the global well posedness and spatial decay of solutions for the derivative complex ginzburg landau equation in h1 abstract the global well posedness for the cauchy problem of the derivative complex ginzburg landau equation is shown in the h1 critical and h1 subcritical cases a spatial decaying estimate of solutions in h 1 is also obtained and the decaying rate is independent of time t 0

stochastic blockmodels and community structure in networks stochastic blockmodels have been proposed as a tool for detecting community structure in networks as well as for generating synthetic networks for use as benchmarks most blockmodels however ignore variation in vertex degree making them unsuitable for applications to real world networks which typically display broad degree distributions that can significantly affect the results here we demonstrate how the generalization of blockmodels to incorporate this missing element leads to an improved objective function for community detection in complex networks we also propose a heuristic algorithm for community detection using this objective function or its non degree corrected counterpart and show that the degree corrected version dramatically outperforms the uncorrected one in both real world and synthetic networks

lattice boltzmann schemes for the nonlinear schrodinger equation the lattice boltzmann lb method is applied to solve the time dependent nonlinear schr odinger nls equation through approximating the reaction term at different orders of accuracy three diffusion reaction lb schemes are constructed for the cubic nls equation a lb initial condition is proposed to include the first order nonequilibrium distribution function these lb schemes are used to solve the one soliton propagation and the homoclinic orbit problems detailed simulation results confirm that the high order reaction term and the lb initial condition are effective in reducing the truncation errors compared with the crank nicolson finite difference scheme the lb scheme is found to give at least comparable and generally more accurate approximation for the cubic nls equation

community detection in complex networks using extremal optimization we propose a method to find the community structure in complex networks based on an extremal optimization of the value of modularity the method outperforms the optimal modularity found by the existing algorithms in the literature giving a better understanding of the community structure we present the results of the algorithm for computer simulated and real networks and compare them with other approaches the efficiency and accuracy of the method make it feasible to be used for the accurate identification of community structure in large complex networks

benchmark graphs for testing community detection algorithms community structure is one of the most important features of real networks and reveals the internal organization of the nodes many algorithms have been proposed but the crucial issue of testing i e the question of how good an algorithm is with respect to others is still open standard tests include the analysis of simple artificial graphs with a built in community structure that the algorithm has to recover however the special graphs adopted in actual tests have a structure that does not reflect the real properties of nodes and communities found in real networks here we introduce a class of benchmark graphs that account for the heterogeneity in the distributions of node degrees and of community sizes we use this benchmark to test two popular methods of community detection modularity optimization and potts model clustering the results show that the benchmark poses a much more severe test to algorithms than standard benchmarks revealing limits that may not be apparent at a first analysis

lattice boltzmann equation hydrodynamics by inserting position and time dependent source or forcing terms into the microscopic evolution equation of a lattice boltzmann fluid and treating the generalized scheme within the usual chapman enskog methodology we show that the emergent dynamics of the lattice fluid may be usefully transformed our method of adjustment is demonstrated by implementing the cylindrical polar coordinate form of the continuity and momentum equations on a rectangular lattice and generating results for pipe flow with straightforward systematic adjustment of the simulation our approach produces results in excellent agreement with theory

the cauchy problem for critical and subcritical semilinear parabolic equations in lr ii initial data in critical sobolev spaces abstract by presenting some time space l p l r estimates we will establish the local and global existence and uniqueness of solutions for semilinear parabolic equations with the cauchy data in critical sobolev spaces of negative indices our results contain the complex derivative ginzburg landau equation and the cahn hilliard equation as special cases

lattice boltzmann model for free surface flow and its application to filling process in casting a generalized lattice boltzmann model to simulate free surface is constructed in both two and three dimensions the proposed model satisfies the interfacial boundary conditions accurately a distinctive feature of the model is that the collision processes is carried out only on the points occupied partially or fully by the fluid to maintain a sharp interfacial front the method includes an anti diffusion algorithm the unknown distribution functions at the interfacial region are constructed according to the first order chapman enskog analysis the interfacial boundary conditions are satisfied exactly by the coefficients in the chapman enskog expansion the distribution functions are naturally expressed in the local interfacial coordinates the macroscopic quantities al the interface are extracted from the least square solutions of a locally linearized system obtained from the known distribution functions the proposed method does not require any geometric front construction and is robust for any interfacial topology simulation results of realistic filling process are presented rectangular cavity in two dimensions and hammer box campbell box sheffield box and motorblock in three dimensions to enhance the stability at high reynolds numbers various upwind type schemes are developed free slip and no slip boundary conditions are also discussed

cellular automaton fluids a model for flow in porous media numerical models of fluid flow through porous media can be developed from either microscopic or macroscopic properties the large scale viewpoint is perhaps the most prevalent darcy s law relates the chief macroscopic parameters of interest flow rate permeability viscosity and pressure gradient and may be invoked to solve for any of these parameters when the others are known in practical situations however this solution may not be possible attention is then typically focused on the estimation of permeability and numerous numerical methods based on knowledge of the microscopic pore space geometry have been proposed because the intrinsic inhomogeneity of porous media makes the application of proper boundary conditions difficult microscopic flow calculations have typically been achieved with idealized arrays of geometrically simple pores throats and cracks i propose here an attractive alternative which can freely and accurately model fluid flow in grossly irregular geometries this new method s

random walks for image segmentation a novel method is proposed for performing multilabel interactive image segmentation given a small number of pixels with user defined or predefined labels one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels by assigning each pixel to the label for which the greatest probability is calculated a high quality image segmentation may be obtained theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits this algorithm is formulated in discrete space i e on a graph using combinatorial analogues of standard operators and principles from continuous potential theory allowing it to be applied in arbitrary dimension on arbitrary graphs

a new scheme for source term in lbgk model for convection diffusion equation a new scheme for source term in the lattice bgk lbgk model for convection diffusion equation is proposed unlike the models proposed previously the present scheme only requires the source term in order of the knudsen number by adding a differential operator of the source term to the evolution equation the scheme can be applied to reaction diffusion systems directly numerical results are found to be in excellent agreement with the analytical solutions it is also found that the numerical accuracy of the present scheme is generally much better than that of the existing models

semisupervised learning based on generalized point charge models the recent years have witnessed a surge of interest in semisupervised learning numerous methods have been proposed for learning from partially labeled data in this brief a novel semisupervised learning approach based on an electrostatic field model is proposed we treat the labeled data points as point charges therefore the remaining unlabeled data points are placed in the electrostatic fields generated by these charges the labels of these unlabeled data points can be regarded as the electric potentials of the electrostatic field at their corresponding places moreover we also develop an efficient way to extend our method for out of sample data and analyze theoretically the relationship between our method and the traditional graph based methods finally the experimental results on both toy and real world data sets are provided to show the effectiveness of our method

a hybrid multi time step framework for pore scale and continuum scale modeling of solute transport in porous media abstract in this paper we propose a computational framework which is based on a domain decomposition technique to employ both finite element method which is a popular continuum modeling approach and lattice boltzmann method which is a popular pore scale modeling approach in the same computational domain to bridge the gap across the disparate length and time scales we first propose a new method to enforce continuum scale boundary conditions i e dirichlet and neumann boundary conditions onto the numerical solution from the lattice boltzmann method this method is based on maximization of entropy and preserve the non negativity of discrete distributions under the lattice boltzmann method the proposed computational framework allows different grid sizes orders of interpolation and time steps in different subdomains this allows for different desired resolutions in the numerical solution in different subdomains through numerical experiments the effect of grid and time step refinement disparity of time steps in different subdomains domain partitioning and the number of iteration steps on the accuracy and rate of convergence of the proposed methodology are studied finally to showcase the performance of this framework in porous media applications we use it to simulate the dissolution of calcium carbonate in a porous structure

accurate boundary treatments for lattice boltzmann simulations of electric fields and electro kinetic applications in this paper a novel boundary method is proposed for lattice boltzmann simulations of electric potential fields with complex boundary shapes and conditions a shifted boundary from the physical surface location is employed in simulations to achieve a better finite difference approximation of the potential gradient at the physical surface simulations are presented to demonstrate the accuracy and capability of this method in dealing with complex surface situations an example simulation of the electrical double layer and electro osmotic flow around a three dimensional spherical particle is also presented these simulated results are compared with analytical predictions and are found to be in excellent agreement this method could be useful for electro kinetic and colloidal simulations with complex boundaries and can also be readily extended to other phenomena and processes such as heat transfer and convection diffusion systems

a two dimensional lattice boltzmann model for uniform channel flows in this paper a novel two dimensional lattice boltzmann model lbm is developed for uniform channel flows the axial velocity is solved from a momentum diffusion equation over the cross sectional plane an extrapolation boundary condition is also introduced to enhance the no slip boundary in the momentum equation this boundary treatment can also be applied to lbm simulations of other diffusion processes the algorithm and boundary treatment are validated by simulations of steady poiseuille and pulsatile womersley flows in circular pipes the numerical convergence and accuracy are comparable to those of existing models moreover comparison with general three dimensional lattice boltzmann simulations demonstrates the advantages of our two dimensional model including lower computational resource requirements memory and time easier boundary treatment for arbitrary cross sectional shapes and no velocity constraint these features are attractive for practical applications with uniform channel flows

semi supervised community detection based on non negative matrix factorization with node popularity based on the ideas of graph regularization we present a semi supervised and nmf based model to utilize the prior information of networks by introducing the parameters of node popularities we propose a refined pssnmf model which is particularly suitable for networks with large degree heterogeneity and unbalanced community structure the prior information with node popularity being introduced into the model is more effective than being directly encoded into the adjacent matrix a plethora of exhaustive studies have proved that the community detection merely based on topological information often leads to relatively low accuracy several approaches aim to achieve performance improvement by utilizing the background information but they ignore the effect of node degrees on the availability of prior information in this paper by combining the idea of graph regularization with the pairwise constraints we present a semi supervised non negative matrix factorization ssnmf model for community detection and then to alleviate the influence of the heterogeneity of node degrees and community sizes we propose an improved ssnmf model by introducing the node popularity namely pssnmf which helps to utilize the prior information more effectively at last the extensive experiments on both artificial and real world networks show that the proposed method improves as expected the accuracy of community detection especially on networks with large degree heterogeneity and unbalanced community structure

solutions for semilinear parabolic equations in lp and regularity of weak solutions of the navier stokes system abstract we construct a unique local regular solution in l q 0 t l p for a class of semilinear parabolic equations which includes the semilinear heat equation u t u u u 0 and the navier stokes system here p and q are so chosen that the norm of l q 0 t l p is dimensionless or scaling invariant the main relation between p and q for the semilinear heat equation is 1 q 1 p 1 q n 2 provided that initial data are in l r with r n 2 1 where n is the space dimension applying our regular solutions to the navier stokes system we show that the k 2 dimensional hausdorff measure of possible time singularities of a turbulent solution is zero if the turbulent solution is in l q 0 t l p where k 2 q nq p p n 1 q we show moreover that a turbulent solution is regular if it is in c 0 t l n

on global solutions and blow up for kuramoto sivashinsky type models and well posed burnett equations abstract the initial boundary value problem ibvp and the cauchy problem for the kuramoto sivashinsky equation v t v x x x x v x x 1 2 v 2 x and other related 2 m th order semilinear parabolic partial differential equations in one dimension and in r n are considered global existence and blow up as well as l bounds are reviewed by using i classic tools of interpolation theory and galerkin methods ii eigenfunction and nonlinear capacity methods iii henry s version of weighted gronwall s inequalities iv two types of scaling blow up arguments for the ibvps existence of global solutions is proved for both dirichlet and navier boundary conditions for some related 2 m th order pdes in r n r uniform boundedness of global solutions of the cauchy problem are established as another related application the well posed burnett type equations v t v v p m v div v 0 in r n r m 1 are considered for m 1 these are the classic navier stokes equations as a simple illustration it is shown that a uniform l p r n bound on locally sufficiently smooth v x t for p n 2 m 1 implies a uniform l r n bound hence the solutions do not blow up for m 1 and n 3 this gives p 3 which reflects the famous leray prodi serrin ladyzhenskaya regularity results l p q criteria and re derives kato s class of unique mild solutions in r n truly bounded classic l 2 solutions are shown to exist in dimensions n 2 2 m 1

heat transfer in lattice bgk modeled fluid the thermal lattice bgk model is a recently suggested numerical tool aiming at solving problems of thermohydrodynamics the quality of the lattice bgk simulation is checked in this paper by calculating temperature profiles in the couette flow under different eckert and mach numbers a revised lower order model is proposed to improve the accuracy and the higher order model is proved to be advantageous in this respect especially in the flow regime with a higher mach number

modified lattice boltzmann model for axisymmetric flows a modified lattice boltzmann model based on the two dimensional nine velocity lattice bhatnagar gross krook fluid is presented for axisymmetric flows a spatially and temporally varying source term is incorporated into the evolution equation for the momentum distribution function on a two dimensional cartesian lattice the precise form of the source term is derived through a chapman enskog analysis so that the additional axisymmetric contributions in the navier stokes equations are furnished when written in the cylindrical polar coordinate system

potts model based on a markov process computation solves the community structure problem effectively the potts model is a powerful tool to uncover community structure in complex networks here we propose a framework to reveal the optimal number of communities and stability of network structure by quantitatively analyzing the dynamics of the potts model specifically we model the community structure detection potts procedure by a markov process which has a clear mathematical explanation then we show that the local uniform behavior of spin values across multiple timescales in the representation of the markov variables could naturally reveal the network s hierarchical community structure in addition critical topological information regarding multivariate spin configuration could also be inferred from the spectral signatures of the markov process finally an algorithm is developed to determine fuzzy communities based on the optimal number of communities and the stability across multiple timescales the effectiveness and efficiency of our algorithm are theoretically analyzed as well as experimentally validated

study of the 1d lattice boltzmann shallow water equation and its coupling to build a canal network the d1q3 lattice boltzmann lb shallow water equation is analyzed in detail and compared with other numerical schemes analytical results are derived and used to discuss the accuracy and stability of the model we show how such d1q3 lb models for canal reaches may be easily coupled with various hydraulic interconnection structures to build models of complex irrigation networks

finding community structure in very large networks the discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community but most methods proposed so far are unsuitable for very large networks because of their computational cost here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms its running time on a network with n vertices and m edges is o md phantom rule 0 2em 0ex mathrm log phantom rule 0 2em 0ex n where d is the depth of the dendrogram describing the community structure many real world networks are sparse and hierarchical with m ensuremath sim n and d ensuremath sim mathrm log phantom rule 0 2em 0ex n in which case our algorithm runs in essentially linear time o n phantom rule 0 2em 0ex mathrm log 2 phantom rule 0 2em 0ex n as an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on line retailer items in the network being linked if they are frequently purchased by the same buyer the network has more than 400 000 vertices and 2 ifmmode times else texttimes fi 10 6 edges we show that our algorithm can extract meaningful communities from this network revealing large scale patterns present in the purchasing habits of customers

semi supervised clustering algorithm for community structure detection in complex networks abstract discovering a community structure is fundamental for uncovering the links between structure and function in complex networks in this paper we discuss an equivalence of the objective functions of the symmetric nonnegative matrix factorization snmf and the maximum optimization of modularity density based on this equivalence we develop a new algorithm named the so called snmf ss by combining snmf and a semi supervised clustering approach previous nmf based algorithms often suffer from the restriction of measuring network topology from only one perspective but our algorithm uses a semi supervised mechanism to get rid of the restriction the algorithm is illustrated and compared with spectral clustering and nmf by using artificial examples and other classic real world networks experimental results show the significance of the proposed approach particularly in the cases when community structure is obscure

isometric decomposition operators function spaces ep qλ and applications to nonlinear evolution equations abstract by using the isometric decomposition to the frequency spaces we will introduce a new class of function spaces e p q which is a subspace of gevrey 1 class g 1 r n c r n for 0 and we will study the cauchy problem for the nonlinear schrodinger equation the complex ginzburg landau equation and the navier stokes equation some well posed results are obtained for the cauchy data in e 2 1 0 and the regularity behavior in e 2 1 ct g 1 r n for the complex ginzburg landau equation and the navier stokes equation is also obtained as time t 0

the lattice boltzmann equation a new tool for computational fluid dynamics abstract we present a series of applications which demonstrate that the lattice boltzmann equation is an adequate computational tool to address problems spanning a wide spectrum of fluid regimes ranging from laminar to fully turbulent flows in two and three dimensions

l and decay estimates for higher order semilinear diffusion absorption equations abstract we derive estimates of solutions of the semilinear 2mth order parabolic equation of diffusion absorption type u t m u u p 1 u in r n r m 2 p 1 with bounded initial data u 0 from l q or other functional spaces for m 1 i e for the semilinear heat equation with absorption intensively studied from the 1970s basic global l estimates are straightforward and guaranteed by the maximum principle we show that for m 2 where comparison or order preserving properties of parabolic flows fail some similar estimates can be obtained by scaling techniques establishing the rates of decay of the solutions as t and the behaviour as t 0

fuzzy overlapping community detection based on local random walk and multidimensional scaling a b s t r a c t a fuzzy overlapping community is an important kind of overlapping community in which each node belongs to each community to different extents it exists in many real networks but how to identify a fuzzy overlapping community is still a challenging task in this work the concept of local random walk and a new distance metric are introduced based on the new distance measurement the dissimilarity index between each node of a network is calculated firstly then in order to keep the original node distance as much as possible the network structure is mapped into low dimensional space by the multidimensional scaling mds finally the fuzzy c means clustering is employed to find fuzzy communities in a network the experimental results show that the proposed algorithm is effective and efficient to identify the fuzzy overlapping communities in both artificial networks and real world networks

an improved immersed boundary lattice boltzmann method for simulating three dimensional incompressible flows the recently proposed boundary condition enforced immersed boundary lattice boltzmann method ib lbm 14 is improved in this work to simulate three dimensional incompressible viscous flows in the conventional ib lbm the restoring force is pre calculated and the non slip boundary condition is not enforced as compared to body fitted solvers as a result there is a flow penetration to the solid boundary this drawback was removed by the new version of ib lbm 14 in which the restoring force is considered as unknown and is determined in such a way that the non slip boundary condition is enforced since eulerian points are also defined inside the solid boundary the computational domain is usually regular and the cartesian mesh is used on the other hand to well capture the boundary layer and in the meantime to save the computational effort we often use non uniform mesh in ib lbm applications in our previous two dimensional simulations 14 the taylor series expansion and least squares based lattice boltzmann method tllbm was used on the non uniform cartesian mesh to get the flow field the final expression of tllbm is an algebraic formulation with some weighting coefficients these coefficients could be computed in advance and stored for the following computations however this way may become impractical for 3d cases as the memory requirement often exceeds the machine capacity the other way is to calculate the coefficients at every time step as a result extra time is consumed significantly to overcome this drawback in this study we propose a more efficient approach to solve lattice boltzmann equation on the non uniform cartesian mesh as compared to tllbm the proposed approach needs much less computational time and virtual storage its good accuracy and efficiency are well demonstrated by its application to simulate the 3d lid driven cubic cavity flow to valid the combination of proposed approach with the new version of ibm 14 for 3d flows with curved boundaries the flows over a sphere and torus are simulated the obtained numerical results compare very well with available data in the literature

regular article an accurate curved boundary treatment in the lattice boltzmann method the lattice boltzmann equation lbe is an alternative kinetic method capable of solving hydrodynamics for various systems major advantages of the method are due to the fact that the solution for the particle distribution functions is explicit easy to implement and natural to parallelize because the method often uses uniform regular cartesian lattices in space curved boundaries are often approximated by a series of stairs that leads to reduction in computational accuracy in this work a second order accurate treatment of the boundary condition in the lbe method is developed for a curved boundary the proposed treatment of the curved boundaries is an improvement of a scheme due to o filippova and d hanel 1998 j comput phys 147 219 the proposed treatment for curved boundaries is tested against several flow problems 2 d channel flows with constant and oscillating pressure gradients for which analytic solutions are known flow due to an impulsively started wall lid driven square cavity flow and uniform flow over a column of circular cylinders the second order accuracy is observed with a solid boundary arbitrarily placed between lattice nodes the proposed boundary condition has well behaved stability characteristics when the relaxation time is close to 1 2 the zero limit of viscosity the improvement can make a substantial contribution toward simulating practical fluid flow problems using the lattice boltzmann method

semi supervised community detection based on discrete potential theory abstract in recent studies of the complex network most of the community detection methods only consider the network topological structure without background information this leads to a relatively low accuracy in this paper a novel semi supervised community detection algorithm is proposed based on the discrete potential theory it effectively incorporates individual labels the labels of corresponding communities to guide the community detection process for achieving better accuracy specifically a number of vertices with user defined labels are first identified to act as unit elementary charges which can generate different electrostatic fields then community detection can be translated into a potential transmission problem by formulating the problem using combinational dirichlet labels of those unlabeled vertices can be determined by the labels for which the greatest potential is calculated finally a better community partition can be obtained our extensive numerical experiments in both artificial and real networks lead to two key observations first individual labels play an important role in community detection and second our proposed semi supervised community detection algorithm outperforms existing counterparts in both accuracy and time complexity especially for obscure networks

lattice boltzmann computational fluid dynamics in three dimensions the recent development of the lattice gas method and its extension to the lattice boltzmann method have provided new computational schemes for fluid dynamics both methods are fully paralleled and can easily model many different physical problems including flows with complicated boundary conditions in this paper basic principles of a lattice boltzmann computational method are described and applied to several three dimensional benchmark problems in most previous lattice gas and lattice boltzmann methods a face centered hyper cubic lattice in four dimensional space was used to obtain an isotropic stress tensor to conserve computer memory we develop a model which requires 14 moving directions instead of the usual 24 directions lattice boltzmann models describing two phase fluid flows and magnetohydrodynamics can be developed based on this simpler 14 directional lattice comparisons between three dimensional spectral code results and results using our method are given for simple periodic geometries an important property of the lattice boltzmann method is that simulations for flow in simple and complex geometries have the same speed and efficiency while all other methods including the spectral method are unable to model complicated geometries efficiently

cellular automaton fluids 1 basic theory continuum equations are derived for the large scale behavior of a class of cellular automaton models for fluids the cellular automata are discrete analogues of molecular dynamics in which particles with discrete velocities populate the links of a fixed array of sites kinetic equations for microscopic particle distributions are constructed hydrodynamic equations are then derived using the chapman enskog expansion slightly modified navier stokes equations are obtained in two and three dimensions with certain lattices viscosities and other transport coefficients are calculated using the boltzmann transport equation approximation some corrections to the equations of motion for cellular automaton fluids beyond the navier stokes order are given

two dimensional turbulence with the lattice boltzmann equation the authors investigate the ability of the lattice boltzmann equation to reproduce the basic physics of fully turbulent two dimensional flows and present a qualitative estimate of its computational efficiency with respect to other conventional techniques