Search NASA⌕ Search

SEARCH · Search NASA

Results for “dimension:2”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Parallelized domain decomposition for multi-dimensional Lagrangian random walk mass-transfer particle tracking schemes

Lagrangian particle tracking schemes allow a wide range of flow and transport processes to be simulated accurately, but a major challenge is numerically implementing the inter-particle interactions in an efficient manner. This article develops a multi-dimensional, parallelized domain decomposition (DDC) strategy for mass-transfer particle tracking (MTPT) methods in which particles exchange mass dynamically. We show that this can be efficiently parallelized by employing large numbers of CPU cores to accelerate run times. In order to validate the approach and our theoretical predictions we focus our efforts on a well-known benchmark problem with pure diffusion, where analytical solutions in any number of dimensions are well established. In this work, we investigate different procedures for “tiling” the domain in two and three dimensions (2-D and 3-D), as this type of formal DDC construction is currently limited to 1-D. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-D for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work. For an optimally subdivided diffusion problem, the 2-D parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run-up to around 2700 cores, reducing a 5 h simulation to 8 s, while the 3-D algorithm maintains appreciable speedup up to 1700 cores.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Simulating Large PEPs Tensor Networks on Small Quantum Devices

We systematically map low bond dimension PEPs tensor networks to quantum circuits. By measuring and reusing qubits, we are in principle able to simulate an N×M square lattice PEPs network (for arbitrary M) of bond dimension 2 using N+ 2 qubits. We then seek to determine if this mapping can yield useful values for long-range loop observables in the presence of quantum device noise in the topological Wen plaquette model by mapping a 3×3 PEPs tensor network to a 5-qubit quantum circuit and executing it on the Honeywell System Model H1-1 trapped-ion device. We find that, for this system size, the noisy observable values are indeed sufficient for diagnosing topological vs. trivial order as the Wen model is perturbed by a magnetic field term in the Hamiltonian. We provide an overview of the experimental procedure and its results. We then explain in greater detail our method for mapping 2D tensor networks to quantum circuits and its scaling properties. This serves as a proof-of-concept of the utilty of the measure-and-reuse approach for simulating large 2D quantum systems on small quantum devices.

MacCormack, Ian↗
DOE OSTI2021

Dirac fast scramblers

In this work, we introduce a family of Gross-Neveu-Yukawa models with a large number of fermion and boson flavors as higher dimensional generalizations of the Sachdev-Ye-Kitaev model. The models may be derived from local lattice couplings and give rise to Lorentz invariant critical solutions in 1+1 and 2+1 dimensions. These solutions imply anomalous dimensions of both bosons and fermions tuned by the number ratio of boson to fermion flavors. In 1+1 dimension the solution represents a stable critical phase, while in 2+1 dimension it governs a quantum phase transition. We compute the out of time order correlators in the 1+1 dimensional model, showing that it exhibits growth with the maximal Lyapunov exponent λ L =2πT in the low temperature limit.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Frustration-induced diffusive scattering anomaly and dimension change in FeGe 2

Magnetic frustration, arising from the competition of exchange interactions, has received great attention because of its relevance to exotic quantum phenomena in materials. In the current work, we report an unusual checkerboard-shaped scattering anomaly in FeGe 2 , far from the known incommensurate magnetic satellite peaks, by inelastic neutron scattering. More surprisingly, such phenomenon appears as spin dynamics at low temperature, but it becomes prominent above Néel transition as elastic scattering. Here, a model Hamiltonian that includes an intraplane next-nearest neighbor was proposed and such anomaly is attributed to the near-perfect magnetic frustration and the emergence of unexpected two-dimensional magnetic order in the quasi-one-dimensional FeGe 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Quantum Statistics of Vortices from a Dual Theory of the X Y Ferromagnet

In this work, we extend the well-known mapping between the easy-plane ferromagnet and electrostatics in d = 2 spatial dimensions to dynamical and quantum phenomena in a d = 2+1 spacetime. Ferromagnetic vortices behave like quantum particles with an electric charge equal to the vortex number and a magnetic flux equal to the transverse spin of the vortex core. Vortices with half-integer core spin exhibit fermionic statistics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

From trivial to topological paramagnets: The case of Z 2 and Z 2 3 symmetries in two dimensions

Using quantum Monte Carlo simulations, we map out the phase diagram of Hamiltonians interpolating between trivial and nontrivial bosonic symmetry-protected topological phases, protected by Z 2 and Z 2 3 symmetries, in two dimensions. In all cases, we find that the trivial and the topological phases are separated by an intermediate phase in which the protecting symmetry is spontaneously broken. Depending on the model, we identify a variety of magnetic orders on the triangular lattice, including ferromagnetism, 3 × 3 order, and stripe orders (both commensurate and incommensurate). Critical properties are determined through a finite-size scaling analysis. Possible scenarios regarding the nature of the phase transitions are discussed.

2-dimensional systems↗
DOE OSTI2021

Revisiting the multi-monopole point of SU( N ) $\mathcal{N}$ = 2 gauge theory in four dimensions

Motivated by applications to soft supersymmetry breaking, we revisit the expansion of the Seiberg-Witten solution around the multi-monopole point on the Coulomb branch of pure SU(N) $\mathcal{N}$ = 2 gauge theory in four dimensions. At this point N - 1 mutually local magnetic monopoles become massless simultaneously, and in a suitable duality frame the gauge couplings logarithmically run to zero. We explicitly calculate the leading threshold corrections to this logarithmic running from the Seiberg-Witten solution by adapting a method previously introduced by D’Hoker and Phong. We compare our computation to existing results in the literature; this includes results specific to SU(2) and SU(3) gauge theories, the large-N results of Douglas and Shenker, as well as results obtained by appealing to integrable systems or topological strings. We find broad agreement, while also clarifying some lingering inconsistencies. Finally, we explicitly extend the results of Douglas and Shenker to finite N, finding exact agreement with our first calculation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Quantum computing for energy correlators

In recent years, energy correlators have emerged as powerful observables for probing the fragmentation dynamics of high-energy collisions. We introduce the first numerical strategy for calculating energy correlators using the Hamiltonian lattice approach, providing access to the intriguing nonperturbative dynamics of these observables. Furthermore, motivated by rapid advances in quantum computing hardware and algorithms, we propose a quantum algorithm for calculating energy correlators in quantum field theories. This algorithm includes ground state preparation, the application of source, sink, energy flux and real-time evolution operators, and the Hadamard test. We validate our approach by applying it to the SU(2) pure gauge theory in 2 + 1 dimensions on 3 × 3 and 5 × 5 honeycomb lattices with 𝑗 max = $\frac{1}{2}$ at various couplings, utilizing both classical methods and the quantum algorithm, the latter tested using the IBM emulator for specific configurations. The results are consistent with the expected behavior of the strong coupling regime and motivate a more comprehensive study to probe the confinement dynamics across the weak and strong coupling regimes.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Implement and Test 3D Mortar Contact in BISON

We leverage the extension of the generation of mortar segment meshes to three dimensions in MOOSE’s framework to extend thermomechanical modeling capabilities to problems with three dimensions. A modular approach to gap heat transfer physics using the mortar finite element method was created and documented, mechanical contact was extended to three dimensions—including frictional behavior, performance and ease of use were improved, and steps towards scalability of solid mechanics problems involving contact were taken. Many of these new developments are demonstrated in the simulation of 3D light-water reactor (LWR) problems, where the thermomechanical interface problem is solved using the mortar finite element method. Usage of the mortar framework has improved convergence in 2D problems and has enabled employing friction in 3D problems, of which we show results of a short, local stack of 3D pellets. Consequently, the benefits of mortar in terms of solution convergence and quality are extended to three dimensions. Section 2 discusses fundamental developments that enabled the simulation of practical mortar problems in three dimensions and other general improvements, including the reduction of the derivative container size, the modification of dual basis computations when edge dropping (lack of secondary element projection) takes place, the improvement of conditioning when employing the VCP in-edge dropping conditions, and code usability and quality improvements. These latter code enhancements include the migration of tests using “old” mortar contact constraints to using dual mortar with a semi-smooth Newton solution strategy and the reuse of lower dimensional domains for straightforwardly setting up a mortar thermomechanical LWR problem, i.e. the MOOSE action is employed for mechanical contact and the thermal LWR action is employed to capture the gas conductance, contact, and radiation components of gap heat transfer physics. Independently of the mortar LWR thermal action, we developed a modular approach to gap heat transfer that resides in MOOSE and can be leveraged, e.g., in metallic fuel problems. This approach, whose code design based on MOOSE’s user objects to model specific physics was proposed by the maintenance activity, is detailed in Section 3. Based on the dual mortar finite element method, the frictional contact constraints were extended to three dimensions. A block sheared in two directions in and out of contact with a rigid plane is employed in Section 4 to show the way the approach handles changes in frictional states (e.g. stick to slip) within a competitive number of Newton iterations. Equations and numerical results on the use of the VCP with Cartesian Lagrange multipliers, whose combination enables their direct condensation, are described in Section 5.3. Two-dimensional and three-dimensional BISON LWR simulations are discussed in Section 6. Particularly, a stack of five eccentric pellets with a surface defect is simulated and the effect of pellet-cladding friction is assessed. Finally, conclusions are outlined in Section 7.

42 ENGINEERING↗
DOE OSTI2023

One-dimensionality signature in optical conductivity of heavy-fermion CeIr 3 B 2

In low dimensions, the combined effects of interactions and quantum fluctuations can lead to dramatically new physics distinct from that existing in higher dimensions. Here, we investigate the electronic and optical properties of CeIr 3 ⁢B 2 , a quasione-dimensional (1D) Kondo lattice system, using ab initio calculations. The Ce atoms in the hexagonal crystal structure form 1D chains along the c axis, with extremely short Ce-Ce distances. The quasi-1D nature of the crystal structure is well reflected in its electronic structure. Extremely flat bands emerge within the ab plane of the Brillouin zone, yielding sharp optical transitions in the corresponding optical conductivity. Further, our calculations indicate that these prominent peaks in the optical conductivity provide a clear signature of quasi-1D heavy fermion systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Interacting CFTs for all couplings: thermal versus entanglement entropy at large N

In this paper, I calculate the large N limit of marginal O(N) models with non-polynomial potentials in arbitrary odd dimensions d. This results in a new class of interacting pure conformal field theories (CFTs) in d = 3 + 4n for any n ϵ $\mathbb{Z}$ + . Similarly, in d = 3 + 4n I calculate the thermal entropy for all couplings on R 2+4n × S 1 for n = 0, 1, 2, 3. In 2+1 dimensions I find the strong-to-weak coupling ratio of the thermal entropy to be 4/5, matching recent results, and further extend this analysis to higher odd dimensions. Next, I calculated the vacuum entanglement entropy ${s}_{\textrm{EE}}^d$ on S d–2 for all couplings in arbitrary odd d in the large N limit. I find the vacuum entanglement entropy on S d–2 to be not only solvable but also constant for all couplings λ. Thus, in the large N limit, the vacuum entanglement entropy on S d–2 for odd d is constant for all λ, in contrast to the thermal entropy which is shown to also be monotonically decreasing with λ in d = 3 + 4n.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Knots and entanglement

We extend the entanglement bootstrap program to (3+1)-dimensions. We study knotted excitations of (3+1)-dimensional liquid topological orders and exotic fusion processes of loops. As in previous work in (2+1)-dimensions [Ann. Phys. 418, 168164 (2020), Phys. Rev. B 103, 115150 (2021)], we define a variety of superselection sectors and fusion spaces from two axioms on the ground state entanglement entropy. In particular, we identify fusion spaces associated with knots. We generalize the information convex set to a new class of regions called immersed regions, promoting various theorems to this new context. Examples from solvable models are provided; for instance, a concrete calculation of knot multiplicity shows that the knot complement of a trefoil knot can store quantum information. We define spiral maps that allow us to understand consistency relations for torus knots as well as spiral fusions of fluxes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality

Motivated by the fermion-bag approach, in this work we construct a new class of Hamiltonian lattice field theories that can help us to study fermionic quantum critical points, particularly those with four-fermion interactions. Although these theories are constructed in discrete time with a finite temporal lattice spacing ϵ, when ϵ → 0, conventional continuous-time Hamiltonian lattice field theories are recovered. The fermion-bag algorithms run relatively faster when ϵ = 1 as compared to ϵ → 0 but still allow us to compute universal quantities near the quantum critical point even at such a large value of ϵ. As an example of this new approach, here we study the $N_f$ = 1 Gross-Neveu chiral-Ising universality class in 2 + 1 dimensions by calculating the critical scaling of the staggered mass order parameter. We show that we are able to study lattice sizes up to 100 2 sites when ϵ = 1, while with comparable resources we can reach lattice sizes of only up to 64 2 when ϵ → 0. The critical exponents obtained in both these studies match within errors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Quantum Gauge Networks: A New Kind of Tensor Network

Although tensor networks are powerful tools for simulating low-dimensional quantum physics, tensor network algorithms are very computationally costly in higher spatial dimensions. We introduce quantum gauge networks: a different kind of tensor network ansatz for which the computation cost of simulations does not explicitly increase for larger spatial dimensions. We take inspiration from the gauge picture of quantum dynamics, which consists of a local wavefunction for each patch of space, with neighboring patches related by unitary connections. A quantum gauge network (QGN) has a similar structure, except the Hilbert space dimensions of the local wavefunctions and connections are truncated. We describe how a QGN can be obtained from a generic wavefunction or matrix product state (MPS). All 2k-point correlation functions of any wavefunction for M many operators can be encoded exactly by a QGN with bond dimension O(M k ). In comparison, for just k = 1, an exponentially larger bond dimension of 2 M/6 is generically required for an MPS of qubits. We provide a simple QGN algorithm for approximate simulations of quantum dynamics in any spatial dimension. The approximate dynamics can achieve exact energy conservation for time-independent Hamiltonians, and spatial symmetries can also be maintained exactly. We benchmark the algorithm by simulating the quantum quench of fermionic Hamiltonians in up to three spatial dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Characterization and classification of interacting ( 2 + 1 )-dimensional topological crystalline insulators with orientation-preserving wallpaper groups

While free fermion topological crystalline insulators have been largely classified, the analogous problem in the strongly interacting case has been only partially solved. In this work, we develop a characterization and classification of interacting, invertible fermionic topological phases in (2+1) dimensions with charge conservation, discrete magnetic translation and M-fold point group rotation symmetries, which form the group G f = U(1) f × Φ [Z 2 $\rtimes$Z M ] for M = 1,2,3,4, and 6. Φ is the magnetic flux per unit cell. We derive a topological response theory in terms of background crystalline gauge fields, which gives a complete classification of different phases and a physical characterization in terms of quantized response to symmetry defects. We then derive the same classification in terms of a set of real space invariants {$Θ^±_o$} that can be obtained from ground state expectation values of suitable partial rotation operators. We explicitly relate these real space invariants to the quantized coefficients in the topological response theory, and find the dependence of the invariants on the chiral central charge c – of the invertible phase. Finally, when Φ = 0 we derive an explicit map between the free and interacting classifications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Stability of exact solutions of the (2 + 1)-dimensional nonlinear Schrödinger equation with arbitrary nonlinearity parameter κ

In this work, we consider the nonlinear Schrödinger equation (NLSE) in 2+1 dimensions with arbitrary nonlinearity exponent κ in the presence of an external confining potential. Exact solutions to the system are constructed, and their stability as we increase the 'mass' (i.e., the L 2 norm) and the nonlinearity parameter κ is explored. Here we observe both theoretically and numerically that the presence of the confining potential leads to wider domains of stability over the parameter space compared to the unconfined case. Our analysis suggests the existence of a stable regime of solutions for all κ as long as their mass is less than a critical value M*(κ). Furthermore, we find that there are two different critical masses, one corresponding to width perturbations and the other one to translational perturbations. The results of Derrick's theorem are also obtained by studying the small amplitude regime of a four-parameter collective coordinate (4CC) approximation. A numerical stability analysis of the NLSE shows that the instability curve M*(κ) versus κ lies below the two curves found by Derrick's theorem and the 4CC approximation. In the absence of the external potential, κ = 1 demarcates the separation between the blowup regime and the stable regime. In this 4CC approximation, for κ < 1, when the mass is above the critical mass for the translational instability, quite complicated motions of the collective coordinates are possible. Energy conservation prevents the blowup of the solution as well as confines the center of the solution to a finite spatial domain. We call this regime the 'frustrated' blowup regime and give some illustrations. In an appendix, we show how to extend these results to arbitrary initial ground state solution data and arbitrary spatial dimension d.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Classification of all $\mathcal{N}\geq 3$ moduli space orbifold geometries at rank 2

We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional \mathcal{N}\geq 3 𝒩 ≥ 3 superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to moduli spaces of known theories or discretely gauged version of them. Remarkably, we find 6 geometries which are not realized by any known theory, of which 3 have an \mathcal{N}=2 𝒩 = 2 Coulomb branch slice with a non-freely generated coordinate ring, suggesting the existence of new, exotic \mathcal{N}=3 𝒩 = 3 theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Nonperturbative dynamics of (2+1)d φ 4 -theory from Hamiltonian truncation

We use Lightcone Conformal Truncation (LCT) - a version of Hamiltonian truncation - to study the nonperturbative, real-time dynamics of φ 4 -theory in 2+1 dimensions. This theory has UV divergences that need to be regulated. We review how, in a Hamiltonian framework with a total energy cutoff, renormalization is necessarily state-dependent, and UV sensitivity cannot be canceled with standard local operator counter-terms. To overcome this problem, we present a prescription for constructing the appropriate state-dependent counterterms for (2+1)d φ 4 -theory in lightcone quantization. We then use LCT with this counterterm prescription to study φ 4 -theory, focusing on the $\mathbb{Z}$ 2 symmetry-preserving phase. Specifically, we compute the spectrum as a function of the coupling and demonstrate the closing of the mass gap at a (scheme-dependent) critical coupling. We also compute Lorentz-invariant two-point functions, both at generic strong coupling and near the critical point, where we demonstrate IR universality and the vanishing of the trace of the stress tensor.

field theories in lower dimensions↗