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25
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 27 (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...
Role of van der Waals interaction in forming moleculemetal junctions: flat organic molecules
 on the Au(111) surface. PHYSICAL CHEMISTRY CHEMICAL PHYSICS 2010
"... The selfassembly of flat organic molecules on metal surfaces is controlled, apart from the kinetic factors, by the interplay between the molecule–molecule and molecule–surface interactions. These are typically calculated using standard density functional theory within the generalized gradient appro ..."
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Cited by 2 (0 self)
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The selfassembly of flat organic molecules on metal surfaces is controlled, apart from the kinetic factors, by the interplay between the molecule–molecule and molecule–surface interactions. These are typically calculated using standard density functional theory within the generalized gradient approximation, which significantly underestimates nonlocal correlations, i.e. van der Waals (vdW) contributions, and thus affects interactions between molecules and the metal surface in the junction. In this paper we address this question systematically for the Au(111) surface and a number of popular flat organic molecules which form directional hydrogen bonds with each other. This is done using the recently developed firstprinciples vdWDF method which takes into account the nonlocal nature of electron correlation [M. Dion et al., Phys. Rev. Lett. 2004, 92, 246401]. We report here a systematic study of such systems involving completely selfconsistent vdWDF calculations with full geometry relaxation. We find that the hydrogen bonding between the molecules is only insignificantly affected by the vdW contribution, both in the gas phase and on the gold surface. However, the adsorption energies of these molecules on the surface increase dramatically as compared with the ordinary density functional (within the generalized gradient approximation, GGA) calculations, in agreement with available experimental data and previous
HEAVY QUARKS IN THE QUARKGLUON PLASMA
, 2009
"... Heavyflavor particles are believed to provide valuable probes of the medium produced in ultrarelativistic collisions of heavy nuclei. In this article we review recent progress in our understanding of the interactions of charm and bottom quarks in the QuarkGluon Plasma (QGP). For individual heavy q ..."
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Cited by 1 (0 self)
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Heavyflavor particles are believed to provide valuable probes of the medium produced in ultrarelativistic collisions of heavy nuclei. In this article we review recent progress in our understanding of the interactions of charm and bottom quarks in the QuarkGluon Plasma (QGP). For individual heavy quarks, we focus on elastic interactions for which the large quark mass enables a Brownian motion treatment. This opens a unique access to thermalization mechanisms for heavy quarks at low momentum, and thus to their transport coefficients in the quarkgluon fluid. Different approaches to evaluate heavyquark diffusion are discussed and compared, including perturbative QCD, effective potential models utilizing input from lattice QCD and stringtheoretic estimates in conformal field theories. Applications to heavyquark observables in heavyion collisions are realized via relativistic Langevin simulations, where we illustrate the important role of a realistic medium evolution to quantitatively extract the heavyquark diffusion constant. In the heavy quarkonium sector, we briefly review the current status in potentialmodel based interpretations of correlation functions computed in lattice QCD, followed by an evaluation of quarkonium dissociation reactions in the QGP. The discussion of the phenomenology in heavyion reactions focuses on thermal model frameworks paralleling the open heavyflavor sector. We also emphasize connections to the heavyquark diffusion problem in both potential models and quarkonium regeneration processes. 1.