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At least 127 records · Page 7
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DOE OSTI2024

An unstructured body-of-revolution electromagnetic particle-in-cell algorithm with radial perfectly matched layers and dual polarizations

A novel electromagnetic particle-in-cell algorithm has been developed for fully kinetic plasma simulations on unstructured (irregular) meshes in complex body-of-revolution geometries. The algorithm, implemented in the BORPIC++ code, utilizes a set of field scalings and a coordinate mapping, reducing the Maxwell field problem in a cylindrical system to a Cartesian finite element Maxwell solver in the meridian plane. The latter obviates the cylindrical coordinate singularity in the symmetry axis. The choice of an unstructured finite element discretization enhances the geometrical flexibility of the BORPIC++ solver compared to the more traditional finite difference solvers. Symmetries in Maxwell’s equations are explored to decompose the problem into two dual polarization states with isomorphic representations that enable code reuse. The particle-in-cell scatter and gather steps preserve charge conservation at the discrete level. Our previous algorithm (BORPIC+) discretized the E and B field components of TE Φ and TM Φ polarizations on the finite element (primal) mesh. Here, we employ a new field-update scheme. Using the same finite element (primal) mesh, this scheme advances two sets of field components independently: (1) E and B of TE Φ polarized fields, (E z , E ρ , B Φ ) and (2) D and H of TM Φ polarized fields, (D Φ , H z , H ρ ). Since these field updates are not explicitly coupled, the new field solver obviates the coordinate singularity, which otherwise arises at the cylindrical symmetric axis, ρ = 0 when defining the discrete Hodge matrices (generalized finite element mass matrices). Here, a cylindrical perfectly matched layer is implemented as a boundary condition in the radial direction to simulate open space problems, with periodic boundary conditions in the axial direction. We investigate effects of charged particles moving next to the cylindrical perfectly matched layer. We model azimuthal currents arising from rotational motion of charged rings, which produce TMΦ polarized fields. Several numerical examples are provided to illustrate the first application of the algorithm.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Minimal area surfaces in AdS n+1 and Wilson loops

The AdS/CFT correspondence relates the expectation value of Wilson loops in N = 4 SYM to the area of minimal surfaces in AdS 5 . In this paper we consider minimal area surfaces in generic Euclidean AdS n+1 using the Pohlmeyer reduction in a similar way as we did previously in Euclidean AdS 3 . As in that case, the main obstacle is to find the correct parameterization of the curve in terms of a conformal parameter. Once that is done, the boundary conditions for the Pohlmeyer fields are obtained in terms of conformal invariants of the curve. After solving the Pohlmeyer equations, the area can be expressed as a boundary integral involving a generalization of the conformal arc-length, curvature and torsion of the curve. Furthermore, one can introduce the λ-deformation symmetry of the contours by a simple change in the conformal invariants. This determines the λ-deformed contours in terms of the solution of a boundary linear problem. In fact the condition that all λ deformed contours are periodic can be used as an alternative to solving the Pohlmeyer equations and is equivalent to imposing the vanishing of an infinite set of conserved charges derived from integrability.

't Hooft and Polyakov loops↗
DOE OSTI2019

Vacuum structure of the left-right symmetric model

The left-right symmetric model (LRSM), originally proposed to explain parity violation in low energy processes, has since emerged as an attractive framework for light neutrino masses via the seesaw mechanism. The scalar sector of the minimal LRSM consists of an SU(2) bi-doublet, as well as left- and right-handed weak isospin triplets, thus making the corresponding vacuum structure much more complicated than that of the Standard Model. In particular, the desired ground state of the Higgs potential should be a charge conserving, and preferably global, minimum with parity violation at low scales. We show that this is not a generic feature of the LRSM potential and happens only for a small fraction of the parameter space of the potential. We also analytically study the potential for some simplified cases and obtain sufficient conditions (though not necessary) to achieve successful symmetry breaking. We then carry out a detailed statistical analysis of the minima of the Higgs potential using numerical minimization and find that for a large fraction of the parameter space, the potential does not have a good vacuum. Imposing the analytically obtained conditions, we can readily find the small part of the parameter space with good vacua. Consequences for some scalar masses are also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

$$ T\overline{T},J\overline{T},T\overline{J} $$ partition sums from string theory

We calculate the torus partition sum of a general CFT 2 with left and right moving conserved currents J and $ \overline{J} $ J ¯ , perturbed by a combination of the irrelevant operators $ T\overline{T},J\overline{T} $ T T ¯ , J T ¯ and $ T\overline{J} $ T J ¯ . We use string theory techniques to write it as an integral transform of the partition sum of the unperturbed CFT with chemical potentials for the left and right moving conserved charges. The resulting expression transforms in the right way under the modular group, and reproduces the known spectrum of these models. We also derive a formula for the partition function of deformed CFT 2 with non-vanishing chemical potentials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Revisiting non-relativistic limits

Here, we show that the full spurionic symmetry of Galilean-invariant field theories can be deduced when those theories are the limits of relativistic parents. Under the limit, the non-relativistic daughter couples to Newton-Cartan geometry together with all of the symmetries advocated in previous work, including the recently revived Milne boosts. Our limit is a covariant version of the usual one, where we start with a gapped relativistic theory with a conserved charge, turn on a chemical potential equal to the rest mass of the lightest charged state, and then zoom in to the low energy sector. This procedure gives a simple physical interpretation for the Milne boosts. Our methods even apply when there is a magnetic moment, which is known to modify the non-relativistic symmetry transformations. We focus on two examples. Free scalars are used to demonstrate the basic procedure, whereas hydrodynamics is used in order to exhibit the power of this approach in a fully dynamical setting, correcting several inaccuracies in the existing literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Lorentz symmetry and IR structure of the BFSS matrix model

The BFSS matrix model relates flat space M-theory to a large N limit of matrix quantum mechanics describing N non-relativistic D0-branes. M-theory, being a theory of gravity in flat space, has a rich infrared structure that includes various soft theorems and an infinite set of conserved charges associated to asymptotic symmetries. In this work, we ask: to what extent is this infrared structure present in BFSS? We find that all the salient features concerning the infrared structure of M-theory carry over naturally to the quantum mechanics dual. Moreover, we demonstrate that the dual statement of the soft graviton theorem in the matrix model implies that D0-brane scattering amplitudes in BFSS enjoy the full 11d Lorentz symmetry of M-theory, a claim which has been long anticipated. We also offer several first-principle consistency checks for our findings, including a computation of the soft theorem which does not presuppose the BFSS duality and a non-trivial match between several known symmetries of M-theory and BFSS that appear naturally in this formalism. These calculations give non-perturbative evidence in support of the BFSS duality as a model of flat space holography.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

The holographic dual of Rényi relative entropy

The relative entropy is a measure of the distinguishability of two quantum states. A great deal of progress has been made in the study of the relative entropy between an excited state and the vacuum state of a conformal field theory (CFT) reduced to a spherical region. For example, when the excited state is a small perturbation of the vacuum state, the relative entropy is known to have a universal expression for all CFT’s. Specifically, the perturbative relative entropy can be written as the symplectic flux of a certain scalar field in an auxiliary AdS-Rindler spacetime. Moreover, if the CFT has a semi-classical holographic dual, the relative entropy is known to be related to conserved charges in the bulk dual spacetime. In this paper, we introduce a one-parameter generalization of the relative entropy which we call refined Rényi relative entropy. We study this quantity in CFT’s and find a one-parameter generalization of the aforementioned known results about the relative entropy. We also discuss a new family of positive energy theorems in asymptotically locally AdS spacetimes that arises from the holographic dual of the refined Rényi relative entropy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

The attractor flow for AdS 5 black holes in $\mathcal{N}$ = 2 gauged supergravity

We study the flow equations for BPS black holes in $\mathcal{N}$ = 2 five-dimensional gauged supergravity coupled to any number of vector multiplets via FI couplings. We develop the Noether-Wald procedure in this context and exhibit the conserved charges as explicit integrals of motion, in the sense that they can be computed at any radius on the rotating spacetime. The boundary conditions needed to solve the first order differential equations are discussed in great detail. We extremize the entropy function that controls the near horizon geometry and give explicit formulae for all geometric variables at their supersymmetric extrema. We have also considered a complexification of the near-horizon variables that elucidates some features of the theory from the near-horizon perspective.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Extending the thermodynamic form factor bootstrap program: multiple particle-hole excitations, crossing symmetry, and reparameterization invariance

In this study, we further the thermodynamic bootstrap program which involves a set of recently developed ideas used to determine thermodynamic form factors of local operators in integrable quantum field theories. These form factors are essential building blocks for dynamic correlation functions at finite temperatures or non-equilibrium stationary states. In this work we extend this program in three ways. Firstly, we demonstrate that the conjectured annihilation pole axiom is valid in the low energy particle-hole excitations. Secondly, we introduce a crossing relation, which establishes a connection between form factors with different excitation content. Typically, the crossing relation is a consequence of Lorentz invariance, but due to the finite energy density of the considered states, Lorentz invariance is broken. Nonetheless a crossing relation involving excitations with both particles and holes can established using the finite volume representation of the thermodynamic form factors. Finally, we demonstrate that the thermodynamic form factors satisfy a reparameterization invariance, an invariance which encompasses crossing. Reparameterization invariance exploits the fact that the details of the representation of the thermodynamic state are unimportant. In the course of developing these results, we demonstrate the internal consistency of the thermodynamic form factor bootstrap program in a number of ways. Finally, we provide explicit computations of form factors of conserved charges and densities with crossed excitations and show our results can be used to infer information about thermodynamic form factors in the Lieb-Liniger model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Probing the chiral magnetic wave with charge-dependent flow measurements in Pb-Pb collisions at the LHC

The Chiral Magnetic Wave (CMW) phenomenon is essential to provide insights into the strong interaction in QCD, the properties of the quark-gluon plasma, and the topological characteristics of the early universe, offering a deeper understanding of fundamental physics in high-energy collisions. Measurements of the charge-dependent anisotropic flow coefficients are studied in Pb-Pb collisions at center-of-mass energy per nucleon-nucleon collision $\sqrt{s_{\textrm{NN}}}$ = 5.02 TeV to probe the CMW. In particular, the slope of the normalized difference in elliptic (v 2 ) and triangular (v 3 ) flow coefficients of positively and negatively charged particles as a function of their event-wise normalized number difference, is reported for inclusive and identified particles. The slope ${r}_3^{\textrm{Norm}}$ is found to be larger than zero and to have a magnitude similar to ${r}_2^{\textrm{Norm}}$, thus pointing to a large background contribution for these measurements. Furthermore, ${r}_2^{\textrm{Norm}}$ can be described by a blast wave model calculation that incorporates local charge conservation. In addition, using the event shape engineering technique yields a fraction of CMW (f CMW ) contribution to this measurement which is compatible with zero. This measurement provides the very first upper limit for f CMW , and in the 10–60% centrality interval it is found to be 26% (38%) at 95% (99.7%) confidence level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation

Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

General N=2 supersymmetric quantum mechanical model: Supervariable approach to its off-shell nilpotent symmetries

Using the supersymmetric (SUSY) invariant restrictions on the (anti-)chiral supervariables, we derive the off-shell nilpotent symmetries of the general one (0+1)-dimensional N=2 SUSY quantum mechanical (QM) model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables θ and θ-bar with θ{sup 2}=(θ-bar){sup 2}=0,θ(θ-bar)+(θ-bar)θ=0). We provide the geometrical meanings to the two SUSY transformations of our present theory which are valid for any arbitrary type of superpotential. We express the conserved charges and Lagrangian of the theory in terms of the supervariables (that are obtained after the application of SUSY invariant restrictions) and provide the geometrical interpretation for the nilpotency property and SUSY invariance of the Lagrangian for the general N=2 SUSY quantum theory. We also comment on the mathematical interpretation of the above symmetry transformations. - Highlights: • A novel method has been proposed for the derivation of N=2 SUSY transformations. • General N=2 SUSY quantum mechanical (QM) model with a general superpotential, is considered. • The above SUSY QM model is generalized onto a (1, 2)-dimensional supermanifold. • SUSY invariant restrictions are imposed on the (anti-)chiral supervariables. • Geometrical meaning of the nilpotency property is provided.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A multi-phase-field model of topological pattern formation during electrochemical dealloying of binary alloys

Porous metal structures produced by electrochemical dealloying have been extensively studied for use in various applications that require high surface areas. A new comprehensive multi-phase-field (MPF) model is proposed to study topological porous patterns formed by spontaneously etching a bulk binary alloy that involves electrochemical reactions, bulk and surface diffusion, ion transport, applied electrode potential, and charge conservation. The governing equations for the alloy-porous cluster-electrolyte system account for a generalized Butler-Volmer electrochemical reaction and are in accordance with the classical nucleation theory. Based on a quantitative examination of the effects of electrode potential and precursor composition, the simulation results reproduce typical phenomena including passive surface dealloying, active porosity evolution, critical potential, and characteristic length scale in two-dimension (2-D) and three-dimension (3-D). To consider more complicated dealloying systems, the evolutions of a bimodal porous metal structure, nanocomposite, and nested porous network with a structured hierarchy are investigated. Finally, the proposed model can be a useful tool for understanding and predicting the morphology evolution of diverse porous structures during electrochemical dealloying.

Hierarchical porous structure↗
DOE OSTI2015

Implementation of a hybrid particle code with a PIC description in r–z and a gridless description in ϕ into OSIRIS

For many plasma physics problems, three-dimensional and kinetic effects are very important. However, such simulations are very computationally intensive. Fortunately, there is a class of problems for which there is nearly azimuthal symmetry and the dominant three-dimensional physics is captured by the inclusion of only a few azimuthal harmonics. Recently, it was proposed [1] to model one such problem, laser wakefield acceleration, by expanding the fields and currents in azimuthal harmonics and truncating the expansion. The complex amplitudes of the fundamental and first harmonic for the fields were solved on an r–z grid and a procedure for calculating the complex current amplitudes for each particle based on its motion in Cartesian geometry was presented using a Marder's correction to maintain the validity of Gauss's law. In this paper, we describe an implementation of this algorithm into OSIRIS using a rigorous charge conserving current deposition method to maintain the validity of Gauss's law. We show that this algorithm is a hybrid method which uses a particles-in-cell description in r–z and a gridless description in ϕ. We include the ability to keep an arbitrary number of harmonics and higher order particle shapes. Examples for laser wakefield acceleration, plasma wakefield acceleration, and beam loading are also presented and directions for future work are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

A scalable DG solver for the electroneutral Nernst-Planck equations

The robust, scalable simulation of flowing electrochemical systems is increasingly important due to the synergy between intermittent renewable energy and electrochemical technologies such as energy storage and chemical manufacturing. The high Péclet regime of many such applications prevents the use of off-the-shelf discretization methods. In this work, we present a high-order Discontinuous Galerkin scheme for the electroneutral Nernst-Planck equations. The chosen charge conservation formulation allows for the specific treatment of the different physics: upwinding for advection and migration, and interior penalty for diffusion of ionic species as well the electric potential. Similarly, the formulation enables different treatments in the preconditioner: AMG for the potential blocks and ILU-based methods for the advection-dominated concentration blocks. Here we evaluate the convergence rate of the discretization scheme through numerical tests. Strong scaling results for two preconditioning approaches are shown for a large 3D flow-plate reactor example.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

The QCD Equation of state and critical end-point estimates at O ( μ B 6 )

Here, we present results for the QCD Equation of State at non-zero chemical potentials corresponding to the conserved charges in QCD using Taylor expansion upto sixth order in the baryon number, electric charge and strangeness chemical potentials. The latter two are constrained by the strangeness neutrality and a fixed electric charge to baryon number ratio. In our calculations, we use the Highly Improved Staggered Quarks (HISQ) discretization scheme at physical quark masses and at different values of the lattice spacings to control lattice cut-off effects. Furthermore we calculate the pressure along lines of constant energy density, which serve as proxies for the freeze-out conditions and discuss their dependence on μ Β , which is necessary for hydrodynamic modelling near freezeout. We also provide an estimate of the radius of convergence of the Taylor series from the 6th order coefficients which provides a new constraint on the location of the critical end-point in the T-μ Β plane of the QCD phase diagram.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Dynamical initialization and hydrodynamic modeling of relativistic heavy-ion collisions

We present a fully three-dimensional model providing initial conditions for energy and conserved charge density distributions in heavy ion collisions at RHIC Beam Energy Scan (BES) collision energies. The model includes the dynamical deceleration of participating nucleons or valence quarks. It provides a realistic estimation of the initial baryon stopping during the early stage of collisions. We also present the implementation of the model with 3+1 dimensional hydrodynamics, which involves the addition of source terms that deposit energy and net-baryon densities produced by the initial state model at proper times greater than the initial time for the hydrodynamic simulation. The importance of this dynamical initialization stage on hadronic flow observables at the RHIC BES is quantified.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Search for CME in U+U and Au+Au collisions in STAR with different approaches of handling backgrounds

We report the chiral magnetic effect (CME) refers to charge separation along a strong magnetic field between left- and right-handed quarks, caused by interactions with topological gluon fields from QCD vacuum fluctuations. We present two approaches to handle the dominant elliptic flow (v 2 ) background in the three-particle correlator (Δγ 112 ), sensitive to CME. In the first approach, we present the Δγ 112 and Δγ 123 measurements in U+U and Au+Au collisions. While hydrodynamic simulations including resonance decays and local charge conservation predict that Δγ 112 scaled by N part /ν 2 will be similar in U+U and Au+Au collisions, the projected B-field exhibits a distinct difference between the two systems and with varying N part . Therefore, U+U and Au+Au collisions provide configurations with different expectations for both CME signal and background. Moreover, the three-particle observable Δγ 123 scaled by N part /ν 3 provide baseline measurement for only the background. In the second approach, we handle the ν 2 background by measuring Δγ 112 with respect to the planes of spectators measured by Zero Degree Calorimeters and participants measured by Time Projection Chamber. These measurements contain different amounts of contributions from CME signal (along B-field, due to spectators) and ν 2 background (determined by the participant geometry). With the two Δγ 112 measurements, the possible CME signal and the background contribution can be determined. We report such a measurement in Au+Au collisions at $\sqrt{s_{NN}}$ = 27GeV with the newly installed event plane detector, and report the new findings in U+U system where the spectator-participant plane correlations are expected to differ from those in Au+Au collisions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗