The Experts below are selected from a list of 93105 Experts worldwide ranked by ideXlab platform
Adriaan Beukers - One of the best experts on this subject based on the ideXlab platform.
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a novel design solution for improving the performance of composite toroidal hydrogen storage tanks
International Journal of Hydrogen Energy, 2012Co-Authors: Lei Zu, Sotiris Koussios, Adriaan BeukersAbstract:Abstract This paper presents a novel design approach combining isotensoidal structures with non-Geodesic winding patterns, which is able to significantly improve the geometric flexibility and structural performance of composite toroidal hydrogen storage tanks. The fiber trajectories are allowed to deviate from Geodesics and the slippage coefficient is introduced to enlarge the design opportunities of toroidal pressure vessels. With the aid of the netting theory and fiber slippage law, the governing equations for specifying the meridian profiles of non-Geodesic-isotensoids are derived based on the condition of uniform fiber stress. The desired toroids are then obtained by forcing the non-Geodesic isotensoidal meridian profiles to become closed. The resulting cross-sectional shapes and winding angle distributions are outlined, corresponding to various slippage coefficients of non-Geodesics. The vessel performance factors are determined to demonstrate the better structural efficiency that the application of non-Geodesics can achieve. The results show that the vessel performance improves by using non-Geodesics, due to the overall decrease in winding angles of the fiber trajectories. It is also concluded that the structural performance of isotensoidal toroids can be further improved with increasing the slippage coefficient of the non-Geodesic trajectories.
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design of filament wound isotensoid pressure vessels with unequal polar openings
Composite Structures, 2010Co-Authors: Sotiris Koussios, Adriaan BeukersAbstract:Abstract Previous studies on filament-wound isotensoids are mostly based on Geodesic winding. However, the geometry of Geodesics is certainly limiting the available design space. A typical restriction is the inability to create isotensoids with unequal openings at both ends. In this paper, a simplified method for designing isotensoid pressure vessels with unequal polar opening is outlined, using non-Geodesic trajectories. Firstly we present the non-Geodesic equations on general shells of revolution. Next, a direct relation among the shell curvatures, roving force, internal pressure and slippage coefficient, as a basis for determining non-Geodesics-based isotensoid shapes, is provided. The governing equations for specifying meridian profiles are derived in terms of the slippage coefficient. The meridian profiles of non-Geodesics-based isotensoids corresponding to various opening radii and slippage coefficients are determined, and the performance factors of the obtaining domes are calculated to demonstrate the effect the application of non-Geodesics has on the structural efficiency. A stable and easily accessible solution procedure is proposed to determine the slippage coefficients fulfilling the winding requirements. Results show that the present method is suitable for the design of isotensoid structures with unequal polar openings. Results also indicate that the non-Geodesics-based isotensoid domes show better performance than the Geodesic–isotensoid.
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Design of filament-wound circular toroidal hydrogen storage vessels based on non-Geodesic fiber trajectories
International Journal of Hydrogen Energy, 2010Co-Authors: Sotiris Koussios, Adriaan BeukersAbstract:One of the most important design issues for filament-wound hydrogen storage vessels reflects on the determination of the optimal winding trajectories. The goal of this paper is to determine the optimal fiber paths and the resulting laminated structures for non-Geodesically overwound circular toroidal hydrogen storage vessels. With the aid of the continuum theory and the non-Geodesic law, the differential equations describing non-Geodesic paths on a toroidal surface are given. The general criteria for avoiding fiber-bridging and slippage on a torus are formulated by differential geometry. The relation between the slippage coefficient and the winding angle is obtained to meet stable winding requirements. The initial winding angle and the slippage coefficient of non-Geodesics are considered as the design variables, while the minimum shell mass acts as the objective function. The optimal non-Geodesic trajectories, corresponding to various relative bending radii, are determined in order to evaluate the effect of non-Geodesics on the structural performance of toroids. Results indicate that circular toroidal vessels designed using the present method show better performance than Geodesics-based ones, mainly triggered by maximum utilization of the laminate strength. The results also reveal that the structural efficiency of circular toroidal vessels can be significantly improved using non-Geodesic winding.
Sotiris Koussios - One of the best experts on this subject based on the ideXlab platform.
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a novel design solution for improving the performance of composite toroidal hydrogen storage tanks
International Journal of Hydrogen Energy, 2012Co-Authors: Lei Zu, Sotiris Koussios, Adriaan BeukersAbstract:Abstract This paper presents a novel design approach combining isotensoidal structures with non-Geodesic winding patterns, which is able to significantly improve the geometric flexibility and structural performance of composite toroidal hydrogen storage tanks. The fiber trajectories are allowed to deviate from Geodesics and the slippage coefficient is introduced to enlarge the design opportunities of toroidal pressure vessels. With the aid of the netting theory and fiber slippage law, the governing equations for specifying the meridian profiles of non-Geodesic-isotensoids are derived based on the condition of uniform fiber stress. The desired toroids are then obtained by forcing the non-Geodesic isotensoidal meridian profiles to become closed. The resulting cross-sectional shapes and winding angle distributions are outlined, corresponding to various slippage coefficients of non-Geodesics. The vessel performance factors are determined to demonstrate the better structural efficiency that the application of non-Geodesics can achieve. The results show that the vessel performance improves by using non-Geodesics, due to the overall decrease in winding angles of the fiber trajectories. It is also concluded that the structural performance of isotensoidal toroids can be further improved with increasing the slippage coefficient of the non-Geodesic trajectories.
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design of filament wound isotensoid pressure vessels with unequal polar openings
Composite Structures, 2010Co-Authors: Sotiris Koussios, Adriaan BeukersAbstract:Abstract Previous studies on filament-wound isotensoids are mostly based on Geodesic winding. However, the geometry of Geodesics is certainly limiting the available design space. A typical restriction is the inability to create isotensoids with unequal openings at both ends. In this paper, a simplified method for designing isotensoid pressure vessels with unequal polar opening is outlined, using non-Geodesic trajectories. Firstly we present the non-Geodesic equations on general shells of revolution. Next, a direct relation among the shell curvatures, roving force, internal pressure and slippage coefficient, as a basis for determining non-Geodesics-based isotensoid shapes, is provided. The governing equations for specifying meridian profiles are derived in terms of the slippage coefficient. The meridian profiles of non-Geodesics-based isotensoids corresponding to various opening radii and slippage coefficients are determined, and the performance factors of the obtaining domes are calculated to demonstrate the effect the application of non-Geodesics has on the structural efficiency. A stable and easily accessible solution procedure is proposed to determine the slippage coefficients fulfilling the winding requirements. Results show that the present method is suitable for the design of isotensoid structures with unequal polar openings. Results also indicate that the non-Geodesics-based isotensoid domes show better performance than the Geodesic–isotensoid.
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Design of filament-wound circular toroidal hydrogen storage vessels based on non-Geodesic fiber trajectories
International Journal of Hydrogen Energy, 2010Co-Authors: Sotiris Koussios, Adriaan BeukersAbstract:One of the most important design issues for filament-wound hydrogen storage vessels reflects on the determination of the optimal winding trajectories. The goal of this paper is to determine the optimal fiber paths and the resulting laminated structures for non-Geodesically overwound circular toroidal hydrogen storage vessels. With the aid of the continuum theory and the non-Geodesic law, the differential equations describing non-Geodesic paths on a toroidal surface are given. The general criteria for avoiding fiber-bridging and slippage on a torus are formulated by differential geometry. The relation between the slippage coefficient and the winding angle is obtained to meet stable winding requirements. The initial winding angle and the slippage coefficient of non-Geodesics are considered as the design variables, while the minimum shell mass acts as the objective function. The optimal non-Geodesic trajectories, corresponding to various relative bending radii, are determined in order to evaluate the effect of non-Geodesics on the structural performance of toroids. Results indicate that circular toroidal vessels designed using the present method show better performance than Geodesics-based ones, mainly triggered by maximum utilization of the laminate strength. The results also reveal that the structural efficiency of circular toroidal vessels can be significantly improved using non-Geodesic winding.
Dusa Mcduff - One of the best experts on this subject based on the ideXlab platform.
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Hofer's L?-geometry: energy and stability of Hamiltonian flows, part I
Inventiones Mathematicae, 1996Co-Authors: François Lalonde, Dusa McduffAbstract:Consider the group $\Ham^c(M)$ of compactly supported Hamiltonian symplectomorphisms of the symplectic manifold $(M,\om)$ with the Hofer $L^{\infty}$-norm. A path in $\Ham^c(M)$ will be called a Geodesic if all sufficiently short pieces of it are local minima for the Hofer length functional $\Ll$. In this paper, we give a necessary condition for a path $\ga$ to be a Geodesic. We also develop a necessary condition for a Geodesic to be stable, that is, a local minimum for $\Ll$. This condition is related to the existence of periodic orbits for the linearization of the path, and so extends Ustilovsky's work on the second variation formula. Using it, we construct a symplectomorphism of $S^2$ which cannot be reached from the identity by a shortest path. In later papers in this series, we will use holomorphic methods to prove the sufficiency of the condition given here for the characterisation of Geodesics as well as the sufficiency of the condition for the stability of Geodesics. We will also investigate conditions under which Geodesics are absolutely length-minimizing
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Hofer'sL ^∞-geometry: energy and stability of Hamiltonian flows, part I
Inventiones mathematicae, 1995Co-Authors: François Lalonde, Dusa McduffAbstract:Consider the group Ham^ c ( M ) of compactly supported Hamiltonian symplectomorphisms of the symplectic manifold ( M , ω) with the Hofer L ^∞-norm. A path in Ham^ c ( M ) will be called a Geodesic if all sufficiently short pieces of it are local minima for the Hofer length functional ℒ. In this paper, we give a necessary condition for a path γ to be a Geodesic. We also develop a necessary condition for a Geodesic to be stable, that is, a local minimum for ℒ. This condition is related to the existence of periodic orbits for the linearization of the path, and so extends Ustilovsky's work on the second variation formula. Using it, we construct a symplectomorphism of S ^2 which cannot be reached from the identity by a shortest path. In later papers in this series, we will use holomorphic methods to prove the sufficiency of the condition given here for the characterisation of Geodesics as well as the sufficiency of the condition for the stability of Geodesics. We will also investigate conditions under which Geodesics are absolutely length-minimizing.
Michael A Nielsen - One of the best experts on this subject based on the ideXlab platform.
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the geometry of quantum computation
arXiv: Quantum Physics, 2006Co-Authors: Mark R. Dowling, Michael A NielsenAbstract:Determining the quantum circuit complexity of a unitary operation is closely related to the problem of finding minimal length paths in a particular curved geometry [Nielsen et al, Science 311, 1133-1135 (2006)]. This paper investigates many of the basic geometric objects associated to this space, including the Levi-Civita connection, the Geodesic equation, the curvature, and the Jacobi equation. We show that the optimal Hamiltonian evolution for synthesis of a desired unitary necessarily obeys a simple universal Geodesic equation. As a consequence, once the initial value of the Hamiltonian is set, subsequent changes to the Hamiltonian are completely determined by the Geodesic equation. We develop many analytic solutions to the Geodesic equation, and a set of invariants that completely determine the Geodesics. We investigate the problem of finding minimal Geodesics through a desired unitary, U, and develop a procedure which allows us to deform the (known) Geodesics of a simple and well understood metric to the Geodesics of the metric of interest in quantum computation. This deformation procedure is illustrated using some three-qubit numerical examples. We study the computational complexity of evaluating distances on Riemmanian manifolds, and show that no efficient classical algorithm for this problem exists, subject to the assumption that good pseudorandom generators exist. Finally, we develop a canonical extension procedure for unitary operations which allows ancilla qubits to be incorporated into the geometric approach to quantum computing.
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a geometric approach to quantum circuit lower bounds
Quantum Information & Computation, 2006Co-Authors: Michael A NielsenAbstract:What is the minimal size quantum circuit required to exactly implement a specified n-qubit unitary operation, U, without the use of ancilla qubits? We sbow that a lowerbound on the minimal size is provided by the length of the minimal Geodesic between Uand the identity, I, where length is defined by a suitable Finsler metric on the manifoldSU(2n). The Geodesic curves on these manifolds have the striking property that oncean initial position and velocity are set, the remMnder of the Geodesic is completelydeternfined by a second order differential equation known as the Geodesic equation. Thisis in contrast with the usual case in circuit design, either classical or quantum, wherebeing given part of an optimal circuit does not obviously assist in the design of therest of the circuit. Geodesic analysis thus offers a potentially powerful approacb to theproblem of proving quantum circuit lower bounds. In this paper we construct severalFinsler metrics whose minimal length Geodesics provide lower bounds on quantum circuitsize. For eacb Finsler metric we give a procedure to compute the corresponding Geodesicequation. We also construct a large class of solutions to the Geodesic equation, whichwe call Pauli Geodesics, since they arise from isometries generated by the Pauli group.For any unitary U diagonal in the computational basis, we sbow that: (a) proposed theminimal length Geodesic is unique, it must be a Pauli Geodesic; (b) finding the length ofthe minimal Pauli Geodesic passing from I to U is equivalent to solving an exponentialsize instance of the closest vector in a lattice problem (CVP); and (c) all but a doublyexponentially small fraction of sucb unit aries have nfinimal Pauli Geodesics of exponentiallength.
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a geometric approach to quantum circuit lower bounds
arXiv: Quantum Physics, 2005Co-Authors: Michael A NielsenAbstract:What is the minimal size quantum circuit required to exactly implement a specified n-qubit unitary operation, U, without the use of ancilla qubits? We show that a lower bound on the minimal size is provided by the length of the minimal Geodesic between U and the identity, I, where length is defined by a suitable Finsler metric on SU(2^n). The Geodesic curves of such a metric have the striking property that once an initial position and velocity are set, the remainder of the Geodesic is completely determined by a second order differential equation known as the Geodesic equation. This is in contrast with the usual case in circuit design, either classical or quantum, where being given part of an optimal circuit does not obviously assist in the design of the rest of the circuit. Geodesic analysis thus offers a potentially powerful approach to the problem of proving quantum circuit lower bounds. In this paper we construct several Finsler metrics whose minimal length Geodesics provide lower bounds on quantum circuit size, and give a procedure to compute the corresponding Geodesic equation. We also construct a large class of solutions to the Geodesic equation, which we call Pauli Geodesics, since they arise from isometries generated by the Pauli group. For any unitary U diagonal in the computational basis, we show that: (a) provided the minimal length Geodesic is unique, it must be a Pauli Geodesic; (b) finding the length of the minimal Pauli Geodesic passing from I to U is equivalent to solving an exponential size instance of the closest vector in a lattice problem (CVP); and (c) all but a doubly exponentially small fraction of such unitaries have minimal Pauli Geodesics of exponential length.
François Lalonde - One of the best experts on this subject based on the ideXlab platform.
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Hofer's L?-geometry: energy and stability of Hamiltonian flows, part I
Inventiones Mathematicae, 1996Co-Authors: François Lalonde, Dusa McduffAbstract:Consider the group $\Ham^c(M)$ of compactly supported Hamiltonian symplectomorphisms of the symplectic manifold $(M,\om)$ with the Hofer $L^{\infty}$-norm. A path in $\Ham^c(M)$ will be called a Geodesic if all sufficiently short pieces of it are local minima for the Hofer length functional $\Ll$. In this paper, we give a necessary condition for a path $\ga$ to be a Geodesic. We also develop a necessary condition for a Geodesic to be stable, that is, a local minimum for $\Ll$. This condition is related to the existence of periodic orbits for the linearization of the path, and so extends Ustilovsky's work on the second variation formula. Using it, we construct a symplectomorphism of $S^2$ which cannot be reached from the identity by a shortest path. In later papers in this series, we will use holomorphic methods to prove the sufficiency of the condition given here for the characterisation of Geodesics as well as the sufficiency of the condition for the stability of Geodesics. We will also investigate conditions under which Geodesics are absolutely length-minimizing
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Hofer'sL ^∞-geometry: energy and stability of Hamiltonian flows, part I
Inventiones mathematicae, 1995Co-Authors: François Lalonde, Dusa McduffAbstract:Consider the group Ham^ c ( M ) of compactly supported Hamiltonian symplectomorphisms of the symplectic manifold ( M , ω) with the Hofer L ^∞-norm. A path in Ham^ c ( M ) will be called a Geodesic if all sufficiently short pieces of it are local minima for the Hofer length functional ℒ. In this paper, we give a necessary condition for a path γ to be a Geodesic. We also develop a necessary condition for a Geodesic to be stable, that is, a local minimum for ℒ. This condition is related to the existence of periodic orbits for the linearization of the path, and so extends Ustilovsky's work on the second variation formula. Using it, we construct a symplectomorphism of S ^2 which cannot be reached from the identity by a shortest path. In later papers in this series, we will use holomorphic methods to prove the sufficiency of the condition given here for the characterisation of Geodesics as well as the sufficiency of the condition for the stability of Geodesics. We will also investigate conditions under which Geodesics are absolutely length-minimizing.
