The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform
David Avnir - One of the best experts on this subject based on the ideXlab platform.
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Continuous Symmetry Analysis of the Cis-Trans Isomerizations of Diazene Derivatives: The Symmetry Transition Point
2020Co-Authors: Inbal Tuvi-arad, David AvnirAbstract:Intrinsic reaction coordinate calculations were performed for the cis-trans isomerization reaction of diazene and its dihalogeno derivatives. The Continuous Symmetry Measures (CSM) method was applied for calculating the deviation from perfect Symmetry along the reaction path. A unique Symmetry-profile, which describes the change in Symmetry along the reaction coordinate, was obtained for each case. A "Symmetry transition point" is identified at the extremum point along the Symmetry-profile. At this point, the deviation of the molecule from the rotational Symmetry of the reactant is the same as its deviation from the rotational Symmetry of the product. The results also show that CSM can be used as an alternative reaction coordinate. Calculations at the DFT, HF and MP2 levels result in similar Symmetry profiles, thus showing that the description of reaction paths in terms of CSM is a robust method that provides a new type of understanding of the structural and the geometrical changes that take place during a reaction.
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Continuous Symmetry analyses c nv and d n measures of molecules complexes and proteins
Journal of Computational Chemistry, 2013Co-Authors: Mark Pinsky, Amir Zait, Maayan Bonjack, David AvnirAbstract:The Continuous Symmetry methodology has been developed to provide a quantitative estimation for the degree of a selected Symmetry point-group in a molecular structure. Previous developed measures included the CS, Cn, Sn (including Ci) symmetries, several polyhedral symmetries, and the related chirality measure. Motivated by the abundance and importance of Cnv Symmetry in many key molecules and by the abundance of Dn Symmetry in many organometallic complexes and in many protein clusters, measures for these symmetries, based on the general definition of the Continuous Symmetry measure, were developed. Detailed description of the derivation of the measures, along with plenty of examples for their application, is provided. © 2012 Wiley Periodicals, Inc.
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a Continuous Symmetry analysis of chemical bonding
Chemistry: A European Journal, 2011Co-Authors: Chaim Dryzun, Pere Alemany, David Casanova, David AvnirAbstract:The ability to quantify the Symmetry content of a given molecular system is important both for the quan- titative prediction of its physical and chemical properties, as well as for the establishment of powerful theoretical concepts that can be derived solely from Symmetry considerations. The Symmetry content of a complex object such as a molecule relies, however, on the level of structural description that is chosen. This may range form a simple geometrical picture in which only the position of the nuclei is indi- cated, to a more or less detailed de- scription of the electronic structure given by the different quantum chemi- cal methods. Recently, a paper was published describing a new general methodology for calculating the sym- metry content of diverse mathematical objects, such as vectors, operators, ma- trices, functions and more. In the pres- ent work we apply that approach to ex- plore the inversion Symmetry for dia- tomic molecules. Although it is a very simple system, general physical conclu- sions on the phenomenon of chemical bonding can be easily obtained from the Symmetry analysis at different levels of description.
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Continuous Symmetry measures of density maps
Journal of Physical Chemistry C, 2010Co-Authors: Mark Pinsky, David Danovich, David AvnirAbstract:Density maps are commonly used for data presentation, and their Symmetry is a central characteristic. Quite often near Symmetry can be detected but not the exact one. Here we present a method for estimating the Symmetry content of density maps. We thus extend the application of the Continuous Symmetry measure (CSM) methodology to many-points problems. We demonstrate the applicability of the method on electron-density probability maps and use, as a model, a series of copper clusters: 1Cu3+, 1Cu4 (planar and tetrahedral), 2Cu7, and 1Cu6. These were distorted in various ways, and the electron density maps of the distorted clusters were analyzed with respect to the content of the elementary Symmetry point groups, namely reflection, inversion rotation, and improper rotation. In general, it has been found that Symmetry distortions of nuclei arrangement are amplified in the electronic arrangement.
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generalization of the Continuous Symmetry measure the Symmetry of vectors matrices operators and functions
Physical Chemistry Chemical Physics, 2009Co-Authors: Chaim Dryzun, David AvnirAbstract:In this paper we generalize a method for evaluating the Continuous Symmetry measure, which is a quantitative estimate of the degree of Symmetry of a given object. The generalization makes it possible to calculate the degree of Symmetry content for any mathematical entity that is part of metric spaces such as vectors, matrices, operators and functions. Furthermore, by this new approach one can calculate the Symmetry-content values for any compact Symmetry groups either finite or infinite. An advantage of the new methodology is the ability to investigate analytically problems of Symmetry changes. Examples of Symmetry evaluation calculations are provided, including mixing of ideal gases, evaluation of the Symmetry content of a Hamiltonian operator, the 2pz orbital of the hydrogen atom, and more.
Erhard Seiler - One of the best experts on this subject based on the ideXlab platform.
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Does conformal quantum field theory describe the continuum limits of 2D spin models with Continuous Symmetry?
Physics Letters B, 1998Co-Authors: Adrian Patrascioiu, Erhard SeilerAbstract:It is generally taken for granted that two-dimensional critical phenomena can be fully classified by the well known two-dimensional (rational) conformal quantum field theories (CQFTs). In particular it is believed that in models with a Continuous Symmetry characterized by a Lie group $G$ the continuum theory enjoys an enhanced Symmetry $G\times G$ due to the decoupling of right and left movers. In this letter we review the conventional arguments leading to this conclusion, point out two gaps and provide a conterexample. Nevertheless we justify in the end the conventional conclusions by additional arguments.Comment: 9 page
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does conformal quantum field theory describe the continuum limits of 2d spin models with Continuous Symmetry
Physics Letters B, 1998Co-Authors: Adrian Patrascioiu, Erhard SeilerAbstract:Abstract It is generally taken for granted that two-dimensional critical phenomena can be fully classified by the well known two-dimensional (rational) conformal quantum field theories (CQFTs). In particular it is believed that in models with a Continuous Symmetry characterized by a Lie group G the continuum theory enjoys an enhanced Symmetry G × G due to the decoupling of right and left movers. In this letter we review the conventional arguments leading to this conclusion, point out two gaps and provide a counterexample. Nevertheless we justify in the end the conventional conclusions by additional arguments.
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continuum limit of two dimensional spin models with Continuous Symmetry and conformal quantum field theory
Physical Review E, 1998Co-Authors: Adrian Patrascioiu, Erhard SeilerAbstract:According to the standard classification of conformal quantum field theory (CQFT) in two dimensions, the massless continuum limit of the O(2) model at the Kosterlitz-Thouless transition point should be given by the massless free scalar field; in particular the Noether current of the model should be proportional to (the dual of) the gradient of the massless free scalar field, reflecting a Symmetry enhanced from O(2) to $\mathrm{O}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{}\mathrm{O}(2)$. More generally, the massless continuum limit of a spin model with a Symmetry given by a Lie group $G$ should have an enhanced Symmetry $G\ifmmode\times\else\texttimes\fi{}G$. We point out that the arguments leading to this conclusion contain two serious gaps: (i) the possibility of ``nontrivial local cohomology'' and (ii) the possibility that the current is an ultralocal field. For the two-dimensional O(2) model we give analytic arguments that rule out the first possibility and use numerical methods to dispose of the second one. We conclude that the standard CQFT predictions appear to be borne out in the O(2) model, but give an example where they would fail. We also point out that all our arguments apply equally well to any $G$ symmetric spin model, provided it has a critical point at a finite temperature.
Agostino Martinelli - One of the best experts on this subject based on the ideXlab platform.
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State Estimation based on the Concept of Continuous Symmetry and Observability Analysis: The Case of Calibration
IEEE Transactions on Robotics, 2011Co-Authors: Agostino MartinelliAbstract:This paper considers the problem of state estimation in autonomous navigation from a theoretical perspective. In particular, the investigation regards problems where the information provided by the sensor data is not sufficient to carry out the state estimation (i.e. the state is not observable). For these systems, the concept of Continuous Symmetry is introduced. Detecting the Continuous symmetries of a given system has a very practical importance. It allows us to detect an observable state whose components are non linear functions of the original non observable state. So far this theoretical and very general concept has been applied to deal with two distinct fundamental estimation problems in the framework of mobile robotics. The former is in the framework of self-calibration and the latter is in the framework of the fusion of the data provided by inertial sensors and vision sensors. For reasons of length, only the former is discussed. In particular, the theoretical machinery is used to address a specific calibration problem. The solution constrains the robot to move along specific trajectories in order to be able to apply the calibration algorithm. This paper provides two distinct contributions. The first is the introduction of this concept of Continuous Symmetry. The second is the introduction of a simple and efficient strategy to extrinsically calibrate a bearing sensor (e.g. a vision sensor) mounted on a vehicle and, simultaneously estimate the parameters describing the systematic error of its odometry system. Many accurate simulations and real experiments show the robustness, the efficiency and the accuracy of the proposed strategy.
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State Estimation Based on the Concept of Continuous Symmetry and Observability Analysis: The Case of Calibration
IEEE Transactions on Robotics, 2011Co-Authors: Agostino MartinelliAbstract:This paper considers the problem of state estimation in autonomous navigation from a theoretical perspective. In particular, the investigation concerns problems where the information provided by the sensor data is not sufficient to carry out the state estimation (i.e., the state is not observable). For these systems, the concept of Continuous Symmetry is introduced. Detection of the Continuous symmetries of a given system has a very practical importance. It allows the detection of an observable state whose components are nonlinear functions of the original nonobservable state. So far, this theoretical and very general concept has been applied to deal with two distinct fundamental estimation problems in the framework of mobile robotics. The former is in the framework of self-calibration, and the latter is in the framework of the fusion of the data provided by inertial sensors and vision sensors. For reasons of length, only the former is discussed. In particular, the theoretical machinery is used to address a specific calibration problem. The solution constrains the robot to move along specific trajectories in order to be able to apply the calibration algorithm. This paper provides two distinct contributions. The first is the introduction of this concept of Continuous Symmetry. The second is the introduction of a simple and efficient strategy to extrinsically calibrate a bearing sensor (e.g., a vision sensor) mounted on a vehicle and, simultaneously, estimate the parameters describing the systematic error of its odometry system. Many accurate simulations and real experiments show the robustness, the efficiency, and the accuracy of the proposed strategy.
Adrian Patrascioiu - One of the best experts on this subject based on the ideXlab platform.
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Does conformal quantum field theory describe the continuum limits of 2D spin models with Continuous Symmetry?
Physics Letters B, 1998Co-Authors: Adrian Patrascioiu, Erhard SeilerAbstract:It is generally taken for granted that two-dimensional critical phenomena can be fully classified by the well known two-dimensional (rational) conformal quantum field theories (CQFTs). In particular it is believed that in models with a Continuous Symmetry characterized by a Lie group $G$ the continuum theory enjoys an enhanced Symmetry $G\times G$ due to the decoupling of right and left movers. In this letter we review the conventional arguments leading to this conclusion, point out two gaps and provide a conterexample. Nevertheless we justify in the end the conventional conclusions by additional arguments.Comment: 9 page
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does conformal quantum field theory describe the continuum limits of 2d spin models with Continuous Symmetry
Physics Letters B, 1998Co-Authors: Adrian Patrascioiu, Erhard SeilerAbstract:Abstract It is generally taken for granted that two-dimensional critical phenomena can be fully classified by the well known two-dimensional (rational) conformal quantum field theories (CQFTs). In particular it is believed that in models with a Continuous Symmetry characterized by a Lie group G the continuum theory enjoys an enhanced Symmetry G × G due to the decoupling of right and left movers. In this letter we review the conventional arguments leading to this conclusion, point out two gaps and provide a counterexample. Nevertheless we justify in the end the conventional conclusions by additional arguments.
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continuum limit of two dimensional spin models with Continuous Symmetry and conformal quantum field theory
Physical Review E, 1998Co-Authors: Adrian Patrascioiu, Erhard SeilerAbstract:According to the standard classification of conformal quantum field theory (CQFT) in two dimensions, the massless continuum limit of the O(2) model at the Kosterlitz-Thouless transition point should be given by the massless free scalar field; in particular the Noether current of the model should be proportional to (the dual of) the gradient of the massless free scalar field, reflecting a Symmetry enhanced from O(2) to $\mathrm{O}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{}\mathrm{O}(2)$. More generally, the massless continuum limit of a spin model with a Symmetry given by a Lie group $G$ should have an enhanced Symmetry $G\ifmmode\times\else\texttimes\fi{}G$. We point out that the arguments leading to this conclusion contain two serious gaps: (i) the possibility of ``nontrivial local cohomology'' and (ii) the possibility that the current is an ultralocal field. For the two-dimensional O(2) model we give analytic arguments that rule out the first possibility and use numerical methods to dispose of the second one. We conclude that the standard CQFT predictions appear to be borne out in the O(2) model, but give an example where they would fail. We also point out that all our arguments apply equally well to any $G$ symmetric spin model, provided it has a critical point at a finite temperature.
Shahar Keinan - One of the best experts on this subject based on the ideXlab platform.
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Continuous Symmetry analysis of tetrahedral planar distortions copper chlorides and other ab4 species
Inorganic Chemistry, 2001Co-Authors: Shahar Keinan, David AvnirAbstract:The Symmetry of tetracoordinated copper complexes, especially of CuCl42-, is analyzed in terms of quantitative Continuous Symmetry. These complexes acquire structures that span from tetrahedral to planar, with all gradual variations in between, a property that is evaluated here in terms of their degrees of tetrahedricity (S(Td)) and square planarity (S(D4h)). It was found that out of the large arsenal of geometry-allowed tetrahedral structures, each of which is characterized by specific S(Td) and S(D4h) pair values, copper complexes concentrate on an extremely well-defined correlation line linking these two Symmetry-content measures; that is, only very specific pairs of S(Td) and S(D4h) values that dictate each other are allowed. Furthermore, it was found that of the various routes that can lead from a tetrahedron to a planar square, the mode known as spread fits exactly in its Symmetry S(Td)/S(D4h) characteristics the observed Symmetry behavior of the copper complexes. Interestingly, the spread mode refl...
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Continuous Symmetry analysis of tetrahedral/planar distortions. Copper chlorides and other AB4 species.
Inorganic Chemistry, 2001Co-Authors: Shahar Keinan, David AvnirAbstract:The Symmetry of tetracoordinated copper complexes, especially of CuCl42-, is analyzed in terms of quantitative Continuous Symmetry. These complexes acquire structures that span from tetrahedral to planar, with all gradual variations in between, a property that is evaluated here in terms of their degrees of tetrahedricity (S(Td)) and square planarity (S(D4h)). It was found that out of the large arsenal of geometry-allowed tetrahedral structures, each of which is characterized by specific S(Td) and S(D4h) pair values, copper complexes concentrate on an extremely well-defined correlation line linking these two Symmetry-content measures; that is, only very specific pairs of S(Td) and S(D4h) values that dictate each other are allowed. Furthermore, it was found that of the various routes that can lead from a tetrahedron to a planar square, the mode known as spread fits exactly in its Symmetry S(Td)/S(D4h) characteristics the observed Symmetry behavior of the copper complexes. Interestingly, the spread mode refl...