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M Coppey - One of the best experts on this subject based on the ideXlab platform.
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Lattice Theory of trapping reactions with mobile species.
Physical review. E Statistical nonlinear and soft matter physics, 2004Co-Authors: M Moreau, G Oshanin, O Bénichou, M CoppeyAbstract:We present a stochastic Lattice Theory describing the kinetic behavior of trapping reactions A+B-->B, in which both the A and B particles perform an independent stochastic motion on a regular hypercubic Lattice. Upon an encounter of an A particle with any of the B particles, A is annihilated with a finite probability; finite reaction rate is taken into account by introducing a set of two-state random variables--"gates," imposed on each B particle, such that an open (closed) gate corresponds to a reactive (passive) state. We evaluate here a formal expression describing the time evolution of the A particle survival probability, which generalizes our previous results. We prove that for quite a general class of random motion of the species involved in the reaction process, for infinite or finite number of traps, and for any time t, the A particle survival probability is always larger in the case when A stays immobile, than in situations when it moves.
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Lattice Theory of trapping reactions with mobile species.
Physical Review E, 2004Co-Authors: M Moreau, G Oshanin, O Bénichou, M CoppeyAbstract:We present a stochastic Lattice Theory describing the kinetic behavior of trapping reactions $A+\stackrel{\ensuremath{\rightarrow}}{B}B,$ in which both the A and B particles perform an independent stochastic motion on a regular hypercubic Lattice. Upon an encounter of an A particle with any of the B particles, A is annihilated with a finite probability; finite reaction rate is taken into account by introducing a set of two-state random variables\char22{}``gates,'' imposed on each B particle, such that an open (closed) gate corresponds to a reactive (passive) state. We evaluate here a formal expression describing the time evolution of the A particle survival probability, which generalizes our previous results. We prove that for quite a general class of random motion of the species involved in the reaction process, for infinite or finite number of traps, and for any time t, the A particle survival probability is always larger in the case when A stays immobile, than in situations when it moves.
M Moreau - One of the best experts on this subject based on the ideXlab platform.
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Lattice Theory of trapping reactions with mobile species.
Physical review. E Statistical nonlinear and soft matter physics, 2004Co-Authors: M Moreau, G Oshanin, O Bénichou, M CoppeyAbstract:We present a stochastic Lattice Theory describing the kinetic behavior of trapping reactions A+B-->B, in which both the A and B particles perform an independent stochastic motion on a regular hypercubic Lattice. Upon an encounter of an A particle with any of the B particles, A is annihilated with a finite probability; finite reaction rate is taken into account by introducing a set of two-state random variables--"gates," imposed on each B particle, such that an open (closed) gate corresponds to a reactive (passive) state. We evaluate here a formal expression describing the time evolution of the A particle survival probability, which generalizes our previous results. We prove that for quite a general class of random motion of the species involved in the reaction process, for infinite or finite number of traps, and for any time t, the A particle survival probability is always larger in the case when A stays immobile, than in situations when it moves.
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Lattice Theory of trapping reactions with mobile species.
Physical Review E, 2004Co-Authors: M Moreau, G Oshanin, O Bénichou, M CoppeyAbstract:We present a stochastic Lattice Theory describing the kinetic behavior of trapping reactions $A+\stackrel{\ensuremath{\rightarrow}}{B}B,$ in which both the A and B particles perform an independent stochastic motion on a regular hypercubic Lattice. Upon an encounter of an A particle with any of the B particles, A is annihilated with a finite probability; finite reaction rate is taken into account by introducing a set of two-state random variables\char22{}``gates,'' imposed on each B particle, such that an open (closed) gate corresponds to a reactive (passive) state. We evaluate here a formal expression describing the time evolution of the A particle survival probability, which generalizes our previous results. We prove that for quite a general class of random motion of the species involved in the reaction process, for infinite or finite number of traps, and for any time t, the A particle survival probability is always larger in the case when A stays immobile, than in situations when it moves.
Rudolf Wille - One of the best experts on this subject based on the ideXlab platform.
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restructuring Lattice Theory an approach based on hierarchies of concepts
International Conference on Formal Concept Analysis, 2009Co-Authors: Rudolf WilleAbstract:Lattice Theory today reflects the general Status of current mathematics: there is a rich production of theoretical concepts, results, and developments, many of which are reached by elaborate mental gymnastics; on the other hand, the connections of the Theory to its surroundings are getting weaker and weaker, with the result that the Theory and even many of its parts become more isolated. Restructuring Lattice Theory is an attempt to reinvigorate connections with our general culture by interpreting the Theory as concretely as possible, and in this way to promote better communication between Lattice theorists and potential users of Lattice Theory.
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ICFCA - RESTRUCTURING Lattice Theory: AN APPROACH BASED ON HIERARCHIES OF CONCEPTS
Formal Concept Analysis, 2009Co-Authors: Rudolf WilleAbstract:Lattice Theory today reflects the general Status of current mathematics: there is a rich production of theoretical concepts, results, and developments, many of which are reached by elaborate mental gymnastics; on the other hand, the connections of the Theory to its surroundings are getting weaker and weaker, with the result that the Theory and even many of its parts become more isolated. Restructuring Lattice Theory is an attempt to reinvigorate connections with our general culture by interpreting the Theory as concretely as possible, and in this way to promote better communication between Lattice theorists and potential users of Lattice Theory.
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CLA - Formal concept analysis as applied Lattice Theory
Lecture Notes in Computer Science, 1Co-Authors: Rudolf WilleAbstract:Formal Concept Analysis is a mathematical Theory of concept hierarchies which is based on Lattice Theory. It has been developed to support humans in their thought and knowledge. The aim of this paper is to show how successful the Lattice-theoretic foundation can be in applying Formal Concept Analysis in a wide range. This is demonstrated in three sections dealing with representation, processing, and measurement of conceptual knowledge. Finally, further relationships between abstract Lattice Theory and Formal Concept Analysis are briefly discussed.
Martin Hÿtch - One of the best experts on this subject based on the ideXlab platform.
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Application of the O-Lattice Theory for the reconstruction of the high-angle near 90? tilt Si(1 1 0)/(0 0 1) boundary created by wafer bonding
Acta Materialia, 2012Co-Authors: Nikolay Cherkashin, O. Kononchuk, Shay Reboh, Martin HÿtchAbstract:This work presents an experimental and theoretical identification of defects and morphologies of a high-angle near-90° tilt Si boundary created by direct wafer bonding. Two samples with different twist misorientations, between the layer and the (0 0 1) substrate, were studied using conventional transmission electron microscopy (TEM) and geometric phase analysis of high-resolution TEM images. The O-Lattice Theory was used for atom reconstruction of the interface along the direction. It is demonstrated that to preserve covalent bonding across the interface, it should consist of facets intersected by maximum of six planes with three 90° Shockley dislocations per facet. It is shown that a particular atom reconstruction is needed at transition points from one facet to another. The presence or absence of deviation from exact 90° tilt of the layer with respect to the substrate is shown to be related directly to the undulations of the interface. It is demonstrated that the latter has an influence on the Burgers vector of the dislocations adjusting in-plane twist misorientation. A general model for cubic face-centered materials for an arbitrary 〈1 1 0〉sub,lay tilt interface is proposed, which predicts the net Burgers vector and the spacing between dislocations necessary to realize transition from the Lattice of the substrate (layer) to the layer (substrate).
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Reconstruction of a high angle tilt (110)/(001) boundary in Si using O-Lattice Theory
Solid State Phenomena, 2011Co-Authors: Nikolay Cherkashin, O. Kononchuk, Martin HÿtchAbstract:High angle close to 90° tilt Si boundary created by direct wafer bonding (DWB) using SmartCut® technology is studied in this work. Experimental identification of defects and morphologies at the interface is realized using conventional transmission electron microscopy (TEM) and geometric phase analysis (GPA) of high-resolution TEM images. Atom reconstruction of the interface along the direction is carried out within the frame of the O-Lattice Theory. We demonstrate that to preserve covalent bonding across the interface it should consist of facets intersected by a maximum of six planes with three 90° Shockley dislocations per facet. For a long enough interface the formation of Frank dislocations is predicted with a period equal 6 times that of Shockley dislocations. Long range undulations of the interface are shown to be related directly to a deviation from exact 90° tilt of the layer with respect to the substrate.
G Oshanin - One of the best experts on this subject based on the ideXlab platform.
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Lattice Theory of trapping reactions with mobile species.
Physical review. E Statistical nonlinear and soft matter physics, 2004Co-Authors: M Moreau, G Oshanin, O Bénichou, M CoppeyAbstract:We present a stochastic Lattice Theory describing the kinetic behavior of trapping reactions A+B-->B, in which both the A and B particles perform an independent stochastic motion on a regular hypercubic Lattice. Upon an encounter of an A particle with any of the B particles, A is annihilated with a finite probability; finite reaction rate is taken into account by introducing a set of two-state random variables--"gates," imposed on each B particle, such that an open (closed) gate corresponds to a reactive (passive) state. We evaluate here a formal expression describing the time evolution of the A particle survival probability, which generalizes our previous results. We prove that for quite a general class of random motion of the species involved in the reaction process, for infinite or finite number of traps, and for any time t, the A particle survival probability is always larger in the case when A stays immobile, than in situations when it moves.
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Lattice Theory of trapping reactions with mobile species.
Physical Review E, 2004Co-Authors: M Moreau, G Oshanin, O Bénichou, M CoppeyAbstract:We present a stochastic Lattice Theory describing the kinetic behavior of trapping reactions $A+\stackrel{\ensuremath{\rightarrow}}{B}B,$ in which both the A and B particles perform an independent stochastic motion on a regular hypercubic Lattice. Upon an encounter of an A particle with any of the B particles, A is annihilated with a finite probability; finite reaction rate is taken into account by introducing a set of two-state random variables\char22{}``gates,'' imposed on each B particle, such that an open (closed) gate corresponds to a reactive (passive) state. We evaluate here a formal expression describing the time evolution of the A particle survival probability, which generalizes our previous results. We prove that for quite a general class of random motion of the species involved in the reaction process, for infinite or finite number of traps, and for any time t, the A particle survival probability is always larger in the case when A stays immobile, than in situations when it moves.
