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Computation of Minimum Energy Paths for Quasi-Linear Problems

JOURNAL OF SCIENTIFIC COMPUTING 2011年第2期49卷 180-194页

作者： Chamard, Jeremy Otta, Josef Lloyd, David J. B. Univ Surrey Dept Math Guildford GU2 7XH Surrey England Univ W Bohemia Dept Math Plzen 30614 Czech Republic

We investigate minimum energy paths of the quasi-linear problem with the p-Laplacian operator and a double-well potential. We adapt the string method of E, Ren, and Vanden-Eijnden (J. Chem. Phys. 126, 2007) to locate saddle-type solutions. In one-dimension, the string method is shown to find a minimum energy path that can align along one-dimensional "ridges" of saddle-continua. We then apply the same method to locate saddle solutions and transition paths of the two-dimensional quasi-linear problem. The method developed is applicable to a general class of quasi-linear PDEs.

关键词： p-Laplacian string method Mountain pass algorithm

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A numerical method for the study of nucleation of ordered phases

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JOURNAL OF COMPUTATIONAL PHYSICS 2010年第5期229卷 1797-1809页

作者： Lin, Ling Cheng, Xiuyuan E, Weinan Shi, An-Chang Zhang, Pingwen Peking Univ Sch Math Sci Beijing 100871 Peoples R China Peking Univ LMAM Beijing 100871 Peoples R China Princeton Univ Dept Math Princeton NJ 08544 USA Princeton Univ PACM Princeton NJ 08544 USA McMaster Univ Dept Phys & Astron Hamilton ON L8S 4M1 Canada

A numerical approach based on the string method is developed to study nucleation of ordered phases in first-order phase transitions. Among other things, this method allows an efficient computation of the minimum energy path (MEP) during the nucleation process. The MEP provides information about the size, shape and free energy barrier of the critical nucleus. To improve the efficiency of the string method, a special initialization process is proposed. Constraints from physical models are treated using two methods, a generalized coordinates method and a projection method. Strategies for choosing the computational domain and defining the nucleus boundary are also introduced. The validity of our approach is illustrated by two nontrivial examples from soft condensed matter physics, namely the nematic-isotropic transition of liquid crystals and the ordered-to-ordered phase transition of diblock copolymers. (C) 2009 Elsevier Inc. All rights reserved.

关键词： Nucleation Ordered phase Critical nuclei Minimum energy path (MEP) string method Liquid crystal Block copolymer

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Unveiling the Mechanist i c Singulariti e s of Caspases: A Computational Analysis of the Reaction Mechanism in Human Caspase-1

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ACS CATALYSIS 2023年第7期13卷 4348-4361页

作者： Ramos-Guzman, Carlos A. . Ruiz-Pernia, J. Javier Zinovjev, Kirill Tunon, Inaki Univ Valencia Dept Quim Fis Burjassot 46100 Spain Univ Jaume 1 Inst Mat Avanzados Castellon de La Plana 12071 Spain

Caspases are cysteine proteases in charge of breaking a peptide bond next to an aspartate residue. Caspases constitute an important family of enzymes involved in cell death and inflammatory processes. A plethora of diseases, including neurological and metabolic diseases and cancer, are associated with the poor regulation of caspase-mediated cell death and inflammation. Human caspase-1 in particular carries out the transformation of the pro-inflammatory cytokine pro-interleukin-1 beta into its active form, a key process in the inflammatory response and then in many diseases, such as Alzheimer's disease. Despite its importance, the reaction mechanism of caspases has remained elusive. The standard mechanistic proposal valid for other cysteine proteases and that involves the formation of an ion pair in the catalytic dyad is not supported by experimental evidence. Using a combination of classical and hybrid DFT/MM simulations, we propose a reaction mechanism for the human caspase-1 that explains experimental observations, including mutagenesis, kinetic, and structural data. In our mechanistic proposal, the catalytic cysteine, Cys285, is activated after a proton transfer to the amide group of the scissile peptide bond, a process facilitated by hydrogen-bond interactions with Ser339 and His237. The catalytic histidine does not directly participate in any proton transfer during the reaction. After formation of the acylenzyme intermediate, the deacylation step takes place through the activation of a water molecule by the terminal amino group of the peptide fragment formed during the acylation step. The overall activation free energy obtained from our DFT/MM simulations is in excellent agreement with the value derived from the experimental rate constant, 18.7 vs 17.9 kcal center dot mol-1, respectively. Simulations of the H237A mutant support our conclusions and agree with the reported reduced activity observed for this caspase-1 variant. We propose that this mechanism can ex

关键词： caspase-1 cysteine proteases CD clan reaction mechanism minimum free energy path QM MM string method

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Directed Self-Assembly of Linear Arrays of Block Copolymer Cylinders

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JOURNAL OF POLYMER SCIENCE PART B-POLYMER PHYSICS 2015年第5期53卷 317-326页

作者： Laachi, Nabil Iwama, Tatsuhiro Delaney, Kris T. Shykind, David Weinheimer, Corey J. Fredrickson, Glenn H. Univ Calif Santa Barbara Mat Res Lab Santa Barbara CA 93106 USA Intel Corp Hillsboro OR 97124 USA

We investigate the directed self-assembly (DSA) of cylinder-forming block copolymers inside extended guiding templates of different sizes and shapes. We focus in particular on templates that promote the formation of linear arrays of two or three cylinders for contact hole multiplication. Using self-consistent field theory (SCFT) simulations, we uncover the existence windows for two- and three-cylinder arrays and assess their stability relative to other defective morphologies present in the templates. From SCFT simulations, templates in which three DSA cylinders are the lowest free energy configuration are more prone to defective morphologies in comparison to narrower templates with a two cylinder ground state. The size, placement and pitch of the defect-free structures are estimated for different template sizes and shapes. Beyond the thermodynamic description of the self-assembly process and the ensuing equilibrium properties, we also consider the equally important issue of the kinetics of melting of defects into perfect structures. Using the string method, we compute the most probable kinetic pathways that anneal elementary defects into a desired perfect array of cylinders. Similar to our findings on defectivity levels, defects in three-cylinder-friendly templates are associated with high kinetic barriers > 8 kT while their counterparts in narrower templates more readily dissipate into two-cylinder states after crossing barriers < 2 kT. (c) 2014 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys. 2015, 53, 317-326

关键词： Computer Modeling contact hole multiplication cylinder-forming block copolymers Diblock copolymers directed self-assembly self-consistent field theory Statistical thermodynamics string method transition pathways VIA Lithography

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Self-Consistent Field Theory Investigation of Directed Self-Assembly in Cylindrical Confinement

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JOURNAL OF POLYMER SCIENCE PART B-POLYMER PHYSICS 2015年第2期53卷 142-153页

作者： Laachi, Nabil Delaney, Kris T. Kim, Bongkeun Hur, Su-Mi Bristol, Robert Shykind, David Weinheimer, Corey J. Fredrickson, Glenn H. Univ Calif Santa Barbara Mat Res Lab Santa Barbara CA 93106 USA Univ Calif Santa Barbara Dept Chem Engn Santa Barbara CA 93106 USA Intel Corp Hillsboro OR 97124 USA

We use self-consistent field theory to study the self-assembly of cylinder-forming diblock copolymers confined in a cylindrical prepattern. This situation arises in contact holesthe hole shrink problemwhere the goal is to produce a cylindrical hole with reduced dimensions relative to a guiding prepattern. In this study, we focus on systems with a critical prepattern dimension ranging from 50 nm to 100 nm that consequently lead to the formation of a single cylinder in the middle of the hole. We find that a variety of defect morphologies arise from the self-assembly process and are strongly governed by the prepattern dimensions, wetting conditions as well as the polymer molecular weight. We also consider blends of diblock copolymers and homopolymers and determine optimal blending configurations that not only favor the formation of the desired cylindrical morphology but also extend the processing window relative to the pure diblock case. When defective structures form inside the prepattern, we compute their formation energy and use the string method to examine the kinetic pathways for the transition from the defective state to the perfect cylindrical state. (c) 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015, 53, 142-153

关键词： computer modeling contact holes diblock copolymers directed self-assembly graphoepitaxy hole shrink problem self-assembly self-consistent field theory string method vertical interconnect access lithography

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Harmonic Fourier beads method for studying rare events on rugged energy surfaces

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JOURNAL OF CHEMICAL PHYSICS 2006年第17期125卷 174108,1-7页

作者： Khavrutskii, Ilja V. Arora, Karunesh Brooks, Charles L., III Scripps Res Inst Dept Mol Biol La Jolla CA 92037 USA

We present a robust, distributable method for computing minimum free energy paths of large molecular systems with rugged energy landscapes. The method, which we call harmonic Fourier beads (HFB), exploits the Fourier representation of a path in an appropriate coordinate space and proceeds iteratively by evolving a discrete set of harmonically restrained path points-beads-to generate positions for the next path. The HFB method does not require explicit knowledge of the free energy to locate the path. To compute the free energy profile along the final path we employ an umbrella sampling method in two generalized dimensions. The proposed HFB method is anticipated to aid the study of rare events in biomolecular systems. Its utility is demonstrated with an application to conformational isomerization of the alanine dipeptide in gas phase. (c) 2006 American Institute of Physics.

关键词： CLASSICAL STATISTICAL-MECHANICS NUDGED ELASTIC BAND MOLECULAR-DYNAMICS REACTION PATHS TRANSITION-STATES CONFORMATIONAL TRANSITIONS FUNCTIONAL TRANSITIONS FINITE-TEMPERATURE string method CONSTRAINTS

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Hyperbolic periodic orbits in nongradient systems and small-noise-induced metastable transitions

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PHYSICA D-NONLINEAR PHENOMENA 2018年 363卷 1-17页

作者： Tao, Molei Georgia Inst Technol Sch Math Atlanta GA 30332 USA

Small noise can induce rare transitions between metastable states, which can be characterized by Maximum Likelihood Paths (MLPs). Nongradient systems contrast gradient systems in that MLP does not have to cross the separatrix at a saddle point, but instead possibly at a point on a hyperbolic periodic orbit. A numerical approach for identifying such unstable periodic orbits is proposed based on string method. In a special class of nongradient systems ('orthogonal-type'), there are provably local MLPs that cross such saddle point or hyperbolic periodic orbit, and the separatrix crossing location determines the associated local maximum of transition rate. In general cases, however, the separatrix crossing may not determine a unique local maximum of the rate, as we numerically observed a counter-example in a sheared 2D-space Allen-Cahn SPDE. It is a reasonable conjecture that there are always local MLPs associated with each attractor on the separatrix, such as saddle point or hyperbolic periodic orbit;our numerical experiments did not disprove so. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Freidlin-Wentzell large deviation theory Nongradient systems Hyperbolic periodic orbit Heteroclinic orbit string method gMAM

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Proposal of a Multistate Memory Using Voltage Controlled Magnetic Anisotropy of a Cross-Shaped Ferromagnet

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IEEE TRANSACTIONS ON NANOTECHNOLOGY 2015年第5期14卷 883-888页

作者： Pramanik, Tanmoy Roy, Urmimala Register, Leonard F. Banerjee, Sanjay K. Univ Texas Austin Microelect Res Ctr Austin TX 78758 USA

Voltage controlled magnetic anisotropy (VCMA)-induced precessional magnetization dynamics of a cross-shaped ferromagnet (FM) is studied by micromagnetic simulation. A cross-shaped FM, which has four minima in its energy landscape, can be used to store two bits. We show that, by selecting appropriate dimensions and taking into account interfacial perpendicular magnetic anisotropy, the cross-shaped FM can be switched from one state to the other states using VCMA, while the in-plane component of magnetization provides multistate functionality. VCMA-induced switching provides a low-power alternative to spin-transfer-torque switching of a similar cross-shaped FM studied previously. We estimate the thermal stability using the string method to capture the complex micromagnetic nature of the switching along the minimum energy path. The results could be useful toward development of a low-power multistate nonvolatile memory.

关键词： Multistate memory shape anisotropy string method voltage controlled magnetic anisotropy

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A temperature-based method for determination of the two-dimensional trajectory of an air jet

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BUILDING AND ENVIRONMENT 2005年第10期40卷 1323-1328页

作者： Özcan, SE Vranken, E Berckmans, D Lab Agr Bldg Res B-3001 Heverlee Belgium

In previous studies, a temperature based, arc-shaped airflow pattern (AFP) sensor positioned downstream of inlet opening was developed to measure and control the trajectory of an air jet in mechanically ventilated buildings. Image analysis using smoke was used as a reference technique for quantification of the airflow pattern. However, for further development and validation of the AFP sensor in real installations, such as livestock houses, smoke experiments are not practical since they do not allow continuous measurements. Therefore a new, temperature-based reference method was developed to determine the trajectory of an incoming cold air jet in a mechanically ventilated room. The experimental set-up consists of two strings with six thermocouples that are placed vertically against the direction of the flow. The basic principle is that the cold air passing through these strings creates a coldest zone on each. A curve is fit through these coldest points on the strings and inlet direction, representing the centreline of the flow pattern. This curve was compared with the one that was determined by smoke experiments in a real scale test facility (SE = 0.84 m). Afterwards, a model was constructed to estimate the airflow pattern from the AFP sensor (R-2 = 0.85, SE = 0.51 m). (c) 2004 Elsevier Ltd. All rights reserved.

关键词： airflow pattern image analysis string method temperature sensor mechanical ventilation

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A mean field approach of nucleation

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SCRIPTA MATERIALIA 2012年第1期67卷 77-80页

作者： Philippe, T. Blavette, D. Univ Rouen GPM UMR CNRS 6634 F-76801 St Etienne De Rouvray France Inst Univ France Paris France

The nucleation pathway in binary solid solution was investigated using mean field theory coupled to the string method. The string method has been used to locate the minimum free energy pathway for thermally activated nucleation, i.e. the most probable path for the phase transition. The overall behaviour of the system and the properties of the nucleus, composition and size were found to be in good agreement with other non-classical nucleation theories. It was found that the size of the critical nucleus diverges near the spinodal line. (C) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

关键词： Mean field Nucleation string method Minimum free energy path

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