Folkert Tangerman - Academia.edu (original) (raw)

Papers by Folkert Tangerman

У статті проведено удосконалення діючої моделі виробничої демократії; на базі цієї моделі запроп... more У статті проведено удосконалення діючої моделі виробничої демократії; на базі цієї моделі запропоновано систему управління з досягнення тривалої соціально-економічної стабільності на виробничому рівні. В статье проведено усовершенствование действующей модели производственной демократии; на базе этой модели предложена система управления по достижению длительной социально-экономической стабильности на производственном уровне. The improvement of operating model of production democracy has been performed in the article. It has been offered the control system on achievement of the protracted socio-economic stability in production level on the basis of this model.

The movement of a flock with a single leader (and a directed path from it to every agent) can be ... more The movement of a flock with a single leader (and a directed path from it to every agent) can be stabilized. Nonetheless for large flocks perturbations in the movement of the leader may grow to a considerable size as they propagate throughout the flock and before they die out over time. As an example we consider a string of N+1 oscillators moving in the line. Each one `observes' the relative velocity and position of only its nearest neighbors. This information is then used to determine its own acceleration. Now we fix all parameters except the number of oscillators. We then show (within a certain class of systems) that a perturbation in the leader's orbit is almost always amplified exponentially in N as it propagates towards the outlying members of the flock. The only exception is when there is a symmetry present in the interaction: in that case the growth of the perturbation is linear in N. Comment: 9 pages, 5 figures

Journal of Statistical Physics, 1990

ABSTRACT In this paper we study the well-ordered Cantor sets in hyperbolic sets on the line and t... more ABSTRACT In this paper we study the well-ordered Cantor sets in hyperbolic sets on the line and the plane. Examples of such sets occur in circle maps and in area-preserving twist maps. We set up a renormalization scheme employing in both cases the first return map. We prove convergence of this scheme. The convergence implies that the asymptotic geometry of such a well-ordered set with irrational rotation number and their nearby well-ordered orbits is determined by the Lyapunov exponent of this set.

Communications in Mathematical Physics, 1991

We consider the space N of C 2 twist maps that satisfy the following requirements. The action is ... more We consider the space N of C 2 twist maps that satisfy the following requirements. The action is the sum of a purely quadratic term and a periodic potential times a constant k (hereafter called the nonlinearity). The potential restricted to the unit circle is bimodal, i.e. has one local minimum and one local maximum. The following statements are proven for maps in JV with nonlinearity k large enough. The intersection of the unstable and stable invariant manifolds to the hyperbolic minimizing periodic points contains minimizing homoclinic points. Consider two finite pieces of these manifolds that connect two adjacent homoclinic minimizing points (hereafter called fundamental domains). We prove that all such fundamental domains have precisely one point in their intersection (the Single Intersection theorem). In addition, we show that limit points of minimizing points are recurrent, which implies that Aubry Mather sets (with irrational rotation number) are contained in diamonds formed by local stable and unstable manifolds of nearby minimizing periodic orbits (the Diamond Configuration theorem). Another corollary concerns the intersection of the minimax orbits with certain symmetry lines of the map.

Communications in Mathematical Physics, 1991

In this paper we consider one parameter families of circle maps with nonlinear flat spot singular... more In this paper we consider one parameter families of circle maps with nonlinear flat spot singularities. Such circle maps were studied in [Circles I] where in particular we studied the geometry of closest returns to the critical interval for irrational rotation numbers of constant type. In this paper we apply those results to obtain exact relations between scalings in the parameter space to dynamical scalings near parameter values where the rotation number is the golden mean. Then results on [Circles I] can be used to compute the scalings in the parameter space. As far as we are aware, this constitutes the first case in which parameter scalings can be rigorously computed in the presence of highly nonlinear (and nonhyperbolic) dynamics.

Ergodic Theory and Dynamical Systems, 1986

Kupka-Smale like theorems are proven in the real analytic case, using existing perturbation schem... more Kupka-Smale like theorems are proven in the real analytic case, using existing perturbation schemes for the smooth case and the heat operator. As a consequence, a topological proof is obtained of Siegel's theorem on the generic divergence of normal form transformations.

We study Birkhoff sums S(k,a) = g(a)+g(2a)+...+g(ka) at the golden mean rotation number a with pe... more We study Birkhoff sums S(k,a) = g(a)+g(2a)+...+g(ka) at the golden mean rotation number a with periodic continued fraction approximations p(n)/q(n), where g(x) = log(2-2 cos(2 pi x). The summation of such quantities with logarithmic singularity is motivated by critical KAM phenomena. We relate the boundedness of log- averaged Birkhoff sums S(k,a)/log(k) and the convergence of S(q(n),a) with the existence of an experimentally established limit function f(x) = lim S([x q(n)])(p(n+1)/q(n+1))-S([x q(n)])(p(n)/q(n)) for n to infinity on the interval [0,1]. The function f satisfies a functional equation f(ax) + (1-a) f(x)= b(x) with a monotone function b. The limit lim S(q(n),a) for n going to infinity can be expressed in terms of the function f.

Ergodic Theory and Dynamical Systems, 1986

We show that entire functions which are critically finite and which meet certain growth condition... more We show that entire functions which are critically finite and which meet certain growth conditions admit ‘Cantor bouquets’ in their Julia sets. These are invariant subsets of the Julia set which are homeomorphic to the product of a Cantor set and the line [0, ∞). All of the curves in the bouquet tend to ∞ in the same direction, and the map behaves like the shift automorphism on the Cantor set. Hence the dynamics near ∞ for these types of maps may be analyzed completely. Among the entire maps to which our methods apply are exp (z), sin (z), and cos (z).

Front tracking capability has been encorporated into the Partnership in Computational Science (PI... more Front tracking capability has been encorporated into the Partnership in Computational Science (PICS) GCT code, version 1.0. This merge adds a two dimensional, discontinuity tracking capability to the GCT 1.0 code. It supports the ability to run both on scalar platforms, specifically UNIX workstations, and on the INTEL iPSC/860 hypercube parallel architecture. Porting to the INTEL Paragon architecture will be accomplished once a stable version of the software for said architecture is available. 1 Introduction We report on our encorporation of front tracking capabilities into the PICS GCT code, version 1.0. We begin with a background sketch and outline of the merge, and provide more detailed information in the following sections. Work supported by US Department of Energy under subcontract with Oak Ridge National Laboratory, subcontract number 19XSK964C. The design criteria for the PICS GCT (Groundwater Contaminant Transport) code, version 1.0, is to provide a three dimensional, gro...

The Hamilton-Jacobi equation describes the dynamics of a hypersurface in R n. This equation is a ... more The Hamilton-Jacobi equation describes the dynamics of a hypersurface in R n. This equation is a nonlinear conservation law and thus has discontinuous solutions. The dependent variable is a surface gradient and the discontinuity is a surface cusp. Here we investigate the intersection of cusp hypersurfaces. These intersections define (n \Gamma 1)-dimensional Riemann problems for the HamiltonJacobi equation. We propose the class of Hamilton-Jacobi equations as a natural higher-dimensional generalization of scalar equations which allow a satisfactory theory of higher-dimensional Riemann problems. The first main result of this paper is a general framework for the study of higherdimensional Riemann problems for Hamilton-Jacobi equations. The purpose of the framework is to understand the structure of Hamilton-Jacobi wave interactions in an explicit and constructive manner. Specialized to two-dimensional Riemann problems (i.e., the intersection of cusp curves on surfaces imbedded in R 3), ...

Resin Transfer Molding (RTM), as a method for the manufacture of advanced fiber reinforced compos... more Resin Transfer Molding (RTM), as a method for the manufacture of advanced fiber reinforced composite materials, is attractive because it offers the possibility of lower manufacturing costs and more complex shapes than traditional methods. A major issue in this new manufacturing process is the elimination of void spaces in the resin fill operation, so that products with high quality are manufactured. Process modeling is particularly useful in understanding, designing, and optimizing the process conditions to achieve this goal. In this paper we report on our program with the Advanced Technology & Development Center at Northrop Grumman and demonstrate how modeling could improve the manufacturing process and enhance product quality. We review the manufacturing process and related issues and present a manufacturing process model, developed recently by the authors. This model is applied to study the formation and migration of air bubbles in the preform, a major RTM manufacturing problem, ...

This paper describes surface evolution formulated in terms of a Hamilton-Jacobi equation and a so... more This paper describes surface evolution formulated in terms of a Hamilton-Jacobi equation and a solution algorithm based on a three-dimensional front tracking algorithm. Our method achieves sharp resolution in the evolution of surface edges and corners. This study is motivated by semiconductor chip evolution during deposition and resputtering processes. For this reason, we discuss here the effects of diffuse rescattering on surface features. We illustrate some of the three-dimensional capabilities of the front tracking algorithm. We also present a validation study by display of two-dimensional cross sections of threedimensional simulations of a finite length trench. The cross sections correspond to twodimensional simulations of S. Hamaguchi and S. M. Rossnagel. Supported in part by the Applied Mathematics Subprogram of the U.S. Department of Energy DE-FG0290ER25084, the National Science Foundation grants DMS-9312098 and 9500568, and the Army Research Office grant DAAH04-95-10414. 1 ...

Resin Transfer Molding, as a method for the manufacture of advanced fiber reinforced composite ma... more Resin Transfer Molding, as a method for the manufacture of advanced fiber reinforced composite materials, is attractive because it offers the possibility of lower manufacturing costs and more complex shapes than the traditional manufacturing methods. A major issue in this new manufacturing process is the elimination of void spaces in the resin fill operation, so that products with high quality are manufactured. In this paper we present a two phase, two component air solubility model to study the formation and migration of the macro and micro voids. The numerical solutions of the model are obtained through a front tracking code. The front tracking method has the distinguishing feature of preserving sharp interfaces throughout the simulation. The results demonstrate that the model proposed here has desirable qualitative agreement with experimental results. Based on these results, we make numerical predictions to show how modeling could improve the manufacturing process and hence enhan...

The reduction of porosity is an important requirement in the manufacture of reliable composite co... more The reduction of porosity is an important requirement in the manufacture of reliable composite components. In the Resin Transfer Molding (RTM) process, porosity results from the formation and growth of gas bubbles during the fill and cure stages of the process. Understanding the dynamics of the formation and motion of these bubbles will allow design of RTM processes that provide optimum quality and performance. In this paper, we demonstrate that an unsaturated flow model for gas bubble migration is in qualitative agreement with experimental results. 1 INTRODUCTION The high cost of autoclave-processed composites has led to interest in alternative processing concepts. Resin transfer molding (RTM) is one particularly attractive technique for many applications since it combines cost savings with potential performance improvements (e.g., 3-D strength characteristics). In the past, tool design decisions, component design decisions, and processing cycles for composites have been devel- 1 T...

We consider the rational maps given by z 7 ! jzj 2 ?2 z 2 + c, for z and c complex and > 1 2 fixe... more We consider the rational maps given by z 7 ! jzj 2 ?2 z 2 + c, for z and c complex and > 1 2 fixed and real. The case = 1 corresponds to quadratic polynomials: some of the well-known results for this conformal case still hold for near 1, while others break down. Among the differences between the two cases are the possibility, for 6 = 1, of periodic attractors that do not attract the critical point, and the fact that for < 1 the Julia set is smooth for an open set of values of c. Numerical evidence suggests that the analogue of the Mandelbrot set for this family is connected, but not locally connected if 6 = 1.

Circle maps with a flat spot are studied which are differentiable, even on the boundary of the fl... more Circle maps with a flat spot are studied which are differentiable, even on the boundary of the flat spot. Estimates on the Lebesgue measure and the Hausdorff dimension of the non-wandering set are obtained. Also, a sharp transition is found from degenerate geometry similar to what was found earlier for non-differentiable maps with a flat spot to bounded geometry as in critical maps without a flat spot.

this paper. The semiconductor manufacturing industry has various codes for studying the two dimen... more this paper. The semiconductor manufacturing industry has various codes for studying the two dimensional problem: the evolution of cross-sections of trenches. For instance, a front tracking algorithm for moving curves in R

Abstract. We present a numerical model of two fluid mixing based on hyperbolic equations hav-ing ... more Abstract. We present a numerical model of two fluid mixing based on hyperbolic equations hav-ing complete state variables (velocity, pressure, temperature) for each fluid. The model is designed for the study of acceleration driven mixing layers in a chunk mix regime dominated by large scale coherent mixing structures. The numerical solution of the model is validated by comparison to the incompressible limit. For the purpose of this comparison, we present a newly obtained analytic solu-tion of the pressure equation for this model and an analytic constraint derived from the asymptotic limit of the compressible pressures, which determines uniquely the incompressible pressure solution. The numerical solution is also validated by a mesh convergence study.

Front Tracking is a methodology which uses computational geometry to provide numerical solutions ... more Front Tracking is a methodology which uses computational geometry to provide numerical solutions of enhanced quality for problems of computational physics. It is particularly applicable to the computation of solutions with important jump discontinuities, or fronts. Fronts are represented as lower dimensional data structures, which in the spirit of non-manifold geometries used in CAD systems, support surfaces, curves (at surface intersections) and nodes (at common intersection points of three surfaces). These are expressed in the front tracking algorithm as a simplicial complex: data structures representing non intersecting smooth objects of given dimension, and boundary and coboundary operators to link them to lower and higher dimensional smooth objects. In the solution to problems of computational physics, these fronts evolve and can change their topology, forcing the need for fast retriangulation, intersection detection, and intersection removal routines. The methodology has been ...

У статті проведено удосконалення діючої моделі виробничої демократії; на базі цієї моделі запроп... more У статті проведено удосконалення діючої моделі виробничої демократії; на базі цієї моделі запропоновано систему управління з досягнення тривалої соціально-економічної стабільності на виробничому рівні. В статье проведено усовершенствование действующей модели производственной демократии; на базе этой модели предложена система управления по достижению длительной социально-экономической стабильности на производственном уровне. The improvement of operating model of production democracy has been performed in the article. It has been offered the control system on achievement of the protracted socio-economic stability in production level on the basis of this model.

The movement of a flock with a single leader (and a directed path from it to every agent) can be ... more The movement of a flock with a single leader (and a directed path from it to every agent) can be stabilized. Nonetheless for large flocks perturbations in the movement of the leader may grow to a considerable size as they propagate throughout the flock and before they die out over time. As an example we consider a string of N+1 oscillators moving in the line. Each one `observes' the relative velocity and position of only its nearest neighbors. This information is then used to determine its own acceleration. Now we fix all parameters except the number of oscillators. We then show (within a certain class of systems) that a perturbation in the leader's orbit is almost always amplified exponentially in N as it propagates towards the outlying members of the flock. The only exception is when there is a symmetry present in the interaction: in that case the growth of the perturbation is linear in N. Comment: 9 pages, 5 figures

Journal of Statistical Physics, 1990

ABSTRACT In this paper we study the well-ordered Cantor sets in hyperbolic sets on the line and t... more ABSTRACT In this paper we study the well-ordered Cantor sets in hyperbolic sets on the line and the plane. Examples of such sets occur in circle maps and in area-preserving twist maps. We set up a renormalization scheme employing in both cases the first return map. We prove convergence of this scheme. The convergence implies that the asymptotic geometry of such a well-ordered set with irrational rotation number and their nearby well-ordered orbits is determined by the Lyapunov exponent of this set.

Communications in Mathematical Physics, 1991

We consider the space N of C 2 twist maps that satisfy the following requirements. The action is ... more We consider the space N of C 2 twist maps that satisfy the following requirements. The action is the sum of a purely quadratic term and a periodic potential times a constant k (hereafter called the nonlinearity). The potential restricted to the unit circle is bimodal, i.e. has one local minimum and one local maximum. The following statements are proven for maps in JV with nonlinearity k large enough. The intersection of the unstable and stable invariant manifolds to the hyperbolic minimizing periodic points contains minimizing homoclinic points. Consider two finite pieces of these manifolds that connect two adjacent homoclinic minimizing points (hereafter called fundamental domains). We prove that all such fundamental domains have precisely one point in their intersection (the Single Intersection theorem). In addition, we show that limit points of minimizing points are recurrent, which implies that Aubry Mather sets (with irrational rotation number) are contained in diamonds formed by local stable and unstable manifolds of nearby minimizing periodic orbits (the Diamond Configuration theorem). Another corollary concerns the intersection of the minimax orbits with certain symmetry lines of the map.

Communications in Mathematical Physics, 1991

In this paper we consider one parameter families of circle maps with nonlinear flat spot singular... more In this paper we consider one parameter families of circle maps with nonlinear flat spot singularities. Such circle maps were studied in [Circles I] where in particular we studied the geometry of closest returns to the critical interval for irrational rotation numbers of constant type. In this paper we apply those results to obtain exact relations between scalings in the parameter space to dynamical scalings near parameter values where the rotation number is the golden mean. Then results on [Circles I] can be used to compute the scalings in the parameter space. As far as we are aware, this constitutes the first case in which parameter scalings can be rigorously computed in the presence of highly nonlinear (and nonhyperbolic) dynamics.

Ergodic Theory and Dynamical Systems, 1986

Kupka-Smale like theorems are proven in the real analytic case, using existing perturbation schem... more Kupka-Smale like theorems are proven in the real analytic case, using existing perturbation schemes for the smooth case and the heat operator. As a consequence, a topological proof is obtained of Siegel's theorem on the generic divergence of normal form transformations.

We study Birkhoff sums S(k,a) = g(a)+g(2a)+...+g(ka) at the golden mean rotation number a with pe... more We study Birkhoff sums S(k,a) = g(a)+g(2a)+...+g(ka) at the golden mean rotation number a with periodic continued fraction approximations p(n)/q(n), where g(x) = log(2-2 cos(2 pi x). The summation of such quantities with logarithmic singularity is motivated by critical KAM phenomena. We relate the boundedness of log- averaged Birkhoff sums S(k,a)/log(k) and the convergence of S(q(n),a) with the existence of an experimentally established limit function f(x) = lim S([x q(n)])(p(n+1)/q(n+1))-S([x q(n)])(p(n)/q(n)) for n to infinity on the interval [0,1]. The function f satisfies a functional equation f(ax) + (1-a) f(x)= b(x) with a monotone function b. The limit lim S(q(n),a) for n going to infinity can be expressed in terms of the function f.

Ergodic Theory and Dynamical Systems, 1986

We show that entire functions which are critically finite and which meet certain growth condition... more We show that entire functions which are critically finite and which meet certain growth conditions admit ‘Cantor bouquets’ in their Julia sets. These are invariant subsets of the Julia set which are homeomorphic to the product of a Cantor set and the line [0, ∞). All of the curves in the bouquet tend to ∞ in the same direction, and the map behaves like the shift automorphism on the Cantor set. Hence the dynamics near ∞ for these types of maps may be analyzed completely. Among the entire maps to which our methods apply are exp (z), sin (z), and cos (z).

Front tracking capability has been encorporated into the Partnership in Computational Science (PI... more Front tracking capability has been encorporated into the Partnership in Computational Science (PICS) GCT code, version 1.0. This merge adds a two dimensional, discontinuity tracking capability to the GCT 1.0 code. It supports the ability to run both on scalar platforms, specifically UNIX workstations, and on the INTEL iPSC/860 hypercube parallel architecture. Porting to the INTEL Paragon architecture will be accomplished once a stable version of the software for said architecture is available. 1 Introduction We report on our encorporation of front tracking capabilities into the PICS GCT code, version 1.0. We begin with a background sketch and outline of the merge, and provide more detailed information in the following sections. Work supported by US Department of Energy under subcontract with Oak Ridge National Laboratory, subcontract number 19XSK964C. The design criteria for the PICS GCT (Groundwater Contaminant Transport) code, version 1.0, is to provide a three dimensional, gro...

The Hamilton-Jacobi equation describes the dynamics of a hypersurface in R n. This equation is a ... more The Hamilton-Jacobi equation describes the dynamics of a hypersurface in R n. This equation is a nonlinear conservation law and thus has discontinuous solutions. The dependent variable is a surface gradient and the discontinuity is a surface cusp. Here we investigate the intersection of cusp hypersurfaces. These intersections define (n \Gamma 1)-dimensional Riemann problems for the HamiltonJacobi equation. We propose the class of Hamilton-Jacobi equations as a natural higher-dimensional generalization of scalar equations which allow a satisfactory theory of higher-dimensional Riemann problems. The first main result of this paper is a general framework for the study of higherdimensional Riemann problems for Hamilton-Jacobi equations. The purpose of the framework is to understand the structure of Hamilton-Jacobi wave interactions in an explicit and constructive manner. Specialized to two-dimensional Riemann problems (i.e., the intersection of cusp curves on surfaces imbedded in R 3), ...

Resin Transfer Molding (RTM), as a method for the manufacture of advanced fiber reinforced compos... more Resin Transfer Molding (RTM), as a method for the manufacture of advanced fiber reinforced composite materials, is attractive because it offers the possibility of lower manufacturing costs and more complex shapes than traditional methods. A major issue in this new manufacturing process is the elimination of void spaces in the resin fill operation, so that products with high quality are manufactured. Process modeling is particularly useful in understanding, designing, and optimizing the process conditions to achieve this goal. In this paper we report on our program with the Advanced Technology & Development Center at Northrop Grumman and demonstrate how modeling could improve the manufacturing process and enhance product quality. We review the manufacturing process and related issues and present a manufacturing process model, developed recently by the authors. This model is applied to study the formation and migration of air bubbles in the preform, a major RTM manufacturing problem, ...

This paper describes surface evolution formulated in terms of a Hamilton-Jacobi equation and a so... more This paper describes surface evolution formulated in terms of a Hamilton-Jacobi equation and a solution algorithm based on a three-dimensional front tracking algorithm. Our method achieves sharp resolution in the evolution of surface edges and corners. This study is motivated by semiconductor chip evolution during deposition and resputtering processes. For this reason, we discuss here the effects of diffuse rescattering on surface features. We illustrate some of the three-dimensional capabilities of the front tracking algorithm. We also present a validation study by display of two-dimensional cross sections of threedimensional simulations of a finite length trench. The cross sections correspond to twodimensional simulations of S. Hamaguchi and S. M. Rossnagel. Supported in part by the Applied Mathematics Subprogram of the U.S. Department of Energy DE-FG0290ER25084, the National Science Foundation grants DMS-9312098 and 9500568, and the Army Research Office grant DAAH04-95-10414. 1 ...

Resin Transfer Molding, as a method for the manufacture of advanced fiber reinforced composite ma... more Resin Transfer Molding, as a method for the manufacture of advanced fiber reinforced composite materials, is attractive because it offers the possibility of lower manufacturing costs and more complex shapes than the traditional manufacturing methods. A major issue in this new manufacturing process is the elimination of void spaces in the resin fill operation, so that products with high quality are manufactured. In this paper we present a two phase, two component air solubility model to study the formation and migration of the macro and micro voids. The numerical solutions of the model are obtained through a front tracking code. The front tracking method has the distinguishing feature of preserving sharp interfaces throughout the simulation. The results demonstrate that the model proposed here has desirable qualitative agreement with experimental results. Based on these results, we make numerical predictions to show how modeling could improve the manufacturing process and hence enhan...

The reduction of porosity is an important requirement in the manufacture of reliable composite co... more The reduction of porosity is an important requirement in the manufacture of reliable composite components. In the Resin Transfer Molding (RTM) process, porosity results from the formation and growth of gas bubbles during the fill and cure stages of the process. Understanding the dynamics of the formation and motion of these bubbles will allow design of RTM processes that provide optimum quality and performance. In this paper, we demonstrate that an unsaturated flow model for gas bubble migration is in qualitative agreement with experimental results. 1 INTRODUCTION The high cost of autoclave-processed composites has led to interest in alternative processing concepts. Resin transfer molding (RTM) is one particularly attractive technique for many applications since it combines cost savings with potential performance improvements (e.g., 3-D strength characteristics). In the past, tool design decisions, component design decisions, and processing cycles for composites have been devel- 1 T...

We consider the rational maps given by z 7 ! jzj 2 ?2 z 2 + c, for z and c complex and > 1 2 fixe... more We consider the rational maps given by z 7 ! jzj 2 ?2 z 2 + c, for z and c complex and > 1 2 fixed and real. The case = 1 corresponds to quadratic polynomials: some of the well-known results for this conformal case still hold for near 1, while others break down. Among the differences between the two cases are the possibility, for 6 = 1, of periodic attractors that do not attract the critical point, and the fact that for < 1 the Julia set is smooth for an open set of values of c. Numerical evidence suggests that the analogue of the Mandelbrot set for this family is connected, but not locally connected if 6 = 1.

Circle maps with a flat spot are studied which are differentiable, even on the boundary of the fl... more Circle maps with a flat spot are studied which are differentiable, even on the boundary of the flat spot. Estimates on the Lebesgue measure and the Hausdorff dimension of the non-wandering set are obtained. Also, a sharp transition is found from degenerate geometry similar to what was found earlier for non-differentiable maps with a flat spot to bounded geometry as in critical maps without a flat spot.

this paper. The semiconductor manufacturing industry has various codes for studying the two dimen... more this paper. The semiconductor manufacturing industry has various codes for studying the two dimensional problem: the evolution of cross-sections of trenches. For instance, a front tracking algorithm for moving curves in R

Abstract. We present a numerical model of two fluid mixing based on hyperbolic equations hav-ing ... more Abstract. We present a numerical model of two fluid mixing based on hyperbolic equations hav-ing complete state variables (velocity, pressure, temperature) for each fluid. The model is designed for the study of acceleration driven mixing layers in a chunk mix regime dominated by large scale coherent mixing structures. The numerical solution of the model is validated by comparison to the incompressible limit. For the purpose of this comparison, we present a newly obtained analytic solu-tion of the pressure equation for this model and an analytic constraint derived from the asymptotic limit of the compressible pressures, which determines uniquely the incompressible pressure solution. The numerical solution is also validated by a mesh convergence study.

Front Tracking is a methodology which uses computational geometry to provide numerical solutions ... more Front Tracking is a methodology which uses computational geometry to provide numerical solutions of enhanced quality for problems of computational physics. It is particularly applicable to the computation of solutions with important jump discontinuities, or fronts. Fronts are represented as lower dimensional data structures, which in the spirit of non-manifold geometries used in CAD systems, support surfaces, curves (at surface intersections) and nodes (at common intersection points of three surfaces). These are expressed in the front tracking algorithm as a simplicial complex: data structures representing non intersecting smooth objects of given dimension, and boundary and coboundary operators to link them to lower and higher dimensional smooth objects. In the solution to problems of computational physics, these fronts evolve and can change their topology, forcing the need for fast retriangulation, intersection detection, and intersection removal routines. The methodology has been ...