random tree type partitions as a model for acyclic polymerization holtsmark 3 2 stable distribution of the supercritical gel we study the asymptotic behavior in the thermodynamic limit as n of a particular probability distribution on the set of all forests of trees on a set of n elements monomers we establish the existence of three stages of polymerization dependent upon the ration of association and dissociation rates of monomers and we analyse the near critical and supercritical stages in the supercritical stage we discover that the molecular weight of the largest connected component gel has the holtsmark distribution

the asymptotic distributions of the size of the largest length of a reversible markov process of polymerization in this paper the subcritical near critical and supercritical asymptotic behaviour of a reversible markov process as a chemical model for polymerization was studied we establish the existence of three distinct stages subcritical near critical and supercritical stages of polymerization in the thermodynamic limit as n depending on the value of strength of the fragmentation reaction these three stages correspond to the size of the largest length of polymers of size n to be itself of order log n na 1 2 a 1 and n respectively especially a 2 2 1 when the coagulation reaction rate constant rij of the polymers satisfies rij i j with 1 2 3 2

lattice boltzmann model for the incompressible navier stokes equation in this paper a lattice boltzmann lb model to simulate incompressible flow is developed the main idea is to explicitly eliminate the terms of o m2 where m is the mach number due to the density fluctuation in the existing lb models in the proposed incompressible lb model the pressure p instead of the mass density is the independent dynamic variable the incompressible navier stokes equations are derived from the incompressible lb model via chapman enskog procedure numerical results of simulations of the plane poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2d womersley flow are presented the numerical results are found to be in excellent agreement with theory

applied optimal shape design abstract this paper is a short survey of optimal shape design osd for fluids osd is an interesting field both mathematically and for industrial applications existence sensitivity correct discretization are important theoretical issues practical implementation issues for airplane designs are critical too the paper is also a summary of the material covered in our recent book applied optimal shape design oxford university press 2001

a high level programming language implementation of topology optimization applied to steady state navier stokes flow we present a versatile high level programming language implementation of non linear topology optimization our implementation is based on the commercial software package femlab and it allows a wide range of optimization objectives to be dealt with easily we exemplify our method by studies of steady state navier stokes flow problems thus extending the work by borrvall and petersson on topology optimization of fluids in stokes flow int j num meth fluids 2003 41 77 107 we analyse the physical aspects of the solutions and how they are affected by different parameters of the optimization algorithm a complete example of our implementation is included as femlab code in an appendix copyright 2005 john wiley sons ltd

level set based topology optimization for electromagnetic dipole antenna design this paper presents a level set framework for a typical electromagnetic design problem of dipole antenna in this study the geometrical configuration of an antenna is represented by the zero level contour of a higher dimensional level set function the governing equation for the induced current flow on a metal surface is the electric field integral equation efie which takes into account the electric component of the incident wave the design objective is formulated in terms of the surface current and incident electric field the normal velocity of the level set model which reflects the sensitivity of the objective function is derived from the adjoint variable method and shape derivative by optimizing the objective function the area with the highest current density to which the voltage feeding should be applied can be reshaped the advantages of adopting the level set technique for electromagnetic design lie in its capacity for capturing sophisticated topological changes and facilitation in mathematical representation of the design configuration the demonstrative examples of dipole antenna design show that the level set method results in a fairly smooth optimization process where the vacuum metal interface gradually attains its optimal configuration a series of design cases with self adjoint and non self adjoint sensitivity analyses are studied and compared to the benchmarking problems in dipole antenna

neutral fractional integro differential equation with nonlinear term depending on lower order derivative by applying an iterative technique sufficient conditions are obtained for the existence of the unique solution of the nonlinear neutral fractional integro differential equation involving two riemann liouville derivatives of different fractional orders finally an example is also given to illustrate the availability of our main results

structural topology optimization based on non local shepard interpolation of density field abstract this paper presents a non local density interpolation strategy for topology optimization based on nodal design variables in this method design variable points can be positioned at any locations in the design domain and may not necessarily coincide with elemental nodes by using the shepard family of interpolants the density value of any given computational point is interpolated by design variable values within a certain circular influence domain of the point the employed interpolation scheme has an explicit form and satisfies non negative and range restricted properties required by a physically significant density interpolation since the discretizations of the density field and the displacement field are implemented on two independent sets of points the method is well suited for a topology optimization problem with a design domain containing higher order elements or non quadrilateral elements moreover it has the ability to yield mesh independent solutions if the radius of the influence domain is reasonably specified numerical examples demonstrate the validity of the proposed formulation and numerical techniques it is also confirmed that the method can successfully avoid checkerboard patterns as well as islanding phenomenon

aerodynamic shape optimization using computational fluid dynamics and parallel simulated annealing algorithms aerodynamic shape design using stochastic optimization methods such as simulated annealing method to optimize objective functions evaluated by modern state of the art computational fluid dynamics solvers normally requires enormous computation time to search for the global optimal design aerodynamic shape optimization of internal flow systems is studied using euler navier stokes solvers and parallel simulated annealing algorithm which is implemented on parallel computing platforms a variety of inverse and direct design of internal flow systems are carried out to examine the efficiency and speedup of the parallel simulated annealing algorithms

fractional problems with advanced arguments abstract this paper concerns boundary fractional differential problems with advanced arguments we investigate the existence of initial value problems when the initial point is given at the end point of an interval nonhomogeneous linear fractional differential equations are also studied the existence of solutions for fractional differential equations with advanced arguments and with boundary value problems has been investigated by using a monotone iterative technique we also discuss corresponding fractional inequalities several examples illustrate the results

topology optimization for turbulent flow with spalart allmaras model abstract in this research a new finite element fe based topology optimization to for turbulent flow was developed using the spalart allmaras s a equation which is one of the reynolds averaged navier stokes rans equations despite many innovative works on the subject of fluidic to it is rare to consider the influence of turbulent flow in to to consider the effect of complex turbulent fluid motion this research considered the s a model developed mainly for aerodynamic flows for a successful to one primary issue is modification of the s a turbulent model to account for topological evolution during the optimization process to address this issue we proposed the addition of penalization terms to the original governing equations to show the validity of the present approach and the effect of turbulent flow on optimal layouts some two dimensional benchmark designs studied for laminar flow were reconsidered by considering the effect of turbulent flow the eddy viscosity values were increased at some local regions due to the boussinesq hypothesis and naturally optimal layouts affected by the spatially varying viscosity were obtained in turbulent flow it was also found that the balance between the inertia force and the viscosity force plays an important role in topological designs

a variational level set approach for surface area minimization of triply periodic surfaces in this paper we study triply periodic surfaces with minimal surface area under a constraint in the volume fraction of the regions phases that the surface separates using a variational level set method formulation we present a theoretical characterization of and a numerical algorithm for computing these surfaces we use our theoretical and computational formulation to study the optimality of the schwartz primitive p schwartz diamond d and schoen gyroid g surfaces when the volume fractions of the two phases are equal and explore the properties of optimal structures when the volume fractions of the two phases are not equal due to the computational cost of the fully three dimensional shape optimization problem we implement our numerical simulations using a parallel level set method software package

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

discrete adjoint sensitivity analysis for fluid flow topology optimization based on the generalized lattice boltzmann method abstract a discrete adjoint sensitivity analysis for fluid flow topology optimization based on the lattice boltzmann method lbm with multiple relaxation times mrt is developed the lattice boltzmann fluid solver is supplemented by a porosity model using a darcy force the continuous transition from fluid to solid facilitates a gradient based optimization process of the design topology of fluidic channels the adjoint lbm equation which is used to compute the gradient of the optimization objective with respect to the design variables is derived in moment space and found to be as simple as the original lbm the moment based spatial momentum derivatives used to express the discrete objective functional cost function have the advantage that the local stress tensor is a local quantity avoiding the numerical computation of gradients of the discrete velocity field this is particularly useful if dissipation is a design criterion as demonstrated in this paper the method is validated by a detailed comparison with results obtained by borrvall et al for stokes flow while their approach is only valid for stokes flow i e very low reynolds numbers our approach in its present form can in principle be applied for flows of different reynolds numbers just like the navier stokes equation based approaches this point is demonstrated with a bending pipe example for various reynolds numbers

topology optimization of the shear thinning non newtonian fluidic systems for minimizing wall shear stress this paper suggests the topology optimization process to minimize wall shear stress by considering shear thinning non newtonian fluid effects in the systematic design of fluidic systems dealing with blood topology optimization was originally developed for mechanical design problems and within the last decade the method has been extended to a range of fluidic applications in this paper the carreau yasuda constitutive equation model is used for shear thinning non newtonian fluid modeling the fundamental idea is that the material density of each element or grid point is a design variable thus the geometry is parameterized in a pixel like pattern then material interpolation functions for inverse permeability and dynamic viscosity are used to ensure convergence of the solution and resolve non linearity in order to define wall shear stress on implicit boundary between solid and fluid i e blood occurring in fluidic topology optimization the relaxation method of wall shear stress is first proposed in this study we then apply the proposed fluidic topology optimization to actual fluidic systems dealing with blood e g a femoral bypass graft these design examples validate the efficiency of the proposed approach and show that topology optimization can be used for the initial conceptual design of various fluidic systems

shape topology optimization for navier stokes problem using variational level set method we consider the shape topology optimization of the navier stokes problem a new algorithm is proposed based on the variational level set method by this algorithm a relatively smooth evolution can be maintained without re initialization and drastic topology change can be handled easily finally the promising features of the proposed method are illustrated by two benchmark examples

a level set method for structural topology optimization this paper presents a new approach to structural topology optimization we represent the structural boundary by a level set model that is embedded in a scalar function of a higher dimension such level set models are flexible in handling complex topological changes and are concise in describing the boundary shape of the structure furthermore a well founded mathematical procedure leads to a numerical algorithm that describes a structural optimization as a sequence of motions of the implicit boundaries converging to an optimum solution and satisfying specified constraints the result is a 3d topology optimization technique that demonstrates outstanding flexibility of handling topological changes fidelity of boundary representation and degree of automation we have implemented the algorithm with the use of several robust and efficient numerical techniques of level set methods the benefit and the advantages of the proposed method are illustrated with several 2d examples that are widely used in the recent literature of topology optimization especially in the homogenization based methods

design of maximum permeability material structures this paper extends recent advances in the topology optimization of fluid flows to the design of periodic porous material microstructures operating in a characteristic base cell of the material the goal is to determine the layout of solid and fluid phases that will yield maximum permeability and prescribed flow symmetries in the bulk material darcy s law governs flow through the macroscopic material while stokes equations govern flow through the microscopic channels permeability is computed via numerical homogenization of the base cell using finite elements solutions to the proposed inverse homogenization design problem feature simply connected pore spaces that closely resemble minimal surfaces such as the triply periodic schwartz p minimal surface for 3 d isotropic maximum permeability materials

topology optimization of steady navier stokes flow with body force abstract this paper presents the topology optimization of steady navier stokes flows with body forces that influence the optimal shape and topology of fluid flows based on the implicit expression of the fluid flow with the level set method an optimization problem is formulated and analyzed using the continuous adjoint method the shape and topological sensitivities are computed based on the adjoint and asymptotic analysis of the optimization problem in the optimization procedure the level set surface is evolved based on the shape sensitivity and nucleated based on the topological sensitivity simultaneously three kinds of body forces that are commonly used in the design of fluid devices i e constant nonuniform and solution dependent body forces are considered in the two dimensional and three dimensional numerical examples numerical results demonstrate that this method can effectively achieve the topology optimization of the navier stokes flows with body forces

combination of topology optimization and optimal control method this paper presents the combination of topology optimization and optimal control method to find the optimal match between the material topology and control in the presented method the material topology is determined using the simp solid isotropic material with penalization method which has been popularly used in topology optimization in the simp method the design variable is relaxed and bounded in the interval 0 1 and the evolution of the design variable is usually implemented by the method of moving asymptotes mma which can be used to deal with optimization problem with multiple integral constraints and bound constraint of the design variable in the combination of topology optimization and optimal control method the control variable appears along with the design variable in order to evolve the control variable and design variable using mma simultaneously the control variable is regularized using a bound constraint and the corresponding bound constraint is projected onto the interval 0 1 which is the same as the bound constraint of the design variable the optimization problem is analyzed using the adjoint method to obtain the adjoint sensitivity during the optimization procedure the design and control variables are filtered by the helmholtz filters to ensure the smoothness of the distribution to ensure the minimum scale length and remove the gray area in the material topology the filtered design variable is projected by the threshold method the feasibility and robustness of the combination of these two methods are demonstrated by several test problems including heat transfer fluid flow and compliance minimization

a consistent grayscale free topology optimization method using the level set method and zero level boundary tracking mesh summary this paper proposes a level set based topology optimization method incorporating a boundary tracking mesh generating method and nonlinear programming because the boundary tracking mesh is always conformed to the structural boundary good approximation to the boundary is maintained during optimization therefore structural design problems are solved completely without grayscale material previously we introduced the boundary tracking mesh generating method into level set based topology optimization and updated the design variables by solving the level set equation in order to adapt our previous method to general structural optimization frameworks the incorporation of the method with nonlinear programming is investigated in this paper to successfully incorporate nonlinear programming the optimization problem is regularized using a double well potential furthermore the sensitivities with respect to the design variables are strictly derived to maintain consistency in mathematical programming we expect the investigation to open up a new class of grayscale free topology optimization the usefulness of the proposed method is demonstrated using several numerical examples targeting two dimensional compliant mechanism and metallic waveguide design problems copyright 2014 john wiley sons ltd

an improved implicit re initialization method for the level set function applied to shape and topology optimization of fluid this paper presents an accurate implicit re initialization approach in the framework of a level set method the improved method includes two schemes for keeping the zero level set unperturbed the first scheme is to derive and use a new formula for the smoothing parameter in the conventional re initialization equation based on the principle of the interface not moving the second scheme is to reduce the local time step to avoid the interface moving across grid points when the sign of the level set function near the interface is changed the example presented suggests that the new algorithm has a better approximation to the signed distance function and obtains a more accurate interface than the algorithm presented by sussman et al 1994 for shape and topology optimization of fluid the effectiveness of the developed method in this paper was demonstrated by the internal and external flow examples

critical behavior of the heterogeneous random coagulation fragmentation processes in this paper we study the asymptotic distributions of the heterogeneous random coagulation fragmentation processes hcfp which model the coagulation fragmentation and diffusion of clusters of particles on a lattice based on a closed form of the stationary distribution for the hcfp we prove that the mutually dependent clusters with a finite size finite particles in the sub critical stage will become independent in the critical and super critical stages and the asymptotic distributions of the number of clusters may converge to gaussian or poisson distribution according to its size to be small or large in the critical and super critical stages

existence results to delay fractional differential equations with nonlinear boundary conditions this paper concerns boundary value problems for delay fractional differential equations we formulate sufficient conditions under which such problems have extremal solutions in the corresponding region delay differential inequalities are also discussed examples are given to illustrate the effectiveness of the results

level set topology optimization of fluids in stokes flow we propose the level set method of topology optimization as a viable robust and efficient alternative to density based approaches in the setting of fluid flow the proposed algorithm maintains the discrete nature of the optimization problem throughout the optimization process leading to significant advantages over density based topology optimization algorithms specifically the no slip boundary condition is implemented directly this is accurate removes the need for interpolation schemes and continuation methods and gives significant computational savings by only requiring flow to be modeled in fluid regions topological sensitivity information is utilized to give a robust algorithm in two dimensions and familiar two dimensional power dissipation minimization problems are solved successfully computational efficiency of the algorithm is also clearly demonstrated on large scale three dimensional problems

stress based topology optimization method for steady state fluid structure interaction problems abstract this research developed a new stress based topology optimization method stom for a steady state fluid structure interaction fsi problem that minimizes the volume subject to the local stress constraints despite numerous studies on stom challenging optimization issues related to stress based topology optimization to procedures for fluid structure multiphysics systems still exist critical issues involved in creating a successful to for an fsi structure include the interpolation approach between the fluid equation and the structure equation with respect to locally defined design variables the mutual multiphysics coupling boundary conditions at dramatically evolving interfacing boundaries and a clear interpretation of the governing equations and the interaction boundary conditions for spatially varying intermediate design variables in addition to these three issues which are related to multiphysics equations there are three important considerations related to the stom the stress singularity issue the issues of multiple constraints and the highly nonlinear behavior of the stress constraints to resolve all of the aforementioned issues we applied a monolithic analysis integrating the qp relaxation method and the global p norm approach using the present method we created optimal layouts that minimize the volume constraining local stress values for a steady state fluid and structural interaction system

heuristic optimality criterion algorithm for shape design of fluid flow this paper presents a heuristic optimality criterion algorithm for shape design of fluid flow in this algorithm the lattice boltzmann method lbm is utilized to calculate the flow field of a fluid domain which is divided into elemental cells a heuristic optimality criterion is applied for cells at the solid fluid interface i e the dynamic pressure for fluid cells and the viscous stress on their neighboring solid cells an automatic program is processed step by step to exchange the positions of solid and fluid cells identified by the optimality criterion with the objective of decreasing the flow resistance at the constraint of constant fluid volume to illustrate the procedure of this algorithm for shape design of fluid flow two simple examples are presented one with fluid flowing through a right angle elbow and the other through a converging t junction numerical results show that this algorithm can successfully reduce the total pressure drop of the system demonstrating its potential applications in engineering optimal design

brittle and ductile failure constraints of stress based topology optimization method for fluid structure interactions abstract this study considers failure theories for brittle and ductile materials in the stress based topology optimization method stom for steady state fluid structure interactions fsi in some relevant studies the subject of the stress based topology optimization to minimize volumes with local von mises stress constraints has been researched however the various failure theories for ductile and brittle materials such as the maximum shear stress theory the brittle and ductile mohr coulomb theory and the drucker prager theory have not been considered for successful stom for fsi in addition to alleviating physics interpolation issues between structure and fluid and some numerical issues related to stom the mathematical characteristics of the various failure theories should be properly formulated and constrained to resolve all the involved computational issues the present study applies the monolithic analysis method the qp relaxation method and the p norm approach to the failure constraints the present topology optimization method can create optimal layouts while minimizing volume constraining local failure constraints for ductile and brittle materials for steady state fluid and structural interaction system

size of the largest cluster under zero range invariant measures we study the finite zero range process with occupancy dependent rate function g under the invariant measure which can be written explicitly in terms of g particles are distributed over sites and we regard all particles at a fixed site as a cluster in the density one case that is equal numbers of particles and sites we determine asymptotically the size of the largest cluster as the number of particles tends to infinity and determine its dependence on the rate function

level set based topology optimization of transient flow using lattice boltzmann method considering an oscillating flow condition abstract topology optimization is widely applied to various design problems in both structure and fluid dynamics engineering specifically the development of energy dissipation devices with vibration control remains a key consideration the aim of this study is to improve devices that maximize the absorption or dissipation of the vibration of an oscillating object and propose an approach in which the level set based topology optimization of transient flow using the lattice boltzmann method is simultaneously applied to forward and reverse direction flows to deal with oscillating flows in real world engineering designs although several studies have examined topology optimization to minimize dissipated kinetic energy this study introduces an objective function for maximizing the dissipated kinetic energy in time varying fluid flows via velocity gradients

topology optimization using the lattice boltzmann method incorporating level set boundary expressions this paper presents a topology optimization method for fluid dynamics problems based on the level set method and using the lattice boltzmann method lbm in this optimization method the optimization problems are formulated based on the original boltzmann equation and the design sensitivities are precisely obtained without the time consuming numerical operations encountered when dealing with a large scale asymmetric matrix in contrast to previous research in which the lbm uses the lattice boltzmann equation lbe for the formulations of optimization problems and the derivation of their adjoint equations that is we newly derive sensitivity formulations from the original boltzmann equation not the lbe that can be said to be an approximated equation and these formulations yield strictly correct sensitivities that are error free based on the above formulations we construct a level set based topology optimization method incorporating a fictitious interface energy for the design of a fluid channel that minimizes flow friction furthermore two and three dimensional numerical examples are provided to confirm the validity and utility of the presented method

on a random graph evolving by degrees abstract we consider a random multi graph growth process g m on a vertex set n which is a special case of a more general process proposed by laci lovasz in 2002 g 0 is empty and g m 1 is obtained from g m by inserting a new edge e at random specifically the conditional probability that e joins two currently disjoint vertices i and j is proportional to d i d j where d i d j are the degrees of i j in g m and 0 is a fixed parameter the limiting case is the erd s renyi graph process we show that whp g m contains a unique giant component iff c 2 m n c 1 and the size of this giant is asymptotic to n 1 c c where c c is the root of c c 2 c c 2 a phase transition window is proved to be contained essentially in c a n 1 3 c b n 1 4 and we conjecture that 1 4 may be replaced with 1 3 for the multigraph version mg m we show that mg m is connected whp iff m m n n 1 1 we conjecture that for 1 m n is the threshold for connectedness of g m itself

initial value problems for neutral fractional differential equations involving a riemann liouville derivative we present the application of a monotone iterative method to neutral fractional problems given are sufficient conditions which guarantee that a neutral fractional differential equations with initial condition has a unique solution two examples illustrate the results

level set methods for optimization problems involving geometry and constraints i frequencies of a two density inhomogeneous drum many problems in engineering design involve optimizing the geometry to maximize a certain design objective geometrical constraints are often imposed in this paper we use the level set method devised in osher and sethian j comput phys 79 12 1988 the variational level set calculus presented in zhao et al j comput phys 127 179 1996 and the projected gradient method as in rudin et al physica d 60 259 1992 to construct a simple numerical approach for problems of this type we apply this technique to a model problem involving a vibrating system whose resonant frequency or whose spectral gap is to be optimized subject to constraints on geometry our numerical results are quite promising we expect to use this approach to deal with a wide class of optimal design problems in the future

phase field method to optimize dielectric devices for electromagnetic wave propagation we discuss a phase field method for shape optimization in the context of electromagnetic wave propagation the proposed method has the same functional capabilities as the level set method for shape optimization the first advantage of the method is the simplicity of computation since extra operations such as re initialization of functions are not required the second is compatibility with the topology optimization method due to the similar domain representation and the sensitivity analysis structural shapes are represented by the phase field function defined in the design domain and this function is optimized by solving a time dependent reaction diffusion equation the artificial double well potential function used in the equation is derived from sensitivity analysis we study four types of 2d or 2 5d axisymmetric optimization problems two are the classical problems of photonic crystal design based on the bloch theory and photonic crystal wave guide design and two are the recent topics of designing dielectric left handed metamaterials and dielectric ring resonators

existence of solutions of boundary value problems for differential equations with delayed arguments we study the existence and approximation of solution of boundary value problems for differential equations with delayed arguments sufficient conditions are established for the existence of a unique solution or extremal ones of the given problem a monotone iterative technique is applied

a graph valued markov process as rings allowed polymerization model subcritical behavior in previous papers random tree type partitions of a finite set as a stochastic model for acyclic polymerization were studied in this paper the model is extended one important step further by allowing rings formation the main result is that in the subcritical domain the asymptotic behavior of the process remains essentially the same as in the acyclic case despite the fact that cycles are not excluded

on monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations abstract in this paper we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions of first and second order periodic boundary value problems and periodic solutions of functional differential equations we obtain some new results relative to the lower solution and upper solution with

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

an extended level set method for shape and topology optimization in this paper the conventional level set methods are extended as an effective approach for shape and topology optimization by the introduction of the radial basis functions rbfs the rbf multiquadric splines are used to construct the implicit level set function with a high level of accuracy and smoothness and to discretize the original initial value problem into an interpolation problem the motion of the dynamic interfaces is thus governed by a system of coupled ordinary differential equations odes and a relatively smooth evolution can be maintained without reinitialization a practical implementation of this method is further developed for solving a class of energy based optimization problems in which approximate solution to the original hamilton jacobi equation may be justified and nucleation of new holes inside the material domain is allowed for furthermore the severe constraints on the temporal and spatial discretizations can be relaxed leading to a rapid convergence to the final design insensitive to initial guesses the normal velocities are chosen to perform steepest gradient based optimization by using shape sensitivity analysis and a bi sectioning algorithm a physically meaningful and efficient extension velocity method is also presented the proposed method is implemented in the framework of minimum compliance design and its efficiency over the existing methods is highlighted numerical examples show its accuracy convergence speed and insensitivity to initial designs in shape and topology optimization of two dimensional 2d problems that have been extensively investigated in the literature

structural optimization using sensitivity analysis and a level set method in the context of structural optimization we propose a new numerical method based on a combination of the classical shape derivative and of the level set method for front propagation we implement this method in two and three space dimensions for a model of linear or nonlinear elasticity we consider various objective functions with weight and perimeter constraints the shape derivative is computed by an adjoint method the cost of our numerical algorithm is moderate since the shape is captured on a fixed eulerian mesh although this method is not specifically designed for topology optimization it can easily handle topology changes however the resulting optimal shape is strongly dependent on the initial guess

topology optimization of regions of darcy and stokes flow this paper treats the topology optimization problem of obtaining an optimal layout of regions of darcy and stokes flow where the objective is the total potential power functional representing aver

a variational level set method for the topology optimization of steady state navier stokes flow the smoothness of topological interfaces often largely affects the fluid optimization and sometimes makes the density based approaches though well established in structural designs inadequate this paper presents a level set method for topology optimization of steady state navier stokes flow subject to a specific fluid volume constraint the solid fluid interface is implicitly characterized by a zero level contour of a higher order scalar level set function and can be naturally transformed to other configurations as its host moves a variational form of the cost function is constructed based upon the adjoint variable and lagrangian multiplier techniques to satisfy the volume constraint effectively the lagrangian multiplier derived from the first order approximation of the cost function is amended by the bisection algorithm the procedure allows evolving initial design to an optimal shape and or topology by solving the hamilton jacobi equation two classes of benchmarking examples are presented in this paper 1 periodic microstructural material design for the maximum permeability and 2 topology optimization of flow channels for minimizing energy dissipation a number of 2d and 3d examples well demonstrated the feasibility and advantage of the level set method in solving fluid solid shape and topology optimization problems

vortex design problem in this investigation we propose a computational approach for the solution of optimal control problems for vortex systems with compactly supported vorticity the problem is formulated as a pde constrained optimization in which the solutions are found using a gradient based descent method recognizing such euler flows as free boundary problems the proposed approach relies on shape differentiation combined with adjoint analysis to determine cost functional gradients in explicit tracking of interfaces vortex boundaries this method offers an alternative to grid based techniques such as the level set methods and represents a natural optimization formulation for vortex problems computed using the contour dynamics technique we develop and validate this approach using the design of 2d equilibrium euler flows with finite area vortices as a model problem it is also discussed how the proposed methodology can be applied to euler flows featuring other vorticity distributions such as vortex sheets and to time dependent phenomena

topology optimization for three dimensional electromagnetic waves using an edge element based finite element method this paper develops a topology optimization procedure for three dimensional electromagnetic waves with an edge element based finite element method in contrast to the two dimensional case three dimensional electromagnetic waves must include an additional divergence free condition for the field variables the edge element based finite element method is used to both discretize the wave equations and enforce the divergence free condition for wave propagation described in terms of the magnetic field in the widely used class of non magnetic materials the divergence free condition is imposed on the magnetic field this naturally leads to a nodal topology optimization method when wave propagation is described using the electric field the divergence free condition must be imposed on the electric displacement in this case the material in the design domain is assumed to be piecewise homogeneous to impose the divergence free condition on the electric field this results in an element wise topology optimization algorithm the topology optimization problems are regularized using a helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method in order to ensure the applicability of the filter in the element wise topology optimization version a regularization method is presented to project the nodal into an element wise physical density variable

computing minimal surfaces via level set curvature flow given a fixed closed curve or curves in r sp3 there is an associated problem of finding a surface with mean curvature zero which has that curve or curves as its boundary in this paper a new approach to numerically solving the minimal surface problem is introduced the surface is represented as a level set of a global function phi r sp3 to r the family of surfaces evolve in time according to mean curvature flow a solution is found when a steady state condition is achieved a new system of interpolatory boundary conditions are used to maintain the connection between the surface and the fixed boundary contour several computer surfaces are shown including examples of topological changes

a variational level set approach to multiphase motion a coupled level set method for the motion of multiple junctions of e g solid liquid and grain boundaries which follows the gradient flow for an energy functional consisting of surface tension proportional to length and bulk energies proportional to area is developed the approach combines the level set method of s osher and j a sethian with a theoretical variational formulation of the motion by f reitich and h m soner the resulting method uses as many level set functions as there are regions and the energy functional is evaluated entirely in terms of level set functions the gradient projection method leads to a coupled system of perturbed by curvature terms hamilton jacobi equations the coupling is enforced using a single lagrange multiplier associated with a constraint which essentially prevents a regions from overlapping and b the development of a vacuum the numerical implementation is relatively simple and the results agree with and go beyond the theory as given in 12 other applications of this methodology including the decomposition of a domain into subregions with minimal interface length are discussed finally some new techniques and results in level set methodology are presented

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

structural boundary design via level set and immersed interface methods we develop and test an algorithmic approach to the boundary design of elastic structures the goal of our approach is two fold first to develop a method which allows one to rapidly solve the two dimensional lam equations in arbitrary domains and compute for example the stresses and second to develop a systematic way of modifying the design to optimize chosen properties at the core our approach relies on two distinct steps given a design we first apply an explicit jump immersed interface method to compute the stresses for a given design shape we then use a narrow band level set method to perturb this shape and progress towards an improved design the equations of 2d linear elastostatics in the displacement formulation on arbitrary domains are solved quickly by domain embedding and the use of fast elastostatic solvers this effectively reduces the dimensionality of the problem by one once the stresses are found the level set method which represents the design structure through an embedded implicit function is used in the second step to alter the shape with velocities depending on the stresses in the current design criteria are provided for advancing the shape in an appropriate direction and for correcting the evolving shape when given constraints are violated

phase transitions on markovian bipartite graphs an application of the zero range process we analyze the existence and the size of the giant component in the stationary state of a markovian model for bipartite multigraphs in which the movement of the edge ends on one set of vertices of the bipartite graph is a zero range process the degrees being static on the other set the analysis is based on approximations by independent variables and on the results of molloy and reed for graphs with prescribed degree sequences the possible types of phase diagrams are identified by studying the behavior below the zero range condensation point as a specific example we consider the so called evans interaction in particular we examine the values of a critical exponent describing the growth of the giant component as the value of the dilution parameter controlling the connectivity is increased above the critical threshold rigorous analysis spans a large portion of the parameter space of the model exactly at the point of zero range condensation these results supplemented with conjectures supported by monte carlo simulations suggest that the phenomenological landau theory for percolation on graphs is not broken by the fluctuations

fluid flow in a porous tree shaped network optimal design and extension of hess murray s law abstract this paper aims to contribute to the ongoing research on tree shaped flow structures here we focuses on porous walled tree shaped networks namely the laminar fluid flow analytical models are developed for pressure distribution along the porous tree network and for the hydraulic resistance of the network in terms of geometry of successive vessel segments number of branches branching levels and intrinsic permeability of walls we also rely on constructal design to find important insights regarding the allometric relationships between the sizes of successive vessel segments of tree networks among other results we show that the flow distribution depends on the aspect ratio of the branching vessels as well as on the wall permeability of vessels maximum physical efficiency to connect successive vessel segments is homothetic with a size ratio of 2 1 3 hess murray law only for impermeable tree networks our results indicate that for porous vessels this homothetic ratio increases with the intrinsic permeability of the vessel wall this result may help to understand the occurrence of different optimal relationships between the vessel diameters such as in the branching hierarchy of the conductive and respiratory zones of the lungs