The Experts below are selected from a list of 76488 Experts worldwide ranked by ideXlab platform
Simone Warzel - One of the best experts on this subject based on the ideXlab platform.
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absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on Tree Graphs
Journal of Mathematical Physics, 2012Co-Authors: Michael Aizenman, Simone WarzelAbstract:We discuss the dynamical implications of the recent proof that for a quantum particle in a random potential on a regular Tree Graph absolutely continuous (ac) spectrum occurs non-perturbatively through rare fluctuation-enabled resonances. The main result is spelled in the title.
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absolutely continuous spectra of quantum Tree Graphs with weak disorder
Communications in Mathematical Physics, 2006Co-Authors: Michael Aizenman, Robert Sims, Simone WarzelAbstract:We consider the Laplacian on a rooted metric Tree Graph with branching number K≥2 and random edge lengths given by independent and identically distributed bounded variables. Our main result is the stability of the absolutely continuous spectrum for weak disorder. A useful tool in the discussion is a function which expresses a directional transmission amplitude to infinity and forms a generalization of the Weyl-Titchmarsh function to Trees. The proof of the main result rests on upper bounds on the range of fluctuations of this quantity in the limit of weak disorder.
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absolutely continuous spectra of quantum Tree Graphs with weak disorder
arXiv: Mathematical Physics, 2005Co-Authors: Michael Aizenman, Robert Sims, Simone WarzelAbstract:We consider the Laplacian on a rooted metric Tree Graph with branching number $ K \geq 2 $ and random edge lengths given by independent and identically distributed bounded variables. Our main result is the stability of the absolutely continuous spectrum for weak disorder. A useful tool in the discussion is a function which expresses a directional transmission amplitude to infinity and forms a generalization of the Weyl-Titchmarsh function to Trees. The proof of the main result rests on upper bounds on the range of fluctuations of this quantity in the limit of weak disorder.
Michael Aizenman - One of the best experts on this subject based on the ideXlab platform.
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absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on Tree Graphs
Journal of Mathematical Physics, 2012Co-Authors: Michael Aizenman, Simone WarzelAbstract:We discuss the dynamical implications of the recent proof that for a quantum particle in a random potential on a regular Tree Graph absolutely continuous (ac) spectrum occurs non-perturbatively through rare fluctuation-enabled resonances. The main result is spelled in the title.
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absolutely continuous spectra of quantum Tree Graphs with weak disorder
Communications in Mathematical Physics, 2006Co-Authors: Michael Aizenman, Robert Sims, Simone WarzelAbstract:We consider the Laplacian on a rooted metric Tree Graph with branching number K≥2 and random edge lengths given by independent and identically distributed bounded variables. Our main result is the stability of the absolutely continuous spectrum for weak disorder. A useful tool in the discussion is a function which expresses a directional transmission amplitude to infinity and forms a generalization of the Weyl-Titchmarsh function to Trees. The proof of the main result rests on upper bounds on the range of fluctuations of this quantity in the limit of weak disorder.
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absolutely continuous spectra of quantum Tree Graphs with weak disorder
arXiv: Mathematical Physics, 2005Co-Authors: Michael Aizenman, Robert Sims, Simone WarzelAbstract:We consider the Laplacian on a rooted metric Tree Graph with branching number $ K \geq 2 $ and random edge lengths given by independent and identically distributed bounded variables. Our main result is the stability of the absolutely continuous spectrum for weak disorder. A useful tool in the discussion is a function which expresses a directional transmission amplitude to infinity and forms a generalization of the Weyl-Titchmarsh function to Trees. The proof of the main result rests on upper bounds on the range of fluctuations of this quantity in the limit of weak disorder.
Dimos V Dimarogonas - One of the best experts on this subject based on the ideXlab platform.
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robust formation control in se 3 for Tree Graph structures with prescribed transient and steady state performance
Automatica, 2019Co-Authors: Christos K Verginis, Alexandros Nikou, Dimos V DimarogonasAbstract:This paper presents a novel control protocol for distance and orientation formation control of rigid bodies, whose sensing Graph is a static and undirected Tree, in the special Euclidean group SE(3 ...
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robust formation control in se 3 for Tree Graph structures with prescribed transient and steady state performance
arXiv: Systems and Control, 2018Co-Authors: Christos K Verginis, Alexandros Nikou, Dimos V DimarogonasAbstract:This paper presents a novel control protocol for distance and orientation formation control of rigid bodies, whose communication Graph is a static and undirected Tree, in the special Euclidean group SE(3). The proposed control laws are decentralized, in the sense that each agent uses only local relative information from its neighbors to calculate its control signal, as well as robust with respect to modeling (parametric and structural) uncertainties and external disturbances. The proposed methodology guarantees the satisfaction of inter-agent distance constraints that resemble collision avoidance and connectivity maintenance properties. Moreover, certain predefined functions characterize the transient and steady state performance of the closed loop system. Finally, simulation results verify the validity and efficiency of the proposed approach.
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family of controllers for attitude synchronization in s2
Conference on Decision and Control, 2015Co-Authors: Pedro O Pereira, Dimos V DimarogonasAbstract:In this paper we study a family of controllers that guarantees attitude synchronization for a network of elements in the unit sphere domain, i.e., S2. We propose distributed continuous controllers for elements whose dynamics are controllable (i.e., control with torque as command), and which can be implemented by each individual agent without the need of a common global orientation frame among the network, i.e., it requires only local information that can be measured by each individual agent from its own orientation frame. The controllers are specified according to arbitrary distance functions in S2, and we provide conditions on those distance functions that guarantee that i) a synchronized network of agents is locally asymptotically stable for an arbitrary connected network topology; ii) a synchronized network can be achieved for almost all initial conditions in a Tree Graph network. We also study the equilibria configurations that come with specific types of network Graphs. The proposed strategies can be used in attitude synchronization of swarms of fully actuated rigid bodies, such as satellites.
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family of controllers for attitude synchronization on the sphere
arXiv: Systems and Control, 2015Co-Authors: Pedro O Pereira, Dimos V DimarogonasAbstract:In this paper we study a family of controllers that guarantees attitude synchronization for a network of elements in the unit sphere domain, i.e. $\mathcal{S}^2$. We propose distributed continuous controllers for elements whose dynamics are controllable (i.e. control with torque as command), and which can be implemented by each individual agent without the need of a common global orientation frame among the network, i.e. it requires only local information that can be measured by each individual agent from its own orientation frame. The controllers are specified according to arbitrary distance functions in $\mathcal{S}^2$, and we provide conditions on those distance functions that guarantee that i) a synchronized network of agents is locally asymptotically stable for an arbitrary network Graph; ii) a synchronized network can be achieved for almost all initial conditions in a Tree Graph network. We also study the equilibria configurations that come with specific types of network Graphs. The proposed strategies can be used in attitude synchronization of swarms of fully actuated rigid bodies, such as satellites.
Sergio A Yuhjtman - One of the best experts on this subject based on the ideXlab platform.
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Convergence of Mayer and Virial expansions and the Penrose Tree-Graph identity
Letters in Mathematical Physics, 2017Co-Authors: Aldo Procacci, Sergio A YuhjtmanAbstract:We establish new lower bounds for the convergence radius of the Mayer series and the Virial series of a continuous particle system interacting via a stable and tempered pair potential. Our bounds considerably improve those given by Penrose (J Math Phys 4:1312, 1963 ) and Ruelle (Ann Phys 5:109–120, 1963 ) for the Mayer series and by Lebowitz and Penrose (J Math Phys 7:841–847, 1964 ) for the Virial series. To get our results, we exploit the Tree-Graph identity given by Penrose (Statistical mechanics: foundations and applications. Benjamin, New York, 1967 ) using a new partition scheme based on minimum spanning Trees.
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convergence of mayer and virial expansions and the penrose Tree Graph identity
arXiv: Mathematical Physics, 2015Co-Authors: Aldo Procacci, Sergio A YuhjtmanAbstract:We establish new lower bounds for the convergence radius of the Mayer series and the Virial series of a continuous particle system interacting via a stable and tempered pair potential. Our bounds considerably improve those given by Penrose and Ruelle in 1963 for the Mayer series and by Lebowitz and Penrose in 1964 for the Virial series. To get our results we exploit the Tree-Graph identity given by Penrose in 1967 using a new partition scheme based on minumum spanning Trees.
Robert Sims - One of the best experts on this subject based on the ideXlab platform.
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absolutely continuous spectra of quantum Tree Graphs with weak disorder
Communications in Mathematical Physics, 2006Co-Authors: Michael Aizenman, Robert Sims, Simone WarzelAbstract:We consider the Laplacian on a rooted metric Tree Graph with branching number K≥2 and random edge lengths given by independent and identically distributed bounded variables. Our main result is the stability of the absolutely continuous spectrum for weak disorder. A useful tool in the discussion is a function which expresses a directional transmission amplitude to infinity and forms a generalization of the Weyl-Titchmarsh function to Trees. The proof of the main result rests on upper bounds on the range of fluctuations of this quantity in the limit of weak disorder.
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absolutely continuous spectra of quantum Tree Graphs with weak disorder
arXiv: Mathematical Physics, 2005Co-Authors: Michael Aizenman, Robert Sims, Simone WarzelAbstract:We consider the Laplacian on a rooted metric Tree Graph with branching number $ K \geq 2 $ and random edge lengths given by independent and identically distributed bounded variables. Our main result is the stability of the absolutely continuous spectrum for weak disorder. A useful tool in the discussion is a function which expresses a directional transmission amplitude to infinity and forms a generalization of the Weyl-Titchmarsh function to Trees. The proof of the main result rests on upper bounds on the range of fluctuations of this quantity in the limit of weak disorder.
