29,978 research outputs found

    MAS: A versatile Landau-fluid eigenvalue code for plasma stability analysis in general geometry

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    We have developed a new global eigenvalue code, Multiscale Analysis for plasma Stabilities (MAS), for studying plasma problems with wave toroidal mode number n and frequency omega in a broad range of interest in general tokamak geometry, based on a five-field Landau-fluid description of thermal plasmas. Beyond keeping the necessary plasma fluid response, we further retain the important kinetic effects including diamagnetic drift, ion finite Larmor radius, finite parallel electric field, ion and electron Landau resonances in a self-consistent and non-perturbative manner without sacrificing the attractive efficiency in computation. The physical capabilities of the code are evaluated and examined in the aspects of both theory and simulation. In theory, the comprehensive Landau-fluid model implemented in MAS can be reduced to the well-known ideal MHD model, electrostatic ion-fluid model, and drift-kinetic model in various limits, which clearly delineates the physics validity regime. In simulation, MAS has been well benchmarked with theory and other gyrokinetic and kinetic-MHD hybrid codes in a manner of adopting the unified physical and numerical framework, which covers the kinetic Alfven wave, ion sound wave, low-n kink, high-n ion temperature gradient mode and kinetic ballooning mode. Moreover, MAS is successfully applied to model the Alfven eigenmode (AE) activities in DIII-D discharge #159243, which faithfully captures the frequency sweeping of RSAE, the tunneling damping of TAE, as well as the polarization characteristics of KBAE and BAAE being consistent with former gyrokinetic theory and simulation. With respect to the key progress contributed to the community, MAS has the advantage of combining rich physics ingredients, realistic global geometry and high computation efficiency together for plasma stability analysis in linear regime.Comment: 40 pages, 21 figure

    An incremental input-to-state stability condition for a generic class of recurrent neural networks

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    This paper proposes a novel sufficient condition for the incremental input-to-state stability of a generic class of recurrent neural networks (RNNs). The established condition is compared with others available in the literature, showing to be less conservative. Moreover, it can be applied for the design of incremental input-to-state stable RNN-based control systems, resulting in a linear matrix inequality constraint for some specific RNN architectures. The formulation of nonlinear observers for the considered system class, as well as the design of control schemes with explicit integral action, are also investigated. The theoretical results are validated through simulation on a referenced nonlinear system

    Entanglement in the full state vector of boson sampling

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    The full state vector of boson sampling is generated by passing S single photons through beam splitters of M modes. The initial Fock state is expressed withgeneralized coherent states, and an exact application of the unitary evolution becomes possible. Due to the favorable polynomial scaling in M , we can investigate Renyi entanglement entropies for moderate particle and huge mode numbers. We find (almost) Renyi index independent symmetric Page curves with maximum entropy at equal partition. Furthermore, the maximum entropy as a function of mode index saturates as a function of M in the collision-free subspace case. The asymptotic value of the entropy increases linearly with S. Furthermore, we show that the build-up of the entanglement leads to a cusp at subsystem size equal to S in the asymmetric entanglement curve. The maximum entanglement is reached surprisingly early before the mode population is distributed over the whole system

    Optimal universal quantum circuits for unitary complex conjugation

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    Let UdU_d be a unitary operator representing an arbitrary dd-dimensional unitary quantum operation. This work presents optimal quantum circuits for transforming a number kk of calls of UdU_d into its complex conjugate Udˉ\bar{U_d}. Our circuits admit a parallel implementation and are proven to be optimal for any kk and dd with an average fidelity of ⟹F⟩=k+1d(d−k)\left\langle{F}\right\rangle =\frac{k+1}{d(d-k)}. Optimality is shown for average fidelity, robustness to noise, and other standard figures of merit. This extends previous works which considered the scenario of a single call (k=1k=1) of the operation UdU_d, and the special case of k=d−1k=d-1 calls. We then show that our results encompass optimal transformations from kk calls of UdU_d to f(Ud)f(U_d) for any arbitrary homomorphism ff from the group of dd-dimensional unitary operators to itself, since complex conjugation is the only non-trivial automorphisms on the group of unitary operators. Finally, we apply our optimal complex conjugation implementation to design a probabilistic circuit for reversing arbitrary quantum evolutions.Comment: 19 pages, 5 figures. Improved presentation, typos corrected, and some proofs are now clearer. Closer to the published versio

    Sensitivity analysis for ReaxFF reparameterization using the Hilbert-Schmidt independence criterion

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    We apply a global sensitivity method, the Hilbert-Schmidt independence criterion (HSIC), to the reparameterization of a Zn/S/H ReaxFF force field to identify the most appropriate parameters for reparameterization. Parameter selection remains a challenge in this context as high dimensional optimizations are prone to overfitting and take a long time, but selecting too few parameters leads to poor quality force fields. We show that the HSIC correctly and quickly identifies the most sensitive parameters, and that optimizations done using a small number of sensitive parameters outperform those done using a higher dimensional reasonable-user parameter selection. Optimizations using only sensitive parameters: 1) converge faster, 2) have loss values comparable to those found with the naive selection, 3) have similar accuracy in validation tests, and 4) do not suffer from problems of overfitting. We demonstrate that an HSIC global sensitivity is a cheap optimization pre-processing step that has both qualitative and quantitative benefits which can substantially simplify and speedup ReaxFF reparameterizations.Comment: author accepted manuscrip

    A Spatio-temporal Decomposition Method for the Coordinated Economic Dispatch of Integrated Transmission and Distribution Grids

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    With numerous distributed energy resources (DERs) integrated into the distribution networks (DNs), the coordinated economic dispatch (C-ED) is essential for the integrated transmission and distribution grids. For large scale power grids, the centralized C-ED meets high computational burden and information privacy issues. To tackle these issues, this paper proposes a spatio-temporal decomposition algorithm to solve the C-ED in a distributed and parallel manner. In the temporal dimension, the multi-period economic dispatch (ED) of transmission grid (TG) is decomposed to several subproblems by introducing auxiliary variables and overlapping time intervals to deal with the temporal coupling constraints. Besides, an accelerated alternative direction method of multipliers (A-ADMM) based temporal decomposition algorithm with the warm-start strategy, is developed to solve the ED subproblems of TG in parallel. In the spatial dimension, a multi-parametric programming projection based spatial decomposition algorithm is developed to coordinate the ED problems of TG and DNs in a distributed manner. To further improve the convergence performance of the spatial decomposition algorithm, the aggregate equivalence approach is used for determining the feasible range of boundary variables of TG and DNs. Moreover, we prove that the proposed spatio-temporal decomposition method can obtain the optimal solution for bilevel convex optimization problems with continuously differentiable objectives and constraints. Numerical tests are conducted on three systems with different scales, demonstrating the high computational efficiency and scalability of the proposed spatio-temporal decomposition method

    A hybrid quantum algorithm to detect conical intersections

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    Conical intersections are topologically protected crossings between the potential energy surfaces of a molecular Hamiltonian, known to play an important role in chemical processes such as photoisomerization and non-radiative relaxation. They are characterized by a non-zero Berry phase, which is a topological invariant defined on a closed path in atomic coordinate space, taking the value π\pi when the path encircles the intersection manifold. In this work, we show that for real molecular Hamiltonians, the Berry phase can be obtained by tracing a local optimum of a variational ansatz along the chosen path and estimating the overlap between the initial and final state with a control-free Hadamard test. Moreover, by discretizing the path into NN points, we can use NN single Newton-Raphson steps to update our state non-variationally. Finally, since the Berry phase can only take two discrete values (0 or π\pi), our procedure succeeds even for a cumulative error bounded by a constant; this allows us to bound the total sampling cost and to readily verify the success of the procedure. We demonstrate numerically the application of our algorithm on small toy models of the formaldimine molecule (\ce{H2C=NH}).Comment: 15 + 10 pages, 4 figure

    Layout optimization of structures with distributed self-weight, lumped masses and frictional supports

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    The well-known ‘ground structure’-based truss layout optimization method has recently been extended to allow accurate modelling of distributed self-weight. By incorporating equally stressed catenaries in the ground structure, non-conservative errors caused by neglecting bending effects within members carrying their own weight are eliminated. However, in cases where the self-weight of a structure has a favourable role in supporting the applied loads, solutions that include convoluted arrangements of overlapping elements may often be generated. To address this, an enhanced layout optimization formulation is proposed that explicitly allows inclusion of favourable unstressed masses, such as counterweights. Frictional supports are also modelled and the cost of abutments and anchorages taken account of in the formulation. The efficacy of the proposed methodology is demonstrated through application to benchmark examples and to the conceptual design of a simplified long-span bridge structure, considering both ground anchored and self-anchored alternatives

    Exploring the Structure of Scattering Amplitudes in Quantum Field Theory: Scattering Equations, On-Shell Diagrams and Ambitwistor String Models in Gauge Theory and Gravity

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    In this thesis I analyse the structure of scattering amplitudes in super-symmetric gauge and gravitational theories in four dimensional spacetime, starting with a detailed review of background material accessible to a non-expert. I then analyse the 4D scattering equations, developing the theory of how they can be used to express scattering amplitudes at tree level. I go on to explain how the equations can be solved numerically using a Monte Carlo algorithm, and introduce my Mathematica package treeamps4dJAF which performs these calculations. Next I analyse the relation between the 4D scattering equations and on-shell diagrams in N = 4 super Yang-Mills, which provides a new perspective on the tree level amplitudes of the theory. I apply a similar analysis to N = 8 supergravity, developing the theory of on-shell diagrams to derive new Grassmannian integral formulae for the amplitudes of the theory. In both theories I derive a new worldsheet expression for the 4 point one loop amplitude supported on 4D scattering equations. Finally I use 4D ambitwistor string theory to analyse scattering amplitudes in N = 4 conformal supergravity, deriving new worldsheet formulae for both plane wave and non-plane wave amplitudes supported on 4D scattering equations. I introduce a new prescription to calculate the derivatives of on-shell variables with respect to momenta, and I use this to show that certain non-plane wave amplitudes can be calculated as momentum derivatives of amplitudes with plane wave states

    Advance in Keyless Cryptography

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    The term “keyless cryptography” as it is commonly adopted, applies to secure message transmission either directly without any key distribution in advance or as key sharing protocol between communicating users, based on physical layer security, before ordinary encryption/decryption procedures. In the current chapter the results are presented concerning to keyless cryptography that have been obtained by authors recently. Firstly Shamir’s protocol of secure communication is considered where commutative encryption procedure is executed. It has been found out which of the public key algorithms can be used with such protocol. Next item of consideration concerns Dean’s and Goldsmith’s cryptosystem based on multiple-input, multiple-output (MIMO) technology. It has been established under which conditions this cryptosystem is in fact secure. The third example under consideration is EVSkey scheme proposed recently by D. Qin and Z. Ding. It has been proven that such key distribution method is in fact insecure, in spite of the authors’ claims. Our main result is a description of a key sharing protocol executing over public noiseless channels (like internet) that provides a key sharing reliability and security without any cryptographic assumptions
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