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Didina Serban - One of the best experts on this subject based on the ideXlab platform.
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determinant formula for the Octagon form factor in n 4 supersymmetric yang mills theory
Physical Review Letters, 2019Co-Authors: Ivan Kostov, V B Petkova, Didina SerbanAbstract:We present a closed expression for the Octagon form factor which appears as a building block in a class of four-point correlation functions in N=4 supersymmetric Yang-Mills theory considered recently by Coronado. The Octagon form factor is expressed, to all loop orders, as the determinant of a semi-infinite matrix. We find that perturbatively at weak coupling the entries of this matrix are linear combinations of ladder functions with simple rational coefficients.
Fei Duan - One of the best experts on this subject based on the ideXlab platform.
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wetting transition at a threshold surfactant concentration of evaporating sessile droplets on a patterned surface
Langmuir, 2019Co-Authors: Kian Soo Ong, Xin Zhong, Junheng Ren, Karen Siewling Chong, Fei DuanAbstract:Wetting transitions induced by varying the components in a solution of a drying droplet can lead to its evolving shape on a textured surface. It can provide new insights on liquid pattern control through manipulating droplet solutions. We show the pronounced transitions of wetting for surfactant solution droplets drying on a micropyramid-patterned surface. At low initial surfactant concentrations, the droplet maintains an Octagonal shape until the end of drying. At intermediate initial surfactant concentrations, the early Octagon spreads to a square, which later evolves to a stretched rectangle. At high initial surfactant concentrations, the droplet mainly exhibits the “Octagon-to-square” transition, and the square shape is maintained until the end. The Octagon-to-square transition occurs at similar temporal volume-averaged surfactant concentrations for the various initial surfactant concentrations. It results from the dependence of the surface energy change of spread over the micropyramid structure on th...
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Wetting Transition at a Threshold Surfactant Concentration of Evaporating Sessile Droplets on a Patterned Surface
2019Co-Authors: Xin Zhong, Kian Soo Ong, Junheng Ren, Karen Siewling Chong, Fei DuanAbstract:Wetting transitions induced by varying the components in a solution of a drying droplet can lead to its evolving shape on a textured surface. It can provide new insights on liquid pattern control through manipulating droplet solutions. We show the pronounced transitions of wetting for surfactant solution droplets drying on a micropyramid-patterned surface. At low initial surfactant concentrations, the droplet maintains an Octagonal shape until the end of drying. At intermediate initial surfactant concentrations, the early Octagon spreads to a square, which later evolves to a stretched rectangle. At high initial surfactant concentrations, the droplet mainly exhibits the “Octagon-to-square” transition, and the square shape is maintained until the end. The Octagon-to-square transition occurs at similar temporal volume-averaged surfactant concentrations for the various initial surfactant concentrations. It results from the dependence of the surface energy change of spread over the micropyramid structure on the temporal volume-averaged surfactant concentration. At high initial surfactant concentrations, the accumulation of the surfactant near the contact line driven by outward flows could raise the local viscosity and enhance the pinning effect, leading to the great suppression of the “square-to-rectangle” transition
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Octagon to square wetting area transition of water ethanol droplets on a micropyramid substrate by increasing ethanol concentration
Langmuir, 2017Co-Authors: Huicheng Feng, Karen S. L. Chong, Kian Soo Ong, Fei DuanAbstract:The wettability and evaporation of water–ethanol binary droplets on the substrate with micropyramid cavities are studied by controlling the initial ethanol concentrations. The droplets form Octagonal initial wetting areas on the substrate. As the ethanol concentration increases, the side ratio of the initial wetting Octagon increases from 1.5 at 0% ethanol concentration to 3.5 at 30% ethanol concentration. The increasing side ratio indicates that the wetting area transforms from an Octagon to a square if we consider the Octagon to be a square with its four corners cut. The droplets experience a pinning–depinning transition during evaporation. The pure water sessile droplet evaporation demonstrates three stages from the constant contact line (CCL) stage, and then the constant contact angle (CCA) stage, to the mixed stage. An additional mixed stage is found between the CCL and CCA stages in the evaporation of water–ethanol binary droplets due to the anisotropic depinning along the two different axes of symm...
Ivan Kostov - One of the best experts on this subject based on the ideXlab platform.
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Octagon with finite bridge: free fermions and determinant identities
'Springer Science and Business Media LLC', 2021Co-Authors: Ivan Kostov, Valentina B. PetkovaAbstract:Abstract We continue the study of the Octagon form factor which helps to evaluate a class of four-point correlation functions in N $$ \mathcal{N} $$ = 4 SYM theory. The Octagon is characterised, besides the kinematical parameters, by a “bridge” of ℓ propagators connecting two nonadjacent operators. In this paper we construct an operator representation of the Octagon with finite bridge as an expectation value in the Fock space of free complex fermions. The bridge ℓ appears as the level of filling of the Dirac sea. We obtain determinant identities relating Octagons with different bridges, which we derive from the expression of the Octagon in terms of discrete fermionic oscillators. The derivation is based on the existence of a previously conjectured similarity transformation, which we find here explicitly
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determinant formula for the Octagon form factor in n 4 supersymmetric yang mills theory
Physical Review Letters, 2019Co-Authors: Ivan Kostov, V B Petkova, Didina SerbanAbstract:We present a closed expression for the Octagon form factor which appears as a building block in a class of four-point correlation functions in N=4 supersymmetric Yang-Mills theory considered recently by Coronado. The Octagon form factor is expressed, to all loop orders, as the determinant of a semi-infinite matrix. We find that perturbatively at weak coupling the entries of this matrix are linear combinations of ladder functions with simple rational coefficients.
Xin Zhong - One of the best experts on this subject based on the ideXlab platform.
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wetting transition at a threshold surfactant concentration of evaporating sessile droplets on a patterned surface
Langmuir, 2019Co-Authors: Kian Soo Ong, Xin Zhong, Junheng Ren, Karen Siewling Chong, Fei DuanAbstract:Wetting transitions induced by varying the components in a solution of a drying droplet can lead to its evolving shape on a textured surface. It can provide new insights on liquid pattern control through manipulating droplet solutions. We show the pronounced transitions of wetting for surfactant solution droplets drying on a micropyramid-patterned surface. At low initial surfactant concentrations, the droplet maintains an Octagonal shape until the end of drying. At intermediate initial surfactant concentrations, the early Octagon spreads to a square, which later evolves to a stretched rectangle. At high initial surfactant concentrations, the droplet mainly exhibits the “Octagon-to-square” transition, and the square shape is maintained until the end. The Octagon-to-square transition occurs at similar temporal volume-averaged surfactant concentrations for the various initial surfactant concentrations. It results from the dependence of the surface energy change of spread over the micropyramid structure on th...
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Wetting Transition at a Threshold Surfactant Concentration of Evaporating Sessile Droplets on a Patterned Surface
2019Co-Authors: Xin Zhong, Kian Soo Ong, Junheng Ren, Karen Siewling Chong, Fei DuanAbstract:Wetting transitions induced by varying the components in a solution of a drying droplet can lead to its evolving shape on a textured surface. It can provide new insights on liquid pattern control through manipulating droplet solutions. We show the pronounced transitions of wetting for surfactant solution droplets drying on a micropyramid-patterned surface. At low initial surfactant concentrations, the droplet maintains an Octagonal shape until the end of drying. At intermediate initial surfactant concentrations, the early Octagon spreads to a square, which later evolves to a stretched rectangle. At high initial surfactant concentrations, the droplet mainly exhibits the “Octagon-to-square” transition, and the square shape is maintained until the end. The Octagon-to-square transition occurs at similar temporal volume-averaged surfactant concentrations for the various initial surfactant concentrations. It results from the dependence of the surface energy change of spread over the micropyramid structure on the temporal volume-averaged surfactant concentration. At high initial surfactant concentrations, the accumulation of the surfactant near the contact line driven by outward flows could raise the local viscosity and enhance the pinning effect, leading to the great suppression of the “square-to-rectangle” transition
Hongseok Yang - One of the best experts on this subject based on the ideXlab platform.
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Learning analysis strategies for Octagon and context sensitivity from labeled data generated by static analyses
Formal Methods in System Design, 2018Co-Authors: Kihong Heo, Hongseok YangAbstract:We present a method for automatically learning an effective strategy for clustering variables for the Octagon analysis from a given codebase. This learned strategy works as a preprocessor of Octagon. Given a program to be analyzed, the strategy is first applied to the program and clusters variables in it. We then run a partial variant of the Octagon analysis that tracks relationships among variables within the same cluster, but not across different clusters. The notable aspect of our learning method is that although the method is based on supervised learning, it does not require manually-labeled data. The method does not ask human to indicate which pairs of program variables in the given codebase should be tracked. Instead it uses the impact pre-analysis for Octagon from our previous work and automatically labels variable pairs in the codebase as positive or negative. We implemented our method on top of a static buffer-overflow detector for C programs and tested it against open source benchmarks. Our experiments show that the partial Octagon analysis with the learned strategy scales up to 100KLOC and is 33 $$\times $$ × faster than the one with the impact pre-analysis (which itself is significantly faster than the original Octagon analysis), while increasing false alarms by only 2%. The general idea behind our methodis applicable to other types of static analyses as well. We demonstrate that our method is also effective to learn a strategy for context-sensitivity of interval analysis.
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learning a variable clustering strategy for Octagon from labeled data generated by a static analysis
Static Analysis Symposium, 2016Co-Authors: Kihong Heo, Hongseok YangAbstract:We present a method for automatically learning an effective strategy for clustering variables for the Octagon analysis from a given codebase. This learned strategy works as a preprocessor of Octagon. Given a program to be analyzed, the strategy is first applied to the program and clusters variables in it. We then run a partial variant of the Octagon analysis that tracks relationships among variables within the same cluster, but not across different clusters. The notable aspect of our learning method is that although the method is based on supervised learning, it does not require manually-labeled data. The method does not ask human to indicate which pairs of program variables in the given codebase should be tracked. Instead it uses the impact pre-analysis for Octagon from our previous work and automatically labels variable pairs in the codebase as positive or negative. We implemented our method on top of a static buffer-overflow detector for C programs and tested it against open source benchmarks. Our experiments show that the partial Octagon analysis with the learned strategy scales up to 100KLOC and is 33x faster than the one with the impact pre-analysis (which itself is significantly faster than the original Octagon analysis), while increasing false alarms by only 2 %.
