The Experts below are selected from a list of 87390 Experts worldwide ranked by ideXlab platform
Danial S Forghani - One of the best experts on this subject based on the ideXlab platform.
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behavior of a free quantum particle in the poincare upper half Plane Geometry
Annals of Physics, 2020Co-Authors: Parham Dehghani, Habib S Mazharimousavi, Danial S ForghaniAbstract:Abstract Inspired by the recent work of Filho et al. (2016) a Hermitian momentum operator is introduced in a general curved space with diagonal metric. The modified Hamiltonian associated with this new momentum is calculated and discussed. Furthermore, granting the validity of the Heisenberg equation in a curved space, the Ehrenfest theorem is generalized and interpreted with the new position-dependent differential operator in a curved space. The modified Hamiltonian leads to a modified time-independent Schrodinger equation, which is solved explicitly for a free particle in the Poincare upper half-Plane Geometry. It is shown that a “free particle” does not behave as it is totally free due to the curved background Geometry.
Roberto Onofrio - One of the best experts on this subject based on the ideXlab platform.
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anomalies in electrostatic calibrations for the measurement of the casimir force in a sphere Plane Geometry
Physical Review A, 2008Co-Authors: W J Kim, Michael Brownhayes, Diego A R Dalvit, J H Brownell, Roberto OnofrioAbstract:Dipartimento di Fisica “Galileo Galilei”, Universit`a di Padova, Via Marzolo 8, Padova 35131, Italy(Dated: December 1, 2008)We have performed precision electrostatic calibrations in the sphere-Plane Geometry, and observedanomalous behavior. Namely, the scaling exponent of the electrostatic signal with distance was foundto be smaller than expected on the basis of the pure Coulombian contribution, and the residualpotential found to be distance dependent. We argue that these findings affect the accuracy of theelectrostatic calibrations and invite reanalysis of previous determinations of the Casimir force.
Linghua Chang - One of the best experts on this subject based on the ideXlab platform.
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achievable angles between two compressed sparse vectors under norm distance constraints imposed by the restricted isometry property a Plane Geometry approach
IEEE Transactions on Information Theory, 2013Co-Authors: Linghua ChangAbstract:The angle between two compressed sparse vectors subject to the norm/distance constraints imposed by the restricted isometry property (RIP) of the sensing matrix plays a crucial role in the studies of many compressive sensing (CS) problems. Assuming that u and v are two sparse vectors with∠ (u, v) = θ and the sensing matrix Φ satisfies RIP, this paper is aimed at analytically characterizing the achievable angles between Φu and Φv. Motivated by geometric interpretations of RIP and with the aid of the well-known law of cosines, we propose a Plane-Geometry-based formulation for the study of the considered problem. It is shown that all the RIP-induced norm/distance constraints on Φu and Φv can be jointly depicted via a simple geometric diagram in the 2-D Plane. This allows for a joint analysis of all the considered algebraic constraints from a geometric perspective. By conducting Plane Geometry analyses based on the constructed diagram, closed-form formulas for the maximal and minimal achievable angles are derived. Computer simulations confirm that the proposed solution is tighter than an existing algebraic-based estimate derived using the polarization identity. The obtained results are used to derive a tighter restricted isometry constant of structured sensing matrices of a certain kind, to wit, those in the form of a product of an orthogonal projection matrix and a random sensing matrix. Follow-up applications in CS are also discussed.
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achievable angles between two compressed sparse vectors under norm distance constraints imposed by the restricted isometry property a Plane Geometry approach
arXiv: Information Theory, 2012Co-Authors: Linghua ChangAbstract:The angle between two compressed sparse vectors subject to the norm/distance constraints imposed by the restricted isometry property (RIP) of the sensing matrix plays a crucial role in the studies of many compressive sensing (CS) problems. Assuming that (i) u and v are two sparse vectors separated by an angle thetha, and (ii) the sensing matrix Phi satisfies RIP, this paper is aimed at analytically characterizing the achievable angles between Phi*u and Phi*v. Motivated by geometric interpretations of RIP and with the aid of the well-known law of cosines, we propose a Plane Geometry based formulation for the study of the considered problem. It is shown that all the RIP-induced norm/distance constraints on Phi*u and Phi*v can be jointly depicted via a simple geometric diagram in the two-dimensional Plane. This allows for a joint analysis of all the considered algebraic constraints from a geometric perspective. By conducting Plane Geometry analyses based on the constructed diagram, closed-form formulae for the maximal and minimal achievable angles are derived. Computer simulations confirm that the proposed solution is tighter than an existing algebraic-based estimate derived using the polarization identity. The obtained results are used to derive a tighter restricted isometry constant of structured sensing matrices of a certain kind, to wit, those in the form of a product of an orthogonal projection matrix and a random sensing matrix. Follow-up applications to three CS problems, namely, compressed-domain interference cancellation, RIP-based analysis of the orthogonal matching pursuit algorithm, and the study of democratic nature of random sensing matrices are investigated.
Anne Bourdon - One of the best experts on this subject based on the ideXlab platform.
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Large Conical Discharge Structure of an Air Discharge at Atmospheric Pressure in a Point-to-Plane Geometry
IEEE Transactions on Plasma Science, 2014Co-Authors: Franois Pechereau, Pierre Le Delliou, Jaroslav Jánský, Pierre Tardiveau, Stéphane Pasquiers, Anne BourdonAbstract:The experimental and simulated optical emissions of an air discharge at atmospheric pressure propagating in a point-to-Plane Geometry with a sharp point and a high overvoltage are compared. A conical discharge structure is observed. A good agreement on the maximum diameter of the discharge and its propagation velocity is obtained.
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numerical simulation of filamentary discharges with parallel adaptive mesh refinement
Journal of Computational Physics, 2008Co-Authors: Sergey Pancheshnyi, Pierre Segur, Julien Capeillere, Anne BourdonAbstract:Direct simulation of filamentary gas discharges like streamers or dielectric barrier micro-discharges requires the use of an adaptive mesh. The objective of this paper is to develop a strategy which can use a set of grids with suitable local refinements for the continuity equations and Poisson's equation in 2D and 3D geometries with a high-order discretization. The advantages of this approach are presented with a filamentary discharge simulation in Plane-Plane Geometry in nitrogen within the diffusion-drift approximation.
Parham Dehghani - One of the best experts on this subject based on the ideXlab platform.
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behavior of a free quantum particle in the poincare upper half Plane Geometry
Annals of Physics, 2020Co-Authors: Parham Dehghani, Habib S Mazharimousavi, Danial S ForghaniAbstract:Abstract Inspired by the recent work of Filho et al. (2016) a Hermitian momentum operator is introduced in a general curved space with diagonal metric. The modified Hamiltonian associated with this new momentum is calculated and discussed. Furthermore, granting the validity of the Heisenberg equation in a curved space, the Ehrenfest theorem is generalized and interpreted with the new position-dependent differential operator in a curved space. The modified Hamiltonian leads to a modified time-independent Schrodinger equation, which is solved explicitly for a free particle in the Poincare upper half-Plane Geometry. It is shown that a “free particle” does not behave as it is totally free due to the curved background Geometry.
