ranging from biology and social sciences to ecosystems and materials processing. These processes often exhibit disparate scales that render their simulation prohibitive even for massive computational resources. The problem is resolved by introducing a novel stochastic multiresolution method that enables the efficient simulation of reaction-diffusion processes as modeled by ...
Reaction-diffusion problems in the physics of hot plasmas
Wilhelmsson, H
2000-01-01
The physics of hot plasmas is of great importance for describing many phenomena in the universe and is fundamental for the prospect of future fusion energy production on Earth. Nontrivial results of nonlinear electromagnetic effects in plasmas include the self-organization and self-formation in the plasma of structures compact in time and space. These are the consequences of competing processes of nonlinear interactions and can be best described using reaction-diffusion equations. Reaction-Diffusion Problems in the Physics of Hot Plasmas is focused on paradigmatic problems of a reaction-diffusion type met in many branches of science, concerning in particular the nonlinear interaction of electromagnetic fields with plasmas.
Simple computation of reaction-diffusion processes on point clouds.
Macdonald, Colin B; Merriman, Barry; Ruuth, Steven J
2013-06-04
The study of reaction-diffusion processes is much more complicated on general curved surfaces than on standard Cartesian coordinate spaces. Here we show how to formulate and solve systems of reaction-diffusion equations on surfaces in an extremely simple way, using only the standard Cartesian form of differential operators, and a discrete unorganized point set to represent the surface. Our method decouples surface geometry from the underlying differential operators. As a consequence, it becomes possible to formulate and solve rather general reaction-diffusion equations on general surfaces without having to consider the complexities of differential geometry or sophisticated numerical analysis. To illustrate the generality of the method, computations for surface diffusion, pattern formation, excitable media, and bulk-surface coupling are provided for a variety of complex point cloud surfaces.
Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion
Del Razo, Mauricio J; Qian, Hong; Lin, Guang
2014-01-01
The currently existing theory of fluorescence correlation spectroscopy(FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered in single-cell biochemistry, it is expected that FCS time correlation functions of a reaction-diffusion system can deviate from the classic results of Elson and Magde. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems here are no closed solutions; therefore, stochastic Monte-Carlo simulations are carried out. We show that the deviation is small for a simple bimolecular reaction; the most significant deviations occur when the number of molecules is small and of the same order. Our results show that current linear FCS theory could be adequate ...
Adaptive mesh refinement for stochastic reaction-diffusion processes
Bayati, Basil; Chatelain, Philippe; Koumoutsakos, Petros
2011-01-01
We present an algorithm for adaptive mesh refinement applied to mesoscopic stochastic simulations of spatially evolving reaction-diffusion processes. The transition rates for the diffusion process are derived on adaptive, locally refined structured meshes. Convergence of the diffusion process is presented and the fluctuations of the stochastic process are verified. Furthermore, a refinement criterion is proposed for the evolution of the adaptive mesh. The method is validated in simulations of reaction-diffusion processes as described by the Fisher-Kolmogorov and Gray-Scott equations.
Reaction Diffusion and Chemotaxis for Decentralized Gathering on FPGAs
Bernard Girau
2009-01-01
and rapid simulations of the complex dynamics of this reaction-diffusion model. Then we describe the FPGA implementation of the environment together with the agents, to study the major challenges that must be solved when designing a fast embedded implementation of the decentralized gathering model. We analyze the results according to the different goals of these hardware implementations.
Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion
Del Razo, Mauricio; Pan, Wenxiao; Qian, Hong; Lin, Guang
2014-05-30
The currently existing theory of fluorescence correlation spectroscopy (FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered in single-cell biochemistry, it is expected that FCS time correlation functions of a reaction-diffusion system can deviate from the classic results of Elson and Magde [Biopolymers (1974) 13:1-27]. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems there are no closed solutions; therefore, stochastic Monte-Carlo simulations are carried out. We show that the deviation is small for a simple bimolecular reaction; the most significant deviations occur when the number of molecules is small and of the same order. Extending Delbrück-Gillespie’s theory for stochastic nonlinear reactions with rapidly stirring to reaction-diffusion systems provides a mesoscopic model for chemical and biochemical reactions at nanometric and mesoscopic level such as a single biological cell.
Internal Stabilization of a Mutualistic Reaction Diffusion System
Wang Yuan DONG
2007-01-01
We study the internal stabilization of steady-state solutions to a 2-species mutualistic reaction diffusion system via finite-dimensional feedback controllers. Our main idea is to use differ- ent internal controllers to stabilize different steady-state solutions. The controllers are provided by considering LQ problems associated with the lineaxized systems at steady-state solutions.
Turing instability in reaction-diffusion systems with nonlinear diffusion
Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
2013-10-15
The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.
Hamiltonian perspective on compartmental reaction-diffusion networks
Seslija, Marko; van der Schaft, Arjan; Scherpen, Jacquelien M. A.
2014-01-01
Inspired by the recent developments in modeling and analysis of reaction networks, we provide a geometric formulation of the reversible reaction networks under the influence of diffusion. Using the graph knowledge of the underlying reaction network, the obtained reaction diffusion system is a distri
Hubert, Julie; Dufour, Thierry; Vandencasteele, Nicolas; Reniers, François; Viville, Pascal; Lazzaroni, Roberto; Raes, M; Terryn, Herman
2016-01-01
The synthesis and texturization processes of fluorinated surfaces by means of atmospheric plasma are investigated and presented through an integrated study of both the plasma phase and the resulting material surface. Three methods enhancing the surface hydrophobicity up to the production of super-hydrophobic surfaces are evaluated: (i) the modification of a polytetrafluoroethylene (PTFE) surface, (ii) the plasma deposition of fluorinated coatings and (iii) the incorporation of nanoparticles into those fluorinated films. In all the approaches, the nature of the plasma gas appears to be a crucial parameter for the desired property. Although a higher etching of the PTFE surface can be obtained with a pure helium plasma, the texturization can only be created if O2 is added to the plasma, which simultaneously decreases the total etching. The deposition of CxFy films by a dielectric barrier discharge leads to hydrophobic coatings with water contact angles (WCAs) of 115{\\textdegree}, but only the filamentary argon d...
Reaction-diffusion pattern in shoot apical meristem of plants.
Hironori Fujita
Full Text Available A fundamental question in developmental biology is how spatial patterns are self-organized from homogeneous structures. In 1952, Turing proposed the reaction-diffusion model in order to explain this issue. Experimental evidence of reaction-diffusion patterns in living organisms was first provided by the pigmentation pattern on the skin of fishes in 1995. However, whether or not this mechanism plays an essential role in developmental events of living organisms remains elusive. Here we show that a reaction-diffusion model can successfully explain the shoot apical meristem (SAM development of plants. SAM of plants resides in the top of each shoot and consists of a central zone (CZ and a surrounding peripheral zone (PZ. SAM contains stem cells and continuously produces new organs throughout the lifespan. Molecular genetic studies using Arabidopsis thaliana revealed that the formation and maintenance of the SAM are essentially regulated by the feedback interaction between WUSHCEL (WUS and CLAVATA (CLV. We developed a mathematical model of the SAM based on a reaction-diffusion dynamics of the WUS-CLV interaction, incorporating cell division and the spatial restriction of the dynamics. Our model explains the various SAM patterns observed in plants, for example, homeostatic control of SAM size in the wild type, enlarged or fasciated SAM in clv mutants, and initiation of ectopic secondary meristems from an initial flattened SAM in wus mutant. In addition, the model is supported by comparing its prediction with the expression pattern of WUS in the wus mutant. Furthermore, the model can account for many experimental results including reorganization processes caused by the CZ ablation and by incision through the meristem center. We thus conclude that the reaction-diffusion dynamics is probably indispensable for the SAM development of plants.
Distributed order reaction-diffusion systems associated with Caputo derivatives
Saxena, R. K.; Mathai, A. M.; Haubold, H. J.
2014-08-01
This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the joint Laplace and Fourier transforms in compact and closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by other authors, notably by Mainardi et al. ["The fundamental solution of the space-time fractional diffusion equation," Fractional Calculus Appl. Anal. 4, 153-202 (2001); Mainardi et al. "Fox H-functions in fractional diffusion," J. Comput. Appl. Math. 178, 321-331 (2005)] for the fundamental solution of the space-time fractional equation, including Haubold et al. ["Solutions of reaction-diffusion equations in terms of the H-function," Bull. Astron. Soc. India 35, 681-689 (2007)] and Saxena et al. ["Fractional reaction-diffusion equations," Astrophys. Space Sci. 305, 289-296 (2006a)] for fractional reaction-diffusion equations. The advantage of using the Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation, containing this derivative, includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of fractional diffusion, space-time fraction diffusion, and time-fractional diffusion, see Schneider and Wyss ["Fractional diffusion and wave equations," J. Math. Phys. 30, 134-144 (1989)]. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-function in compact forms. The convergence conditions for the double series occurring in the solutions are investigated. It is interesting to observe that the double series comes out to be a special case of the Srivastava-Daoust hypergeometric function of two variables
Cohabitation reaction-diffusion model for virus focal infections
Amor, Daniel R.; Fort, Joaquim
2014-12-01
The propagation of virus infection fronts has been typically modeled using a set of classical (noncohabitation) reaction-diffusion equations for interacting species. However, for some single-species systems it has been recently shown that noncohabitation reaction-diffusion equations may lead to unrealistic descriptions. We argue that previous virus infection models also have this limitation, because they assume that a virion can simultaneously reproduce inside a cell and diffuse away from it. For this reason, we build a several-species cohabitation model that does not have this limitation. Furthermore, we perform a sensitivity analysis for the most relevant parameters of the model, and we compare the predicted infection speed with observed data for two different strains of the T7 virus.
Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation
Petr Stehlík
2015-01-01
Full Text Available We study reaction-diffusion equations with a general reaction function f on one-dimensional lattices with continuous or discrete time ux′ (or Δtux=k(ux-1-2ux+ux+1+f(ux, x∈Z. We prove weak and strong maximum and minimum principles for corresponding initial-boundary value problems. Whereas the maximum principles in the semidiscrete case (continuous time exhibit similar features to those of fully continuous reaction-diffusion model, in the discrete case the weak maximum principle holds for a smaller class of functions and the strong maximum principle is valid in a weaker sense. We describe in detail how the validity of maximum principles depends on the nonlinearity and the time step. We illustrate our results on the Nagumo equation with the bistable nonlinearity.
Does reaction-diffusion support the duality of fragmentation effect?
Roques, Lionel
2009-01-01
There is a gap between single-species model predictions, and empirical studies, regarding the effect of habitat fragmentation per se, i.e., a process involving the breaking apart of habitat without loss of habitat. Empirical works indicate that fragmentation can have positive as well as negative effects, whereas, traditionally, single-species models predict a negative effect of fragmentation. Within the class of reaction-diffusion models, studies almost unanimously predict such a detrimental effect. In this paper, considering a single-species reaction-diffusion model with a removal -- or similarly harvesting -- term, in two dimensions, we find both positive and negative effects of fragmentation of the reserves, i.e. the protected regions where no removal occurs. Fragmented reserves lead to higher population sizes for time-constant removal terms. On the other hand, when the removal term is proportional to the population density, higher population sizes are obtained on aggregated reserves, but maximum yields ar...
Untangling knots via reaction-diffusion dynamics of vortex strings
Maucher, Fabian
2016-01-01
We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to initialize the knot as a vortex string in the FitzHugh-Nagumo equation. Remarkably, we find that the subsequent evolution preserves the topology of the knot and can untangle an unknot into a circle. Illustrative test case examples are presented, including the untangling of a hard unknot known as the culprit. Our approach to the unknotting problem has two novel features, in that it applies field theory rather than particle mechanics and uses reaction-diffusion dynamics in place of energy minimization.
Multiresolution stochastic simulations of reaction-diffusion processes.
Bayati, Basil; Chatelain, Philippe; Koumoutsakos, Petros
2008-10-21
Stochastic simulations of reaction-diffusion processes are used extensively for the modeling of complex systems in areas ranging from biology and social sciences to ecosystems and materials processing. These processes often exhibit disparate scales that render their simulation prohibitive even for massive computational resources. The problem is resolved by introducing a novel stochastic multiresolution method that enables the efficient simulation of reaction-diffusion processes as modeled by many-particle systems. The proposed method quantifies and efficiently handles the associated stiffness in simulating the system dynamics and its computational efficiency and accuracy are demonstrated in simulations of a model problem described by the Fisher-Kolmogorov equation. The method is general and can be applied to other many-particle models of physical processes.
Parametric spatiotemporal oscillation in reaction-diffusion systems.
Ghosh, Shyamolina; Ray, Deb Shankar
2016-03-01
We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.
Reaction diffusion equation with spatio-temporal delay
Zhao, Zhihong; Rong, Erhua
2014-07-01
We investigate reaction-diffusion equation with spatio-temporal delays, the global existence, uniqueness and asymptotic behavior of solutions for which in relation to constant steady-state solution, included in the region of attraction of a stable steady solution. It is shown that if the delay reaction function satisfies some conditions and the system possesses a pair of upper and lower solutions then there exists a unique global solution. In terms of the maximal and minimal constant solutions of the corresponding steady-state problem, we get the asymptotic stability of reaction-diffusion equation with spatio-temporal delay. Applying this theory to Lotka-Volterra model with spatio-temporal delay, we get the global solution asymptotically tend to the steady-state problem's steady-state solution.
Untangling Knots Via Reaction-Diffusion Dynamics of Vortex Strings
Maucher, Fabian; Sutcliffe, Paul
2016-04-01
We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to initialize the knot as a vortex string in the FitzHugh-Nagumo equation. Remarkably, we find that the subsequent evolution preserves the topology of the knot and can untangle an unknot into a circle. Illustrative test case examples are presented, including the untangling of a hard unknot known as the culprit. Our approach to the unknotting problem has two novel features, in that it applies field theory rather than particle mechanics and uses reaction-diffusion dynamics in place of energy minimization.
Reaction-diffusion master equation in the microscopic limit
Hellander, Stefan; Hellander, Andreas; Petzold, Linda
2012-04-01
Stochastic modeling of reaction-diffusion kinetics has emerged as a powerful theoretical tool in the study of biochemical reaction networks. Two frequently employed models are the particle-tracking Smoluchowski framework and the on-lattice reaction-diffusion master equation (RDME) framework. As the mesh size goes from coarse to fine, the RDME initially becomes more accurate. However, recent developments have shown that it will become increasingly inaccurate compared to the Smoluchowski model as the lattice spacing becomes very fine. Here we give a general and simple argument for why the RDME breaks down. Our analysis reveals a hard limit on the voxel size for which no local RDME can agree with the Smoluchowski model and lets us quantify this limit in two and three dimensions. In this light we review and discuss recent work in which the RDME has been modified in different ways in order to better agree with the microscale model for very small voxel sizes.
On the Reaction Diffusion Master Equation in the Microscopic Limit
Hellander, Stefan; Petzold, Linda
2011-01-01
Stochastic modeling of reaction-diffusion kinetics has emerged as a powerful theoretical tool in the study of biochemical reaction networks. Two frequently employed models are the particle-tracking Smoluchowski framework and the on-lattice Reaction-Diffusion Master Equation (RDME) framework. As the mesh size goes from coarse to fine, the RDME initially becomes more accurate. However, recent developments have shown that it will become increasingly inaccurate compared to the Smoluchowski model as the lattice spacing becomes very fine. In this paper we give a new, general and simple argument for why the RDME breaks down. Our analysis reveals a hard limit on the voxel size for which no local RDME can agree with the Smoluchowski model.
ALTERNATING DIRECTION FINITE ELEMENT METHOD FOR SOME REACTION DIFFUSION MODELS
江成顺; 刘蕴贤; 沈永明
2004-01-01
This paper is concerned with some nonlinear reaction - diffusion models. To solve this kind of models, the modified Laplace finite element scheme and the alternating direction finite element scheme are established for the system of patrical differential equations. Besides, the finite difference method is utilized for the ordinary differential equation in the models. Moreover, by the theory and technique of prior estimates for the differential equations, the convergence analyses and the optimal L2- norm error estimates are demonstrated.
Controllability of Degenerating Reaction-Diffusion System in Electrocardiology
Bendahmane, Mostafa
2011-01-01
This paper is devoted to analyze the null controllability of a nonlinear reaction-diffusion system approximating a parabolic-elliptic system modeling electrical activity in the heart. The uniform, with respect to the degenerating parameter, null controllability of the approximating system by a single control force acting on a subdomain is shown. The proof needs a precisely estimate with respect to the degenerating parameter and it is done combining Carleman estimates and energy inequalities.
The speed of reaction-diffusion wavefronts in nonsteady media
Mendez, Vicenc [Departament de Medicina, Facultat de Ciencies de la Salut, Universitat Internacional de Catalunya. c/Gomera s/n, 08190-Sant Cugat del Valles (Barcelona) (Spain); Fort, Joaquim [Departament de Fisica, Universitat de Girona, Campus Montilivi, 17071 Girona, Catalonia (Spain); Pujol, Toni [Departament de Fisica, Universitat de Girona, Campus Montilivi, 17071 Girona, Catalonia (Spain)
2003-04-11
The evolution of the speed of wavefronts for reaction-diffusion equations with time-varying parameters is analysed. We make use of singular perturbative analysis to study the temporal evolution of the speed for pushed fronts. The analogy with Hamilton-Jacobi dynamics allows us to consider the problem for pulled fronts, which is described by Kolmogorov-Petrovskii-Piskunov (KPP) reaction kinetics. Both analytical studies are in good agreement with the results of numerical solutions.
The speed of reaction-diffusion wavefronts in nonsteady media
Méndez, V; Pujol, T
2003-01-01
The evolution of the speed of wavefronts for reaction-diffusion equations with time-varying parameters is analysed. We make use of singular perturbative analysis to study the temporal evolution of the speed for pushed fronts. The analogy with Hamilton-Jacobi dynamics allows us to consider the problem for pulled fronts, which is described by Kolmogorov-Petrovskii-Piskunov (KPP) reaction kinetics. Both analytical studies are in good agreement with the results of numerical solutions.
An Application of Equivalence Transformations to Reaction Diffusion Equations
Mariano Torrisi
2015-10-01
Full Text Available In this paper, we consider a quite general class of advection reaction diffusion systems. By using an equivalence generator, derived in a previous paper, the authors apply a projection theorem to determine some special forms of the constitutive functions that allow the extension by one of the two-dimensional principal Lie algebra. As an example, a special case is discussed at the end of the paper.
Resonant Phase Patterns in a Reaction-Diffusion System
Lin, Anna L.; Bertram, Matthias; Martinez, Karl; Swinney, Harry L.; Ardelea, Alexandre; Carey, Graham F.
2000-05-01
Resonance regions similar to the Arnol'd tongues found in single oscillator frequency locking are observed in experiments using a spatially extended periodically forced Belousov-Zhabotinsky system. We identify six distinct 2:1 subharmonic resonant patterns and describe them in terms of the position-dependent phase and magnitude of the oscillations. Some experimentally observed features are also found in numerical studies of a forced Brusselator reaction-diffusion model. (c) 2000 The American Physical Society.
Reaction rates for a generalized reaction-diffusion master equation.
Hellander, Stefan; Petzold, Linda
2016-01-01
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach, in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is of the order of the reaction radius of a reacting pair of molecules.
Distributed order reaction-diffusion systems associated with Caputo derivatives
Saxena, R K; Haubold, H J
2011-01-01
This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the joint Laplace and Fourier transforms in compact and closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by other authors, notably by Mainardi et al. [23,24], for the fundamental solution of the space-time fractional equation, including Haubold et al. [13] and Saxena et al. [38] for fractional reaction-diffusion equations. The advantage of using the Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation, containing this derivative, includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of fractional diffusion, space-time fraction diffusion...
Reaction rates for a generalized reaction-diffusion master equation
Hellander, Stefan; Petzold, Linda
2016-01-01
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach, in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is of the order of the reaction radius of a reacting pair of molecules.
Reaction diffusion and solid state chemical kinetics handbook
Dybkov, V I
2010-01-01
This monograph deals with a physico-chemical approach to the problem of the solid-state growth of chemical compound layers and reaction-diffusion in binary heterogeneous systems formed by two solids; as well as a solid with a liquid or a gas. It is explained why the number of compound layers growing at the interface between the original phases is usually much lower than the number of chemical compounds in the phase diagram of a given binary system. For example, of the eight intermetallic compounds which exist in the aluminium-zirconium binary system, only ZrAl3 was found to grow as a separate
A Weak Comparison Principle for Reaction-Diffusion Systems
José Valero
2012-01-01
Full Text Available We prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation, and to a model of fractional-order chemical autocatalysis with decay. Moreover, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functions L∞ is proved for at least one solution of the problem.
Global dynamics of a reaction-diffusion system
Yuncheng You
2011-02-01
Full Text Available In this work the existence of a global attractor for the semiflow of weak solutions of a two-cell Brusselator system is proved. The method of grouping estimation is exploited to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of coupled reaction-diffusion systems with cubic autocatalytic nonlinearity and linear coupling. It is proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite. Moreover, the existence of an exponential attractor for this solution semiflow is shown.
Exact solutions for logistic reaction-diffusion equations in biology
Broadbridge, P.; Bradshaw-Hajek, B. H.
2016-08-01
Reaction-diffusion equations with a nonlinear source have been widely used to model various systems, with particular application to biology. Here, we provide a solution technique for these types of equations in N-dimensions. The nonclassical symmetry method leads to a single relationship between the nonlinear diffusion coefficient and the nonlinear reaction term; the subsequent solutions for the Kirchhoff variable are exponential in time (either growth or decay) and satisfy the linear Helmholtz equation in space. Example solutions are given in two dimensions for particular parameter sets for both quadratic and cubic reaction terms.
On the solutions of fractional reaction-diffusion equations
Jagdev Singh
2013-05-01
Full Text Available In this paper, we obtain the solution of a fractional reaction-diffusion equation associated with the generalized Riemann-Liouville fractional derivative as the time derivative and Riesz-Feller fractional derivative as the space-derivative. The results are derived by the application of the Laplace and Fourier transforms in compact and elegant form in terms of Mittag-Leffler function and H-function. The results obtained here are of general nature and include the results investigated earlier by many authors.
Reaction-diffusion-branching models of stock price fluctuations
Tang, Lei-Han; Tian, Guang-Shan
Several models of stock trading (Bak et al., Physica A 246 (1997) 430.) are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent H=1/4. Biased diffusion towards the market price and blind-eyed copying lead to crossovers to the empirically observed random-walk behavior ( H=1/2) at long times. The calculated crossover forms and diffusion constants are shown to agree well with simulation data.
Parametric pattern selection in a reaction-diffusion model.
Michael Stich
Full Text Available We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function of a natural control parameter (feed-rate where degenerate patterns with different numbers of spots coexist for a fixed feed-rate. While it is possible to generate identical patterns via both mechanisms, we show that replication cascades lead to a wider choice of pattern profiles that can be selected through a tuning of the feed-rate, exploiting hysteresis and directionality effects of the different pattern pathways.
A weak comparison principle for reaction-diffusion systems
Valero, José
2012-01-01
In this paper we prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation and to a model of fractional-order chemical autocatalysis with decay. Morever, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functions $L^{\\infty}$ is proved for at least one solution of the problem.
Reaction rates for mesoscopic reaction-diffusion kinetics.
Hellander, Stefan; Hellander, Andreas; Petzold, Linda
2015-02-01
The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.
Reaction rates for reaction-diffusion kinetics on unstructured meshes
Hellander, Stefan; Petzold, Linda
2017-02-01
The reaction-diffusion master equation is a stochastic model often utilized in the study of biochemical reaction networks in living cells. It is applied when the spatial distribution of molecules is important to the dynamics of the system. A viable approach to resolve the complex geometry of cells accurately is to discretize space with an unstructured mesh. Diffusion is modeled as discrete jumps between nodes on the mesh, and the diffusion jump rates can be obtained through a discretization of the diffusion equation on the mesh. Reactions can occur when molecules occupy the same voxel. In this paper, we develop a method for computing accurate reaction rates between molecules occupying the same voxel in an unstructured mesh. For large voxels, these rates are known to be well approximated by the reaction rates derived by Collins and Kimball, but as the mesh is refined, no analytical expression for the rates exists. We reduce the problem of computing accurate reaction rates to a pure preprocessing step, depending only on the mesh and not on the model parameters, and we devise an efficient numerical scheme to estimate them to high accuracy. We show in several numerical examples that as we refine the mesh, the results obtained with the reaction-diffusion master equation approach those of a more fine-grained Smoluchowski particle-tracking model.
Stochastic reaction-diffusion kinetics in the microscopic limit
Fange, David; Berg, Otto G.; Sjöberg, Paul; Elf, Johan
2010-01-01
Quantitative analysis of biochemical networks often requires consideration of both spatial and stochastic aspects of chemical processes. Despite significant progress in the field, it is still computationally prohibitive to simulate systems involving many reactants or complex geometries using a microscopic framework that includes the finest length and time scales of diffusion-limited molecular interactions. For this reason, spatially or temporally discretized simulations schemes are commonly used when modeling intracellular reaction networks. The challenge in defining such coarse-grained models is to calculate the correct probabilities of reaction given the microscopic parameters and the uncertainty in the molecular positions introduced by the spatial or temporal discretization. In this paper we have solved this problem for the spatially discretized Reaction-Diffusion Master Equation; this enables a seamless and physically consistent transition from the microscopic to the macroscopic frameworks of reaction-diffusion kinetics. We exemplify the use of the methods by showing that a phosphorylation-dephosphorylation motif, commonly observed in eukaryotic signaling pathways, is predicted to display fluctuations that depend on the geometry of the system. PMID:21041672
A discrete model to study reaction-diffusion-mechanics systems.
Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V
2011-01-01
This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
A discrete model to study reaction-diffusion-mechanics systems.
Louis D Weise
Full Text Available This article introduces a discrete reaction-diffusion-mechanics (dRDM model to study the effects of deformation on reaction-diffusion (RD processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material. Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
Cumulative signal transmission in nonlinear reaction-diffusion networks.
Diego A Oyarzún
Full Text Available Quantifying signal transmission in biochemical systems is key to uncover the mechanisms that cells use to control their responses to environmental stimuli. In this work we use the time-integral of chemical species as a measure of a network's ability to cumulatively transmit signals encoded in spatiotemporal concentrations. We identify a class of nonlinear reaction-diffusion networks in which the time-integrals of some species can be computed analytically. The derived time-integrals do not require knowledge of the solution of the reaction-diffusion equation, and we provide a simple graphical test to check if a given network belongs to the proposed class. The formulae for the time-integrals reveal how the kinetic parameters shape signal transmission in a network under spatiotemporal stimuli. We use these to show that a canonical complex-formation mechanism behaves as a spatial low-pass filter, the bandwidth of which is inversely proportional to the diffusion length of the ligand.
Reaction rates for mesoscopic reaction-diffusion kinetics
Hellander, Stefan; Hellander, Andreas; Petzold, Linda
2015-02-01
The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.
Theory and application of stability for stochastic reaction diffusion systems
LUO Qi; DENG FeiQi; MAO XueRong; BAO JunDong; ZHANG YuTian
2008-01-01
So far, the Lyapunov direct method is still the moat effective technique in the study of stability for ordinary differential equations and stochastic differential equations. Due to the shortage of the corresponding Ito formula, this useful method has not been popularized in stochastic partial differential equations. The aim of this work is to try to extend the Lyapunov direct method to the Ito stochastic reaction diffusion systems and to establish the corresponding Lyapunov stability theory, including stability in probablity, asymptotic stability in probablity, end exponential stability in mean square. As the application of the obtained theorems, this paper addresses the stability of the Hopfield neural network and points out that the main results ob-tained by Holden Helge and Liao Xiaoxin et al. can be all regarded as the corollaries of the theorems presented in this paper.
Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations
Alzahrani, Hasnaa H.
2016-07-26
A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge-Kutta- Chebyshev (RKC) scheme is adjusted to integrate diffusion. Spatial operator is de- scretised by second-order finite differences on a uniform grid. The overall solution is advanced over S fractional stiff integrations, where S corresponds to the number of RKC stages. The behavior of the scheme is analyzed by applying it to three simple problems. The results show that it achieves second-order accuracy, thus, preserving the formal accuracy of the original RKC. The presented development sets the stage for future extensions, particularly, to multidimensional reacting flows with detailed chemistry.
A Lattice Boltzmann Model for Oscillating Reaction-Diffusion
Rodríguez-Romo, Suemi; Ibañez-Orozco, Oscar; Sosa-Herrera, Antonio
2016-07-01
A computational algorithm based on the lattice Boltzmann method (LBM) is proposed to model reaction-diffusion systems. In this paper, we focus on how nonlinear chemical oscillators like Belousov-Zhabotinsky (BZ) and the chlorite-iodide-malonic acid (CIMA) reactions can be modeled by LBM and provide with new insight into the nature and applications of oscillating reactions. We use Gaussian pulse initial concentrations of sulfuric acid in different places of a bidimensional reactor and nondiffusive boundary walls. We clearly show how these systems evolve to a chaotic attractor and produce specific pattern images that are portrayed in the reactions trajectory to the corresponding chaotic attractor and can be used in robotic control.
Mechanical reaction-diffusion model for bacterial population dynamics
Ngamsaad, Waipot
2015-01-01
The effect of mechanical interaction between cells on the spreading of bacterial population was investigated in one-dimensional space. A nonlinear reaction-diffusion equation has been formulated as a model for this dynamics. In this model, the bacterial cells are treated as the rod-like particles that interact, when contacting each other, through the hard-core repulsion. The repulsion introduces the exclusion process that causes the fast diffusion in bacterial population at high density. The propagation of the bacterial density as the traveling wave front in long time behavior has been analyzed. The analytical result reveals that the front speed is enhanced by the exclusion process---and its value depends on the packing fraction of cell. The numerical solutions of the model have been solved to confirm this prediction.
Turing instability in reaction-diffusion models on complex networks
Ide, Yusuke; Izuhara, Hirofumi; Machida, Takuya
2016-09-01
In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erdős-Rényi, the Watts-Strogatz, and the threshold network models. From analysis of the Laplacian matrices of graphs generated by these models, we numerically reveal that stable and unstable regions of a homogeneous steady state on the parameter space of two diffusion coefficients completely differ, depending on the network architecture. In addition, we theoretically discuss the stable and unstable regions in the cases of regular enhanced ring lattices which include regular circles, and networks generated by the threshold network model when the number of vertices is large enough.
Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations
Indekeu, Joseph O.; Smets, Ruben
2017-08-01
Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.
Multiscale Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics
Franz, Benjamin
2013-06-19
Two algorithms that combine Brownian dynami cs (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface, which partitions the domain, and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that the overlap region is required to accurately compute variances using PBD simulations. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented. © 2013 Society for Industrial and Applied Mathematics.
Multiscale reaction-diffusion algorithms: PDE-assisted Brownian dynamics
Franz, Benjamin; Chapman, S Jonathan; Erban, Radek
2012-01-01
Two algorithms that combine Brownian dynamics (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface which partitions the domain and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that to accurately compute variances using the PBD simulation requires the overlap region. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented.
Guiding brine shrimp through mazes by solving reaction diffusion equations
Singal, Krishma; Fenton, Flavio
Excitable systems driven by reaction diffusion equations have been shown to not only find solutions to mazes but to also to find the shortest path between the beginning and the end of the maze. In this talk we describe how we can use the Fitzhugh-Nagumo model, a generic model for excitable media, to solve a maze by varying the basin of attraction of its two fixed points. We demonstrate how two dimensional mazes are solved numerically using a Java Applet and then accelerated to run in real time by using graphic processors (GPUs). An application of this work is shown by guiding phototactic brine shrimp through a maze solved by the algorithm. Once the path is obtained, an Arduino directs the shrimp through the maze using lights from LEDs placed at the floor of the Maze. This method running in real time could be eventually used for guiding robots and cars through traffic.
Ohmori, Shousuke; Yamazaki, Yoshihiro
2016-01-01
Ultradiscrete equations are derived from a set of reaction-diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction-diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction-diffusion equations.
Characterization of Cocycle Attractors for Nonautonomous Reaction-Diffusion Equations
Cardoso, C. A.; Langa, J. A.; Obaya, R.
In this paper, we describe in detail the global and cocycle attractors related to nonautonomous scalar differential equations with diffusion. In particular, we investigate reaction-diffusion equations with almost-periodic coefficients. The associated semiflows are strongly monotone which allow us to give a full characterization of the cocycle attractor. We prove that, when the upper Lyapunov exponent associated to the linear part of the equations is positive, the flow is persistent in the positive cone, and we study the stability and the set of continuity points of the section of each minimal set in the global attractor for the skew product semiflow. We illustrate our result with some nontrivial examples showing the richness of the dynamics on this attractor, which in some situations shows internal chaotic dynamics in the Li-Yorke sense. We also include the sublinear and concave cases in order to go further in the characterization of the attractors, including, for instance, a nonautonomous version of the Chafee-Infante equation. In this last case we can show exponentially forward attraction to the cocycle (pullback) attractors in the positive cone of solutions.
Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces.
Dhillon, Daljit Singh J; Milinkovitch, Michel C; Zwicker, Matthias
2017-04-01
In this paper, we present computational techniques to investigate the effect of surface geometry on biological pattern formation. In particular, we study two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD systems and extend them to operate on large-scale meshes for arbitrary surfaces. In particular, we use spectral techniques for a linear stability analysis to characterise and directly compose patterns emerging from homogeneities. We develop an implementation using surface finite element methods and a numerical eigenanalysis of the Laplace-Beltrami operator on surface meshes. In addition, we describe a technique to explore solutions of the nonlinear RD equations using numerical continuation. Here, we present a multiresolution approach that allows us to trace solution branches of the nonlinear equations efficiently even for large-scale meshes. Finally, we demonstrate the working of our framework for two RD systems with applications in biological pattern formation: a Brusselator model that has been used to model pattern development on growing plant tips, and a chemotactic model for the formation of skin pigmentation patterns. While these models have been used previously on simple geometries, our framework allows us to study the impact of arbitrary geometries on emerging patterns.
A Reaction-Diffusion Model of Cholinergic Retinal Waves
Lansdell, Benjamin; Ford, Kevin; Kutz, J. Nathan
2014-01-01
Prior to receiving visual stimuli, spontaneous, correlated activity in the retina, called retinal waves, drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh) manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs), whose dense, recurrent connectivity then propagates this activity laterally. Their inter-wave interval and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In addition to simulation, we are thus able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how parameters such as the spontaneous activation rate and sAHP refractory period contribute to critical wave size variability. PMID:25474327
Stochastic flows, reaction-diffusion processes, and morphogenesis
Kozak, J.J.; Hatlee, M.D.; Musho, M.K.; Politowicz, P.A.; Walsh, C.A.
1983-02-01
Recently, an exact procedure has been introduced (C. A. Walsh and J. J. Kozak, Phys. Rev. Lett.. 47: 1500 (1981)) for calculating the expected walk length
Reaction Diffusion Voronoi Diagrams: From Sensors Data to Computing
Alejandro Vázquez-Otero
2015-05-01
Full Text Available In this paper, a new method to solve computational problems using reaction diffusion (RD systems is presented. The novelty relies on the use of a model configuration that tailors its spatiotemporal dynamics to develop Voronoi diagrams (VD as a part of the system’s natural evolution. The proposed framework is deployed in a solution of related robotic problems, where the generalized VD are used to identify topological places in a grid map of the environment that is created from sensor measurements. The ability of the RD-based computation to integrate external information, like a grid map representing the environment in the model computational grid, permits a direct integration of sensor data into the model dynamics. The experimental results indicate that this method exhibits significantly less sensitivity to noisy data than the standard algorithms for determining VD in a grid. In addition, previous drawbacks of the computational algorithms based on RD models, like the generation of volatile solutions by means of excitable waves, are now overcome by final stable states.
Accelerated Parallel Texture Optimization
Hao-Da Huang; Xin Tong; Wen-Cheng Wang
2007-01-01
Texture optimization is a texture synthesis method that can efficiently reproduce various features of exemplar textures. However, its slow synthesis speed limits its usage in many interactive or real time applications. In this paper, we propose a parallel texture optimization algorithm to run on GPUs. In our algorithm, k-coherence search and principle component analysis (PCA) are used for hardware acceleration, and two acceleration techniques are further developed to speed up our GPU-based texture optimization. With a reasonable precomputation cost, the online synthesis speed of our algorithm is 4000+ times faster than that of the original texture optimization algorithm and thus our algorithm is capable of interactive applications. The advantages of the new scheme are demonstrated by applying it to interactive editing of flow-guided synthesis.
Da Costa, Jean-Pierre; Germain, Christian
2010-01-01
We propose a novel parametric approach which aims at the synthesis of anisotropic solid textures from the analysis of a single 2D exemplar. This approach is an extension of the pyramidal scheme of Portilla and Simoncelli. It proceeds in three main steps: first, a 2D analysis of the example is performed which produces a set of reference statistics. Then, 3D reference statistics are inferred from the 2D ones thanks to specific anisotropy assumptions. The final step aims at the synthesis itself: the 3D target statistics are imposed on a random 3D block according to a specific multi resolution pyramidal scheme. The approach is applied to the synthesis of solid textures representative of the structure of dense pre-graphitic carbons. The samples are lattice fringe images obtained by high resolution transmission electronic microscopy (HRTEM). HRTEM samples with increasing structural order are used for the experimental evaluation. The produced solid textures exhibit anisotropy properties similar to those observed in the HRTEM samples. Such an approach can easily be extended to any 3D anisotropic structures showing stacks of layers such as wood grain images, seismic data, etc.
Low Temperature Synthesis of Li2SiO3: Effect on Its Morphological and Textural Properties
Georgina Mondragón-Gutiérrez
2008-01-01
Full Text Available Synthesis, at low temperature, of Li2SiO3 was investigated using different Li : Si molar ratios and urea, which was used as template. This new synthesis was performed in order to look for different textural and morphological properties than those obtained usually by conventional methods in this kind of ceramics. XRD and SEM analyses showed that Li2SiO3 was obtained pure and with ceramic particle morphology of hollow spheres of 2–6 μm. TEM analysis showed that those spheres were composed by needle-like particles crosslinked among them. This morphology provided a high surface area, probed by N2 adsorption. Therefore, this method of synthesis may be used to obtain other similar ceramics and test them in different applications.
SDDEs limits solutions to sublinear reaction-diffusion SPDEs
Hassan Allouba
2003-11-01
Full Text Available We start by introducing a new definition of solutions to heat-based SPDEs driven by space-time white noise: SDDEs (stochastic differential-difference equations limits solutions. In contrast to the standard direct definition of SPDEs solutions; this new notion, which builds on and refines our SDDEs approach to SPDEs from earlier work, is entirely based on the approximating SDDEs. It is applicable to, and gives a multiscale view of, a variety of SPDEs. We extend this approach in related work to other heat-based SPDEs (Burgers, Allen-Cahn, and others and to the difficult case of SPDEs with multi-dimensional spacial variable. We focus here on one-spacial-dimensional reaction-diffusion SPDEs; and we prove the existence of a SDDEs limit solution to these equations under less-than-Lipschitz conditions on the drift and the diffusion coefficients, thus extending our earlier SDDEs work to the nonzero drift case. The regularity of this solution is obtained as a by-product of the existence estimates. The uniqueness in law of our SPDEs follows, for a large class of such drifts/diffusions, as a simple extension of our recent Allen-Cahn uniqueness result. We also examine briefly, through order parameters $epsilon_1$ and $epsilon_2$ multiplied by the Laplacian and the noise, the effect of letting $epsilon_1,epsilon_2o 0$ at different speeds. More precisely, it is shown that the ratio $epsilon_2/epsilon_1^{1/4}$ determines the behavior as $epsilon_1,epsilon_2o 0$.
A reaction-diffusion model of human brain development.
Julien Lefèvre
2010-04-01
Full Text Available Cortical folding exhibits both reproducibility and variability in the geometry and topology of its patterns. These two properties are obviously the result of the brain development that goes through local cellular and molecular interactions which have important consequences on the global shape of the cortex. Hypotheses to explain the convoluted aspect of the brain are still intensively debated and do not focus necessarily on the variability of folds. Here we propose a phenomenological model based on reaction-diffusion mechanisms involving Turing morphogens that are responsible for the differential growth of two types of areas, sulci (bottom of folds and gyri (top of folds. We use a finite element approach of our model that is able to compute the evolution of morphogens on any kind of surface and to deform it through an iterative process. Our model mimics the progressive folding of the cortical surface along foetal development. Moreover it reveals patterns of reproducibility when we look at several realizations of the model from a noisy initial condition. However this reproducibility must be tempered by the fact that a same fold engendered by the model can have different topological properties, in one or several parts. These two results on the reproducibility and variability of the model echo the sulcal roots theory that postulates the existence of anatomical entities around which the folding organizes itself. These sulcal roots would correspond to initial conditions in our model. Last but not least, the parameters of our model are able to produce different kinds of patterns that can be linked to developmental pathologies such as polymicrogyria and lissencephaly. The main significance of our model is that it proposes a first approach to the issue of reproducibility and variability of the cortical folding.
A Lagrangian particle method for reaction-diffusion systems on deforming surfaces.
Bergdorf, Michael; Sbalzarini, Ivo F; Koumoutsakos, Petros
2010-11-01
Reaction-diffusion processes on complex deforming surfaces are fundamental to a number of biological processes ranging from embryonic development to cancer tumor growth and angiogenesis. The simulation of these processes using continuum reaction-diffusion models requires computational methods capable of accurately tracking the geometric deformations and discretizing on them the governing equations. We employ a Lagrangian level-set formulation to capture the deformation of the geometry and use an embedding formulation and an adaptive particle method to discretize both the level-set equations and the corresponding reaction-diffusion. We validate the proposed method and discuss its advantages and drawbacks through simulations of reaction-diffusion equations on complex and deforming geometries.
A CLASS OF REACTION-DIFFUSION EQUATIONS WITH HYSTERESIS DIFFERENTIAL OPERATOR
XuLongfeng
2002-01-01
In this paper, the classical and weak derivatives with respect to spatial variable of a class of hysteresis functional are discussed. Some conclusions about solutions of a class of reaction-diffusion equations with hysteresis differential operator are given.
The First Integral Method to Study a Class of Reaction-Diffusion Equations
KE Yun-Quan; YU Jun
2005-01-01
In this letter, a class of reaction-diffusion equations, which arise in chemical reaction or ecology and other fields of physics, are investigated. A more general analytical solution of the equation is obtained by using the first integral method.
Nonlinear predator-prey singularly perturbed Robin Problems for reaction diffusion systems
莫嘉琪; 韩祥临
2003-01-01
The nonlinear predator-prey reaction diffusion systems for singularly perturbed Robin Problems are considered. Under suitable conditions, the theory of differential inequalities can be used to study the asymptotic behavior of the solution for initial boundary value problems.
莫嘉琪
2003-01-01
The nonlinear predator-prey singularly perturbed Robin initial boundary value problems for reaction diffusion systems were considered. Under suitable conditions, using theory of differential inequalities the existence and asymptotic behavior of solution for initial boundary value problems were studied.
Jia-qi Mo; Wan-tao Lin
2006-01-01
In this paper the singularly perturbed initial boundary value problems for the nonlocal reaction diffusion system are considered. Using the iteration method and the comparison theorem, the existence and its asymptotic behavior of the solution for the problem are studied.
An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems.
Chiu, Chichia; Yu, Jui-Ling
2007-04-01
Reaction-diffusion-chemotaxis systems have proven to be fairly accurate mathematical models for many pattern formation problems in chemistry and biology. These systems are important for computer simulations of patterns, parameter estimations as well as analysis of the biological systems. To solve reaction-diffusion-chemotaxis systems, efficient and reliable numerical algorithms are essential for pattern generations. In this paper, a general reaction-diffusion-chemotaxis system is considered for specific numerical issues of pattern simulations. We propose a fully explicit discretization combined with a variable optimal time step strategy for solving the reaction-diffusion-chemotaxis system. Theorems about stability and convergence of the algorithm are given to show that the algorithm is highly stable and efficient. Numerical experiment results on a model problem are given for comparison with other numerical methods. Simulations on two real biological experiments will also be shown.
THE CORNER LAYER SOLUTION TO ROBIN PROBLEM FOR REACTION DIFFUSION EQUATION
无
2012-01-01
A class of Robin boundary value problem for reaction diffusion equation is considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of the corner layer solution to the initial boundary value problem are studied.
A CLASS OF SINGULARLY PERTURBED INITIAL BOUNDARY PROBLEM FOR REACTION DIFFUSION EQUATION
Xie Feng
2003-01-01
The singularly perturbed initial boundary value problem for a class of reaction diffusion equation isconsidered. Under appropriate conditions, the existence-uniqueness and the asymptotic behavior of the solu-tion are showed by using the fixed-point theorem.
A reaction diffusion model of pattern formation in clustering of adatoms on silicon surfaces
Trilochan Bagarti
2012-12-01
Full Text Available We study a reaction diffusion model which describes the formation of patterns on surfaces having defects. Through this model, the primary goal is to study the growth process of Ge on Si surface. We consider a two species reaction diffusion process where the reacting species are assumed to diffuse on the two dimensional surface with first order interconversion reaction occuring at various defect sites which we call reaction centers. Two models of defects, namely a ring defect and a point defect are considered separately. As reaction centers are assumed to be strongly localized in space, the proposed reaction-diffusion model is found to be exactly solvable. We use Green's function method to study the dynamics of reaction diffusion processes. Further we explore this model through Monte Carlo (MC simulations to study the growth processes in the presence of a large number of defects. The first passage time statistics has been studied numerically.
Spreading speeds and traveling waves for non-cooperative reaction-diffusion systems
Wang, Haiyan
2010-01-01
Much has been studied on the spreading speed and traveling wave solutions for cooperative reaction-diffusion systems. In this paper, we shall establish the spreading speed for a large class of non-cooperative reaction-diffusion systems and characterize the spreading speed as the slowest speed of a family of non-constant traveling wave solutions. As an application, our results are applied to a partially cooperative system describing interactions between ungulates and grass.
AUTO-DARBOUX TRANSFORMATION AND EXACT SOLUTIONS OF THE BRUSSELATOR REACTION DIFFUSION MODEL
闫振亚; 张鸿庆
2001-01-01
Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known.Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine- cosine method, more exact solutions are found which contain soliton solutions.
Cross-diffusional effect in a telegraph reaction diffusion Lotka-Volterra two competitive system
Abdusalam, H.A E-mail: hosny@operamail.com; Fahmy, E.S
2003-10-01
It is known now that, telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion in several branches of sciences. Telegraph reaction diffusion Lotka-Volterra two competitive system is considered. We observed that this system can give rise to diffusive instability only in the presence of cross-diffusion. Local and global stability analysis in the cross-diffusional effect are studied by considering suitable Lyapunov functional.
A practical guide to stochastic simulations of reaction-diffusion processes
Erban, Radek; Chapman, Jonathan; Maini, Philip
2007-01-01
A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the classical Gillespie algorithm for the stochastic modelling of chemical reactions. Then stochastic algorithms for modelling molecular diffusion are given. Finally, basic stochastic reaction-diffusion methods are presented. The connections between stochastic simul...
Synthesis and textural properties of unsupported and supported rutile (TiO2) membranes
Kumar, Krishnankutty-Nair P.; Keizer, Klaas; Burggraaf, Anthonie J.; Okubo, Tatsuya; Nagamoto, Hidetoshi
1993-01-01
Two approaches were postulated for improving the stability of porous texture of titania membranes: (1) retarding the phase transformation and grain growth; (2) avoiding the phase transformation. Based on the second approach, rutile membranes were made directly from a rutile sol, prepared by the prec
Synthesis of chiral networks for polymer stabilized cholesteric texture (PSCT) displays
Rego, J.A.; Cahill, P.A.
1997-03-01
New mono- and di-functional polymerizable twist agents for formation of polymer stabilized cholesteric texture liquid crystal displays have been synthesized. Degree of crosslinking has a pronounced effect on electrooptic response of the cell and the stability of oriented states.
Diffusion synthesis of textured YBa2Cu3O(7-delta) ceramic
Kalanda, N. A.; Shambalev, V. N.; Pan'kov, V. V.
1991-07-01
A method is described whereby a textured high-temperature superconductor ceramic of the system Y-Ba-Cu-O is synthesized by the diffusion method using various mixtures of Y-Ba-Cu-O and Ba-Cu-O systems. The basal plane of the perovskite structure is shown to be formed in the direction of the diffusion flow. Critical current densities in excess of 1000 A/sq cm at 77 K have been demonstrated for the best specimens.
Wang Tiles Texture Synthesis utilizing Bee Evolutionary Genetic Algorithm%基于蜜蜂进化型遗传算法的Wang tiles纹理合成
孙涛; 徐蔚鸿
2012-01-01
In texture synthesis process,the thesis introduces Bee Evolution Genetic Algorithm,and uses the BEGA to realize global optimization of the sample texture selection,and solve diamond juncture problem in the synthesized textures.Therefore,and the quality of Tile sets is improved,and the synthesis speed is grown up.Through the experiment,make the ideal synthetic effect.%在基于Wang Tiles的纹理合成中引入蜜蜂进化型遗传算法,用它来实现样本纹理块选择的全局优化,解决纹理合成出现的菱形接缝问题,提高了Wang Tile集的质量,加快了合成速度。通过实验得到了理想的合成效果。
Control of DNA replication by anomalous reaction-diffusion kinetics
Bechhoefer, John; Gauthier, Michel
2010-03-01
DNA replication requires two distinct processes: the initiation of pre-licensed replication origins and the propagation of replication forks away from the fired origins. Experiments indicate that these origins are triggered over the whole genome at a rate I(t) (the number of initiations per unreplicated length per time) that increases throughout most of the synthesis (S) phase, before rapidly decreasing to zero at the end of the replication process. We propose a simple model for the control of DNA replication in which the rate of initiation of replication origins is controlled by protein-DNA interactions. Analyzing recent data from Xenopus frog embryos, we find that the initiation rate is reaction limited until nearly the end of replication, when it becomes diffusion limited. Initiation of origins is suppressed when the diffusion-limited search time dominates. To fit the experimental data, we find that the interaction between DNA and the rate-limiting protein must be subdiffusive.
Cherniha, Roman
2017-01-01
This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception,...
Cox process representation and inference for stochastic reaction-diffusion processes
Schnoerr, David; Grima, Ramon; Sanguinetti, Guido
2016-05-01
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction-diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.
A Domain Decomposition Method for Time Fractional Reaction-Diffusion Equation
Chunye Gong
2014-01-01
Full Text Available The computational complexity of one-dimensional time fractional reaction-diffusion equation is O(N2M compared with O(NM for classical integer reaction-diffusion equation. Parallel computing is used to overcome this challenge. Domain decomposition method (DDM embodies large potential for parallelization of the numerical solution for fractional equations and serves as a basis for distributed, parallel computations. A domain decomposition algorithm for time fractional reaction-diffusion equation with implicit finite difference method is proposed. The domain decomposition algorithm keeps the same parallelism but needs much fewer iterations, compared with Jacobi iteration in each time step. Numerical experiments are used to verify the efficiency of the obtained algorithm.
Simulation of reaction-diffusion processes in three dimensions using CUDA
Molnar, Ferenc; Meszaros, Robert; Lagzi, Istvan
2010-01-01
Numerical solution of reaction-diffusion equations in three dimensions is one of the most challenging applied mathematical problems. Since these simulations are very time consuming, any ideas and strategies aiming at the reduction of CPU time are important topics of research. A general and robust idea is the parallelization of source codes/programs. Recently, the technological development of graphics hardware created a possibility to use desktop video cards to solve numerically intensive problems. We present a powerful parallel computing framework to solve reaction-diffusion equations numerically using the Graphics Processing Units (GPUs) with CUDA. Four different reaction-diffusion problems, (i) diffusion of chemically inert compound, (ii) Turing pattern formation, (iii) phase separation in the wake of a moving diffusion front and (iv) air pollution dispersion were solved, and additionally both the Shared method and the Moving Tiles method were tested. Our results show that parallel implementation achieves t...
Gan, Qintao; Lv, Tianshi; Fu, Zhenhua
2016-04-01
In this paper, the synchronization problem for a class of generalized neural networks with time-varying delays and reaction-diffusion terms is investigated concerning Neumann boundary conditions in terms of p-norm. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. By establishing a new inequality, some simple and useful conditions are obtained analytically to guarantee the global exponential synchronization of the addressed neural networks under the periodically intermittent control. According to the theoretical results, the influences of diffusion coefficients, diffusion space, and control rate on synchronization are analyzed. Finally, the feasibility and effectiveness of the proposed methods are shown by simulation examples, and by choosing different diffusion coefficients, diffusion spaces, and control rates, different controlled synchronization states can be obtained.
A Series Solution of the Cauchy Problem for Turing Reaction-diffusion Model
L. Päivärinta
2011-12-01
Full Text Available In this paper, the series pattern solution of the Cauchy problem for Turing reaction-diffusion model is obtained by using the homotopy analysis method (HAM. Turing reaction-diffusion model is nonlinear reaction-diffusion system which usually has power-law nonlinearities or may be rewritten in the form of power-law nonlinearities. Using the HAM, it is possible to find the exact solution or an approximate solution of the problem. This technique provides a series of functions which converges rapidly to the exact solution of the problem. The efficiency of the approach will be shown by applying the procedure on two problems. Furthermore, the so-called homotopy-Pade technique (HPT is applied to enlarge the convergence region and rate of solution series given by the HAM.
Sample Duplication Method for Monte Carlo Simulation of Large Reaction-Diffusion System
张红东; 陆建明; 杨玉良
1994-01-01
The sample duplication method for the Monte Carlo simulation of large reaction-diffusion system is proposed in this paper. It is proved that the sample duplication method will effectively raise the efficiency and statistical precision of the simulation without changing the kinetic behaviour of the reaction-diffusion system and the critical condition for the bifurcation of the steady-states. The method has been applied to the simulation of spatial and time dissipative structure of Brusselator under the Dirichlet boundary condition. The results presented in this paper definitely show that the sample duplication method provides a very efficient way to sol-’e the master equation of large reaction-diffusion system. For the case of two-dimensional system, it is found that the computation time is reduced at least by a factor of two orders of magnitude compared to the algorithm reported in literature.
Realistic boundary conditions for stochastic simulations of reaction-diffusion processes
Erban, R; Erban, Radek
2006-01-01
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic partial-differential equations or stochastic simulation algorithms. The latter provide a more detailed and precise picture, and several stochastic simulation algorithms have been proposed in recent years. Such models typically give the same description of the reaction-diffusion processes far from the boundary of the simulated domain, but the behaviour close to a reactive boundary (e.g. a membrane with receptors) is unfortunately model-dependent. In this paper, we study four different approaches to stochastic modelling of reaction-diffusion problems and show the correct choice of the boundary condition for each model. The reactive boundary is treated as partially reflective, which means that some molecules hitting the boundary are adsorbed (e.g. bound to the receptor) and some molecul...
Finite volume element method for analysis of unsteady reaction-diffusion problems
Sutthisak Phongthanapanich; Pramote Dechaumphai
2009-01-01
A finite volume element method is developed for analyzing unsteady scalar reaction--diffusion problems in two dimensions. The method combines the concepts that are employed in the finite volume and the finite element method together. The finite volume method is used to discretize the unsteady reaction--diffusion equation, while the finite element method is applied to estimate the gradient quantities at cell faces. Robustness and efficiency of the combined method have been evaluated on uniform rectangular grids by using available numerical solutions of the two-dimensional reaction-diffusion problems. The numerical solutions demonstrate that the combined method is stable and can provide accurate solution without spurious oscillation along the highgradient boundary layers.
Chen, Weiliang
2016-01-01
Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of simulated models and morphologies have exceeded the capacity of any serial implementation. This led to development of parallel solutions that benefit from the boost in performance of modern large-scale supercomputers. In this paper, we describe an MPI-based, parallel Operator-Splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its usage in real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies. Simulation results indicate that our implementation is capable of achieving super-linear speedup for balanced loading simulations with reasonable molecul...
MAXIMAL ATTRACTORS OF CLASSICAL SOLUTIONS FOR REACTION DIFFUSION EQUATIONS WITH DISPERSION
Li Yanling; Ma Yicheng
2005-01-01
The paper first deals with the existence of the maximal attractor of classical solution for reaction diffusion equation with dispersion, and gives the sup-norm estimate for the attractor. This estimate is optimal for the attractor under Neumann boundary condition. Next, the same problem is discussed for reaction diffusion system with uniformly contracting rectangle, and it reveals that the maximal attractor of classical solution for such system in the whole space is only necessary to be established in some invariant region.Finally, a few examples of application are given.
Instability and pattern formation in reaction-diffusion systems: a higher order analysis.
Riaz, Syed Shahed; Sharma, Rahul; Bhattacharyya, S P; Ray, D S
2007-08-14
We analyze the condition for instability and pattern formation in reaction-diffusion systems beyond the usual linear regime. The approach is based on taking into account perturbations of higher orders. Our analysis reveals that nonlinearity present in the system can be instrumental in determining the stability of a system, even to the extent of destabilizing one in a linearly stable parameter regime. The analysis is also successful to account for the observed effect of additive noise in modifying the instability threshold of a system. The analytical study is corroborated by numerical simulation in a standard reaction-diffusion system.
Modeling cardiac mechano-electrical feedback using reaction-diffusion-mechanics systems
Keldermann, R. H.; Nash, M. P.; Panfilov, A. V.
2009-06-01
In many practically important cases, wave propagation described by the reaction-diffusion equation initiates deformation of the medium. Mathematically, such processes are described by coupled reaction-diffusion-mechanics (RDM) systems. RDM systems were recently used to study the effects of deformation on wave propagation in cardiac tissue, so called mechano-electrical feedback (MEF). In this article, we review the results of some of these studies, in particular those relating to the effects of deformation on pacemaker activity and spiral wave dynamics in the heart. We also provide brief descriptions of the numerical methods used, and the underlying cardiac physiology.
Anne Galarneau
2016-04-01
Full Text Available Silica monoliths featuring either mesopores or flow-through macropores and mesopores in their skeleton are prepared by combining spinodal phase separation and sol-gel condensation. The macroporous network is first generated by phase separation in acidic medium in the presence of polyethyleneoxides while mesoporosity is engineered in a second step in alkaline medium, possibly in the presence of alkylammonium cations as surfactants. The mesoporous monoliths, also referred as aerogels, are obtained in the presence of alkylpolyethylene oxides in acidic medium without the use of supercritical drying. The impact of the experimental conditions on pore architecture of the monoliths regarding the shape, the ordering, the size and the connectivity of the mesopores is comprehensively discussed based on a critical appraisal of the different models used for textural analysis.
Synthesis of Nanosilver Particles in the Texture of Bank Notes to Produce Antibacterial Effect
Lari, Mohammad Hossein Asadi; Esmaili, Vahid; Naghavi, Seyed Mohammad Ebrahim; Kimiaghalam, Amir Hossein; Sharifaskari, Emadaldin
Silver particles show antibacterial and antiseptic properties at the nanoscale. Such properties result from an alteration in the binding capacity of silver atoms in bits of less than 6.5nm which enables them to kill harmful organisms. Silver nanoparticles are now the most broadly used agents in the area of nanotechnology after carbon nanotubes. Given that currency bills are one of the major sources of bacterial disseminations and their contamination has recently been nominated as a critical factor in gastrointestinal infections and possibly colon cancers, here we propose a new method for producing antibacterial bank notes by using silver nanoparticles. Older bank notes are sprayed with acetone to clean the surface. The bank note is put into a petri-dish containing a solution of silver nitrate and ammonia so that it is impregnated. The bank notes are then reduced with the formaldehyde gas, which penetrates its texture and produces silver nanoparticles in the cellulose matrix. The side products of the reactions are quickly dried off and the procedure ends with the drying of the bank note. The transmission electron microscope (TEM) images confirmed the nanoscale size range for the formed particles while spectroscopy methods, such as XRD, provided proof for the metallic nature of the particles. Bacterial challenge tests then showed that no colonies of the three tested bacterium (Escherichia coli, Staphylococcus aureus and Pseudomonas aeruginosa survived on the sample after a 72h incubation period. This study has provided a method for synthesizing silver NPs directly into the texture of fabrics and textiles (like that of bank notes) which can result in lower production costs, making the use of silver NPs economically beneficial. The method, specifically works on the fabric of bank notes, suggesting a method to tackle the transmission of bacteria through bank notes. Moreover, this study is a testament to the strong antibacterial nature of even low concentrations of
Convective wave front locking for a reaction-diffusion system in a conical flow reactor
Kuptsov, P.V.; Kuznetsov, S.P.; Knudsen, Carsten
2002-01-01
We consider reaction-diffusion instabilities in a flow reactor whose cross-section slowly expands with increasing longitudinal coordinate (cone shaped reactor). Due to deceleration of the flow in this reactor, the instability is convective near the inlet to the reactor and absolute at the downstr...
The constructive technique and its application in solving a nonlinear reaction diffusion equation
Lai Shao-Yong; Guo Yun-Xi; Qing Yin; Wu Yong-Hong
2009-01-01
A mathematical technique based on the consideration of a nonlinear partial differential equation together with an additional condition in the form of an ordinary differential equation is employed to study a nonlinear reaction diffusion equation which describes a real process in physics and in chemistry. Several exact solutions for the equation are acquired under certain circumstances.
Weakly nonlinear dynamics in reaction-diffusion systems with Levy flights
Nec, Y; Nepomnyashchy, A A [Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000 (Israel); Golovin, A A [Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208 (United States)], E-mail: flyby@techunix.technion.ac.il
2008-12-15
Reaction-diffusion equations with a fractional Laplacian are reduced near a long wave Hopf bifurcation. The obtained amplitude equation is shown to be the complex Ginzburg-Landau equation with a fractional Laplacian. Some of the properties of the normal complex Ginzburg-Landau equation are generalized for the fractional analogue. In particular, an analogue of the Kuramoto-Sivashinsky equation is derived.
Asymptotic Speed of Wave Propagation for A Discrete Reaction-Diffusion Equation
Xiu-xiang Liu; Pei-xuan Weng
2006-01-01
We deal with asymptotic speed of wave propagation for a discrete reaction-diffusion equation. We find the minimal wave speed c* from the characteristic equation and show that c* is just the asymptotic speed of wave propagation. The isotropic property and the existence of solution of the initial value problem for the given equation are also discussed.
Simulating Some Complex Phenomena in Hydrothermal Ore-Forming Processes by Reaction-Diffusion CNN
Xu Deyi; Yu Chongwen; Bao Zhengyu
2003-01-01
Complexity phenomena like dynamic and static patterns, order from disorder, chaos and catastrophe were simulated by the application of 2-D reaction-diffusion CNN of two state variables and two diffusion coefficients transformed from Zhabotinksii model. They revealed somehow the mechanism of hydrothermal ore-forming processes, and answered several questions about the onset of ore forming.
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
Travelling Wave Solutions in Delayed Reaction Diffusion Systems with Partial Monotonicity
Jian-hua Huang; Xing-fu Zou
2006-01-01
This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of "desirable pair of upper-lower solutions", through which a subset can be constructed. We then apply the Schauder's fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts.
LONG-TIME BEHAVIOR OF A CLASS OF REACTION DIFFUSION EQUATIONS WITH TIME DELAYS
无
2006-01-01
The present paper devotes to the long-time behavior of a class of reaction diffusion equations with delays under Dirichlet boundary conditions. The stability and global attractability for the zero solution are provided, and the existence, stability and attractability for the positive stationary solution are also obtained.
Spreading Speed for a Periodic Reaction-diffusion Model with Nonmonotone Birth Function
HUANG Ye-hui; WENG Pei-xuan
2012-01-01
A reaction-diffusion model for a single spccies with age structure and nonlocal reaction for periodic time t is derived.Some results about the model with monotone birth function are firstly introduced,and then by constructing two auxiliary equations and squeezing method,the spreading speed for the system with nonmonotone birth function is obtained.
Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case
Bedeaux, D.; Ortiz de Zárate, J.M.; Pagonabarraga, I.; Sengers, J.V.; Kjelstrup, S.
2011-01-01
In this paper, we consider a simple reaction-diffusion system, namely, a binary fluid mixture with an association-dissociation reaction between two species. We study fluctuations at hydrodynamic spatiotemporal scales when this mixture is driven out of equilibrium by the presence of a temperature gra
Existence of global solutions to reaction-diffusion systems via a Lyapunov functional
Said Kouachi
2001-10-01
Full Text Available The purpose of this paper is to construct polynomial functionals (according to solutions of the coupled reaction-diffusion equations which give $L^{p}$-bounds for solutions. When the reaction terms are sufficiently regular, using the well known regularizing effect, we deduce the existence of global solutions. These functionals are obtained independently of work done by Malham and Xin [11].
Konukoglu, Ender; Clatz, Olivier; Menze, Bjoern H; Stieltjes, Bram; Weber, Marc-André; Mandonnet, Emmanuel; Delingette, Hervé; Ayache, Nicholas
2010-01-01
Reaction-diffusion based tumor growth models have been widely used in the literature for modeling the growth of brain gliomas. Lately, recent models have started integrating medical images in their formulation. Including different tissue types, geometry of the brain and the directions of white matter fiber tracts improved the spatial accuracy of reaction-diffusion models. The adaptation of the general model to the specific patient cases on the other hand has not been studied thoroughly yet. In this paper, we address this adaptation. We propose a parameter estimation method for reaction-diffusion tumor growth models using time series of medical images. This method estimates the patient specific parameters of the model using the images of the patient taken at successive time instances. The proposed method formulates the evolution of the tumor delineation visible in the images based on the reaction-diffusion dynamics; therefore, it remains consistent with the information available. We perform thorough analysis of the method using synthetic tumors and show important couplings between parameters of the reaction-diffusion model. We show that several parameters can be uniquely identified in the case of fixing one parameter, namely the proliferation rate of tumor cells. Moreover, regardless of the value the proliferation rate is fixed to, the speed of growth of the tumor can be estimated in terms of the model parameters with accuracy. We also show that using the model-based speed, we can simulate the evolution of the tumor for the specific patient case. Finally, we apply our method to two real cases and show promising preliminary results.
Surfactantless synthesis and textural properties of self-assembled mesoporous SnO{sub 2}
Velasquez, Celso [Departamento de QuImica, Universidad Autonoma Metropolitana-Iztapalapa, PO Box 55-534, Mexico, DF 09340 (Mexico); Ojeda, MarIa Luisa [Instituto de QuImica, UNAM, Circuito Exterior, Ciudad Universitaria, CP 04510, Mexico, DF (Mexico); Campero, Antonio [Departamento de QuImica, Universidad Autonoma Metropolitana-Iztapalapa, PO Box 55-534, Mexico, DF 09340 (Mexico); Esparza, Juan Marcos [Departamento de QuImica, Universidad Autonoma Metropolitana-Iztapalapa, PO Box 55-534, Mexico, DF 09340 (Mexico); Rojas, Fernando [Departamento de QuImica, Universidad Autonoma Metropolitana-Iztapalapa, PO Box 55-534, Mexico, DF 09340 (Mexico)
2006-07-28
Ordered surfactantless self-assembled, mesoporous SnO{sub 2} adsorbents, consisting of tubular voids of nanometric sizes, are prepared by the sol-gel processing of tin (IV) tetra-tert-amyloxide, Sn(OAm{sup t}){sub 4}, whose molecules have been previously chelated with acetylacetone in the absence of water, to modulate their reactivity and to promote an incipient self-assembling of -O-Sn-O oligomeric species; ultimately, the necessary amount of water to induce the hydrolysis-condensation reactions is added to this aged sol, then producing tubular pore templates within the SnO{sub 2} xerogel network. A collection of mesoporous SnO{sub 2} xerogels of assorted structural properties has been obtained after calcination in air of precursory gels proceeding from an aged mixture of Sn(OAm{sup t}){sub 4} and acetylacetone at temperatures in the range 200-1000 deg. C. N{sub 2} sorption isotherms measured on these SnO{sub 2} solids evidence mesoporous structures of diverse textural characteristics (i.e. pore widths of 3-50 nm and surface areas of 10-140 m{sup 2} g{sup -1}) in which voids virtually behave as if they are independent cylindrical pores during capillary condensation and evaporation.
Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach
Kim, Changho; Nonaka, Andy; Bell, John B.; Garcia, Alejandro L.; Donev, Aleksandar
2017-03-01
We develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuating hydrodynamics (FHD). For hydrodynamic systems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poisson fluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules, to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamic fluctuations to the formation of a two
Yochelis, Arik; Bar-On, Tomer; Gov, Nir S.
2016-04-01
Unconventional myosins belong to a class of molecular motors that walk processively inside cellular protrusions towards the tips, on top of actin filament. Surprisingly, in addition, they also form retrograde moving self-organized aggregates. The qualitative properties of these aggregates are recapitulated by a mass conserving reaction-diffusion-advection model and admit two distinct families of modes: traveling waves and pulse trains. Unlike the traveling waves that are generated by a linear instability, pulses are nonlinear structures that propagate on top of linearly stable uniform backgrounds. Asymptotic analysis of isolated pulses via a simplified reaction-diffusion-advection variant on large periodic domains, allows to draw qualitative trends for pulse properties, such as the amplitude, width, and propagation speed. The results agree well with numerical integrations and are related to available empirical observations.
Dichotomous-noise-induced pattern formation in a reaction-diffusion system
Das, Debojyoti; Ray, Deb Shankar
2013-06-01
We consider a generic reaction-diffusion system in which one of the parameters is subjected to dichotomous noise by controlling the flow of one of the reacting species in a continuous-flow-stirred-tank reactor (CSTR) -membrane reactor. The linear stability analysis in an extended phase space is carried out by invoking Furutzu-Novikov procedure for exponentially correlated multiplicative noise to derive the instability condition in the plane of the noise parameters (correlation time and strength of the noise). We demonstrate that depending on the correlation time an optimal strength of noise governs the self-organization. Our theoretical analysis is corroborated by numerical simulations on pattern formation in a chlorine-dioxide-iodine-malonic acid reaction-diffusion system.
An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems
Padgett, Jill M. A.; Ilie, Silvana, E-mail: silvana@ryerson.ca [Department of Mathematics, Ryerson University, Toronto, ON, M5B 2K3 (Canada)
2016-03-15
Stochastic modelling is critical for studying many biochemical processes in a cell, in particular when some reacting species have low population numbers. For many such cellular processes the spatial distribution of the molecular species plays a key role. The evolution of spatially heterogeneous biochemical systems with some species in low amounts is accurately described by the mesoscopic model of the Reaction-Diffusion Master Equation. The Inhomogeneous Stochastic Simulation Algorithm provides an exact strategy to numerically solve this model, but it is computationally very expensive on realistic applications. We propose a novel adaptive time-stepping scheme for the tau-leaping method for approximating the solution of the Reaction-Diffusion Master Equation. This technique combines effective strategies for variable time-stepping with path preservation to reduce the computational cost, while maintaining the desired accuracy. The numerical tests on various examples arising in applications show the improved efficiency achieved by the new adaptive method.
Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains
Madzvamuse, Anotida
2009-08-29
By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth. © Springer-Verlag 2009.
An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
Burrage, Kevin
2012-01-01
Fractional differential equations are becoming increasingly used as a modelling tool for processes associated with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues that impose a number of computational constraints. In this paper we develop efficient, scalable techniques for solving fractional-in-space reaction diffusion equations using the finite element method on both structured and unstructured grids via robust techniques for computing the fractional power of a matrix times a vector. Our approach is show-cased by solving the fractional Fisher and fractional Allen-Cahn reaction-diffusion equations in two and three spatial dimensions, and analyzing the speed of the traveling wave and size of the interface in terms of the fractional power of the underlying Laplacian operator. © 2012 Society for Industrial and Applied Mathematics.
Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds
Desvillettes, Laurent
2008-01-01
In the continuation of [Desvillettes, L., Fellner, K.: Exponential Decay toward Equilibrium via Entropy Methods for Reaction-Diffusion Equations. J. Math. Anal. Appl. 319 (2006), no. 1, 157-176], we study reversible reaction-diffusion equations via entropy methods (based on the free energy functional) for a 1D system of four species. We improve the existing theory by getting 1) almost exponential convergence in L1 to the steady state via a precise entropy-entropy dissipation estimate, 2) an explicit global L∞ bound via interpolation of a polynomially growing H1 bound with the almost exponential L1 convergence, and 3), finally, explicit exponential convergence to the steady state in all Sobolev norms.
Reaction-diffusion equation for quark-hadron transition in heavy-ion collisions
Bagchi, Partha; Sengupta, Srikumar; Srivastava, Ajit M
2015-01-01
Reaction-diffusion equations with suitable boundary conditions have special propagating solutions which very closely resemble the moving interfaces in a first order transition. We show that the dynamics of chiral order parameter for chiral symmetry breaking transition in heavy-ion collisions, with dissipative dynamics, is governed by one such equation, specifically, the Newell-Whitehead equation. Further, required boundary conditions are automatically satisfied due to the geometry of the collision. The chiral transition is, therefore, completed by a propagating interface, exactly as for a first order transition, even though the transition actually is a crossover for relativistic heavy-ion collisions. Same thing also happens when we consider the initial confinement-deconfinement transition with Polyakov loop order parameter. The resulting equation, again with dissipative dynamics, can then be identified with the reaction-diffusion equation known as the Fitzhugh-Nagumo equation which is used in population genet...
Modelling the impact of an invasive insect via reaction-diffusion.
Roques, Lionel; Auger-Rozenberg, Marie-Anne; Roques, Alain
2008-11-01
An exotic, specialist seed chalcid, Megastigmus schimitscheki, has been introduced along with its cedar host seeds from Turkey to southeastern France during the early 1990s. It is now expanding in plantations of Atlas Cedar (Cedrus atlantica). We propose a model to predict the expansion and impact of this insect. This model couples a time-discrete equation for the ovo-larval stage with a two-dimensional reaction-diffusion equation for the adult stage, through a formula linking the solution of the reaction-diffusion equation to a seed attack rate. Two main diffusion operators, of Fokker-Planck and Fickian types, are tested. We show that taking account of the dependence of the insect mobility with respect to spatial heterogeneity, and choosing the appropriate diffusion operator, are critical factors for obtaining good predictions.
STOCHASTIC CRACKING AND HEALING BEHAVIORS OF THIN FILMS DURING REACTION-DIFFUSION GROWTH
S.L. Zhu; S.L. Yang; Y.M. Xiong; M.S. Li; S.J. Geng; C.S. Hu; Fuhui Wang; W. T. Wu
2001-01-01
The stochastic cracking and healing behaviors of reaction-diffusion growth of thin filmswere studied by means of Markov processes analysis. We chose the thermal growth ofoxide scales on metals as an example of reaction-diffusion growth. The thermal growthof oxide films follows power law when no cracking occurs. Our results showed that thegrowth kinetics under stochastic cracking and healing conditions was different fromthat without cracking. It might be altered to either pseudo-linear or pseudo-power lawsdependent upon the intensity and frequency of the cracking of the films. When thehoping items dominated, the growth followed pseudo-linear law; when the diffusionalitems dominated, it followed pseudo-power law with the exponentials lower than theintrinsical values. The numerical results were in good agreement with the meassuredkinetics of isothermal and cyclic oxidation of NiAl-0.1 Y (at. %) alloys in air at 1273K.
Turing Bifurcation and Pattern Formation of Stochastic Reaction-Diffusion System
Qianiqian Zheng
2017-01-01
Full Text Available Noise is ubiquitous in a system and can induce some spontaneous pattern formations on a spatially homogeneous domain. In comparison to the Reaction-Diffusion System (RDS, Stochastic Reaction-Diffusion System (SRDS is more complex and it is very difficult to deal with the noise function. In this paper, we have presented a method to solve it and obtained the conditions of how the Turing bifurcation and Hopf bifurcation arise through linear stability analysis of local equilibrium. In addition, we have developed the amplitude equation with a pair of wave vector by using Taylor series expansion, multiscaling, and further expansion in powers of small parameter. Our analysis facilitates finding regions of bifurcations and understanding the pattern formation mechanism of SRDS. Finally, the simulation shows that the analytical results agree with numerical simulation.
Dynamical Behavior of Core 3 He Nuclear Reaction-Diffusion Systems and Sun's Gravitational Field
DU Jiulin; SHEN Hong
2005-01-01
The coupling of the sun's gravitational field with processes of diffusion and convection exerts a significant influence on the dynamical behavior of the core 3He nuclear reaction-diffusion system. Stability analyses of the system are made in this paper by using the theory of nonequilibrium dynamics. It is showed that, in the nuclear reaction regions extending from the center to about 0.38 times of the radius of the sun, the gravitational field enables the core 3He nuclear reaction-diffusion system to become unstable and, after the instability, new states to appear in the system have characteristic of time oscillation. This may change the production rates of both 7Be and 8B neutrinos.
Effect of mixing on reaction-diffusion kinetics for protein hydrogel-based microchips.
Zubtsov, D A; Ivanov, S M; Rubina, A Yu; Dementieva, E I; Chechetkin, V R; Zasedatelev, A S
2006-03-09
Protein hydrogel-based microchips are being developed for high-throughput evaluation of the concentrations and activities of various proteins. To shorten the time of analysis, the reaction-diffusion kinetics on gel microchips should be accelerated. Here we present the results of the experimental and theoretical analysis of the reaction-diffusion kinetics enforced by mixing with peristaltic pump. The experiments were carried out on gel-based protein microchips with immobilized antibodies under the conditions utilized for on-chip immunoassay. The dependence of fluorescence signals at saturation and corresponding saturation times on the concentrations of immobilized antibodies and antigen in solution proved to be in good agreement with theoretical predictions. It is shown that the enhancement of transport with peristaltic pump results in more than five-fold acceleration of binding kinetics. Our results suggest useful criteria for the optimal conditions for assays on gel microchips to balance high sensitivity and rapid fluorescence saturation kinetics.
An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems
Padgett, Jill M. A.; Ilie, Silvana
2016-03-01
Stochastic modelling is critical for studying many biochemical processes in a cell, in particular when some reacting species have low population numbers. For many such cellular processes the spatial distribution of the molecular species plays a key role. The evolution of spatially heterogeneous biochemical systems with some species in low amounts is accurately described by the mesoscopic model of the Reaction-Diffusion Master Equation. The Inhomogeneous Stochastic Simulation Algorithm provides an exact strategy to numerically solve this model, but it is computationally very expensive on realistic applications. We propose a novel adaptive time-stepping scheme for the tau-leaping method for approximating the solution of the Reaction-Diffusion Master Equation. This technique combines effective strategies for variable time-stepping with path preservation to reduce the computational cost, while maintaining the desired accuracy. The numerical tests on various examples arising in applications show the improved efficiency achieved by the new adaptive method.
Qualitative Analysis on a Reaction-Diffusion Prey Predator Model and the Corresponding Steady-States
Qunyi BIE; Rui PENG
2009-01-01
The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem.The local and global stability of the positive constant steady-state are discussed,and then some results for nonexistence of positive non-constant steady-states are derived.
Limiting behavior of non-autonomous stochastic reaction-diffusion equations on thin domains
Li, Dingshi; Wang, Bixiang; Wang, Xiaohu
2017-02-01
This paper deals with the limiting behavior of stochastic reaction-diffusion equations driven by multiplicative noise and deterministic non-autonomous terms defined on thin domains. We first prove the existence, uniqueness and periodicity of pullback tempered random attractors for the equations in an (n + 1)-dimensional narrow domain, and then establish the upper semicontinuity of these attractors when a family of (n + 1)-dimensional thin domains collapses onto an n-dimensional domain.
An analytic algorithm for the space-time fractional reaction-diffusion equation
M. G. Brikaa
2015-11-01
Full Text Available In this paper, we solve the space-time fractional reaction-diffusion equation by the fractional homotopy analysis method. Solutions of different examples of the reaction term will be computed and investigated. The approximation solutions of the studied models will be put in the form of convergent series to be easily computed and simulated. Comparison with the approximation solution of the classical case of the studied modeled with their approximation errors will also be studied.
Accelerated stochastic and hybrid methods for spatial simulations of reaction-diffusion systems
Rossinelli, D; Bayati, B; Koumoutsakos, P.
2008-01-01
Spatial distributions characterize the evolution of reaction-diffusion models of several physical, chemical, and biological systems. We present two novel algorithms for the efficient simulation of these models: Spatial т-Leaping (Sт -Leaping), employing a unified acceleration of the stochastic simulation of reaction and diffusion, and Hybrid т-Leaping (Hт-Leaping), combining a deterministic diffusion approximation with a т-Leaping acceleration of the stochastic reactions. The algorithms are v...
Compact-like kink in a real electrical reaction-diffusion chain
Comte, J.C. [Laboratoire de Physiopathologie des Reseaux Neuronaux du Cycle Veille-Sommeil, CNRS UMR 5167, Faculte de Medecine Laennec 7, Rue Guillaume Paradin, 69372 Lyon Cedex 08 (France)]. E-mail: comtejc@sommeil.univ-lyon1.fr; Marquie, P. [Laboratoire d' Electronique, Informatique et Image (LE2i) UMR CNRS 5158, Aile des Sciences de l' Ingenieur, BP 47870, 21078 Dijon Cedex (France)
2006-07-15
We demonstrate experimentally the compact-like kinks existence in a real electrical reaction-diffusion chain. Our measures show that such entities are strictly localized and consequently present a finite spatial extent. We show equally that the kink velocity is threshold-dependent. A theoretical quantification of the critical coupling under which propagation fails is also achieved and reveals that nonlinear coupling leads to a propagation failure reduction.
Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models
Narcisa Apreutesei
2014-05-01
Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.
ASYMPTOTIC SOLUTION OF ACTIVATOR INHIBITOR SYSTEMS FOR NONLINEAR REACTION DIFFUSION EQUATIONS
Jiaqi MO; Wantao LIN
2008-01-01
A nonlinear reaction diffusion equations for activator inhibitor systems is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the variables of multiple scales and the expanding theory of power series the formal asymptotic expansions of the solution are constructed, and finally, using the theory of differential inequalities the uniform validity and asymptotic behavior of the solution are studied.
Xiang-Chao Shi
2016-02-01
Full Text Available The fractional reaction diffusion equation is one of the popularly used fractional partial differential equations in recent years. The fast Adomian decomposition method is used to obtain the solution of the Cauchy problem. Also, the analytical scheme is extended to the fractional one where the Taylor series is employed. In comparison with the classical Adomian decomposition method, the ratio of the convergence is increased. The method is more reliable for the fractional partial differential equations.
Chuangxia Huang
2011-01-01
Full Text Available Stability of reaction-diffusion recurrent neural networks (RNNs with continuously distributed delays and stochastic influence are considered. Some new sufficient conditions to guarantee the almost sure exponential stability and mean square exponential stability of an equilibrium solution are obtained, respectively. Lyapunov's functional method, M-matrix properties, some inequality technique, and nonnegative semimartingale convergence theorem are used in our approach. The obtained conclusions improve some published results.
INFLUENCE OF NOISE AND DELAY ON REACTION-DIFFUSION RECURRENT NEURAL NETWORKS
Li Wu
2006-01-01
In this paper, the influence of the noise and delay upon the stability property of reaction-diffusion recurrent neural networks (RNNs) with the time-varying delay is discussed. The new and easily verifiable conditions to guarantee the mean value exponential stability of an equilibrium solution are derived. The rate of exponential convergence can be estimated by means of a simple computation based on these criteria.
Finite Travelling Waves for a Semilinear Degenerate Reaction-Diffusion System
Shu WANG; Cheng Fu WANG; Dang LUO
2001-01-01
In this paper, the existence and nonexistence of finite travelling waves (FTWs) for a semilinear degenerate reaction-diffusion systemis studied, where 0 ＜αi ＜ 1, mij ≥ 0 and ∑nj=1mij ＞ 0, i,j = 1,.. N. Necessary and sufficientconditions on existence and large time behaviours of FTWs of (I) are obtained by using the matrixtheory, Schauder's fixed point theorem, and upper and lower solutions method.
Generalized monotone method and numerical approach for coupled reaction diffusion systems
Sowmya, M.; Vatsala, Aghalaya S.
2017-01-01
Study of coupled reaction diffusion systems are very useful in various branches of science and engineering. In this paper, we provide a methodology to construct the solution for the coupled reaction diffusion systems, with initial and boundary conditions, where the forcing function is the sum of an increasing and decreasing function. It is known that the generalized monotone method coupled with coupled lower and upper solutions yield monotone sequences which converges uniformly and monotonically to coupled minimal and maximal solutions. In addition, the interval of existence is guaranteed by the lower and upper solutions, which are relatively easy to compute. Using the lower and upper solutions as the initial approximation, we develop a method to compute the sequence of coupled lower and upper solutions on the interval or on the desired interval of existence. Further, if the uniqueness conditions are satisfied, the coupled minimal and maximal solutions converge to the unique solution of the reaction diffusion systems. We will provide some numerical results as an application of our numerical methodology.
Contribution to an effective design method for stationary reaction-diffusion patterns
Szalai, István; Horváth, Judit [Laboratory of Nonlinear Chemical Dynamics, Institute of Chemistry, Eötvös Loránd University, P.O. Box 32, H-1518 Budapest 112 (Hungary); De Kepper, Patrick [Centre de Recherche Paul Pascal, CNRS, University of Bordeaux, 115, Avenue Schweitzer, F-33600 Pessac (France)
2015-06-15
The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences.
Contribution to an effective design method for stationary reaction-diffusion patterns
Szalai, István; Horváth, Judit; De Kepper, Patrick
2015-06-01
The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences.
Solutions of fractional reaction-diffusion equations in terms of the H-function
Haubold, H. J.; Mathai, A. M.; Saxena, R. K.
2007-12-01
This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation associated with the Caputo derivative as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the Laplace and Fourier transforms in closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by many authors, notably by Mainardi et al. (2001, 2005) for the fundamental solution of the space-time fractional diffusion equation, and Saxena et al. (2006a, b) for fractional reaction-diffusion equations. The advantage of using Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation containing this derivative includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of neutral fractional diffusion, space-fractional diffusion, and time-fractional diffusion. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-functions in compact form.
Ram K. Saxena
2015-04-01
Full Text Available This article is in continuation of the authors research attempts to derive computational solutions of an unified reaction-diffusion equation of distributed order associated with Caputo derivatives as the time-derivative and Riesz-Feller derivative as space derivative. This article presents computational solutions of distributed order fractional reaction-diffusion equations associated with Riemann-Liouville derivatives of fractional orders as the time-derivatives and Riesz-Feller fractional derivatives as the space derivatives. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is derived in a closed and computational form in terms of the familiar Mittag-Leffler function. It provides an elegant extension of results available in the literature. The results obtained are presented in the form of two theorems. Some results associated specifically with fractional Riesz derivatives are also derived as special cases of the most general result. It will be seen that in case of distributed order fractional reaction-diffusion, the solution comes in a compact and closed form in terms of a generalization of the Kampé de Fériet hypergeometric series in two variables. The convergence of the double series occurring in the solution is also given.
Contribution to an effective design method for stationary reaction-diffusion patterns.
Szalai, István; Horváth, Judit; De Kepper, Patrick
2015-06-01
The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences.
Wang, Jin-Liang; Wu, Huai-Ning; Huang, Tingwen; Ren, Shun-Yan
2016-04-01
Two types of coupled neural networks with reaction-diffusion terms are considered in this paper. In the first one, the nodes are coupled through their states. In the second one, the nodes are coupled through the spatial diffusion terms. For the former, utilizing Lyapunov functional method and pinning control technique, we obtain some sufficient conditions to guarantee that network can realize synchronization. In addition, considering that the theoretical coupling strength required for synchronization may be much larger than the needed value, we propose an adaptive strategy to adjust the coupling strength for achieving a suitable value. For the latter, we establish a criterion for synchronization using the designed pinning controllers. It is found that the coupled reaction-diffusion neural networks with state coupling under the given linear feedback pinning controllers can realize synchronization when the coupling strength is very large, which is contrary to the coupled reaction-diffusion neural networks with spatial diffusion coupling. Moreover, a general criterion for ensuring network synchronization is derived by pinning a small fraction of nodes with adaptive feedback controllers. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of the theoretical results.
Jacquemet, Vincent
2010-09-01
Microscale electrical propagation in the heart can be modeled by a reaction-diffusion system, describing cell and tissue electrophysiology. Macroscale features of wavefront propagation can be reproduced by an eikonal model, a reduced formulation involving only wavefront shape. In this paper, these two approaches are combined to incorporate global information about reentrant pathways into a reaction-diffusion model. The eikonal-diffusion formulation is generalized to handle reentrant activation patterns and wavefront collisions. Boundary conditions are used to specify pathways of reentry. Finite-element-based numerical methods are presented to solve this nonlinear equation on a coarse triangular mesh. The macroscale eikonal model serves to construct an initial condition for the microscale reaction-diffusion model. Electrical propagation simulated from this initial condition is then compared to the isochrones predicted by the eikonal model. Results in 2-D and thin 3-D test-case geometries demonstrate the ability of this technique to initiate anatomical and functional reentries along prescribed pathways, thus facilitating the development of dedicated models aimed at better understanding clinical case reports.
Saliba, Daniel; Al-Ghoul, Mazen
2016-11-01
We report the synthesis of magnesium-aluminium layered double hydroxide (LDH) using a reaction-diffusion framework (RDF) that exploits the multiscale coupling of molecular diffusion with chemical reactions, nucleation and growth of crystals. In an RDF, the hydroxide anions are allowed to diffuse into an organic gel matrix containing the salt mixture needed for the precipitation of the LDH. The chemical structure and composition of the synthesized magnesium-aluminium LDHs are determined using powder X-ray diffraction (PXRD), thermo-gravimetric analysis, differential scanning calorimetry, solid-state nuclear magnetic resonance (SSNMR), Fourier transform infrared and energy dispersive X-ray spectroscopy. This novel technique also allows the investigation of the mechanism of intercalation of some fluorescent probes, such as the neutral three-dimensional rhodamine B (RhB) and the negatively charged two-dimensional 8-hydroxypyrene-1,3,6-trisulfonic acid (HPTS), using in situ steady-state fluorescence spectroscopy. The incorporation of these organic dyes inside the interlayer region of the LDH is confirmed via fluorescence microscopy, solid-state lifetime, SSNMR and PXRD. The activation energies of intercalation of the corresponding molecules (RhB and HPTS) are computed and exhibit dependence on the geometry of the involved probe (two or three dimensions), the charge of the fluorescent molecule (anionic, cationic or neutral) and the cationic ratio of the corresponding LDH. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.
Gabor transform in texture analysis
Chen, Chien-Chang; Chen, Chaur-Chin
1994-10-01
Gabor transform has recently been exploited to do texture analysis, including texture edge detection, texture segmentation/discrimination, and texture synthesis. For most of the applications using Gabor transform, people convolve the given texture image with a set of Gabor filters with some user specified parameters. Although the mathematical formulation of applications involve the Fourier transform, few have investigated mathematical properties of the relationship between Gabor filters and their Fourier transform. This paper mainly studies mathematical properties of real Gabor filters and their corresponding Fourier transform. The goal is to select a set of `interesting' Gabor filters, or say, a set of parameters for Gabor filters to do texture analysis. We demonstrate, by means of 3-D graphical displays, that a Gabor filter or its corresponding Fourier transform may have a single peak or double peaks according to different parameters. Experiments for texture discrimination are given to demonstrate the applications of Gabor transform.
Yamada, H; Ito, M
1998-01-01
The amoeboid organism, the plasmodium of Physarum polycephalum, behaves on the basis of spatio-temporal pattern formation by local contraction-oscillators. This biological system can be regarded as a reaction-diffusion system which has spatial interaction by active flow of protoplasmic sol in the cell. Paying attention to the physiological evidence that the flow is determined by contraction pattern in the plasmodium, a reaction-diffusion system having self-determined flow arises. Such a coupling of reaction-diffusion-advection is a characteristic of the biological system, and is expected to relate with control mechanism of amoeboid behaviours. Hence, we have studied effects of the self-determined flow on pattern formation of simple reaction-diffusion systems. By weakly nonlinear analysis near a trivial solution, the envelope dynamics follows the complex Ginzburg-Landau type equation just after bifurcation occurs at finite wave number. The flow term affects the nonlinear term of the equation through the critic...
BHARDWAJ S B; SINGH RAM MEHAR; SHARMA KUSHAL; MISHRA S C
2016-06-01
Attempts have been made to explore the exact periodic and solitary wave solutions of nonlinear reaction diffusion (RD) equation involving cubic–quintic nonlinearity along with timedependent convection coefficients. Effect of varying model coefficients on the physical parameters of solitary wave solutions is demonstrated. Depending upon the parametric condition, the periodic,double-kink, bell and antikink-type solutions for cubic–quintic nonlinear reaction-diffusion equation are extracted. Such solutions can be used to explain various biological and physical phenomena.
A reaction-diffusion model of ROS-induced ROS release in a mitochondrial network.
Lufang Zhou
2010-01-01
Full Text Available Loss of mitochondrial function is a fundamental determinant of cell injury and death. In heart cells under metabolic stress, we have previously described how the abrupt collapse or oscillation of the mitochondrial energy state is synchronized across the mitochondrial network by local interactions dependent upon reactive oxygen species (ROS. Here, we develop a mathematical model of ROS-induced ROS release (RIRR based on reaction-diffusion (RD-RIRR in one- and two-dimensional mitochondrial networks. The nodes of the RD-RIRR network are comprised of models of individual mitochondria that include a mechanism of ROS-dependent oscillation based on the interplay between ROS production, transport, and scavenging; and incorporating the tricarboxylic acid (TCA cycle, oxidative phosphorylation, and Ca(2+ handling. Local mitochondrial interaction is mediated by superoxide (O2.- diffusion and the O2.(--dependent activation of an inner membrane anion channel (IMAC. In a 2D network composed of 500 mitochondria, model simulations reveal DeltaPsi(m depolarization waves similar to those observed when isolated guinea pig cardiomyocytes are subjected to a localized laser-flash or antioxidant depletion. The sensitivity of the propagation rate of the depolarization wave to O(2.- diffusion, production, and scavenging in the reaction-diffusion model is similar to that observed experimentally. In addition, we present novel experimental evidence, obtained in permeabilized cardiomyocytes, confirming that DeltaPsi(m depolarization is mediated specifically by O2.-. The present work demonstrates that the observed emergent macroscopic properties of the mitochondrial network can be reproduced in a reaction-diffusion model of RIRR. Moreover, the findings have uncovered a novel aspect of the synchronization mechanism, which is that clusters of mitochondria that are oscillating can entrain mitochondria that would otherwise display stable dynamics. The work identifies the
Lacitignola, Deborah; Bozzini, Benedetto; Frittelli, Massimo; Sgura, Ivonne
2017-07-01
The present paper deals with the pattern formation properties of a specific morpho-electrochemical reaction-diffusion model on a sphere. The physico-chemical background to this study is the morphological control of material electrodeposited onto spherical particles. The particular experimental case of interest refers to the optimization of novel metal-air flow batteries and addresses the electrodeposition of zinc onto inert spherical supports. Morphological control in this step of the high-energy battery operation is crucial to the energetic efficiency of the recharge process and to the durability of the whole energy-storage device. To rationalise this technological challenge within a mathematical modeling perspective, we consider the reaction-diffusion system for metal electrodeposition introduced in [Bozzini et al., J. Solid State Electr.17, 467-479 (2013)] and extend its study to spherical domains. Conditions are derived for the occurrence of the Turing instability phenomenon and the steady patterns emerging at the onset of Turing instability are investigated. The reaction-diffusion system on spherical domains is solved numerically by means of the Lumped Surface Finite Element Method (LSFEM) in space combined with the IMEX Euler method in time. The effect on pattern formation of variations in the domain size is investigated both qualitatively, by means of systematic numerical simulations, and quantitatively by introducing suitable indicators that allow to assign each pattern to a given morphological class. An experimental validation of the obtained results is finally presented for the case of zinc electrodeposition from alkaline zincate solutions onto copper spheres.
Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK.
Wang, Kaier; Steyn-Ross, Moira L; Steyn-Ross, D Alistair; Wilson, Marcus T; Sleigh, Jamie W; Shiraishi, Yoichi
2014-04-11
Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system's set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This "code-based" approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution. As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations. The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming
Breathing spiral waves in the chlorine dioxide-iodine-malonic acid reaction-diffusion system
Berenstein, Igal; Muñuzuri, Alberto P.; Yang, Lingfa; Dolnik, Milos; Zhabotinsky, Anatol M.; Epstein, Irving R.
2008-08-01
Breathing spiral waves are observed in the oscillatory chlorine dioxide-iodine-malonic acid reaction-diffusion system. The breathing develops within established patterns of multiple spiral waves after the concentration of polyvinyl alcohol in the feeding chamber of a continuously fed, unstirred reactor is increased. The breathing period is determined by the period of bulk oscillations in the feeding chamber. Similar behavior is obtained in the Lengyel-Epstein model of this system, where small amplitude parametric forcing of spiral waves near the spiral wave frequency leads to the formation of breathing spiral waves in which the period of breathing is equal to the period of forcing.
Threshold phenomena for symmetric decreasing solutions of reaction-diffusion equations
Muratov, C B
2012-01-01
We study the long time behavior of solutions of the Cauchy problem for nonlinear reaction-diffusion equations in one space dimension with the nonlinearity of bistable, ignition or monostable type. We prove a one-to-one relation between the long time behavior of the solution and the limit value of its energy for symmetric decreasing initial data in $L^2$ under minimal assumptions on the nonlinearities. The obtained relation allows to establish sharp threshold results between propagation and extinction for monotone families of initial data in the considered general setting.
Extension of Newman's method to electrochemical reaction-diffusion in a fuel cell catalyst layer
Duan, Tianping; Weidner, John W.; White, Ralph E.
A numerical technique is developed for solving coupled electrochemical reaction-diffusion equations. Through analyzing the nonlinearity of the problem, a trial and error iterating procedure is constructed. The coefficient matrix is arranged as a tridiagonal form with elements of block matrix and is decomposed to LU form. A compact forward and backward substitution algorithm based on the shift of inversing block matrix by Gauss-Jordan full pivoting is developed. A large number of node points is required to converge the calculation. Computation experiences show that the iteration converges very quickly. The effects of inner diffusion on the electrochemical reaction are analyzed by numerical solutions.
A reaction-diffusion SIS epidemic model in an almost periodic environment
Wang, Bin-Guo; Li, Wan-Tong; Wang, Zhi-Cheng
2015-12-01
A susceptible-infected-susceptible almost periodic reaction-diffusion epidemic model is studied by means of establishing the theories and properties of the basic reproduction ratio {R0}. Particularly, the asymptotic behaviors of {R0} with respect to the diffusion rate {DI} of the infected individuals are obtained. Furthermore, the uniform persistence, extinction and global attractivity are presented in terms of {R0}. Our results indicate that the interaction of spatial heterogeneity and temporal almost periodicity tends to enhance the persistence of the disease.
Relation between the complex Ginzburg-Landau equation and reaction-diffusion System
Shao Xin; Ren Yi; Ouyang Qi
2006-01-01
The complex Ginzburg-Landau equation(CGLE)has been used to describe the travelling wave behaviour in reaction-diffusion (RD) systems. We argue that this description is valid only when the RD system is close to the Hopf bifurcation,and is not valid when a RD system is away from the onset.To test this,we study spirals and anti-spirals in the chlorite-iodide-malonic acid (CIMA) reaction and the corresponding CGLE.Numerical simulations confirm that the CGLE can only be applied to the CIMA reaction when it is very near the Hopf onset.
Asymptotic solution for a class of weakly nonlinear singularly perturbed reaction diffusion problem
TANG Rong-rong
2009-01-01
Under appropriate conditions, with the perturbation method and the theory of differential inequalities, a class of weakly nonlinear singularly perturbed reaction diffusion problem is considered. The existence of solution of the original problem is proved by constructing the auxiliary functions. The uniformly valid asymptotic expansions of the solution for arbitrary mth order approximation are obtained through constructing the formal solutions of the original problem, expanding the nonlinear terms to the power in small parameter e and comparing the coefficient for the same powers of ε. Finally, an example is provided, resulting in the error of O(ε2).
Turing patterns in a reaction-diffusion model with the Degn-Harrison reaction scheme
Li, Shanbing; Wu, Jianhua; Dong, Yaying
2015-09-01
In this paper, we consider a reaction-diffusion model with Degn-Harrison reaction scheme. Some fundamental analytic properties of nonconstant positive solutions are first investigated. We next study the stability of constant steady-state solution to both ODE and PDE models. Our result also indicates that if either the size of the reactor or the effective diffusion rate is large enough, then the system does not admit nonconstant positive solutions. Finally, we establish the global structure of steady-state bifurcations from simple eigenvalues by bifurcation theory and the local structure of the steady-state bifurcations from double eigenvalues by the techniques of space decomposition and implicit function theorem.
Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)
2013-01-01
In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.
Dulos, E.; Hunding, A.; Boissonade, J.; de Kepper, P.
Since the seminal paper "The chemical basis of morphogenesis" by Alan Turing, the temporal and spatial self-organization phenomena produced in chemically reacting and diffusing systems are often thought as paradigms for biological development. The basic theoretical principles on which the development of stationary concentration patterns (Turing structures) rely on are briefly presented. We review different aspects of our contribution to the experimental observation of reaction-diffusion patterns in iodine-oxychlorine systems. The experimental techniques are emphasized. Phase diagrams gathering different standing and travelling patterns are presented, analyzed and modeled. A special attention is also given to some peculiar pattern growth dynamics (spot division, finger splitting).
Traveling waves in a nonlocal, piecewise linear reaction-diffusion population model
Autry, E. A.; Bayliss, A.; Volpert, V. A.
2017-08-01
We consider an analytically tractable switching model that is a simplification of a nonlocal, nonlinear reaction-diffusion model of population growth where we take the source term to be piecewise linear. The form of this source term allows us to consider both the monostable and bistable versions of the problem. By transforming to a traveling frame and choosing specific kernel functions, we are able to reduce the problem to a system of algebraic equations. We construct solutions and examine the propagation speed and monotonicity of the resulting waves.
Luisa Malaguti
2011-01-01
Full Text Available The paper deals with a degenerate reaction-diffusion equation, including aggregative movements and convective terms. The model also incorporates a real parameter causing the change from a purely diffusive to a diffusive-aggregative and to a purely aggregative regime. Existence and qualitative properties of traveling wave solutions are investigated, and estimates of their threshold speeds are furnished. Further, the continuous dependence of the threshold wave speed and of the wave profiles on a real parameter is studied, both when the process maintains its diffusion-aggregation nature and when it switches from it to another regime.
Unfolding-based corrector estimates for a reaction-diffusion system predicting concrete corrosion
Fatima, Tasnim; Ptashnyk, Mariya
2011-01-01
We use the periodic unfolding technique to derive corrector estimates for a reaction-diffusion system describing concrete corrosion penetration in the sewer pipes. The system, defined in a periodically-perforated domain, is semi-linear, partially dissipative, and coupled via a non-linear ordinary differential equation posed on the solid-water interface at the pore level. After discussing the solvability of the pore scale model, we apply the periodic unfolding techniques (adapted to treat the presence of perforations) not only to get upscaled model equations, but also to prepare a proper framework for getting a convergence rate (corrector estimates) of the averaging procedure.
Wave reflection in a reaction-diffusion system: breathing patterns and attenuation of the echo.
Tsyganov, M A; Ivanitsky, G R; Zemskov, E P
2014-05-01
Formation and interaction of the one-dimensional excitation waves in a reaction-diffusion system with the piecewise linear reaction functions of the Tonnelier-Gerstner type are studied. We show that there exists a parameter region where the established regime of wave propagation depends on initial conditions. Wave phenomena with a complex behavior are found: (i) the reflection of waves at a growing distance (the remote reflection) upon their collision with each other or with no-flux boundaries and (ii) the periodic transformation of waves with the jumping from one regime of wave propagation to another (the periodic trigger wave).
A Reaction-diffusion System with Nonlinear Absorption Terms and Boundary Flux
2008-01-01
This paper deals with a reaction-diffusion system with nonlinear absorption terms and boundary flux. As results of interactions among the six nonlinear terms in the system, some sufficient conditions on global existence and finite time blow-up of the solutions are described via all the six nonlinear exponents appearing in the six nonlinear terms. In addition, we also show the influence of the coefficients of the absorption terms as well as the geometry of the domain to the global existence and finite time blow-up of the solutions for some cases. At last, some numerical results are given.
Dierckx, Hans; Bernus, Olivier; Verschelde, Henri
2011-09-02
The dependency of wave velocity in reaction-diffusion (RD) systems on the local front curvature determines not only the stability of wave propagation, but also the fundamental properties of other spatial configurations such as vortices. This Letter gives the first derivation of a covariant eikonal-curvature relation applicable to general RD systems with spatially varying anisotropic diffusion properties, such as cardiac tissue. The theoretical prediction that waves which seem planar can nevertheless possess a nonvanishing geometrical curvature induced by local anisotropy is confirmed by numerical simulations, which reveal deviations up to 20% from the nominal plane wave speed.
Jingsun Yao; Jiaqi Mo
2005-01-01
The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
Positional information and reaction-diffusion: two big ideas in developmental biology combine.
Green, Jeremy B A; Sharpe, James
2015-04-01
One of the most fundamental questions in biology is that of biological pattern: how do the structures and shapes of organisms arise? Undoubtedly, the two most influential ideas in this area are those of Alan Turing's 'reaction-diffusion' and Lewis Wolpert's 'positional information'. Much has been written about these two concepts but some confusion still remains, in particular about the relationship between them. Here, we address this relationship and propose a scheme of three distinct ways in which these two ideas work together to shape biological form.
WANG Wen-jing; ZHAN Hai-hong
2008-01-01
Three kinds of soil texture (clay-loam, mid-loam, and sand-loam soil) were used to study the effects of soil texture on starch accumulating rate and the changes in activities of the key enzymes of starch synthesis in the kernel during grain filling in high gluten content wheat ZM 9023, under conditions of pond culture. The content of starch and its components were measured according to the method of double-wave length described by Bao (1996). ADP-glucose pyrophosphorylase (AGPP) activity was tested according to the method described by Doehlert et al. (1988). Soluble starch synthase (SSS) and starch branching enzyme (SBE) activities were tested according to the method described by Nakamura et al. (1989). The amylose, amylopectin, and total starch accumulating rate in the kernel of ZM 9023 were found to be a single-peak curve in three different soil textures during grain filling, and peaked 20, 15, and 15 d after anthesis, respectively. The activities of the enzymes, AGPP, SSS, and SBE, in the kernel of ZM 9023 had a single-peaked curve, which peaked 20, 15, and 15 d after anthesis, respectively. The activities of the above three enzymes of ZM 9023 were higher in the sand-loam soil. The accumulating peak of amylose formed later compared to that of amylopectin. The sand-loam soil could help high gluten content cultivars to synthesize starch.
The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems
Di Francesco, M.
2008-12-08
We study the long-time asymptotics of reaction-diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion-convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid-state physics as a paradigm for general nonlinear systems. © 2008 The Royal Society.
Self-similar fast-reaction limits for reaction-diffusion systems on unbounded domains
Crooks, E. C. M.; Hilhorst, D.
2016-08-01
We present a unified approach to characterising fast-reaction limits of systems of either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary differential equation, on unbounded domains, motivated by models of fast chemical reactions where either one or both reactant(s) is/are mobile. For appropriate initial data, solutions of four classes of problems each converge in the fast-reaction limit k → ∞ to a self-similar limit profile that has one of four forms, depending on how many components diffuse and whether the spatial domain is a half or whole line. For fixed k, long-time convergence to these same self-similar profiles is also established, thanks to a scaling argument of Kamin. Our results generalise earlier work of Hilhorst, van der Hout and Peletier to a much wider class of problems, and provide a quantitative description of the penetration of one substance into another in both the fast-reaction and long-time regimes.
Le Novère Nicolas
2010-03-01
Full Text Available Abstract Background Most cellular signal transduction mechanisms depend on a few molecular partners whose roles depend on their position and movement in relation to the input signal. This movement can follow various rules and take place in different compartments. Additionally, the molecules can form transient complexes. Complexation and signal transduction depend on the specific states partners and complexes adopt. Several spatial simulator have been developed to date, but none are able to model reaction-diffusion of realistic multi-state transient complexes. Results Meredys allows for the simulation of multi-component, multi-feature state molecular species in two and three dimensions. Several compartments can be defined with different diffusion and boundary properties. The software employs a Brownian dynamics engine to simulate reaction-diffusion systems at the reactive particle level, based on compartment properties, complex structure, and hydro-dynamic radii. Zeroth-, first-, and second order reactions are supported. The molecular complexes have realistic geometries. Reactive species can contain user-defined feature states which can modify reaction rates and outcome. Models are defined in a versatile NeuroML input file. The simulation volume can be split in subvolumes to speed up run-time. Conclusions Meredys provides a powerful and versatile way to run accurate simulations of molecular and sub-cellular systems, that complement existing multi-agent simulation systems. Meredys is a Free Software and the source code is available at http://meredys.sourceforge.net/.
Studies of the accuracy of time integration methods for reaction-diffusion equations
Ropp, David L.; Shadid, John N.; Ober, Curtis C.
2004-03-01
In this study we present numerical experiments of time integration methods applied to systems of reaction-diffusion equations. Our main interest is in evaluating the relative accuracy and asymptotic order of accuracy of the methods on problems which exhibit an approximate balance between the competing component time scales. Nearly balanced systems can produce a significant coupling of the physical mechanisms and introduce a slow dynamical time scale of interest. These problems provide a challenging test for this evaluation and tend to reveal subtle differences between the various methods. The methods we consider include first- and second-order semi-implicit, fully implicit, and operator-splitting techniques. The test problems include a prototype propagating nonlinear reaction-diffusion wave, a non-equilibrium radiation-diffusion system, a Brusselator chemical dynamics system and a blow-up example. In this evaluation we demonstrate a "split personality" for the operator-splitting methods that we consider. While operator-splitting methods often obtain very good accuracy, they can also manifest a serious degradation in accuracy due to stability problems.
Hybrid approaches for multiple-species stochastic reaction-diffusion models
Spill, Fabian; Alarcon, Tomas; Maini, Philip K; Byrne, Helen
2015-01-01
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains ...
Spatiotemporal patterns in reaction-diffusion system and in a vibrated granular bed
Swinney, H.L.; Lee, K.J.; McCormick, W.D. [Univ. of Texas, Austin, TX (United States)
1995-12-31
Experiments on a quasi-two-dimensional reaction-diffusion system reveal transitions from a uniform state to stationary hexagonal, striped, and rhombic spatial patterns. For other reactor conditions lamellae and self-replicating spot patterns are observed. These patterns form in continuously fed thin gel reactors that can be maintained indefinitely in well-defined nonequilibrium states. Reaction-diffusion models with two chemical species yield patterns similar to those observed in the experiments. Pattern formation is also being examined in vertically oscillated thin granular layers (typically 3-30 particle diameters deep). For small acceleration amplitudes, a granular layer is flat, but above a well-defined critical acceleration amplitude, spatial patterns spontaneously form. Disordered time-dependent granular patterns are observed as well as regular patterns of squares, stripes, and hexagons. A one-dimensional model consisting of a completely inelastic ball colliding with a sinusoidally oscillating platform provides a semi-quantitative description of most of the observed bifurcations between the different spatiotemporal regimes.
Structural texture synthesis method based on L neighbor segmentation%基于L邻域分割的结构性纹理合成方法
张雨禾; 耿国华; 刘伦椿; 周子骏
2014-01-01
针对纹理合成过程中L邻域整体匹配造成的误差，充分考虑了结构性纹理中像点之间的相关性信息，提出了一种新的L邻域匹配方法。取4个特殊的方向，对L邻域进行分割，利用纹理样图的灰度共生矩阵的相关值，对各个分割区域确定匹配优先级。采用基于优先级的多次匹配，找出L邻域的最佳匹配块。实验证明，该方法减少了传统的L邻域在匹配搜索过程中存在的计算复杂性和匹配误差，有效地提高了纹理合成中预处理的速度，在结构性纹理合成中获得了好的效果。%This paper proposes a new L neighbor matching method for errors caused by overall L neighbor matching during the texture synthesis process with full consideration of the correlation information between pixels in structural texture. It segments the L neighbor along 4 special directions, marks each divided region with matching priority based on the Grey⁃level co⁃occurrence matrix ( GLCM)′s IDM, and thereby determines the matching priority of each divided region. It also uses the multi⁃matching method based on priority to identify the best matching block of L neighbor. Experimental results proved that this method reduces the computational complexity and matching errors caused by traditional L neighbor matching. It effectively improves the preprocessing speed of texture synthesis and obtains good structured texture synthesis effect.
Hynek Lauschmann
2011-05-01
Full Text Available The reconstitution of the history of a fatigue process is based on the knowledge of any correspondences between the morphology of the crack surface and the velocity of the crack growth (crack growth rate - CGR. The textural fractography is oriented to mezoscopic SEM magnifications (30 to 500x. Images contain complicated textures without distinct borders. The aim is to find any characteristics of this texture, which correlate with CGR. Pre-processing of images is necessary to obtain a homogeneous texture. Three methods of textural analysis have been developed and realized as computational programs: the method based on the spectral structure of the image, the method based on a Gibbs random field (GRF model, and the method based on the idealization of light objects into a fibre process. In order to extract and analyze the fibre process, special methods - tracing fibres and a database-oriented analysis of a fibre process - have been developed.
A Two-grid Method with Expanded Mixed Element for Nonlinear Reaction-diffusion Equations
Wei Liu; Hong-xing Rui; Hui Guo
2011-01-01
Expanded mixed finite element approximation of nonlinear reaction-diffusion equations is discussed. The equations considered here are used to model the hydrologic and bio-geochemical phenomena. To linearize the mixed-method equations, we use a two-grid method involving a small nonlinear system on a coarse gird of size H and a linear system on a fine grid of size h. Error estimates are derived which demonstrate that the error is O(△t + hk+1 + H2k+2-d/2) (k ≥ 1), where k is the degree of the approximating space for the primary variable and d is the spatial dimension. The above estimates are useful for determining an appropriate H for the coarse grid problems.
Turing bifurcation in a reaction-diffusion system with density-dependent dispersal
Kumar, Niraj; Horsthemke, Werner
2010-05-01
Motivated by the recent finding [N. Kumar, G.M. Viswanathan, V.M. Kenkre, Physica A 388 (2009) 3687] that the dynamics of particles undergoing density-dependent nonlinear diffusion shows sub-diffusive behaviour, we study the Turing bifurcation in a two-variable system with this kind of dispersal. We perform a linear stability analysis of the uniform steady state to find the conditions for the Turing bifurcation and compare it with the standard Turing condition in a reaction-diffusion system, where dispersal is described by simple Fickian diffusion. While activator-inhibitor kinetics are a necessary condition for the Turing instability as in standard two-variable systems, the instability can occur even if the diffusion constant of the inhibitor is equal to or smaller than that of the activator. We apply these results to two model systems, the Brusselator and the Gierer-Meinhardt model.
Numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory
Ramos, J. I.
1987-01-01
A review of numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory is presented. The methods reviewed include explicit, implicit, quasi-linearization, time linearization, operator-splitting, random walk and finite-element techniques and methods of lines. Adaptive and nonadaptive procedures are also reviewed. These techniques are applied first to solve two model problems which have exact traveling wave solutions with which the numerical results can be compared. This comparison is performed in terms of both the wave profile and computed wave speed. It is shown that the computed wave speed is not a good indicator of the accuracy of a particular method. A fourth-order time-linearized, Hermitian compact operator technique is found to be the most accurate method for a variety of time and space sizes.
The dynamics of nonlinear reaction-diffusion equations with small Lévy noise
Debussche, Arnaud; Imkeller, Peter
2013-01-01
This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose domains of attraction meet in a separating manifold with several saddle points. Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and transition times between the domains of attraction depend polynomially on the noise intensity in the small intensity limit. Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.
Reaction-diffusion theory in the presence of an attractive harmonic potential
Spendier, K.; Sugaya, S.; Kenkre, V. M.
2013-12-01
Problems involving the capture of a moving entity by a trap occur in a variety of physical situations, the moving entity being an electron, an excitation, an atom, a molecule, a biological object such as a receptor cluster, a cell, or even an animal such as a mouse carrying an epidemic. Theoretical considerations have almost always assumed that the particle motion is translationally invariant. We study here the case when that assumption is relaxed, in that the particle is additionally subjected to a harmonic potential. This tethering to a center modifies the reaction-diffusion phenomenon. Using a Smoluchowski equation to describe the system, we carry out a study which is explicit in one dimension but can be easily extended for arbitrary dimensions. Interesting features emerge depending on the relative location of the trap, the attractive center, and the initial placement of the diffusing particle.
Existence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations
Ducrot, Arnaud; Matano, Hiroshi
2012-01-01
We consider one-dimensional reaction-diffusion equations for a large class of spatially periodic nonlinearities (including multistable ones) and study the asymptotic behavior of solutions with Heaviside type initial data. Our analysis reveals some new dynamics where the profile of the propagation is not characterized by a single front, but by a layer of several fronts which we call a terrace. Existence and convergence to such a terrace is proven by using an intersection number argument, without much relying on standard linear analysis. Hence, on top of the peculiar phenomenon of propagation that our work highlights, several corollaries will follow on the existence and convergence to pulsating traveling fronts even for highly degenerate nonlinearities that have not been treated before.
THE EXTINCTION BEHAVIOR OF THE SOLUTIONS FOR A CLASS OF REACTION-DIFFUSION EQUATIONS
陈松林
2001-01-01
The methods of Lp estimation are used to discuss the extinction phenomena of the solutions to the following reaction-diffusion equations with initial-boudnary values u/ t = Au-λ |u|γ-1u-βu ((x,t) ∈Ω×(0,+∞)),u(x,t) | Ω×(0.+∞) = 0,u(x,0) = uo(x) ∈ H1 0(Ω) ∩ L1+γ(Ω) (x ∈Ω).Sufficient and necessary conditions about the extinction of the solutions is given Here λ＞0, γ＞ 0, β＞ 0 are constants, Ω∈ RN is bounded with smooth boundary Ω At last,it is simulated with a higher order equation by using the present methods.
Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system.
Muhammad Abbas
Full Text Available In this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretize the time derivative while cubic B-spline is used as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann method. The accuracy of the proposed scheme is demonstrated by applying it on a test problem. The performance of this scheme is shown by computing L∞ and L2 error norms for different time levels. The numerical results are found to be in good agreement with known exact solutions.
Numerical method using cubic B-spline for a strongly coupled reaction-diffusion system.
Abbas, Muhammad; Majid, Ahmad Abd; Md Ismail, Ahmad Izani; Rashid, Abdur
2014-01-01
In this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretize the time derivative while cubic B-spline is used as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann method. The accuracy of the proposed scheme is demonstrated by applying it on a test problem. The performance of this scheme is shown by computing L∞ and L2 error norms for different time levels. The numerical results are found to be in good agreement with known exact solutions.
STEPS: modeling and simulating complex reaction-diffusion systems with Python
Stefan Wils
2009-06-01
Full Text Available We describe how the use of the Python language improved the user interface of the program STEPS. STEPS is a simulation platform for modeling and stochastic simulation of coupled reaction-diffusion systems with complex 3-dimensional boundary conditions. Setting up such models is a complicated process that consists of many phases. Initial versions of STEPS relied on a static input format that did not cleanly separate these phases, limiting modelers in how they could control the simulation and becoming increasingly complex as new features and new simulation algorithms were added. We solved all of these problems by tightly integrating STEPS with Python, using SWIG to expose our existing simulation code.
Oscillatory pulses and wave trains in a bistable reaction-diffusion system with cross diffusion.
Zemskov, Evgeny P; Tsyganov, Mikhail A; Horsthemke, Werner
2017-01-01
We study waves with exponentially decaying oscillatory tails in a reaction-diffusion system with linear cross diffusion. To be specific, we consider a piecewise linear approximation of the FitzHugh-Nagumo model, also known as the Bonhoeffer-van der Pol model. We focus on two types of traveling waves, namely solitary pulses that correspond to a homoclinic solution, and sequences of pulses or wave trains, i.e., a periodic solution. The effect of cross diffusion on wave profiles and speed of propagation is analyzed. We find the intriguing result that both pulses and wave trains occur in the bistable cross-diffusive FitzHugh-Nagumo system, whereas only fronts exist in the standard bistable system without cross diffusion.
On the Statistics of Reaction-Diffusion Simulations for Molecular Communication
Noel, Adam; Schober, Robert
2015-01-01
A molecule traveling in a realistic propagation environment can experience stochastic interactions with other molecules and the environment boundary. The statistical behavior of some isolated phenomena, such as dilute unbounded molecular diffusion, are well understood. However, the coupling of multiple interactions can impede closed-form analysis, such that simulations are required to determine the statistics. This paper compares the statistics of molecular reaction-diffusion simulation models from the perspective of molecular communication systems. Microscopic methods track the location and state of every molecule, whereas mesoscopic methods partition the environment into virtual containers that hold molecules. The properties of each model are described and compared with a hybrid of both models. Simulation results also assess the accuracy of Poisson and Gaussian approximations of the underlying Binomial statistics.
Accelerated stochastic and hybrid methods for spatial simulations of reaction diffusion systems
Rossinelli, Diego; Bayati, Basil; Koumoutsakos, Petros
2008-01-01
Spatial distributions characterize the evolution of reaction-diffusion models of several physical, chemical, and biological systems. We present two novel algorithms for the efficient simulation of these models: Spatial τ-Leaping ( Sτ-Leaping), employing a unified acceleration of the stochastic simulation of reaction and diffusion, and Hybrid τ-Leaping ( Hτ-Leaping), combining a deterministic diffusion approximation with a τ-Leaping acceleration of the stochastic reactions. The algorithms are validated by solving Fisher's equation and used to explore the role of the number of particles in pattern formation. The results indicate that the present algorithms have a nearly constant time complexity with respect to the number of events (reaction and diffusion), unlike the exact stochastic simulation algorithm which scales linearly.
Global existence and asymptotic stability of equilibria to reaction-diffusion systems
Wang, Rong-Nian; Tang, Zhong Wei
2009-06-01
In this paper, we study weakly coupled reaction-diffusion systems in unbounded domains of {\\bb R}^2 or {\\bb R}^3 , where the reaction terms are sums of quasimonotone nondecreasing and nonincreasing functions. Such systems are more complicated than those in many previous publications and little is known about them. A comparison principle and global existence, and boundedness theorems for solutions to these systems are established. Sufficient conditions on the nonlinearities, ensuring the positively Ljapunov stability of the zero solution with respect to H2-perturbations, are also obtained. As samples of applications, these results are applied to an autocatalytic chemical model and a concrete problem, whose nonlinearities are nonquasimonotone. Our results are novel. In particular, we present a solution to an open problem posed by Escher and Yin (2005 J. Nonlinear Anal. Theory Methods Appl. 60 1065-84).
Critical behavior in reaction-diffusion systems exhibiting absorbing phase transition
Ódor, G
2003-01-01
Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n>1 parents and where explicit diffusion of single particles (A) exists are reviewed. Arguments based on mean-field approximation and simulations are given which support novel kind of non-equilibrium criticality. These are in contradiction with the implications of a suggested phenomenological, multiplicative noise Langevin equation approach and with some of recent numerical analysis. Simulation results for the one and two dimensional binary spreading 2A -> 4A, 4A -> 2A model display a new type of mean-field criticality characterized by alpha=1/3 and beta=1/2 critical exponents suggested in cond-mat/0210615.
Liang, Xiao; Wang, Linshan; Wang, Yangfan; Wang, Ruili
2016-09-01
In this paper, we focus on the long time behavior of the mild solution to delayed reaction-diffusion Hopfield neural networks (DRDHNNs) driven by infinite dimensional Wiener processes. We analyze the existence, uniqueness, and stability of this system under the local Lipschitz function by constructing an appropriate Lyapunov-Krasovskii function and utilizing the semigroup theory. Some easy-to-test criteria affecting the well-posedness and stability of the networks, such as infinite dimensional noise and diffusion effect, are obtained. The criteria can be used as theoretic guidance to stabilize DRDHNNs in practical applications when infinite dimensional noise is taken into consideration. Meanwhile, considering the fact that the standard Brownian motion is a special case of infinite dimensional Wiener process, we undertake an analysis of the local Lipschitz condition, which has a wider range than the global Lipschitz condition. Two samples are given to examine the availability of the results in this paper. Simulations are also given using the MATLAB.
Judd, S L; Judd, Stephen L.; Silber, Mary
1998-01-01
This paper investigates the competition between both simple (e.g. stripes, hexagons) and ``superlattice'' (super squares, super hexagons) Turing patterns in two-component reaction-diffusion systems. ``Superlattice'' patterns are formed from eight or twelve Fourier modes, and feature structure at two different length scales. Using perturbation theory, we derive simple analytical expressions for the bifurcation equation coefficients on both rhombic and hexagonal lattices. These expressions show that, no matter how complicated the reaction kinectics, the nonlinear reaction terms reduce to just four effective terms within the bifurcation equation coefficients. Moreover, at the hexagonal degeneracy -- when the quadratic term in the hexagonal bifurcation equation disappears -- the number of effective system parameters drops to two, allowing a complete characterization of the possible bifurcation results at this degeneracy. The general results are then applied to specific model equations, to investigate the stabilit...
Vorticity field, helicity integral and persistence of entanglement in reaction-diffusion systems
Trueba, J L; Arrayas, M [Area de Electromagnetismo, Universidad Rey Juan Carlos, Camino del Molino s/n, 28943 Fuenlabrada, Madrid (Spain)
2009-07-17
We show that a global description of the stability of entangled structures in reaction-diffusion systems can be made by means of a helicity integral. A vorticity vector field is defined for these systems, as in electromagnetism or fluid dynamics. We have found under which conditions the helicity is conserved or lost through the boundaries of the medium, so the entanglement of structures observed is preserved or disappears during time evolution. We illustrate the theory with an example of knotted entanglement in a FitzHugh-Nagumo model. For this model, we introduce new non-trivial initial conditions using the Hopf fibration and follow the time evolution of the entanglement. (fast track communication)
Wavefronts in time-delayed reaction-diffusion systems. Theory and comparison to experiment
Fort, Joaquim [Departament de Fisica, Universitat de Girona, Girona (Spain)]. E-mail: joaquim.fort@udg.es; Mendez, Vicenc [Facultat de Ciencies de la Salut, Universitat Internacional de Catalunya, Ssant Cugat del Valles (Spain)]. E-mail: vmendez@csc.unica.edu
2002-06-01
We review the recent theoretical progress in the formulation and solution of the front speed problem for time-delayed reaction-diffusion systems. Most of the review is focused on hyperbolic equations. They have been widely used in recent years, because they allow for analytical solutions and yield a realistic description of some relevant phenomena. The theoretical methods are applied to a range of applications, including population dynamics, forest fire models, bistable systems and combustion wavefronts. We also present a detailed account of successful predictions of the models, as assessed by comparison to experimental data for some biophysical systems, without making use of any free parameters. Areas where the work reviewed may contribute to future progress are discussed. (author)
An observer for an occluded reaction-diffusion system with spatially varying parameters
Kramer, Sean; Bollt, Erik M.
2017-03-01
Spatially dependent parameters of a two-component chaotic reaction-diffusion partial differential equation (PDE) model describing ocean ecology are observed by sampling a single species. We estimate the model parameters and the other species in the system by autosynchronization, where quantities of interest are evolved according to misfit between model and observations, to only partially observed data. Our motivating example comes from oceanic ecology as viewed by remote sensing data, but where noisy occluded data are realized in the form of cloud cover. We demonstrate a method to learn a large-scale coupled synchronizing system that represents the spatio-temporal dynamics and apply a network approach to analyze manifold stability.
Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics
Strehl, Robert; Ilie, Silvana, E-mail: silvana@ryerson.ca [Department of Mathematics, Ryerson University, Toronto, Ontario M5B 2K3 (Canada)
2015-12-21
In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated on three benchmarking systems, with special focus on approximation accuracy and efficiency.
Hepburn, I.; Chen, W.; De Schutter, E.
2016-08-01
Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realistic biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.
KPP reaction-diffusion equations with a non-linear loss inside a cylinder
Giletti, Thomas
2010-01-01
We consider in this paper a reaction-diffusion system in presence of a flow and under a KPP hypothesis. While the case of a single-equation has been extensively studied since the pioneering Kolmogorov-Petrovski-Piskunov paper, the study of the corresponding system with a Lewis number not equal to 1 is still quite open. Here, we will prove some results about the existence of travelling fronts and generalized travelling fronts solutions of such a system with the presence of a non-linear spacedependent loss term inside the domain. In particular, we will point out the existence of a minimal speed, above which any real value is an admissible speed. We will also give some spreading results for initial conditions decaying exponentially at infinity.
KPP reaction-diffusion system with a nonlinear loss inside a cylinder
Giletti, Thomas
2010-09-01
We consider in this paper a reaction-diffusion system in the presence of a flow and under a KPP hypothesis. While the case of a single-equation has been extensively studied since the pioneering Kolmogorov-Petrovski-Piskunov paper, the study of the corresponding system with a Lewis number not equal to 1 is still quite open. Here, we will prove some results about the existence of travelling fronts and generalized travelling fronts solutions of such a system with the presence of a nonlinear space-dependent loss term inside the domain. In particular, we will point out the existence of a minimal speed, above which any real value is an admissible speed. We will also give some spreading results for initial conditions decaying exponentially at infinity.
TRAVELING WAVE SPEED AND SOLUTION IN REACTION-DIFFUSION EQUATION IN ONE DIMENSION
周天寿; 张锁春
2001-01-01
By Painlevé analysis, traveling wave speed and solution of reaction-diffusion equations for the concentration of one species in one spatial dimension are in detail investigated. When the exponent of the creation term is larger than the one of the annihilation term, two typical cases are studied, one with the exact traveling wave solutions, yielding the values of speeds, the other with the series expansion solution, also yielding the value of speed. Conversely, when the exponent of creation term is smaller than the one of the annihilation term, two typical cases are also studied, but only for one of them, there is a series development solution, yielding the value of speed, and for the other, traveling wave solution cannot exist. Besides, the formula of calculating speeds and solutions of planar wave within the thin boundary layer are given for a class of typical excitable media.
Grytskyy, Dmytro; Diesmann, Markus; Helias, Moritz
2016-06-01
Self-organized structures in networks with spike-timing dependent synaptic plasticity (STDP) are likely to play a central role for information processing in the brain. In the present study we derive a reaction-diffusion-like formalism for plastic feed-forward networks of nonlinear rate-based model neurons with a correlation sensitive learning rule inspired by and being qualitatively similar to STDP. After obtaining equations that describe the change of the spatial shape of the signal from layer to layer, we derive a criterion for the nonlinearity necessary to obtain stable dynamics for arbitrary input. We classify the possible scenarios of signal evolution and find that close to the transition to the unstable regime metastable solutions appear. The form of these dissipative solitons is determined analytically and the evolution and interaction of several such coexistent objects is investigated.
Grytskyy, Dmytro; Diesmann, Markus; Helias, Moritz
2016-06-01
Self-organized structures in networks with spike-timing dependent synaptic plasticity (STDP) are likely to play a central role for information processing in the brain. In the present study we derive a reaction-diffusion-like formalism for plastic feed-forward networks of nonlinear rate-based model neurons with a correlation sensitive learning rule inspired by and being qualitatively similar to STDP. After obtaining equations that describe the change of the spatial shape of the signal from layer to layer, we derive a criterion for the nonlinearity necessary to obtain stable dynamics for arbitrary input. We classify the possible scenarios of signal evolution and find that close to the transition to the unstable regime metastable solutions appear. The form of these dissipative solitons is determined analytically and the evolution and interaction of several such coexistent objects is investigated.
A reaction-diffusion-based coding rate control mechanism for camera sensor networks.
Yamamoto, Hiroshi; Hyodo, Katsuya; Wakamiya, Naoki; Murata, Masayuki
2010-01-01
A wireless camera sensor network is useful for surveillance and monitoring for its visibility and easy deployment. However, it suffers from the limited capacity of wireless communication and a network is easily overflown with a considerable amount of video traffic. In this paper, we propose an autonomous video coding rate control mechanism where each camera sensor node can autonomously determine its coding rate in accordance with the location and velocity of target objects. For this purpose, we adopted a biological model, i.e., reaction-diffusion model, inspired by the similarity of biological spatial patterns and the spatial distribution of video coding rate. Through simulation and practical experiments, we verify the effectiveness of our proposal.
Cluster geometry and survival probability in systems driven by reaction-diffusion dynamics
Windus, Alastair; Jensen, Henrik J [The Institute for Mathematical Sciences, 53 Prince' s Gate, South Kensington, London SW7 2PG (United Kingdom)], E-mail: h.jensen@imperial.ac.uk
2008-11-15
We consider a reaction-diffusion model incorporating the reactions A{yields}{phi}, A{yields}2A and 2A{yields}3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order absorbing phase transition to an extinct state. A tricritical point separates the two phase lines. While we comment on this critical behaviour, the main focus of the paper is on the geometry of the population clusters that form. We observe the different cluster structures that arise at criticality for the three different types of critical behaviour and show that there exists a linear relationship for the survival probability against initial cluster size at the tricritical point only.
Complex patterns in reaction-diffusion systems a tale of two front instabilities
Hagberg, A; Aric Hagberg; Ehud Meron
1994-01-01
Two front instabilities in a reaction-diffusion system are shown to lead to the formation of complex patterns. The first is an instability to transverse modulations that drives the formation of labyrinthine patterns. The second is a Nonequilibrium Ising-Bloch (NIB) bifurcation that renders a stationary planar front unstable and gives rise to a pair of counterpropagating fronts. Near the NIB bifurcation the relation of the front velocity to curvature is highly nonlinear and transitions between counterpropagating fronts become feasible. Nonuniformly curved fronts may undergo local front transitions that nucleate spiral-vortex pairs. These nucleation events provide the ingredient needed to initiate spot splitting and spiral turbulence. Similar spatio-temporal processes have been observed recently in the ferrocyanide-iodate-sulfite reaction.
Scenarios of domain pattern formation in a reaction-diffusion system
Muratov, C B
1996-01-01
We performed an extensive numerical study of a two-dimensional reaction-diffusion system of the activator-inhibitor type in which domain patterns can form. We showed that both multidomain and labyrinthine patterns may form spontaneously as a result of Turing instability. In the stable homogeneous system with the fast inhibitor one can excite both localized and extended patterns by applying a localized stimulus. Depending on the parameters and the excitation level of the system stripes, spots, wriggled stripes, or labyrinthine patterns form. The labyrinthine patterns may be both connected and disconnected. In the the stable homogeneous system with the slow inhibitor one can excite self-replicating spots, breathing patterns, autowaves and turbulence. The parameter regions in which different types of patterns are realized are explained on the basis of the asymptotic theory of instabilities for patterns with sharp interfaces developed by us in Phys. Rev. E. 53, 3101 (1996). The dynamics of the patterns observed i...
Robustness of the Critical Behaviour in a Discrete Stochastic Reaction-Diffusion Medium
Fatès, Nazim; Berry, Hugues
We study the steady states of a reaction-diffusion medium modelled by a stochastic 2D cellular automaton. We consider the Greenberg-Hastings model where noise and topological irregularities of the grid are taken into account. The decrease of the probability of excitation changes qualitatively the behaviour of the system from an "active" to an "extinct" steady state. Simulations show that this change occurs near a critical threshold; it is identified as a nonequilibrium phase transition which belongs to the directed percolation universality class. We test the robustness of the phenomenon by introducing persistent defects in the topology : directed percolation behaviour is conserved. Using experimental and analytical tools, we suggest that the critical threshold varies as the inverse of the average number of neighbours per cell.
Xu Rui [Department of Applied Mathematics, Xi' an Jiaotong University, Xi' an 710049 (China)]. E-mail: rxu88@yahoo.com.cn; Chaplain, M.A.J. [Department of Mathematics, University of Dundee, Dundee DD1 4HN (United Kingdom); Davidson, F.A. [Department of Mathematics, University of Dundee, Dundee DD1 4HN (United Kingdom)
2006-11-15
In this paper, we first investigate a stage-structured competitive model with time delays, harvesting, and nonlocal spatial effect. By using an iterative technique recently developed by Wu and Zou (Wu J, Zou X. Travelling wave fronts of reaction-diffusion systems with delay. J Dynam Differen Equat 2001;13:651-87), sufficient conditions are established for the existence of travelling front solution connecting the two boundary equilibria in the case when there is no positive equilibrium. The travelling wave front corresponds to an invasion by a stronger species which drives the weaker species to extinction. Secondly, we consider a stage-structured competitive model with time delays and nonlocal spatial effect when the domain is finite. We prove the global stability of each of the nonnegative equilibria and demonstrate that the more complex model studied here admits three possible long term behaviors: coexistence, bistability and dominance as is the case for the standard Lotka-Voltera competitive model.
Cluster geometry and survival probability in systems driven by reaction diffusion dynamics
Windus, Alastair; Jensen, Henrik J.
2008-11-01
We consider a reaction-diffusion model incorporating the reactions A→phi, A→2A and 2A→3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order absorbing phase transition to an extinct state. A tricritical point separates the two phase lines. While we comment on this critical behaviour, the main focus of the paper is on the geometry of the population clusters that form. We observe the different cluster structures that arise at criticality for the three different types of critical behaviour and show that there exists a linear relationship for the survival probability against initial cluster size at the tricritical point only.
Scalable implicit methods for reaction-diffusion equations in two and three space dimensions
Veronese, S.V.; Othmer, H.G. [Univ. of Utah, Salt Lake City, UT (United States)
1996-12-31
This paper describes the implementation of a solver for systems of semi-linear parabolic partial differential equations in two and three space dimensions. The solver is based on a parallel implementation of a non-linear Alternating Direction Implicit (ADI) scheme which uses a Cartesian grid in space and an implicit time-stepping algorithm. Various reordering strategies for the linearized equations are used to reduce the stride and improve the overall effectiveness of the parallel implementation. We have successfully used this solver for large-scale reaction-diffusion problems in computational biology and medicine in which the desired solution is a traveling wave that may contain rapid transitions. A number of examples that illustrate the efficiency and accuracy of the method are given here; the theoretical analysis will be presented.
Hybrid approaches for multiple-species stochastic reaction-diffusion models.
Spill, Fabian
2015-10-01
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.
Fan, Xiaofei; Zhang, Xian; Wu, Ligang; Shi, Michael
2017-01-01
This paper is concerned with the finite-time stability problem of the delayed genetic regulatory networks (GRNs) with reaction-diffusion terms under Dirichlet boundary conditions. By constructing a Lyapunov-Krasovskii functional including quad-slope integrations, we establish delay-dependent finite-time stability criteria by employing the Wirtinger-type integral inequality, Gronwall inequality, convex technique, and reciprocally convex technique. In addition, the obtained criteria are also reaction-diffusion-dependent. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.
Wazwaz, Abdul-Majid
2017-07-01
In this work we address the Lane-Emden boundary value problems which appear in chemical applications, biochemical applications, and scientific disciplines. We apply the variational iteration method to solve two specific models. The first problem models reaction-diffusion equation in a spherical catalyst, while the second problem models the reaction-diffusion process in a spherical biocatalyst. We obtain reliable analytical expressions of the concentrations and the effectiveness factors. Proper graphs will be used to illustrate the obtained results. The proposed analysis demonstrates reliability and efficiency applicability of the employed method.
反应扩散方程的奇摄动%SINGULAR PERTURBATION FOR REACTION DIFFUSION EQUATIONS
莫嘉琪; 王辉; 朱江
2003-01-01
The singularly perturbed initial boundary value problems for reaction diffusion equations are considered. Under suitable conditions and by using the theory of differential inequality, the asymptotic behavior of solution for initial boundary value problems are studied, where the reduced problems possess two intersecting solutions.
Accumulations of T-points in a model for solitary pulses in an excitable reaction-diffusion medium.
Homburg, A.J.; Natiello, M.A.
2005-01-01
We consider a family of differential equations that describes traveling waves in a reaction-diffusion equation modeling oxidation of carbon oxide on a platinum surface, near the onset of spatio-temporal chaos. The organizing bifurcation for the bifurcation structure with small carbon oxide
Salem Abdelmalek
2014-11-01
Full Text Available In this article we construct the invariant regions for m-component reaction-diffusion systems with a tridiagonal symmetric Toeplitz matrix of diffusion coefficients and with nonhomogeneous boundary conditions. We establish the existence of global solutions, and use Lyapunov functional methods. The nonlinear reaction term is assumed to be of polynomial growth.
Liming WU; Zhengliang ZHANG
2006-01-01
We establish Talagrand's T2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type's approximations and the known results in the finite dimensional case. Furthermore in the additive noise case we prove also logarithmic Sobolev inequalities with sharp constants. Applications to ReactionDiffusion equations are provided.
Chuangxia Huang
2009-01-01
Full Text Available This paper is concerned with pth moment exponential stability of stochastic reaction-diffusion Cohen-Grossberg neural networks with time-varying delays. With the help of Lyapunov method, stochastic analysis, and inequality techniques, a set of new suffcient conditions on pth moment exponential stability for the considered system is presented. The proposed results generalized and improved some earlier publications.
Siebert, Julien; Alonso, Sergio; Bär, Markus; Schöll, Eckehard
2014-05-01
A one-component bistable reaction-diffusion system with asymmetric nonlocal coupling is derived as a limiting case of a two-component activator-inhibitor reaction-diffusion model with differential advection. The effects of asymmetric nonlocal couplings in such a bistable reaction-diffusion system are then compared to the previously studied case of a system with symmetric nonlocal coupling. We carry out a linear stability analysis of the spatially homogeneous steady states of the model and numerical simulations of the model to show how the asymmetric nonlocal coupling controls and alters the steady states and the front dynamics in the system. In a second step, a third fast reaction-diffusion equation is included which induces the formation of more complex patterns. A linear stability analysis predicts traveling waves for asymmetric nonlocal coupling, in contrast to a stationary Turing patterns for a system with symmetric nonlocal coupling. These findings are verified by direct numerical integration of the full equations with nonlocal coupling.
Pham, Tuan D.; Watanabe, Yuzuru; Higuchi, Mitsunori; Suzuki, Hiroyuki
2017-02-01
Texture analysis of computed tomography (CT) imaging has been found useful to distinguish subtle differences, which are in- visible to human eyes, between malignant and benign tissues in cancer patients. This study implemented two complementary methods of texture analysis, known as the gray-level co-occurrence matrix (GLCM) and the experimental semivariogram (SV) with an aim to improve the predictive value of evaluating mediastinal lymph nodes in lung cancer. The GLCM was explored with the use of a rich set of its derived features, whereas the SV feature was extracted on real and synthesized CT samples of benign and malignant lymph nodes. A distinct advantage of the computer methodology presented herein is the alleviation of the need for an automated precise segmentation of the lymph nodes. Using the logistic regression model, a sensitivity of 75%, specificity of 90%, and area under curve of 0.89 were obtained in the test population. A tenfold cross-validation of 70% accuracy of classifying between benign and malignant lymph nodes was obtained using the support vector machines as a pattern classifier. These results are higher than those recently reported in literature with similar studies.
Pham, Tuan D; Watanabe, Yuzuru; Higuchi, Mitsunori; Suzuki, Hiroyuki
2017-02-24
Texture analysis of computed tomography (CT) imaging has been found useful to distinguish subtle differences, which are in- visible to human eyes, between malignant and benign tissues in cancer patients. This study implemented two complementary methods of texture analysis, known as the gray-level co-occurrence matrix (GLCM) and the experimental semivariogram (SV) with an aim to improve the predictive value of evaluating mediastinal lymph nodes in lung cancer. The GLCM was explored with the use of a rich set of its derived features, whereas the SV feature was extracted on real and synthesized CT samples of benign and malignant lymph nodes. A distinct advantage of the computer methodology presented herein is the alleviation of the need for an automated precise segmentation of the lymph nodes. Using the logistic regression model, a sensitivity of 75%, specificity of 90%, and area under curve of 0.89 were obtained in the test population. A tenfold cross-validation of 70% accuracy of classifying between benign and malignant lymph nodes was obtained using the support vector machines as a pattern classifier. These results are higher than those recently reported in literature with similar studies.
Turing pattern formation in the chlorine dioxide-iodine- malonic acid reaction-diffusion system
Setayeshgar, Sima
The formation of localized structures in the chlorine dioxide-idodine-malonic acid (CDIMA) reaction-diffusion system is investigated numerically using a realistic model of this system. We analyze the one-dimensional patterns formed along the gradients imposed by boundary feeds, and study their linear stability to symmetry- breaking perturbations (the Turing instability) in the plane transverse to these gradients. We establish that an often-invoked simple local linear analysis which neglects longitudinal diffusion is inappropriate for predicting the linear stability of these patterns. Using a fully nonuniform analysis, we investigate the structure of the patterns formed along the gradients and their stability to transverse Turing pattern formation as a function of the values of two control parameters: the malonic acid feed concentration and the size of the reactor in the dimension along the gradients. The results from this investigation are compared with existing experimental results. We also verify that the two-variable reduction of the chemical model employed in the linear stability analysis is justified. Finally, we present numerical solution of the CDIMA system in two dimensions which is in qualitative agreement with experiments. This result also confirms our linear stability analysis, while demonstrating the feasibility of numerical exploration of realistic chemical models.
Parallel Solutions for Voxel-Based Simulations of Reaction-Diffusion Systems
Daniele D’Agostino
2014-01-01
Full Text Available There is an increasing awareness of the pivotal role of noise in biochemical processes and of the effect of molecular crowding on the dynamics of biochemical systems. This necessity has given rise to a strong need for suitable and sophisticated algorithms for the simulation of biological phenomena taking into account both spatial effects and noise. However, the high computational effort characterizing simulation approaches, coupled with the necessity to simulate the models several times to achieve statistically relevant information on the model behaviours, makes such kind of algorithms very time-consuming for studying real systems. So far, different parallelization approaches have been deployed to reduce the computational time required to simulate the temporal dynamics of biochemical systems using stochastic algorithms. In this work we discuss these aspects for the spatial TAU-leaping in crowded compartments (STAUCC simulator, a voxel-based method for the stochastic simulation of reaction-diffusion processes which relies on the Sτ-DPP algorithm. In particular we present how the characteristics of the algorithm can be exploited for an effective parallelization on the present heterogeneous HPC architectures.
Bursting regimes in a reaction-diffusion system with action potential-dependent equilibrium.
Stephen R Meier
Full Text Available The equilibrium Nernst potential plays a critical role in neural cell dynamics. A common approximation used in studying electrical dynamics of excitable cells is that the ionic concentrations inside and outside the cell membranes act as charge reservoirs and remain effectively constant during excitation events. Research into brain electrical activity suggests that relaxing this assumption may provide a better understanding of normal and pathophysiological functioning of the brain. In this paper we explore time-dependent ionic concentrations by allowing the ion-specific Nernst potentials to vary with developing transmembrane potential. As a specific implementation, we incorporate the potential-dependent Nernst shift into a one-dimensional Morris-Lecar reaction-diffusion model. Our main findings result from a region in parameter space where self-sustaining oscillations occur without external forcing. Studying the system close to the bifurcation boundary, we explore the vulnerability of the system with respect to external stimulations which disrupt these oscillations and send the system to a stable equilibrium. We also present results for an extended, one-dimensional cable of excitable tissue tuned to this parameter regime and stimulated, giving rise to complex spatiotemporal pattern formation. Potential applications to the emergence of neuronal bursting in similar two-variable systems and to pathophysiological seizure-like activity are discussed.
Local traps as nanoscale reaction-diffusion probes: B clustering in c-Si
Pawlak, B. J., E-mail: bartekpawlak72@gmail.com [Globalfoundries, Kapeldreef 75, B-3001 Leuven (Belgium); Cowern, N. E. B.; Ahn, C. [School of Electrical and Electronic Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU (United Kingdom); Vandervorst, W. [IMEC, Kapeldreef 75, B-3001 Leuven, Belgium and IKS, Department of Physics, KU Leuven, Leuven (Belgium); Gwilliam, R. [Surrey Ion Beam Centre, Nodus Laboratory, University of Surrey, Guildford, Surrey GU2 7XH (United Kingdom); Berkum, J. G. M. van [Philips CFT, Prof. Holstlaan 4, 5656 AA Eindhoven (Netherlands)
2014-12-01
A series of B implantation experiments into initially amorphized and not fully recrystallized Si, i.e., into an existing a/c-Si bi-layer material, have been conducted. We varied B dose, energy, and temperature during implantation process itself. Significant B migration has been observed within c-Si part near the a/c-interface and near the end-of-range region before any activation annealing. We propose a general concept of local trapping sites as experimental probes of nanoscale reaction-diffusion processes. Here, the a/c-Si interface acts as a trap, and the process itself is explored as the migration and clustering of mobile BI point defects in nearby c-Si during implantation at temperatures from 77 to 573 K. We find that at room temperature—even at B concentrations as high as 1.6 atomic %, the key B-B pairing step requires diffusion lengths of several nm owing to a small, ∼0.1 eV, pairing energy barrier. Thus, in nanostructures doped by ion implantation, the implant distribution can be strongly influenced by thermal migration to nearby impurities, defects, and interfaces.
Tulzer, Gerhard; Heitzinger, Clemens
2016-04-22
In this work, we develop a 2D algorithm for stochastic reaction-diffusion systems describing the binding and unbinding of target molecules at the surfaces of affinity-based sensors. In particular, we simulate the detection of DNA oligomers using silicon-nanowire field-effect biosensors. Since these devices are uniform along the nanowire, two dimensions are sufficient to capture the kinetic effects features. The model combines a stochastic ordinary differential equation for the binding and unbinding of target molecules as well as a diffusion equation for their transport in the liquid. A Brownian-motion based algorithm simulates the diffusion process, which is linked to a stochastic-simulation algorithm for association at and dissociation from the surface. The simulation data show that the shape of the cross section of the sensor yields areas with significantly different target-molecule coverage. Different initial conditions are investigated as well in order to aid rational sensor design. A comparison of the association/hybridization behavior for different receptor densities allows optimization of the functionalization setup depending on the target-molecule density.
Richter, Otto; Moenickes, Sylvia; Suhling, Frank
2012-02-01
The spatial dynamics of range expansion is studied in dependence of temperature. The main elements population dynamics, competition and dispersal are combined in a coherent approach based on a system of coupled partial differential equations of the reaction-diffusion type. The nonlinear reaction terms comprise population dynamic models with temperature dependent reproduction rates subject to an Allee effect and mutual competition. The effect of temperature on travelling wave solutions is investigated for a one dimensional model version. One main result is the importance of the Allee effect for the crossing of regions with unsuitable habitats. The nonlinearities of the interaction terms give rise to a richness of spatio-temporal dynamic patterns. In two dimensions, the resulting non-linear initial boundary value problems are solved over geometries of heterogeneous landscapes. Geo referenced model parameters such as mean temperature and elevation are imported into the finite element tool COMSOL Multiphysics from a geographical information system. The model is applied to the range expansion of species at the scale of middle Europe.
Pattern formation in reaction-diffusion systems: From spiral waves to turbulence
Davidsen, Joern
2009-05-01
Almost all systems we encounter in nature possess some sort of form or structure. In many cases, the structures arise from an initially unstructured state without the action of an agent that predetermines the pattern. Such self-organized structures emerge from cooperative interactions among the constituents of the system and often exhibit properties that are distinct from those of their constituent elements or molecules. For example, chemical waves in reaction-diffusion systems are at the core of a huge variety of physical, chemical, and biological processes. In (quasi) two-dimensional situations, spiral wave patterns are especially prevalent and determine the characteristics of processes such as surface catalytic oxidation reactions, contraction of the heart muscle, and various signaling mechanisms in biological systems. In this talk, I will review and discuss recent theoretical and experimental results regarding the dynamics, properties and stability of spiral waves and their three-dimensional analog (scroll waves). Special emphasis will be given to synchronization defect lines which generically arise in complex-oscillatory media, and the phenomenon of defect-mediated turbulence or filament turbulence where the dynamics of a pattern is dominated by the rapid motion, nucleation, and annihilation of spirals or scroll waves, respectively. The latter is of direct relevance in the context of ventricular fibrillation - a turbulent electrical wave activity that destroys the coherent contraction of the ventricular muscle and its main pumping function leading to sudden cardiac death.
The two-regime method for optimizing stochastic reaction-diffusion simulations
Flegg, M. B.
2011-10-19
Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for stochastic spatio-temporal simulation, ranging from detailed molecular-based approaches to less detailed compartment-based simulations. Compartment-based approaches yield quick and accurate mesoscopic results, but lack the level of detail that is characteristic of the computationally intensive molecular-based models. Often microscopic detail is only required in a small region (e.g. close to the cell membrane). Currently, the best way to achieve microscopic detail is to use a resource-intensive simulation over the whole domain. We develop the two-regime method (TRM) in which a molecular-based algorithm is used where desired and a compartment-based approach is used elsewhere. We present easy-to-implement coupling conditions which ensure that the TRM results have the same accuracy as a detailed molecular-based model in the whole simulation domain. Therefore, the TRM combines strengths of previously developed stochastic reaction-diffusion software to efficiently explore the behaviour of biological models. Illustrative examples and the mathematical justification of the TRM are also presented.
Parallel solutions for voxel-based simulations of reaction-diffusion systems.
D'Agostino, Daniele; Pasquale, Giulia; Clematis, Andrea; Maj, Carlo; Mosca, Ettore; Milanesi, Luciano; Merelli, Ivan
2014-01-01
There is an increasing awareness of the pivotal role of noise in biochemical processes and of the effect of molecular crowding on the dynamics of biochemical systems. This necessity has given rise to a strong need for suitable and sophisticated algorithms for the simulation of biological phenomena taking into account both spatial effects and noise. However, the high computational effort characterizing simulation approaches, coupled with the necessity to simulate the models several times to achieve statistically relevant information on the model behaviours, makes such kind of algorithms very time-consuming for studying real systems. So far, different parallelization approaches have been deployed to reduce the computational time required to simulate the temporal dynamics of biochemical systems using stochastic algorithms. In this work we discuss these aspects for the spatial TAU-leaping in crowded compartments (STAUCC) simulator, a voxel-based method for the stochastic simulation of reaction-diffusion processes which relies on the Sτ-DPP algorithm. In particular we present how the characteristics of the algorithm can be exploited for an effective parallelization on the present heterogeneous HPC architectures.
Deriving reaction-diffusion models in ecology from interacting particle systems.
Cantrell, R S; Cosner, C
2004-02-01
We use a scaling procedure based on averaging Poisson distributed random variables to derive population level models from local models of interactions between individuals. The procedure is suggested by using the idea of hydrodynamic limits to derive reaction-diffusion models for population interactions from interacting particle systems. The scaling procedure is formal in the sense that we do not address the issue of proving that it converges; instead we focus on methods for computing the results of the scaling or deriving properties of rescaled systems. To that end we treat the scaling procedure as a transform, in analogy with the Laplace or Fourier transform, and derive operational formulas to aid in the computation of rescaled systems or the derivation of their properties. Since the limiting procedure is adapted from work by Durrett and Levin, we refer to the transform as the Durrett-Levin transform. We examine the effects of rescaling in various standard models, including Lotka-Volterra models, Holling type predator-prey models, and ratio-dependent models. The effects of scaling are mostly quantitative in models with smooth interaction terms, but ratio-dependent models are profoundly affected by the scaling. The scaling transforms ratio-dependent terms that are singular at the origin into smooth terms. Removing the singularity at the origin eliminates some of the unique dynamics that can arise in ratio-dependent models.
Fourier spectral methods for fractional-in-space reaction-diffusion equations
Bueno-Orovio, Alfonso
2014-04-01
© 2014, Springer Science+Business Media Dordrecht. Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains of ℝ. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.
Szalai, István; Cuiñas, Daniel; Takács, Nándor; Horváth, Judit; De Kepper, Patrick
2012-08-06
In his seminal 1952 paper, Alan Turing predicted that diffusion could spontaneously drive an initially uniform solution of reacting chemicals to develop stable spatially periodic concentration patterns. It took nearly 40 years before the first two unquestionable experimental demonstrations of such reaction-diffusion patterns could be made in isothermal single phase reaction systems. The number of these examples stagnated for nearly 20 years. We recently proposed a design method that made their number increase to six in less than 3 years. In this report, we formally justify our original semi-empirical method and support the approach with numerical simulations based on a simple but realistic kinetic model. To retain a number of basic properties of real spatial reactors but keep calculations to a minimal complexity, we introduce a new way to collapse the confined spatial direction of these reactors. Contrary to similar reduced descriptions, we take into account the effect of the geometric size in the confinement direction and the influence of the differences in the diffusion coefficient on exchange rates of species with their feed environment. We experimentally support the method by the observation of stationary patterns in red-ox reactions not based on oxihalogen chemistry. Emphasis is also brought on how one of these new systems can process different initial conditions and memorize them in the form of localized patterns of different geometries.
Bau, Haim; Liu, Changchun; Killawala, Chitvan; Sadik, Mohamed; Mauk, Michael
2014-11-01
Real-time amplification and quantification of specific nucleic acid sequences plays a major role in many medical and biotechnological applications. In the case of infectious diseases, quantification of the pathogen-load in patient specimens is critical to assessing disease progression, effectiveness of drug therapy, and emergence of drug-resistance. Typically, nucleic acid quantification requires sophisticated and expensive instruments, such as real-time PCR machines, which are not appropriate for on-site use and for low resource settings. We describe a simple, low-cost, reactiondiffusion based method for end-point quantification of target nucleic acids undergoing enzymatic amplification. The number of target molecules is inferred from the position of the reaction-diffusion front, analogous to reading temperature in a mercury thermometer. We model the process with the Fisher Kolmogoroff Petrovskii Piscounoff (FKPP) Equation and compare theoretical predictions with experimental observations. The proposed method is suitable for nucleic acid quantification at the point of care, compatible with multiplexing and high-throughput processing, and can function instrument-free. C.L. was supported by NIH/NIAID K25AI099160; M.S. was supported by the Pennsylvania Ben Franklin Technology Development Authority; C.K. and H.B. were funded, in part, by NIH/NIAID 1R41AI104418-01A1.
Interior Controllability of a 2×2 Reaction-Diffusion System with Cross-Diffusion Matrix
Hugo Leiva
2009-01-01
Full Text Available We prove the interior approximate controllability for the following 2×2 reaction-diffusion system with cross-diffusion matrix ut=aΔu−β(−Δ1/2u+bΔv+1ωf1(t,x in (0,τ×Ω, vt=cΔu−dΔv−β(−Δ1/2v+1ωf2(t,x in (0,τ×Ω, u=v=0, on (0,T×∂Ω, u(0,x=u0(x, v(0,x=v0(x, x∈Ω, where Ω is a bounded domain in ℝN (N≥1, u0,v0∈L2(Ω, the 2×2 diffusion matrix D=[abcd] has semisimple and positive eigenvalues 0<ρ1≤ρ2, β is an arbitrary constant, ω is an open nonempty subset of Ω, 1ω denotes the characteristic function of the set ω, and the distributed controls f1,f2∈L2([0,τ];L2(Ω. Specifically, we prove the following statement: if λ11/2ρ1+β>0 (where λ1 is the first eigenvalue of −Δ, then for all τ>0 and all open nonempty subset ω of Ω the system is approximately controllable on [0,τ].
A reaction-diffusion model for radiation-induced bystander effects.
Olobatuyi, Oluwole; de Vries, Gerda; Hillen, Thomas
2017-08-01
We develop and analyze a reaction-diffusion model to investigate the dynamics of the lifespan of a bystander signal emitted when cells are exposed to radiation. Experimental studies by Mothersill and Seymour 1997, using malignant epithelial cell lines, found that an emitted bystander signal can still cause bystander effects in cells even 60 h after its emission. Several other experiments have also shown that the signal can persist for months and even years. Also, bystander effects have been hypothesized as one of the factors responsible for the phenomenon of low-dose hyper-radiosensitivity and increased radioresistance (HRS/IRR). Here, we confirm this hypothesis with a mathematical model, which we fit to Joiner's data on HRS/IRR in a T98G glioma cell line. Furthermore, we use phase plane analysis to understand the full dynamics of the signal's lifespan. We find that both single and multiple radiation exposure can lead to bystander signals that either persist temporarily or permanently. We also found that, in an heterogeneous environment, the size of the domain exposed to radiation and the number of radiation exposures can determine whether a signal will persist temporarily or permanently. Finally, we use sensitivity analysis to identify those cell parameters that affect the signal's lifespan and the signal-induced cell death the most.
Modeling and finite difference numerical analysis of reaction-diffusion dynamics in a microreactor.
Plazl, Igor; Lakner, Mitja
2010-03-01
A theoretical description with numerical experiments and analysis of the reaction-diffusion processes of homogeneous and non-homogeneous reactions in a microreactor is presented considering the velocity profile for laminar flows of miscible and immiscible fluids in a microchannel at steady-state conditions. A Mathematical model in dimensionless form, containing convection, diffusion, and reaction terms are developed to analyze and to forecast the reactor performance. To examine the performance of different types of reactors, the outlet concentrations for the plug-flow reactor (PFR), and the continuous stirred-tank reactor (CSTR) are also calculated for the case of an irreversible homogeneous reaction of two components. The comparison of efficiency between ideal conventional macroscale reactors and the microreactor is presented for a wide range of operating conditions, expressed as different Pe numbers (0.01 < Pe < 10). The numerical procedure of complex non-linear systems based on an implicit finite-difference method improved by non-equidistant differences is proposed.
Saxena, R. K.; Mathai, A. M.; Haubold, H. J.
2015-10-01
This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized fractional time-derivative defined by Hilfer (2000), the space derivative of second order by the Riesz-Feller fractional derivative and adding the function ϕ (x, t) which is a nonlinear function governing reaction. The solution is derived by the application of the Laplace and Fourier transforms in a compact and closed form in terms of the H-function. The main result obtained in this paper provides an elegant extension of the fundamental solution for the space-time fractional diffusion equation obtained earlier by Mainardi et al. (2001, 2005) and a result very recently given by Tomovski et al. (2011). Computational representation of the fundamental solution is also obtained explicitly. Fractional order moments of the distribution are deduced. At the end, mild extensions of the derived results associated with a finite number of Riesz-Feller space fractional derivatives are also discussed.
Parallel Solutions for Voxel-Based Simulations of Reaction-Diffusion Systems
D'Agostino, Daniele; Pasquale, Giulia; Clematis, Andrea; Maj, Carlo; Mosca, Ettore; Milanesi, Luciano; Merelli, Ivan
2014-01-01
There is an increasing awareness of the pivotal role of noise in biochemical processes and of the effect of molecular crowding on the dynamics of biochemical systems. This necessity has given rise to a strong need for suitable and sophisticated algorithms for the simulation of biological phenomena taking into account both spatial effects and noise. However, the high computational effort characterizing simulation approaches, coupled with the necessity to simulate the models several times to achieve statistically relevant information on the model behaviours, makes such kind of algorithms very time-consuming for studying real systems. So far, different parallelization approaches have been deployed to reduce the computational time required to simulate the temporal dynamics of biochemical systems using stochastic algorithms. In this work we discuss these aspects for the spatial TAU-leaping in crowded compartments (STAUCC) simulator, a voxel-based method for the stochastic simulation of reaction-diffusion processes which relies on the Sτ-DPP algorithm. In particular we present how the characteristics of the algorithm can be exploited for an effective parallelization on the present heterogeneous HPC architectures. PMID:25045716
李新政; 白占国; 李燕; 贺亚峰; 赵昆
2015-01-01
The resonance interaction between two modes is investigated using a two-layer coupled Brusselator model. When two different wavelength modes satisfy resonance conditions, new modes will appear, and a variety of superlattice patterns can be obtained in a short wavelength mode subsystem. We find that even though the wavenumbers of two Turing modes are fixed, the parameter changes have infl uences on wave intensity and pattern selection. When a hexagon pattern occurs in the short wavelength mode layer and a stripe pattern appears in the long wavelength mode layer, the Hopf instability may happen in a nonlinearly coupled model, and twinkling-eye hexagon and travelling hexagon patterns will be obtained. The symmetries of patterns resulting from the coupled modes may be different from those of their parents, such as the cluster hexagon pattern and square pattern. With the increase of perturbation and coupling intensity, the nonlinear system will con-vert between a static pattern and a dynamic pattern when the Turing instability and Hopf instability happen in the nonlinear system. Besides the wavenumber ratio and intensity ratio of the two different wavelength Turing modes, perturbation and coupling intensity play an important role in the pattern formation and selection. According to the simulation results, we find that two modes with different symmetries can also be in the spatial resonance under certain conditions, and complex patterns appear in the two-layer coupled reaction diffusion systems.
Kunze, Markus
2011-01-01
We prove convergence of the solutions X_n of semilinear stochastic evolution equations dX_n(t) = (A_nX(t) + F_n(t,X_n(t)))dt + G_n(t,X_n(t))dW_H(t), X_n(0) = x_n, on a Banach space B, driven by a cylindrical Brownian motion W_H in a Hilbert space H. We assume that the operators A_n converge to A and the locally Lipschitz functions F_n and G_n converge to the locally Lipschitz functions F and G in an appropriate sense. Moreover, we obtain estimates for the lifetime of the solution X of the limiting problem in terms of the lifetimes of the approximating solutions X_n. We apply the results to prove global existence for reaction diffusion equations with multiplicative noise and a polynomially bounded reaction term satisfying suitable dissipativity conditions. The operator governing the linear part of the equation can be an arbitrary uniformly elliptic second order elliptic operator.
Bifurcation analysis of a delay reaction-diffusion malware propagation model with feedback control
Zhu, Linhe; Zhao, Hongyong; Wang, Xiaoming
2015-05-01
With the rapid development of network information technology, information networks security has become a very critical issue in our work and daily life. This paper attempts to develop a delay reaction-diffusion model with a state feedback controller to describe the process of malware propagation in mobile wireless sensor networks (MWSNs). By analyzing the stability and Hopf bifurcation, we show that the state feedback method can successfully be used to control unstable steady states or periodic oscillations. Moreover, formulas for determining the properties of the bifurcating periodic oscillations are derived by applying the normal form method and center manifold theorem. Finally, we conduct extensive simulations on large-scale MWSNs to evaluate the proposed model. Numerical evidences show that the linear term of the controller is enough to delay the onset of the Hopf bifurcation and the properties of the bifurcation can be regulated to achieve some desirable behaviors by choosing the appropriate higher terms of the controller. Furthermore, we obtain that the spatial-temporal dynamic characteristics of malware propagation are closely related to the rate constant for nodes leaving the infective class for recovered class and the mobile behavior of nodes.
A nonlocal and periodic reaction-diffusion-advection model of a single phytoplankton species.
Peng, Rui; Zhao, Xiao-Qiang
2016-02-01
In this article, we are concerned with a nonlocal reaction-diffusion-advection model which describes the evolution of a single phytoplankton species in a eutrophic vertical water column where the species relies solely on light for its metabolism. The new feature of our modeling equation lies in that the incident light intensity and the death rate are assumed to be time periodic with a common period. We first establish a threshold type result on the global dynamics of this model in terms of the basic reproduction number R0. Then we derive various characterizations of R0 with respect to the vertical turbulent diffusion rate, the sinking or buoyant rate and the water column depth, respectively, which in turn give rather precise conditions to determine whether the phytoplankton persist or become extinct. Our theoretical results not only extend the existing ones for the time-independent case, but also reveal new interesting effects of the modeling parameters and the time-periodic heterogeneous environment on persistence and extinction of the phytoplankton species, and thereby suggest important implications for phytoplankton growth control.
Brownian-motion based simulation of stochastic reaction-diffusion systems for affinity based sensors
Tulzer, Gerhard; Heitzinger, Clemens
2016-04-01
In this work, we develop a 2D algorithm for stochastic reaction-diffusion systems describing the binding and unbinding of target molecules at the surfaces of affinity-based sensors. In particular, we simulate the detection of DNA oligomers using silicon-nanowire field-effect biosensors. Since these devices are uniform along the nanowire, two dimensions are sufficient to capture the kinetic effects features. The model combines a stochastic ordinary differential equation for the binding and unbinding of target molecules as well as a diffusion equation for their transport in the liquid. A Brownian-motion based algorithm simulates the diffusion process, which is linked to a stochastic-simulation algorithm for association at and dissociation from the surface. The simulation data show that the shape of the cross section of the sensor yields areas with significantly different target-molecule coverage. Different initial conditions are investigated as well in order to aid rational sensor design. A comparison of the association/hybridization behavior for different receptor densities allows optimization of the functionalization setup depending on the target-molecule density.
Hellander, Andreas; Lawson, Michael J.; Drawert, Brian; Petzold, Linda
2014-06-01
The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps were adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the diffusive finite-state projection (DFSP) method, to incorporate temporal adaptivity.
A reaction-diffusion model of the Darien Gap Sterile Insect Release Method
Alford, John G.
2015-05-01
The Sterile Insect Release Method (SIRM) is used as a biological control for invasive insect species. SIRM involves introducing large quantities of sterilized male insects into a wild population of invading insects. A fertile/sterile mating produces offspring that are not viable and the wild insect population will eventually be eradicated. A U.S. government program maintains a permanent sterile fly barrier zone in the Darien Gap between Panama and Columbia to control the screwworm fly (Cochliomyia Hominivorax), an insect that feeds off of living tissue in mammals and has devastating effects on livestock. This barrier zone is maintained by regular releases of massive quantities of sterilized male screwworm flies from aircraft. We analyze a reaction-diffusion model of the Darien Gap barrier zone. Simulations of the model equations yield two types of spatially inhomogeneous steady-state solutions representing a sterile fly barrier that does not prevent invasion and a barrier that does prevent invasion. We investigate steady-state solutions using both phase plane methods and monotone iteration methods and describe how barrier width and the sterile fly release rate affects steady-state behavior.
Cubic autocatalysis in a reaction-diffusion annulus: semi-analytical solutions
Alharthi, M. R.; Marchant, T. R.; Nelson, M. I.
2016-06-01
Semi-analytical solutions for cubic autocatalytic reactions are considered in a circularly symmetric reaction-diffusion annulus. The Galerkin method is used to approximate the spatial structure of the reactant and autocatalyst concentrations. Ordinary differential equations are then obtained as an approximation to the governing partial differential equations and analyzed to obtain semi-analytical results for this novel geometry. Singularity theory is used to determine the regions of parameter space in which the different types of steady-state diagram occur. The region of parameter space, in which Hopf bifurcations can occur, is found using a degenerate Hopf bifurcation analysis. A novel feature of this geometry is the effect, of varying the width of the annulus, on the static and dynamic multiplicity. The results show that for a thicker annulus, Hopf bifurcations and multiple steady-state solutions occur in a larger portion of parameter space. The usefulness and accuracy of the semi-analytical results are confirmed by comparison with numerical solutions of the governing partial differential equations.
Drift and breakup of spiral waves in reaction-diffusion-mechanics systems.
Panfilov, A V; Keldermann, R H; Nash, M P
2007-05-08
Rotating spiral waves organize excitation in various biological, physical, and chemical systems. They underpin a variety of important phenomena, such as cardiac arrhythmias, morphogenesis processes, and spatial patterns in chemical reactions. Important insights into spiral wave dynamics have been obtained from theoretical studies of the reaction-diffusion (RD) partial differential equations. However, most of these studies have ignored the fact that spiral wave rotation is often accompanied by substantial deformations of the medium. Here, we show that joint consideration of the RD equations with the equations of continuum mechanics for tissue deformations (RD-mechanics systems), yield important effects on spiral wave dynamics. We show that deformation can induce the breakup of spiral waves into complex spatiotemporal patterns. We also show that mechanics leads to spiral wave drift throughout the medium approaching dynamical attractors, which are determined by the parameters of the model and the size of the medium. We study mechanisms of these effects and discuss their applicability to the theory of cardiac arrhythmias. Overall, we demonstrate the importance of RD-mechanics systems for mathematics applied to life sciences.
Spatiotemporal Patterns in a Ratio-Dependent Food Chain Model with Reaction-Diffusion
Lei Zhang
2014-01-01
Full Text Available Predator-prey models describe biological phenomena of pursuit-evasion interaction. And this interaction exists widely in the world for the necessary energy supplement of species. In this paper, we have investigated a ratio-dependent spatially extended food chain model. Based on the bifurcation analysis (Hopf and Turing, we give the spatial pattern formation via numerical simulation, that is, the evolution process of the system near the coexistence equilibrium point (u2*,v2*,w2*, and find that the model dynamics exhibits complex pattern replication. For fixed parameters, on increasing the control parameter c1, the sequence “holes → holes-stripe mixtures → stripes → spots-stripe mixtures → spots” pattern is observed. And in the case of pure Hopf instability, the model exhibits chaotic wave pattern replication. Furthermore, we consider the pattern formation in the case of which the top predator is extinct, that is, the evolution process of the system near the equilibrium point (u1*,v1*,0, and find that the model dynamics exhibits stripes-spots pattern replication. Our results show that reaction-diffusion model is an appropriate tool for investigating fundamental mechanism of complex spatiotemporal dynamics. It will be useful for studying the dynamic complexity of ecosystems.
Emotional Effects of Dynamic Textures
Alexander Toet
2011-12-01
Full Text Available This study explores the effects of various spatiotemporal dynamic texture characteristics on human emotions. The emotional experience of auditory (eg, music and haptic repetitive patterns has been studied extensively. In contrast, the emotional experience of visual dynamic textures is still largely unknown, despite their natural ubiquity and increasing use in digital media. Participants watched a set of dynamic textures, representing either water or various different media, and self-reported their emotional experience. Motion complexity was found to have mildly relaxing and nondominant effects. In contrast, motion change complexity was found to be arousing and dominant. The speed of dynamics had arousing, dominant, and unpleasant effects. The amplitude of dynamics was also regarded as unpleasant. The regularity of the dynamics over the textures' area was found to be uninteresting, nondominant, mildly relaxing, and mildly pleasant. The spatial scale of the dynamics had an unpleasant, arousing, and dominant effect, which was larger for textures with diverse content than for water textures. For water textures, the effects of spatial contrast were arousing, dominant, interesting, and mildly unpleasant. None of these effects were observed for textures of diverse content. The current findings are relevant for the design and synthesis of affective multimedia content and for affective scene indexing and retrieval.
Visual texture accurate material appearance measurement, representation and modeling
Haindl, Michal
2013-01-01
This book surveys the state of the art in multidimensional, physically-correct visual texture modeling. Features: reviews the entire process of texture synthesis, including material appearance representation, measurement, analysis, compression, modeling, editing, visualization, and perceptual evaluation; explains the derivation of the most common representations of visual texture, discussing their properties, advantages, and limitations; describes a range of techniques for the measurement of visual texture, including BRDF, SVBRDF, BTF and BSSRDF; investigates the visualization of textural info
Convergence of methods for coupling of microscopic and mesoscopic reaction-diffusion simulations
Flegga, Mark B.; Hellander, Stefan; Erban, Radek
2015-01-01
In this paper, three multiscale methods for coupling of mesoscopic (compartment-based) and microscopic (molecular-based) stochastic reaction-diffusion simulations are investigated. Two of the three methods that will be discussed in detail have been previously reported in the literature; the two-regime method (TRM) and the compartment-placement method (CPM). The third method that is introduced and analysed in this paper is called the ghost cell method (GCM), since it works by constructing a “ghost cell” in which molecules can disappear and jump into the compartment-based simulation. Presented is a comparison of sources of error. The convergent properties of this error are studied as the time step Δt (for updating the molecular-based part of the model) approaches zero. It is found that the error behaviour depends on another fundamental computational parameter h, the compartment size in the mesoscopic part of the model. Two important limiting cases, which appear in applications, are considered: (i) Δt → 0 and h is fixed; (ii) Δt → 0 and h → 0 such that √Δt/h is fixed. The error for previously developed approaches (the TRM and CPM) converges to zero only in the limiting case (ii), but not in case (i). It is shown that the error of the GCM converges in the limiting case (i). Thus the GCM is superior to previous coupling techniques if the mesoscopic description is much coarser than the microscopic part of the model. PMID:26568640
New mechanism of spiral wave initiation in a reaction-diffusion-mechanics system.
Louis D Weise
Full Text Available Spiral wave initiation in the heart muscle is a mechanism for the onset of dangerous cardiac arrhythmias. A standard protocol for spiral wave initiation is the application of a stimulus in the refractory tail of a propagating excitation wave, a region that we call the "classical vulnerable zone." Previous studies of vulnerability to spiral wave initiation did not take the influence of deformation into account, which has been shown to have a substantial effect on the excitation process of cardiomyocytes via the mechano-electrical feedback phenomenon. In this work we study the effect of deformation on the vulnerability of excitable media in a discrete reaction-diffusion-mechanics (dRDM model. The dRDM model combines FitzHugh-Nagumo type equations for cardiac excitation with a discrete mechanical description of a finite-elastic isotropic material (Seth material to model cardiac excitation-contraction coupling and stretch activated depolarizing current. We show that deformation alters the "classical," and forms a new vulnerable zone at longer coupling intervals. This mechanically caused vulnerable zone results in a new mechanism of spiral wave initiation, where unidirectional conduction block and rotation directions of the consequently initiated spiral waves are opposite compared to the mechanism of spiral wave initiation due to the "classical vulnerable zone." We show that this new mechanism of spiral wave initiation can naturally occur in situations that involve wave fronts with curvature, and discuss its relation to supernormal excitability of cardiac tissue. The concept of mechanically induced vulnerability may lead to a better understanding about the onset of dangerous heart arrhythmias via mechano-electrical feedback.
Camley, Brian A.; Zhao, Yanxiang; Li, Bo; Levine, Herbert; Rappel, Wouter-Jan
2017-01-01
We study a minimal model of a crawling eukaryotic cell with a chemical polarity controlled by a reaction-diffusion mechanism describing Rho GTPase dynamics. The size, shape, and speed of the cell emerge from the combination of the chemical polarity, which controls the locations where actin polymerization occurs, and the physical properties of the cell, including its membrane tension. We find in our model both highly persistent trajectories, in which the cell crawls in a straight line, and turning trajectories, where the cell transitions from crawling in a line to crawling in a circle. We discuss the controlling variables for this turning instability and argue that turning arises from a coupling between the reaction-diffusion mechanism and the shape of the cell. This emphasizes the surprising features that can arise from simple links between cell mechanics and biochemistry. Our results suggest that similar instabilities may be present in a broad class of biochemical descriptions of cell polarity.
Camley, Brian A; Li, Bo; Levine, Herbert; Rappel, Wouter-Jan
2016-01-01
We study a minimal model of a crawling eukaryotic cell with a chemical polarity controlled by a reaction-diffusion mechanism describing Rho GTPase dynamics. The size, shape, and speed of the cell emerge from the combination of the chemical polarity, which controls the locations where actin polymerization occurs, and the physical properties of the cell, including its membrane tension. We find in our model both highly persistent trajectories, in which the cell crawls in a straight line, and turning trajectories, where the cell transitions from crawling in a line to crawling in a circle. We discuss the controlling variables for this turning instability, and argue that turning arises from a coupling between the reaction-diffusion mechanism and the shape of the cell. This emphasizes the surprising features that can arise from simple links between cell mechanics and biochemistry. Our results suggest that similar instabilities may be present in a broad class of biochemical descriptions of cell polarity.
陈松林
2002-01-01
@@ The following Lemma stated (in: Applied Mathematics and Mechanics (English Edition),2001,22( 11 ): 1352 - 1356) was applied to describe the asymptotic behaviors of solutions of aclass of reaction-diffusion equation. On account of the special property of the super solution(i.e., a nonzero solution and null solution have C1 smooth connection) constructed in theLemma, we'll give the Lemma a detailed proof as follows.
Wang, Kai; Teng, Zhidong; Jiang, Haijun
2012-10-01
In this paper, the adaptive synchronization in an array of linearly coupled neural networks with reaction-diffusion terms and time delays is discussed. Based on the LaSalle invariant principle of functional differential equations and the adaptive feedback control technique, some sufficient conditions for adaptive synchronization of such a system are obtained. Finally, a numerical example is given to show the effectiveness of the proposed synchronization method.
无
2012-01-01
In this paper,we consider the reaction diffusion equations with strong generic delay kernel and non-local effect,which models the microbial growth in a flow reactor.The existence of traveling waves is established for this model.More precisely,using the geometric singular perturbation theory,we show that traveling wave solutions exist provided that the delay is sufficiently small with the strong generic delay kernel.
Kengne, Emmanuel; Saydé, Michel; Ben Hamouda, Fathi; Lakhssassi, Ahmed
2013-11-01
Analytical entire traveling wave solutions to the 1+1 density-dependent nonlinear reaction-diffusion equation via the extended generalized Riccati equation mapping method are presented in this paper. This equation can be regarded as an extension case of the Fisher-Kolmogoroff equation, which is used for studying insect and animal dispersal with growth dynamics. The analytical solutions are then used to investigate the effect of equation parameters on the population distribution.
Hormuth, David A., II; Weis, Jared A.; Barnes, Stephanie L.; Miga, Michael I.; Rericha, Erin C.; Quaranta, Vito; Yankeelov, Thomas E.
2015-07-01
Reaction-diffusion models have been widely used to model glioma growth. However, it has not been shown how accurately this model can predict future tumor status using model parameters (i.e., tumor cell diffusion and proliferation) estimated from quantitative in vivo imaging data. To this end, we used in silico studies to develop the methods needed to accurately estimate tumor specific reaction-diffusion model parameters, and then tested the accuracy with which these parameters can predict future growth. The analogous study was then performed in a murine model of glioma growth. The parameter estimation approach was tested using an in silico tumor ‘grown’ for ten days as dictated by the reaction-diffusion equation. Parameters were estimated from early time points and used to predict subsequent growth. Prediction accuracy was assessed at global (total volume and Dice value) and local (concordance correlation coefficient, CCC) levels. Guided by the in silico study, rats (n = 9) with C6 gliomas, imaged with diffusion weighted magnetic resonance imaging, were used to evaluate the model’s accuracy for predicting in vivo tumor growth. The in silico study resulted in low global (tumor volume error 0.92) and local (CCC values >0.80) level errors for predictions up to six days into the future. The in vivo study showed higher global (tumor volume error >11.7%, Dice silico study shows that model parameters can be accurately estimated and used to accurately predict future tumor growth at both the global and local scale. However, the poor predictive accuracy in the experimental study suggests the reaction-diffusion equation is an incomplete description of in vivo C6 glioma biology and may require further modeling of intra-tumor interactions including segmentation of (for example) proliferative and necrotic regions.
Simultaneous and non-simultaneous blow-up and uniform blow-up profiles for reaction-diffusion system
Zhengqiu Ling
2012-11-01
Full Text Available This article concerns the blow-up solutions of a reaction-diffusion system with nonlocal sources, subject to the homogeneous Dirichlet boundary conditions. The criteria used to identify simultaneous and non-simultaneous blow-up of solutions by using the parameters p and q in the model are proposed. Also, the uniform blow-up profiles in the interior domain are established.
M.H. Tiwana
2017-04-01
Full Text Available This work investigates the fractional non linear reaction diffusion (FNRD system of Lotka-Volterra type. The system of equations together with the boundary conditions are solved by Homotopy perturbation transform method (HPTM. The series solutions are obtained for the two cases (homogeneous and non-homogeneous of FNRD system. The effect of fractional parameter on the mass concentration of two species are shown and discussed with the help of 3D graphs.
Matthew J Simpson
Full Text Available Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0
基于改进能量优化的透视纹理合成研究%STUDY ON PERSPECTIVE TEXTURE SYNTHESIS BASED ON IMPROVED ENERGY OPTIMISATION
马爽; 史巍; 许刚
2014-01-01
针对传统能量优化方法需要逐点计算的不足，提出一种结合缝合技术的改进能量优化方法用于透视纹理图像的合成。首先，用像素块处理代替逐个像素点的运算，建立基于图像块的能量优化模型；其次，在优化过程中，引入图像缝合技术解决块处理可能存在的接缝、重叠等问题，提高合成图像质量。实验结果表明，改进的能量优化法计算效率大大提高，且可获得更好的视觉效果。%In this paper we propose an energy optimisation improvement algorithm in combination with image quilting technology for perspective texture image synthesis in light of the insufficiency of traditional pixel-based energy optimisation method.First,we replace the pixel-to-pixel calculation with patch processing of pixels,and build the image patch-based energy optimisation model.Secondly,during the optimisation process,we introduce image quilting to solve the problems may having in patch processing such as the joint seams,overlapping, and so on,for improving the quality of synthesis image.Experimental results show that the proposed energy optimisation algorithm greatly improves the computation efficiency,meanwhile,a better visual effect is achieved as well.
I STAMBOLOVA; V BLASKOV; D STOYANOVA; I AVRAMOVA; L DIMITROV; K MILENOVA; K BALASHEV; S SIMEONOVA; A TZONEV; L ALEKSANDROV; A ELIYAS
2017-06-01
Three different precipitating agents (NaOH, NH$_4$(H)CO$_3$ and CO(NH$_2$)$_2$) have been applied for the hydrothermalsynthesis of ZnO powder materials, aiming at obtaining various types of porosity and surface species on ZnO. The synthesis procedures were carried out in the presence and in the absence of tri-block copolymer Pluronic (P123,EO20PO70EO20). These materials were characterized by powder X-ray diffraction (PXRD), X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM)–energy-dispersive X-ray spectroscopy (EDX), BET method and TG–differential thermal analysis (DTA) method, and their photocatalytic activities were tested in the removal azo dye Reactive Black 5 (RB5). The urea precipitant yields spongy-like surface forms and the greatest share of mesopores. It has the highest specific surface area, highest degree of crystallinity of wurtzite ZnO phase and largest content of surface OHgroups in comparison with the other two precipitants. The zinc hydroxycarbonate intermediate phase is missing in the case of NaOH as precipitating agent; therefore, it manifests poorer textural characteristics. The morphology of P123-modified sample is different and consists of needle-shaped particles. The urea-precipitated samples display superior performance inthe photocatalytic oxidation reaction, compared with the other precipitated samples. The other two precipitating agents are inferior in regard to their photocatalytic activity due to greater share of micropores (not well-illuminated inner surface) and different surface morphologies.
Ghosh, Pushpita; Sen, Shrabani; Riaz, Syed Shahed; Ray, Deb Shankar
2009-05-01
The photosensitive chlorine dioxide-iodine-malonic acid reaction-diffusion system has been an experimental paradigm for the study of Turing pattern over the last several years. When subjected to illumination of varied intensity by visible light the patterns undergo changes from spots to stripes, vice versa, and their mixture. We carry out a nonlinear analysis of the underlying model in terms of a Galerkin scheme with finite number of modes to explore the nature of the stability and existence of various modes responsible for the type and crossover of the light-induced patterns.
Hasibun Naher
2012-01-01
Full Text Available We construct new exact traveling wave solutions involving free parameters of the nonlinear reaction diffusion equation by using the improved (G′/G-expansion method. The second-order linear ordinary differential equation with constant coefficients is used in this method. The obtained solutions are presented by the hyperbolic and the trigonometric functions. The solutions become in special functional form when the parameters take particular values. It is important to reveal that our solutions are in good agreement with the existing results.
Dongfang Li
2014-01-01
Full Text Available This paper is concerned with the stability of non-Fickian reaction-diffusion equations with a variable delay. It is shown that the perturbation of the energy function of the continuous problems decays exponentially, which provides a more accurate and convenient way to express the rate of decay of energy. Then, we prove that the proposed numerical methods are sufficient to preserve energy stability of the continuous problems. We end the paper with some numerical experiments on a biological model to confirm the theoretical results.
Fedotov, Sergei
1998-10-01
An asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of the path-integral approach, scaling procedure, and the singular perturbation techniques involving the large deviations theory for the Poisson random walk. The exact formula for the position and speed of reaction front is derived. It is found that the reaction front dynamics is formally associated with the relativistic Hamiltonian/Lagrangian mechanics.
Qiankun Song
2007-06-01
Full Text Available Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of equilibrium point for the addressed neural network are derived by M-matrix theory, analytic methods, and inequality techniques. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper are less restrictive than previously known criteria. Two examples are given to show the effectiveness of the obtained results.
Cao Jinde
2007-01-01
Full Text Available Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of equilibrium point for the addressed neural network are derived by M-matrix theory, analytic methods, and inequality techniques. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper are less restrictive than previously known criteria. Two examples are given to show the effectiveness of the obtained results.
Felicia Shirly Peace
2014-01-01
Full Text Available A mathematical model of the dynamics of the self-ignition of a reaction-diffusion system is studied in this paper. An approximate analytical method (modified Adomian decomposition method is used to solve nonlinear differential equations under steady-state condition. Analytical expressions for concentrations of the gas reactant and the temperature have been derived for Lewis number (Le and parameters β, γ, and ϕ2. Furthermore, in this work, the numerical simulation of the problem is also reported using MATLAB program. An agreement between analytical and numerical results is noted.
Singh, Jagdev; Rashidi, M. M.; Kumar, Devendra; Swroop, Ram
2016-12-01
In this paper, we study a dynamical Brusselator reaction-diffusion system arising in triple collision and enzymatic reactions with time fractional Caputo derivative. The present article involves a more generalized effective approach, proposed for the Brusselator system say q-homotopy analysis transform method (q-HATM), providing the family of series solutions with nonlocal generalized effects. The convergence of the q-HATM series solution is adjusted and controlled by auxiliary parameter ℏ and asymptotic parameter n. The numerical results are demonstrated graphically. The outcomes of the study show that the q-HATM is computationally very effective and accurate to analyze nonlinear fractional differential equations.
Tezuka, Ken-ichi; Wada, Yoshitaka; Takahashi, Akiyuki; Kikuchi, Masanori
2005-01-01
Bone is a complex system with functions including those of adaptation and repair. To understand how bone cells can create a structure adapted to the mechanical environment, we propose a simple bone remodeling model based on a reaction-diffusion system influenced by mechanical stress. Two-dimensional bone models were created and subjected to mechanical loads. The conventional finite element method (FEM) was used to calculate stress distribution. A stress-reactive reaction-diffusion model was constructed and used to simulate bone remodeling under mechanical loads. When an external mechanical stress was applied, stimulated bone formation and subsequent activation of bone resorption produced an efficient adaptation of the internal shape of the model bone to a given stress, and demonstrated major structures of trabecular bone seen in the human femoral neck. The degree of adaptation could be controlled by modulating the diffusion constants of hypothetical local factors. We also tried to demonstrate the deformation of bone structure during osteoporosis by the modulation of a parameter affecting the balance between formation and resorption. This simple model gives us an insight into how bone cells can create an architecture adapted to environmental stress, and will serve as a useful tool to understand both physiological and pathological states of bone based on structural information.
ReaDDy--a software for particle-based reaction-diffusion dynamics in crowded cellular environments.
Johannes Schöneberg
Full Text Available We introduce the software package ReaDDy for simulation of detailed spatiotemporal mechanisms of dynamical processes in the cell, based on reaction-diffusion dynamics with particle resolution. In contrast to other particle-based reaction kinetics programs, ReaDDy supports particle interaction potentials. This permits effects such as space exclusion, molecular crowding and aggregation to be modeled. The biomolecules simulated can be represented as a sphere, or as a more complex geometry such as a domain structure or polymer chain. ReaDDy bridges the gap between small-scale but highly detailed molecular dynamics or Brownian dynamics simulations and large-scale but little-detailed reaction kinetics simulations. ReaDDy has a modular design that enables the exchange of the computing core by efficient platform-specific implementations or dynamical models that are different from Brownian dynamics.
Aristotelous, Andreas C; Haider, Mansoor A
2014-08-01
Macroscopic models accounting for cellular effects in natural or engineered tissues may involve unknown constitutive terms that are highly dependent on interactions at the scale of individual cells. Hybrid discrete models, which represent cells individually, were used to develop and apply techniques for modeling diffusive nutrient transport and cellular uptake to identify a nonlinear nutrient loss term in a macroscopic reaction-diffusion model of the system. Flexible and robust numerical methods were used, based on discontinuous Galerkin finite elements in space and a Crank-Nicolson temporal discretization. Scales were bridged via averaging operations over a complete set of subdomains yielding data for identification of a macroscopic nutrient loss term that was accurately captured via a fifth-order polynomial. Accuracy of the identified macroscopic model was demonstrated by direct, quantitative comparisons of the tissue and cellular scale models in terms of three error norms computed on a mesoscale mesh. Copyright © 2014 John Wiley & Sons, Ltd.
Pattern formation in a two-component reaction-diffusion system with delayed processes on a network
Petit, Julien; Asllani, Malbor; Fanelli, Duccio; Lauwens, Ben; Carletti, Timoteo
2016-11-01
Reaction-diffusion systems with time-delay defined on complex networks have been studied in the framework of the emergence of Turing instabilities. The use of the Lambert W-function allowed us to get explicit analytic conditions for the onset of patterns as a function of the main involved parameters, the time-delay, the network topology and the diffusion coefficients. Depending on these parameters, the analysis predicts whether the system will evolve towards a stationary Turing pattern or rather to a wave pattern associated to a Hopf bifurcation. The possible outcomes of the linear analysis overcome the respective limitations of the single-species case with delay, and that of the classical activator-inhibitor variant without delay. Numerical results gained from the Mimura-Murray model support the theoretical approach.
Fernandes, Ryan I
2012-01-01
An alternating direction implicit (ADI) orthogonal spline collocation (OSC) method is described for the approximate solution of a class of nonlinear reaction-diffusion systems. Its efficacy is demonstrated on the solution of well-known examples of such systems, specifically the Brusselator, Gray-Scott, Gierer-Meinhardt and Schnakenberg models, and comparisons are made with other numerical techniques considered in the literature. The new ADI method is based on an extrapolated Crank-Nicolson OSC method and is algebraically linear. It is efficient, requiring at each time level only $O({\\cal N})$ operations where ${\\cal N}$ is the number of unknowns. Moreover,it is shown to produce approximations which are of optimal global accuracy in various norms, and to possess superconvergence properties.
Basavaraja, C.; Park, Do Young; Yamaguchi, Tomohiko; Huh, Do Sung
2007-06-01
Periodic waves were studied via the process of wet stamping, in a heterogeneous media soaked in different solutions of the Belousov-Zhabotinsky (BZ) reaction system containing ferroin and malonic acid. The experiments were performed by making an initial contact of soaked polyacrylamide (PAA) gel with agarose stamp for a short period of time, and then placing the gel onto the glass plate after exposing both of its surfaces. This led to the development of propagating waves on the surface of the gel. The results show that patterns have a dependence on the concentration of individual species, which are represented in the form of bifurcation diagrams. The behavioral trend of this system is also compared with the current perspectives of the reaction diffusion system.
Kanittha Yimnak
2014-01-01
Full Text Available The meshless local Pretrov-Galerkin method (MLPG with the test function in view of the Heaviside step function is introduced to solve the system of coupled nonlinear reaction-diffusion equations in two-dimensional spaces subjected to Dirichlet and Neumann boundary conditions on a square domain. Two-field velocities are approximated by moving Kriging (MK interpolation method for constructing nodal shape function which holds the Kronecker delta property, thereby enhancing the arrangement nodal shape construction accuracy, while the Crank-Nicolson method is chosen for temporal discretization. The nonlinear terms are treated iteratively within each time step. The developed formulation is verified in two numerical examples with investigating the convergence and the accuracy of numerical results. The numerical experiments revealing the solutions by the developed formulation are stable and more precise.
Ram K. Saxena
2014-08-01
Full Text Available This paper deals with the investigation of the computational solutions of a unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann–Liouville fractional derivative defined by others and the space derivative of second order by the Riesz–Feller fractional derivative and adding a function ɸ(x, t. The solution is derived by the application of the Laplace and Fourier transforms in a compact and closed form in terms of Mittag–Leffler functions. The main result obtained in this paper provides an elegant extension of the fundamental solution for the space-time fractional diffusion equation obtained by others and the result very recently given by others. At the end, extensions of the derived results, associated with a finite number of Riesz–Feller space fractional derivatives, are also investigated.
One-Dimensional Reaction-Diffusion Simulation of Cu Migration in Polycrystalline CdTe Solar Cells
Guo, Da [Arizona State University; Akis, Richard [Arizona State University; Brinkman, Daniel [Arizona State University; Sankin, Igor [First Solar; Fang, Tian [First Solar; Vasileska, Dragica [Arizona State University; Ringhofer, Christain [Arizona State University
2014-06-13
In this work, we report on developing 1D reaction-diffusion solver to understand the kinetics of p-type doping formation in CdTe absorbers and to shine some light on underlying causes of metastabilities observed in CdTe PV devices. Evolution of intrinsic and Cu-related defects in CdTe solar cell has been studied in time-space domain self-consistently with free carrier transport and Poisson equation. Resulting device performance was simulated as a function of Cu diffusion anneal time showing pronounced effect the evolution of associated acceptor and donor states can cause on device characteristics. Although 1D simulation has intrinsic limitations when applied to poly-crystalline films, the results suggest strong potential of the approach in better understanding of the performance and metastabilities of CdTe photovoltaic device.
Comte, J C; Marquié, P; Remoissenet, M
1999-12-01
We introduce a nonlinear Klein-Gordon lattice model with specific double-well on-site potential, additional constant external force and dissipation terms, which admits exact discrete kink or traveling wave fronts solutions. In the non-dissipative or conservative regime, our numerical simulations show that narrow kinks can propagate freely, and reveal that static or moving discrete breathers, with a finite but long lifetime, can emerge from kink-antikink collisions. In the general dissipative regime, the lifetime of these breathers depends on the importance of the dissipative effects. In the overdamped or diffusive regime, the general equation of motion reduces to a discrete reaction diffusion equation; our simulations show that, for a given potential shape, discrete wave fronts can travel without experiencing any propagation failure but their collisions are inelastic.
Lund, Halvor; Simonsen, Ingve
2012-01-01
We review and introduce a generalized reaction-diffusion approach to epidemic spreading in a metapopulation modeled as a complex network. The metapopulation consists of susceptible and infected individuals that are grouped in subpopulations symbolising cities and villages that are coupled by human travel in a transportation network. By analytic methods and numerical simulations we calculate the fraction of infected people in the metaopoluation in the long time limit, as well as the relevant parameters characterising the epidemic threshold that separates an epidemic from a non-epidemic phase. Within this model, we investigate the effect of a heterogeneous network topology and a heterogeneous subpopulation size distribution. Such a system is suited for epidemic modeling where small villages and big cities exist simultaneously in the metapopulation. We find that the heterogeneous conditions cause the epidemic threshold to be a non-trivial function of the reaction rates (local parameters), the network's topology ...
Adam, A. M. A.; Bashier, E. B. M.; Hashim, M. H. A.; Patidar, K. C.
2017-07-01
In this work, we design and analyze a fitted numerical method to solve a reaction-diffusion model with time delay, namely, a delayed version of a population model which is an extension of the logistic growth (LG) equation for a food-limited population proposed by Smith [F.E. Smith, Population dynamics in Daphnia magna and a new model for population growth, Ecology 44 (1963) 651-663]. Seeing that the analytical solution (in closed form) is hard to obtain, we seek for a robust numerical method. The method consists of a Fourier-pseudospectral semi-discretization in space and a fitted operator implicit-explicit scheme in temporal direction. The proposed method is analyzed for convergence and we found that it is unconditionally stable. Illustrative numerical results will be presented at the conference.
Chalupecký, Vladimír; Kruschwitz, Jens; Muntean, Adrian
2012-01-01
We consider a two-scale reaction diffusion system able to capture the corrosion of concrete with sulfates. Our aim here is to define and compute two macroscopic corrosion indicators: typical pH drop and gypsum profiles. Mathematically, the system is coupled, endowed with micro-macro transmission conditions, and posed on two different spatially-separated scales: one microscopic (pore scale) and one macroscopic (sewer pipe scale). We use a logarithmic expression to compute values of pH from the volume averaged concentration of sulfuric acid which is obtained by resolving numerically the two-scale system (microscopic equations with direct feedback with the macroscopic diffusion of one of the reactants). Furthermore, we also evaluate the content of the main sulfatation reaction (corrosion) product---the gypsum---and point out numerically a persistent kink in gypsum's concentration profile. Finally, we illustrate numerically the position of the free boundary separating corroded from not-yet-corroded regions.
Budroni, M. A.; De Wit, A.
2016-06-01
When two solutions containing separate reactants A and B of an oscillating reaction are put in contact in a gel, localized spatiotemporal patterns can develop around the contact zone thanks to the interplay of reaction and diffusion processes. Using the Brusselator model, we explore analytically the deployment in space and time of the bifurcation diagram of such an A +B → oscillator system. We provide a parametric classification of possible instabilities as a function of the ratio of the initial reactant concentrations and of the reaction intermediate species diffusion coefficients. Related one-dimensional reaction-diffusion dynamics are studied numerically. We find that the system can spatially localize waves and Turing patterns as well as induce more complex dynamics such as zigzag spatiotemporal waves when Hopf and Turing modes interact.
Tsibidis, George D
2008-01-01
Temporally and spatially resolved measurements of protein transport inside cells provide important clues to the functional architecture and dynamics of biological systems. Fluorescence Recovery After Photobleaching (FRAP) technique has been used over the past three decades to measure the mobility of macromolecules and protein transport and interaction with immobile structures inside the cell nucleus. A theoretical model is presented that aims to describe protein transport inside the nucleus, a process which is influenced by the presence of a boundary (i.e. membrane). A set of reaction-diffusion equations is employed to model both the diffusion of proteins and their interaction with immobile binding sites. The proposed model has been designed to be applied to biological samples with a Confocal Laser Scanning Microscope (CLSM) equipped with the feature to bleach regions characterised by a scanning beam that has a radially Gaussian distributed profile. The proposed model leads to FRAP curves that depend on the o...
Sato, Makoto; Yasugi, Tetsuo; Minami, Yoshiaki; Miura, Takashi; Nagayama, Masaharu
2016-08-30
Notch-mediated lateral inhibition regulates binary cell fate choice, resulting in salt and pepper patterns during various developmental processes. However, how Notch signaling behaves in combination with other signaling systems remains elusive. The wave of differentiation in the Drosophila visual center or "proneural wave" accompanies Notch activity that is propagated without the formation of a salt and pepper pattern, implying that Notch does not form a feedback loop of lateral inhibition during this process. However, mathematical modeling and genetic analysis clearly showed that Notch-mediated lateral inhibition is implemented within the proneural wave. Because partial reduction in EGF signaling causes the formation of the salt and pepper pattern, it is most likely that EGF diffusion cancels salt and pepper pattern formation in silico and in vivo. Moreover, the combination of Notch-mediated lateral inhibition and EGF-mediated reaction diffusion enables a function of Notch signaling that regulates propagation of the wave of differentiation.
Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems
Woolley, Thomas E.
2012-05-22
Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.
Texture Repairing by Unified Low Rank Optimization
Xiao Liang; Xiang Ren; Zhengdong Zhang; Yi Ma
2016-01-01
In this paper, we show how to harness both low-rank and sparse structures in regular or near-regular textures for image completion. Our method is based on a unified formulation for both random and contiguous corruption. In addition to the low rank property of texture, the algorithm also uses the sparse assumption of the natural image: because the natural image is piecewise smooth, it is sparse in certain transformed domain (such as Fourier or wavelet transform). We combine low-rank and sparsity properties of the texture image together in the proposed algorithm. Our algorithm based on convex optimization can automatically and correctly repair the global structure of a corrupted texture, even without precise information about the regions to be completed. This algorithm integrates texture rectification and repairing into one optimization problem. Through extensive simulations, we show our method can complete and repair textures corrupted by errors with both random and contiguous supports better than existing low-rank matrix recovery methods. Our method demonstrates significant advantage over local patch based texture synthesis techniques in dealing with large corruption, non-uniform texture, and large perspective deformation.
Stato dell’arte nella sintesi di texture sonore
Diemo Schwarz
2016-06-01
Full Text Available The synthesis of sound textures, such as rain, wind, or crowds, is an important application for cinema, multimedia creation, games and installations. However, despite the clearly defined requirements of naturalness and flexibility, no automatic method has yet found widespread use. After clarifying the definition, terminology, and usages of sound texture synthesis, we will give an overview of the many existing methods and approaches, and the few available software implementations, and classify them by the synthesis model they are based on, such as subtractive or additive synthesis, granular synthesis, corpus-based concatenative synthesis, wavelets, or physical modeling. Additionally, an overview is given over analysis methods used for sound texture synthesis, such as segmentation, statistical modeling, timbral analysis, and modeling of transitions.
Simultaneous structure and texture image inpainting.
Bertalmio, Marcelo; Vese, Luminita; Sapiro, Guillermo; Osher, Stanley
2003-01-01
An algorithm for the simultaneous filling-in of texture and structure in regions of missing image information is presented in this paper. The basic idea is to first decompose the image into the sum of two functions with different basic characteristics, and then reconstruct each one of these functions separately with structure and texture filling-in algorithms. The first function used in the decomposition is of bounded variation, representing the underlying image structure, while the second function captures the texture and possible noise. The region of missing information in the bounded variation image is reconstructed using image inpainting algorithms, while the same region in the texture image is filled-in with texture synthesis techniques. The original image is then reconstructed adding back these two sub-images. The novel contribution of this paper is then in the combination of these three previously developed components, image decomposition with inpainting and texture synthesis, which permits the simultaneous use of filling-in algorithms that are suited for different image characteristics. Examples on real images show the advantages of this proposed approach.
徐龙封
2002-01-01
In this paper, the classical and weak derivatives with respect to spatial variab le of a class of hysteresis functional are discussed. Some conclusions about sol utions of a class of reaction-diffusion equations with hysteresis differential operator are given.
Ducrot, Arnaud; Giletti, Thomas
2014-09-01
In this work we study the asymptotic behaviour of the Kermack-McKendrick reaction-diffusion system in a periodic environment with non-diffusive susceptible population. This problem was proposed by Kallen et al. as a model for the spatial spread for epidemics, where it can be reasonable to assume that the susceptible population is motionless. For arbitrary dimensional space we prove that large classes of solutions of such a system have an asymptotic spreading speed in large time, and that the infected population has some pulse-like asymptotic shape. The analysis of the one-dimensional problem is more developed, as we are able to uncover a much more accurate description of the profile of solutions. Indeed, we will see that, for some initially compactly supported infected population, the profile of the solution converges to some pulsating travelling wave with minimal speed, that is to some entire solution moving at a constant positive speed and whose profile's shape is periodic in time.
Shishkin, G. I.; Shishkina, L. P.
2009-05-01
The boundary value problem for the singularly perturbed reaction-diffusion parabolic equation in a ball in the case of spherical symmetry is considered. The derivatives with respect to the radial variable appearing in the equation are written in divergent form. The third kind boundary condition, which admits the Dirichlet and Neumann conditions, is specified on the boundary of the domain. The Laplace operator in the differential equation involves a perturbation parameter ɛ2, where ɛ takes arbitrary values in the half-open interval (0, 1]. When ɛ → 0, the solution of such a problem has a parabolic boundary layer in a neighborhood of the boundary. Using the integro-interpolational method and the condensing grid technique, conservative finite difference schemes on flux grids are constructed that converge ɛ-uniformly at a rate of O( N -2ln2 N + N {0/-1}), where N + 1 and N 0 + 1 are the numbers of the mesh points in the radial and time variables, respectively.
Pattern Formation in the Turing-Hopf Codimension-2 Phase Space in a Reaction-Diffusion System
YUAN Xu-Jin; SHAO Xin; LIAO Hui-Min; OUYANG Qi
2009-01-01
We systematically investigate the behaviour of pattern formation in a reaction-diffusion system when the system is located near the Turing-Hopf codimension-2 point in phase space. The chloride-iodide-malonic acid (CIMA) reaction is used in this study. A phase diagram is obtained using the concentration of polyvinyl alcohol (PVA) and malonic acid (MA) as control parameters. It is found that the Turing-Hopf mixed state appears only in a small vicinity near the codimension-2 point, and has the form of hexagonal pattern overlapped with anti-target wave; the boundary line separating the Thring state and the wave state is independent of the concentration of MA, only relies on the concentration of PVA. The corresponding numerical simulation using the Lengyel-Epstein (LE) model gives a similar phase diagram as the experiment; it reproduces most patterns observed in the experiment. However, the mixed state we obtain in simulation only appears in the anti-wave tip area, implying that the 3-D effect in the experiments may change the pattern forming behaviour in the codimension-2 regime.
Giletti, Thomas
2010-01-01
We consider in this paper a reaction-diffusion system under a KPP hypothesis in a cylindrical domain in the presence of a shear flow. Such systems arise in predator-prey models as well as in combustion models with heat losses. Similarly to the single equation case, the existence of a minimal speed c* and of traveling front solutions for every speed c > c* has been shown both in the cases of heat losses distributed inside the domain or on the boundary. Here, we deal with the accordance between the two models by choosing heat losses inside the domain which tend to a Dirac mass located on the boundary. First, using the characterizations of the corresponding minimal speeds, we will see that they converge to the minimal speed of the limiting problem. Then, we will take interest in the convergence of the traveling front solutions of our reaction-di?usion systems. We will show the convergence under some assumptions on those solutions, which in particular can be satis?ed in dimension 2.
von Kameke, A.; Huhn, F.; Muñuzuri, A. P.; Pérez-Muñuzuri, V.
2013-02-01
In the absence of advection, reaction-diffusion systems are able to organize into spatiotemporal patterns, in particular spiral and target waves. Whenever advection is present that can be parametrized in terms of effective or turbulent diffusion D*, these patterns should be attainable on a much greater, boosted length scale. However, so far, experimental evidence of these boosted patterns in a turbulent flow was lacking. Here, we report the first experimental observation of boosted target and spiral patterns in an excitable chemical reaction in a quasi-two-dimensional turbulent flow. The wave patterns observed are ˜50 times larger than in the case of molecular diffusion only. We vary the turbulent diffusion coefficient D* of the flow and find that the fundamental Fisher-Kolmogorov-Petrovsky-Piskunov equation, vf∝D*, for the asymptotic speed of a reactive wave remains valid. However, not all measures of the boosted wave scale with D* as expected from molecular diffusion, since the wave fronts turn out to be highly filamentous.
Fatima, Tasnim; Aiki, Toyohiko
2012-01-01
This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: $x$ - macro and $y$ - micro. The system's origin connects to the modeling of concrete corrosion in sewer concrete pipes. It consists of three partial differential equations which are mass-balances of concentrations, as well as, one ordinary differential equation tracking the damage-by-corrosion. The system is semilinear, partially dissipative, and coupled via the solid-water interface at the microstructure (pore) level. The structure of the model equations is obtained in \\cite{tasnim1} by upscaling of the physical and chemical processes taking place within the microstructure of the concrete. Herein we ensure the positivity and $L^\\infty-$bounds on concentrations, and then prove the global-in-time existence and uniqueness of a suitable class of positive and bounded solutions that are stable with respect to the two-scale data and m...
An exact and efficient first passage time algorithm for reaction-diffusion processes on a 2D-lattice
Bezzola, Andri; Bales, Benjamin B.; Alkire, Richard C.; Petzold, Linda R.
2014-01-01
We present an exact and efficient algorithm for reaction-diffusion-nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands.
Lueptow, Richard M.; Schlick, Conor P.; Umbanhowar, Paul B.; Ottino, Julio M.
2013-11-01
We investigate chaotic advection and diffusion in competitive autocatalytic reactions. To study this subject, we use a computationally efficient method for solving advection-reaction-diffusion equations for periodic flows using a mapping method with operator splitting. In competitive autocatalytic reactions, there are two species, B and C, which both react autocatalytically with species A (A +B -->2B and A +C -->2C). If there is initially a small amount of spatially localized B and C and a large amount of A, all three species will be advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that the small scale interactions associated with the chaotic velocity field, specifically the local finite-time Lyapunov exponents (FTLEs), can accurately predict the final average concentrations of B and C after the reaction is complete. The species, B or C, that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If species B and C start in regions having similar FTLEs, their average concentrations at the end of the reaction will also be similar. Funded by NSF Grant CMMI-1000469.
Hallock, Michael J; Stone, John E; Roberts, Elijah; Fry, Corey; Luthey-Schulten, Zaida
2014-05-01
Simulation of in vivo cellular processes with the reaction-diffusion master equation (RDME) is a computationally expensive task. Our previous software enabled simulation of inhomogeneous biochemical systems for small bacteria over long time scales using the MPD-RDME method on a single GPU. Simulations of larger eukaryotic systems exceed the on-board memory capacity of individual GPUs, and long time simulations of modest-sized cells such as yeast are impractical on a single GPU. We present a new multi-GPU parallel implementation of the MPD-RDME method based on a spatial decomposition approach that supports dynamic load balancing for workstations containing GPUs of varying performance and memory capacity. We take advantage of high-performance features of CUDA for peer-to-peer GPU memory transfers and evaluate the performance of our algorithms on state-of-the-art GPU devices. We present parallel e ciency and performance results for simulations using multiple GPUs as system size, particle counts, and number of reactions grow. We also demonstrate multi-GPU performance in simulations of the Min protein system in E. coli. Moreover, our multi-GPU decomposition and load balancing approach can be generalized to other lattice-based problems.
Image statistics underlying natural texture selectivity of neurons in macaque V4
Okazawa, Gouki; Tajima, Satohiro; Komatsu, Hidehiko
2015-01-01
Our daily visual experiences are inevitably linked to recognizing the rich variety of textures. However, how the brain encodes and differentiates a plethora of natural textures remains poorly understood. Here, we show that many neurons in macaque V4 selectively encode sparse combinations of higher-order image statistics to represent natural textures. We systematically explored neural selectivity in a high-dimensional texture space by combining texture synthesis and efficient-sampling techniques. This yielded parameterized models for individual texture-selective neurons. The models provided parsimonious but powerful predictors for each neuron’s preferred textures using a sparse combination of image statistics. As a whole population, the neuronal tuning was distributed in a way suitable for categorizing textures and quantitatively predicts human ability to discriminate textures. Together, we suggest that the collective representation of visual image statistics in V4 plays a key role in organizing the natural texture perception. PMID:25535362
Dando, O
1999-01-01
We examine the field equations of a self-gravitating texture in low-energy superstring gravity, allowing for an arbitrary coupling of the texture field to the dilaton. Both massive and massless dilatons are considered. For the massless dilaton, we find that non-singular spacetimes only exist for certain values of the coupling, dependent on the gravitational strength of the texture. For the massive dilaton, the texture induces a long-range dilaton cloud, but we expect the gravitational behaviour of the defect to be similar to that found in Einstein theory. We compare these results with those found for other global topological defects.
Stamova, Ivanka; Stamov, Gani
2017-09-08
In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.
Hoang, M.A.; Geusebroek, J.M.; Chantler, M.
2002-01-01
In computer vision, measurement of image properties such as color or texture is essential. In this paper, we propose a solid framework for the local measurement of texture in color images. We give a physical basis for the integration of the well-known Gabor filters with the measurement of color. Our
Hoang, M.A.; Geusebroek, J.M.; Deprettere, E.F.; Belloum, A.; Heijnsdijk, J.W.J.; van der Stappen, F.
2002-01-01
In computer vision, measurement of image properties such as color or texture is essential. However, existing methods for measuring color and texture in combination are not well-defined neither from a measurement theoretical basis nor from a physical point of view. We propose a solid framework for th
Beaghton, Andrea; Beaghton, Pantelis John; Burt, Austin
2016-04-01
Some genes or gene complexes are transmitted from parents to offspring at a greater-than-Mendelian rate, and can spread and persist in populations even if they cause some harm to the individuals carrying them. Such genes may be useful for controlling populations or species that are harmful. Driving-Y chromosomes may be particularly potent in this regard, as they produce a male-biased sex ratio that, if sufficiently extreme, can lead to population elimination. To better understand the potential of such genes to spread over a landscape, we have developed a series of reaction-diffusion models of a driving-Y chromosome in 1-D and radially-symmetric 2-D unbounded domains. The wild-type system at carrying capacity is found to be unstable to the introduction of driving-Y males for all models investigated. Numerical solutions exhibit travelling wave pulses and fronts, and analytical and semi-analytical solutions for the asymptotic wave speed under bounded initial conditions are derived. The driving-Y male invades the wild-type equilibrium state at the front of the wave and completely replaces the wild-type males, leaving behind, at the tail of the wave, a reduced- or zero-population state of females and driving-Y males only. In our simplest model of a population with one life stage and density-dependent mortality, wave speed depends on the strength of drive and the diffusion rate of Y-drive males, and is independent of the population dynamic consequences (suppression or elimination). Incorporating an immobile juvenile stage of fixed duration into the model reduces wave speed approximately in proportion to the relative time spent as a juvenile. If females mate just once in their life, storing sperm for subsequent reproduction, then wave speed depends on the movement of mated females as well as Y-drive males, and may be faster or slower than in the multiple-mating model, depending on the relative duration of juvenile and adult life stages. Numerical solutions are shown for
1980-01-01
security applications of scene analysis are reconnaissance, night vision, mapping and terrain classification, target detection and tracking, traffic ... stereopsis and relative motion. 5 *’"." * * m - _- , . _ . . . b -.- -, . ..,. .. . .. . ... . ..... . .... .. . Texture perception is itself a
Wani, Kohmei
Quantitative determination of textural quality of frozen food due to freezing and storage conditions is complicated,since the texture is consisted of multi-dimensiona1 factors. The author reviewed the importance of texture in food quality and the factors which is proposed by a priori estimation. New classification of expression words of textural properties by subjective evaluation and an application of four elements mechanical model for analysis of physical characteristics was studied on frozen meat patties. Combination of freezing-thawing condition on the subjective properties and physiochemical characteristics of beef lean meat and hamachi fish (Yellow-tail) meat was studied. Change of the plasticity and the deformability of these samples differed by freezing-thawing rate and cooking procedure. Also optimum freezing-thawing condition was differed from specimens.
Dierking, Ingo
2006-01-01
A unique compendium of knowledge on all aspects of the texture of liquid crystals, providing not just detailed information on texture formation and determination, but also an in-depth discussion of different characterization methods. Experts as well as graduates entering the field will find all the information they need in this handbook, while the magnitude of the color images make it valuable hands-on-reference.
Gan, Qintao
2017-01-01
In this paper, the exponential synchronization problem of generalized reaction-diffusion neural networks with mixed time-varying delays is investigated concerning Dirichlet boundary conditions in terms of p-norm. Under the framework of the Lyapunov stability method, stochastic theory, and mathematical analysis, some novel synchronization criteria are derived, and an aperiodically intermittent control strategy is proposed simultaneously. Moreover, the effects of diffusion coefficients, diffusion space, and stochastic perturbations on the synchronization process are explicitly expressed under the obtained conditions. Finally, some numerical simulations are performed to illustrate the feasibility of the proposed control strategy and show different synchronization dynamics under a periodically/aperiodically intermittent control.
无
2007-01-01
Taking the Lindemann model as a sample system in which there exist chemical reactions, diffusion and heat conduction, we found the theoretical framework of linear stability analysis for a unidimensional nonhomogeneous two-variable system with one end subject to Dirichlet conditions, while the other end no-flux conditions. Furthermore, the conditions for the emergence of temperature waves are found out by the linear stabiliy analysis and verified by a diagram for successive steps of evolution of spatial profile of temperature during a period that is plotted by numerical simulations on a computer. Without doubt, these results are in favor of the heat balance in chemical reactor designs.
Relighting multiple color textures
DIAO Chang-yu; LU Dong-ming; LIU Gang
2005-01-01
With the development of digital library technology, library books made of paper can be digital released and read, and Endangered Cultural Heritages can be preserved. Traditional library's contents and functions can be greatly enhanced by digital technologies. For these new library objects, the primary key problem is precisely reconstructing their 3D models. When constructing complete 3D models, multiple color texture maps are often necessary. A commonly encountered problem uncounted during fusing of textures from multiple color images is color distortion. Each texture of a single 3D model may be obtained under possibly different lighting conditions and color response of the camera. To remove any visible seam and improve color consistency between the textures while avoiding color distortion, we propose a new efficient algorithm to relight all the texture images globally,spread residual light difference, and recolor each image by homogeneous transformation. A relative illumination model was adopted to obtain the relighting function. We choose lαβ color space with minimal correlation between channels for many natural scenes, for calculating the relighting result. Looking into two overlapped images A and B, we can pairwise relight B into A's luminosity condition in two steps. We first scale B's l channel by the lA/lB ratio of the overlapped region. We can assume A and B are in a same color plane now. Then a homogeneous transformation is applied to B's α and β channels which moves B into A's hue and saturation condition. For multiple overlapped color textures, a patch based weighted global relighting method was proposed to minimize the total color difference. The pairwise relighting method was used between each two overlapped images, and the difference in every overlapped region after relighting was weighted and summed up to construct an energy value. We used Nelder-Mead method to find a minimal energy value and the relighting parameters for every image. After
Lapidus, A.L.; Bruk, I.A.; Mal' tsev, V.V.; Iem, K.C.; Yakerson, V.I.; Golosman, Y.Z.; Mamayeva, I.A.; Kalacheva, N.B.; Danyushevskii, V.Y.; Nissenbaum, V.D.
1981-01-01
A study was made of the mechanism of formation of catalysts; a special feature of this mechanism is the interaction of components (calcium aluminates and basic carbonates of cobalt and magnesium); the carrier with a developed surface and the active component distributed on this surface are formed during this process. Catalysts show maximum selectivity in synthesis of liquid hydrocarbons from CO and H/sub 2/ with a degree of reduction of the metal of 65-84% and a dispersion (according to chemisorption of CO) of 6 x 10/sup -3/ - 10 x 10/sup -3/. Maximum yield of liquid hydrocarbons (114.1 g/nm/sup 3/) was obtained in the pressure of a system of 33Co-3MgO-64 talum treated with hydrogen at 550/sup 0/C.
Computer Texture Mapping for Laser Texturing of Injection Mold
Yongquan Zhou
2014-04-01
Full Text Available Laser texturing is a relatively new multiprocess technique that has been used for machining 3D curved surfaces; it is more flexible and efficient to create decorative texture on 3D curved surfaces of injection molds so as to improve the surface quality and achieve cosmetic surface of molded plastic parts. In this paper, a novel method of laser texturing 3D curved surface based on 3-axis galvanometer scanning unit has been presented to prevent the texturing of injection mold surface from much distortion which is often caused by traditional texturing processes. The novel method has been based on the computer texture mapping technology which has been developed and presented. The developed texture mapping algorithm includes surface triangulation, notations, distortion measurement, control, and numerical method. An interface of computer texture mapping has been built to implement the algorithm of texture mapping approach to controlled distortion rate of 3D texture math model from 2D original texture applied to curvature surface. Through a case study of laser texturing of a high curvature surface of injection mold of a mice top case, it shows that the novel method of laser texturing meets the quality standard of laser texturing of injection mold.
Scarle, Simon
2009-08-01
In the arsenal of tools that a computational modeller can bring to bare on the study of cardiac arrhythmias, the most widely used and arguably the most successful is that of an excitable medium, a special case of a reaction-diffusion model. These are used to simulate the internal chemical reactions of a cardiac cell and the diffusion of their membrane voltages. Via a number of different methodologies it has previously been shown that reaction-diffusion systems are at multiple levels Turing complete. That is, they are capable of computation in the same manner as a universal Turing machine. However, all such computational systems are subject to a limitation known as the Halting problem. By constructing a universal logic gate using a cardiac cell model, we highlight how the Halting problem therefore could limit what it is possible to predict about cardiac tissue, arrhythmias and re-entry. All simulations for this work were carried out on the GPU of an XBox 360 development console, and we also highlight the great gains in computational power and efficiency produced by such general purpose processing on a GPU for cardiac simulations.
Sigaut, Lorena; Villarruel, Cecilia; Ponce, María Laura; Ponce Dawson, Silvina
2017-06-01
Many cell signaling pathways involve the diffusion of messengers that bind and unbind to and from intracellular components. Quantifying their net transport rate under different conditions then requires having separate estimates of their free diffusion coefficient and binding or unbinding rates. In this paper, we show how performing sets of fluorescence correlation spectroscopy (FCS) experiments under different conditions, it is possible to quantify free diffusion coefficients and on and off rates of reaction-diffusion systems. We develop the theory and present a practical implementation for the case of the universal second messenger, calcium (Ca2 +) and single-wavelength dyes that increase their fluorescence upon Ca2 + binding. We validate the approach with experiments performed in aqueous solutions containing Ca2 + and Fluo4 dextran (both in its high and low affinity versions). Performing FCS experiments with tetramethylrhodamine-dextran in Xenopus laevis oocytes, we infer the corresponding free diffusion coefficients in the cytosol of these cells. Our approach can be extended to other physiologically relevant reaction-diffusion systems to quantify biophysical parameters that determine the dynamics of various variables of interest.
Travelling Wave Solutions to a Kind of Reaction Diffusion Equations%一类反应扩散方程新的行波解
行珊; 段卫国
2012-01-01
介绍了一种求解非线性偏微分方程行波解的方法——双函数法。利用该方法求得一类反应扩散方程在不同情况下的新的行波解，Chaffee-Infane方程和Huxley方程作为这一类反应扩散方程的特例也得到了相应的行波解。该方法还可推广到高维非线性反应扩散方程（组）进行求解。%A method to solve nonlinear partial differential equations is introduced. By using the double- function method, new travelling wave solutions to a kind of reaction diffusion equations are obtained under different circumstances. The corresponding travelling wave solutions for the particular case of the reaction diffusion equations, as Chaffee-Infane equation and be used to solve high-dimensional nonlinear reaction Huxley equation, are obtained. This method can also diffusion equations.
C. Alegre
2012-01-01
Full Text Available Carbon xerogels (CXs have been prepared by polycondensation of resorcinol and formaldehyde. Two synthesis pHs were studied in order to evaluate its influence on the electrochemical behaviour of Pt catalysts supported on previous carbon xerogels, synthesized by conventional impregnation method. Catalysts were also synthesized over a commercial carbon black (Vulcan-XC-72R for comparison purposes. Characterization techniques included nitrogen physisorption, scanning electron microscopy, and X-ray diffraction. Catalysts electrochemical activity towards the oxidation of carbon monoxide and methanol was studied by cyclic voltammetry and chronoamperometry to establish the effect of the carbon support on the catalysts performance. Commercial Pt/C catalyst (E-TEK was analyzed for comparison purposes. It was observed that the more developed and mesopore-enriched porous structure of the carbon xerogel synthesized at a higher initial pH resulted in an optimal utilization of the active phase and in an enhanced and promising catalytic activity in the electrooxidation of methanol, in comparison with commercial catalysts.
Birefringent Electroweak Textures
Thatcher, M J; Thatcher, Marcus J.; Morgan, Michael J.
1999-01-01
The behaviour of electromagnetic waves propagating through an electroweak homilia string network is examined. This string network is topologically stable as a cosmic texture, and is characterized by the spatial variation of the isospin rotation of the Higgs field. As a consequence the photon field couples to the intermediate vector bosons, producing a finite range electromagnetic field. It is found that the propagation speed of the photon depends on its polarization vector, whence an homilia string network acts as a birefringent medium. We estimate the birefringent scale for this texture and show that it depends on the frequency of the electromagnetic wave and the length scale of the homilia string network.
Petersen, Hugh
2009-01-01
This article presents an art project inspired by a drawing of a chameleon the author saw in an art-supply catalog. Chameleons prove to be a good subject to highlight shape, color and texture with eigth-graders. In this project, middle- and high-school students draw a chameleon, learn how to use shapes to add to their chameleon drawing, learn how…
Lucassen, M.P.; Gevers, T.; Gijsenij, A.
2011-01-01
Several studies have recorded color emotions in subjects viewing uniform color (UC) samples. We conduct an experiment to measure and model how these color emotions change when texture is added to the color samples. Using a computer monitor, our subjects arrange samples along four scales: warm-cool,
Skophammer, Karen
2010-01-01
Clay is one of the most satisfying mediums for children to work with. It's relatively inexpensive, and the texture and changes that take place with the clay during firing make it irresistible. Molding clay from rolled-out slabs of clay is an easy way to make simple, shallow vessels or display pots. In this article, the author describes how her…
Guhin, Paula
2011-01-01
Creating a painting with texture is easy, although using heavy gel medium or modeling paste may be pricey ways to go about it. High school artists generally like making collages and mixed-media. In this article, the author suggests ways to capitalize on that interest with inexpensive fabric in a painting project.
Lucassen, M.P.; Gevers, T.; Gijsenij, A.
2011-01-01
Several studies have recorded color emotions in subjects viewing uniform color (UC) samples. We conduct an experiment to measure and model how these color emotions change when texture is added to the color samples. Using a computer monitor, our subjects arrange samples along four scales: warm-cool,
Characterization of color texture: color texture based sorting of tiles
Bourada, Y.; Lafon, Dominique; Eterradossi, O.
1998-09-01
Many materials used by the building industry show a color texture which affects the product commercial value. This texture can be seen as the spatial arrangement of regions of acceptable color differences. This work describes an appearance based automated sorting via color texture analysis, using ceramic tiles as example. Textural analysis of the tiles digital images expressed in CIEL*a*b* color system is performed through the analysis of intrinsic features of each region and relationships between regions. Results obtained through the automated process are compared to a visual sorting which leads to calculation of application dependant color and texture tolerances.
Basan, Markus; Lenz, Martin; Joanny, Jean-François; Risler, Thomas
2015-01-01
Contact inhibition is the process by which cells switch from a motile growing state to a passive and stabilized state upon touching their neighbors. When two cells touch, an adhesion link is created between them by means of transmembrane E-cadherin proteins. Simultaneously, their actin filaments stop polymerizing in the direction perpendicular to the membrane and reorganize to create an apical belt that colocalizes with the adhesion links. Here, we propose a detailed quantitative model of the role of the cytoplasmic $\\beta$-catenin and $\\alpha$-catenin proteins in this process, treated as a reaction-diffusion system. Upon cell-cell contact, the concentration in $\\alpha$-catenin dimers increases, inhibiting actin branching and thereby reducing cellular motility and expansion pressure. This model provides a mechanism for contact inhibition that could explain previously unrelated experimental findings on the role played by E-cadherin, $\\beta$-catenin and $\\alpha$-catenin in the cellular phenotype and in tumorige...
Parallel-Sequential Texture Analysis
Broek, E.L. van den; Rikxoort, E.M. van
2005-01-01
Color induced texture analysis is explored, using two texture analysis techniques: the co-occurrence matrix and the color correlogram as well as color histograms. Several quantization schemes for six color spaces and the human-based 11 color quantization scheme have been applied. The VisTex texture
Parallel-Sequential Texture Analysis
van den Broek, Egon; Singh, Sameer; Singh, Maneesha; van Rikxoort, Eva M.; Apte, Chid; Perner, Petra
2005-01-01
Color induced texture analysis is explored, using two texture analysis techniques: the co-occurrence matrix and the color correlogram as well as color histograms. Several quantization schemes for six color spaces and the human-based 11 color quantization scheme have been applied. The VisTex texture
From food structure to texture
Wilkinson, C.; Dijksterhuis, G.B.; Minekus, M.
2000-01-01
Understanding the relationship between food texture perception and food structure is of increasing importance for companies wishing to produce texturally attractive food products. The perception of texture is a complex process involving the senses of vision, hearing, somesthesis and kinesthesis. Tex
Seirin Lee, S.
2010-03-23
Turing\\'s pattern formation mechanism exhibits sensitivity to the details of the initial conditions suggesting that, in isolation, it cannot robustly generate pattern within noisy biological environments. Nonetheless, secondary aspects of developmental self-organisation, such as a growing domain, have been shown to ameliorate this aberrant model behaviour. Furthermore, while in-situ hybridisation reveals the presence of gene expression in developmental processes, the influence of such dynamics on Turing\\'s model has received limited attention. Here, we novelly focus on the Gierer-Meinhardt reaction diffusion system considering delays due the time taken for gene expression, while incorporating a number of different domain growth profiles to further explore the influence and interplay of domain growth and gene expression on Turing\\'s mechanism. We find extensive pathological model behaviour, exhibiting one or more of the following: temporal oscillations with no spatial structure, a failure of the Turing instability and an extreme sensitivity to the initial conditions, the growth profile and the duration of gene expression. This deviant behaviour is even more severe than observed in previous studies of Schnakenberg kinetics on exponentially growing domains in the presence of gene expression (Gaffney and Monk in Bull. Math. Biol. 68:99-130, 2006). Our results emphasise that gene expression dynamics induce unrealistic behaviour in Turing\\'s model for multiple choices of kinetics and thus such aberrant modelling predictions are likely to be generic. They also highlight that domain growth can no longer ameliorate the excessive sensitivity of Turing\\'s mechanism in the presence of gene expression time delays. The above, extensive, pathologies suggest that, in the presence of gene expression, Turing\\'s mechanism would generally require a novel and extensive secondary mechanism to control reaction diffusion patterning. © 2010 Society for Mathematical Biology.
The Visual N1 Is Sensitive to Deviations from Natural Texture Appearance.
Balas, Benjamin; Conlin, Catherine
2015-01-01
Disruptions of natural texture appearance are known to negatively impact performance in texture discrimination tasks, for example, such that contrast-negated textures, synthetic textures, and textures depicting abstract art are processed less efficiently than natural textures. Presently, we examined how visual ERP responses (the P1 and the N1 in particular) were affected by violations of natural texture appearance. We presented participants with images depicting either natural textures or synthetic textures made from the original stimuli. Both stimulus types were additionally rendered either in positive or negative contrast. These appearance manipulations (negation and texture synthesis) preserve a range of low-level features, but also disrupt higher-order aspects of texture appearance. We recorded continuous EEG while participants completed a same/different image discrimination task using these images and measured both the P1 and N1 components over occipital recording sites. While the P1 exhibited no sensitivity to either contrast polarity or real/synthetic appearance, the N1 was sensitive to both deviations from natural appearance. Polarity reversal and synthetic appearance affected the N1 latency differently, however, suggesting a differential impact on processing. Our results suggest that stages of visual processing indexed by the P1 and N1 are sensitive to high-order statistical regularities in natural textures and also suggest that distinct violations of natural appearance impact neural responses differently.
The Visual N1 Is Sensitive to Deviations from Natural Texture Appearance.
Benjamin Balas
Full Text Available Disruptions of natural texture appearance are known to negatively impact performance in texture discrimination tasks, for example, such that contrast-negated textures, synthetic textures, and textures depicting abstract art are processed less efficiently than natural textures. Presently, we examined how visual ERP responses (the P1 and the N1 in particular were affected by violations of natural texture appearance. We presented participants with images depicting either natural textures or synthetic textures made from the original stimuli. Both stimulus types were additionally rendered either in positive or negative contrast. These appearance manipulations (negation and texture synthesis preserve a range of low-level features, but also disrupt higher-order aspects of texture appearance. We recorded continuous EEG while participants completed a same/different image discrimination task using these images and measured both the P1 and N1 components over occipital recording sites. While the P1 exhibited no sensitivity to either contrast polarity or real/synthetic appearance, the N1 was sensitive to both deviations from natural appearance. Polarity reversal and synthetic appearance affected the N1 latency differently, however, suggesting a differential impact on processing. Our results suggest that stages of visual processing indexed by the P1 and N1 are sensitive to high-order statistical regularities in natural textures and also suggest that distinct violations of natural appearance impact neural responses differently.
Spatial Arrangement in Texture Discrimination and Texture Segregation
Kathleen Vancleef
2013-02-01
Full Text Available We investigated the role of spatial arrangement of texture elements in three psychophysical experiments on texture discrimination and texture segregation. In our stimuli, oriented Gabor elements formed an iso-oriented and a randomly oriented texture region. We manipulated (1 the orientation similarity in the iso-oriented region by adding orientation jitter to the orientation of each Gabor; (2 the spatial arrangement of the Gabors: quasi-random or regular; and (3 the shape of the edge between the two texture regions: straight or curved. In Experiment 1, participants discriminated an iso-oriented stimulus from a stimulus with only randomly oriented elements. Experiment 2 required texture segregation to judge the shape of the texture edge. Experiment 3 replicated Experiment 2 with Gabors of a smaller spatial extent in a denser arrangement. We found comparable performance levels with regular and quasi-random Gabor positions in the discrimination task but not in the segregation tasks. We conclude that spatial arrangement plays a role in a texture segregation task requiring shape discrimination of the texture edge but not in a texture discrimination task in which it is sufficient to discriminate an iso-oriented region from a completely random region.
Adaptive Electronic Camouflage Using Texture Synthesis
2012-04-01
Figure 1. Figure 1. A mixed variety of camouflage patterns found in moths (left), reptiles (center), mammals (right). *narek.pezeshkian@navy.mil...camouflaging ships, aircraft, vehicles, uniforms, weapons, and many other devices (Figure 3). Military camouflage colors and patterns have evolved throughout...As robots continue to evolve technologically, they will be used in more complex missions. For example, a robot may be used for information
[Visual Texture Agnosia in Humans].
Suzuki, Kyoko
2015-06-01
Visual object recognition requires the processing of both geometric and surface properties. Patients with occipital lesions may have visual agnosia, which is impairment in the recognition and identification of visually presented objects primarily through their geometric features. An analogous condition involving the failure to recognize an object by its texture may exist, which can be called visual texture agnosia. Here we present two cases with visual texture agnosia. Case 1 had left homonymous hemianopia and right upper quadrantanopia, along with achromatopsia, prosopagnosia, and texture agnosia, because of damage to his left ventromedial occipitotemporal cortex and right lateral occipito-temporo-parietal cortex due to multiple cerebral embolisms. Although he showed difficulty matching and naming textures of real materials, he could readily name visually presented objects by their contours. Case 2 had right lower quadrantanopia, along with impairment in stereopsis and recognition of texture in 2D images, because of subcortical hemorrhage in the left occipitotemporal region. He failed to recognize shapes based on texture information, whereas shape recognition based on contours was well preserved. Our findings, along with those of three reported cases with texture agnosia, indicate that there are separate channels for processing texture, color, and geometric features, and that the regions around the left collateral sulcus are crucial for texture processing.
Seismic texture classification. Final report
Vinther, R.
1997-12-31
The seismic texture classification method, is a seismic attribute that can both recognize the general reflectivity styles and locate variations from these. The seismic texture classification performs a statistic analysis for the seismic section (or volume) aiming at describing the reflectivity. Based on a set of reference reflectivities the seismic textures are classified. The result of the seismic texture classification is a display of seismic texture categories showing both the styles of reflectivity from the reference set and interpolations and extrapolations from these. The display is interpreted as statistical variations in the seismic data. The seismic texture classification is applied to seismic sections and volumes from the Danish North Sea representing both horizontal stratifications and salt diapers. The attribute succeeded in recognizing both general structure of successions and variations from these. Also, the seismic texture classification is not only able to display variations in prospective areas (1-7 sec. TWT) but can also be applied to deep seismic sections. The seismic texture classification is tested on a deep reflection seismic section (13-18 sec. TWT) from the Baltic Sea. Applied to this section the seismic texture classification succeeded in locating the Moho, which could not be located using conventional interpretation tools. The seismic texture classification is a seismic attribute which can display general reflectivity styles and deviations from these and enhance variations not found by conventional interpretation tools. (LN)
Texture Enhanced Appearance Models
Larsen, Rasmus; Stegmann, Mikkel Bille; Darkner, Sune;
2007-01-01
to excessive storage and computational requirements. We propose to reduce the dimensionality of the textural components by selecting a subset of basis functions from a larger dictionary, estimate regression splines and model only the coeffcients of the retained basis functions. We demonstrate the use of two...... types of bases, namely wavelets and wedgelets. Theformer extends the previous work of Wolstenholme and Taylor where Haar wavelet coeffcients subsets were applied. The latter introduces the wedgelet regression tree based on triangulated domains. The wavelet and wedgelet regression splines are functional...
Height and Tilt Geometric Texture
Andersen, Vedrana; Desbrun, Mathieu; Bærentzen, Jakob Andreas
2009-01-01
We propose a new intrinsic representation of geometric texture over triangle meshes. Our approach extends the conventional height field texture representation by incorporating displacements in the tangential plane in the form of a normal tilt. This texture representation offers a good practical...... compromise between functionality and simplicity: it can efficiently handle and process geometric texture too complex to be represented as a height field, without having recourse to full blown mesh editing algorithms. The height-and-tilt representation proposed here is fully intrinsic to the mesh, making...
Marco A. Velasco
2016-10-01
Full Text Available Scaffolds are essential in bone tissue engineering, as they provide support to cells and growth factors necessary to regenerate tissue. In addition, they meet the mechanical function of the bone while it regenerates. Currently, the multiple methods for designing and manufacturing scaffolds are based on regular structures from a unit cell that repeats in a given domain. However, these methods do not resemble the actual structure of the trabecular bone which may work against osseous tissue regeneration. To explore the design of porous structures with similar mechanical properties to native bone, a geometric generation scheme from a reaction-diffusion model and its manufacturing via a material jetting system is proposed. This article presents the methodology used, the geometric characteristics and the modulus of elasticity of the scaffolds designed and manufactured. The method proposed shows its potential to generate structures that allow to control the basic scaffold properties for bone tissue engineering such as the width of the channels and porosity. The mechanical properties of our scaffolds are similar to trabecular tissue present in vertebrae and tibia bones. Tests on the manufactured scaffolds show that it is necessary to consider the orientation of the object relative to the printing system because the channel geometry, mechanical properties and roughness are heavily influenced by the position of the surface analyzed with respect to the printing axis. A possible line for future work may be the establishment of a set of guidelines to consider the effects of manufacturing processes in designing stages.
Shankar, Varun; Wright, Grady B.; Fogelson, Aaron L.; Kirby, Robert M.
2014-05-01
We present a computational method for solving the coupled problem of chemical transport in a fluid (blood) with binding/unbinding of the chemical to/from cellular (platelet) surfaces in contact with the fluid, and with transport of the chemical on the cellular surfaces. The overall framework is the Augmented Forcing Point Method (AFM) (\\emph{L. Yao and A.L. Fogelson, Simulations of chemical transport and reaction in a suspension of cells I: An augmented forcing point method for the stationary case, IJNMF (2012) 69, 1736-52.}) for solving fluid-phase transport in a region outside of a collection of cells suspended in the fluid. We introduce a novel Radial Basis Function-Finite Difference (RBF-FD) method to solve reaction-diffusion equations on the surface of each of a collection of 2D stationary platelets suspended in blood. Parametric RBFs are used to represent the geometry of the platelets and give accurate geometric information needed for the RBF-FD method. Symmetric Hermite-RBF interpolants are used for enforcing the boundary conditions on the fluid-phase chemical concentration, and their use removes a significant limitation of the original AFM. The efficacy of the new methods are shown through a series of numerical experiments; in particular, second order convergence for the coupled problem is demonstrated.
Johnson, Margaret E.; Hummer, Gerhard
2014-07-01
We present a new algorithm for simulating reaction-diffusion equations at single-particle resolution. Our algorithm is designed to be both accurate and simple to implement, and to be applicable to large and heterogeneous systems, including those arising in systems biology applications. We combine the use of the exact Green's function for a pair of reacting particles with the approximate free-diffusion propagator for position updates to particles. Trajectory reweighting in our free-propagator reweighting (FPR) method recovers the exact association rates for a pair of interacting particles at all times. FPR simulations of many-body systems accurately reproduce the theoretically known dynamic behavior for a variety of different reaction types. FPR does not suffer from the loss of efficiency common to other path-reweighting schemes, first, because corrections apply only in the immediate vicinity of reacting particles and, second, because by construction the average weight factor equals one upon leaving this reaction zone. FPR applications include the modeling of pathways and networks of protein-driven processes where reaction rates can vary widely and thousands of proteins may participate in the formation of large assemblies. With a limited amount of bookkeeping necessary to ensure proper association rates for each reactant pair, FPR can account for changes to reaction rates or diffusion constants as a result of reaction events. Importantly, FPR can also be extended to physical descriptions of protein interactions with long-range forces, as we demonstrate here for Coulombic interactions.
LOCAL TEXTURE DESCRIPTION FRAMEWORK FOR TEXTURE BASED FACE RECOGNITION
R. Reena Rose
2014-02-01
Full Text Available Texture descriptors have an important role in recognizing face images. However, almost all the existing local texture descriptors use nearest neighbors to encode a texture pattern around a pixel. But in face images, most of the pixels have similar characteristics with that of its nearest neighbors because the skin covers large area in a face and the skin tone at neighboring regions are same. Therefore this paper presents a general framework called Local Texture Description Framework that uses only eight pixels which are at certain distance apart either circular or elliptical from the referenced pixel. Local texture description can be done using the foundation of any existing local texture descriptors. In this paper, the performance of the proposed framework is verified with three existing local texture descriptors Local Binary Pattern (LBP, Local Texture Pattern (LTP and Local Tetra Patterns (LTrPs for the five issues viz. facial expression, partial occlusion, illumination variation, pose variation and general recognition. Five benchmark databases JAFFE, Essex, Indian faces, AT&T and Georgia Tech are used for the experiments. Experimental results demonstrate that even with less number of patterns, the proposed framework could achieve higher recognition accuracy than that of their base models.
A Novel Technique of Error Concealment Method Selection in Texture Images Using ALBP Classifier
Z. Tothova
2010-06-01
Full Text Available There are many error concealment techniques for image processing. In the paper, the focus is on restoration of image with missing blocks or macroblocks. Different methods can be optimal for different kinds of images. In recent years, great attention was dedicated to textures, and specific methods were developed for their processing. Many of them use classification of textures as an integral part. It is also of an advantage to know the texture classification to select the best restoration technique. In the paper, selection based on texture classification with advanced local binary patterns and spatial distribution of dominant patterns is proposed. It is shown, that for classified textures, optimal error concealment method can be selected from predefined ones, resulting then in better restoration. For testing, three methods of extrapolation and texture synthesis were used.
Laser textured surface gradients
Ta, Van Duong; Dunn, Andrew; Wasley, Thomas J.; Li, Ji; Kay, Robert W.; Stringer, Jonathan; Smith, Patrick J.; Esenturk, Emre; Connaughton, Colm; Shephard, Jonathan D.
2016-05-01
This work demonstrates a novel technique for fabricating surfaces with roughness and wettability gradients and their subsequent applications for chemical sensors. Surface roughness gradients on brass sheets are obtained directly by nanosecond laser texturing. When these structured surfaces are exposed to air, their wettability decreases with time (up to 20 days) achieving both spatial and temporal wettability gradients. The surfaces are responsive to organic solvents. Contact angles of a series of dilute isopropanol solutions decay exponentially with concentration. In particular, a fall of 132° in contact angle is observed on a surface gradient, one order of magnitude higher than the 14° observed for the unprocessed surface, when the isopropanol concentration increased from 0 to 15.6 wt%. As the wettability changes gradually over the surface, contact angle also changes correspondingly. This effect offers multi-sensitivity at different zones on the surface and is useful for accurate measurement of chemical concentration.
Emotional effects of dynamic textures
Toet, A.; Henselmans, M.; Lucassen, M.P.; Gevers, T.
2011-01-01
This study explores the effects of various spatiotemporal dynamic texture characteristics on human emotions. The emotional experience of auditory (eg, music) and haptic repetitive patterns has been studied extensively. In contrast, the emotional experience of visual dynamic textures is still largely
Color texture measurement and segmentation
Hoang, M.A.; Geusebroek, J.M.; Smeulders, A.W.M.
2005-01-01
In computer vision, meaurement of image properties such as color or texture is essential. In this paper, we propose a solid framework for the local measurement of texture in color images. We give a physical basis for the integration of the well-known Gabor filters with the measurement of color. Our
Quantitative Characterisation of Surface Texture
De Chiffre, Leonardo; Lonardo, P.M.; Trumpold, H.
2000-01-01
This paper reviews the different methods used to give a quantitative characterisation of surface texture. The paper contains a review of conventional 2D as well as 3D roughness parameters, with particular emphasis on recent international standards and developments. It presents new texture...
Texture of mayonnaise and dressing
Terpstra, M.E.J.; Janssen, A.M.; Gemert, van L.J.; Doorn, van R.J.M.; Wijk, de R.A.; Weenen, H.; Linden, van der E.
2003-01-01
Relationships between sensory texture attributes and physical properties of mayonnaise and dressings have been explored. The focus of the work was in creaminess and related texture attributes. Samples ranging from 0-70% oil were tested sensorially by QDA-panels. Physical caharacterisation of these
肖娟; 王嵩; 张雯雰
2014-01-01
Criminisi提出的基于样本的图像修复技术需要在整幅图像中遍历样本，代价太大，并可能因选择错误的样本，不断迭代更新后而导致错误信息累积，使修复结果出现较大的偏差。同时，考虑到Criminisi算法中优先权函数的计算失误可能导致修复结果中出现结构失真，由此提出一种基于聚类分割和纹理合成的图像修复改进算法，将目标样本块的搜索限定在与源样本块所覆盖的类别一致的区域当中。在像素点优先权计算中，引入该像素点邻域灰度梯度差值信息，提出更为合理的优先权计算公式，以最大限度保证复杂场景中边缘优先传递，并在置信度更新项中有差别地对待新填充像素点。通过实验证明，改进算法不仅解决了Criminisi算法可能存在的结构偏差延续问题，修复视觉效果更加符合人们的主观感受，而且大大缩短了修复时间。%Criminisi proposed exemplar-based image inpainting techniques need to traverse the whole image exemplar, it is too costly, and may choose the wrong exemplar, constantly updates iteration error messages resulting cumulative, so that a greater deviation may be in inpainting results. Meanwhile, considering the Criminisi algorithm priority function cal-culation may lead to a structural distortion in inpainting results, which proposes an improved algorithm for image inpainting based on clustering segmentation and texture synthesis, the search will be limited to the same categories zone with the source exemplar covered. In the pixel priority calculation, the pixel neighborhood gray gradient difference information is introduced, the priority of more reasonable formula is proposed to ensure maximum edge preferentially transmitted in complex scenes and update entries in confidence difference to treat newly filled pixels. The experimental results show that the improved algorithm not only solves the Criminisi algorithm possible
Zhao, Qi; Yi, Ming; Liu, Yan
2011-10-01
The mitogen-activated protein kinase (MAPK) cascade plays a critical role in the control of cell growth. Deregulation of this pathway contributes to the development of many cancers. To better understand its signal transduction, we constructed a reaction-diffusion model for the MAPK pathway. We modeled the three layers of phosphorylation-dephosphorylation reactions and diffusion processes from the cell membrane to the nucleus. Based on different types of feedback in the MAPK cascade, four operation modes are introduced. For each of the four modes, spatial distributions and dose-response curves of active kinases (i.e. ppMAPK) are explored by numerical simulation. The effects of propagation length, diffusion coefficient and feedback strength on the pathway dynamics are investigated. We found that intrinsic bistability in the MAPK cascade can generate a traveling wave of ppMAPK with constant amplitude when the propagation length is short. ppMAPK in this mode of intrinsic bistability decays more slowly than it does in all other modes as the propagation length increases. Moreover, we examined the global and local responses to Ras-GTP of these four modes, and demonstrated how the shapes of these dose-response curves change as the propagation length increases. Also, we found that larger diffusion constant gives a higher response level on the zero-order regime and makes the ppMAPK profiles flatter under strong Ras-GTP stimulus. Furthermore, we observed that spatial responses of ppMAPK are more sensitive to negative feedback than to positive feedback in the broader signal range. Finally, we showed how oscillatory signals pass through the kinase cascade, and found that high frequency signals are damped faster than low frequency ones.
魏纯辉; 李俐玫
2011-01-01
作者应用谱理论和规范化Lyapunov-Schmidt约化方法研究了关于基因繁殖的反应扩散系统(0,1)解的定态分歧,在特征值的代数重数为1的情况下,在一定条件下得到了定态方程从二阶非退化奇点处分歧出的正则分歧解.%By using the Spectrum Theory and normalized Lyapunov-Schmidt Reduction method, the steady state bifurcation of the reaction-diffusion system from (0,1)for Gene Propagation model is discussed,bifurcated branches from a second order nondegenerate singular point with algebraic multiplicity one of eigenvalue raised from the given reaction-diffusion equations are investigated. And under some conditions, the regular bifurcated branches are obtained.
Motion texture using symmetric property and graphcut algorithm
SHEN Jian-bing; JIN Xiao-gang; ZHOU Chuan; ZHAO Han-li
2006-01-01
In this paper, a novel motion texture approach is presented for synthesizing long character motion (e.g., kungfu) that is similar to the original short input motion. First, a new motion with repeated frames is genterated by exploiting the symmetric properties of the frames and reversing the motion sequence playback in a given motion sequence. Then, the order of the above motion sequence is rearranged by putting the start and the end frames together. The graphcut algorithm is used to seamlessly synthesize the transition between the start and the end frames, which is noted as graphcut-based motion-texton. Finally, we utilize the motion-textons to synthesize long motion texture, which can be patched together like the image texture synthesis method using graphcut algorithm, and automatically form a long motion texture endlessly. Our approach is demonstrated by synthesizing the long kungfu motion texture without visual artifacts, together with post-processing including our new developed graphcut-based motion blending and Poisson-based motion smoothing techniques.
徐琛梅
2008-01-01
This paper deals with the special nonlinear reaction-diffusion equation.The finite difference scheme with incremental unknowns approximating to the differential equation (2.1) is set up by means of introducing incremental unknowns methods.Through the stability analyzing for the scheme,it was shown that the stability conditions of the finite difference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.
徐琛梅
2008-01-01
In the article,the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established.Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space.The approach used is of a simple characteristic in gaining the stability condition of the scheme.
Symmetry realization of texture zeros
Grimus, W. [Institut fuer Theoretische Physik, Universitaet Wien, Boltzmanngasse 5, 1090, Wien (Austria); Joshipura, A.S. [Physical Research Laboratory, 380009, Ahmedabad (India); Lavoura, L. [Centro de Fisica das Interaccoes Fundamentais, Instituto Superior Tecnico, Universidade Tecnica de Lisboa, 1049-001, Lisboa (Portugal); Tanimoto, M. [Department of Physics, Niigata University, Ikarashi 2-8050, 950-2181, Niigata (Japan)
2004-08-01
We show that it is possible to enforce texture zeros in arbitrary entries of the fermion mass matrices by means of Abelian symmetries; in this way, many popular mass-matrix textures find a symmetry justification. We propose two alternative methods which allow one to place zeros in any number of elements of the mass matrices that one wants. They are applicable simultaneously in the quark and lepton sectors. They are also applicable in grand unified theories. The number of scalar fields required by our methods may be large; still, in many interesting cases this number can be reduced considerably. The larger the desired number of texture zeros is, the simpler are the models which reproduce the texture. (orig.)
Symmetry realization of texture zeros
Grimus, Walter; Lavoura, L; Tanimoto, M
2004-01-01
We show that it is possible to enforce texture zeros in arbitrary entries of the fermion mass matrices by means of Abelian symmetries; in this way, many popular mass-matrix textures find a symmetry justification. We propose two alternative methods which allow to place zeros in any number of elements of the mass matrices that one wants. They are applicable simultaneously in the quark and lepton sectors. They are also applicable in Grand Unified Theories. The number of scalar fields required by our methods may be large; still, in many interesting cases this number can be reduced considerably. The larger the desired number of texture zeros is, the simpler are the models which reproduce the texture.
EUROMET SUPPLEMENTARY COMPARISON - SURFACE TEXTURE
Koenders, L.; Andreasen, Jan Lasson; De Chiffre, Leonardo
At the length meeting in Prague in Oct. 1999 a new comparison was suggested on surface texture. The last comparison on this field was finished in 1989. In the meantime the instrumentation, the standards and the written standards have been improved including some software filters. The pilot...... laboratories for this supplementary comparison on surface texture are the Centre for Geometrical Metrology at the Technical University of Denmark and the Micro- and Nanotopography laboratory at the Physikalisch-Technische Bundesanstalt, Germany....
Laser surface texturing: chosen problems
Antoszewski, Bogdan; Sek, Piotr
2013-01-01
In modern machines for realization of goals like lubrication intesyfication, heat flow intensyfiacation, microflow simulation; more and more often surface texturing is used. It became possible due to develepment of technologies that use sources of concentrated energy stream like microlasers. The paper shows results of experimental investigation on seal rings made of silicon carbide. Experiments were conducted using seal rings without surface modifications and a seal rings with a geometrical surface textures made with Nd:Yag laser.
Joanna Korczyk-Szabó
2013-12-01
Full Text Available Abstract The bread quality is considerably dependent on the texture characteristic of bread crumb. Crumb texture is an important quality indicator, as consumer prefer different bread taste. Texture analysis is primarily concerned with the evaluation of mechanical characteristics where a material is subjected to a controlled force from which a deformation curve of its response is generated. It is an objective physical examination of baked products and gives direct information on the product quality, oppositely to dough rheology tests what inform on the baking suitability of the flour, as raw material. This is why the texture analysis is one of the most helpful analytical methods of the product development. In the framework of our research during the years 2008 – 2009 were analyzed selected indicators for bread texture quality of five Triticum spelta L. varieties – Altgold, Oberkulmer Rotkorn, Ostro, Rubiota and Franckenkorn grown in an ecological system. The bread texture quality was evaluated on texture analyzer TA.XT Plus (Stable Micro Systems, Surrey, UK, following the AACC (74-09 standard method and expressed as crumb firmness (N, stiffness (N.mm-1 and relative elasticity (%. Our research proved that all selected indicators were significantly influenced by the year of growing and variety. The most soft bread was achieved in Rubiota, whereas bread crumb samples from Franckenkorn and Altgold were the most firm and stiff. Correlation analysis showed strong negative correlation between relative elasticity and bread crumb firmness as well as bread stiffness (-0.81++, -0.78++. The spelt grain can be a good source for making bread flour, but is closely dependent on choice of spelt variety. The spelt wheat bread crumb texture need further investigation as it can be a reliable quality parameter.
Audio Classification from Time-Frequency Texture
Yu, Guoshen
2008-01-01
Time-frequency representations of audio signals often resemble texture images. This paper derives a simple audio classification algorithm based on treating sound spectrograms as texture images. The algorithm is inspired by an earlier visual classification scheme particularly efficient at classifying textures. While solely based on time-frequency texture features, the algorithm achieves surprisingly good performance in musical instrument classification experiments.
Texture analysis methods for the characterisation of biological and medical images
Ştefan Ţălu
2012-06-01
Full Text Available Adaptations can be extreme in many cases and they help organisms survive in their habitat or ecological niche. These adaptations can affect their anatomy, ethology or physiology. Anatomical adaptations are physical features such as animal's shape, particularities at the skeleton level, texture of exoskeleton, surface of the skin in animals or cuticula in plants etc. The purpose of this paper is to present a synthesis concerning the texture analysis methods used for the characterisation of biological and medical images. Texture analysis methods of biological and medical images provide noninvasive tools that allow biologists, physicians and researchers the early detection and diagnosis of diseases.
Spherical harmonics in texture analysis
Schaeben, Helmut; van den Boogaart, K. Gerald
2003-07-01
The objective of this contribution is to emphasize the fundamental role of spherical harmonics in constructive approximation on the sphere in general and in texture analysis in particular. The specific purpose is to present some methods of texture analysis and pole-to-orientation probability density inversion in a unifying approach, i.e. to show that the classic harmonic method, the pole density component fit method initially introduced as a distinct alternative, and the spherical wavelet method for high-resolution texture analysis share a common mathematical basis provided by spherical harmonics. Since pole probability density functions and orientation probability density functions are probability density functions defined on the sphere Ω3⊂ R3 or hypersphere Ω4⊂ R4, respectively, they belong at least to the space of measurable and integrable functions L1( Ωd), d=3, 4, respectively. Therefore, first a basic and simplified method to derive real symmetrized spherical harmonics with the mathematical property of providing a representation of rotations or orientations, respectively, is presented. Then, standard orientation or pole probability density functions, respectively, are introduced by summation processes of harmonic series expansions of L1( Ωd) functions, thus avoiding resorting to intuition and heuristics. Eventually, it is shown how a rearrangement of the harmonics leads quite canonically to spherical wavelets, which provide a method for high-resolution texture analysis. This unified point of view clarifies how these methods, e.g. standard functions, apply to texture analysis of EBSD orientation measurements.
Texture discrimination by Gabor functions.
Turner, M R
1986-01-01
A 2D Gabor filter can be realized as a sinusoidal plane wave of some frequency and orientation within a two dimensional Gaussian envelope. Its spatial extent, frequency and orientation preferences as well as bandwidths are easily controlled by the parameters used in generating the filters. However, there is an "uncertainty relation" associated with linear filters which limits the resolution simultaneously attainable in space and frequency. Daugman (1985) has determined that 2D Gabor filters are members of a class of functions achieving optimal joint resolution in the 2D space and 2D frequency domains. They have also been found to be a good model for two dimensional receptive fields of simple cells in the striate cortex (Jones 1985; Jones et al. 1985). The characteristic of optimal joint resolution in both space and frequency suggests that these filters are appropriate operators for tasks requiring simultaneous measurement in these domains. Texture discrimination is such a task. Computer application of a set of Gabor filters to a variety of textures found to be preattentively discriminable produces results in which differently textured regions are distinguished by first-order differences in the values measured by the filters. This ability to reduce the statistical complexity distinguishing differently textured region as well as the sensitivity of these filters to certain types of local features suggest that Gabor functions can act as detectors of certain "texton" types. The performance of the computer models suggests that cortical neurons with Gabor like receptive fields may be involved in preattentive texture discrimination.
Joanna Korczyk – Szabó
2014-02-01
Full Text Available Texture analysis is an objective physical examination of baked products and gives direct information on the product quality, oppositely to dough rheology tests what inform on the baking suitability of the flour, as raw material. Evaluation of the mechanical properties of bread crumb is important not only for quality assurance in the bakeries, but also for assessing the effects of changes in dough ingredients and processing condition and also for describing the changes in bread crumb during storage. Crumb cellular structure is an important quality criterion used in commercial baking and research laboratories to judge bread quality alongside taste, crumb colour and crumb physical texture. In the framework of our research during the years 2010 – 2011 were analyzed selected indicators of bread crumb for texture quality of three Triticum spelta L. cultivars – Altgold, Rubiota and Ostro grown in an ecological system. The bread texture quality was evaluated on texture analyzer TA.XT Plus (Stable Micro Systems, Surrey, UK, following the AACC (74-09 standard and expressed as crumb firmness (N, stiffness (N.mm-1 and relative elasticity (%. Our research proved that all selected indicators were significantly influenced by the year of growing and variety. The most soft bread was achieved in Rubiota, whereas bread crumb samples from Altgold and Ostro were the most firm and stiff. Correlation analysis showed strong negative correlation between relative elasticity and bread crumb firmness as well as bread stiffness (-0.65++, -0.66++. The spelt wheat bread crumb texture need further investigation as it can be a reliable quality parameter.
Laser surface texturing of tool steel: textured surfaces quality evaluation
Šugár, Peter; Šugárová, Jana; Frnčík, Martin
2016-05-01
In this experimental investigation the laser surface texturing of tool steel of type 90MnCrV8 has been conducted. The 5-axis highly dynamic laser precision machining centre Lasertec 80 Shape equipped with the nano-second pulsed ytterbium fibre laser and CNC system Siemens 840 D was used. The planar and spherical surfaces first prepared by turning have been textured. The regular array of spherical and ellipsoidal dimples with a different dimensions and different surface density has been created. Laser surface texturing has been realized under different combinations of process parameters: pulse frequency, pulse energy and laser beam scanning speed. The morphological characterization of ablated surfaces has been performed using scanning electron microscopy (SEM) technique. The results show limited possibility of ns pulse fibre laser application to generate different surface structures for tribological modification of metallic materials. These structures were obtained by varying the processing conditions between surface ablation, to surface remelting. In all cases the areas of molten material and re-cast layers were observed on the bottom and walls of the dimples. Beside the influence of laser beam parameters on the machined surface quality during laser machining of regular hemispherical and elipsoidal dimple texture on parabolic and hemispherical surfaces has been studied.
Sensory memory and food texture
Mojet, J.; Köster, E.P.
2005-01-01
Memory for texture plays an important role in food expectations. After fasting overnight, subjects (41 women, 35 men, age 19-60 years) received a breakfast including breakfast drink, biscuits and yoghurt. Subsequently, they rated their hunger feelings every hour, and returned for a taste experiment
Sensory memory and food texture
Mojet, J.; Koster, E.P.
2005-01-01
Memory for texture plays an important role in food expectations. After fasting overnight, subjects (41 women, 35 men, age 19¿60 years) received a breakfast including breakfast drink, biscuits and yoghurt. Subsequently, they rated their hunger feelings every hour, and returned for a taste experiment
Colloidal aspects of texture perception
Vliet, T. van; Aken, G.A. van; Jongh, H.H.J. de; Hamer, R.J.
2009-01-01
Recently, considerable attention has been given to the understanding of texture attributes that cannot directly be related to physical properties of food, such as creamy, crumbly and watery. The perception of these attributes is strongly related to the way the food is processed during food intake, m
Colloidal aspects of texture perception
Vliet, van T.
2010-01-01
The perception of complex textures in food is strongly related to the way food is processed during eating, and is modulated by other basic characteristics, such as taste and aroma. An understanding at the colloidal level of the basic processes in the mouth is essential in order to link the compositi
Fast cartoon + texture image filters.
Buades, Antoni; Le, Triet M; Morel, Jean-Michel; Vese, Luminita A
2010-08-01
Can images be decomposed into the sum of a geometric part and a textural part? In a theoretical breakthrough, [Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations. Providence, RI: American Mathematical Society, 2001] proposed variational models that force the geometric part into the space of functions with bounded variation, and the textural part into a space of oscillatory distributions. Meyer's models are simple minimization problems extending the famous total variation model. However, their numerical solution has proved challenging. It is the object of a literature rich in variants and numerical attempts. This paper starts with the linear model, which reduces to a low-pass/high-pass filter pair. A simple conversion of the linear filter pair into a nonlinear filter pair involving the total variation is introduced. This new-proposed nonlinear filter pair retains both the essential features of Meyer's models and the simplicity and rapidity of the linear model. It depends upon only one transparent parameter: the texture scale, measured in pixel mesh. Comparative experiments show a better and faster separation of cartoon from texture. One application is illustrated: edge detection.
Bigham, Gary
2010-01-01
Off-road motorcycle racing and ATV riding. Gardening and fishing. What do these high-adrenaline and slower-paced pastimes have in common? Each requires soil, and the texture of that soil has an effect on all of them. In the inquiry-based lessons described here, students work both in the field or laboratory and in the classroom to collect soil…
Colloidal aspects of texture perception
Vliet, T. van; Aken, G.A. van; Jongh, H.H.J. de; Hamer, R.J.
2009-01-01
Recently, considerable attention has been given to the understanding of texture attributes that cannot directly be related to physical properties of food, such as creamy, crumbly and watery. The perception of these attributes is strongly related to the way the food is processed during food intake,
Sensory memory and food texture
Mojet, J.; Köster, E.P.
2005-01-01
Memory for texture plays an important role in food expectations. After fasting overnight, subjects (41 women, 35 men, age 19-60 years) received a breakfast including breakfast drink, biscuits and yoghurt. Subsequently, they rated their hunger feelings every hour, and returned for a taste experiment
Sensory memory and food texture
Mojet, J.; Koster, E.P.
2005-01-01
Memory for texture plays an important role in food expectations. After fasting overnight, subjects (41 women, 35 men, age 19¿60 years) received a breakfast including breakfast drink, biscuits and yoghurt. Subsequently, they rated their hunger feelings every hour, and returned for a taste experiment
莫嘉琪
2006-01-01
A class of nonlinear nonlocal singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained; secondly, by using the stretched variable, the composing expansion method and the expanding theory of power series, the initial layer is constructed; and finally,by using the theory of differential inequalities the asymptotic behavior of solutions for initial boundary value problems is studied, and including some relational inequalities the existence and uniqueness of solutions for the original problem and the uniformly valid asymptotic estimation are discussed.
Garcia Velarde, M.
1977-07-01
Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.
王智诚; 王双明
2013-01-01
利用动力系统方法及持久性理论研究了一类时间周期的时滞非局部反应扩散单种群增长模型，建立了解的全局存在性以及一致持久性。%The paper was concerned with a class of delayed nonlocal reaction-diffusion equation with a time period, which modelled the growth of a single species. By using the monotone dynamical system method and practice persistence theory, the global existence and uniform persistence of solutions were established.
Computing negentropy based signatures for texture recognition
Daniela COLTUC
2007-12-01
Full Text Available The proposed method aims to provide a new tool for texture recognition. For this purpose, a set of texture samples are decomposed by using the FastICA algorithm and characterized by a negentropy based signature. In order to do recognition, the texture signatures are compared by means of Minkowski distance. The recognition rates, computed for a set of 320 texture samples, show a medium recognition accuracy and the method may be further improved.
Applications of pattern recognition in aluminum alloy texture characterization
Liu, Guizhong; Rehbein, D. K.; Foley, James C.; Thompson, R. B.
2000-05-01
This paper presents a methodology to extract texture information in Aluminum alloys using pattern recognition algorithm. The orientation of the samples can be obtained by the orientation Image Microscope (OIM) technique. The ISO DATA pattern recognition algorithm is implemented to classify the OIM data into different clusters. Based on the classification results, the probability density function (pdf) is estimated. Then, the pdf is expanded as a series of Legendre functions with coefficients, i.e., the orientation distribution coefficients (ODC) as texture parameters. Three of these ODC's are of special interests, namely W400, W420, and W440. This paper includes results from ultrasonic NDE and this novel algorithm.—Ames Laboratory is operated for U.S. Department of Energy by Iowa State University under Contract W-7405-ENG-82. This work was supported by the Office of Basic Energy Sciences as a part of the Center of Excellence of the Synthesis and Processing of Advanced Materials.
Statistical representation of sound textures in the impaired auditory system
McWalter, Richard Ian; Dau, Torsten
2015-01-01
Many challenges exist when it comes to understanding and compensating for hearing impairment. Traditional methods, such as pure tone audiometry and speech intelligibility tests, offer insight into the deficiencies of a hearingimpaired listener, but can only partially reveal the mechanisms...... that underlie the hearing loss. An alternative approach is to investigate the statistical representation of sounds for hearing-impaired listeners along the auditory pathway. Using models of the auditory periphery and sound synthesis, we aimed to probe hearing impaired perception for sound textures – temporally...... homogenous sounds such as rain, birds, or fire. It has been suggested that sound texture perception is mediated by time-averaged statistics measured from early auditory representations (McDermott et al., 2013). Changes to early auditory processing, such as broader “peripheral” filters or reduced compression...
Modeling Human Aesthetic Perception of Visual Textures
Thumfart, Stefan; Jacobs, Richard H. A. H.; Lughofer, Edwin; Eitzinger, Christian; Cornelissen, Frans W.; Groissboeck, Werner; Richter, Roland
2011-01-01
Texture is extensively used in areas such as product design and architecture to convey specific aesthetic information. Using the results of a psychological experiment, we model the relationship between computational texture features and aesthetic properties of visual textures. Contrary to previous a
Geometric Total Variation for Texture Deformation
Bespalov, Dmitriy; Dahl, Anders Lindbjerg; Shokoufandeh, Ali
2010-01-01
of features in texture images leads to significant improvements in localization of these features, when textures undergo geometrical transformations. Accurate localization of features in the presense of unkown deformations is a crucial property for texture characterization methods, and we intend to expoit...
Modeling Human Aesthetic Perception of Visual Textures
Thumfart, Stefan; Jacobs, Richard H. A. H.; Lughofer, Edwin; Eitzinger, Christian; Cornelissen, Frans W.; Groissboeck, Werner; Richter, Roland
2011-01-01
Texture is extensively used in areas such as product design and architecture to convey specific aesthetic information. Using the results of a psychological experiment, we model the relationship between computational texture features and aesthetic properties of visual textures. Contrary to previous
Evaluation of color representation for texture analysis
Broek, E.L. van den; Rikxoort, E.M. van
2005-01-01
Since more than 50 years texture in image material is a topic of research. Hereby, color was ignored mostly. This study compares 70 diferent con- figurations for texture analysis, using four features. For the configurations we used: (i) a gray value texture descriptor: the co-occurrence matrix and a
Real-time Texture Error Detection
Dan Laurentiu Lacrama
2008-01-01
Full Text Available This paper advocates an improved solution for the real-time error detection of texture errors that occurs in the production process in textile industry. The research is focused on the mono-color products with 3D texture model (Jacquard fabrics. This is a more difficult task than, for example, 2D multicolor textures.
Evaluation of color representation for texture analysis
Verbrugge, R.; van den Broek, Egon; van Rikxoort, E.M.; Taatgen, N.; Schomaker, L.
2004-01-01
Since more than 50 years texture in image material is a topic of research. Hereby, color was ignored mostly. This study compares 70 different configurations for texture analysis, using four features. For the configurations we used: (i) a gray value texture descriptor: the co-occurrence matrix and a
周凤燕
2012-01-01
研究了一类反应扩散广义时滞细胞神经网络在噪声干扰下的指数稳定性.利用Ito公式,Holder不等式,M矩阵性质和微分不等式技巧,给出了系统均值指数稳定的充分条件,并且判断方法简单易操作.最后给出了主要定理的两个应用实例,表明结论的有效性.%The exponential stability of a class of reaction-diffusion general cellular neural network with time delay and noise perturbation is studied. Using the Ito formula, Holder inequality, M-matric properties and a skill of differential inequality, some sufficient conditions are given to guarantee the mean value exponential stability of the equilibrium for the stochastic reaction-diffusion general cellular neural network with time delay and the sufficient conditions are easier to operate. In the end, two examples are given to illustrate the main theoretical results.
谢溪庄
2011-01-01
In this paper, the author proposed and considered a Schoner reaction-diffusion equation in competing model with nonlocal delays . Each species in the discrete delay type model has a corresponding constant maturation time. Only the adult members are involved competition and immature members are in the absence of competition. We established the existence of traveling wave fronts connecting two boundary equilibriums. The approach used in this paper is the upper-lower solutions technique and monotone iteration by Wang, Li and Ruan for reaction-diffusion systems with spatio-temporal delays.%构造并研究了一类具有非局部时滞Schoner竞争反应扩散模型．每一个种群的成熟期是一个常数，而且只有成年种群存在竞争，幼年的种群并不存在竞争，此外种群个体在空间区域中的运动是随机行走的．我们利用Wang，Li和Ruan建立的具有非局部时滞的反应扩散系统的波前解存在性理论，证明了连接两个边界平衡解的行波解的存在性．
田慧洁; 李艳玲; 郭改慧
2016-01-01
研究了具有饱和项和毒素影响的反应扩散模型的平衡态方程,在齐次Neumann边界条件下常数平衡解的分歧与稳定性.利用谱分析和分歧理论的方法,分别以r1、r2为分歧参数,讨论了系统在常数平衡解附近出现分歧现象;同时运用线性算子的扰动理论和分歧解的稳定理论给出分歧解的稳定性.%The steady-states of reaction diffusion model with saturating terms and effects of toxic substances is studied, the bifurcation and the stability of a reaction-diffusion system with homogeneous Neumann boundary are investigated by the method of spectral analysis and bifurcation theory. The bifurcation at the steady-state solutions is acquired by treating r1, r2 as bifurcation parameters. Moreover, some stability results of the bifurcation solutions are obtained by using pertur-bation theory of linear operators and stability theory of bifurcation solutions.
Texture induced microwave background anisotropies
Borrill, Julian; Copeland, Edmund J.; Liddle, Andrew R.; Stebbins, Albert; Veeraraghavan, Shoba
1994-03-01
We use numerical simulations to calculate the cosmic microwave background anisotropy induced by the evolution of a global texture field, with special emphasis on individual textures. Both spherically symmetric and general configurations are analyzed, and in the latter case we consider field configurations which exhibit unwinding events and also ones which do not. We compare the results given by evolving the field numerically under both the expanded core (XCORE) and non-linear sigma model (NLSM) approximations with the analytic predictions of the NLSM exact solution for a spherically symmetric self-similar (SSSS) unwinding. We find that the random unwinding configuration spots' typical peak height is 60-75\\% and angular size typically only 10% of those of the SSSS unwinding, and that random configurations without an unwinding event nonetheless may generate indistinguishable hot and cold spots. A brief comparison is made with other work.
Watermarking textures in video games
Liu, Huajian; Berchtold, Waldemar; Schäfer, Marcel; Lieb, Patrick; Steinebach, Martin
2014-02-01
Digital watermarking is a promising solution to video game piracy. In this paper, based on the analysis of special challenges and requirements in terms of watermarking textures in video games, a novel watermarking scheme for DDS textures in video games is proposed. To meet the performance requirements in video game applications, the proposed algorithm embeds the watermark message directly in the compressed stream in DDS files and can be straightforwardly applied in watermark container technique for real-time embedding. Furthermore, the embedding approach achieves high watermark payload to handle collusion secure fingerprinting codes with extreme length. Hence, the scheme is resistant to collusion attacks, which is indispensable in video game applications. The proposed scheme is evaluated in aspects of transparency, robustness, security and performance. Especially, in addition to classical objective evaluation, the visual quality and playing experience of watermarked games is assessed subjectively in game playing.
Quantitative Characterisation of Surface Texture
De Chiffre, Leonardo; Lonardo, P.M.; Trumpold, H.;
2000-01-01
This paper reviews the different methods used to give a quantitative characterisation of surface texture. The paper contains a review of conventional 2D as well as 3D roughness parameters, with particular emphasis on recent international standards and developments. It presents new texture...... characterisation methods, such as fractals, wavelets, change trees and others, including for each method a short review, the parameters that the new methods calculate, and applications of the methods to solve surface problems. The paper contains a discussion on the relevance of the different parameters...... and quantification methods in terms of functional correlations, and it addresses the need for reducing the large number of existing parameters. The review considers the present situation and gives suggestions for future activities....
Texture of lipid bilayer domains
Jensen, Uffe Bernchou; Brewer, Jonathan R.; Midtiby, Henrik Skov
2009-01-01
chains. By imaging the intensity variations as a function of the polarization angle, we map the lateral variations of the lipid tilt within domains. Results reveal that gel domains are composed of subdomains with different lipid tilt directions. We have applied a Fourier decomposition method......We investigate the texture of gel (g) domains in binary lipid membranes composed of the phospholipids DPPC and DOPC. Lateral organization of lipid bilayer membranes is a topic of fundamental and biological importance. Whereas questions related to size and composition of fluid membrane domain...... are well studied, the possibility of texture in gel domains has so far not been examined. When using polarized light for two-photon excitation of the fluorescent lipid probe Laurdan, the emission intensity is highly sensitive to the angle between the polarization and the tilt orientation of lipid acyl...
Textural discrimination in unconstrained environment
Albalooshi, Fatema A.; Asari, Vijayan K.
2014-03-01
Object region segmentation for object detection and identi cation in images captured in a complex background environment is one of the most challenging tasks in image processing and computer vision areas especially for objects that have non-homogeneous body textures. This paper presents an object segmentation technique in an unconstrained environment based on textural descriptors to extract the object region of interest from other surrounding objects and backgrounds in order to get an accurate identi cation of the segmented area precisely. The proposed segmentation method is developed on a textural based analysis and employs Seeded Region Growing (SRG) segmentation algorithm to accomplish the process. In our application of obtaining the region of a chosen object for further manipulation through data mining, human input is used to choose the object of interest through which seed points are identi ed and employed. User selection of the object of interest could be achieved in di erent ways, one of which is using mouse based point and click procedure. Therefore, the proposed system provides the user with the choice to select the object of interest that will be segmented out from other background regions and objects. It is important to note that texture information gives better description of objects and plays an important role for the characterization of regions. In region growing segmentation, three key factors are satis ed such as choice of similarity criteria, selection of seed points, and stopping rule. The choice of similarity criteria is accomplished through texture descriptors and connectivity properties. The selection of seed points is determined interactively by the user when they choose the object of interest. The de nition of a stopping rule is achieved using a test for homogeneity and connectivity measures, therefore, a region would stop growing when there are no further pixels that satisfy the homogeneity and connectivity criteria. The segmentation region
Formations of Bacteria-like Textures by dynamic reactions in Meteorite and Syntheses
Miura, Y.
2009-05-01
1. Introduction Spherule texture can be formed in dynamic reaction during meteoritic impact in air. However, there are no reports on nano-bacteria-like (i.e. spherule-chained) textures with iron (and Nickel) oxides (with chlorine) in composition and micro-texture with 100nm order [1] in meteorite and synthetic experiment. The purpose of the present study is to elucidate spherule-chained texture with micro-texture of 100nm in order found in the Kuga iron meteorite, Iwakuni, Yamaguchi, Japan, and its first artificial synthesis in laboratory. 2. Two textures in the Kuga meteorite: The Kuga iron meteorite found in Kuga, Iwakuni, Yamaguchi, Japan reveals spherule-chained texture with Fe, Ni-rich composition with 10μm in size, where each spherule contained "long micro-texture in 100nm in size"[1,2]. The complex texture of flow and chained shapes can be found only in the fusion crust of the meteorite formed by quenched and random processes with vapor-melting process in air of the Earth. The FE-ASEM with EDX analyses by an in-situ observation indicate that the matrix of the spherule-chained texture with Fe, Ni, O-rich (with minor Cl) composition is carbon-rich composition formed by impact reactions in air. 3. Comparison with Martian meteorite Remnant of life in ocean can be found by mineralized fossil, which can be found in the Martian meteorite ALH84001 as bacteria-like chained texture of magnetite in composition (in 100nm order) around carbonate spherules [3]. Similarity of bacteria-like texture of the ALH84001 compared with the Kuga meteorites in this study are composition of Fe-rich, C-bearing, and chained texture of small size replaced by Fe and O-rich composition in air. Major difference of these textures is no carbonates minerals in the Kuga meteorite at dynamic reaction in air [1, 2, 3]. 4. First synthesis of bacteria- like akaganeite: A bacteria-like texture with Fe oxides (with minor chlorine as akaganeite-like compositions) is synthesized by chlorine and water
Influence of initial textures on dynamic recrystallization and textures in AZ31 magnesium alloys
YANG Ping(杨平); CUI Feng-e(崔凤娥); MA Shi-cai(马世才); G Gottstein
2003-01-01
Microscopy and X-ray diffractometry were applied to inspect the influence of initial texture on dynamic recrystallization and texture formation in AZ31 magnesium alloys during channel die compression. The results show that stress-strain curves, microstructures and textures depend on initial textures. Two types of nucleation sites are detected which are in different proportions depending on initial textures. Dynamic recrystallization proceeds faster in samples with more inhomogeneity. When the basal planes of grains are parallel to rolling plane of sample with scattering around transverse direction, no new texture component occurs and texture is strengthened together with dynamic recrystallization. By other initial textures there are texture changes during hot deformation. New grains rotate gradually to basal orientation at heavy strain.
Jianli eLiu
2015-11-01
Full Text Available Modeling human aesthetic perception of visual textures is important and valuable in numerous industrial domains, such as product design, architectural design and decoration. Based on results from a semantic differential rating experiment, we modeled the relationship between low-level basic texture features and aesthetic properties involved in human aesthetic texture perception. First, we compute basic texture features from textural images using four classical methods. These features are neutral, objective and independent of the socio-cultural context of the visual textures. Then, we conduct a semantic differential rating experiment to collect from evaluators their aesthetic perceptions of selected textural stimuli. In semantic differential rating experiment, eights pairs of aesthetic properties are chosen, which are strongly related to the socio-cultural context of the selected textures and to human emotions. They are easily understood and connected to everyday life. We propose a hierarchical feed-forward layer model of aesthetic texture perception and assign 8 pairs of aesthetic properties to different layers. Finally, we describe the generation of multiple linear and nonlinear regression models for aesthetic prediction by taking dimensionality-reduced texture features and aesthetic properties of visual textures as dependent and independent variables, respectively. Our experimental results indicate that the relationships between each layer and its neighbors in the hierarchical feed-forward layer model of aesthetic texture perception can be fitted well by linear functions, and the models thus generated can successfully bridge the gap between computational texture features and aesthetic texture properties.
Configuration effects on texture transparency.
Kawabe, Takahiro; Miura, Kayo
2004-01-01
This study examined the factors producing the perception of transparency between overlaid regions composed of Gabor micro-patterns as functions of their spatial frequency, separation of overlaid regions, and types of orientation modulation. The results showed that the likelihood of perceiving transparency was high both when (1) the difference in Gabor spatial frequency between regions was large, and (2) the region boundary, which was formed by short-range orientation differences in the Gabor micro-patterns, clearly emerged. We conclude that texture transparency appears to result from an interaction between a boundary-detection mechanism defining the shape of each region and a surface-detection mechanism assigning the boundary.
黄建华; 路钢
2000-01-01
In this paper, we discuss the asymptotic behaviour of spatial disretization of Fitz-Hugh-Nagumo equations and bistable reaction diffusion equations with Neumamn boundary conditions, and the invariant regions, absorbing sets and global attractors are obtained and the estimation of Hausdorff dimension is given.%本文利用扰动方法，研究了Fitz-Hugh-Nagumo方程和双稳反应扩散方程在Neuman边值条件下空间离散后的渐近行为，证明了两个格微分方程组的不变区域、吸引集和整体吸引子的存在性，并给出了离散Fitz-Hugh-Nagumo方程的整体吸引子的Hausdorff维数估计．
Optical devices featuring textured semiconductor layers
Moustakas, Theodore D.; Cabalu, Jasper S.
2011-10-11
A semiconductor sensor, solar cell or emitter, or a precursor therefor, has a substrate and one or more textured semiconductor layers deposited onto the substrate. The textured layers enhance light extraction or absorption. Texturing in the region of multiple quantum wells greatly enhances internal quantum efficiency if the semiconductor is polar and the quantum wells are grown along the polar direction. Electroluminescence of LEDs of the invention is dichromatic, and results in variable color LEDs, including white LEDs, without the use of phosphor.
Texture and anisotropy in ferroelectric lead metaniobate
Iverson, Benjamin John
Ferroelectric lead metaniobate, PbNb2O6, is a piezoelectric ceramic typically used because of its elevated Curie temperature and anisotropic properties. However, the piezoelectric constant, d33, is relatively low in randomly oriented ceramics when compared to other ferroelectrics. Crystallographic texturing is often employed to increase the piezoelectric constant because the spontaneous polarization axes of grains are better aligned. In this research, crystallographic textures induced through tape casting are distinguished from textures induced through electrical poling. Texture is described using multiple quantitative approaches utilizing X-ray and neutron time-of-flight diffraction. Tape casting lead metaniobate with an inclusion of acicular template particles induces an orthotropic texture distribution. Templated grain growth from seed particles oriented during casting results in anisotropic grain structures. The degree of preferred orientation is directly linked to the shear behavior of the tape cast slurry. Increases in template concentration, slurry viscosity, and casting velocity lead to larger textures by inducing more particle orientation in the tape casting plane. The maximum 010 texture distributions were two and a half multiples of a random distribution. Ferroelectric texture was induced by electrical poling. Electric poling increases the volume of material oriented with the spontaneous polarization direction in the material. Samples with an initial paraelectric texture exhibit a greater change in the domain volume fraction during electrical poling than randomly oriented ceramics. In tape cast samples, the resulting piezoelectric response is proportional to the 010 texture present prior to poling. This results in property anisotropy dependent on initial texture. Piezoelectric properties measured on the most textured ceramics were similar to those obtained with a commercial standard.
Silicon superficial texturing bypulsed laser
Ponce, L.
1998-04-01
Full Text Available Texturing of silicon surfaces with pulsed laser is made. The method is based on the formation of laser- induced periodic surface structure (LIPSS. The process is temporary characterized through the dynamic reflectance, thus determining the formation threshold of the structure. Relation between the different textures and the spectral reflectance of the samples before and after the treatment is also characterized. The mean value of spectral reflectance decreases up to a 6 %.
Se realiza el texturado de superficies de silicio con un láser pulsado mediante la formación de una estructura periódica inducida por láser (LIPSS. Se caracteriza el proceso mediante reflectancia dinámica, determinándose el umbral de formación de la estructura. Se caracteriza el nivel de texturado midiendo la reflectancia espectral de las muestras antes y después del tratamiento. El valor medio de la reflectancia espectral disminuye hasta el 6 %.
Texture Image Classification Based on Gabor Wavelet
DENG Wei-bing; LI Hai-fei; SHI Ya-li; YANG Xiao-hui
2014-01-01
For a texture image, by recognizining the class of every pixel of the image, it can be partitioned into disjoint regions of uniform texture. This paper proposed a texture image classification algorithm based on Gabor wavelet. In this algorithm, characteristic of every image is obtained through every pixel and its neighborhood of this image. And this algorithm can achieve the information transform between different sizes of neighborhood. Experiments on standard Brodatz texture image dataset show that our proposed algorithm can achieve good classification rates.
G. Madasamy Raja
2013-01-01
Full Text Available Texture analysis is one of the important as well as useful tasks in image processing applications. Many texture models have been developed over the past few years and Local Binary Patterns (LBP is one of the simple and efficient approach among them. A number of extensions to the LBP method have been also presented but the problem remains challenging in feature vector generation and comparison. As textures are oriented and scaled differently, a texture model should effectively handle grey-scale variation, rotation variation, illumination variation and noise. The length of the feature vector in a texture model also plays an important role in deciding the time complexity of the texture analysis. This study proposes a new texture model, called Optimized Local Ternary Patterns (OLTP in the spatial methods of texture analysis. The proposed texture model is based on Local Ternary Patterns (LTP, which in turn is based on LBP. A new concept called âLevel of Optimalityâ to select the optimal set of patterns is discussed in this study. This proposed texture model uses only optimal patterns to extract the textural information from the digital images and thereby reducing the length of the feature vector. This proposed model is robust to image rotation, grey-scale transformation, histogram equalization and noise. The results are compared with other widely used texture models by applying classification tests to variety of texture images from the standard Brodatz texture database. Experimental results prove that the proposed texture model is robust to grey-scale variation, image rotation, histogram equalization and noise. Experimental results also show that the proposed texture model improves the classification accuracy and the speed of the classification process. In all tested tasks, the proposed method outperforms the earlier methods.
The brass-type texture and its deviation from the copper-type texture
Leffers, Torben; Ray, R.K.
2009-01-01
-type texture. However, since there is by now reasonable agreement about the description of and the explanation for the development of the copper-type texture (though not about all the details), we have chosen to focus on the brass-type texture for which there is no such general agreement. First we introduce...
Mechanical seal with textured sidewall
Khonsari, Michael M.; Xiao, Nian
2017-02-14
The present invention discloses a mating ring, a primary ring, and associated mechanical seal having superior heat transfer and wear characteristics. According to an exemplary embodiment of the present invention, one or more dimples are formed onto the cylindrical outer surface of a mating ring sidewall and/or a primary ring sidewall. A stationary mating ring for a mechanical seal assembly is disclosed. Such a mating ring comprises an annular body having a central axis and a sealing face, wherein a plurality of dimples are formed into the outer circumferential surface of the annular body such that the exposed circumferential surface area of the annular body is increased. The texture added to the sidewall of the mating ring yields superior heat transfer and wear characteristics.
Intergranular strains in textured steel
Daymond, M.R. [Los Alamos Neutron Science Center (LANSCE), Los Alamos, NM (United States); Tome, C.N. [Los Alamos National Lab., NM (United States). Materials Science and Technology Div.; Bourke, M.A.M. [Los Alamos Neutron Science Center (LANSCE), Los Alamos, NM (United States); Los Alamos National Lab., NM (United States). Materials Science and Technology Div.
2000-07-01
Tensile specimens were machined from heat treated austenitic stainless steel plate prior to and after 70% reduction by uni-directional rolling. In addition to a specimen from the as-received plate, two specimens were cut from the rolled plate, with axes parallel and perpendicular to the rolling direction respectively. In situ measurements of the strain response of multiple hkl lattice planes to an applied uniaxial tensile load were made using neutron diffraction. The experimental results are compared with predictions from a self-consistent Hill-Hutchinson model. The measured texture in the plate was approximately 3 times random, however its effect on the hkl response was small compared to the residual strains left by rolling. The apparent elastic modulus and Poisson's ratios of the planes is affected by the residual strains, which is attributed to the effect of micro-plasticity. Interpretation of residual stress measurements is considered in light of these results. (orig.)
On the origin of recrystallization textures
K T Kashyap
2001-02-01
The development of recrystallization textures has been debated for the past 50 years. Essentially the rival theories of evolution of recrystallization textures i.e. oriented nucleation (ON) and oriented growth (OG) has been under dispute. In the ON model, it has been argued that a higher frequency of the special orientation (grains) than random occur, thus accounting for the texture. In the OG model, it has been argued that the specially oriented grains have a high mobility boundary and thus can migrate faster and grow to a larger size as compared to random orientations thus contributing to the final recrystallization texture. In FCC metals and alloys like aluminium, cube orientation [(001) $\\langle$100$\\rangle$] is the recrystallization texture component. In the classic OG model, cube orientation is supposed to be misoriented from -orientation [(123) $\\langle$63$\\bar{4}\\rangle$] which is a deformation texture component by a 40° about $\\langle$111$\\rangle$ relationship which is supposed to be a high mobility boundary leading to faster growth of cube grains. Stereographic calculations and analytical calculations are presented in this paper to the effect that the -orientation (123) $\\langle$63$\\bar{4}\\rangle$ is not misoriented from cube (100) $\\langle$001$\\rangle$ by 40° (111) whereas another deformation texture component (123) $\\langle$41$\\bar{2}\\rangle$ which is termed the -component is misoriented from cube component by 40°$\\ \\langle$111$\\rangle$ . -component is also seen in deformation textures of aluminium and hence the classic OG model remains valid with respect to the -component.
On Texture and Geometry in Image Analysis
Gustafsson, David Karl John
2009-01-01
fields and Maximum Entropy (FRAME) model [213, 214] is used for inpaining texture. We argue that many ’textures’ contain details that must be inpainted exactly. Simultaneous reconstruction of geometric structure and texture is a difficult problem, therefore, a two-phase reconstruction procedure...
A Noise Robust Statistical Texture Model
Hilger, Klaus Baggesen; Stegmann, Mikkel Bille; Larsen, Rasmus
2002-01-01
This paper presents a novel approach to the problem of obtaining a low dimensional representation of texture (pixel intensity) variation present in a training set after alignment using a Generalised Procrustes analysis.We extend the conventional analysis of training textures in the Active...
On texture formation of chromium electrodeposits
Nielsen, Christian Bergenstof; Leisner, Peter; Horsewell, Andy
1998-01-01
The microstructure, texture and hardness of electrodeposited hard, direct current (DC) chromium and pulsed reversed chromium has been investigated. These investigations suggest that the growth and texture of hard chromium is controlled by inhibition processes and reactions. Further, it has been...... established that codeposition of Cr2O3 nanoparticles is a general feature of DC chromium electrodeposition....
Texture and anisotropy of ferroelectric bismuth titanate
Jones, Jacob Leo
Ferroelectric bismuth titanate, Na0.5Bi4.5 Ti4O15, is a piezoelectric ceramic used as an electromechanical sensor in high temperature environments (T piezoelectric constant, d33, is relatively low in randomly oriented ceramics. Crystallographic texturing is often employed to increase the piezoelectric constant because the spontaneous polarization axes of the grains are better aligned. This research distinguishes between the crystallographic texture induced to the grains from tape casting and crystallographic texture induced to the ferroelectric domains from electrical poling. Novel quantitative approaches describe texture of both types independently using conventional and synchrotron X-ray sources as well as time-of-flight neutron diffraction with multiple detectors. Furthermore, methods are developed to describe the combined effect of a ferroelectric texture superimposed on a paraelectric texture. Texture of the paraelectric crystallographic axes was induced by novel processing approaches. An alternative to using plate-shaped template particles was developed utilizing calcined powder. Paraelectric texture develops from particle settling and strong surface energy anisotropy during sintering. The 00l textures induced from this process are on the order of two to four multiples of a random distribution. These textures create property anisotropies between the casting plane and normal directions of 6.4 and 5.7 in piezoelectric d33 constant and remanent polarization, respectively. Texture of the ferroelectric crystallographic axes was induced by electrical poling at different temperatures and in different orientations. Ceramics with an initial paraelectric texture can exhibit greater change in the domain volume fractions during electrical poling than randomly oriented ceramics. This is demonstrated by applying novel quantitative approaches to reflection X-ray spectra from many sample directions. Because orthorhombic Na0.5Bi 4.5Ti4O15 has two ferroelectric domains that
Texture boundary classification using Gabor elementary functions
Dunn, Dennis F.; Higgins, William E.; Maida, Anthony; Wakeley, Joseph
1991-11-01
Many texture-segmentation mechanisms take the form of an elaborate bank of filters. Commonly used within such mechanisms are the Gabor elementary functions (GEFs). While filter-bank-based mechanisms show promise and some analytical work has been done to demonstrate the efficacy of GEFs, the relationships between texture differences and the filter configurations required to discriminate these differences remain largely unknown. In this paper, we given analytical and experimental evidence that suggests that various types of discontinuities can occur at texture boundaries when appropriately 'tuned' GEF-based filters are applied to a textured image; thus, by applying a discontinuity-detection scheme (i.e., edge detector) to such a filtered image, one can segment the image into different textured regions.
ISOTROPIC TEXTURING OF POLYCRYSTALLINE SILICON WAFERS
L. Wang; H. Shen; Y.F. Hu
2005-01-01
An isotropic etching technique of texturing silicon solar cells has been applied to polycrystalline silicon wafers with different acid concentrations. Optimal etching conditions have been determined by etching rate calculation, scanning electron microscope (SEM) image and reflectance measurement. The surface morphology of the textured wafers varies in accordance with the different etchant concentration which in turn leads to the dissimilarity of etching speed. Textured polycrystalline silicon wafer surfaces display randomly located etched pits which can reduce the surface reflection and enhance the light absorption. The special relationship between reflectivity and etching rate was studied. Reflectance measurements show that isotropic texturing is one of the suitable techniques for texturing polycrystalline silicon wafers and benefits solar cells performances.
Layered Textures for Image-Based Rendering
en-Cheng Wang; ui-Yu Li; in Zheng; n-Hua Wu
2004-01-01
An extension to texture mapping is given in this paper for improving the efficiency of image-based rendering. For a depth image with an orthogonal displacement at each pixel, it is decomposed by the displacement into a series of layered textures (LTs) with each one having the same displacement for all its texels. Meanwhile,some texels of the layered textures are interpolated for obtaining a continuous 3D approximation of the model represented in the depth image. Thus, the plane-to-plane texture mapping can be used to map these layered textures to produce novel views and the advantages can be obtained as follows: accelerating the rendering speed,supporting the 3D surface details and view motion parallax, and avoiding the expensive task of hole-filling in the rendering stage. Experimental results show the new method can produce high-quality images and run faster than many famous image-based rendering techniques.
Photoconductive terahertz generation from textured semiconductor materials.
Collier, Christopher M; Stirling, Trevor J; Hristovski, Ilija R; Krupa, Jeffrey D A; Holzman, Jonathan F
2016-01-01
Photoconductive (PC) terahertz (THz) emitters are often limited by ohmic loss and Joule heating-as these effects can lead to thermal runaway and premature device breakdown. To address this, the proposed work introduces PC THz emitters based on textured InP materials. The enhanced surface recombination and decreased charge-carrier lifetimes of the textured InP materials reduce residual photocurrents, following the picosecond THz waveform generation, and this diminishes Joule heating in the emitters. A non-textured InP material is used as a baseline for studies of fine- and coarse-textured InP materials. Ultrafast pump-probe and THz setups are used to measure the charge-carrier lifetimes and THz response/photocurrent consumption of the respective materials and emitters. It is found that similar temporal and spectral characteristics can be achieved with the THz emitters, but the level of photocurrent consumption (yielding Joule heating) is greatly reduced in the textured materials.
Bayesian exploration for intelligent identification of textures
Jeremy A. Fishel
2012-06-01
Full Text Available In order to endow robots with humanlike abilities to characterize and identify objects, they must be provided with tactile sensors and intelligent algorithms to select, control and interpret data from useful exploratory movements. Humans make informed decisions on the sequence of exploratory movements that would yield the most information for the task, depending on what the object may be and prior knowledge of what to expect from possible exploratory movements. This study is focused on texture discrimination, a subset of a much larger group of exploratory movements and percepts that humans use to discriminate, characterize, and identify objects. Using a testbed equipped with a biologically inspired tactile sensor (the BioTac® we produced sliding movements similar to those that humans make when exploring textures. Measurement of tactile vibrations and reaction forces when exploring textures were used to extract measures of textural properties inspired from psychophysical literature (traction, roughness, and fineness. Different combinations of normal force and velocity were identified to be useful for each of these three properties. A total of 117 textures were explored with these three movements to create a database of prior experience to use for identifying these same textures in future encounters. When exploring a texture, the discrimination algorithm adaptively selects the optimal movement to make and property to measure based on previous experience to differentiate the texture from a set of plausible candidates, a process we call Bayesian exploration. Performance of 99.6% in correctly discriminating pairs of similar textures was found to exceed human capabilities. Absolute classification from the entire set of 117 textures generally required a small number of well-chosen exploratory movements (median=5 and yielded a 95.4% success rate. The method of Bayesian exploration developed and tested in this paper may generalize well to other
Bayesian exploration for intelligent identification of textures.
Fishel, Jeremy A; Loeb, Gerald E
2012-01-01
In order to endow robots with human-like abilities to characterize and identify objects, they must be provided with tactile sensors and intelligent algorithms to select, control, and interpret data from useful exploratory movements. Humans make informed decisions on the sequence of exploratory movements that would yield the most information for the task, depending on what the object may be and prior knowledge of what to expect from possible exploratory movements. This study is focused on texture discrimination, a subset of a much larger group of exploratory movements and percepts that humans use to discriminate, characterize, and identify objects. Using a testbed equipped with a biologically inspired tactile sensor (the BioTac), we produced sliding movements similar to those that humans make when exploring textures. Measurement of tactile vibrations and reaction forces when exploring textures were used to extract measures of textural properties inspired from psychophysical literature (traction, roughness, and fineness). Different combinations of normal force and velocity were identified to be useful for each of these three properties. A total of 117 textures were explored with these three movements to create a database of prior experience to use for identifying these same textures in future encounters. When exploring a texture, the discrimination algorithm adaptively selects the optimal movement to make and property to measure based on previous experience to differentiate the texture from a set of plausible candidates, a process we call Bayesian exploration. Performance of 99.6% in correctly discriminating pairs of similar textures was found to exceed human capabilities. Absolute classification from the entire set of 117 textures generally required a small number of well-chosen exploratory movements (median = 5) and yielded a 95.4% success rate. The method of Bayesian exploration developed and tested in this paper may generalize well to other cognitive problems.
A textural approach based on Gabor functions for texture edge detection in ultrasound images.
Chen, C M; Lu, H H; Han, K C
2001-04-01
Edge detection is an important, but difficult, step in quantitative ultrasound (US) image analysis. In this paper, we present a new textural approach for detecting a class of edges in US images; namely, the texture edges with a weak regional mean gray-level difference (RMGD) between adjacent regions. The proposed approach comprises a vision model-based texture edge detector using Gabor functions and a new texture-enhancement scheme. The experimental results on the synthetic edge images have shown that the performances of the four tested textural and nontextural edge detectors are about 20%-95% worse than that of the proposed approach. Moreover, the texture enhancement may improve the performance of the proposed texture edge detector by as much as 40%. The experiments on 20 clinical US images have shown that the proposed approach can find reasonable edges for real objects of interest with the performance of 0.4 +/- 0.08 in terms of the Pratt's figure.
Texture in Metallic and Ceramic Films and Coatings
Czerwinski, F; J. A. Szpunar
1999-01-01
The properties of films and coatings can be optimized for a variety of applications by modifying their texture. Understanding how the texture in thin films is formed and how it can be controlled during film growth process is one of the most important areas of texture research. Several examples were selected to illustrate how the texture in films and coatings is developed and to explain how various properties of films are affected by texture. In particular, texture development during electrode...
BHQ revisited (2): Texture development
Kilian, Rüdiger; Heilbronner, Renée
2016-04-01
Analysis of crystallographic preferred orientations (CPO) is mostly used to derive the kinematics of flow or conditions and processes of deformation. Observations from naturally and experimentally deformed rocks indicate that specific texture types might relate to deformation conditions or flow laws - with a number of variables being based on assumptions that are not fully tested. For example, the activity of certain slip systems is interpreted from pole figure geometries assuming that grains are oriented such that the shear stress is minimized, thus enforcing specific c-axis and a-xis directions, so-called "easy glide" orientations. Black Hills Quartzite (BHQ) deformed experimentally in the dislocation creep regime reveals a CPO development that depends on finite strain (Heilbronner & Tullis, 2006). In that study the CPO development was tracked through the analysis of optically derived C-axis pole figures and corresponding orientation maps indicating a transition from a girdle distribution to a single maximum around the kinematic y-axis with increasing strain. In this contribution, we re-measure the same samples using EBSD. The availability of the full crystal orientations in combination with novel techniques of orientation and misorientation mapping and combinations of fabric and texture data allow us to analyze the texture development in more detail. Special emphasis is on (a) the ratio of glide to dynamic recrystallization, (b) the relation of grain scale strain to bulk strain and (c) the development of intragranular misorientations with increasing recrystallization and strain. One interesting result of our analysis concerns the inference of "easy glide" grains based on their c-axis direction. As it turns out, the alignment of -directions at the periphery of the pole figure is more rapidly attained than the clustering of the c-axis about the y-axis (classical interpretation for prism glide) or at the periphery (classical interpretation for basal glide). It
Vertically aligned biaxially textured molybdenum thin films
Krishnan, Rahul [Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180 (United States); Riley, Michael [Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180 (United States); Lee, Sabrina [US Army Armament Research, Development and Engineering Center, Benet Labs, Watervliet, New York 12189 (United States); Lu, Toh-Ming [Department of Physics, Applied Physics and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180 (United States)
2011-09-15
Vertically aligned, biaxially textured molybdenum nanorods were deposited using dc magnetron sputtering with glancing flux incidence (alpha = 85 degrees with respect to the substrate normal) and a two-step substrate-rotation mode. These nanorods were identified with a body-centered cubic crystal structure. The formation of a vertically aligned biaxial texture with a [110] out-of-plane orientation was combined with a [-110] in-plane orientation. The kinetics of the growth process was found to be highly sensitive to an optimum rest time of 35 seconds for the two-step substrate rotation mode. At all other rest times, the nanorods possessed two separate biaxial textures each tilted toward one flux direction. While the in-plane texture for the vertical nanorods maintains maximum flux capture area, inclined Mo nanorods deposited at alpha = 85 degrees without substrate rotation display a [-1-1-4] in-plane texture that does not comply with the maximum flux capture area argument. Finally, an in situ capping film was deposited with normal flux incidence over the biaxially textured vertical nanorods resulting in a thin film over the porous nanorods. This capping film possessed the same biaxial texture as the nanorods and could serve as an effective substrate for the epitaxial growth of other functional materials.
Texture and wettability of metallic lotus leaves
Frankiewicz, C.; Attinger, D.
2016-02-01
Superhydrophobic surfaces with the self-cleaning behavior of lotus leaves are sought for drag reduction and phase change heat transfer applications. These superrepellent surfaces have traditionally been fabricated by random or deterministic texturing of a hydrophobic material. Recently, superrepellent surfaces have also been made from hydrophilic materials, by deterministic texturing using photolithography, without low-surface energy coating. Here, we show that hydrophilic materials can also be made superrepellent to water by chemical texturing, a stochastic rather than deterministic process. These metallic surfaces are the first analog of lotus leaves, in terms of wettability, texture and repellency. A mechanistic model is also proposed to describe the influence of multiple tiers of roughness on wettability and repellency. This demonstrated ability to make hydrophilic materials superrepellent without deterministic structuring or additional coatings opens the way to large scale and robust manufacturing of superrepellent surfaces.Superhydrophobic surfaces with the self-cleaning behavior of lotus leaves are sought for drag reduction and phase change heat transfer applications. These superrepellent surfaces have traditionally been fabricated by random or deterministic texturing of a hydrophobic material. Recently, superrepellent surfaces have also been made from hydrophilic materials, by deterministic texturing using photolithography, without low-surface energy coating. Here, we show that hydrophilic materials can also be made superrepellent to water by chemical texturing, a stochastic rather than deterministic process. These metallic surfaces are the first analog of lotus leaves, in terms of wettability, texture and repellency. A mechanistic model is also proposed to describe the influence of multiple tiers of roughness on wettability and repellency. This demonstrated ability to make hydrophilic materials superrepellent without deterministic structuring or additional
Unsupervised Color-texture Image Segmentation
YU Sheng-yang; ZHANG Fan; WANG Yong-gang; YANG Jie
2008-01-01
The measure J in J value segmentation (JSEG) falls to represent the discontinuity of color, which degrades the robustness and discrimination of JSEG. An improved approach for JSEG algorithm was proposed for unsupervised color-texture image segmentation. The texture and photometric invariant edge information were combined, which results in a discriminative measure for color-texture homogeneity. Based on the image whose pixel values are values of the new measure, region growing-merging algorithm used in JSEG was then employed to segment the image. Finally, experiments on a variety of real color images demonstrate performance improvement due to the proposed method.
Texture development in Galfenol wire
Boesenberg, A. J.; Restorff, J. B.; Wun-Fogle, M.; Sailsbury, H.; Summers, E.
2013-05-01
Galfenol (Fe-Ga alloy) wire fabrication provides a low cost alternative to directional solidification methods. This work evaluates the compositional dependence of the wire drawing suitability of Fe-Ga and characterizes the microstructural and magnetic properties of these wires. Wire has been produced with Ga contents between 10 at. % and 17 at. % to allow determination of the ductile to brittle transition (DTBT) in wire manufacture. Published results on chill cast bend specimens indicated that a DTBT occurs at roughly 15 at. % Ga. This DTBT was observed under tensile loading with a corresponding change in fracture behavior from transverse fracture to intergranular fracture. For improved magnetostrictive performance, higher Ga contents are desired, closer to the 17 at. % Ga evaluated in this work. Electron backscattered diffraction B-H loop and resonance measurements as a function of magnetic field (to determine modulus and coupling factor) are presented for as-drawn, furnace, and direct current (DC) annealed wire. Galfenol wire produced via traditional drawing methods is found to have a strong (α) texture parallel to the drawing direction. As-drawn wire was observed to have a lower magnetic permeability and larger hysteresis than DC annealed wire. This is attributed to the presence of a large volume of crystalline defects; such as vacancies and dislocations.
2007-01-01
[figure removed for brevity, see original site] Figure 1 The south polar region of Mars is covered seasonally with translucent carbon dioxide ice. In the spring gas subliming (evaporating) from the underside of the seasonal layer of ice bursts through weak spots, carrying dust from below with it, to form numerous dust fans aligned in the direction of the prevailing wind. The dust gets trapped in the shallow grooves on the surface, helping to define the small-scale structure of the surface. The surface texture is reminiscent of lizard skin (figure 1). Observation Geometry Image PSP_003730_0945 was taken by the High Resolution Imaging Science Experiment (HiRISE) camera onboard the Mars Reconnaissance Orbiter spacecraft on 14-May-2007. The complete image is centered at -85.2 degrees latitude, 181.5 degrees East longitude. The range to the target site was 248.5 km (155.3 miles). At this distance the image scale is 24.9 cm/pixel (with 1 x 1 binning) so objects 75 cm across are resolved. The image shown here has been map-projected to 25 cm/pixel . The image was taken at a local Mars time of 06:04 PM and the scene is illuminated from the west with a solar incidence angle of 69 degrees, thus the sun was about 21 degrees above the horizon. At a solar longitude of 237.5 degrees, the season on Mars is Northern Autumn.
Factors Involved in Tactile Texture Perception through Probes
Yoshioka, Takashi; Zhou, Julia
2008-01-01
An understanding of texture perception by robotic systems can be developed by examining human texture perception through a probe. Like texture perception through direct touch with the finger, texture perception by indirect means of a probe is multi-dimensional, comprising rough, hard, and sticky texture continua. In this study, we describe the individual subject variability in probe-mediated texture perception, and compare similarities and differences of texture perception between direct touch and indirect touch. The results show variability among subjects, as individual subjects may choose to rely on different degrees of three texture dimensions and do so at different scanning velocities. Despite this variability between scanning conditions within each subject, the subjects make consistently reliable discriminations of textures and subjective magnitude estimates along texture continua when indirectly exploring texture surfaces with a probe. These data contribute information that is valuable to the design of robotic sensory systems, and to the understanding of sensory feedback, which is essential in teleoperations. PMID:19617927
张忠文
2015-01-01
A nonlocal and time-delayed reaction-diffusion predator-prey model was studied, where prey individuals undergo two stages, i.e. immature and mature, and the conversion of consumed from prey biomass to predator biomass has a retardation. The growth of the prey population obeys general Beverton-Holt function. By discussing the principal eigenvalue of nonlocal elliptic problems, we showed an explicit expression of the principal eigenvalue, the suﬃcient conditions for the uniform persistence and global extinction for the model could be established. By the fluctuation method, the global attractivity of the unique positive constant steady state was obtained.%考虑一类带阶段结构的扩散捕食者食饵模型，其中食饵个体经历两个生命阶段，未成熟和成熟阶段，捕食者生物量的转化有一个延迟，食饵生物量的增长遵循一般化的Beverton-Holt函数。就非局部椭圆特征问题的主特征值，建立一致持久性与全局灭绝性。利用波动方法，给出唯一正常数稳态解的全局吸引性。
Evolution of solidification texture during additive manufacturing
Wei, H L; Mazumder, J; DebRoy, T
2015-01-01
Striking differences in the solidification textures of a nickel based alloy owing to changes in laser scanning pattern during additive manufacturing are examined based on theory and experimental data...
Texture and Wettability of Metallic Lotus Leaves
Frankiewicz, Christophe
2015-01-01
Superhydrophobic surfaces with the self-cleaning behavior of lotus leaves are sought for drag reduction and phase change heat transfer applications. These superrepellent surfaces have traditionally been fabricated by random or deterministic texturing of a hydrophobic material. Recently, superrepellent surfaces have also been made from hydrophilic materials, by deterministic texturing using photolithography, without low-surface energy coating. Here, we show that hydrophilic materials can also be made superrepellent to water by chemical texturing, a stochastic rather than deterministic process. These metallic surfaces are the first analog of lotus leaves, in terms of wettability, texture and repellency. A mechanistic model is also proposed to describe the influence of multiple tiers of roughness on wettability and repellency. This demonstrated ability to make hydrophilic materials superrepellent without deterministic structuring or additional coatings opens the way to large scale and robust manufacturing of sup...
One Channel Image Texture Based Interpretation
Rodinova, N. V.
2011-03-01
In single band and single polarized synthetic aperture radar (SAR) images, in individual channels of polarimetric SAR and multispectral images, in panchromatic images, magnetic resonance imaging, etc., the information is limited to the intensity and texture, and it is very difficult to interpret such images without any a priori information.This paper proposes to use the textural features (contrast, entropy and inverse moment), obtained from grey level co-occurrence matrix (GLCM), to segment one channel images. The interpretation of received texture merged color images are performed based on calculated texture feature values for various surface objects (forest, town, water, and so on) in initial image.SIR-C/X-SAR SLC L-band images, SPOT 4 multispectral and panchromatic images are used for illustration.
Monitoring Thermal Coagulation with Ultrasonic Textures
YANG Wei; ZHANG Su; CHEN Ya-zhu; CHEN Lei; HU Bing; MA Wei-yin
2007-01-01
The feasibility of using B-mode ultrasound image textures and pattern recognition technique to characterize the thermal coagulation in vitro during radiofrequency ablation was investigated.The changes of ultrasonic textures in the different regions of samples varied with the heating time in the in-vitro experiments, which would result in that the coagulated and noncoagulated regions of tissue had different ultrasonic textures.Using support vector machine to extract the ultrasonic texture features and characterize the state of tissue, the size and boundaries of thermal lesions could be detected and measured more exactly than only using the gray scale information of B-mode ultrasound image.The proposed method would be applied to the image-guided radiofrequency ablation (IGRA) procedure for monitoring the thermal coagulation.
Texture classification based on EMD and FFT
XIONG Chang-zhen; XU Jun-yi; ZOU Jian-cheng; QI Dong-xu
2006-01-01
Empirical mode decomposition (EMD) is an adaptive and approximately orthogonal filtering process that reflects human's visual mechanism of differentiating textures. In this paper, we present a modified 2D EMD algorithm using the FastRBF and an appropriate number of iterations in the shifting process (SP), then apply it to texture classification. Rotation-invariant texture feature vectors are extracted using auto-registration and circular regions of magnitude spectra of 2D fast Fourier transform(FFT). In the experiments, we employ a Bayesion classifier to classify a set of 15 distinct natural textures selected from the Brodatz album. The experimental results, based on different testing datasets for images with different orientations, show the effectiveness of the proposed classification scheme.
Probing Majorana Neutrino Textures at DUNE
Bora, Kalpana; Dutta, Debajyoti
2016-01-01
We study the possibility of probing different texture zero neutrino mass matrices at long baseline neutrino experiment DUNE. Assuming a diagonal charged lepton basis and Majorana nature of light neutrinos, we first classify the possible light neutrino mass matrices with one and two texture zeros and then numerically evaluate the parameter space in terms of atmospheric mixing angle $\\theta_{23}$ and Dirac CP phase $\\delta_{\\text{CP}}$ which satisfies the texture zero conditions. We then feed these parameter values into the numerical analysis in order to study the sensitivity of DUNE experiment to them. We find that the DUNE will be able to exclude some of these texture zero mass matrices which restrict the $(\\theta_{23}-\\delta_{\\text{CP}})$ to a very specific range of values.
Evolution of solidification texture during additive manufacturing.
Wei, H L; Mazumder, J; DebRoy, T
2015-11-10
Striking differences in the solidification textures of a nickel based alloy owing to changes in laser scanning pattern during additive manufacturing are examined based on theory and experimental data. Understanding and controlling texture are important because it affects mechanical and chemical properties. Solidification texture depends on the local heat flow directions and competitive grain growth in one of the six preferred growth directions in face centered cubic alloys. Therefore, the heat flow directions are examined for various laser beam scanning patterns based on numerical modeling of heat transfer and fluid flow in three dimensions. Here we show that numerical modeling can not only provide a deeper understanding of the solidification growth patterns during the additive manufacturing, it also serves as a basis for customizing solidification textures which are important for properties and performance of components.
Friction tensor concept for textured surfaces
K R Y Simha; Anirudhan Pottirayil; Pradeep L Menezes; Satish V Kailas
2008-06-01
Directionality of grinding marks inﬂuences the coefﬁcient of friction during sliding. Depending on the sliding direction the coefﬁcient of friction varies between maximum and minimum for textured surfaces. For random surfaces without any texture the friction coefﬁcient becomes independent of the sliding direction. This paper proposes the concept of a friction tensor analogous to the heat conduction tensor in anisotropic media. This implies that there exists two principal friction coefﬁcients $\\mu_{1,2}$ analogous to the principal conductivities $k_{1,2}$. For symmetrically textured surfaces the principal directions are orthogonal with atleast one plane of symmetry. However, in the case of polished single crystalline solids in relative sliding motion, crystallographic texture controls the friction tensor.
Textural properties of mango cultivars during ripening.
Jha, Shyam Narayan; Jaiswal, Pranita; Narsaiah, Kairam; Kaur, Poonam Preet; Singh, Ashish Kumar; Kumar, Ramesh
2013-12-01
Firmness and toughness of fruit, peel and pulp of seven different mango cultivars were studied over a ripening period of ten days to investigate the effects of harvesting stages (early, mid and late) on fruit quality. Parameters were measured at equatorial region of fruits using TA-Hdi Texture Analyzer. The textural characteristics showed a rapid decline in their behaviour until mangoes got ripened and thereafter, the decline became almost constant indicating the completion of ripening. However, the rate of decline in textural properties was found to be cultivar specific. In general, the changes in textural attributes were found to be significantly influenced by ripening period and stage of harvesting, but firmness attributes (peel, fruit and pulp) of early harvested mangoes did not differ significantly from mid harvested mangoes, while peel, fruit and pulp firmness of late harvested mangoes were found to be significantly lower than early and mid harvested mangoes.
Perez, Lidia Lopez; Zarubina, Valeriya; Mayoral, Alvaro; Melian-Cabrera, Ignacio
2015-01-01
This paper investigates the effect of silica addition on the structural, textural and acidic properties of an evaporation induced self-assembled (EISA) mesoporous alumina. Two silica addition protocols were applied while maintaining the EISA synthesis route. The first route is based on the addition
An image processing analysis of skin textures
Sparavigna, A
2008-01-01
Colour and coarseness of skin are visually different. When image processing is involved in the skin analysis, it is important to quantitatively evaluate such differences using texture features. In this paper, we discuss a texture analysis and measurements based on a statistical approach to the pattern recognition. Grain size and anisotropy are evaluated with proper diagrams. The possibility to determine the presence of pattern defects is also discussed.
Cascade Textures and SUSY SO(10) GUT
Adulpravitchai, Adisorn; Takahashi, Ryo
2010-01-01
We give texture analyses of cascade hierarchical mass matrices in supersymmetric SO(10) grand unified theory. We embed cascade mass textures of the standard model fermion with right-handed neutrinos into the theory, which gives relations among the mass matrices of the fermions. The related phenomenologies, such as the lepton flavor violating processes and leptogenesis, are also investigated in addition to the PMNS mixing angles.
Proposal of Unified Fermion Texture
Krolikowski, W.
1998-03-01
unified form of mass matrix is proposed for neutrinos, charged leptons, up quarks and down quarks. Some constraints for the parameters involved are tentatively postulated. Then, the predictions are neatly consistent with available experimental data. Among the predictions are: (i) mτ ~1776.80 MeV (with the inputs of me and mμ ), (ii) mν_0 ≪ mν_1~(0.6 to )× 10-2 eV and mν_2~ (0.2 to 1)× 10-1 eV (with the atmospheric-neutrino inputs of |mν_22 - mν_12| × (0.0003 to 0.01) eV2 and the νμ → ντ oscillation amplitude × 0.8), and also ( iii) ms ~270 MeV, |Vub/Vcb| ~0.082 and argVub ~-640 (with the inputs of mc = 1.3 GeV, mb = 4.5 GeV, |Vus| = 0.221 and |Vcb| = 0.041, where mu ≪ mc ≪ mt and md ≪ ms ≪ mb ). All elements of the Cabibbo--Kobayashi--Maskawa matrix are evaluated. All elements of its lepton counterpart are calculated up to an unknown phase (Appendix B). Some items related to dynamical aspects of the proposed fermion ``texture'' are briefly commented on (Appendix A). In particular, the notion of a novel dark matter, free of any Standard Model interactions (and their supersymmetric variants), appears in the case of preon option.
TEXTURE ANALYSIS OF SPELT WHEAT BREAD
Magdaléna Lacko - Bartošová
2013-02-01
Full Text Available The bread quality is considerably dependent on the texture characteristic of bread crumb. Texture analysis is primarily concerned with the evaluation of mechanical characteristics where a material is subjected to a controlled force from which a deformation curve of its response is generated. It is an objective physical examination of baked products and gives direct information on the product quality, oppositely to dough rheology tests what are inform on the baking suitability of the flour, as raw material. This is why the texture analysis is one of the most helpful analytical methods of the product development. In the framework of our research during the years 2008 – 2009 were analyzed selected indicators of bread crumb for texture quality of three Triticum spelta L. cultivars – Oberkulmer Rotkorn, Rubiota and Franckenkorn grown in an ecological system at the locality of Dolna Malanta near Nitra. The bread texture quality was evaluated on texture analyzer TA.XT Plus and expressed as crumb firmness (N, stiffness (N.mm-1 and relative elasticity (%.Our research proved that all selected indicators were significantly influenced by the year of growing and variety. The most soft bread was measured in Rubiota, whereas bread crumb samples from Franckenkorn were the most firm and stiff. Relative elasticity confirmed that the lowest firmness and stiffness was found in Rubiota bread. The spelt grain can be a good source for making bread flour, but is closely dependent on choice of spelt variety.
Texture feature based liver lesion classification
Doron, Yeela; Mayer-Wolf, Nitzan; Diamant, Idit; Greenspan, Hayit
2014-03-01
Liver lesion classification is a difficult clinical task. Computerized analysis can support clinical workflow by enabling more objective and reproducible evaluation. In this paper, we evaluate the contribution of several types of texture features for a computer-aided diagnostic (CAD) system which automatically classifies liver lesions from CT images. Based on the assumption that liver lesions of various classes differ in their texture characteristics, a variety of texture features were examined as lesion descriptors. Although texture features are often used for this task, there is currently a lack of detailed research focusing on the comparison across different texture features, or their combinations, on a given dataset. In this work we investigated the performance of Gray Level Co-occurrence Matrix (GLCM), Local Binary Patterns (LBP), Gabor, gray level intensity values and Gabor-based LBP (GLBP), where the features are obtained from a given lesion`s region of interest (ROI). For the classification module, SVM and KNN classifiers were examined. Using a single type of texture feature, best result of 91% accuracy, was obtained with Gabor filtering and SVM classification. Combination of Gabor, LBP and Intensity features improved the results to a final accuracy of 97%.
Fast Image Texture Classification Using Decision Trees
Thompson, David R.
2011-01-01
Texture analysis would permit improved autonomous, onboard science data interpretation for adaptive navigation, sampling, and downlink decisions. These analyses would assist with terrain analysis and instrument placement in both macroscopic and microscopic image data products. Unfortunately, most state-of-the-art texture analysis demands computationally expensive convolutions of filters involving many floating-point operations. This makes them infeasible for radiation- hardened computers and spaceflight hardware. A new method approximates traditional texture classification of each image pixel with a fast decision-tree classifier. The classifier uses image features derived from simple filtering operations involving integer arithmetic. The texture analysis method is therefore amenable to implementation on FPGA (field-programmable gate array) hardware. Image features based on the "integral image" transform produce descriptive and efficient texture descriptors. Training the decision tree on a set of training data yields a classification scheme that produces reasonable approximations of optimal "texton" analysis at a fraction of the computational cost. A decision-tree learning algorithm employing the traditional k-means criterion of inter-cluster variance is used to learn tree structure from training data. The result is an efficient and accurate summary of surface morphology in images. This work is an evolutionary advance that unites several previous algorithms (k-means clustering, integral images, decision trees) and applies them to a new problem domain (morphology analysis for autonomous science during remote exploration). Advantages include order-of-magnitude improvements in runtime, feasibility for FPGA hardware, and significant improvements in texture classification accuracy.
TEXTURE PRESERVING IMAGE CODING USING ORTHOGONAL POLYNOMIALS
R. Krishnamoorthi
2010-08-01
Full Text Available In order to replace the artifacts in the textured background, a new texture preserving image coder using the set of orthogonal polynomials is proposed in this paper. The proposed scheme is based on the model that represents textures using points spread operator relating to a linear system. In the proposed texture based image coding scheme, the encoder first identifies textured regions, which are then analyzed to produce the model features. Then these features are later transmitted to decoder which decodes to form a synthetic texture and results into synthetic stage. The proposed modeling delivers to attain high compression ratio by maintaining constantly excellent visual quality. 92.31% with a PSNR value of 31.93dB when the quality factor is 5 for D96 image is achieved by the proposed scheme. By keeping up the quality factor as a constant constrained, we obtain 91.11% of compression ratio with a PSNR value of 33.26dB for different set of image that is, D38 image.
Reaction-diffusion basis of retroviral infectivity
Sadiq, S. Kashif
2016-11-01
Retrovirus particle (virion) infectivity requires diffusion and clustering of multiple transmembrane envelope proteins (Env3) on the virion exterior, yet is triggered by protease-dependent degradation of a partially occluding, membrane-bound Gag polyprotein lattice on the virion interior. The physical mechanism underlying such coupling is unclear and only indirectly accessible via experiment. Modelling stands to provide insight but the required spatio-temporal range far exceeds current accessibility by all-atom or even coarse-grained molecular dynamics simulations. Nor do such approaches account for chemical reactions, while conversely, reaction kinetics approaches handle neither diffusion nor clustering. Here, a recently developed multiscale approach is considered that applies an ultra-coarse-graining scheme to treat entire proteins at near-single particle resolution, but which also couples chemical reactions with diffusion and interactions. A model is developed of Env3 molecules embedded in a truncated Gag lattice composed of membrane-bound matrix proteins linked to capsid subunits, with freely diffusing protease molecules. Simulations suggest that in the presence of Gag but in the absence of lateral lattice-forming interactions, Env3 diffuses comparably to Gag-absent Env3. Initial immobility of Env3 is conferred through lateral caging by matrix trimers vertically coupled to the underlying hexameric capsid layer. Gag cleavage by protease vertically decouples the matrix and capsid layers, induces both matrix and Env3 diffusion, and permits Env3 clustering. Spreading across the entire membrane surface reduces crowding, in turn, enhancing the effect and promoting infectivity. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.
Target Patterns in Reaction-Diffusion Systems,
1981-01-01
new variable xd, the diffusion matrix in (1.1) is just DM and the velocities Vph and v,, in (4.20) and (4.21) are multiplied by C-I/2, Finally except...the (ksr)-’ / factors in (4.4), (4.19), (5.1), and (5.2) are absent in one dimension. However, the analysis for three dimensions hinges on whether (4.2
Reaction-diffusion models of decontamination
Hjorth, Poul G.
A contaminant, which also contains a polymer is in the form of droplets on a solid surface. It is to be removed by the action of a decontaminant, which is applied in aqueous solution. The contaminant is only sparingly soluble in water, so the reaction mechanism is that it slowly dissolves...... in the aqueous solution and then is oxidized by the decontaminant. The polymer is insoluble in water, and so builds up near the interface, where its presence can impede the transport of contaminant. In these circumstances, Dstl wish to have mathematical models that give an understanding of the process, and can...
Distribution in flowing reaction-diffusion systems
Kamimura, Atsushi
2009-12-28
A power-law distribution is found in the density profile of reacting systems A+B→C+D and 2A→2C under a flow in two and three dimensions. Different densities of reactants A and B are fixed at both ends. For the reaction A+B, the concentration of reactants asymptotically decay in space as x-1/2 and x-3/4 in two dimensions and three dimensions, respectively. For 2A, it decays as log (x) /x in two dimensions. The decay of A+B is explained considering the effect of segregation of reactants in the isotropic case. The decay for 2A is explained by the marginal behavior of two-dimensional diffusion. A logarithmic divergence of the diffusion constant with system size is found in two dimensions. © 2009 The American Physical Society.