The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
I Y Dodin - One of the best experts on this subject based on the ideXlab platform.
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zonal flow dynamics from a Phase Space perspective
Physics of Plasmas, 2016Co-Authors: D E Ruiz, Jeffrey B Parker, E L Shi, I Y DodinAbstract:The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in the studies of zonal flows (ZFs) emerging from DW turbulence. However, this formulation neglects the exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometrical-optics limit. We derive a modified theory that takes both of these effects into account, while still treating DW quanta (“driftons”) as particles in Phase Space. The drifton dynamics is described by an equation of the Wigner–Moyal type, which is commonly known in the Phase-Space formulation of quantum mechanics. In the geometrical-optics limit, this formulation features additional terms missing in the traditional WKE that ensure exact conservation of the total enstrophy of the system, in addition to the total energy, which is the only conserved invariant in previous theories based on the WKE. Numerical simulations are presented to illustrate the importance of these additional terms. The proposed formulation can be considered as a p...
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zonal flow dynamics from a Phase Space perspective
arXiv: Plasma Physics, 2016Co-Authors: D E Ruiz, Jeffrey B Parker, E L Shi, I Y DodinAbstract:The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in studies of zonal flows (ZFs) emerging from DW turbulence. However, this formulation neglects the exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometrical-optics limit. We derive a modified theory that takes both of these effects into account, while still treating DW quanta ("driftons") as particles in Phase Space. The drifton dynamics is described by an equation of the Wigner-Moyal type, which is commonly known in the Phase-Space formulation of quantum mechanics. In the geometrical-optics limit, this formulation features additional terms missing in the traditional WKE that ensure exact conservation of the total enstrophy of the system, in addition to the total energy, which is the only conserved invariant in previous theories based on the WKE. Numerical simulations are presented to illustrate the importance of these additional terms. The proposed formulation can be considered as a Phase-Space representation of the second-order cumulant expansion, or CE2.
Stephen Wiggins - One of the best experts on this subject based on the ideXlab platform.
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Phase Space structure and transport in a caldera potential energy surface
arXiv: Chaotic Dynamics, 2018Co-Authors: Matthaios Katsanikas, Stephen WigginsAbstract:We study Phase Space transport in a 2D caldera potential energy surface (PES) using techniques from nonlinear dynamics. The caldera PES is characterized by a flat region or shallow minimum at its center surrounded by potential walls and multiple symmetry related index one saddle points that allow entrance and exit from this intermediate region.We have discovered four qualitatively distinct cases of the structure of the Phase Space that govern Phase Space transport. These cases are categorized according to the total energy and the stability of the periodic orbits associated with the family of the central minimum, the bifurcations of the same family, and the energetic accessibility of the index one saddles. In each case we have computed the invariant manifolds of the unstable periodic orbits of the central region of the potential and the invariant manifolds of the unstable periodic orbits of the families of periodic orbits associated with the index one saddles. We have found that there are three distinct mechanisms determined by the invariant manifold structure of the unstable periodic orbits govern the Phase Space transport. The first mechanism explains the nature of the entrance of the trajectories from the region of the low energy saddles into the caldera and how they may become trapped in the central region of the potential. The second mechanism describes the trapping of the trajectories that begin from the central region of the caldera, their transport to the regions of the saddles, and the nature of their exit from the caldera. The third mechanism describes the Phase Space geometry responsible for the dynamical matching of trajectories originally proposed by Carpenter and described in Collins et al. (2014) for the two dimensional caldera PES that we consider.
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quantum theory of reactive scattering in Phase Space
arXiv: Quantum Physics, 2010Co-Authors: Arseni Goussev, Roman Schubert, Holger Waalkens, Stephen WigginsAbstract:We review recent results on quantum reactive scattering from a Phase Space perspective. The approach uses classical and quantum versions of normal form theory and the perspective of dynamical systems theory. Over the past ten years the classical normal form theory has provided a method for realizing the Phase Space structures that are responsible for determining reactions in high dimensional Hamiltonian systems. This has led to the understanding that a new (to reaction dynamics) type of Phase Space structure, a {\em normally hyperbolic invariant manifold} (or, NHIM) is the "anchor" on which the Phase Space structures governing reaction dynamics are built. The quantum normal form theory provides a method for quantizing these Phase Space structures through the use of the Weyl quantization procedure. We show that this approach provides a solution of the time-independent Schr\"odinger equation leading to a (local) S-matrix in a neighborhood of the saddle point governing the reaction. It follows easily that the quantization of the directional flux through the dividing surface with the properties noted above is a flux operator that can be expressed in a "closed form". Moreover, from the local S-matrix we easily obtain an expression for the cumulative reactio probability (CRP). Significantly, the expression for the CRP can be evaluated without the need to compute classical trajectories. The quantization of the NHIM is shown to lead to the activated complex, and the lifetimes of quantum states initialized on the NHIM correspond to the Gamov-Siegert resonances. We apply these results to the collinear nitrogen exchange reaction and a three degree-of-freedom system corresponding to an Eckart barrier coupled to two Morse oscillators.
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quantum theory of reactive scattering in Phase Space
Advances in Quantum Chemistry, 2010Co-Authors: Arseni Goussev, Roman Schubert, Holger Waalkens, Stephen WigginsAbstract:We review recent results on quantum reactive scattering from a Phase Space perspective. The approach uses classical and quantum versions of Poincare-Birkhoff normal form theory and the perspective of dynamical systems theory. Over the past 10 years the classical normal form theory has provided a method for realizing the Phase Space structures that are responsible for determining reactions in high-dimensional Hamiltonian systems. This has led to the understanding that a new (to reaction dynamics) type of Phase Space structure, a normally hyperbolic invariant manifold (or NHIM), is the "anchor" on which the Phase Space structures governing reaction dynamics are built, e.g., it is the classical analogue of the chemists notion of the "activated complex" and it is essential for the construction of a surface that divides reactants from products which has the "no-recrossing" property for trajectories and minimal flux. The quantum normal form (QNF) theory provides a method for quantizing these Phase Space structures through the use of the Weyl quantization procedure. We show that this approach provides a solution of the time-independent Schrodinger equation leading to a (local) S-matrix in a neighborhood of the saddle point governing the reaction. These results can be obtained for any dimensional system for which an accurate normal form can be computed, and it does not require numerical solution of the Schrodinger equation or the generation of any classical trajectories. It follows easily that the quantization of the directional flux through the dividing surface with the properties noted above is a flux operator that can be expressed in a "closed form." Moreover, from the local S-matrix we easily obtain an expression for the cumulative reaction probability (CRP), which is the essential ingredient for the computation of microcanonical reaction rates and thermal reaction rates. Significantly, the expression for the CRP can be evaluated without the need to compute classical trajectories. This is a by-product of the quantization of classical Phase Space structures that govern "exact" classical dynamics. The quantization of the NHIM is shown to lead to the activated complex, and the lifetimes of quantum states initialized on the NHIM correspond to the Gamov-Siegert resonances. We apply these results to the collinear nitrogen exchange reaction and a three degree-of-freedom system corresponding to an Eckart barrier coupled to two Morse oscillators. We end by describing some further challenges that are topics of current research, but where some preliminary results are known: corner-cutting tunneling, state-to-state reaction rates, the flux flux autocorrelation function formalism, and the convergence of the QNF. We emphasize that this dynamical system, Phase Space approach to quantum reactive scattering through the QNF provides a completely new approach to the computation of the relevant quantum scattering quantities (e.g., CRP, resonances) which shows promise in leading to computationally efficient methods for "high-dimensional" systems.
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impenetrable barriers in Phase Space for deterministic thermostats
arXiv: Statistical Mechanics, 2008Co-Authors: Gregory S Ezra, Stephen WigginsAbstract:We investigate the relation between the Phase Space structure of Hamiltonian and non-Hamiltonian deterministic thermostats. We show that Phase Space structures governing reaction dynamics in Hamiltonian systems map to the same type of Phase Space structures for the non-Hamiltonian isokinetic equations of motion for the thermostatted Hamiltonian. Our results establish a framework for analyzing thermostat dynamics using concepts and methods developed in reaction rate theory.
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Phase Space conduits for reaction in multidimensional systems hcn isomerization in three dimensions
Journal of Chemical Physics, 2004Co-Authors: Holger Waalkens, Andrew Burbanks, Stephen WigginsAbstract:The three-dimensional hydrogen cyanide/isocyanide isomerization problem is taken as an example to present a general theory for computing the Phase Space structures which govern classical reaction dynamics in systems with an arbitrary (finite) number of degrees of freedom. The theory, which is algorithmic in nature, comprises the construction of a dividing surface of minimal flux which is locally a “surface of no return.” The theory also allows for the computation of the global Phase Space transition pathways that trajectories must follow in order to react. The latter are enclosed by the stable and unstable manifolds of a so-called normally hyperbolic invariant manifold (NHIM). A detailed description of the geometrical structures and the resulting constraints on reaction dynamics is given, with particular emphasis on the three degrees of freedom case. A procedure is given which uses these structures to compute orbits homoclinic to, and heteroclinic between, NHIMs. The role of homoclinic and heteroclinic orbits in global recrossings of dividing surfaces and transport in complex systems is explained. The complete description provided here is inherently one within Phase Space; it cannot be inferred from a configuration Space picture. A complexification of the classical Phase Space structures to incorporate quantum effects is also discussed. The results presented here call into question certain assumptions routinely made on the global dynamics; this paper provides methods that enable one to understand and quantify the Phase Space dynamics of reactions without making such assumptions.
M C Thompson - One of the best experts on this subject based on the ideXlab platform.
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horizontal Phase Space distortions arising from magnetic pulse compression of an intense relativistic electron beam
Physical Review Letters, 2003Co-Authors: S Anderson, J B Rosenzweig, P Musumeci, M C ThompsonAbstract:We report detailed measurements of the transverse Phase Space distortions induced by magnetic chicane compression of a high brightness, relativistic electron beam to subpicosecond length. A strong bifurcation in the Phase Space is observed when the beam is strongly compressed. This effect is analyzed using several computational models and is correlated to the folding of longitudinal Phase Space. The impact of these results on current research in collective beam effects in bending systems and implications for future short wavelength free-electron lasers and linear colliders are discussed.
Laura Waller - One of the best experts on this subject based on the ideXlab platform.
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computational Phase Space measurements using multiplexed coded apertures conference presentation
SPIE Commercial + Scientific Sensing and Imaging, 2017Co-Authors: Hsiou Yuan Liu, Benjamin Recht, Nicholas Boyd, Fanglin Liu, Laura WallerAbstract:Phase-Space refers to simultaneous Space-frequency information (e.g. Wigner functions, light fields), which is directly related to spatial coherence properties (e.g. Mutual Intensity). We introduce a binary pupil masking technique that allows us to computationally reconstruct the Phase Space distribution of optical beams from a series of images. Previous work has shown Phase Space to be useful for 3D imaging and localization in a multiple scattering environment. Binary masks are easy to implement compared to gray masks or Phase masks and the proposed scheme requires no interferometry. After designing the masks with nonredundant arrays, we measure an intensity image for each aperture mask and reconstruct the Phase Space through an auxiliary coherence function. We demonstrate experimentally the reconstruction of the Phase Space of a collection of 3D incoherent sources.
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3D imaging in volumetric scattering media using Phase-Space measurements
Optics Express, 2015Co-Authors: Hsiou Yuan Liu, Jingshan Zhong, Eric Jonas, Benjamin Recht, Lei Tian, Laura WallerAbstract:We demonstrate the use of Phase-Space imaging for 3D localization of multiple point sources inside scattering material. The effect of scattering is to spread angular (spatial frequency) information, which can be measured by Phase Space imaging. We derive a multi-slice forward model for homogenous volumetric scattering, then develop a reconstruction algorithm that exploits sparsity in order to further constrain the problem. By using 4D measurements for 3D reconstruction, the dimensionality mismatch provides significant robustness to multiple scattering, with either static or dynamic diffusers. Experimentally, our high-resolution 4D Phase-Space data is collected by a spectrogram setup, with results successfully recovering the 3D positions of multiple LEDs embedded in turbid scattering media.
Julio F Navarro - One of the best experts on this subject based on the ideXlab platform.
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the Phase Space density profiles of cold dark matter halos
The Astrophysical Journal, 2001Co-Authors: James E. Taylor, Julio F NavarroAbstract:We examine the coarse-grained Phase-Space density pro—les of a set of recent, high-resolution simula- tions of galaxy-sized cold dark matter (CDM) halos. Over two and a half decades in radius the Phase- Space density closely follows a power law, o/p3 P r~a, with aB 1.875. This behavior closely matches the self-similar solution obtained by Bertschinger for secondary infall of gas onto a point-mass perturber in a uniformly expanding universe. On the other hand, the density pro—le corresponding to Bertschingers solution (a power law of slope r2a~6) diUers signi—cantly from the density pro—les of CDM halos. CDM halo density pro—les are clearly not power laws, and they have logarithmic slopes that steepen gradually with radius, roughly as described by Navarro, Frenk, & White (NFW). We show that isotropic, spher- ically symmetric equilibrium mass distributions with power-law Phase-Space density pro—les form a one- parameter family of structures controlled by the ratio of the local velocity dispersion to the ii natural ˇˇ velocity dispersion at some —ducial radius For i \ a \ 1.875, one recovers the r 0 ; i \ 4nGo(r 0 )r2 0 /p2(r 0 ). power-law solution o P r2a~6 .A si increases, the density pro—les become quite complex but still diverge as r2a~6 near the center. For i larger than some critical value solutions become nonphysical, i crit (a), leading to negative densities near the center. The critical solution, corresponds to the case i \ i crit , where the Phase-Space density distribution is the narrowest compatible with the power-law Phase-Space density strati—cation constraint. Over three decades in radius, the critical solution follows closely an NFW pro—le, although its logarithmic slope asymptotically approaches (2a/5 \( 0.75 (rather than (1) at very small radii. Our results thus suggest that the NFW pro—le is the result of a hierarchical assembly process that preserves the Phase-Space strati—cation of Bertschingers spherical infall model but ii mixes ˇˇ the system maximally, perhaps as a result of repeated merging, leading to a relatively uniform Phase- Space density distribution across the system. This —nding oUers intriguing clues as to the origin of the similarity in the structure of dark matter halos formed in hierarchically clustering universes. Subject headings: cosmology: theorydark mattergalaxies: formationgalaxies: structure ¨ methods: analyticalmethods: numerical On-line material: color —gures
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the Phase Space density profiles of cold dark matter halos
arXiv: Astrophysics, 2001Co-Authors: James E. Taylor, Julio F NavarroAbstract:We examine the coarse-grained Phase-Space density profiles of a set of recent, high-resolution simulations of galaxy-sized Cold Dark Matter (CDM) halos. Over two and a half decades in radius the Phase-Space density closely follows a power-law, $\rho/\sigma^3 \propto r^{-\alpha}$, with $\alpha = 1.875$. This behaviour matches the self-similar solution obtained by Bertschinger for secondary infall in a uniformly expanding universe. On the other hand, the density profile corresponding to Bertschinger's solution (a power-law of slope $r^{2\alpha-6}$) differs significantly from the density profiles of CDM halos. We show that isotropic mass distributions with power-law Phase-Space density profiles form a one-parameter family of structures controlled by $\kappa$, the ratio of the velocity dispersion to the peak circular velocity. For $\kappa=\alpha=1.875$ one recovers the power-law solution $\rho \propto r^{2\alpha-6}$. For $\kappa$ larger than some critical value, $\kappa_{cr}$, solutions become non-physical, leading to negative densities near the center. The critical solution, $\kappa =\kappa_{cr}$, has the narrowest Phase-Space density distribution compatible with the power-law Phase-Space density stratification constraint. Over three decades in radius the critical solution is indistinguishable from an NFW profile. Our results thus suggest that the NFW profile is the result of a hierarchical assembly process that preserves the Phase-Space stratification of Bertschinger's infall model but which ``mixes'' the system maximally, perhaps as a result of repeated merging.
