45,898 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

    Quantum Mechanics Lecture Notes. Selected Chapters

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    These are extended lecture notes of the quantum mechanics course which I am teaching in the Weizmann Institute of Science graduate physics program. They cover the topics listed below. The first four chapter are posted here. Their content is detailed on the next page. The other chapters are planned to be added in the coming months. 1. Motion in External Electromagnetic Field. Gauge Fields in Quantum Mechanics. 2. Quantum Mechanics of Electromagnetic Field 3. Photon-Matter Interactions 4. Quantization of the Schr\"odinger Field (The Second Quantization) 5. Open Systems. Density Matrix 6. Adiabatic Theory. The Berry Phase. The Born-Oppenheimer Approximation 7. Mean Field Approaches for Many Body Systems -- Fermions and Boson

    A family of total Lagrangian Petrov-Galerkin Cosserat rod finite element formulations

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    The standard in rod finite element formulations is the Bubnov-Galerkin projection method, where the test functions arise from a consistent variation of the ansatz functions. This approach becomes increasingly complex when highly nonlinear ansatz functions are chosen to approximate the rod's centerline and cross-section orientations. Using a Petrov-Galerkin projection method, we propose a whole family of rod finite element formulations where the nodal generalized virtual displacements and generalized velocities are interpolated instead of using the consistent variations and time derivatives of the ansatz functions. This approach leads to a significant simplification of the expressions in the discrete virtual work functionals. In addition, independent strategies can be chosen for interpolating the nodal centerline points and cross-section orientations. We discuss three objective interpolation strategies and give an in-depth analysis concerning locking and convergence behavior for the whole family of rod finite element formulations.Comment: arXiv admin note: text overlap with arXiv:2301.0559

    Quantum resonances and analysis of the survival amplitude in the nonlinear Winter's model

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    In this paper we show that the typical effects of quantum resonances, namely, the exponential-type decay of the survival amplitude, continue to exist even when a nonlinear perturbative term is added to the time-dependent Schroedinger equation. The difficulty in giving a rigorous and appropriate definition of quantum resonances by means of the notions already used for linear equations is also highlighted.Comment: 31 pages, 8 figure

    Rational-approximation-based model order reduction of Helmholtz frequency response problems with adaptive finite element snapshots

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    We introduce several spatially adaptive model order reduction approaches tailored to non-coercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz problems. The offline information is computed by means of adaptive finite elements, so that each snapshot lives in a different discrete space that resolves the local singularities of the analytical solution and is adjusted to the considered frequency value. A rational surrogate is then assembled adopting either a least squares or an interpolatory approach, yielding a function-valued version of the standard rational interpolation method (V-SRI) and the minimal rational interpolation method (MRI). In the context of building an approximation for linear or quadratic functionals of the Helmholtz solution, we perform several numerical experiments to compare the proposed methodologies. Our simulations show that, for interior resonant problems (whose singularities are encoded by poles on the V-SRI and MRI work comparably well. Instead, when dealing with exterior scattering problems, whose frequency response is mostly smooth, the V-SRI method seems to be the best performing one

    Stability for the Surface Diffusion Flow

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    We study the global existence and stability of surface diffusion flow (the normal velocity is given by the Laplacian of the mean curvature) of smooth boundaries of subsets of the nn--dimensional flat torus. More precisely, we show that if a smooth set is ``close enough'' to a strictly stable critical set for the Area functional under a volume constraint, then the surface diffusion flow of its boundary hypersurface exists for all time and asymptotically converges to the boundary of a ``translated'' of the critical set. This result was obtained in dimension n=3n=3 by Acerbi, Fusco, Julin and Morini (extending previous results for spheres of Escher, Mayer and Simonett and Elliott and Garcke in dimension n=2n=2). Our work generalizes such conclusion to any dimension nNn\in\mathbb N. For sake of clarity, we show all the details in dimension n=4n=4 and we list the necessary modifications to the quantities involved in the proof in the general nn--dimensional case, in the last section

    Neuroanatomical and gene expression features of the rabbit accessory olfactory system. Implications of pheromone communication in reproductive behaviour and animal physiology

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    Mainly driven by the vomeronasal system (VNS), pheromone communication is involved in many species-specific fundamental innate socio-sexual behaviors such as mating and fighting, which are essential for animal reproduction and survival. Rabbits are a unique model for studying chemocommunication due to the discovery of the rabbit mammary pheromone, but paradoxically there has been a lack of knowledge regarding its VNS pathway. In this work, we aim at filling this gap by approaching the system from an integrative point of view, providing extensive anatomical and genomic data of the rabbit VNS, as well as pheromone-mediated reproductive and behavioural studies. Our results build strong foundation for further translational studies which aim at implementing the use of pheromones to improve animal production and welfare

    Stochastic integration in Riemannian manifolds from a functional-analytic point of view

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    This article presents a construction of the concept of stochastic integration in Riemannian manifolds from a purely functional-analytic point of view. We show that there are infinitely many such integrals, and that any two of them are related by a simple formula. We also find that the Stratonovich and It\^o integrals known to probability theorists are two instances of the general concept constructed herein.Comment: Minor corrections and additions. Final draft, accepted for publication in "Journal of Functional Analysis

    Quantum Integrability vs Experiments: Correlation Functions and Dynamical Structure Factors

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    Integrable Quantum Field Theories can be solved exactly using bootstrap techniques based on their elastic and factorisable S-matrix. While knowledge of the scattering amplitudes reveals the exact spectrum of particles and their on-shell dynamics, the expression of the matrix elements of the various operators allows the reconstruction of off-shell quantities such as two-point correlation functions with a high level of precision. In this review, we summarise results relevant to the contact point between theory and experiment providing a number of quantities that can be computed theoretically with great accuracy. We concentrate on universal amplitude ratios which can be determined from the measurement of generalised susceptibilities, and dynamical structure factors, which can be accessed experimentally e.g. via inelastic neutron scattering or nuclear magnetic resonance. Besides an overview of the subject and a summary of recent advances, we also present new results regarding generalised susceptibilities in the tricritical Ising universality class.Comment: 53 pages, 12 figures. arXiv admin note: text overlap with arXiv:2109.0976

    Dispersive formalism for the nuclear structure correction δNS\delta_\mathrm{NS} to the β\beta decay rate

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    We analyze the axial γW\gamma W-box diagram for I(JP)=1(0+)I(J^P)=1(0^+) nuclei and provide a dispersion representation of the nuclear-structure correction δNS\delta_\text{NS} including its energy-dependent part. We also summarize useful isospin rotation formula and representations in nuclear theory that could facilitate the calculation of the parity-odd nuclear structure function F3(ν,Q2)F_3(\nu,Q^2). They provide a rigorous theory framework for the future, high-precision calculation of the nuclear structure correction δNS\delta_\text{NS} necessary for the extraction of the Cabibbo-Kobayashi-Maskawa matrix element Vud|V_{ud}| from superallowed nuclear β\beta decays.Comment: Version accepted by Physical Review
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