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29
An EnergyMinimizing Interpolation For Robust Multigrid Methods
 SIAM J. SCI. COMPUT
, 1998
"... We propose a robust interpolation for multigrid based on the concepts of energy minimization and approximation. The formulation is general; it can be applied to any dimensions. The analysis for one dimension proves that the convergence rate of the resulting multigrid method is independent of the coe ..."
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Cited by 47 (6 self)
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We propose a robust interpolation for multigrid based on the concepts of energy minimization and approximation. The formulation is general; it can be applied to any dimensions. The analysis for one dimension proves that the convergence rate of the resulting multigrid method is independent of the coefficient of the underlying PDE, in addition to being independent of the mesh size. We demonstrate numerically the effectiveness of the multigrid method in two dimensions by applying it to a discontinuous coefficient problem and an oscillatory coefficient problem. We also show using a onedimensional Helmholtz problem that the energy minimization principle can be applied to solving elliptic problems that are not positive definite.
Chaperonin function: folding by forced unfolding
 Science
, 1999
"... 24. AntiOVA (DO11.10) T cell receptor (TCR) transgenic lymph node cells (5 3 106 cells) were transferred to BALB/c mice that were immunized 1 day later with 100mg OVA in FreundÕs complete adjuvant (25). Draining (pool of brachial, axillary, and inguinal) and nondraining (mesenteric) lymph node cel ..."
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Cited by 36 (1 self)
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24. AntiOVA (DO11.10) T cell receptor (TCR) transgenic lymph node cells (5 3 106 cells) were transferred to BALB/c mice that were immunized 1 day later with 100mg OVA in FreundÕs complete adjuvant (25). Draining (pool of brachial, axillary, and inguinal) and nondraining (mesenteric) lymph node cells were isolated 1 to 5 days later and used in MDC chemotaxis assays. The frequency of OVAspeciÞc T cells that migrated was measured with the clonotypic antibody to TCR KJ126 (28). Overnight incubation of day 2 draining lymph node cells (at 107 cells/ml) in medium containing interleukin2 (IL2) (4 ng/ml) increased the sensitivity of activated KJ1261 cells to MDC (14). Therefore, IL2—cultured cells were used in experiments to detect chemokine production by puriÞed lymph node DCs and stromal cells.
An Odyssey Into Local Refinement And Multilevel Preconditioning I: Optimality Of . . .
 SIAM J. NUMER. ANAL
, 2002
"... In this article, we examine the BramblePasciakXu (BPX) preconditioner in the setting of local 2D and 3D mesh refinement. While the available optimality results for the BPX preconditioner have been constructed primarily in the setting of uniformly refined meshes, a notable exception is the 2D resul ..."
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Cited by 26 (14 self)
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In this article, we examine the BramblePasciakXu (BPX) preconditioner in the setting of local 2D and 3D mesh refinement. While the available optimality results for the BPX preconditioner have been constructed primarily in the setting of uniformly refined meshes, a notable exception is the 2D result due to Dahmen and Kunoth, which established BPX optimality on meshes produced by a restricted class of local 2D redgreen refinement. The purpose of this article is to extend the original 2D DahmenKunoth result to several additional types of local 2D and 3D redgreen (conforming) and red (nonconforming) refinement procedures. The extensions are accomplished through a 3D extension of the 2D framework in the original DahmenKunoth work, by which the question of optimality is reduced to establishing that locally enriched finite element subspaces allow for the construction of a scaled basis which is formally Riesz stable. This construction in turn rests entirely on establishing a number of geometrical properties between neighboring simplices produced by the local refinement algorithms. These properties are then used to build Rieszstable scaled bases for use in the BPX optimality framework. Since the theoretical framework supports arbitrary spatial dimension d 1, we indicate clearly which geometrical properties, established here for several 2D and 3D local refinement procedures, must be reestablished to show BPX optimality for spatial dimension 4. Finally, we also present a simple alternative optimality proof of the BPX preconditioner on quasiuniform meshes in two and three spatial dimensions, through the use of Kfunctionals and H stability of L 2 projection for s 1. The proof techniques we use are quite general; in particular, the results require no smoothnes...
Macroscopic Evolution of Particle Systems with Short and Long Range
, 2000
"... We consider a lattice gas with general short range interactions and a Kac potential Jγ(r) of range γ −1, γ> 0, evolving via particles hopping to nearest neighbor empty sites with rates which satisfy detailed balance with respect to the equilibrium measure. Scaling space like γ −1 and time like γ ..."
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Cited by 12 (0 self)
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We consider a lattice gas with general short range interactions and a Kac potential Jγ(r) of range γ −1, γ> 0, evolving via particles hopping to nearest neighbor empty sites with rates which satisfy detailed balance with respect to the equilibrium measure. Scaling space like γ −1 and time like γ −2, we prove that in the limit γ → 0 the macroscopic density profile ρ(r, t) satisfies the equation ρ(r, t) = ∇ ·
Stimulusdriven traveling solutions in continuum neuronal models with a general smooth firing rate function
 SIAM J. Appl. Math
"... Abstract. We examine the existence of traveling wave solutions for a continuum neuronal network modeled by integrodifferential equations. First, we consider a scalar field model with a general smooth firing rate function and a spatiotemporally varying stimulus. We prove that a traveling front solut ..."
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Cited by 11 (1 self)
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Abstract. We examine the existence of traveling wave solutions for a continuum neuronal network modeled by integrodifferential equations. First, we consider a scalar field model with a general smooth firing rate function and a spatiotemporally varying stimulus. We prove that a traveling front solution that is locked to the stimulus exists for a certain interval of stimulus speeds. Next, we include a slow adaptation equation and obtain a formula, which involves a certain adjoint solution, for the stimulus speeds that induce locked traveling pulse solutions. Further, we use singular perturbation analysis to characterize an approximation to the adjoint solution that we compare to a numerically computed adjoint. Numerical simulations are used to illustrate the traveling fronts and pulses that we study and to make comparisons with our analytically computed bounds for stimuluslocked wave behavior.
A guidingcenter FokkerPlanck collision operator for nonuniform magnetic fields, Phys. Plasmas 11
, 2004
"... A new formulation for collisional kinetic theory is presented based on the use of Lietransform methods to eliminate fast orbital time scales from a general bilinear collision operator. As an application of this new formalism, a general guidingcenter bilinear FokkerPlanck (FP) collision operator is ..."
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Cited by 6 (0 self)
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A new formulation for collisional kinetic theory is presented based on the use of Lietransform methods to eliminate fast orbital time scales from a general bilinear collision operator. As an application of this new formalism, a general guidingcenter bilinear FokkerPlanck (FP) collision operator is derived following the elimination of the fast gyromotion time scale of a charged particle moving in a nonuniform magnetic field. It is expected that classical transport processes in a strongly magnetized nonuniform plasma can, thus, be described in terms of this reduced guidingcenter FP kinetic theory. The present paper introduces the reducedcollision formalism only while its applications are left to future work. PACS numbers: 52.25.Dg, 52.25.Fi, 52.20.Dq 1 I.
Scalable and Multilevel Iterative Methods
, 1998
"... In this dissertation, we analyze three classes of iterative methods which are often used as preconditioners for Krylov subspace methods, for the solution of large and sparse linear systems arising from the discretization of partial differential equations. In addition, we propose algorithms for imag ..."
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Cited by 6 (1 self)
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In this dissertation, we analyze three classes of iterative methods which are often used as preconditioners for Krylov subspace methods, for the solution of large and sparse linear systems arising from the discretization of partial differential equations. In addition, we propose algorithms for image processing applications and multiple righthand side problems. The first class is the incomplete LU factorization preconditioners, an intrinsic sequential algorithm. We develop a parallel implementation of ILU(0) and devise a strategy for a priori memory allocation crucial for ILU(k) parallelization. The second class is the sparse approximate inverse (SPAI) preconditioners. We improve and extend its applicability to elliptic PDEs by using wavelets which converts smoothness, often found in the Green's function...
An EnergyMinimizing Interpolation For Multigrid Methods
 Stanford University, Juli
, 1997
"... . We shall study multigrid methods from energy minimizations and approximations. Through the analysis of an multigrid method in 1D, we introduce the concepts of stability and the approximation property in the classical theory. Based on them, we derive an energyminimizing interpolation and present a ..."
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Cited by 5 (0 self)
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. We shall study multigrid methods from energy minimizations and approximations. Through the analysis of an multigrid method in 1D, we introduce the concepts of stability and the approximation property in the classical theory. Based on them, we derive an energyminimizing interpolation and present a two level analysis for it. Issues on coarsening are also addressed. Finally, we demonstrate the effectiveness of the multigrid method by applying it to unstructured grids computations and discontinuous coefficient problems. 1. Introduction. Multigrid methods have been widely used as an efficient solver for second order elliptic PDE's yet it is still not completely understood. This is partially revealed by the poor convergence of the standard multigrid methods applying to PDE's whose coefficients are anisotropic [16], discontinuous [1, 6, 9] or oscillatory [12, 31]. Special techniques, for instance, block smoothing [6], semicoarsening [10, 30], matrixdependent interpolations [24, 26], fre...
The Tricontinuous Double Gyroid Cubic Phase in Triblock Copolymers of the ABA Type, submitted to Macromolecules
"... ABSTRACT: We report the synthesis and morphological characterization of two triblock copolymers of the ABA type, where A is polystyrene (PS) and B polyisoprene (PI). The volume fraction of the minority component, PS or PI, is approximately 1/3. Cubic microdomain morphologies, already found in diblo ..."
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Cited by 3 (1 self)
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ABSTRACT: We report the synthesis and morphological characterization of two triblock copolymers of the ABA type, where A is polystyrene (PS) and B polyisoprene (PI). The volume fraction of the minority component, PS or PI, is approximately 1/3. Cubic microdomain morphologies, already found in diblock and star block copolymers with the same composition range, are observed for the first time in the case of linear triblock copolymers. The two ABA triblocks are on opposite sides of the phase diagram, which signifies that both the A end blocks and the B midblock are capable of forming the interconnected double network structure. Investigation of the morphology was done via birefringence, smallangle Xray scattering (SAXS), and transmission electron microscopy (TEM). Birefringence measurements showed each triblock structure to have isotropic optical properties. The characteristic ratio of the observed Bragg peaks, q2/q1, was approximately 4/ 3 for each sample, indicating a set of eight possible cubic space groups. TEM data showed an interconnected tricontinuous microdomain structure. Since the two triblocks have essentially complementary structures (PS ) 0.32 in one and PI ) 0.36 in the other), the TEM images of OsO4stained thin sections are complementary and the diffraction patterns of the images are approximately equal according to Babinet's principle. Examination of highsymmetry projections demonstrated p6mm, p4mm, and c2mm symmetry present in the TEM images. Comparison with the 〈111〉, 〈100〉, and 〈110〉 projections of the eight cubic space groups satisfying the SAXS data eliminated all but the Fm3 hm and Ia3 hd groups as possible structures. Due to the observed connectivity of the structure, the Fm3 hm structure could be eliminated by inspection of possible network structures and the resultant symmetries. Computer simulations of a model structure (double gyroid) based on level surfaces with Ia3 hd symmetry and their Fourier transforms showed excellent agreement with the highsymmetry projections and their respective optical transforms.
A lightweight authentication protocol with local security association control in mobile networks
 in Proc. IEEE MILCOM’04
, 2004
"... Abstract — In this paper, we propose a new lightweight authentication protocol with local security association (SA) control to locally authenticate an interdomain roaming user efficiently based on its mobility and traffic patterns in mobile networks. We first design a protocol to establish a local ..."
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Abstract — In this paper, we propose a new lightweight authentication protocol with local security association (SA) control to locally authenticate an interdomain roaming user efficiently based on its mobility and traffic patterns in mobile networks. We first design a protocol to establish a local SA for authenticating the roaming user securely. Then, in order to determine the life time for the local SA, an authentication cost function is proposed to evaluate the authentication efficiency with the concern of risk, mobility and traffic patterns. The optimal life time of the local SA is determined by minimizing the authentication cost function. The performance of the proposed protocol is analyzed with respect to authentication cost under different mobility and traffic patterns. Comparing to DIAMETER, the proposed approach outperforms DIAMETER for macromobility users with high volume of authentication requests. Key Words: Mobile networks, authentication, security association.